tag:blogger.com,1999:blog-89398555437748309212024-03-19T05:20:42.455-05:00Fundamental NerveEstamos migrando a www.asanchezyali.comTipillito Sánchezhttp://www.blogger.com/profile/17968576148255423366noreply@blogger.comBlogger13125tag:blogger.com,1999:blog-8939855543774830921.post-68039637522864223662021-04-26T07:33:00.001-05:002021-04-26T07:33:04.829-05:00Álgebra Lineal Parte 2/4: Valores propios, vectores propios y subespacios propios<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
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<p>En esta entrada vamos a regresar a la pregunta original que motivó nuestra discusión de los valores propios y vectores propios en primer lugar: dada una transformación lineal $T: V\to V$ sobre un espacio finito dimensional $V$, ¿Es posible encontrar una base $\beta$ de $V$ tal que la matriz asociada $[T]_{\beta}^{\beta}$ es una matriz diagonal?</p>
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<blockquote><p><strong>Definición 1.</strong> <em>Un operador lineal $T:V \to V$ sobre un espacio finito dimensional $V$ es <strong>diagonalizable</strong> si existe una base $\beta$ de $V$ tal que la matriz asociada $[T]_{\beta}^{\beta}$ es una matriz diagonal.</em></p>
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<p>Esta definición también se puede formular para matrices; si $A$ es una matriz de orden $n\times n$, entonces $A$ es la matriz de $T:F^{n}\to F^{n}$ dada por la multiplicación a izquierda por $A$. En este caso podemos decir que $A$ es diagonalizable cuando $T$ es diagonalizable. De los resultados para cambios de base, esto es equivalente a decir que existe una matriz invertible $Q\in M_{n\times n}(F)$, denominada <strong>matriz de cambio de base</strong> $Q=[I]_{\beta}^{\gamma}$, para la cual $Q^{-1}A Q = [I]_{\gamma}^{\beta}[T]_{\gamma}^{\gamma}[I]_{\beta}^{\gamma} = [T]_{\beta}^{\beta}$ es una matriz diagonal.</p>
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<p><strong>Definición 2.</strong> Una matriz $A\in M_{n\times n}(F)$ es diagonalizables sobre $F$ si existe una matriz invertible, $Q\in M_{n\times n}(F)$ para cual $Q^{-1}AQ$ es una matriz diagonal.</p>
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<p>Recuerden que hay que tener un particular cuidado con el campo $F$, ya que la diagonalización de una matriz depende parcialmente del campo $F$ sobre el cual se esté trabajando.</p>
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<p>Recuerde que se dice que dos matrices $A$ y $B$ de orden $n\times n$ son similares si existe una matriz invertible $n\times n$ tal que $B= Q^{-1}AQ$. Por lo tanto, una matriz es diagonalizable precisamente cuando es similar a una matriz diagonal.</p>
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<p>Nuestro objetivo es caracterizar las transformaciones lineales.</p>
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<blockquote><p><strong>Polinomio característico y similaridad</strong>. <em>Si $A$ y $B$ son similares, entonces ellas tienen el mismo polinomio característico, determinante, traza y valores propios (y sus valores propios tienen las mismas multiplicidades).</em></p>
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<p><em>Demostración</em>. <em>Suponga que $B = Q^{-1}AQ$. Para el polinomio característico, se computa simplemente $\det(\lambda I - B) =$ $\det(Q^{-1}(\lambda I)Q - Q^{-1}AQ)=$ $\det(Q^{-1}(\lambda I - A)Q) = $ $ \det(Q^{-1})\det(\lambda I -A)\det(Q)= $ $\det(\lambda I - A)$.</em></p>
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<p><em>El determinante y la traza son ambos coeficientes para el polinomio característico así que ellos son también iguales.</em></p>
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<p><em>Finalmente, los valores propios son las raíces del polinomio característico, así que llos son los mismos y ocurren con la misma multiplicidad para $A$ y $B$</em>.</p>
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<p>Los vectores propios para matrices similares también esta cercanamente relacionados:</p>
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<blockquote><p><strong>Valores propios y similaridad.</strong> <em>Si $B = Q^{-1}AQ$, entonces $v$ es un vector propios de $B$ con valor propio $\lambda$ si y solo si $Qv$ es un vector propio de $A$ con valor propio $\lambda$.</em></p>
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<p><em>Demostración. Dado que $Q$ es invertible, $v=0$ si y sólo si $Qv=0$. Ahora asumamos que $v\neq 0$. Primero suponemos que $v$ es un vector propio de $B$ con valor propio $\lambda$. Entonces $A(Qv)=Q(Q^{-1}AQ)v=Q(Bv)=Q(\lambda v) = \lambda (Qv)$, esto quiere decir que $Qv$ es un vector propio de $A$ con valor propio $\lambda$.</em></p>
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<p><em>Inversamente, si $Qv$ es un vector propio de $A$ con valor propio $\lambda$. Entonces $Bv = Q^{-1}A(Qv) = Q^{-1}\lambda (Qv) = \lambda (Q^{-1}Qv) = \lambda v$, así $v$ es un vector propio de $B$ con valor propio $\lambda$.</em></p>
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<blockquote><p><strong>Corolario</strong>. <em>Si $B = Q^{-1}AQ$, entonces los subespacios propios para $B$ tienen las mismas dimensiones como los subespacios propios para $A$.</em></p>
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<p>En esencia, diaganalizabilidad es equivalente a la existencia de una base de vectores propios:</p>
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<blockquote><p><strong>Diagonalizabilidad</strong>. <em>Un operador lineal $T:V\to V$ es diagonalizable si y solo si existe una base $\beta$ de $V$ que consiste de vectores propios de $T$.</em></p>
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<p><em>Demostración</em>. <em>Suponga primero que $V$ tiene una base de vectores propios $\beta = \{v_1, v_2,\dots, v_n\}$ con sus respectivos valores propios $\lambda_1, \lambda_2, \dots, \lambda_n$. Entonces por hipótesis, $T(v_i)=\lambda_i v_i$, y así $[T]_{\beta}^{\beta}$ es la matriz diagonal con entradas en la diagonal principal $\lambda_1,\dots, \lambda_n$.</em></p>
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<p><em>Inversamente, suponga que $T$ es diagonalizable y sea $\beta = \{v_1,\dots, v_n\}$ una base tal que $[T]_{\beta}^{\beta}$ es una matriz diagonal cuyas entradas son $\lambda_1, \cdots, \lambda_n.$ Entonces por hipótesis, cada $v_1$ es no cero y $T(v_i)=\lambda_i v_i$ para cada $v_i$ es un vector propio de $T$.</em></p>
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<p>Aunque el resultado anterior da una caracterización de las transformaciones diagonalizables, no es enteramente obvio como para determinar que tal bases de vectores propios existe</p>
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<p>Resulta que esencialmente se puede verificar esta propiedad en cada espacio propio. Se ha provado antes, que la dimensión de cada $\lambda$ - subespacio propio de $T$ es menor o igual que la multiplicidad de $\lambda$ como una raíz del polinomio característico.</p>
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<p>Dado que que el polinomio característico tiene grado $n$, esto quiere decir que la suma de las dimensiones de los $\lambda$ - subespacios no es superios a $n$, y puede ser superior a $n$ solo cuando cada subespacio propio tiene dimensión igual a la multiplicidad de sus correspondientes valores propios.</p>
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<p>El objetivo ahora, es mostrar que si cada subespacio propio tiene dimensión igual a la multiplicidad de sus correspondientes valores propios, entonces la matriz será diagonalizable.</p>
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<p>Pero para hacer esto, antes se necesita un resultado intermedio acerca de la independencia de los vectores propios que tienen distintos valores propios.</p>
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<blockquote><p><strong>Independencia de los vectores propios.</strong> <em>Si $v_1$, $v_2$,..., $v_n$ son vectores propios de $T$ asociados a los distintos valores propios $\lambda_1, \lambda_2, \dots, \lambda_n$ cuando $v_1,\dots, v_{n}$ son linealmente independientes.</em></p>
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<p><em>Demostración</em>. <em>Razonando por inducción sobre $n$. Es caso base para $n=1$ es trivial, dado que por definición un vector propio no puede ser zero. Suponga ahora que $n\leq 2$ y eque se tiene la dependencia lineal $a_1v_1+\cdots + a_nv_n=0$ para los vectores propios $v_1, \dots, v_n$ teniendo distintos valores propios $\lambda_1, \cdots \lambda_n$.</em></p>
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<p><em>Aplicando ahora $T$ a ambos lados $T(a_1v_1+\cdots + a_nv_n) = a_1(\lambda_1 v_1) +\cdots + a_n(\lambda_n v_n) = 0$. Pero si ahora restamos la dependencia original por un factor de $\lambda_1$ se ontiene la nueva relacipon:</em></p>
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\begin{equation}
a_2(\lambda_2-\lambda_1)v_2 + a_3(\lambda_3 - \lambda_1)v_3 + \cdots a_n(\lambda_n - \lambda_1)v_n = 0.
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<p><em>Por la hipótesis inductiva, todos los coeficientes de esta dependencia debe ser cero, y así se tienen $\lambda_k \neq \lambda_1$ para cada $k$, así se concluye que $a_2 = \cdots = a_n = 0$. Entonces $a_1 v_1 = 0$ implica que $a_1 = 0$, con lo que se concluye la prueba.</em></p>
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<p>A continuación vamos a formalizar la noción de tener todos los valores propios en $F$.</p>
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<blockquote><p><strong>Definición</strong>. <em>Si $p(x)\in F[x]$, se dice que $p(x)$ es <strong>factorizable</strong> en $F$ si $p(x)$ se puede escribir como el producto de factores lineales en $F[x]$, es decir $p(x)=a(a-r_1)(x-r_2)\cdot\cdots \cdot(x-r_d)$ para algún $a, r_1, r_2, \dots, r_d\in F$.</em></p>
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<p>Informalmente, un polinomio es factorizable sobre $F$ cuando todas sus raíces son elementos de $F$.</p>
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<p><strong>Ejemplo 1.</strong> El polinomio $x^2 -2$ no es factorizable en $\mathbb{Q}$, pero si es completamente factorizable sobre $\mathbb{R}$ dado que se puede escribir $x^2-2 =(x-\sqrt{2})(x-\sqrt{2})\in \mathbb{R}[x]$. Observe que las raíces $\sqrt{2}$ y $-\sqrt{2}$ del polinomio no son elementos de $\mathbb{Q}$ pero si son elementos de $\mathbb{R}$.</p>
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<p><strong>Ejemplo 2.</strong> El polinomio $x^2-1$ es factorizable sobre $\mathbb{Q}$, dado que se puede escribir $x^2-1 = (x-1)(x+1)$ en $\mathbb{Q}[x]$.</p>
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<p>Si $A$ es una matriz de orden $n\times n$, se dice que todos sus valores propios están en $F$ cuando el polinomio característico de $A$ es factorizable en $F$.</p>
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<p>Ahora vamos a establecer un criterio de diagonalización de matrices:</p>
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<blockquote><p><strong>Creterio de diagonalización</strong>. <em>Una matriz $A\in M_{n\times n}(F)$ es diagonalizable sobre $F$ si y solo si todos los valores propios están den $F$, y para cada valor propio $\lambda$, la dimensión del $\lambda$ - espacio es igual a la multplicidad de $\lambda$ como una raíz del polinomio característico.</em></p>
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<p><em>Demostración</em>. <em>Si la matriz $A$ de orden $n\times n$ es diagonalizable, entonces las entradas de la diagonal de sus diagonalización son los valores propios de $A$, así ellos deberán estár en el campo escalar $F$.</em></p>
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<p><em>Además, por teorema anterior sobre diagonalización, $V$ tiene una base $\beta$ de vectores propios para $A$. Ahora, para cualquier valor propio $\lambda_i$ de $A$, sea $b_i$ el número de elementos de $\beta$ que tienen valor propio $\lambda_i$, y sea $d_i$ la multiplicidad de $\lambda_i$ como una raíz del polinomio característico.</em></p>
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<p><em>Por lo tanto $\sum_i b_i = n$ dado que $\beta$ es una base para $V$, y $\sum_i d_i = n$, de los resultados anteriores el polinomio característico $b_i \leq d_i$. Por lo tanto $n = \sum_i b_i \leq \sum_i d_i = n$, así $b_i = d_i$ para cada $i$.</em></p>
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<p><em>Por otro lado, suponga que los valores propios de $A$ están en $F$ y que $b_i = d_i$ para todo $i$. Entonces sea $\beta$ la unión de las bases para cada subespacio propio de $A$. Por hipótesis, $\beta$ contiene $\sum_i b_i = \sum_i d_i = n$ vectores, así se concluye que es una base $n$ - dimensional para el espacio $V$, ahora solo debemos demostrar que son linealmente indipendientes.</em></p>
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<p><em>Explicitamente, sea $\beta_i = \{v_{i, 1}, \dots, v_{i, j_i}\}$ la base de los $\lambda_i$ - subespacios para cada $i$, así que $\beta = \{v_{1, 1}, v_{1, 2},\dots, v_{k, j}\}$ y $Av_{i, j} = \lambda_i v_{i, j}$ para cada par $(i, j)$.</em></p>
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<p><em>Suponga que hay dependencia $a_{1, 1} v_{1, 1} + \cdots + a_{k, j} = 0$. Sea $w_i = \sum_{j} a_{i, j} v_{i, j}$, y observe que $w_i$ tiene $Aw_i = \lambda_i w_i$, y sea $w_1 + w_2 +\cdots + w_k = 0$.</em></p>
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<p><em>Si alguno de los $w_i$ es no nulo, entonces se tendría un dependecia linela no trivial entre los valores propios de $A$ con distinto valores propios, pero estos es imposible por teorema anterior.</em></p>
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<p><em>Por lo tanto, cada $w_i=0$, quiere decir que $a_{i, 1}v_{i, 1}+\cdots + a_{k, j_i}v_{i, j_i} = 0$. Pero como $\beta_i$ es linealmente independiente, todos los coeficientes $a_{i, j}$ deben ser cero. Por lo tanto, $\beta$ debe ser linealmente independiente y por lo tanto es una base para $V$.</em></p>
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<blockquote><p><strong>Corolario</strong>. <em>Si $A\in M_{n\times n} (F)$ tiene $n$ valores propios distintos en $F$, entonces $A$ es diagonalizable sobre $F$.</em></p>
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<p><em>Demostración</em>. <em>Para cada valor propio se debe tener multiplicidad uno como una raíz del polinomio característico. Dado que hay $n$ valores propios y la suma de sus multiplicidades es también $n$. Entonces la dimensión de cada valor propio es igual a uno (dado que la dimensión siempre está entre uno y la multiplicidad). Así por el teorema anterior, $A$ es diagonalizable.</em></p>
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<div style="text-align: right"> $\Box$ </div>
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<p>La prueba del teorema de diagonalización da un procedimiento explicito para determinar la diagonalizabilidad y la diagonalización de una matriz. Para determinar cuando una transformación lineal $T$ (o matriz) es diagonalizable, y hallar una base $\beta$ tal que $[T]_{\beta}^{\beta}$ es diagonal (o una matriz $Q$ con $Q^{-1}AQ$ diagonal), se siguen los siguientes pasos:</p>
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<li>Encontrar el polinomio característico y los valores propios de $T$ (o $A$).</li>
<li>Encontrar una base para cada subespacio propio de $T$ (o A).</li>
<li>Determinar si $T$ (o $A$) es diagonalizable. Si la dimensión de cada subespacio propio es igual a número de veces que los valores propios aparecen como raíces del polinomio característico, en otro caso $T$ es no diagonalizable. </li>
<li>Para una transformación lineal $T$ diagonalizable, sea $\beta$ una base de los vectores propios para $T$. Para una matriz $A$, la matriz $Q$ de diagonalización puede ser tomada como la matriz cuyas columnas son una base de vectores propios de $A$. </li>
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<p><strong>Ejemplo 3.</strong> Para $T:\mathbb{R}^{2}\to \mathbb{R}^{2}$ dado por $T(x, y)=\langle -2y, 3x + 5y\rangle$, determinar cuando $T$ es diagonalizable y si es así, hallar una base $\beta$ tal que $[T]_{\beta}^{\beta}$ es diagonal.</p>
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<p>La matriz $A$ asociada para $T$ relativa a la base estandar es:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">Matrix</span><span class="p">,</span> <span class="n">factor</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">A</span> <span class="o">=</span> <span class="n">Matrix</span><span class="p">([[</span><span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">5</span><span class="p">]])</span>
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<p>Computamos el polinomio característico</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">polynomial</span> <span class="o">=</span> <span class="n">A</span><span class="o">.</span><span class="n">charpoly</span><span class="p">()</span>
<span class="n">factor</span><span class="p">(</span><span class="n">polynomial</span><span class="o">.</span><span class="n">as_expr</span><span class="p">())</span>
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$\displaystyle \left(\lambda - 3\right) \left(\lambda - 2\right)$
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<p>Por lo tanto los valores propios son $\lambda = 2, 3$. Datoa que los valores propios son distintos, entonces $T$ es diagonalizables.</p>
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<p>Usaremos la siguiente función para calcular las transformaciones $T_\lambda = \lambda I - A$:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">eye</span>
<span class="k">def</span> <span class="nf">eigen_transformation</span><span class="p">(</span><span class="n">eigenvalue</span><span class="p">,</span> <span class="n">A</span><span class="p">):</span>
<span class="n">identity</span> <span class="o">=</span> <span class="n">eye</span><span class="p">(</span><span class="n">A</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
<span class="k">return</span> <span class="n">eigenvalue</span> <span class="o">*</span> <span class="n">identity</span> <span class="o">-</span> <span class="n">A</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">T_2</span> <span class="o">=</span> <span class="n">eigen_transformation</span><span class="p">(</span><span class="n">eigenvalue</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">A</span><span class="o">=</span><span class="n">A</span><span class="p">)</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">T_3</span> <span class="o">=</span> <span class="n">eigen_transformation</span><span class="p">(</span><span class="n">eigenvalue</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">A</span><span class="o">=</span><span class="n">A</span><span class="p">)</span>
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<p>Luego los espacios propios para las transformaciones propias $T_2$ y $T_3$ son:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">T_2</span><span class="o">.</span><span class="n">nullspace</span><span class="p">()</span>
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<pre>[Matrix([
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">T_3</span><span class="o">.</span><span class="n">nullspace</span><span class="p">()</span>
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<pre>[Matrix([
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<p>Esto quiere decir que $[1, -1]^{\top}$ es una base para el $2$ - subespacio propio, y $[-2, 3]^{\top}$ es una base para el $3$ - subespacio.</p>
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<p>Por lo tanto para $\beta = \{[1, -1]^{\top}, [-2, 3]^{\top}\}$, se puede ver que:</p>
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\begin{equation}
[T]_{\beta}^{\beta} = \begin{bmatrix} 2 & 0 \\ 0 & 3 \end{bmatrix}
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<p>En efecto:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">Q</span> <span class="o">=</span> <span class="n">Matrix</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">]])</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">Q</span><span class="o">.</span><span class="n">inv</span><span class="p">()</span><span class="o">*</span><span class="n">A</span><span class="o">*</span><span class="n">Q</span>
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$\displaystyle \left[\begin{matrix}2 & 0\\0 & 3\end{matrix}\right]$
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<p><strong>Ejemplo 4</strong>. Para la matriz $A = \begin{bmatrix} 1 & -1 & -1 \\ 0 & 1 & -1 \\ 0 & 0 & 1 \end{bmatrix}$ determinar si existe una matriz diagonal $D$ y matriz $A$ con $D = Q^{-1}AQ$, y si es así, encontrarla.</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">Matrix</span><span class="p">,</span> <span class="n">factor</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">A</span> <span class="o">=</span> <span class="n">Matrix</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]])</span>
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<p>Sus valores propios son:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">A</span><span class="o">.</span><span class="n">eigenvals</span><span class="p">()</span>
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<pre>{1: 3}</pre>
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<p>Los valores propios son $\lambda = 1, 1, 1$. Esto se puede comprobar fácilmente debido a que $A$ es una matriz triangular y por lo tanto su polinomio característico es $\det(\lambda I - A) = (\lambda - 1)^3$.</p>
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<p>Por otro lado la transformación propio $T_1$ es:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">T_1</span> <span class="o">=</span> <span class="n">eigen_transformation</span><span class="p">(</span><span class="n">eigenvalue</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">A</span><span class="o">=</span><span class="n">A</span><span class="p">)</span>
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$\displaystyle \left[\begin{matrix}0 & 1 & 1\\0 & 0 & 1\\0 & 0 & 0\end{matrix}\right]$
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<p>Donde su espacio nulo es:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">T_1</span><span class="o">.</span><span class="n">nullspace</span><span class="p">()</span>
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<pre>[Matrix([
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<p>Por lo tanto el $1$ - subespacio propio es generado por $[1, 0, 0]^{\top}$. Dado que la dimensionalidad de este espacio no es igual a la multiplicidad de $\lambda = 1$, entonces la matriz $A$ no es diagonalizable y por lo tanto no existen las matrices $D$ y $Q$.</p>
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<p><strong>Ejemplo 5.</strong> Para la matriz $\begin{bmatrix} 1 & -1 & 0 \\ 0 & 2 & 0 \\ 0 & 2 & 1 \end{bmatrix}$, determine si existe una matriz diagonal $D$ y una matriz invertible $Q$ tal que $D = Q^{-1}AQ$, si es así, encontrarlas.</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">A</span> <span class="o">=</span> <span class="n">Matrix</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">]])</span>
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$\displaystyle \left(\lambda - 2\right) \left(\lambda - 1\right)^{2}$
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<p>Así, los valores propios son $\lambda = 1, 1, 2$.</p>
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<p>Las tranformaciones propias sociadas respectivamente a cada valor de $\lambda$ son:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">T_1</span> <span class="o">=</span> <span class="n">eigen_transformation</span><span class="p">(</span><span class="n">eigenvalue</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">A</span><span class="o">=</span><span class="n">A</span><span class="p">)</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">T_2</span> <span class="o">=</span> <span class="n">eigen_transformation</span><span class="p">(</span><span class="n">eigenvalue</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">A</span><span class="o">=</span><span class="n">A</span><span class="p">)</span>
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<p>Sus respectivos subespacios serían:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">T_1</span><span class="o">.</span><span class="n">nullspace</span><span class="p">()</span>
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<pre>[Matrix([
[1],
[0],
[0]]),
Matrix([
[0],
[0],
[1]])]</pre>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">T_2</span><span class="o">.</span><span class="n">nullspace</span><span class="p">()</span>
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<pre>[Matrix([
[-1/2],
[ 1/2],
[ 1]])]</pre>
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<p>Por lo tanto $\{[1, 0, 0]^{\top}, [0, 0, 1]^{\top}\}$ es una base para el $1$ - subespacio propio y $\{[-1, 1, 2]^{\top}$ es una base para el $2$ - subespacio propio.</p>
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<p>Dado que la dimensionalidad de cada subespacio propio es igual a su multiplicidad de su respectivo valor propio, entonces $A$ es diagonaizable y se toma a $D$ y $Q$ como:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">D</span> <span class="o">=</span> <span class="n">Matrix</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">]])</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">Q</span> <span class="o">=</span> <span class="n">Matrix</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">]])</span>
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<p>Ahora hay que comprobar que $D = Q^{-1}AQ$ y en efecto se tiene:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">D</span> <span class="o">==</span> <span class="n">Q</span><span class="o">.</span><span class="n">inv</span><span class="p">()</span><span class="o">*</span><span class="n">A</span><span class="o">*</span><span class="n">Q</span>
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<pre>True</pre>
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<p><strong>Observación.</strong> Se puede tomar tambień las siguientes matrices $D$ y $Q$:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">D</span> <span class="o">=</span> <span class="n">Matrix</span><span class="p">([[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]])</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">Q</span> <span class="o">=</span> <span class="n">Matrix</span><span class="p">([[</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]])</span>
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<p>Y nuevamente se comprueba que $D = Q^{-1}A Q$.</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">D</span> <span class="o">==</span> <span class="n">Q</span><span class="o">.</span><span class="n">inv</span><span class="p">()</span><span class="o">*</span><span class="n">A</span><span class="o">*</span><span class="n">Q</span>
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<pre>True</pre>
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<p>Es decir no hay una razón particular para para preocuparse mucho sobre qué matriz diagonal diagonal, siempre que se organicen los vectores propios y los valores propios de manera correspondiente. También se podría haber utilizado cualquier otra base de los espacios propios para construir $Q$.</p>
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<p>Sabiedno que una matriz es diagonalizable, esta puede ser muy útil para realizar algunos cálculos complejos.</p>
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<p>Por ejemplo, si $A$ es una matriz diagonalizable con $D = Q^{-1}A Q$, entonces es muy fácil computar cualquier pontencia de $A$. Explicitamente, dado que se puede escribir $A = QD^{-1}$, entonces $A^{k}=(QDQ^{-1})^{k}=QD^{k}Q^{-1}$. Pero como $D$ es diagonal, entonces $D^{k}$ es simplemente una matriz diagonal cuyas entradas son las $k$ potencias de las entradas de $D$.</p>
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<p><strong>Ejemplo 5.</strong> Si $A = \begin{bmatrix} -2 & -6 \\ 3 & 7 \end{bmatrix}$, encontrar una formula de la $k$ potencia $A^{k}$, para un entero positivo.</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">Matrix</span><span class="p">,</span> <span class="n">factor</span><span class="p">,</span> <span class="n">symbols</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">k</span> <span class="o">=</span> <span class="n">symbols</span><span class="p">(</span><span class="s1">'k'</span><span class="p">)</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">A</span> <span class="o">=</span> <span class="n">Matrix</span><span class="p">([[</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="o">-</span><span class="mi">6</span><span class="p">],</span> <span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">7</span><span class="p">]])</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">A</span><span class="o">.</span><span class="n">eigenvals</span><span class="p">()</span>
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<pre>{4: 1, 1: 1}</pre>
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<p>Los valores propios son $\lambda = 4, 1$. Así las transformaciones propias serían:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">T_4</span> <span class="o">=</span> <span class="n">eigen_transformation</span><span class="p">(</span><span class="n">eigenvalue</span><span class="o">=</span><span class="mi">4</span><span class="p">,</span> <span class="n">A</span><span class="o">=</span><span class="n">A</span><span class="p">)</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">T_1</span> <span class="o">=</span> <span class="n">eigen_transformation</span><span class="p">(</span><span class="n">eigenvalue</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">A</span><span class="o">=</span><span class="n">A</span><span class="p">)</span>
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<p>Y sus respectivos espacios nulos serían:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">T_4</span><span class="o">.</span><span class="n">nullspace</span><span class="p">()</span>
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<pre>[Matrix([
[-1],
[ 1]])]</pre>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">T_1</span><span class="o">.</span><span class="n">nullspace</span><span class="p">()</span>
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<pre>[Matrix([
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<p>Por lo tanto una base para el $4$ - subespacio propio es $\{[-1, 1]^{\top}\}$ y una base para el $1$ - subespacio propio es $\{[-2, 1]^{\top}\}$. Así las matrices $D$ y $Q$ serían:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">D</span> <span class="o">=</span> <span class="n">Matrix</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">4</span><span class="p">]])</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">Q</span> <span class="o">=</span> <span class="n">Matrix</span><span class="p">([[</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">]])</span>
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<p>Luego, $D^{k}$ y $A^{k}$ son:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">D</span><span class="o">**</span><span class="n">k</span>
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$\displaystyle \left[\begin{matrix}1 & 0\\0 & 4^{k}\end{matrix}\right]$
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">A</span><span class="o">**</span><span class="n">k</span>
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$\displaystyle \left[\begin{matrix}2 - 4^{k} & 2 - 2 \cdot 4^{k}\\4^{k} - 1 & 2 \cdot 4^{k} - 1\end{matrix}\right]$
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<p>Finalmente, hay que verificar que $A^{k} = QD^{k}Q^{-1}$.</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">A</span><span class="o">**</span><span class="n">k</span> <span class="o">==</span> <span class="n">Q</span><span class="o">*</span> <span class="n">D</span><span class="o">**</span><span class="n">k</span> <span class="o">*</span> <span class="n">Q</span><span class="o">.</span><span class="n">inv</span><span class="p">()</span>
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<pre>True</pre>
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<p>También se puede usar la diagonalización de una matriz para probar nuevos teoremas de una forma más simple. He aquí un ejemplo típico.</p>
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<blockquote><p><strong>Definición.</strong> <em>Si $T:V\to V$ es un operador y $p(x) = a_0 + a_1 x+\cdots a_nx^n$ es un polinomio, se define:
$$p(T)= a_0 I + a_1 T + \cdots a_n T^{n}.$$
Similarmente, si $A$ es una matriz de orden $n\times n$, se define:
$$p(A) = a_0 I + a_1 A + \cdots a_n A^{n}.$$
Es fácil comprobar que $Q^{-1}p(A)Q = p(Q^{-1}AQ)$.</em></p>
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<blockquote><p><strong>Caley-Hamilton.</strong> Si $p(x)$ es el polinómio característico de la matriz $A$, entonces $p(A)$ es la matriz cero.</p>
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<p>El mismo se resultado se dá para el polinomio característico del operador lineal $T:V\to V$.</p>
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<p><strong>Ejemplo 6.</strong> Para la matriz $\begin{bmatrix} 2 & 2 \\ 3 & 1 \end{bmatrix}$, se tiene:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">Matrix</span><span class="p">,</span> <span class="n">factor</span><span class="p">,</span> <span class="n">symbols</span><span class="p">,</span> <span class="n">eye</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">A</span> <span class="o">=</span> <span class="n">Matrix</span><span class="p">([[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">]])</span>
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<p>con polinomio característico:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">A</span><span class="o">.</span><span class="n">charpoly</span><span class="p">()</span><span class="o">.</span><span class="n">as_expr</span><span class="p">()</span>
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$\displaystyle \lambda^{2} - 3 \lambda - 4$
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<p>Se computar fácilmente $A^{2} - 3 A - 4I_{2}$, en efecto:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">A</span><span class="o">**</span><span class="mi">2</span> <span class="o">-</span> <span class="mi">3</span> <span class="o">*</span> <span class="n">A</span> <span class="o">-</span> <span class="mi">4</span> <span class="o">*</span> <span class="n">eye</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
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$\displaystyle \left[\begin{matrix}0 & 0\\0 & 0\end{matrix}\right]$
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<p><em>Demostración</em>. <em>Si $A$ es diagonalizable, entonces $D = Q^{-1} A Q$ con $D$ diagonal, y sea $p(x)$ el polinomio característico de $A$. La diagonal de entradas de $D$ son los valores propios $\lambda_1,\dots, \lambda_n$ de $A$. por lo tanto son raíces del polinómio característico, es decir $p(\lambda_1)=\cdots=p(\lambda_n)=0$.</em></p>
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<p><em>Se puede verificar fácilmente que:</em></p>
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\begin{equation}
p(D)=p\left(\begin{bmatrix} \lambda_1 & & \\ &\ddots & \\ & & \lambda_n\end{bmatrix}\right) = \begin{bmatrix} p(\lambda_1) & & \\ &\ddots & \\ & & p(\lambda_n)\end{bmatrix} = \begin{bmatrix} 0 & & \\ &\ddots & \\ & & 0\end{bmatrix}=0.
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<p><em>Luego $p(A) = Q p(D) Q^{-1} = 0$ cómo se quería probar.</em></p>
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<p>En el caso de una matriz $A$ no diagonalizable, la prueba del teorema de Cayley Hamilton es sustancialmente más dificil. Este caso se tratará en la sigueinte sección usando la forma canónica de Jordan.</p>
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<h2 id="Bibliografía">Bibliografía<a class="anchor-link" href="#Bibliografía">¶</a></h2><ol>
<li>Evan Dummit, 2020, Linear Algebra - part 4: Eingenvalues, Diagonalization, and the Jordan Form.</li>
<li>SymPy Development Team. 2021. <a href="https://docs.sympy.org/latest/index.html">Sympy 1.8 documetation</a>.</li>
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<h2 id="Contacto">Contacto<a class="anchor-link" href="#Contacto">¶</a></h2><ul>
<li>Participa del canal de Nerve a través de <a href="https://discord.gg/edPmghPq8K">Discord</a>.</li>
<li>Se quieres conocer más acerca de este tema me puedes contactar a través de <a href="https://www.classgap.com/me/alejandro-sanchez-yali">Classgap</a>.</li>
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<p>Si el post fue de tu agrado muestra tu apoyo compartiéndolo, suscribiéndote al blog, siguiéndome o realizando una donación.</p>
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www.asanchezyali.comhttp://www.blogger.com/profile/06396258253910042323noreply@blogger.com0tag:blogger.com,1999:blog-8939855543774830921.post-53195953771229476692021-04-11T09:43:00.006-05:002021-04-11T09:54:36.842-05:00Álgebra Lineal Parte 1/4: Valores propios, vectores propios y subespacios propios<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
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<p style="text-align: justify;">En esta ocasión, vamos a hablar de valores propios y vectores propios: estos son valores y vectores característicos asociados a un operador lineal $T:V\to V$ que permiten estudiar a $T$ en una forma particularmente conveniente. Nuestro objetivo final es describir métodos para encontrar una base para $V$ tal que la matriz asociada $T$ tenga una forma especialmente simple.</p>
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<p style="text-align: justify;">Primero vamos a describir el <strong>proceso de diagonalización</strong>, procedimiento que se hace para encontrar una base tal que la matriz asociada a $T$ sea una matriz diagonal, y que caracteriza a los operadores lineales que son diagonalizables.</p>
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<p style="text-align: justify;">Desafortunadamente, no todos los operadores lineales son diagonalizables, así que también vamos a discutir un método para calcular la forma canónica de una matriz, el cual es la representación más cercana posible a una matriz diagonal. Finalmente estudiaremos unas aplicaciones de la forma canónica de Jordan, incluyendo el teorema de Cayley-Hamilton que es para cualquier matriz que satisface su polinómio característico.</p>
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<h2 id="Valores-propios,-vectores-propios-y-el-polinómio-característico" style="text-align: justify;">Valores propios, vectores propios y el polinómio característico<a class="anchor-link" href="#Valores-propios,-vectores-propios-y-el-polinómio-característico">¶</a></h2>
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<p style="text-align: justify;">Suponga que se tiene una transformación lineal $T:V\to V$ de un espacio vectorial finito dimensional en sí mismo. Vamos a probar que existe una base $\beta$ de $V$ tal que la matriz asociada a $T$ es una matriz diagonal. La motivación para resolver esto, es porque es deseable describir a $T$ en la forma más simple posible, ¿Y hay otra forma más simple que una matriz diagonal?</p>
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<p style="text-align: justify;">Suponga que $\beta = \{v_1, \dots, v_n\}$ y que la matriz asociada a $T$ es la matriz diagonal $[T]_{\beta}^{\beta} =\operatorname*{diag\,} (\lambda_1, \dots, \lambda_n)$. Bajo este supuesto, se tiene que $[T]_{\beta}^{\beta}(v_i)=\lambda_i v_i$ para cada $1\leq i\leq n$; la transformación lineal $T$ se comporta como la multiplicación de un escalar $\lambda_i$ por un vector $v_i$. Inversamente, si se tiene una base $\beta$ de $V$ tal que $[T]_{\beta}^{\beta}(v_i)=\lambda_i v_i$ para algún escalar $\lambda_i$, con $1\leq i \leq n$, entonces la matriz asociada $[T]_{\beta}^{\beta}$ es una matriz diagonal.</p>
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<p style="text-align: justify;">Esto sugiere que hay que estudiar los vectores $v$ tal que $T(v) = \lambda v$ para algún escalar $\lambda$.</p>
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<blockquote><p style="text-align: justify;"><strong>Definición.</strong> <em>Si $T:V\to V$ es una transformación lineal, un vector no nulo $v$ con $T(v)=\lambda v$ es una <strong>vector propio</strong> de $T$, y le corresponde un escalar $\lambda$ llamado <strong>valor propio</strong> de $T$</em>.</p>
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<p style="text-align: justify;">No se considera el vector cero como un vector propio. La razón de esta convención es para asegurar que si $v$ es un vector propio, entonces le corresponde un valor propio $\lambda$ único. Tambien observe que implícitamente $\lambda$ debe ser un elemento del campo escalar de $V$, dado que en otro caso $\lambda v$ no tendría sentido.</p>
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<p style="text-align: justify;">Cuando $V$ es un espacio de funciones, se usa a menudo las palabras <strong>funciones propias</strong> en lugar de <strong>vectores propios</strong>.</p>
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<p style="text-align: justify;">Veamos algunos ejemplos de transformaciones lineales y vectores propios</p>
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<p style="text-align: justify;"><strong>Ejemplo 1.</strong> <em>Si $T:\mathbb{R}^2\to \mathbb{R}^2$ es una transformación con $T(x, y) = [2x+3y, x+4y]^\top$, entonces $v=[3, -1]^\top$ es una vector propio de $T$ con valor propio $\lambda = 1$, por lo tanto $T(v) = [3, -1]^\top = v$. En efecto</em>:</p>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="k">def</span> <span class="nf">T</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span></div><span><div style="text-align: justify;"> <span class="k">return</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">x</span> <span class="o">+</span> <span class="mi">3</span> <span class="o">*</span> <span class="n">y</span><span class="p">,</span> <span class="n">x</span> <span class="o">+</span> <span class="mi">4</span> <span class="o">*</span> <span class="n">y</span><span class="p">)</span></div></span></pre></div>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">T</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span> <span class="o">==</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span>
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<p style="text-align: justify;"><strong>Ejemplo 2.</strong> <em>Si $T:M_{2\times 2}(\mathbb{R})\to M_{2\times 2}(\mathbb{R})$ es la transformación transposición, entonces la matriz $\big[\begin{smallmatrix} 1 & 1 \\ 1 & 3 \end{smallmatrix}\big]$ es un vector propio de $T$ con valor propio $\lambda = 1$, en efecto</em>:</p>
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<p style="text-align: justify;"><strong>Ejemplo 3.</strong> <em>Si $T:P(\mathbb{R})\to P(\mathbb{R})$ es la transformación dada por $T(f(x))=xf'(x)$, entonces para cualquier entero $n\geq 0$, el polinomio $p(x) = x^n$ es una función propia de $T$ con valor propio $n$, dado que $T(x^{n})=nx^{n}$. Esto lo vemos en Python así</em>:</p>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="n">x</span> <span class="o">=</span> <span class="n">symbols</span><span class="p">(</span><span class="s1">'x'</span><span class="p">)</span></div><span><div style="text-align: justify;"><span class="n">n</span> <span class="o">=</span> <span class="n">symbols</span><span class="p">(</span><span class="s1">'n'</span><span class="p">)</span></div></span></pre></div>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="k">def</span> <span class="nf">f</span><span class="p">(</span><span class="n">x</span><span class="p">):</span></div><span><div style="text-align: justify;"> <span class="k">return</span> <span class="n">x</span><span class="o">**</span><span class="n">n</span></div></span></pre></div>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="k">def</span> <span class="nf">T</span><span class="p">(</span><span class="n">f</span><span class="p">):</span></div><span><div style="text-align: justify;"> <span class="k">return</span> <span class="n">x</span> <span class="o">*</span> <span class="n">diff</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span></div></span></pre></div>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">T</span><span class="p">(</span><span class="n">f</span><span class="p">(</span><span class="n">x</span><span class="p">))</span> <span class="o">==</span> <span class="n">n</span> <span class="o">*</span> <span class="n">f</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
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<pre style="text-align: justify;">True</pre>
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<p style="text-align: justify;"><strong>Ejemplo 4.</strong> <em>Si $V$ es un espacio infinito diferenciable de funciones y $D:V\to V$ es el operador diferenciación, la función $f(x) = e^{rx}$ es una función propia con valor propio $r$, para cualquier número real $r$, dado que $D(e^{rx})=re^{rx}$.</em></p>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">symbols</span><span class="p">,</span> <span class="n">exp</span><span class="p">,</span> <span class="n">diff</span>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="n">x</span> <span class="o">=</span> <span class="n">symbols</span><span class="p">(</span><span class="s1">'x'</span><span class="p">)</span></div><span><div style="text-align: justify;"><span class="n">r</span> <span class="o">=</span> <span class="n">symbols</span><span class="p">(</span><span class="s1">'r'</span><span class="p">)</span></div></span></pre></div>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="k">def</span> <span class="nf">f</span><span class="p">(</span><span class="n">x</span><span class="p">):</span></div><span><div style="text-align: justify;"> <span class="k">return</span> <span class="n">exp</span><span class="p">(</span><span class="n">r</span><span class="o">*</span><span class="n">x</span><span class="p">)</span></div></span></pre></div>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="k">def</span> <span class="nf">D</span><span class="p">(</span><span class="n">f</span><span class="p">):</span></div><span><div style="text-align: justify;"> <span class="k">return</span> <span class="n">diff</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span></div></span></pre></div>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">D</span><span class="p">(</span><span class="n">f</span><span class="p">(</span><span class="n">x</span><span class="p">))</span> <span class="o">==</span> <span class="n">r</span> <span class="o">*</span> <span class="n">f</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
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<pre style="text-align: justify;">True</pre>
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<p style="text-align: justify;"><strong>Ejemplo 5.</strong> <em>Si $T:V\to V$ es cualquier transformación lineal y $v$ es un vector no nulo en $\ker (T)$, entonces $v$ es un vector propio de $V$ con valor propio cero. En efecto, los vectores propios asociados a cero son precisamente los vectores no nulos en $\ker (T)$.</em></p>
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<p style="text-align: justify;">Encontrar los vectores propios es una generalización del cálculo del kernel de una transformación lineal, en efecto, se puede reducir el problema de encontrar los vectores propios a computar el kernel de una transformación lineal relacionada.</p>
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<blockquote><p style="text-align: justify;"><strong>Criterio del valor propio.</strong> <em>Si $T: V\to V$ es una transformación lineal, el vector no nulo $v$ es un vector propio de $T$ con valor propio $\lambda$ si y sólo si $v$ está en el $\ker(\lambda \operatorname{id} - T) = \ker(T-\lambda \operatorname{id})$, donde $\operatorname{id}$ es la transformación identidad sobre $V$.</em></p>
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<p style="text-align: justify;">Este criterio reduce el cálculo de los vectores propios a computar el kernel de una colección de transformaciones lineales.</p>
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<p style="text-align: justify;"><em>Demostración: Asuma que $v\neq 0$. Entonces $v$ es un vector propio de $T$ con valor propio $\lambda$ si, y solo si $T(v)=\lambda v$ si, y solo si $(\lambda\operatorname{id})v - T(v) =0$ si, y solo si $(\lambda \operatorname{id} - T)(v) = 0$ si, y solo si $v$ pertenece al kernel de $\lambda \operatorname{id}-T$. La equivalencia $\ker (\lambda \operatorname{id} - T) = \ker(T-\lambda \operatorname{id})$ es también inmediata.</em></p>
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<div style="text-align: right;"> $\Box$ </div>
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<p style="text-align: justify;">Es importante resaltar que hay algunos operadores lineales que no tienen vectores propios.</p>
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<p style="text-align: justify;"><strong>Ejemplo 6.</strong> <em>Si $I:\mathbb{R}[x]\to \mathbb{R}[x]$ es el operador integración, $I(p)=\int_{0}^{x}p(t)dt$, no tiene vectores propios. En efecto, si se supone que $I(p)=\lambda p$, esto es $\int_{0}^{x}p(x)dt = \lambda p(x)$. Entonces derivando a ambos lados con respecto a $x$ y aplicando el teorema fundamental del cálculo se deduce que $p(x) = \lambda p'(x)$. Si $p$ tiene un grado positivo $n$, entonces $\lambda p'(x)$ debería tener un grado a lo sumo de $n-1$, que no es igual a $p(x)$. Por lo tanto, $p$ debe ser el polinomio constante. Pero el único polinomio constante con $I(p) = \lambda p$ es el polinomio cero, el cual por definición no es un vector propio. Por lo tanto, $I$ no tiene vectores propios.</em></p>
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<p style="text-align: justify;">En otros casos, la existencia de los vectores propios dependen del campo escalar que se está usando.</p>
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<p style="text-align: justify;"><strong>Ejemplo 7.</strong> <em>Si se considera $T:F^2 \to F^2$ definido por $T(x, y) = \langle y, -x\rangle$, no tiene valores propios cuando $F=\mathbb{R}$, pero si tiene vectores propios cuando $F=\mathbb{C}$. En efecto si $T(x, y) = \lambda \langle x , y\rangle$, se tiene que $y=\lambda x$ y $-x = \lambda x$, así que $(\lambda^{2} + 1)y=0$. Si $y$ fuera cero, entonces $x=-\lambda y$ sería tambien cero, imposible. Por lo tanto $y\neq 0$ y así $\lambda^{2}+1=0$. Cuando $F=\mathbb{R}$ no existe tal escalar $\lambda$, y por lo tanto en este caso no hay vectores propios. Sin embargo, cuando $F=\mathbb{C}$, se tiene que $\lambda =\pm i$, y entonces los vectores propios son $[x, -ix]^{\top}$ con valor propio $i$ y $[x, ix]^{\top}$ con valor propio $-i$.</em></p>
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<p style="text-align: justify;">Calcular los vectores propios en general de transformaciones lineales sobre espacio infinito dimensionales pueder ser muy complicado.</p>
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<p style="text-align: justify;">Por ejemplo, si $V$ es un espacio infinito diferenciable de funciones, entonces calcular los vectores propios de la transformación $T:V\to V$ con $T(f)=f''+xf'$ requiere resolver la ecuación $f''+x f'=\lambda f$ para un $\lambda$ arbitrario. Es bastante díficil resolver esa ecuación diferencial particular para una $\lambda$ en general, al menos sin recurrir a utilizar una expansión en serie infinita para describir las soluciones, además las soluciones para la mayoría de los valores de $\lambda$ son funciones no elementales.</p>
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<p style="text-align: justify;">En el caso finito dimensional, el problema se puede resolver usando matrices</p>
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<blockquote><p style="text-align: justify;"><strong>Valores propios y matrices.</strong> <em>Suponga que $V$ es un espacio vectorial finito dimensional con una base ordenada $\beta$ y tal que $T:V\to V$ es una transformación lineal. Entonces $v$ es un vector propio de $T$ con valor propio $\lambda$ si y solo si $[v]_{\beta}$ es un vector propio de la multiplicación a la izquierda por $[T]_{\beta}^{\beta}$ con valor propio $\lambda$.</em></p>
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<p style="text-align: justify;"><em>Demostración: Observe que $v\neq 0$ si y sólo si $[v]_{\beta}\neq 0$. Entonces cuando $v$ es un vector de propio de $T$ entonces $T(v)=\lambda v$, es decir, $[T(v)]_{\beta} = [\lambda v]_{\beta}$ esto es $[T]_{\beta}^{\beta}[v]_{\beta}$ si y solo si $[v]_{\beta}$ es un vector propio de la multiplicación a la izquirda por $[T]_{\beta}^{\beta}$.</em></p>
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<div style="text-align: right;"> $\Box$ </div>
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<h2 id="Valores-propios-y-vectores-propios-de-una-matriz" style="text-align: justify;">Valores propios y vectores propios de una matriz<a class="anchor-link" href="#Valores-propios-y-vectores-propios-de-una-matriz">¶</a></h2>
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<p style="text-align: justify;">Ahora vamos a estudiar los valores y vectores propios de una matriz. Por conveniencia, vamos a establecer esta definicion:</p>
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<blockquote><p style="text-align: justify;"><strong>Definición.</strong> <em>Para una matriz $A$ de orden $n\times n$, un vector no nulo $x$ con $Ax = \lambda x$ es un <strong>vector propio</strong> de $A$, y le corresponde un escalar $\lambda$ llamado <strong>valor propio</strong> de $A$.</em></p>
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<p style="text-align: justify;"><strong>Ejemplo 8.</strong> <em>Si $\big[\begin{smallmatrix} 2 & 3 \\ 1 & 4 \end{smallmatrix}\big]$, el vector $x = [3, -1]^{\top}$ es un vector propio de $A$ con valor propio $1$. En efecto</em>:</p>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">Matrix</span>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">A</span> <span class="o">=</span> <span class="n">Matrix</span><span class="p">([[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">]])</span>
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<p style="text-align: justify;"><em>En<code>sympy</code>es fácil definir vectores columna, estos se definen mediante una lista de elementos</em>:</p>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">x</span> <span class="o">=</span> <span class="n">Matrix</span><span class="p">([</span><span class="mi">3</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">])</span>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">A</span><span class="o">*</span><span class="n">x</span> <span class="o">==</span> <span class="n">x</span>
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<pre style="text-align: justify;">True</pre>
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<p style="text-align: justify;"><strong>Ejemplo 9</strong>. <em>Si $A = \begin{bmatrix}2 & -4 & 5\\ 2 & -2 & 5 \\ 2 & 1 & 2\end{bmatrix}$, el vector $x = [1, 2, 2]^{\top}$ es un vector propio de $A$ con valor propio cuatro. En efecto</em>:</p>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">Matrix</span>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">A</span> <span class="o">=</span> <span class="n">Matrix</span><span class="p">([[</span><span class="mi">2</span><span class="p">,</span> <span class="o">-</span><span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">],</span> <span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="mi">5</span><span class="p">],</span> <span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">]])</span>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">x</span> <span class="o">=</span> <span class="n">Matrix</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">])</span>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">A</span><span class="o">*</span><span class="n">x</span> <span class="o">==</span> <span class="mi">4</span><span class="o">*</span><span class="n">x</span>
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<pre style="text-align: justify;">True</pre>
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<p style="text-align: justify;"><strong>Ejemplo 10.</strong> <em>Los valores y vectores propios tambien pueden involucrar número complejos, incluso si la matriz $A$ tiene solo entradas de número reales. Usualmente se asumen que el campo escalar del espacio vectorial es $\mathbb{R}$ al menos que se especifíque otro caso. A continuación veamos un ejemplo en $\mathbb{C}$</em>.</p>
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<p style="text-align: justify;"><em>Sea $A = \begin{bmatrix}6 & 3 & -2\\ -2 & 0 & 0 \\ 6 & 4 & 2\end{bmatrix}$, el vector $x = [1-i, 2i, 2]^{\top}$ es una vector propio de $A$ con valor propio $i+1$. En efecto</em>:</p>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">Matrix</span><span class="p">,</span> <span class="n">I</span><span class="p">,</span> <span class="n">expand</span>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">A</span> <span class="o">=</span> <span class="n">Matrix</span><span class="p">([[</span><span class="mi">6</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="o">-</span><span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">]])</span>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">x</span> <span class="o">=</span> <span class="n">Matrix</span><span class="p">([</span><span class="mi">1</span><span class="o">-</span><span class="n">I</span><span class="p">,</span> <span class="mi">2</span><span class="o">*</span><span class="n">I</span><span class="p">,</span> <span class="mi">2</span><span class="p">])</span>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">A</span><span class="o">*</span><span class="n">x</span> <span class="o">==</span> <span class="n">expand</span><span class="p">((</span><span class="n">I</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span><span class="o">*</span><span class="n">x</span><span class="p">)</span>
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<pre style="text-align: justify;">True</pre>
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<p style="text-align: justify;">Para este ejemplo<code>I</code> es el número imaginario $i$, y el comando <code>expand</code> se utilizó para expandir los productos.</p>
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<p style="text-align: justify;">En principio parece que una matriz puede tener muchos vectores propios con muchos valores propios. Pero en efecto, cualquier matriz $n\times n$ tiene unos pocos valores propios, y hay una forma simple de encontrarlos todos utilizando determinantes.</p>
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<blockquote><p style="text-align: justify;"><strong>Cálculando valores propios.</strong> <em>Si $A$ es una matriz de orden $n\times n$, el escalar $\lambda$ es una valor propio de $A$ si y sólo si $\det(\lambda I - A) =0.$</em></p>
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<p style="text-align: justify;"><em>Demostración.</em> <em>Suponga que $\lambda$ es un valor propio asociado con el vector no nulo $x$. Entonces $Ax=\lambda x$, o como vimos antes $(\lambda I - A)x = 0$. De los resultados para matrices invertibles, se sabe que la ecuación $(\lambda I - A)x$ tiene solución no nula para $x$ si y solo si la matrix $\lambda I - A$ es no invertible, lo cual es equivalente a decir $\det (\lambda I - A) =0$.</em></p>
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<div style="text-align: right;"> $\Box$ </div>
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<p style="text-align: justify;">Cuando se expande el determinante $\det(\lambda I - A)$, se obtiene un polinomio de grado $n$ en la variable $\lambda$, como se puede verificar por inducción.</p>
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<blockquote><p style="text-align: justify;"><strong>Definición.</strong> <em>Para una matriz $A$ de orgen $n\times n$, el polinomio de grado $p(\lambda) = \det(\lambda I - A)$ es llamado el</em> <strong><em>polinomio característico de $A$</em></strong>, <em>y precisamente su raíces son los valores propios de $A$</em>.</p>
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<p style="text-align: justify;">Algunos autores define el polinomio característico como el determinante de la matriz $A-\lambda I$ en lugar de $\lambda I - A$. Aca se define de esta forma porque el coficiente de $\lambda^{n}$ siempre será $1$, en llugar de $(-1)^{n}$.</p>
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<p style="text-align: justify;">Así para encontrar los valores propios de una matriz, solo se necesita encontrar las raíces del polinómio característico.</p>
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<p style="text-align: justify;">Cuando se investiga las raíces para un polinomio de grado pequeño, el siguiente caso de test para las raíces racionales es amenudo útil.</p>
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<blockquote><p style="text-align: justify;"><strong>Criterio de las raíces racionales de un polínomio.</strong> <em>Suponga que $p(\lambda) = \lambda^{n}+\cdots + b$ tiene coeficientes enteros y el coeficiente principal igual a uno. Entonces cualquier número racional que es una raíz de $p(\lambda)$ debe ser un entero que divide a $b$.</em></p>
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<p style="text-align: justify;">La proposición reduce la cantidad de prueba y error necesaria para encontrar raíces racionales de polinomios, ya que solo necesitamos considerar los números enteros que dividen al término constante.</p>
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<p style="text-align: justify;">Por supuesto, un polinomio genérico no tendrá una raíz racional, por lo que para calcular valores propios en la práctica generalmente se necesita usar algún tipo de procedimiento de aproximación numérica, como el método de Newton para $n$ raíces.</p>
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<p style="text-align: justify;"><strong>Ejemplo 11.</strong> <em>Encontrar los valores propios de $A = \big[\begin{smallmatrix} 3 & 1 \\ 2 & 4 \end{smallmatrix}\big]$. Primero encontramos su polinomio característico.</em></p>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">A</span> <span class="o">=</span> <span class="n">Matrix</span><span class="p">([[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">4</span><span class="p">]])</span>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="n">polynomial</span> <span class="o">=</span> <span class="n">A</span><span class="o">.</span><span class="n">charpoly</span><span class="p">()</span></div><span><div style="text-align: justify;"><span class="n">factor</span><span class="p">(</span><span class="n">polynomial</span><span class="o">.</span><span class="n">as_expr</span><span class="p">())</span></div></span></pre></div>
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$\displaystyle \left(\lambda - 5\right) \left(\lambda - 2\right)$
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<p style="text-align: justify;"><em>Como vemos los ceros del polinomio característico son $\lambda =2$ $\lambda=5$, por lo tanto los valores propios de $A$ son $2$ y $5$.</em></p>
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<p style="text-align: justify;"><strong>Ejemplo 12.</strong> <em>Encontrar los valores propios de $A = \begin{bmatrix}1 & 4 & \sqrt{3}\\ 0 & 3 & -8 \\ 0 & 0 & \pi\end{bmatrix}$.</em></p>
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<p style="text-align: justify;"><em>Observe que el determinante de $\lambda I - A es$: $$\det(\lambda - A) = \begin{bmatrix}\lambda - 1 & -4 & -\sqrt{3}\\ 0 & \lambda - 3 & 8 \\ 0 & 0 & \lambda -\pi\end{bmatrix} = (\lambda - 1)(\lambda - 3)(\lambda - \pi)$$ debido a que la matriz es triangular superior. Por lo tanto los valores propios son $1, 3, pi$.</em></p>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">A</span> <span class="o">=</span> <span class="n">Matrix</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="n">sqrt</span><span class="p">(</span><span class="mi">3</span><span class="p">)],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="o">-</span><span class="mi">8</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">pi</span><span class="p">]])</span>
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$\displaystyle \left(\lambda - 3\right) \left(\lambda - 1\right) \left(\lambda - \pi\right)$
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<p style="text-align: justify;">La idea del ejemplo anterior funciona en general:</p>
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<blockquote><p style="text-align: justify;"><strong>Valores propios de una matriz triangular.</strong> <em>Los valores propios de una matriz triangular superior o inferior son las entradas de la diagonal principal.</em></p>
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<p style="text-align: justify;"><em>Demostración</em>. <em>Si $A$ es una matriz triangular superior de orden $n\times n$ (o inferior), entonces se tiene que $\lambda I - A$ también es una matriz triangular superior (o inferior). Luego por las propiedades de los determinantes, $\det(\lambda I - A)$ es igual a el producto de las entradas de la diagonal principal de $\lambda I - A$. Dado que estas entradas son simplemente $\lambda - a_{i, i}$ para $1\leq i\leq n$, los valores propios son $a_{i, i}$ para $1\leq i\leq n$, es decir, simplemente las entradas de la diagonal principal de $A$.</em></p>
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<div style="text-align: right;"> $\Box$ </div>
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<p style="text-align: justify;">Puede ocurrir que el polinomio característico tenga raíces repetidas. En tal caso, cada valor propio tiene <strong>multiplicidad</strong> y se incluye el valor propio el número de veces restante cuando son listados todos los valor propios.</p>
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<p style="text-align: justify;">Por ejemplos, si una matriz tiene el polinomio caractístico $\lambda^{2}(\lambda - 1)^{1}$, se puede decir que los valores propios son cero con multiplicidad dos, y uno con multiplicidad tres. Los valores propios se deberían listar como $\lambda = 0, 0, 1, 1, 1$.</p>
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<p style="text-align: justify;"><strong>Ejemplo 12</strong>. <em>Encontrar los valores propios de la matriz $A = \begin{bmatrix}1 & -1 & 0\\ 1 & 3 & 0 \\ 0 & 0 & 0\end{bmatrix}$. En este caso se tiene:</em></p>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">A</span> <span class="o">=</span> <span class="n">Matrix</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]])</span>
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$\displaystyle \lambda \left(\lambda - 2\right)^{2}$
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<p style="text-align: justify;"><em>Por lo tanto, el polinomio característico tiene las raíces $\lambda = 0$ de multiplicidad uno y a $\lambda=2$ de multiplicidad dos. De esta forma la matriz $A$ tiene los valores propios $\lambda = 0$ de multiplicidad uno y a $\lambda = 2$ de multiplicidad dos. Y se listarían como $\lambda = 0, 2, 2.$</em></p>
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<p style="text-align: justify;"><strong>Ejemplo 12</strong>. <em>Encontrar los valores propios de la matriz $A = \begin{bmatrix}1 & 1 & 0\\ 0 & 1 & 1 \\ 0 & 0 & 1\end{bmatrix}$.</em></p>
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<p style="text-align: justify;"><em>En este caso como $A$ es triangular superior, los valores propios son las entradas de la diagonal principal, así $A$ tiene por valor propio a $\lambda = 1$ con multiplicidad tres. Y se listaría como $\lambda = 1, 1, 1.$</em></p>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">Matrix</span><span class="p">,</span> <span class="n">factor</span>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">A</span> <span class="o">=</span> <span class="n">Matrix</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]])</span>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="n">polynomial</span> <span class="o">=</span> <span class="n">A</span><span class="o">.</span><span class="n">charpoly</span><span class="p">()</span></div><span><div style="text-align: justify;"><span class="n">factor</span><span class="p">(</span><span class="n">polynomial</span><span class="o">.</span><span class="n">as_expr</span><span class="p">())</span></div></span></pre></div>
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$\displaystyle \left(\lambda - 1\right)^{3}$
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<p style="text-align: justify;">Note también que un polinomio característico podría tener raíces no reales, incluso si la entradas de la matriz son reales.</p>
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<p style="text-align: justify;">Dado que el polinomio característico tiene coeficientes reales, los valores propios no reales serán pares conjugados de números complejos. Además, los vectores propios para estos valores propios no necesariamente contienen entradas no reales.</p>
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<p style="text-align: justify;"><strong>Ejemplo 13.</strong> <em>Encontrar los valores propios de $A =\big[\begin{smallmatrix} 1 & 1 \\ -2 & 3\end{smallmatrix}\big]$. En este caso se tiene:</em></p>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">Matrix</span><span class="p">,</span> <span class="n">factor</span><span class="p">,</span> <span class="n">I</span>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">A</span> <span class="o">=</span> <span class="n">Matrix</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">]])</span>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="n">polynomial</span> <span class="o">=</span> <span class="n">A</span><span class="o">.</span><span class="n">charpoly</span><span class="p">()</span></div><span><div style="text-align: justify;"><span class="n">factor</span><span class="p">(</span><span class="n">polynomial</span><span class="o">.</span><span class="n">as_expr</span><span class="p">(),</span> <span class="n">extension</span><span class="o">=</span><span class="p">[</span><span class="n">I</span><span class="p">])</span></div></span></pre></div>
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$\displaystyle \left(\lambda - 2 - i\right) \left(\lambda - 2 + i\right)$
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<p style="text-align: justify;"><em>Los valores propios son $\lambda = 2 + i, 2 -i$.</em></p>
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<h2 id="Subespacios-propios" style="text-align: justify;">Subespacios propios<a class="anchor-link" href="#Subespacios-propios">¶</a></h2>
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<p style="text-align: justify;">Usando el polinomio caraterístico, se pueden encontrar todos los valores propios de una matriz $A$ sin calcular los vectores propios asociados. Sin embargo, también se quiere encontrar los vectores propios asociados para cada valor propio.</p>
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<blockquote><p style="text-align: justify;"><strong>Subespacios propios.</strong> <em>Si $T: V\to V$ es una transformación lineal, entonces para cualquier valor fijo de $\lambda$, el conjunto $E_{\lambda}$ de vectores en $V$ que satisface $T(v)=\lambda v$ es un subespacio de $V$. Este espacio $E_{\lambda}$ se denomina <strong>subespacio propio</strong> asociado al vector propio $\lambda$ o simplemente $\lambda$ - <strong>subespacio</strong>.</em></p>
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<p style="text-align: justify;">Observe que $E_{\lambda}$ es precisamente el conjunto de vectores propios asociados a $\lambda$ junto con el vector cero.</p>
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<p style="text-align: justify;">Los subespacios propios de una matriz $A$ son definidos de la misma forma. $E_{\lambda}$ es el espacio de vectores $v$ tal que $Av = \lambda v$.</p>
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<p style="text-align: justify;"><em>Demostración.</em> <em>Por definición, $E_{\lambda}$ es el kernel de la transformación lineal $\lambda \operatorname{id} - T$, y por lo tanto es un subespacio de $V$.</em></p>
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<div style="text-align: right;"> $\Box$ </div>
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<p style="text-align: justify;"><strong>Ejemplo 14.</strong> Encontrar todos los valores propios, y una base para cada subespacio propio, para la matriz $A = \big[\begin{smallmatrix} 2 & 2 \\ 3 & 1 \end{smallmatrix}\big]$.</p>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">Matrix</span><span class="p">,</span> <span class="n">factor</span><span class="p">,</span> <span class="n">eye</span><span class="p">,</span> <span class="n">I</span>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">A</span> <span class="o">=</span> <span class="n">Matrix</span><span class="p">([[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">]])</span>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="n">polynomial</span> <span class="o">=</span> <span class="n">A</span><span class="o">.</span><span class="n">charpoly</span><span class="p">()</span></div><span><div style="text-align: justify;"><span class="n">factor</span><span class="p">(</span><span class="n">polynomial</span><span class="o">.</span><span class="n">as_expr</span><span class="p">(),</span> <span class="n">extension</span><span class="o">=</span><span class="p">[</span><span class="n">I</span><span class="p">])</span></div></span></pre></div>
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$\displaystyle \left(\lambda - 4\right) \left(\lambda + 1\right)$
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<p style="text-align: justify;"><em>En este caso los valores propios son $\lambda = -1, 4$ cada uno de multiplicidad uno.</em></p>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">A</span><span class="o">.</span><span class="n">eigenvals</span><span class="p">()</span>
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<pre style="text-align: justify;">{4: 1, -1: 1}</pre>
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<p style="text-align: justify;"><em>De forma general se puede definir la aplicación $f(\lambda)=\lambda\operatorname{id} - A$ de la siguiente forma:</em></p>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="k">def</span> <span class="nf">eigen_transformation</span><span class="p">(</span><span class="n">eigenvalue</span><span class="p">,</span> <span class="n">A</span><span class="p">):</span></div><span><div style="text-align: justify;"> <span class="n">identity</span> <span class="o">=</span> <span class="n">eye</span><span class="p">(</span><span class="n">A</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span></div></span><div style="text-align: justify;"> <span class="k">return</span> <span class="n">eigenvalue</span> <span class="o">*</span> <span class="n">identity</span> <span class="o">-</span> <span class="n">A</span></div></pre></div>
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<p style="text-align: justify;"><em>Para $\lambda = -1$, se tiene matriz asociada:</em></p>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="n">B</span> <span class="o">=</span> <span class="n">eigen_transformation</span><span class="p">(</span><span class="n">eigenvalue</span><span class="o">=-</span><span class="mi">1</span><span class="p">,</span> <span class="n">A</span><span class="o">=</span><span class="n">A</span><span class="p">)</span></div><span><div style="text-align: justify;">B</div></span></pre></div>
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$\displaystyle \left[\begin{matrix}-3 & -2\\-3 & -2\end{matrix}\right]$
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<p style="text-align: justify;"><em>Y su kernel o espacio nulo es</em></p>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">B</span><span class="o">.</span><span class="n">nullspace</span><span class="p">()</span>
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<pre><div style="text-align: justify;">[Matrix([</div> [-2/3],
<div style="text-align: justify;"> [ 1]])]</div></pre>
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<p style="text-align: justify;"><em>De decir que el $-1$-subspacio propio es $1$-dimensional y es generado por $\big[\begin{smallmatrix} -2 \\ 3 \end{smallmatrix}\big]$.</em></p>
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<p style="text-align: justify;"><em>Para $\lambda=4$ se debe encontrar el espacio nulo de la matriz:</em></p>
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$\displaystyle \left[\begin{matrix}2 & -2\\-3 & 3\end{matrix}\right]$
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<p style="text-align: justify;"><em>Aplicando el método <code>nullspace</code> se tiene:</em></p>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">B</span><span class="o">.</span><span class="n">nullspace</span><span class="p">()</span>
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<pre><div style="text-align: justify;">[Matrix([</div> [1],
<div style="text-align: justify;"> [1]])]</div></pre>
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<p style="text-align: justify;"><em>Así, el $4$-subespacio propio es $1$-dimensional y es generado por $\big[\begin{smallmatrix} 1 \\ 1 \end{smallmatrix}\big]$.</em></p>
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<p style="text-align: justify;"><strong>Ejemplo 15.</strong> <em>Encontrar todos los valores propios y una base para cada subespacio propio, para la matriz</em>:
\begin{equation}\begin{bmatrix} 0 & 0 & 0 \\ 1 & 0 & -1 \\ 0 & 1 & 0 \end{bmatrix}.\end{equation}</p>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">Matrix</span><span class="p">,</span> <span class="n">factor</span><span class="p">,</span> <span class="n">eye</span><span class="p">,</span> <span class="n">I</span>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">A</span> <span class="o">=</span> <span class="n">Matrix</span><span class="p">([[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">]])</span>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="n">polynomial</span> <span class="o">=</span> <span class="n">A</span><span class="o">.</span><span class="n">charpoly</span><span class="p">()</span></div><span><div style="text-align: justify;"><span class="n">factor</span><span class="p">(</span><span class="n">polynomial</span><span class="o">.</span><span class="n">as_expr</span><span class="p">(),</span> <span class="n">extension</span><span class="o">=</span><span class="p">[</span><span class="n">I</span><span class="p">])</span></div></span></pre></div>
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$\displaystyle \lambda \left(\lambda - i\right) \left(\lambda + i\right)$
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<p style="text-align: justify;"><em>En este caso los valores propios son $\lambda = 0, i, -i.$</em></p>
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<p style="text-align: justify;"><em>Para $\lambda = 0$, se busca el espacio nulo de la matriz:</em></p>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="n">B</span> <span class="o">=</span> <span class="n">eigen_transformation</span><span class="p">(</span><span class="n">eigenvalue</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">A</span><span class="o">=</span><span class="n">A</span><span class="p">)</span></div><span><div style="text-align: justify;">B</div></span></pre></div>
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$\displaystyle \left[\begin{matrix}0 & 0 & 0\\-1 & 0 & 1\\0 & -1 & 0\end{matrix}\right]$
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<p style="text-align: justify;"><em>cuyo espacio nulo viene dado por:</em></p>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">B</span><span class="o">.</span><span class="n">nullspace</span><span class="p">()</span>
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<pre><div style="text-align: justify;">[Matrix([</div> [1],
<div style="text-align: justify;"> [1]])]</div><div style="text-align: justify;"> [0],</div></pre>
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<p style="text-align: justify;"><em>por lo tanto el $0$-espacio propio es $1$ - dimensional y es generado por $[1, 0, 1]^{\top}$.</em></p>
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<p style="text-align: justify;"><em>Para $\lambda = i$ se tiene:</em></p>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="n">B</span> <span class="o">=</span> <span class="n">eigen_transformation</span><span class="p">(</span><span class="n">eigenvalue</span><span class="o">=</span><span class="n">I</span><span class="p">,</span> <span class="n">A</span><span class="o">=</span><span class="n">A</span><span class="p">)</span></div><span><div style="text-align: justify;"><span class="n">B</span><span class="o">.</span><span class="n">nullspace</span><span class="p">()</span></div></span></pre></div>
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<pre><div style="text-align: justify;">[Matrix([</div> [0],
<div style="text-align: justify;"> [1]])]</div><div style="text-align: justify;"> [I],</div></pre>
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<p style="text-align: justify;"><em>Así el $i$-espacio propio es generado por $[0,i, 1]^{\top}$.</em></p>
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<p style="text-align: justify;"><em>Y para $\lambda = -i$ se tiene:</em></p>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="n">B</span> <span class="o">=</span> <span class="n">eigen_transformation</span><span class="p">(</span><span class="n">eigenvalue</span><span class="o">=-</span><span class="n">I</span><span class="p">,</span> <span class="n">A</span><span class="o">=</span><span class="n">A</span><span class="p">)</span></div><span><div style="text-align: justify;"><span class="n">B</span><span class="o">.</span><span class="n">nullspace</span><span class="p">()</span></div></span></pre></div>
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<pre><div style="text-align: justify;">[Matrix([</div> [ 0],
<div style="text-align: justify;"> [ 1]])]</div><div style="text-align: justify;"> [-I],</div></pre>
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<p style="text-align: justify;"><em>y finalmente el $(-i)$-espacio propio es generado por $[0, -i, 1]^{\top}$.</em></p>
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<p style="text-align: justify;">Note que en el ejemplo anterior, con una matriz real se pueden encontrar valores propios complejos conjugados asociados a vectores propios que también son complejos conjugados. Estos no es un accidente:</p>
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<blockquote><p style="text-align: justify;"><strong>Valores propios conjugados.</strong> <em>Si $A$ es una matriz real y $v$ es un vector propio con valores propios $\lambda$, entonces el complejo conjugado $\bar{v}$ es un vector propio con valor propio $\bar{\lambda}$. En particular, una base para $\bar{\lambda}$-subespacio propio es dado por el complejo conjugado de una base para el $\lambda$ - subespacio propio.</em></p>
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<p style="text-align: justify;"><em>Demostración</em>. <em>La primera afirmación se sigue de la observación que el complejo conjugado de un producto o una suma es propiamente el producto o la suma de los complejos conjugados, así si $A$ y $B$ son cualquier par de matrices compatibles en tamaño para la multiplicación, se tiene $\overline{A\cdot B} = \overline{A}\cdot\overline{B}$.</em></p>
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<p style="text-align: justify;"><em>Por lo tanto, si $Av= \lambda v$, tomando complejos conjudagos dados por $\overline{A}\overline{v}=\overline{\lambda}\overline{v}$, y dado que $\overline{A} = A$ porque $A$ es una matriz real, se puede ver que $A\overline{v} =\overline{\lambda}\overline{v}$, por lo tanto, $\overline{v}$ es un vector propio con valores propio $\overline{\lambda}.$</em></p>
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<p style="text-align: justify;"><em>La segunda afirmación se sigue de la primera, dado que la conjugación compleja no afecta la independencia lineal o la dimensión.</em></p>
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<div style="text-align: right;"> $\Box$ </div>
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<p style="text-align: justify;"><strong>Ejemplo 16.</strong> <em>Encontrar todos los valores propios, y una base para cada valor propio, para la matriz $A = \big[\begin{smallmatrix} 3 & -1 \\ 2 & 5 \end{smallmatrix} \big]$.</em></p>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">Matrix</span><span class="p">,</span> <span class="n">factor</span><span class="p">,</span> <span class="n">eye</span><span class="p">,</span> <span class="n">I</span>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">A</span> <span class="o">=</span> <span class="n">Matrix</span><span class="p">([[</span><span class="mi">3</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">5</span><span class="p">]])</span>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="n">polynomial</span> <span class="o">=</span> <span class="n">A</span><span class="o">.</span><span class="n">charpoly</span><span class="p">()</span></div><span><div style="text-align: justify;"><span class="n">factor</span><span class="p">(</span><span class="n">polynomial</span><span class="o">.</span><span class="n">as_expr</span><span class="p">(),</span> <span class="n">extension</span><span class="o">=</span><span class="p">[</span><span class="n">I</span><span class="p">])</span></div></span></pre></div>
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$\displaystyle \left(\lambda - 4 - i\right) \left(\lambda - 4 + i\right)$
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<p style="text-align: justify;"><em>El espacio nulo para $\lambda = 4+i$ es:</em></p>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="n">B</span> <span class="o">=</span> <span class="n">eigen_transformation</span><span class="p">(</span><span class="n">eigenvalue</span><span class="o">=</span><span class="mi">4</span><span class="o">+</span><span class="n">I</span><span class="p">,</span> <span class="n">A</span><span class="o">=</span><span class="n">A</span><span class="p">)</span></div><span><div style="text-align: justify;"><span class="n">B</span><span class="o">.</span><span class="n">nullspace</span><span class="p">()</span></div></span></pre></div>
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<pre><div style="text-align: justify;">[Matrix([</div><div style="text-align: justify;"> [-1/2 + I/2],</div><div style="text-align: justify;"> [ 1]])]</div></pre>
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<p style="text-align: justify;"><em>de donde se concluye que el $(4 + i)$ - subespacio propio es $1$ - dimensional y es generado por $[-1/2 + i/2, 1]^{\top}$.</em></p>
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<p style="text-align: justify;"><em>Ahora para $\lambda = 4- i$ el $(4-i)$-subespacio también es $1$ - dimensional y es generado por $[-1/2 - i/2, 1]^{\top}.$</em></p>
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<p style="text-align: justify;">El siguiente resultado sobre valores propios puede ser útil en los cálculos de doble verificación:</p>
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<blockquote><p style="text-align: justify;"><strong>Valores propios, traza y determinantes</strong>. <em>El producto de los valores propios de $A$ es el determinante de $A$ y la suman de los valores propios de $A$ es igual a la traza de $A$.</em></p>
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<p style="text-align: justify;">Recuerde que la traza de una matriz es definida por la suma de las entradas de su diagonal principal.</p>
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<p style="text-align: justify;"><em>Demostración</em>. <em>Sea $p(\lambda)$ el polinomio característico de $A$. Si se expande el producto de $p(\lambda)=(\lambda -\lambda_1)(\lambda -\lambda_2)\cdot\cdots\cdot (\lambda -\lambda_n)$, se encuentra que el termino constante es igual a $(-1)^{n}\lambda_1\lambda_2\cdots\lambda_n$. Pero el termino constante también es $p(0)$, y dado que $p(\lambda) = \det (\lambda I - A)$ se tiene $p(0)=\det(-A)=(-1)^{n}\det(A)$, por lo tanto $\lambda_1\lambda_2\cdots \lambda_n =\det(A)$.</em></p>
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<p style="text-align: justify;"><em>Además también de la expansión de $p(\lambda)=(\lambda -\lambda_1)(\lambda -\lambda_2)\cdot\cdots\cdot (\lambda -\lambda_n)$, se tiene que el coeficiente de $\lambda^{n-1}$ es igual a $-(\lambda_1 +\cdots+\lambda_n)$.</em></p>
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<p style="text-align: justify;"><em>Si se expande el determinante $\det(\lambda I - A)$ para encontrar el coeficiente de $\lambda^{n-1}$, por una proceso de inducción se puede demostrar que el coeficiente es el negativo de la suma de las entradas de la diagonal principal de $A$.</em></p>
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<p style="text-align: justify;"><em>Por lo tanto, igualando las dos expresiones se muestra que la suma de los valores propios es igual a la traza de $A$.</em></p>
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<div style="text-align: right;"> $\Box$ </div>
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<p style="text-align: justify;"><strong>Ejemplo 16.</strong> <em>Encontrar los valores propios de la matriz $$A = \begin{bmatrix} 2 & 1 & 1 \\ -2 & -1 & -2 \\ 2 & 2 & -3 \end{bmatrix}$$ y verificar las formulas para la traza y el determinante en terminos de los valores propios.</em></p>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">Matrix</span><span class="p">,</span> <span class="n">Trace</span>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">A</span> <span class="o">=</span> <span class="n">Matrix</span><span class="p">([[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="o">-</span><span class="mi">3</span><span class="p">]])</span>
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$\displaystyle \lambda^{3} + 2 \lambda^{2} - \lambda - 2$
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<p style="text-align: justify;"><em>Para encontrar los valores propios, se puede resolver la ecuación cúbica $\lambda^3 + 2\lambda^2 - \lambda -2 = 0$ o simplemente:</em></p>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">A</span><span class="o">.</span><span class="n">eigenvals</span><span class="p">()</span>
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<pre style="text-align: justify;">{1: 1, -1: 1, -2: 1}</pre>
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<p style="text-align: justify;"><em>Los valores propios son $\lambda = 1, -1, -2$, y su suma es $1 + (-1) + (-2) = -2$ y el producto $(1)\cdot (-1) \cdot (-2) = 2$. Por otro lado la traza de $A$ es:</em></p>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">Trace</span><span class="p">(</span><span class="n">A</span><span class="p">)</span><span class="o">.</span><span class="n">simplify</span><span class="p">()</span>
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$\displaystyle -2$
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<p style="text-align: justify;"><em>y el determinante de $A$ es:</em></p>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">A</span><span class="o">.</span><span class="n">det</span><span class="p">()</span>
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$\displaystyle 2$
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<p style="text-align: justify;">En todos los ejemplos anteriores, la dimensión de cada subespacio era menor o igual que la multiplicidad de los valores propios como raíces del polinomio característico. Esto es verdad en general.</p>
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<blockquote><p style="text-align: justify;"><strong>Multiplicidad de los valores propios</strong>. <em>Si $\lambda$ es un valor propio de la matriz $A$ el cual aparece exactamente $k$ veces como una raíz del polinomio característico, entonces la dimensión del subespacio propio corresponde a $\lambda$ es a lo menos uno y a lo sumo $k$.</em></p>
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<p style="text-align: justify;">Recuerde que el número de veces que $\lambda$ aparece como una raíz del polinomio característico se denomina usualmente como la <strong>multiplicidad algebraica</strong> de $\lambda$, y la dimensión del subespacio propio correspondiente a $\lambda$ se denomina <strong>multiplicidad geométrica</strong> y es menor o igual que la multiplicidad algebraica.</p>
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<p style="text-align: justify;"><strong>Ejemplo 17</strong>. <em>Si el polinomio característico de una matriz es $(\lambda - 1)^{3}(\lambda -3)^{2}$, entonces el subespacio propio para $\lambda = 1$ es a lo sumo 3 - dimensional y el subespacio propio para $\lambda=3$ es a lo sumo 2 - dimensional.</em></p>
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<p style="text-align: justify;"><em>Demostración</em>. <em>La afirmación de que un subespacio propio tiene al menos dimensión uno es inmediata, porque si $\lambda$ es una raíz del polinomio característico hay al menos un vector no nulo asociado a él.</em></p>
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<p style="text-align: justify;"><em>Para la otra afirmación, observe que la dimensión de el $\lambda$ - subespacio es la dimensión del espacio homogéneo del sistema $(\lambda I - A) x = 0$.</em></p>
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<p style="text-align: justify;"><em>Si $\lambda$ aparece $k$ veces como una raíz del polinomio característico, entonces cuadno se hace $\lambda I - A$ entonces al reducir esta matriz a la forma escalonada por filas $B$, $B$ debe tener al menos $k$ fila no nulas.</em></p>
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<p style="text-align: justify;"><em>Por otro lado, la matriz $B$ (y por lo tanto $\lambda I - A$ también, dado que la nulidad y el rango de una matriz no cambian por las operaciones filas) debería tener a cero como un valor propio más de $k$ veces, porque $B$ está en forma escalonada y por lo tanto es triangular superior.</em></p>
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<p style="text-align: justify;"><em>Pero el número de filas nulas en una matriz cuadrada en la forma escalonada es el mismo número de columnas que no tiene pivote, es decir, es el número de variables libres, el cual es la dimensión del espacio solución.</em></p>
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<p style="text-align: justify;"><em>Así, de todos los argumentos anteriores, se puede ver que la dimensión de los subespacios propios es a lo sumo $k$.</em>
<div style="text-align: right;"> $\Box$ </div>
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<h2 id="Bibliografía" style="text-align: justify;">Bibliografía<a class="anchor-link" href="#Bibliografía">¶</a></h2><ol>
<li style="text-align: justify;">Evan Dummit, 2020, Linear Algebra - part 4: Eingenvalues, Diagonalization, and the Jordan Form.</li>
<li style="text-align: justify;">SymPy Development Team. 2021. <a href="https://docs.sympy.org/latest/index.html">Sympy 1.8 documetation</a>.</li>
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<h2 id="Contacto" style="text-align: justify;">Contacto<a class="anchor-link" href="#Contacto">¶</a></h2><ul>
<li style="text-align: justify;">Participa de la canal de Nerve a través de <a href="https://discord.gg/edPmghPq8K">Discord</a>.</li>
<li style="text-align: justify;">Se quieres conocer más acerca de este tema me puedes contactar a través de <a href="https://www.classgap.com/me/alejandro-sanchez-yali">Classgap</a>.</li>
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www.asanchezyali.comhttp://www.blogger.com/profile/06396258253910042323noreply@blogger.com0tag:blogger.com,1999:blog-8939855543774830921.post-57453341339836833132021-02-26T07:11:00.002-05:002021-02-27T21:59:41.379-05:00Regresión Logística Multinomial<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
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<p style="text-align: justify;">Algunas veces es necesario hacer clasificación para más de dos clases. Quizas se quiere clasificar tres formas de sentimientos (positivo, neutral o negativo). Esto se podría hacer analizando el contenido del habla y asignado un etiquetado semático a cada una de las palabras para poder valores el sentimiento del habla, sin embargo en esta publicación no vamos a hablar de esto por ahora. Vamos a dedicar la atención a la regresión logística multinomial o softmax.</p>
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<p style="text-align: justify;">En estas situaciones en donde es necesario hacer una clasificación para más de dos clases, se puede hacer uso de la <strong>regresión logística multinomial</strong>, o tambien <strong>regresión softmax</strong>. En este tipo de regresión la variable objetivo tiene un rango que varia sobre un conjunto de más de dos clases; el objetivo aquí será determinar cuá es la probabilidad de $y$ de pertenecer a cada una de las clases potenciales $c\in C$, $P(y=c\;|\;x)$.</p>
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<p style="text-align: justify;">La regresión logística multinomial clasifica usando una generalización de la función sigmoide, conocida como la función <strong>softmax</strong>, para calcular la probabilidad $P(y=c\;|\;x)$. La función softmax toma un vector $z=[z_1, z_2, \dots, z_k]^{\top}$ de $k$ valores arbitrarios y los mapea en una distribucción de probalicada, con cada valore en el rango $(0, 1)$, y todos los valores sumando uno. Como la función sigmoide. es una función exponencial.</p>
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<p style="text-align: justify;">Para un vector $z$ de dimensionalidad $k$, la función softmax es definida como:</p>
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$$s(z_i)=\frac{e^{z_i}}{\sum_{j=1}^{k}e^{z_{j}}},\; 1\leq i\leq k.$$
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<p style="text-align: justify;">Así, la función softmax de un vector $z=[z_1, z_2, \dots, z_k]^{\top}$ es por lo tanto una función vectorial:</p>
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$$s(z)=\left[\frac{e^{z_1}}{\sum_{j=1}^{k}e^{z_{1}}}, \frac{e^{z_2}}{\sum_{j=1}^{k}e^{z_{2}}},\dots, \frac{e^{z_k}}{\sum_{j=1}^{k}e^{z_{k}}}\right]$$
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<p style="text-align: justify;">El denominador $\frac{e^{z_i}}{\sum_{j=1}^{k}e^{z_{j}}}$ es usado para normalizar todos los valores en probabilidades. Por ejemplo:</p>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span></div><span><div style="text-align: justify;"><span class="kn">from</span> <span class="nn">scipy.special</span> <span class="kn">import</span> <span class="n">softmax</span></div></span></pre></div>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">z</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">0.6</span><span class="p">,</span> <span class="mf">1.1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span> <span class="mf">1.2</span><span class="p">,</span> <span class="mf">3.2</span><span class="p">,</span> <span class="o">-</span><span class="mf">1.1</span><span class="p">])</span>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">softmax</span><span class="p">(</span><span class="n">z</span><span class="p">)</span>
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<pre><div style="text-align: justify;">array([0.01002305, 0.01652522, 0.00202362, 0.81638616, 0.01826319,</div><div style="text-align: justify;"> 0.13494772, 0.00183105])</div></pre>
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<p style="text-align: justify;">Otra vez como en la función sigmoide, la entrada de la función softmax puede ser el producto punto entre un vector de pesos $w=(w_0, \dots, w_n)$ y un vector $x=(1, x_1,\dots, x_n$. Pero ahora ese necesario separar el vector de pesos para cada una de las clases.</p>
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$$P(y=c\;| \;x)=\frac{e^{w_c^\top x}}{\sum_{j=1}^{k}e^{w_j^\top x}}$$
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<p style="text-align: justify;">Como la función sigmoide, la función softmax tiene la propiedad de transformar los valores hacía $0$ o $1$. Pos lo tanto , si una de las entradas es más grande que los otros, tenderá a aumentar su probabilidad hacia $1$, y suprime las probabilidades de las entradas más pequeñas.</p>
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<h2 id="Aplicaciones-de-la-regresión-logística-multinomial" style="text-align: justify;">Aplicaciones de la regresión logística multinomial<a class="anchor-link" href="#Aplicaciones-de-la-regresión-logística-multinomial">¶</a></h2>
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<p style="text-align: justify;">Para la clasificación de los datos de entrada es necesario definir una función que depende de la observación $x$ y de la potencial clase $c$. Para esto se usará la notación $f_i(c, x)$, que indicará el atributo $i$ para una clases particular $c$ dado por la observación $x$.</p>
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<p style="text-align: justify;">En clasificación binaria, un peso positivo en una característica apunta hacia $y = 1$ y
un peso negativo hacia $y = 0$, pero en la clasificación multiclase una característica podría ser
evidencia a favor o en contra de una clase individual.</p>
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<p style="text-align: justify;">Veamos algunas características de muestra para algunas tareas de PNL para ayudar a comprender este uso quizás poco intuitivo de características que son funciones tanto de la observación $x$ como de la clase $c$.</p>
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<p style="text-align: justify;">Supongamos que estamos haciendo una clasificación de texto y, en lugar de una clasificación binaria, nuestra tarea es asignar una de las 3 clases A, B o C (neutral) a un documento. Ahora, una función relacionada con los signos de exclamación puede tener un peso negativo para C documentos y un peso positivo para documentos A o B:</p>
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$$f_1(C, x)=\begin{cases}1 & \mbox{ si } ! \notin doc \\
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$$f_2(A, x)=\begin{cases}1 & \mbox{ si } ! \notin doc \\
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$$f_3(B, x)=\begin{cases}1 & \mbox{ si } ! \notin doc \\
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<h2 id="¿Cómo-aprende-las-regresión-multinomial-logística?" style="text-align: justify;">¿Cómo aprende las regresión multinomial logística?<a class="anchor-link" href="#¿Cómo-aprende-las-regresión-multinomial-logística?">¶</a></h2>
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<p style="text-align: justify;">La regresión logística multinomial tiene una función de pérdida ligeramente diferente a la regresión logística binaria porque utiliza el clasificador softmax en lugar del sigmoide. La función de pérdida para un solo ejemplo $x$ es la suma de los registros de las $k$ clases de salida:</p>
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$$L_{CE}(\hat{y}, y)=-\sum_{h=1}^{k}\mathbb{1}_{\{y=k\}}\log P(y=k\;|\;x)=-\sum_{k=1}^{k}\mathbb{1}_{\{y=k\}}\log \frac{e^{w_{k}\cdot x + b_{k}}}{\sum_{j=1}^{k}e^{w_j\cdot x + b_{j}}}$$
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<p style="text-align: justify;">La expersión $\mathbb{1}_{\{y=k\}}$ toma el valor de uno cuando la condición en las llaves es verdadera y cero en cualquier otro caso.</p>
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<p style="text-align: justify;">El gradiente para una muestra es muy similar a el gradiente para la regresión logistica, aunque no se mostrará aquí la derivación. Es la diferencia entre el valor de la clase verdadera $k$ y la probabilidad que el clasificador genera para la clase $k$, ponderada por el valor de la entrada $x_{k}$:</p>
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$$\frac{\partial L_{CE}}{\partial w_{k}} = -(\mathbb{1}_{\{y=k\}}-P(y=k\;|\;x))x_{k}=-\left(\mathbb{1}_{\{y=k\}} - \frac{e^{w_{k}\cdot x + b_{k}}}{\sum_{j=1}^{k}e^{w_j\cdot x + b_{j}}}\right)x_k$$
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<h2 id="Implementación-con-Tensorflow---MNIST" style="text-align: justify;">Implementación con Tensorflow - MNIST<a class="anchor-link" href="#Implementación-con-Tensorflow---MNIST">¶</a></h2>
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<p style="text-align: justify;">MNIST es un conjunto de datos de digitos escritos a mano que se en muchos ejemplos introductorios al machine learning. El conjunto de datos contiene 60000 ejemplos para entrenamiento y 10000 ejemplos para testeo. El tamaño de los digitos ha sido normalizado y la imagen centrada (28 x 28 pixeles) con valores de 0 a 1. Por simplicidad, cada imagen ha sido convertido es una matriz númerica 1-D de 784 características (28 x 28). Para más información <a href="http://yann.lecun.com/exdb/mnist/">http://yann.lecun.com/exdb/mnist/</a>.</p>
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<p style="text-align: justify;">Para nuestro ejemplo de regresión logística multinomial usaremos TensorFlow V2 y se implementará a bajo nivel para entender los detalles que hay en el proceso de entrenamiento. Los detalles de este ejemplo se puede encontrar en <a href="https://github.com/aymericdamien/TensorFlow-Examples/blob/master/tensorflow_v2/notebooks/2_BasicModels/logistic_regression.ipynb">TensorFlow Examples - GitHub</a></p>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="kn">import</span> <span class="nn">tensorflow</span> <span class="k">as</span> <span class="nn">tf</span></div><span><div style="text-align: justify;"><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span></div></span></pre></div>
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<p style="text-align: justify;">A continuación se definen las características generales de los datos:</p>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="n">num_classes</span> <span class="o">=</span> <span class="mi">10</span></div><span><div style="text-align: justify;"><span class="n">num_features</span> <span class="o">=</span> <span class="mi">784</span></div></span></pre></div>
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<p style="text-align: justify;">También se definen los parámetros de entrenamiento:</p>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="n">learning_rate</span> <span class="o">=</span> <span class="mf">0.01</span></div><span><div style="text-align: justify;"><span class="n">training_steps</span> <span class="o">=</span> <span class="mi">1000</span> </div></span><span class="n"><div style="text-align: justify;"><span class="n">batch_size</span> <span class="o">=</span> <span class="mi">256</span></div></span></pre></div>
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<h3 id="Lectura-de-los-datos" style="text-align: justify;">Lectura de los datos<a class="anchor-link" href="#Lectura-de-los-datos">¶</a></h3>
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<p style="text-align: justify;">Se cargan los datos y se identifican el conjunto de entrenamiento y el de testeo:</p>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="kn">from</span> <span class="nn">tensorflow.keras.datasets</span> <span class="kn">import</span> <span class="n">mnist</span></div><span><div style="text-align: justify;"><span class="p">(</span><span class="n">x_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">),</span> <span class="p">(</span><span class="n">x_test</span><span class="p">,</span> <span class="n">y_test</span><span class="p">)</span> <span class="o">=</span> <span class="n">mnist</span><span class="o">.</span><span class="n">load_data</span><span class="p">()</span></div></span></pre></div>
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<p style="text-align: justify;">Para visualizar algunos ejemplos hacemos uso de <code>matplotlib</code> de la siguiente forma:</p>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="n">plt</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">x_train</span><span class="p">[</span><span class="mi">5</span><span class="p">],</span> <span class="n">cmap</span><span class="o">=</span><span class="s1">'gray'</span><span class="p">)</span></div><span><div style="text-align: justify;"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></div></span></pre></div>
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<pre style="text-align: justify;"><function matplotlib.pyplot.show(close=None, block=None)></pre>
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<h3 id="Preparación-de-los-datos" style="text-align: justify;">Preparación de los datos<a class="anchor-link" href="#Preparación-de-los-datos">¶</a></h3>
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<p style="text-align: justify;">Estadarización del tipo de dato:</p>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">x_train</span><span class="p">,</span> <span class="n">x_test</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">x_train</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">float32</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">x_test</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span>
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<p style="text-align: justify;">Transformación de los datos a vectores de 784 características:</p>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">x_train</span><span class="p">,</span> <span class="n">x_test</span> <span class="o">=</span> <span class="n">x_train</span><span class="o">.</span><span class="n">reshape</span><span class="p">([</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">num_features</span><span class="p">]),</span> <span class="n">x_test</span><span class="o">.</span><span class="n">reshape</span><span class="p">([</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">num_features</span><span class="p">])</span>
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<p style="text-align: justify;">Normalización de los datos de [0, 255] a [0, 1]:</p>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">x_train</span><span class="p">,</span> <span class="n">x_test</span> <span class="o">=</span> <span class="n">x_train</span> <span class="o">/</span> <span class="mf">255.</span><span class="p">,</span> <span class="n">x_test</span> <span class="o">/</span> <span class="mf">255.</span>
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<p style="text-align: justify;">A continuación particionamos los datos por lotes y los mezclamos:</p>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="n">train_data</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">Dataset</span><span class="o">.</span><span class="n">from_tensor_slices</span><span class="p">((</span><span class="n">x_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">))</span></div><span><div style="text-align: justify;"><span class="n">train_data</span> <span class="o">=</span> <span class="n">train_data</span><span class="o">.</span><span class="n">repeat</span><span class="p">()</span><span class="o">.</span><span class="n">shuffle</span><span class="p">(</span><span class="mi">5000</span><span class="p">)</span><span class="o">.</span><span class="n">batch</span><span class="p">(</span><span class="n">batch_size</span><span class="p">)</span><span class="o">.</span><span class="n">prefetch</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span></div></span></pre></div>
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<h3 id="Construcción-del-módelo:" style="text-align: justify;">Construcción del módelo:<a class="anchor-link" href="#Construcción-del-módelo:">¶</a></h3>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="n">W</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">Variable</span><span class="p">(</span><span class="n">tf</span><span class="o">.</span><span class="n">ones</span><span class="p">([</span><span class="n">num_features</span><span class="p">,</span> <span class="n">num_classes</span><span class="p">]),</span> <span class="n">name</span><span class="o">=</span><span class="s2">"weight"</span><span class="p">)</span></div><span><div style="text-align: justify;"><span class="n">b</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">Variable</span><span class="p">(</span><span class="n">tf</span><span class="o">.</span><span class="n">zeros</span><span class="p">([</span><span class="n">num_classes</span><span class="p">]),</span> <span class="n">name</span><span class="o">=</span><span class="s2">"bias"</span><span class="p">)</span></div></span></pre></div>
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<p style="text-align: justify;">Regresión logistica de (Wx + b):</p>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="k">def</span> <span class="nf">logistic_regression</span><span class="p">(</span><span class="n">x</span><span class="p">):</span></div><span><div style="text-align: justify;"> <span class="k">return</span> <span class="n">tf</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">softmax</span><span class="p">(</span><span class="n">tf</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">W</span><span class="p">)</span> <span class="o">+</span> <span class="n">b</span><span class="p">)</span></div></span></pre></div>
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<p style="text-align: justify;">La función de costo en este caso sería:</p>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="k">def</span> <span class="nf">cross_entropy</span><span class="p">(</span><span class="n">y_pred</span><span class="p">,</span> <span class="n">y_true</span><span class="p">):</span></div><span><div style="text-align: justify;"> <span class="n">y_true</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">one_hot</span><span class="p">(</span><span class="n">y_true</span><span class="p">,</span> <span class="n">depth</span><span class="o">=</span><span class="n">num_classes</span><span class="p">)</span></div></span><div style="text-align: justify;"> <span class="n">y_pred</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">clip_by_value</span><span class="p">(</span><span class="n">y_pred</span><span class="p">,</span> <span class="mf">1e-9</span><span class="p">,</span> <span class="mf">0.9</span><span class="p">)</span></div><div style="text-align: justify;"> <span class="k">return</span> <span class="n">tf</span><span class="o">.</span><span class="n">reduce_mean</span><span class="p">(</span><span class="o">-</span><span class="n">tf</span><span class="o">.</span><span class="n">reduce_sum</span><span class="p">(</span><span class="n">y_true</span> <span class="o">*</span> <span class="n">tf</span><span class="o">.</span><span class="n">math</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">y_pred</span><span class="p">)</span> <span class="o">+</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">y_true</span><span class="p">)</span> <span class="o">*</span> <span class="n">tf</span><span class="o">.</span><span class="n">math</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">y_pred</span><span class="p">),</span><span class="mi">1</span><span class="p">))</span></div></pre></div>
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<p style="text-align: justify;">La medida que se usará para determinar la calidad del modelo será:</p>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="k">def</span> <span class="nf">accuracy</span><span class="p">(</span><span class="n">y_pred</span><span class="p">,</span> <span class="n">y_true</span><span class="p">):</span></div><span><div style="text-align: justify;"> <span class="n">correct_prediction</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">equal</span><span class="p">(</span><span class="n">tf</span><span class="o">.</span><span class="n">argmax</span><span class="p">(</span><span class="n">y_pred</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="n">tf</span><span class="o">.</span><span class="n">cast</span><span class="p">(</span><span class="n">y_true</span><span class="p">,</span> <span class="n">tf</span><span class="o">.</span><span class="n">int64</span><span class="p">))</span></div></span><div style="text-align: justify;"> <span class="k">return</span> <span class="n">tf</span><span class="o">.</span><span class="n">reduce_mean</span><span class="p">(</span><span class="n">tf</span><span class="o">.</span><span class="n">cast</span><span class="p">(</span><span class="n">correct_prediction</span><span class="p">,</span> <span class="n">tf</span><span class="o">.</span><span class="n">float32</span><span class="p">))</span></div></pre></div>
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<p style="text-align: justify;">Para entrenar el modelo, se utilizará el optimizador definido para el gradiente estocástico:</p>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">optimizer</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">optimizers</span><span class="o">.</span><span class="n">SGD</span><span class="p">(</span><span class="n">learning_rate</span><span class="p">)</span>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="k">def</span> <span class="nf">run_optimization</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span></div><span><div style="text-align: justify;"> <span class="k">with</span> <span class="n">tf</span><span class="o">.</span><span class="n">GradientTape</span><span class="p">()</span> <span class="k">as</span> <span class="n">g</span><span class="p">:</span></div></span><div style="text-align: justify;"> <span class="n">pred</span> <span class="o">=</span> <span class="n">logistic_regression</span><span class="p">(</span><span class="n">x</span><span class="p">)</span></div><div style="text-align: justify;"> <span class="n">loss</span> <span class="o">=</span> <span class="n">cross_entropy</span><span class="p">(</span><span class="n">pred</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span></div><div style="text-align: justify;"> </div><div style="text-align: justify;"> <span class="n">gradients</span> <span class="o">=</span> <span class="n">g</span><span class="o">.</span><span class="n">gradient</span><span class="p">(</span><span class="n">loss</span><span class="p">,</span> <span class="p">[</span><span class="n">W</span><span class="p">,</span> <span class="n">b</span><span class="p">])</span></div><div style="text-align: justify;"> </div><div style="text-align: justify;"> <span class="n">optimizer</span><span class="o">.</span><span class="n">apply_gradients</span><span class="p">(</span><span class="nb">zip</span><span class="p">(</span><span class="n">gradients</span><span class="p">,</span> <span class="p">[</span><span class="n">W</span><span class="p">,</span> <span class="n">b</span><span class="p">]))</span></div></pre></div>
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<p style="text-align: justify;">A continuación, se ejecuta el proceso de entrenamiento:</p>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="n">display_step</span> <span class="o">=</span> <span class="mi">50</span></div><span><div style="text-align: justify;"><span class="k">for</span> <span class="n">step</span><span class="p">,</span> <span class="p">(</span><span class="n">batch_x</span><span class="p">,</span> <span class="n">batch_y</span><span class="p">)</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">train_data</span><span class="o">.</span><span class="n">take</span><span class="p">(</span><span class="n">training_steps</span><span class="p">),</span> <span class="mi">1</span><span class="p">):</span></div></span><div style="text-align: justify;"> <span class="n">run_optimization</span><span class="p">(</span><span class="n">batch_x</span><span class="p">,</span> <span class="n">batch_y</span><span class="p">)</span></div><div style="text-align: justify;"> </div><div style="text-align: justify;"> <span class="k">if</span> <span class="n">step</span> <span class="o">%</span> <span class="n">display_step</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span></div><div style="text-align: justify;"> <span class="n">pred</span> <span class="o">=</span> <span class="n">logistic_regression</span><span class="p">(</span><span class="n">batch_x</span><span class="p">)</span></div><div style="text-align: justify;"> <span class="n">loss</span> <span class="o">=</span> <span class="n">cross_entropy</span><span class="p">(</span><span class="n">pred</span><span class="p">,</span> <span class="n">batch_y</span><span class="p">)</span></div><div style="text-align: justify;"> <span class="n">acc</span> <span class="o">=</span> <span class="n">accuracy</span><span class="p">(</span><span class="n">pred</span><span class="p">,</span> <span class="n">batch_y</span><span class="p">)</span></div><div style="text-align: justify;"> <span class="nb">print</span><span class="p">(</span><span class="s1">'step: </span><span class="si">%i</span><span class="s1">, loss: </span><span class="si">%f</span><span class="s1">, accuracy: </span><span class="si">%f</span><span class="s1">'</span> <span class="o">%</span> <span class="p">(</span><span class="n">step</span><span class="p">,</span> <span class="n">loss</span><span class="p">,</span> <span class="n">acc</span><span class="p">))</span></div></pre></div>
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<pre><div style="text-align: justify;">step: 50, loss: 2.691798, accuracy: 0.707031</div><div style="text-align: justify;">step: 100, loss: 2.201120, accuracy: 0.742188</div>step: 150, loss: 1.926627, accuracy: 0.789062
<div style="text-align: justify;">step: 250, loss: 1.502035, accuracy: 0.812500</div>step: 200, loss: 1.788280, accuracy: 0.773438
step: 300, loss: 1.421701, accuracy: 0.812500
<div style="text-align: justify;">step: 450, loss: 1.242893, accuracy: 0.847656</div>step: 350, loss: 1.371978, accuracy: 0.847656
step: 400, loss: 1.382541, accuracy: 0.789062
step: 500, loss: 1.199832, accuracy: 0.839844
<div style="text-align: justify;">step: 700, loss: 0.882333, accuracy: 0.914062</div>step: 550, loss: 1.111963, accuracy: 0.855469
step: 600, loss: 1.156131, accuracy: 0.828125
step: 650, loss: 1.010465, accuracy: 0.871094
step: 750, loss: 1.011202, accuracy: 0.863281
<div style="text-align: justify;">step: 1000, loss: 1.057235, accuracy: 0.820312</div>step: 800, loss: 0.971723, accuracy: 0.855469
step: 850, loss: 1.082722, accuracy: 0.832031
step: 900, loss: 0.912813, accuracy: 0.875000
<div style="text-align: justify;">step: 950, loss: 0.927843, accuracy: 0.863281</div></pre>
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<p style="text-align: justify;">Finalmente se valida el modelo y se visualizan los resultados:</p>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="n">pred</span> <span class="o">=</span> <span class="n">logistic_regression</span><span class="p">(</span><span class="n">x_test</span><span class="p">)</span></div><span><div style="text-align: justify;"><span class="nb">print</span><span class="p">(</span><span class="s2">"Test Accuracy: </span><span class="si">%f</span><span class="s2">"</span> <span class="o">%</span> <span class="n">accuracy</span><span class="p">(</span><span class="n">pred</span><span class="p">,</span> <span class="n">y_test</span><span class="p">))</span></div></span></pre></div>
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<pre style="text-align: justify;">Test Accuracy: 0.877100
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="n">n_images</span> <span class="o">=</span> <span class="mi">2</span></div><span><div style="text-align: justify;"><span class="n">test_images</span> <span class="o">=</span> <span class="n">x_test</span><span class="p">[:</span><span class="n">n_images</span><span class="p">]</span></div></span><span class="n"><div style="text-align: justify;"><span class="n">predictions</span> <span class="o">=</span> <span class="n">logistic_regression</span><span class="p">(</span><span class="n">test_images</span><span class="p">)</span></div></span>
<div style="text-align: justify;"><span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n_images</span><span class="p">):</span></div><div style="text-align: justify;"> <span class="n">plt</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">test_images</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="p">[</span><span class="mi">28</span><span class="p">,</span> <span class="mi">28</span><span class="p">]),</span> <span class="n">cmap</span><span class="o">=</span><span class="s1">'gray'</span><span class="p">)</span></div><div style="text-align: justify;"> <span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span></div><div style="text-align: justify;"> <span class="nb">print</span><span class="p">(</span><span class="s2">"Model prediction: </span><span class="si">%i</span><span class="s2">"</span> <span class="o">%</span> <span class="n">np</span><span class="o">.</span><span class="n">argmax</span><span class="p">(</span><span class="n">predictions</span><span class="o">.</span><span class="n">numpy</span><span class="p">()[</span><span class="n">i</span><span class="p">]))</span></div></pre></div>
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<pre style="text-align: justify;">Model prediction: 7
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<img src="data:image/png;base64,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<pre style="text-align: justify;">Model prediction: 2
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<h2 id="Conclusiones" style="text-align: justify;">Conclusiones<a class="anchor-link" href="#Conclusiones">¶</a></h2>
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<p style="text-align: justify;">En esta ocasión se introduccido los aspectos generales de la regresión logistica multinomial como un modelo de clasificación:</p>
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<li style="text-align: justify;">La regresión logística multinomial se puede utilizar con dos clases (por ejemplo determinar si un sentimiento es positivo o negativo) o con múltiples clases (por ejemplo la clasificación de libros de acuerdo con un genero literario).</li>
<li style="text-align: justify;">Se usa la función softmax para calcular probabilidades.</li>
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<h2 id="Bibliografía" style="text-align: justify;">Bibliografía<a class="anchor-link" href="#Bibliografía">¶</a></h2><ul>
<li style="text-align: justify;">Mustafa Murat Arat. 2019. <a href="https://mmuratarat.github.io/2019-01-07/logistic-regression-in-Tensorflow">Logistic Regression in Tensorflow</a>.</li>
<li style="text-align: justify;"><a href="https://www.andrewng.org">Andrew Ng</a>. <a href="http://cs229.stanford.edu/materials.html">Machine learning course materials</a>. Technical report, University of Stanford.</li>
<li style="text-align: justify;">Aurelien Geron. 2019. Hands-on Machine Learning with Scikit-Learn, Keras and TensorFlow.</li>
<li style="text-align: justify;">Aymeric Damien. <a href="https://github.com/aymericdamien/TensorFlow-Examples">TensorFlow Tutorial and Examples for Beginners (support TF v1 & v2)</a>.</li>
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<h2 id="Contacto" style="text-align: justify;">Contacto<a class="anchor-link" href="#Contacto">¶</a></h2><ul>
<li style="text-align: justify;">Participa de la canal de Nerve a través de <a href="https://discord.gg/edPmghPq8K">Discord</a>.</li>
<li style="text-align: justify;">Se quieres conocer más acerca de este tema me puedes contactar a través de <a href="https://www.classgap.com/me/alejandro-sanchez-yali">Classgap</a>.</li>
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www.asanchezyali.comhttp://www.blogger.com/profile/06396258253910042323noreply@blogger.com0tag:blogger.com,1999:blog-8939855543774830921.post-74667483495342027442021-02-16T05:37:00.005-05:002021-02-27T21:59:14.976-05:00Regresión Logística<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
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<p style="text-align: justify;">La regresión lineal asume que existe una relación lineal entre dos variables $\mathcal{X}$ y $\mathcal{Y}$. Pero esto se viola rápidamente cuando la variable dependiente, $\mathcal{Y}$ es una variable categórica. La <strong>regresión logística</strong> expresa la regresión lineal múltiple en terminos de un logaritmo, superando así la no linealidad.</p>
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<p style="text-align: justify;">La regresión logística es uno de los métodos que se usan para el problema de clasificación. Usualmente se usa para estimar la probabilidad de que una <strong>muestra</strong> sea parte de una clase en particular (por ejemplo, ¿Cuál es la probabilidad de que una persona padeza cancer?). Si la probabilidad estimada es mayor que $50\%$, entonces el modelo predice que la <strong>muestra</strong> pertenece a esa clase y sino entonces predice que no pertenece. Esto es lo que hace en principio un clasificador binario.</p>
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<p style="text-align: justify;">Como se mencióno al principio, el modelo de regresión lineal se comporta pobremente cuando la variable $\mathcal{Y}$ es una variable discreta o categórica. Para resolver esto, hay que cambiar la forma de la hipótesis $h_{\theta}(x)$. Para esto se toma la familia de predictores de la forma,
$$h_{\theta}(x) = \sigma(\theta^\top x) = \frac{1}{1 + e^{\theta^\top x}},$$
donde
$$\sigma(z) = \frac{1}{1 + e^{-z}}$$
es la <strong>función logística</strong> o la <strong>función sigmoide</strong>. Graficamente $\sigma(z)$ luce de la siguiente forma:</p>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span></div><span><div style="text-align: justify;"><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span></div></span><span class="k"><div style="text-align: justify;"><span class="k">def</span> <span class="nf">sigmoid</span><span class="p">(</span><span class="n">z</span><span class="p">):</span></div></span><div style="text-align: justify;"> <span class="k">return</span> <span class="mi">1</span> <span class="o">/</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="n">z</span><span class="p">))</span></div></pre></div>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="n">z</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="o">-</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mf">0.2</span><span class="p">)</span></div><span><div style="text-align: justify;"><span class="n">g_z</span> <span class="o">=</span> <span class="n">sigmoid</span><span class="p">(</span><span class="n">z</span><span class="p">)</span></div></span></pre></div>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">z</span><span class="p">,</span> <span class="n">g_z</span><span class="p">)</span></div><span><div style="text-align: justify;"><span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s1">'Figura 1. Función Sigmoide'</span><span class="p">)</span></div></span><span class="n"><div style="text-align: justify;"><span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span></div></span></pre></div>
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<p style="text-align: justify;">Observe que $\sigma(z)$ tiene a $1$ cuando $z\to \infty$, y $\sigma(z)$ tiene a $0$ cuándo $z\to -\infty$. Ademas, $\sigma(z)$, y por lo tanto $h_{\theta}$ está acotada entre $0$ y $1$. Acá se sigue manteniendo la convención de que $\theta = (\theta_0, \dots, \theta_n)^{\top}$ y $x=(1, x_1, \dots, x_n)^{\top}$, asi que $\theta^{\top}x=\theta\cdot x$.</p>
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<h3 id="Estimando-probabilidades" style="text-align: justify;">Estimando probabilidades<a class="anchor-link" href="#Estimando-probabilidades">¶</a></h3>
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<p style="text-align: justify;">Considere una conjunto de datos $S=\{(x_i, y_i)\}_{i=1}^m$, donde cada $x_i = (1, x_{i,1}, \dots, x_{i,n})^{\top}$ y cada $y_{i}\in \{0, 1\}$. Bajo estas condiciones, la variable $y_i$ se puede ver como una distribución de Bernoulli para la clasificación binaria. La regresión logística dice que la probabilidad de que la variable $y_i=1$, para $i=1,2, \dots, m$ puede ser modelado así:</p>
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$$ h_{\theta}(x_i)=E[y_i\,|\,x_i]=P(y_i=1\,|\,x_i, \theta)=\sigma(\theta^\top x_i)$$
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<p style="text-align: justify;">donde $\sigma$ representa la función sigmode. ¿Pero esto por qué es así?</p>
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<p style="text-align: justify;">La razón viene de la generalización de los modelos lineales. Dado que $y_i$ es una variable binaria, parece natural la elección de una familia de distribuciones de Bernoulli para el modelo de probabilidad condicional de $y_i$ dado $x_i$. En la formulación de la distribución de Bernoulli como una familia de distribuciones exponenciales, se tiene que $p=\frac{1}{1 + e^{-\eta}}$ donde $\eta = \theta^\top x_i$. Además, observe que si $y_i\,|\, x_i; \theta \sim Ber(p)$, entonces $E[y_i\, |\, x_i]=p$.</p>
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<p style="text-align: justify;">Al asumir que $P(y_i=1\,|\,x_i;\theta)=h_{\theta}(x_i)$ y $P(y_i=0\,|\,x_i;\theta)=1 - h_{\theta}(x_i)$. Entonces de forma más compacta se puede escribir que:</p>
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$$P(y_i\,|\,x_i; \theta)=(h_{\theta}(x_i))^{y_i}(1-h_{\theta}(x_i))^{1-y_i}.$$
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<p style="text-align: justify;">Como desde antes se ha asumido que se tiene un conjunto de entrenamiento con $m$ muestras que se supone han sido generadas independientemente, entonces la verosimilitud de los parámetros se puede expresar como:</p>
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$$L(\theta)=p(y\,|\, X; \theta) = \prod_{i=1}^{m}p(y_i\,|\,x_i; \theta),$$
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<p style="text-align: justify;">donde $y=(y_1, \dots, y_m)^{\top}$ y $X$ es la matriz cuyas filas son $x_i^{\top}$ para todo $i=1, \dots, m$.</p>
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<p style="text-align: justify;">El objetivo es maximizar la verosimilitud $L(\theta)$, para esto es más fácil maximizar su logaritmo, es decir:</p>
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$$l(\theta) = \log L(\theta) = \sum_{i=1}^{m} y_{i}\log h_{\theta}(x_i)+(1+y_i)\log(1 - h_{ \theta}(x_i)).$$
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<p style="text-align: justify;">Como en la regresión lineal para encontrar el parámetro $\theta$ hay que minimizar la función de costo, aquí también se mantiene la consistencia, ya que este problema se puede ver como un problema de minimización. Para esto consideramos el costo promedio sobre todo el conjutno de datos. En este caso, se considera $l(\theta)$. La maximización de $l(\theta)$ es equivalente a la minimización de $-l(\theta)$. Y usando la función promedio sobre todo el conjunto de datos, la función de costos para la regresión toma la forma:</p>
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$$J(\theta)=-\frac{1}{m}L(\theta)=-\frac{1}{m}\sum_{i=1}^{m}y_{i}\log(h_{\theta}(x_i)) + (1-y_i)\log(1-h_{\theta}(x_i)).$$
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<p style="text-align: justify;">Esto nos conduce a entender el costo de un solo dato como $-\log(P(x_i\;|\;y_i))$,, el cual se puede escribir como:</p>
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<p style="text-align: justify;">$$-\log(P(x_i\;|\;y_i))=-\big(y_i\log(h_{\theta}(x_i)) + (1-y_i)\log(1-h_{\theta}(x_i))\big).$$</p>
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<p style="text-align: justify;">Esta expresión se puede expresar como una función a tramos, conocida como la <strong>entropía cruzada</strong>, dada por:</p>
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$$L_{EC}(h_{\theta}(\theta_i), y_i) = \begin{cases}-\log(h_\theta(x_i)) & \mbox{ si } y_i=1 \\ -\log(1-h_\theta(x_i)) & \mbox{ si } y_i = 0 \end{cases} $$
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<h3 id="La-entropía-cruzada-y-el-algoritmo-del-gradiente-descendente" style="text-align: justify;">La entropía cruzada y el algoritmo del gradiente descendente<a class="anchor-link" href="#La-entropía-cruzada-y-el-algoritmo-del-gradiente-descendente">¶</a></h3>
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<p style="text-align: justify;">El objetivo con el gradiente descendente es encontrar el valor optimo para $\theta$: minimizar la función de costo. En la siguiente ecuación se representa el hecho explicito de la función de costo $J$ paramétrizada por $\theta$.Así el objetivo es encontrar $\theta$ que para todos los ejemplos del conjunto de entrenamiento, $\theta$ es tal que la función de costo se minimiza:</p>
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$$
\theta \in \operatorname*{argmin\,\,}_{ \theta\in \Omega} \frac{1}{m}\sum_{i=1}^{m}L_{CE}(f(x_i; \theta), y_i)= \operatorname*{argmin\,\,}_{ \theta\in \Omega} J(\theta).
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<p style="text-align: justify;">Para emplear el algoritmo del gradiente descendente es necesario calcular $\nabla_\theta J(\theta)$ de tal manera que al regla de actualización para $\theta$ con base al gradiente es:</p>
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$$\theta_{t+1} = \theta_{t} -\eta \nabla J(\theta_t).$$
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<p style="text-align: justify;">Teniendo presente la que función de entropía cruzada es:</p>
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$$L_{EC}(h_{\theta}(\theta_i), y_i)=-\big(y_i\log(h_{\theta}(x_i)) + (1-y_i)\log(1-h_{\theta}(x_i))\big).$$
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<p style="text-align: justify;">Observe que la derivada para esta función en un vector de observación $x_i$ es:</p>
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$$ \frac{\partial L_{EC}(h_{\theta}(\theta_i), y_i)}{\partial \theta_j} = [h_\theta(x_i)-y]x_{i, j}.$$
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<p style="text-align: justify;">Note que el gradiente con respeto a $\theta_j$ representa de forma intuitiva, la diferencia entre el valor real $y_i$ y el valor estimado $h_\theta(x_i)$ por la observación $x_i$, multiplicado por el valor correspodiente a $x_{ij}$.Así cada derivada parcial del gradiente es de la forma:</p>
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$$\frac{\partial J(\theta)}{\partial \theta_j } = \frac{1}{m}\sum_{i=1}^{m}[h_\theta(x_i)-y_i]x_{i,j}.$$
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<p style="text-align: justify;">Finalmente de la ecuación anterior, es fácil concluir que:</p>
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$$\nabla_{\theta}J = X^{\top}[\hat{y}-y]$$
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<p style="text-align: justify;">en donde $\hat{y} = [h_\theta(x_1),\dots, h_\theta(x_m)]$.</p>
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<h2 id="Implementación-de-la-regresión-logistica-con-Scikit-learn" style="text-align: justify;">Implementación de la regresión logistica con Scikit-learn<a class="anchor-link" href="#Implementación-de-la-regresión-logistica-con-Scikit-learn">¶</a></h2>
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<p style="text-align: justify;">Un ejercicio interesante para el lector es hacer la implementación de este módelo desde cero, sin embargo en esta ocasión no lo haremos así y veremos como hacer una implementación sencilla haciendo uso del modulo Scikit-learn de Python.</p>
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<p style="text-align: justify;">Para vamos a necesitar los siguiente modulos:</p>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span></div><span><div style="text-align: justify;"><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span></div></span><span class="kn"><div style="text-align: justify;"><span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <span class="n">train_test_split</span></div></span><span class="kn"><div style="text-align: justify;"><span class="kn">from</span> <span class="nn">sklearn.linear_model</span> <span class="kn">import</span> <span class="n">LogisticRegression</span></div></span></pre></div>
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<p style="text-align: justify;">Cargamos lo datos, en este caso disponemos de un pequeño conjunto de datos que contiene la información básica (genero, edad, y salario estimado) de unos usuarios que compran ciertos productos en una tienda. El objetivo acá es clasificar los usuarios entre aquellos que compran o no, esto con el objetivo de implementar alguna estrategía comercial</p>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="n">data</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">read_csv</span><span class="p">(</span><span class="s1">'data.csv'</span><span class="p">)</span></div><span><div style="text-align: justify;"><span class="n">data</span><span class="o">.</span><span class="n">head</span><span class="p">()</span></div></span></pre></div>
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<th>User ID</th>
<th>Gender</th>
<th>Age</th>
<th>EstimatedSalary</th>
<th>Purchased</th>
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<th>0</th>
<td>15624510</td>
<td>Male</td>
<td>19</td>
<td>19000</td>
<td>0</td>
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<th>1</th>
<td>15810944</td>
<td>Male</td>
<td>35</td>
<td>20000</td>
<td>0</td>
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<th>2</th>
<td>15668575</td>
<td>Female</td>
<td>26</td>
<td>43000</td>
<td>0</td>
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<th>3</th>
<td>15603246</td>
<td>Female</td>
<td>27</td>
<td>57000</td>
<td>0</td>
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<th>4</th>
<td>15804002</td>
<td>Male</td>
<td>19</td>
<td>76000</td>
<td>0</td>
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<p style="text-align: justify;">Para hacernos una pequeña idea de la estructura de los datos, podemos construir varias visualizaciones entre las variables independientes (genero, edad y salario estimado) en relación con la variable objetivo (comprar). Por ejemplo, para la relación entre la <em>Age</em> y <em>Purchased</em> se obtiene el siguiente gráfico:</p>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="n">plt</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">data</span><span class="o">.</span><span class="n">Age</span><span class="p">,</span> <span class="n">data</span><span class="o">.</span><span class="n">Purchased</span><span class="p">)</span></div><span><div style="text-align: justify;"><span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span></div></span></pre></div>
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<p style="text-align: justify;">Como se puede apreciar los usuarios estan separados en dos clase, entre aquellos que hay comprado y aquellos que no.</p>
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<p style="text-align: justify;">Ahora vamos a dividir nuestro datos en dos partes, una parte sera el conjunto de entrenamiento y la otra el conjunto de testeo. Para hacer esto hacemos uso de <code>train_test_split</code> que se encuentra en el módulo <code>sklearn.model_selection</code>.</p>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">X_train</span><span class="p">,</span> <span class="n">X_test</span><span class="p">,</span> <span class="n">y_train</span><span class="p">,</span> <span class="n">y_test</span> <span class="o">=</span> <span class="n">train_test_split</span><span class="p">(</span><span class="n">data</span><span class="o">.</span><span class="n">Age</span><span class="p">,</span> <span class="n">data</span><span class="o">.</span><span class="n">Purchased</span><span class="p">,</span> <span class="n">test_size</span><span class="o">=</span><span class="mf">0.20</span><span class="p">)</span>
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<p style="text-align: justify;">Finalmente, hacemos uso de <code>LogisticRegression</code> que encuentra en el módulo <code>sklearn.linear_model</code> para entrenar nuestro modelo:</p>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="n">model</span> <span class="o">=</span> <span class="n">LogisticRegression</span><span class="p">()</span></div><span><div style="text-align: justify;"><span class="n">model</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="o">.</span><span class="n">values</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="n">y_train</span><span class="o">.</span><span class="n">values</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">ravel</span><span class="p">())</span></div></span></pre></div>
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<pre style="text-align: justify;">LogisticRegression()</pre>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">y_pred</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test</span><span class="o">.</span><span class="n">values</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
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<p style="text-align: justify;">Una vez se ha estimado la probabilidad $\hat{p}_i=h_\theta(x_i)$ decidir si $x_i$ pertenece a la clase con etiqueta $y_i=1$. Esto se hace con base a la partición de clases que se obtiene al clasicar la probabilidad estimada en clases mediante:</p>
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$$\hat{y}_i=
\begin{cases}
0 & \mbox{ si } \hat{p}_i<0.5; \\
1 & \mbox{ si } \hat{p}_i \geq 0.5
\end{cases}$$
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<p style="text-align: justify;">Observe que $\sigma(t) < 0$ cuando $t<0$ y $\sigma(t)\geq 0.5$ cuando $t\geq 0$, así, una regresión logistica predice $1$ si $\theta^\top x_i$ es positivo, y $0$ si es negativo.</p>
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<p style="text-align: justify;">Analizando la calidad de las prediciones del modelo con los datos de testeo y visualizando los resultados:</p>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="n">plt</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">X_test</span><span class="p">,</span> <span class="n">y_test</span><span class="p">)</span></div><span><div style="text-align: justify;"><span class="n">plt</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">X_test</span><span class="p">,</span> <span class="n">y_pred</span><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="s1">'red'</span><span class="p">)</span></div></span><span class="n"><div style="text-align: justify;"><span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span></div></span></pre></div>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"Accuracy = </span><span class="si">{</span><span class="n">model</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_test</span><span class="o">.</span><span class="n">values</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="n">y_test</span><span class="o">.</span><span class="n">values</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
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<pre style="text-align: justify;">Accuracy = 0.875
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<h2 id="Bibliografía" style="text-align: justify;">Bibliografía<a class="anchor-link" href="#Bibliografía">¶</a></h2><ul>
<li style="text-align: justify;">Mustafa Murat Arat. 2019. <a href="https://mmuratarat.github.io/2019-01-07/logistic-regression-in-Tensorflow">Logistic Regression in Tensorflow</a>.</li>
<li style="text-align: justify;"><a href="https://www.andrewng.org">Andrew Ng</a>. <a href="http://cs229.stanford.edu/materials.html">Machine learning course materials</a>. Technical report, University of Stanford.</li>
<li style="text-align: justify;">Aurelien Geron. 2019. Hands-on Machine Learning with Scikit-Learn, Keras and TensorFlow.</li>
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<h2 id="Contacto" style="text-align: justify;">Contacto<a class="anchor-link" href="#Contacto">¶</a></h2><ul>
<li style="text-align: justify;">Participa de la canal de Nerve a través de <a href="https://discord.gg/edPmghPq8K">Discord</a>.</li>
<li style="text-align: justify;">Se quieres conocer más acerca de este tema me puedes contactar a través de <a href="https://www.classgap.com/me/alejandro-sanchez-yali">Classgap</a>.</li>
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www.asanchezyali.comhttp://www.blogger.com/profile/06396258253910042323noreply@blogger.com0tag:blogger.com,1999:blog-8939855543774830921.post-36240956232004769582020-11-14T12:13:00.010-05:002021-02-19T11:57:50.482-05:00El algoritmo de Prim<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
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<p style="text-align: justify;">Considere un grafo $G$ conexo y no dirigido, se dice que un <b>árbol generador</b> es un subgrafo que contiene todos los vértices de $G$. En un <b>grafo ponderado</b>, el peso de un subgrafo es la suma de los pesos de cada una de las aristas en el subgrafo. Así, un <b>árbol generador mínimo</b> (MST por sus siglas en inglés) es un subgrafo ponderado no dirigido que es un árbol generador con peso mínimo.</p>
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<p style="text-align: justify;">Hay muchos problemas en los que se requiere hallar un MST de un grafo no dirigido. Por ejemplo, la longitud mínima del cable necesaria para conectar un conjunto de computadores en una red, puede ser determinada por un MST del grafo no dirigido que contiene todas las posibles conexiones.</p>
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<p style="text-align: justify;">El Algoritmo de Prim, es el primero y el más sencillo de los algoritmos de la teoría de grafos para encontrar un árbol generador mínimo en un grafo ponderado, conexo y no dirigido, este problema se conoce como <b>el problema del árbol generador mínimo</b>. En otras palabras, el algoritmo encuentra un subconjunto de aristas que forman un árbol con todos los vértices, donde el peso total de todas las aristas en el árbol es el mínimo posible.</p>
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<p style="text-align: justify;">Este algoritmo fue desarrollado por primera vez por el matemático checo Vojtêch Jarník, no sería hasta más tarde, en 1957, cuando aparecería publicado de forma independiente bajo la autoría del ingeniero informático estadounidense Robert C. Prim. Es él quien le dio fama y por cuyo apellido es hoy conocido. Creado durante su etapa en Bell Labs, Prim trataba de abordar el problema de cómo conectar redes, ya fueran de telecomunicaciones o de transporte y distribución, mediante un número reducido o barato de conexiones.</p>
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<h2 id="¿Cómo-funciona-el-algoritmo-Prim?" style="text-align: justify;">¿Cómo funciona el algoritmo Prim?<a class="anchor-link" href="#¿Cómo-funciona-el-algoritmo-Prim?">¶</a></h2>
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<p style="text-align: justify;">La solución al problema del árbol generador propuesta por Prim se basa en la idea de ir conectando vértices secuencialmente hasta alcanzarlos a todos. Si se tiene como dato de entrada un grafo no dirigido $G=(V, A, W)$, donde $V$ son los vértices, $A$ las aristas y $W$ la matriz de pesos. El algoritmo empieza a construir el árbol a partir de un vértice seleccionado arbitrariamente como punto de inicio. A continuación se itera seleccionando en cada etapa la arista de menor peso (una cualquiera si hay varias posibilidades) que une un vértice
del árbol con otro que aún no está en él; luego se incorpora dicha arista y el vértice de destino al árbol. El proceso se repite hasta añadir todos los vértices, obteniendo como resultado un árbol generador cuyo peso será mínimo.</p>
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<p style="text-align: justify;">El algoritmo podría ser informalmente descrito siguiendo los siguientes pasos:</p>
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<li style="text-align: justify;">Inicializar un árbol $T$ con un único vértice, elegido arbitrariamente del grafo $G$.</li>
<li style="text-align: justify;">Aumentar el árbol por una arista. Encontrar la arista de menor costo de las posibles aristas que pueden conectar el árbol a los vértices que no están aún en el árbol y agregarla al árbol.</li>
<li style="text-align: justify;">Repetir el paso 2 hasta que todos los vértices del grafo pertenezcan al árbol.</li>
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<p style="text-align: justify;">Con más detalle, se debe implementar el siguiente pseudocódigo:</p>
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<p style="text-align: justify;"><strong>Algoritmo de Prim</strong></p>
<blockquote><div style="text-align: justify;">Input: $G=(V, A, W), s\in V$ </div><div style="text-align: justify;">1. $V^{\top}\leftarrow \{s\}$ </div><div style="text-align: justify;">2. $A^{\top}\leftarrow \emptyset$ </div><div style="text-align: justify;">3. while $card(V^{\top}) < card(V)$ do: </div><div style="text-align: justify;">4. $\displaystyle (i, j)=\operatorname*{argmin\,\,}_{(i, j)}\{w_{ij}:i\in V^{\top}, j\in V\setminus V^{\top}\}$ </div><div style="text-align: justify;">5. $A^{\top} \leftarrow A^{\top}\cup\{(i, j)\}$ </div><div style="text-align: justify;">6. $V^{\top} \leftarrow V^{\top}\cup\{j\}$ </div><div style="text-align: justify;">8. end </div><div style="text-align: justify;">return: $T$, $V(T)\leftarrow V^{\top}$, $A(T)\leftarrow A^{\top}$.</div></blockquote>
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<h3 id="Ejemplo" style="text-align: justify;">Ejemplo<a class="anchor-link" href="#Ejemplo">¶</a></h3>
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<p style="text-align: justify;">En la figura 1 se ilustra la ejecución del algoritmo de Prim sobre un grafo $G$. Se empieza por el vértice $v_{_0}$. Dado que $(v_{_0},v_{_1})$ es la arista de peso mínimo que incide sobre $v_{_0}$, se incluye en el árbol generador que se está construyendo (figura 1a). En la figura 1a , se añade la arista $(v_{_1}, v_{_5})$ porque es la arista más pequeña entre $\{v_{_0}, v_{_1}\}$ y $V(G)\setminus \{v_{_0}, v_{_1}\}$. Cuando hay un empate, como en la figura 1c, cualquier arista más pequeña podría funcionar bien. Se procede de esta forma hasta que se pasa por todos los vértices. El árbol generador mínimo definitivo se muestra en la figura 1f.</p>
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<p style="text-align: justify;">La complejidad de tiempo del algoritmo de Prim depende de las estructuras de datos usada para el grafo y para ordenar las aristas por peso, lo que se puede hacer usando una cola de prioridad. La siguiente muestra las opciones típicas:</p>
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<li style="text-align: justify;">Para una matriz de adyacencia y un algoritmo de busqueda clásico la complejidad de ejecución es del orden de $O(\operatorname*{card\,\,}(V)^{2})$.</li>
<li style="text-align: justify;">Para una pila binaria y una lista de adyacencia la complejidad de ejecución es del orden de $O((\operatorname*{card\,\,}(V)+\operatorname*{card\,\,}(E))\log\operatorname*{card\,\,}(V))$.</li>
<li style="text-align: justify;">Para una pila de Fibonacci y una lista de adyacencia la complejidad de ejecución es del orden de $O(\operatorname*{card\,\,}(E) + \operatorname*{card\,\,}(V)log(\operatorname*{card\,\,}(V))$.</li>
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<h2 id="¿Cómo-se-implementa-en-Python-el-algoritmo-de-Prim?" style="text-align: justify;">¿Cómo se implementa en Python el algoritmo de Prim?<a class="anchor-link" href="#¿Cómo-se-implementa-en-Python-el-algoritmo-de-Prim?">¶</a></h2>
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<p style="text-align: justify;">Una forma de implementar el algoritmo de Prim es así:</p>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span></div><span><div style="text-align: justify;"><span class="kn">import</span> <span class="nn">timeit</span></div></span></pre></div>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="kn">from</span> <span class="nn">graphs</span> <span class="kn">import</span> <span class="n">NotOrientedGraph</span></div><span><div style="text-align: justify;"><span class="kn">from</span> <span class="nn">graphs</span> <span class="kn">import</span> <span class="n">Vertex</span></div></span></pre></div>
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<p style="text-align: justify;">El módulo <code>graph</code> contiene la estructura de datos utilizada para el grafo y la puedes encontrar en el repositorio de <a href="https://github.com/alejandrosanchezy/nerve/tree/master/Algoritmo%20de%20Prim" rel="nofollow" src="https://github.com/alejandrosanchezy/nerve/tree/master/Algoritmo%20de%20Prim" target="_blank">Nerve</a>. El resto del algoritmo es:</p>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="k">def</span> <span class="nf">prim</span><span class="p">(</span><span class="n">graph</span><span class="p">:</span> <span class="n">NotOrientedGraph</span><span class="p">,</span> <span class="n">initial_vertex</span><span class="p">:</span> <span class="n">Vertex</span><span class="p">)</span> <span class="o">-></span> <span class="n">NotOrientedGraph</span><span class="p">:</span></div><span><div style="text-align: justify;"> <span class="sd">"""</span></div></span><span class="sd"><div style="text-align: justify;"> Input:</div></span><span class="sd"><div style="text-align: justify;"> graph: It's a graph not oriented and connected.</div></span><span class="sd"><div style="text-align: justify;"> initial_vertex: It's one vertex from graph.</div></span><span class="sd"><div style="text-align: justify;"> Output:</div></span><span class="sd"><div style="text-align: justify;"> The return is a graph not oriented and connected.</div></span><span class="sd"><div style="text-align: justify;"> """</div></span><div style="text-align: justify;"> <span class="c1"># Initialize empty edges array and empty minimum spanning tree:</span></div><div style="text-align: justify;"> <span class="n">minimum_spanning_tree</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">()</span></div><div style="text-align: justify;"> <span class="n">visited_vertices</span> <span class="o">=</span> <span class="nb">list</span><span class="p">()</span></div><div style="text-align: justify;"> <span class="n">edges</span> <span class="o">=</span> <span class="nb">list</span><span class="p">()</span></div><div style="text-align: justify;"> <span class="n">min_edge</span> <span class="o">=</span> <span class="p">(</span><span class="kc">None</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">infty</span><span class="p">)</span></div>
<div style="text-align: justify;"> <span class="c1"># Arbitrarily choose initial vertex from graph:</span></div><div style="text-align: justify;"> <span class="n">vertex</span> <span class="o">=</span> <span class="n">initial_vertex</span></div>
<div style="text-align: justify;"> <span class="c1"># Indices:</span></div><div style="text-align: justify;"> <span class="n">start_vertex</span><span class="p">,</span> <span class="n">end_vertex</span><span class="p">,</span> <span class="n">weight</span> <span class="o">=</span> <span class="nb">range</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span></div>
<div style="text-align: justify;"> <span class="c1"># Run prim's algorithm until we create an minimum spanning tree that</span></div><div style="text-align: justify;"> <span class="c1"># contains every vertex from the graph:</span></div><div style="text-align: justify;"> </div><div style="text-align: justify;"> <span class="k">try</span><span class="p">:</span></div><div style="text-align: justify;"> <span class="k">while</span> <span class="nb">len</span><span class="p">(</span><span class="n">visited_vertices</span><span class="p">)</span> <span class="o"><</span> <span class="n">graph</span><span class="o">.</span><span class="n">num_vertices</span> <span class="o">-</span> <span class="mi">1</span><span class="p">:</span></div>
<div style="text-align: justify;"> <span class="c1"># Mark this vertex as visited:</span></div>
<div style="text-align: justify;"> <span class="n">visited_vertices</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">vertex</span><span class="p">)</span></div>
<div style="text-align: justify;"> <span class="c1"># Set of potential edges:</span></div><div style="text-align: justify;"> <span class="n">edges</span> <span class="o">+=</span> <span class="n">vertex</span><span class="o">.</span><span class="n">edges</span></div>
<div style="text-align: justify;"> <span class="c1"># Find edge with the smallest weight to a vertex that has not yet</span></div><div style="text-align: justify;"> <span class="c1"># been visited:</span></div><div style="text-align: justify;"> <span class="k">for</span> <span class="n">edge</span> <span class="ow">in</span> <span class="n">edges</span><span class="p">:</span></div><div style="text-align: justify;"> <span class="n">inequality</span> <span class="o">=</span> <span class="n">edge</span><span class="p">[</span><span class="n">weight</span><span class="p">]</span> <span class="o"><</span> <span class="n">min_edge</span><span class="p">[</span><span class="n">weight</span><span class="p">]</span></div><div style="text-align: justify;"> <span class="n">membership</span> <span class="o">=</span> <span class="n">edge</span><span class="p">[</span><span class="n">end_vertex</span><span class="p">]</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">visited_vertices</span></div><div style="text-align: justify;"> <span class="k">if</span> <span class="n">inequality</span> <span class="ow">and</span> <span class="n">membership</span><span class="p">:</span></div><div style="text-align: justify;"> <span class="n">min_edge</span> <span class="o">=</span> <span class="n">edge</span></div>
<div style="text-align: justify;"> <span class="c1"># Get the start and end node from minimum edge:</span></div><div style="text-align: justify;"> <span class="n">start_min_edge</span> <span class="o">=</span> <span class="n">min_edge</span><span class="p">[</span><span class="n">start_vertex</span><span class="p">]</span></div><div style="text-align: justify;"> <span class="n">end_min_edge</span> <span class="o">=</span> <span class="n">min_edge</span><span class="p">[</span><span class="n">end_vertex</span><span class="p">]</span></div><div style="text-align: justify;"> <span class="n">min_weight</span> <span class="o">=</span> <span class="n">min_edge</span><span class="p">[</span><span class="n">weight</span><span class="p">]</span></div>
<div style="text-align: justify;"> <span class="c1"># Add the minimum edge to minimum spanning tree:</span></div><div style="text-align: justify;"> <span class="k">if</span> <span class="n">minimum_spanning_tree</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">start_min_edge</span><span class="o">.</span><span class="n">id</span><span class="p">):</span></div><div style="text-align: justify;"> <span class="n">edge</span> <span class="o">=</span> <span class="p">(</span><span class="n">end_min_edge</span><span class="o">.</span><span class="n">id</span><span class="p">,</span> <span class="n">min_weight</span><span class="p">)</span></div><div style="text-align: justify;"> <span class="n">minimum_spanning_tree</span><span class="p">[</span><span class="n">start_min_edge</span><span class="o">.</span><span class="n">id</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">edge</span><span class="p">)</span></div><div style="text-align: justify;"> <span class="k">else</span><span class="p">:</span></div><div style="text-align: justify;"> <span class="n">edge</span> <span class="o">=</span> <span class="p">[(</span><span class="n">end_min_edge</span><span class="o">.</span><span class="n">id</span><span class="p">,</span> <span class="n">min_weight</span><span class="p">)]</span></div><div style="text-align: justify;"> <span class="n">minimum_spanning_tree</span><span class="p">[</span><span class="n">start_min_edge</span><span class="o">.</span><span class="n">id</span><span class="p">]</span> <span class="o">=</span> <span class="n">edge</span></div>
<div style="text-align: justify;"> <span class="c1"># Remove min weight edge form list of edges:</span></div><div style="text-align: justify;"> <span class="n">edges</span><span class="o">.</span><span class="n">remove</span><span class="p">(</span><span class="n">min_edge</span><span class="p">)</span></div>
<div style="text-align: justify;"> <span class="c1"># Start at new vertex and reset min edge:</span></div><div style="text-align: justify;"> <span class="n">vertex</span> <span class="o">=</span> <span class="n">end_min_edge</span></div><div style="text-align: justify;"> <span class="n">min_edge</span> <span class="o">=</span> <span class="p">(</span><span class="kc">None</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">infty</span><span class="p">)</span></div><div style="text-align: justify;"> </div><div style="text-align: justify;"> <span class="k">except</span> <span class="ne">Exception</span> <span class="k">as</span> <span class="n">e</span><span class="p">:</span></div><div style="text-align: justify;"> <span class="nb">print</span><span class="p">(</span><span class="s1">'The graph is not connected or has no edges!'</span><span class="p">)</span></div>
<div style="text-align: justify;"> <span class="c1"># Return the optimal tree:</span></div><div style="text-align: justify;"> <span class="k">return</span> <span class="n">NotOrientedGraph</span><span class="p">(</span><span class="n">minimum_spanning_tree</span><span class="p">)</span></div></pre></div>
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<p style="text-align: justify;">Para usar el algoritmo de Prim es necesario tener un grafo no orientado que podemos construir de la siguiente manera:</p>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="n">data</span> <span class="o">=</span> <span class="p">{</span></div><span><div style="text-align: justify;"> <span class="s1">'a'</span><span class="p">:</span> <span class="p">[(</span><span class="s1">'c'</span><span class="p">,</span> <span class="mi">0</span><span class="p">)],</span> </div></span><div style="text-align: justify;"> <span class="s1">'b'</span><span class="p">:</span> <span class="p">[(</span><span class="s1">'c'</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="p">(</span><span class="s1">'e'</span><span class="p">,</span> <span class="mi">3</span><span class="p">)],</span> </div><div style="text-align: justify;"> <span class="s1">'c'</span><span class="p">:</span> <span class="p">[(</span><span class="s1">'a'</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span> <span class="p">(</span><span class="s1">'b'</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span> <span class="p">(</span><span class="s1">'d'</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="p">(</span><span class="s1">'e'</span><span class="p">,</span> <span class="mi">1</span><span class="p">)]</span></div><span class="p"><div style="text-align: justify;">}</div></span></pre></div>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">graph</span> <span class="o">=</span> <span class="n">NotOrientedGraph</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
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<p style="text-align: justify;">La clase <code>NotOrientedGraph</code> tiene varios métodos que permite consultar algunas de las propiedades de nuestro grafo, a continuación veamos algunos ejemplos:</p>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">graph</span><span class="o">.</span><span class="n">get_vertices</span><span class="p">()</span>
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<pre style="text-align: justify;">['a', 'c', 'b', 'e', 'd']</pre>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">graph</span><span class="o">.</span><span class="n">get_edges</span><span class="p">()</span>
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<pre><div style="text-align: justify;">([('a', 'c', 0),</div> ('c', 'a', 3),
<div style="text-align: justify;"> ('c', 'd', 2),</div> ('c', 'b', 3),
('c', 'e', 1),
<div style="text-align: justify;"> ('b', 'e', 3)],</div> ('b', 'c', 1),
<div style="text-align: justify;"> graphs.NotOrientedGraph)</div></pre>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">graph</span><span class="o">.</span><span class="n">weight_matrix</span><span class="p">()</span>
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<pre><div style="text-align: justify;">(matrix([[inf, 0., inf, inf, inf],</div> [ 3., inf, 3., 1., 2.],
<div style="text-align: justify;"> [inf, inf, inf, inf, inf],</div> [inf, 1., inf, 3., inf],
<div style="text-align: justify;"> ['a', 'c', 'b', 'e', 'd'])</div><div style="text-align: justify;"> [inf, inf, inf, inf, inf]]),</div></pre>
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<pre><div style="text-align: justify;">(matrix([[0, 1, 0, 0, 0],</div> [1, 0, 1, 1, 1],
<div style="text-align: justify;"> [0, 0, 0, 0, 0],</div> [0, 1, 0, 1, 0],
<div style="text-align: justify;"> ['a', 'c', 'b', 'e', 'd'])</div><div style="text-align: justify;"> [0, 0, 0, 0, 0]]),</div></pre>
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<p style="text-align: justify;">Además también se necesita de un vértice inicial que para nuestro ejemplo será:</p>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">initial_vertex</span> <span class="o">=</span> <span class="n">graph</span><span class="o">.</span><span class="n">get_vertex</span><span class="p">(</span><span class="s1">'a'</span><span class="p">)</span>
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<p style="text-align: justify;">Al ejecutar el algoritmo de Prim se obtiene un nuevo grafo conexo y no orientado:</p>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">tree</span> <span class="o">=</span> <span class="n">prim</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span> <span class="n">initial_vertex</span><span class="p">)</span>
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<p style="text-align: justify;">Para nuestro ejemplo, se peude verificar que en efecto el grafo obtenido pasa por todos los vertices y además también nos entrega cuales son la arista que se usando para construirlo.</p>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">tree</span><span class="o">.</span><span class="n">get_vertices</span><span class="p">()</span>
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<pre style="text-align: justify;">['a', 'c', 'e', 'd', 'b']</pre>
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<pre><div style="text-align: justify;">([('a', 'c', 0), ('c', 'e', 1), ('c', 'd', 2), ('c', 'b', 3)],</div><div style="text-align: justify;"> graphs.NotOrientedGraph)</div></pre>
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<h2 id="¿Por-qué-funciona-el-algoritmo-de-Prim?" style="text-align: justify;">¿Por qué funciona el algoritmo de Prim?<a class="anchor-link" href="#¿Por-qué-funciona-el-algoritmo-de-Prim?">¶</a></h2>
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<p style="text-align: justify;">A continuación vamos a establecer el siguiente resultado:</p>
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<p style="text-align: justify;"><strong>Teorema.</strong> Sea $G$ un grafo conexo, no orientado y ponderado. Entonces al aplicar el algoritmo de Prim desde cualquier vértice se obtiene un árbol de expansión con costo mínimo.</p>
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<p style="text-align: justify;">Como $G$ es un grafo conexo entonces siempre es posible encontrar una camino $r$ que une a cualquier par de vértices de $G$. Observe que para la $k$ - ésima iteración del algoritmo de Prim el subgrafo $T_{_k}$ es conexo, no orientado y ponderado. Es fácil ver ue cada par de vértices de $T_{_k}$ está conectado por exactamente un camino. Además es claro que existe una $n$ - ésima iteración, $n < \operatorname*{card\,\,}(V(G))$, donde $T_{_n}$ es un grafo que contiene todo los vértices de $G$, es decir $V(T_{_n}) )= V(G)$. Es claro que $T_{_n}$ es un árbol.</p>
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<p style="text-align: justify;">¿Es $T_{_n}$ un árbol de expansión con costo mínimo para el graho $G$? Suponga que $Y_{_1}$ es un árbol de expansión con costo mínimo para el grafo $G$. Si $T_{_n} = Y_{_1}$ entonces $T_{_n}$ es un árbol mínimo. Por otro lado si $T_{_n} \neq Y_{_1}$, entonces considera la $k$ - ésima iteración del algoritmo de Prim donde se agregó la primera arista $e$ al subgrafo $T_{_{k-1}}$ que no está en $Y_{_1}$. Observe que uno de los extremos de $e$ esta en $V(T_{_{k-1}})$ y el otro no. Como $Y_{_1}$ es un árbol de expansión con costo mínimo de $G$, entonces existe un camino $r$ en $Y_{_1}$ que une los extremos de $e$. En el camino $r$ debe existir una arista $f$ que une al subgrafo $T_{_{k-1}}$ con algún vértice que no está en $V(T_{_{k-1}})$. Observe que en la $k$ - ésima iteración en donde se agregó $e$ también era posible agregar $f$ en vez de $e$ si y sólo si el peso $w(f)$ de $f$ era menor o igual al peso $w(e)$ de $e$, como $f$ no se agregó se concluye que $w(f)\geq w(e)$.</p>
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<p style="text-align: justify;">Sea $Y_{2}$ es grafo tal que $A(Y_{_2}) = (A(Y_{_1})\setminus\{f\})\cup \{e\}$, es decir, el grafo que resulta de remover de $Y_{_1}$ la arista $f$ y agregar la arista $e$. Es fácil ver que $Y_{_2}$ es conexo, tiene el mismo número de vértices que $Y_{_1}$ y su costo total no supere al coso total de $Y_{_1}$, por lo tanto $Y_{_2}$ también es un árbol de expansión con costo mínimo de $G$ que contiene a $e$ y a todas las aristas de $T_{_{k-1}}$. Repitiendo este mismo proceso para $Y_{2}$, buscamos la $k$ - ésima iteración en el algoritmo de Prim donde se haya agregado una arista que está en $T_{_{k-1}}$ pero no está en $Y_{_2}$, eventualmente se encontrará un árbol de expansión con costo mínimo para $G$ que será igual a $T_{_n}$. Esto prueba que el árbol obtenido por el algoritmo de Prim es un árbol de expansión con costo mínimo.</p>
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<h2 id="Conclusiones" style="text-align: justify;">Conclusiones<a class="anchor-link" href="#Conclusiones">¶</a></h2>
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<p style="text-align: justify;">Una implementación simple de Prim, usando una matriz de adyacencia o una representación del grafo en una lista de adyacencia y buscando linealmente una matriz de pesos para encontrar el borde de peso mínimo para agregar, requiere un tiempo de ejecución de $O( \operatorname*{card\,\,}(V)^2)$. Sin embargo, este tiempo de ejecución se puede mejorar mucho más mediante el uso de pilas para implementar la búsqueda de aristas de peso mínimo en el bucle interno del algoritmo.</p>
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<p style="text-align: justify;">Una primera versión mejorada usa una pila para almacenar todos las del grafo de entrada, ordenados por su peso. Esto conduce a un tiempo de ejecución en el peor de los casos de $O ( \operatorname*{card\,\,} (E) \log \operatorname*{card\,\,}(E))$. Pero almacenar vértices en lugar de arista puede mejorarlo aún más. La pila debe ordenar los vértices por el peso de borde más pequeño que los conecte a cualquier vértice en el árbol de expansión mínimo parcialmente construido (MST) (o infinito si no existe tal arista). Cada vez que se elige un vértice $v$ y se agrega al MST, se realiza una operación de disminución de clave en todos los vértices $w$ fuera del MST parcial de manera que $v$ está conectado a $w$, estableciendo la clave al mínimo de su valor anterior y el costo de la arista de $(v, w)$.</p>
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<p style="text-align: justify;">Usando una estructura de datos de pila binaria simple, ahora se puede mostrar que el algoritmo de Prim se ejecuta en el tiempo $O ( \operatorname*{card\,\,}(E) \log \operatorname*{card\,\,}( V))$ donde $ \operatorname*{card\,\,}(E)$ es el número de aristas y $\operatorname*{card\,\,}(V)$ es el número de vértices. Usando una pila de Fibonacci más sofisticada, esto se puede reducir a $O ( \operatorname*{card\,\,}( E) + \operatorname*{card\,\,}( V ) \log \operatorname*{card\,\,}( V ))$, que es asintóticamente más rápido cuando el grafo es lo suficientemente denso que $\operatorname*{card\,\,}( E)$ es $\omega ( \operatorname*{card\,\,}(V))$, y el tiempo lineal cuando $\operatorname*{card\,\,}( E)$ es al menos $ \operatorname*{card\,\,}( V ) \log \operatorname*{card\,\,}( V )$. Para grafos de densidad aún mayor (que tienen al menos $c\operatorname*{card\,\,}( V )$ aristas con $c> 1$), se puede hacer que el algoritmo de Prim se ejecute en tiempo lineal de manera aún más simple, utilizando una pila d-aria en lugar de una pila de Fibonacci.</p>
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<p style="text-align: justify;">No olvides comentar y suscribirte al blog para que estés enterando de los posts que voy a ir subiendo semana a semana. También sientete en libertad de seguirme en Twitter, Github e Instagram.</p>
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<h2 id="Contacto" style="text-align: justify;">Contacto<a class="anchor-link" href="#Contacto">¶</a></h2><ul>
<li style="text-align: justify;">Participa de la canal de Nerve a través de <a href="https://discord.gg/edPmghPq8K" rel="nofollow" src="https://discord.gg/edPmghPq8K" target="_blank">Discord</a>.</li>
<li style="text-align: justify;">Se quieres conocer más acerca de este tema me puedes contactar a través de <a href="https://www.classgap.com/me/alejandro-sanchez-yali" rel="nofollow" src="https://www.classgap.com/me/alejandro-sanchez-yali" target="_blank">Classgap</a>.</li>
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www.asanchezyali.comhttp://www.blogger.com/profile/06396258253910042323noreply@blogger.com0tag:blogger.com,1999:blog-8939855543774830921.post-24195588608864539722020-10-31T22:17:00.009-05:002020-11-24T09:29:25.802-05:00Álgebra lineal y redes neuronales<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
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<p style="text-align: justify;">Las redes neuronales son modelos cuantitativos que aprende como asociar una «entrada» y una «salida» con el uso de algoritmos de aprendizaje. El objetivo aquí, será exponer cuatro conceptos principales del álgebra lineal que son esenciales para el análisis de estos modelos: 1) la proyección de un vector, 2) la descomposición por valores propios y singulares, 3) el gradiente de una matriz Hessiana de una función vectorial, y 4) la expansión en Taylor de una función vectorial. Estos conceptos son ilustrados con el análisis de las reglas de Hebbian y Widrow-Hoff y algunas arquitecturas simples de las redes neuronales (es decir, el auto asociador lineal, el heteroasociador y el error de redes por propagación regresiva). Se muestra también que las redes neuronales son equivalente a versiones iterativas de la estadística estándar y modelos de optimización tales como el análisis de regresión multiple y el análisis por componentes principales.</p>
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<p style="text-align: justify;">El álgebra lineal es usada particularmente para analizar la clase de redes neuronales denominadas «asociadores». Estos modelos de aprendizaje cuantitativo asocian una «entrada» y una «salida» mediante patrones adaptativos que hacen uso de algoritmos de aprendizaje. Cuando el conjunto de patrones de entrada es diferente del conjunto de salida, los modelos se denominan <em>heteroasociadores</em>. Cuando los patrones de entrada y los de salida son iguales, el modelo se denomina <em>autoasociador</em>. Los asociadores consisten de capas de unidades elementales denominadas <em>neuronas</em>. La información fluye a través de todas las capas. Algunas arquitecturas puede incluir capas intermedias (capas ocultas). Típicamente las neuronas de una capa están conectadas con las neuronas de otra capa. El objetivo será entender como algunas operaciones del álgebra lineal describe las transformaciones de la información a través de cada una de las capas.</p>
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<p style="text-align: justify;">Como es usual, los vectores serán representados por letras minúsculas (p. ej., $x$), las matrices por letras mayúsculas (p. ej.., $X$). Además se supone que las siguientes nociones son conocidas: La operación de transposición (p. ej., $x^\top$), la norma de un vector (p. ej.,$||x||$), el producto escalar ( p. ej., $x^{\top}w$) y el producto de dos matrices ( p. ej., $AB)$. También se usará el producto de Hadamard (p. ej., $A\odot B$).</p>
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<h3 id="Proyección-de-un-vector" style="text-align: justify;">Proyección de un vector<a class="anchor-link" href="#Proyección-de-un-vector">¶</a></h3>
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<h4 id="Coseno-entre-dos-vectores" style="text-align: justify;">Coseno entre dos vectores<a class="anchor-link" href="#Coseno-entre-dos-vectores">¶</a></h4>
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<p style="text-align: justify;">El <em>coseno</em> entre dos vectores $x$ y $y$ es el coseno del ángulo formado por el origen del espacio y los puntos definidos por las coordenadas de los vectores. Por lo tanto,</p>
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\begin{equation}\nonumber
\cos(x, y) = \frac{x^\top y}{||x||||y||}.
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<p style="text-align: justify;">El coseno indica la <em>similaridad</em> entre los vectores. Cuando dos vectores tienen la misma dirección (p. ej. $v=\lambda w, \lambda >0$), su coseno es igual a uno; si tienen dirección opuesta (p. ej. $v=\lambda w, \lambda <0$), su coseno es igual a menos uno; y cuando ellos son ortogonales (p. ej. $v^{\top}w=0$), su coseno es igual a cero.</p>
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<h4 id="Distancia-entre-vectores" style="text-align: justify;">Distancia entre vectores<a class="anchor-link" href="#Distancia-entre-vectores">¶</a></h4>
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<p style="text-align: justify;">Entre una gran familia de distancias entre vectores, la más popular es la distancia euclidiana. Ésta está relacionada con el coseno entre vectores y se define como</p>
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\begin{equation}\nonumber
d_{2}(x,y)=\sqrt{(x-y)^\top(x-y)}=||(x-y)||
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<h4 id="Proyección-de-un-vector-sobre-otro-vector" style="text-align: justify;">Proyección de un vector sobre otro vector<a class="anchor-link" href="#Proyección-de-un-vector-sobre-otro-vector">¶</a></h4>
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<p style="text-align: justify;">La proyección ortogonal de un vector $x$ sobre un vector $w$ se define como:</p>
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\begin{equation}\nonumber
\operatorname{proy}_{\langle w\rangle} x = \frac{x^{\top} w}{w^{\top}w}w.
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<p style="text-align: justify;">La norma de $\operatorname*{proy}_{\langle w\rangle} x$ es su distancia al origen del espacio. Esto es igual a:</p>
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\begin{equation}\nonumber
||\operatorname{proy}_{\langle w\rangle} x||=\frac{|x^{\top}w|}{||w||}=|\cos(x,y)|||x||.
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<h4 id="Las-reglas-de-aprendizaje-de-Hebbian-y-Widrow-Hoff" style="text-align: justify;">Las reglas de aprendizaje de Hebbian y Widrow-Hoff<a class="anchor-link" href="#Las-reglas-de-aprendizaje-de-Hebbian-y-Widrow-Hoff">¶</a></h4>
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<p style="text-align: justify;">Una red neuronal consiste de células conectadas a otras células vía conexiones de peso denominadas <em>sinapsis</em>. Considere una red neuronal de $m$ entradas dada por una capa de células y solo una célula de salida. La información es transmitida vía la sinapsis, del conjunto de entrada de las células externas a las células de salida con la respuesta correspondiente al estado de activación. Si el patrón de entrada y el conjunto de pesos sinápticos son dados por un vector $m$ - dimensional denotado por $x$, y $w$, la activación de la célula de salida es dada por</p>
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\begin{equation}\nonumber
a = x^{\top}w.
\end{equation}
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<p style="text-align: justify;">Así la activación es proporcional a la norma de la proyección del vector de entradas sobre el vector de pesos. La respuesta o salida de la célula es denotada por $r$. Para una célula lineal, esta es proporcional a la activación (por conveniencia, se asume que la constante de proporcionalidad es igual a uno). Los heteroasociadores lineales y los autoasociadores son construidos con células lineales. En general, la salida de una célula es una función (no necesariamente continua), denominada la función de transferencia, y su activación es:</p>
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\begin{equation}\nonumber
\label{eqn:función}
r = f(a).
\end{equation}
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<p style="text-align: justify;">Por ejemplo, en redes de retropropagación, la función de transferencia (no lineal) suele ser la función logística</p>
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\begin{equation}\nonumber
r = f(a) = \operatorname{logit}(w^{\top}x) = \frac{1}{1 + \exp(-w^{\top}x)}.
\end{equation}
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<p style="text-align: justify;">A menudo,una red neuronal está diseñada para asociar, a una entrada dada, una respuesta específica llamada objetivo, denotada como $t$. El aprendizaje es equivalente a definir una regla que especifique cómo agregar una pequeña cantidad a cada peso sináptico en cada iteración del algoritmo. El algoritmo acerca la salida de la red al objetivo.</p>
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<p style="text-align: justify;">Las reglas de aprendizaje vienen en dos sabores principales: <em>supervisadas</em> (p. ej. Widrow-Hoff) que tienen en cuenta el error o la distancia entre la respuesta de la neurona y el objetivo, y <em>sin supervisión</em> (p ej. Hebbian) que no requieren tal «retroalimentación». La regla de aprendizaje hebbiana modifica el vector de peso en la iteración $k + 1$ como</p>
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\begin{equation}\nonumber
w_{k+1} = w_{k} + \eta t x,
\end{equation}
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<p style="text-align: justify;">donde $\eta$ es una pequeña constante positiva llamada <em>constante de aprendizaje</em>. Entonces, en cada iteración de la relgla aprendizaje hebbiana se mueve el vector de peso en la dirección del vector de entrada en una cantidad proporcional al objetivo.</p>
<p style="text-align: justify;">La regla de aprendizaje de Widrow-Hoff utiliza el error y la derivada de la función de transferencia $f$ para calcular la corrección como:</p>
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\begin{equation}\nonumber
\label{eqn:corrección}
w_{k+1} = w_{k} + \eta (t-r_{k})f'(a_k)x.
\end{equation}
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<p style="text-align: justify;">Entonces, una iteración de aprendizaje de Widrow-Hoff mueve el vector de peso en la dirección del vector de entrada en una cantidad proporcional al error.</p>
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<p style="text-align: justify;">Para redes con varias celulas (p. ej. $n$) en la capa de salida, el patrón de activación, salida y objetivo se convierten en vectores $n$ - dimensionales (denotados $a$, $r$ y $t$, respectivamente), y los pesos sinápticos se almacenan en una matriz $W$ de dimensión $m \times n$. Las ecuaciones de aprendizaje se reescriben de la siguiente forma:</p>
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\begin{equation}\nonumber
W_{k+1} = W_{k}+\eta x t^{\top}\hbox{(Hebbian)}
\end{equation}
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\begin{equation}\nonumber
W_{k+1} = W_{k}+\eta(f'(a_{k})\odot x)(t- r_{k})^{\top} \hbox{ (Widrow-Hoff)},
\end{equation}
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<p style="text-align: justify;">en donde la derivada $f'$ aplica sobre $a$ por cada componente, es decir, $f'(a)=(f'(a_{1}),\dots,f'(a_{n}))$.</p>
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<p style="text-align: justify;">En general, se deben aprender varias ($l$) asociaciones de entrada / destino. Luego, el conjunto de patrones de entrada se almacena en una matriz $m \times l$ denotada como $X$, los patrones de activación y objetivo respectivamente se almacenan en matrices de dimensión $n \times l$ indicadas como $A$ y $T$, respectivamente. Las iteraciones de activación y aprendizaje se pueden calcular para todos los patrones a la vez (esto se llama aprendizaje por lotes). La matriz de salida se calcula como:</p>
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\begin{equation}\nonumber
r = f(A) = f(WX^{T}),
\end{equation}
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<p style="text-align: justify;">en donde $f$ también aplica sobre cada componente de $WX^{\top}$, es decir $f(WX^{\top})=[f([WX^{\top}]_{ij})]$.</p>
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<p style="text-align: justify;">Las ecuaciones de aprendizaje se convierten</p>
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<p style="text-align: justify;"><a id="1"></a>
\begin{equation}\tag{1}
W_{k+1} = W_{k} + \eta X T^{\top} \hbox{ (Hebbian)},
\end{equation}</p>
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<p style="text-align: justify;"><a id="2"></a>
\begin{equation}\tag{2}
W_{k+1} = W_{k} + \eta (f'(A_{k}) \odot X)(T- R_{k})^{\top} \hbox{ (Widrow-Hoff).}
\end{equation}</p>
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<h3 id="Valores-propios,-vectores-propios-y-la-descomposición-en-valores-singulares" style="text-align: justify;">Valores propios, vectores propios y la descomposición en valores singulares<a class="anchor-link" href="#Valores-propios,-vectores-propios-y-la-descomposición-en-valores-singulares">¶</a></h3>
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<p style="text-align: justify;">Los vectores propios de una matriz cuadrada $W$ dada (resultante de su <em>descomposición propia</em>) son vectores invariantes bajo multiplicación por $W$. La descomposición propia se define mejor para una subclase de matrices llamadas matrices <em>semi-definidas</em> positivas. Una matriz $X$ es positiva semi-definida si existe otra matriz $Y$ tal que $X = YY^{\top}$. Este es el caso de la mayoría de las matrices utilizadas en redes neuronales, por lo que se considera solo este caso aquí.</p>
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<p style="text-align: justify;">Formalmente, un vector (distinto de cero) $u$ es un vector propio de una matriz cuadrada $W$ si</p>
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\begin{equation}\nonumber
Wu = \lambda u.
\end{equation}
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<p style="text-align: justify;">El escalar $\lambda$ es el valor propio asociado con $u$. Entonces $u$ es un vector propio de $W$ si su dirección es invariante bajo la multiplicación por $W$ (solo su longitud cambia si $\lambda \neq 1$). En general, hay varios vectores propios para una matriz dada (como máximo, la dimensión de $W$). En general, se ordenan por orden decreciente de su valor propio. Entonces, el primer vector propio, $u_{1}$ tiene el mayor valor propio $\lambda_{1}$. El número de vectores propios con un valor propio distinto de cero es el rango de la matriz.</p>
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<p style="text-align: justify;">Los valores propios de las matrices semidefinidas positivas son siempre positivos o cero (una matriz con valores propios estrictamente positivos, es definida positiva). Además, cualquier par de vectores propios $u_i$, $u_j$, con valores propios diferentes, son ortogonales, es decir:</p>
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\begin{equation}\nonumber
u_i^{\top} u_{j} = 0 \,\, \forall\,\, i \neq j.
\end{equation}
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<p style="text-align: justify;">Además, el conjunto de vectores propios de una matriz constituye una base ortogonal para los espacios fila y columna. Esto se expresa definiendo dos matrices, la matriz de vectores propios $U$, y la matriz diagonal de los valores propios $\Lambda$. Así la descomposición propia de $W$ (con rango $n$) es:</p>
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\begin{equation}\nonumber
W = U \Lambda U^{\top}.
\end{equation}
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<p style="text-align: justify;">La descomposición de valores singulares (SVD) generaliza la descomposición propia en matrices rectangulares. Si $X$ es una matriz $m \times l$, su SVD se define como:</p>
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\begin{equation}\nonumber
X = U \Delta V^{\top}
\end{equation}
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<p style="text-align: justify;">con $U U^{\top} = V^{\top} V = I$ y $\Delta$ una matriz diagonal ($I$ siendo la matriz identidad).</p>
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<p style="text-align: justify;">Los elementos diagonales de $\Delta$ son números reales positivos llamados valores singulares de $X$. Las matrices $U$ y $V$ son las matrices izquierda y derecha de vectores singulares (que también son vectores propios, ver más abajo).</p>
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<p style="text-align: justify;">El SVD está estrechamente relacionado con la descomposición propia porque $U$, $V$ y $\Delta$ pueden obtenerse a partir de la descomposición propia de las matrices $X^{\top} X$ y $X X^{\top}$ como</p>
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\begin{equation}\nonumber
X^{\top} X = U \Lambda U^{\top},\,\, X X^{\top} = V \Lambda V^{\top},\hbox{ y } \Delta = \Lambda^{1/2}.
\end{equation}
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<p style="text-align: justify;">Tenga en cuenta que $X^{\top} X$ y $X X^{\top}$ tienen los mismos valores propios.</p>
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<p style="text-align: justify;">Las descomposiciones de valores propios y singulares se utilizan en la mayoría de los campos de las matemáticas aplicadas, incluidas las estadística, el procesamiento de imágenes, la mecánica y los sistemas dinámicos. Para las redes neuronales, son esenciales para estudiar la dinámica de los autoasociadores y heteroasociadores lineales.</p>
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<h4 id="Procesos-iterativos" style="text-align: justify;">Procesos iterativos<a class="anchor-link" href="#Procesos-iterativos">¶</a></h4>
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<p style="text-align: justify;">Un heteroasociador lineal que usa la regla de Widrow-Hoff, el aprendizaje modifica solo los valores propios de la matriz de peso. Específicamente, si los patrones a aprender se almacenan en una matriz $X$ de orden $m \times l$, con una descomposición de valores singulares como $X = U \Delta V^{\top}$, entonces la <a href="#2">Ecuación 2</a> de la regla aprendizaje de Widrow-Hoff se convierte en</p>
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<p style="text-align: justify;"><a id="1"></a>
\begin{equation}\tag{3}
W_{k+1} = W_{k} + \eta X(T - R_{k})^{\top} = U\Delta^{-1}[I - (I - \eta\Delta^2)^{n+1}] V^{\top} T^{\top},
\end{equation}</p>
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<p style="text-align: justify;">porque para un heteroasociador lineal $A_{k}=R_{k}$ y $f'(R_{k}) = I$. (ver Abdi, 1994, p.54 ff.).</p>
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<p style="text-align: justify;">La matriz de peso de Widrow-Hoff corresponde a la primera iteración del algoritmo, es decir,</p>
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\begin{equation}\nonumber
W_{1} = U\Delta^{-1}[I - (I - \eta \Delta^2)] V^{\top} T^{\top} = \eta U \Delta V^{\top} T^{\top} = \eta X T^{\top}.
\end{equation}
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<p style="text-align: justify;">La ecuación <a href="#3">Ecuación 3</a> caracteriza los valores de $\eta$ que permiten que el proceso iterativo converja. Denotando por $\delta_{max}$ el mayor valor singular de $X$, si $\eta$ es tal que:</p>
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<p style="text-align: justify;"><a id="4"></a>
\begin{equation}\tag{4}
0 < \eta < 2 \delta^{-2}_{max}
\end{equation}</p>
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<p style="text-align: justify;">entonces se puede demostrar que (ver Abdi, 1994)</p>
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<div class="text_cell_render border-box-sizing rendered_html"><div style="text-align: justify;">\begin{equation}\nonumber
\lim_{n \to \infty}(I - \eta \Delta^{2})^{n} = 0
\end{equation}</div><p style="text-align: justify;">y por lo tanto</p><div style="text-align: justify;">\begin{equation}\nonumber
\lim_{n \to \infty} W_{n} = U \Delta^{-1} V^{\top} T^{\top} = X^{+} T.
\end{equation}</div></div>
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<p style="text-align: justify;">La matriz $X^{+} = U \Delta^{-1} V^{\top} $ es el pseudoinverso de $X$. Da una solución óptima de mínimos cuadrados para la asociación entre la entrada y el objetivo. Por lo tanto, el heteroasociador lineal es equivalente a la regresión múltiple lineal. Si $\eta$ está fuera del intervalo definido por la <a href="#4">Ecuación 4</a>, tanto los valores singulares como los elementos de la matriz de peso crecerán en cada iteración. En la práctica, debido a que las redes neuronales son simuladas por computadoras digitales, la matriz de peso eventualmente alcanzará los límites de la precisión de la máquina.</p>
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<p style="text-align: justify;">Cuando los vectores objetivo son los mismos que los vectores de entrada (es decir, cuando cada entrada está asociada a sí misma), el heteroasociador lineal se convierte en un autoasociador lineal. El enfoque anterior muestra que, ahora, la matriz Hebbiana de peso es la matriz de productos cruzados:</p>
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\begin{equation}\nonumber
W_{1} = X X^{\top} = U \Lambda U^{\top}.
\end{equation}
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<p style="text-align: justify;">Con el aprendizaje de Widrow-Hoff, cuando se alcanza la convergencia, todos los valores propios distintos de cero de la matriz de peso son iguales a 1. La matriz de peso se dice que es esférica; esto es igual a:</p>
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\begin{equation}\nonumber
W_{\infty} = U U^{\top}.
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<p style="text-align: justify;">Debido a que la técnica estadística del análisis de componentes principales (PCA) calcula la descomposición propia de una matriz de productos cruzados similar a $W$, el autoasociador lineal se considera como la red neuronal equivalente de PCA.</p>
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<h3 id="Optimización,-Derivadas-y-Matrices" style="text-align: justify;">Optimización, Derivadas y Matrices<a class="anchor-link" href="#Optimización,-Derivadas-y-Matrices">¶</a></h3>
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<p style="text-align: justify;">Las redes neuronales se utilizan a menudo para optimizar una función de los pesos sinápticos. La <em>diferenciación</em> de una función es el concepto principal para explorar problemas de <em>optimización</em> y, para redes neuronales, implica la diferenciación de vectores o funciones matriciales. En este contexto, debemos considerar la función de transferencia como una función del vector de peso. Esto es:</p>
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\begin{equation}\nonumber
r = f(w).
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<p style="text-align: justify;">La derivada de $f(w)$ con respecto al vector $w$ de $m$ - dimensional se denota por $\nabla f (w)$. También se llama el gradiente de $f$, es decir,</p>
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\begin{equation}\nonumber
\nabla f(w) = \frac{\partial f}{\partial w} = \left[\frac{\partial f}{\partial w_{1}},..., \frac{\partial f}{\partial w_{i}},..., \frac{\partial f}{\partial w_{I}} \right]^{\top}.
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<p style="text-align: justify;">Por ejemplo, la derivada de la salida de una neurona lineal es</p>
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\begin{equation}\nonumber
\frac{\partial f}{\partial w} = \left[\frac{\partial w^{\top} x}{\partial w_{1}},\dots, \frac{\partial w^{\top} x}{\partial w_{m}} \right]^{\top} = [x_{1},\dots, x_{m}]^{\top} = x.
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<p style="text-align: justify;">Cuando una función es dos veces diferenciable, las derivadas de segundo orden se almacenan en una matriz llamada matriz Hessiana de la función. A menudo se denota por $\nabla^{2}(f)$ (recuerde que $\nabla^{2}(f) = [\nabla\nabla^{\top}](f)$) y se define formalmente como</p>
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\begin{equation}\nonumber
\nabla^{2}(f) = \left[\begin{array}{cccc}
\frac{\partial^{2}_{f}}{\partial w^{2}_{1}} & \frac{\partial^{2}_{f}}{\partial w_{1} w_{2}} & \cdots & \frac{\partial^{2}_{f}}{\partial w_{1} w_{m}} \\
\frac{\partial^{2}_{f}}{\partial w_{2} w_{1}} & \frac{\partial^{2}_{f}}{\partial w^{2}_{2}} & \cdots & \frac{\partial^{2}_{f}}{\partial w_{2} w_{m}} \\
\vdots & \vdots & \ddots & \vdots \\
\frac{\partial^{2}_{f}}{\partial w_{I}w_{1}} & \frac{\partial^{2}_{f}}{\partial w_{I}w_{2}} & \cdots & \frac{\partial^{2}_{f}}{\partial w^{2}_{m}}.
\end{array} \right].
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<h4 id="Condiciones-para-mínimo" style="text-align: justify;">Condiciones para mínimo<a class="anchor-link" href="#Condiciones-para-mínimo">¶</a></h4>
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<p style="text-align: justify;">Un problema estándar es mostrar que una regla de aprendizaje dada encuentra una solución óptima en el sentido de que una función del vector de peso (o matriz) llamada <em>función de error</em> alcanza su valor mínimo cuando el aprendizaje ha convergido. A menudo, la función de error se define como la suma del error al cuadrado sobre todos los patrones.</p>
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<p style="text-align: justify;">Cuando se puede evaluar el gradiente de la función de error, una condición necesaria para la optimización (es decir, mínimo o máximo) es encontrar un vector de peso $w^{*}$ tal que</p>
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\begin{equation}\nonumber
\nabla f (w^{*}) = 0.
\end{equation}
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<p style="text-align: justify;">Esta condición también es suficiente siempre que $\nabla^{2}(f)$ sea definida positiva (cf. Haykin, 1999).</p>
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<h2 id="Expansión-de-Taylor" style="text-align: justify;">Expansión de Taylor<a class="anchor-link" href="#Expansión-de-Taylor">¶</a></h2>
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<p style="text-align: justify;">La expansión de Taylor es la técnica estándar utilizada para obtener una aproximación lineal o cuadrática de una función de una variable. Recuerde que la expansión de Taylor de una función continua $f(x)$ es</p>
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\begin{equation}\nonumber
f(x) = \sum_{n=0}^{\infty}(x-a)^{n}\frac{f^{(n)}(a)}{n!} = f(a) +(x-a)\frac{f'(a)}{1!} + (x-a)^{2} \frac{f''(a)}{2!} + \mathcal{R}_{2},
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<p style="text-align: justify;">en donde $\mathcal{R}_{2}$ representa todos los términos de orden superior a 2, y $a$ es un valor «conveniente» para evaluar $f$.</p>
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<p style="text-align: justify;">Esta técnica puede extenderse a funciones de matrices y vectores. Implica la noción de gradiente y de Hessiano. Ahora para una función vectorial $f(x)$ se expresa como:</p>
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\begin{equation}\nonumber
f(x) = f(a) + f(x - a)^{\top}\nabla f(a) + f(x - a)^{\top} \nabla^{2}f(a)f(x - a) + \mathcal{R}_{2}.
\end{equation}
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<h2 id="Minimización-iterativa" style="text-align: justify;">Minimización iterativa<a class="anchor-link" href="#Minimización-iterativa">¶</a></h2>
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<p style="text-align: justify;">Se puede demostrar que una regla de aprendizaje converge a un valor óptimo si disminuye el valor de la función de error en cada iteración. Cuando se puede evaluar el gradiente de la función de error, la técnica de <em>gradiente</em> (o <em>descenso más pronunciado</em>) ajusta el vector de peso moviéndolo en la dirección opuesta al gradiente de la función de error. Formalmente, la corrección para la iteración $(k + 1)$ es</p>
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\begin{equation}\nonumber
w_{k+1} = w_{k} + \nabla = w_{k} - \eta \nabla f(w_k)
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<p style="text-align: justify;">Como ejemplo, demostremos que para un heteroasociador lineal, la regla de aprendizaje de Widrow-Hoff minimiza iterativamente el error al cuadrado entre el objetivo y la salida. La función de error es</p>
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\begin{equation}\nonumber
e^{2} = (t-r)^{2} = t^{2} + r^{2} - 2tr = t^{2} + x^{\top}w w^{\top} -2tw^{\top}x.
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<p style="text-align: justify;">El gradiente de la función de error es:</p>
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\begin{equation}\nonumber
\frac{\partial e}{\partial w} = 2(w^{\top} x)x - 2t x = -2(t - w^{\top} x) x.
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<p style="text-align: justify;">El vector de peso se corrige moviéndose en la dirección opuesta del gradiente. Esto proporciona la siguiente corrección para la iteración $k + 1$:</p>
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\begin{equation}\nonumber
w_{k+1} = w_{k} - \eta \frac{\partial e}{\partial w} = w_{k} + \eta (t-w^{\top}_{k}x)x = w_{k} + \eta(t-o_{k})x.
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<p style="text-align: justify;">Esto da la regla de aprendizaje de Widrow-Hoff en su expresión más simple.</p>
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<p style="text-align: justify;">El método de gradiente funciona porque el gradiente de $w_{n}$ es una aproximación de Taylor de primer orden del gradiente del vector de peso óptimo $w^{*}$. Es una técnica favorita en las redes neuronales porque el error de propagación posterior popular es una técnica de gradiente.</p>
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<p style="text-align: justify;">El método de Newton es una aproximación de Taylor de segundo orden, utiliza el inverso del hessiano de $w$ (suponiendo que exista). Proporciona una mejor aproximación numérica pero requiere más cómputo. Aquí la corrección para la iteración $k + 1$ es</p>
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\begin{equation}\nonumber
w_{k+1} = w_{k} - [\nabla^{2}f(w_{k})]^{-1} \nabla_{f(w_{k})}.
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<h2 id="Referencias" style="text-align: justify;">Referencias<a class="anchor-link" href="#Referencias">¶</a></h2><ul>
<li style="text-align: justify;">Hervé Abdi. 2001. Linear Algebra for Neural Networks.</li>
<li style="text-align: justify;">Hervé Abdi et al. 1999. Neural networks. Thousand Oak.</li>
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<h2 id="Contacto" style="text-align: justify;">Contacto<a class="anchor-link" href="#Contacto">¶</a></h2><ul>
<li style="text-align: justify;">Participa de la canal de Nerve a través de <a href="https://discord.gg/edPmghPq8K" target="_blank">Discord</a>.</li>
<li style="text-align: justify;">Se quieres conocer más acerca de este tema me puedes contactar a través de <a href="https://www.classgap.com/es/tutor/alejandro-sanchez-yali" target="_blank">Classgap</a>.</li>
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www.asanchezyali.comhttp://www.blogger.com/profile/06396258253910042323noreply@blogger.com0tag:blogger.com,1999:blog-8939855543774830921.post-50139072001595949092020-10-11T22:44:00.031-05:002021-03-13T16:56:24.517-05:00Geometría de Incidencia<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
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<p style="text-align: justify;">Una <b>geometría de incidencia</b> está formada por un conjunto $\mathbb{E}$ al que se denomina <b>espacio</b> y a cuyos elementos se conocerán como <b>puntos</b>, junto con dos familias disyuntas y no vacías $\mathcal{L}$, $\mathcal{P}$ de subconjuntos no vacíos del espacio a cuyos elementos se denominaran respectivamente <b>rectas</b> y <b>planos</b>, de modo que se satisfacen los siguientes axiomas:</p>
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<li style="text-align: justify;"><strong>Axioma AI1.</strong> Cualquier par de puntos distintos pertenecen a una única recta.</li>
<li style="text-align: justify;"><strong>Axioma AI2.</strong> Para toda recta, existe al menos dos puntos distintos que pertenecen a ella.</li>
<li style="text-align: justify;"><strong>Axioma AI3.</strong> Para cualquier tripleta de puntos distintos, tales que no pertenecen simultáneamente a ninguna recta, pertenecen a un único plano.</li>
<li style="text-align: justify;"><strong>Axioma AI4.</strong> Para todo plano, existe al menos tres puntos distintos que pertenecen a él y no pertenecen simultaneamente a ninguna recta.</li>
<li style="text-align: justify;"><strong>Axioma AI5.</strong> Si un plano y una recta tienen al menos dos puntos en común, entonces la recta está contenida en el plano.</li>
<li style="text-align: justify;"><strong>Axioma AI6.</strong> Si dos planos tienen un punto en común, entonces tienen dos puntos en común. </li>
<li style="text-align: justify;"><strong>Axioma AI7.</strong> Para todo plano existe al menos un punto que no pertenece a él.</li>
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<p style="text-align: justify;">Cuando tres puntos o más pertenecen simultáneamente a una única recta, entonces se dice que son <b>colineales</b>. También se dirá que cuatro puntos o más son <b>coplanares</b> si pertenecen simultáneamente a un único plano.</p>
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<p style="text-align: justify;">Los axiomas anteriores pueden tener muchas interpretaciones, debido a que el espacio $\mathbb{E}$ se considera como un conjunto del cuál no se ha especificado la naturaliza de sus elementos. Con el objetivo de estimular el entendimiento de estos conceptos, inclusive sus limitaciones, se le sugiere al lector que estudie cuidadosamente los siguientes ejemplos, y descubra que estos ejemplos cumplen con la definición de una geometría de incidencia.</p>
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<p style="text-align: justify;"><b>Ejemplo 1.</b> <em> Considere el conjunto $\mathbb{E}=\{A, B, C\}$ y la familia de rectas $\mathcal{L}=\{\{A,B\},\{A,C\}, \{B, C\}\}$. Sin duda el lector podrá verificar que $\mathbb{E}$ y $\mathcal{L}$ satisface los axiomas AI1, AI2, AI3 y AI4. Si asumimos que los demás axiomas se cumplen por vacuidad, entonces el par $(\mathbb{E},\mathcal{L})$ es una geometría de incidencia.</em></p>
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<p style="text-align: justify;"><b>Ejemplo 2.</b> <em> Considere el conjunto $\mathbb{E}=\{A, B, C, D\}$, la familia de rectas $\mathcal{L}=\{\{A,B\},\{A,C\}, \{A, D\}, \{B, C\}, \{B, D\}, \{C, D\}\}$ y la familia de planos definidos por $\mathcal{P}=\{\{A, B, C\}, \{A, B, D\}, \{A, C, D\}, \{B, C, D\}\}$. En esta ejemplo, el lector podrá verificar que $\mathbb{E}$, $\mathcal{L}$ y $\mathcal{P}$ satisface todos los axiomas de una geometría de incidencia. </em></p>
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<p style="text-align: justify;">Ahora que el lector ha entendido los ejemplos 1 y 2, ya está en la capacidad de resolver las siguientes preguntas: ¿Es posible en el conjunto $\mathbb{E}=\emptyset$ definir una geometría de incidencia? ¿Y en $\mathbb{E}=\{\emptyset\}$?</p>
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<p style="text-align: justify;">Para los lectores más atrevidos, les sugiero pensar en el siguiente problema, el cual involucra algunos aspectos de combinatoria:</p>
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<p style="text-align: justify;"><b>Problema 1.</b> <em> Considere un conjunto finito $\mathbb{E}=\{A_{1}, \cdots, A_{n+1}\}$. ¿De cuántas formas se puede definir las familias de rectas y planos de tal forma que $(\mathbb{E}, \mathcal{P}, \mathcal{L})$ sea una geometría de incidencia?</em></p>
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<p style="text-align: justify;"><strong>Ejemplo 3</strong>. <strong>Geometría Incidencia Clásica</strong>. Considere a $\mathbb{E}$ como un «lienzo infinito plano» donde los puntos son todas las posibles posiciones sobre el lienzo y las rectas será todos los «trazos» definidos por una «regla infinita». Bajo esta interpretación, podemos entender cada uno de los axiomas de la siguiente manera:</p>
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<li style="text-align: justify;"><strong>Axioma AI1.</strong> Cualquier par de puntos distintos pertenecen a una única recta. Para representar este axioma en terminos del lienzo y los trazos infinitos, se consideran inicialmente dos posiciones $A$ y $B$ del lienzo como los puntos $A$ y $B$ por los que mediante una «regla» se traza una «trazo infinito». Para indicar que la recta se extiende infinitamente se agregan flechas en los extremos tal como se puede apreciar en la siguiente figura:</li>
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<li style="text-align: justify;"><strong>Axioma AI2.</strong> Para toda recta, existe al menos dos puntos distintos que pertenecen a ella. En este caso, se considera inicialmente una recta y luego de ella se pueden seleccionar dos puntos $A$ y $B$ distintos tal como se puede apreciar a continuación:</li>
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<li style="text-align: justify;"><strong>Axioma AI3.</strong> Para cualquier tripleta de puntos distintos, tales que no pertenecen simultáneamente a ninguna recta, pertenecen a un único plano. Considere inicialmente tres puntos $A$, $B$, $C$ distintos, este axioma afirma que existe único plano o «lienzo» que los contiene. En este caso el plano es el conjunto $\mathbb{E}$ que se ha definido como un lienzo infinito. En la siguiente figura, el plano se representa como un rectángulo de bordes redondeados, es importante aclarar que se extiende infinitamente.</li>
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<li style="text-align: justify;"><strong>Axioma AI4.</strong> Para todo plano, existe al menos tres puntos distintos que pertenecen a él y no pertenecen simultaneamente a ninguna recta. En este caso, en $\mathbb{E}$ existe tres puntos $A$, $B$, $C$ distinto y que no pertenecen simultaneamente a ninguna recta. </li>
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<li style="text-align: justify;"><strong>Axioma AI5.</strong> Si un plano y una recta tienen al menos dos puntos en común, entonces la recta está contenida en el plano. El lector podrá estar de acuerdo en que este axioma se cumple trivialmente ¿o tal vez no?</li>
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<p style="text-align: justify;">En cuanto a los axiomas AI5, AI6 y AI7 se asumen por obviedad, sin embargo el conjunto $\mathbb{E}$ podría ser modificado para que existe una familia de planos o lienzos. ¿Podrías hacer esta modificación?</p>
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<p style="text-align: justify;">En los siguientes ejemplos se verá una definición más formal de este ejemplo.</p>
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<p style="text-align: justify;"><strong>Ejemplo 4</strong>. Considere al espacio $\mathbb{E}$ como el conjunto $\mathbb{R}^{2}$ de los pares ordenados de números reales. Entonces las rectas son los conjuntos de la forma $\lambda_{_{(a, b, c)}}=\{(x,y)\in \mathbb{E}^{2}: ax+by=c\}$ con $a$, $b$ reales y no todos nulos. Este ejemplo tiene muchas similaridades con el ejemplo anterior.</p>
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<p style="text-align: justify;"><strong>Ejemplo 5.</strong> Considere el espacio $\mathbb{E}$ como el conjunto de las tripletas ordenadas de número reales. Los planos son los conjuntos $\pi_{_{(a, b, c, d)}}=\{(x,y,z)\in \mathbb{E}^{3}: ax+by+cz+d =0\}$ con $a$, $b$, $c$ reales y no todos nulos y las rectas son la intersección de dos planos $\pi_{_1}=\{(x,y,z)\in \mathbb{E}^{3}: a_{_1}x+b_{_1}y+c_{_1}z+d_{_1} =0\}$ y $\pi_{_2}=\{(x,y,z)\in \mathbb{E}^{3}: a_{_2}x+b_{_2}y+c_{_2}z+d_{_2} =0\}$, siempre que la tripleta $(a_{_1}, b_{_1}, c_{_1})$ no sea un múltiplo de la tripleta $(a_{_2}, b_{_2}, c_{_2})$.Este ejemplo se puede considerar como una extensión del ejemplo anterior.</p>
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<p style="text-align: justify;">Los siguente ejemplos permiten entender que en una geometría de incidencia las rectas no siempre son las nociones intuitivas usuales.</p>
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<p style="text-align: justify;"><strong>Ejemplo 6.</strong> Considere el espacio $\mathbb{E}$ como el conjunto $\mathbb{H}^{2}=\{(x,y)\in\mathbb{R}^{2}:y>0\}$. Hay dos tipos de rectas, las verticales dadas por $l_{_a}=\{(x,y)\in \mathbb{H}^{2}:x=a\}$ con $a$ un número real y los arcos definidos por $l_{_{p,r}}=\{(x,y)\in \mathbb{H}:(x-p)^{2}+y^{2}=r^{2}\}$ con $p$, $r$ números reales. Te reto a hacer una interpretación gráfica de este ejemplo y probar que es una geometría de incidencia de dimensión dos.</p>
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<p style="text-align: justify;"><strong>Ejemplo 7.</strong> Considere el conjunto $\mathbb{H}^{3}=\{(x,y,z)\in \mathbb{R}^{3}:z>0\}$ como el conjunto de puntos. Los planos son de dos tipos, los planos verticales dados por $\pi_{_{(a, b, c)}}=\{(x,y,z)\in \mathbb{H}:ax+by+c=0\}$ con $a$, $b$, $c$ reales no todos nulos y los semiesféricos $\pi_{_{(p, q, r)}}=\{(x,y,z)\in \mathbb{H}:(x-p)^{2}+(y-q)^{2}+z^2=r^2\}$ con $p$, $q$ y $r$ números reales y las rectas son la intersección de dos de estos planos, resultando también dos tipos de rectas, las verticales y las semiesféricas.</p>
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<p style="text-align: justify;">Los principales resultados de esta teoria son los siguientes:</p>
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<p style="text-align: justify;"><strong>Teorema 1. Punto exterior a una recta.</strong>
<em>En una geometría de incidencia, para toda recta contenida en un plano, existe al menos un punto del plano dado que no pertenece a ella.</em></p>
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<p style="text-align: justify;">En efecto si $l$ es una recta y $\pi$ es un plano tales que $l\subset \pi$. Por el axioma AI2 existe dos puntos $A$, $B$ distintos tales que $A, B\in l$ y por lo tanto $A, B\in \pi$. Finalmente por el axioma AI3 debe existir un tercer punto $C\in \pi$ tal que $C\notin l$ lo que confirma el teorema.</p>
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<p style="text-align: justify;"><strong>Teorema 2. Intersección de rectas.</strong> <em>Dos rectas distintas en una geometría de incidencia tienen como máximo un punto en común.</em></p>
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<p style="text-align: justify;">Si se consideran a $\lambda_{1}, \lambda_{2}$ como dos rectas diferentes del espacio. Si se supone que se cortan en más de un punto, entonces por el axioma AI1 ellas tienen que ser iguales. Es muy imporante que el lector hace énfasis en la unicidad de la recta que pasan por cualquier par de puntos.</p>
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<p style="text-align: justify;"><strong>Teorema 3. Colinealidad.</strong> <em>En una geometría de incidencia, si $A$, $B$ son puntos de una recta $\lambda$ y $C$ es un punto exterior a $\lambda$, entonces los puntos $A, B, C$ no son colineales.</em></p>
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<p style="text-align: justify;">Si $A$, $B$, $C$ fueran colineales existiría una recta $\gamma$ tal que $A, B, C\in \gamma$ y por el axioma AI1 se concluye que $\gamma =\lambda$, esto quiere decir que $C\in \lambda$ lo que contradice la hipótesis del teorema. Por lo tanto $A$, $B$, $C$ no son colineales.</p>
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<p style="text-align: justify;"><strong>Teorema 4. Coplanaridad de rectas.</strong> <em>En un geometría de incidencia, si dos rectas tiene un punto en común, entonces existe un único plano que las contiene.</em></p>
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<p style="text-align: justify;">Sean $l$ y $m$ dos rectas diferentes que se cortan. Sea $A$ el punto de intersección (Teorema de la intercepción de rectas). Por el
axioma AI2 existen otro punto $B$ diferente de $A$ en $l$ y otro punto $C$ diferente de $A$ en $m$. Luego $A, B, C$ son no colineales ya que
$B$ no está en la recta $m$ y $C$ no está en la recta $l$. Entonces por el axioma AI3, los puntos $A, B,C$ determinan un plano único. Por el axioma AI5 las rectas $l$ y $m$ están contenidas en ese plano. Este es el único plano que las contiene. Si existiera otro, $A, B, C$ estarán en él, contradiciendo el axioma AI3.</p>
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<p style="text-align: justify;"><strong>Teorema 5.</strong> <em>Si $l_{_1}$ y $l_{_2}$ son rectas en una geometría de incidencia y $l_{_1}\cap l_{_2}$ tiene dos o más puntos distintos en común, entonces $l_{_1}=l_{_2}$.</em></p>
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<p style="text-align: justify;">¿Cómo se demostraría este teorema?</p>
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<p style="text-align: justify;"><strong>Definición 1.</strong> Se dirá que dos rectas son <strong>paralelas</strong> si son iguales o bien ambas están contenidas en un mismo plano y no tienen puntos en común. Si dos rectas no tienen puntos en común, pero no están contenidas en el mismo plano, se dirá que se <strong>cruzan</strong>. La única alternativa a estos casos es que las rectas tengan un único punto en común, en cuyo caso se dice que son <strong>secantes</strong>.</p>
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<p style="text-align: justify;">Los siguientes teoremas se sugierene como ejercicios para el lector:</p>
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<p style="text-align: justify;"><strong>Teorema 6.</strong> <em>En una geometría de incidencia, dados un plano y una recta, o bien no tienen puntos comunes, o bien tienen un único punto en común, o bien la recta está contenida en el plano.</em></p>
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<p style="text-align: justify;"><strong>Teorema 7.</strong> <em>En una geometría de incidencia, una recta y un punto exterior a ella están contenidos en un único plano</em></p>
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<p style="text-align: justify;"><strong>Teorema 8.</strong> <em>En una geometría de incidencai, dos planos no paralelos en una geometría de incidencia se cortan en una única recta.</em></p>
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<h2 id="Bibliografía" style="text-align: justify;">Bibliografía<a class="anchor-link" href="#Bibliografía">¶</a></h2><ol>
<li style="text-align: justify;">Jaime Escobar Acosta. 1992. Elementos de geometría. Universidad de Antioquia.</li>
<li style="text-align: justify;">David Hilbert. 1950. The Foundations of Geometry. University of Göttingen.</li>
<li style="text-align: justify;">Carlos Ivorra Castillo. 2013. Geometría. Universidad de Valencia.</li>
<li style="text-align: justify;">John Haas. 2018. What is a geometry?</li>
<li style="text-align: justify;">Gerard A. Venema. 2016. Exploring Advanced Euclidean Geometry with GeoGebra.</li>
<li style="text-align: justify;">Ian Biringer. 2015. Euclidean and Non-Euclidean Geometry.</li>
<li style="text-align: justify;">Millman and Parke. Geometry: A Metric Approach with Models.</li>
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<h2 id="Contacto" style="text-align: justify;">Contacto<a class="anchor-link" href="#Contacto">¶</a></h2><ul>
<li style="text-align: justify;">Participa de la canal de Nerve a través de <a href="https://discord.gg/edPmghPq8K" rel="nofollow" src="https://discord.gg/edPmghPq8K" target="_blank">Discord</a>.</li>
<li style="text-align: justify;">Se quieres conocer más acerca de este tema me puedes contactar a través de <a href="https://www.classgap.com/me/alejandro-sanchez-yali" rel="nofollow" src="https://www.classgap.com/me/alejandro-sanchez-yali" target="_blank">Classgap</a>.</li>
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www.asanchezyali.comhttp://www.blogger.com/profile/06396258253910042323noreply@blogger.com0tag:blogger.com,1999:blog-8939855543774830921.post-53764115684244015752020-10-07T17:31:00.010-05:002021-02-19T11:57:15.230-05:00Sistema formal MIU - Acertijo MU<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
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<p style="text-align: justify;">En esta ocasión se hará una breve introdución a el acertijo $MU$; el cual representa un pequeño <em>sistema formal</em>. Este acertijo fue planteado por Hofstadter en 1979 en su libro Godel, Escher, Bach. An Eternal Golden Braid. El objetivo del acertijo propuesto por Hofstadter es producir la cadena MU (de ahí su nombre de Acertijo $MU$) dentro de un sistema formal conocido como el sistema $MIU$; el nombre del sistema se toma del hecho de que sólo emplea tres letras del alfabeto: $M$, $I$, $U$. Esto significa que las cadenas del sistema $MIU$ estarán formadas exclusivamente por esas tres letras. Para comenzar, el sistema $MIU$ parte de una cadena inicial, la cadena $MI$, es decir, $MI$ es el único axioma del sistema en cuestión. Las cadenas que sean producidas deberán conseguirse aplicando las reglas que se mencionan a continuación:</p>
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<li><p style="text-align: justify;"><strong>Regla 1</strong>. Si se tiene una cadena cuya última letra sea $I$, se le puede agregar una $U$ al final. Dicho en otras palabras, si $xI$ es un teorema, también lo es $xIU$. En este caso $x$ representa cualquier cadena arbitraria. Por ejemplo, si se tiene la cadena $MII$, entonces se puede obtener $MIIU$.</p>
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<li><p style="text-align: justify;"><strong>Regla 2</strong>. Suponga que $Mx$ es un teorema. En tal caso también $Mxx$ es un teorema. Por ejemplo, si se tiene la cadena $MIU$ se puede obtener la cadena $MIUIU$.</p>
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<li><p style="text-align: justify;"><strong>Regla 3</strong>. Si en una de las cadenas de la colección aparece la secuencia $III$, puede elaborarse una nueva cadena sustituyendo $III$ por $U$. Por ejemplo, si se tiene la cadena $UMIIIMU$ se puede elaborar $UMUMU$. Observe que las tres $III$ deben ser consecutivas.</p>
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<li><p style="text-align: justify;"><strong>Regla 4</strong>. Si aparece $UU$ en el interior de una de las cadenas, está permitida su eliminación. Por ejemplo, dado $MUUUIII$ se puede obtener $MUIII$.</p>
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<p style="text-align: justify;">Un primer intento para resolver este acertijo, es proceder a generar de manera manual algunas cadenas, como primer paso, se observa que a partir de el axioma $MI$ y aplicando las reglas, se pueden obtener las siguientes cadenas:</p>
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<li style="text-align: justify;">$MIU$</li>
<li style="text-align: justify;">$MII$</li>
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<p style="text-align: justify;">La primera cadena se obtiene después de aplicar la regla 1, y la segunda, casualmente después de aplicar la regla 2. Es posible observar que no se pueden aplicar las reglas 3 y 4 a $MI$.</p>
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<p style="text-align: justify;">Después se tiene que ver qué cadenas se pueden generar de $MIU$ y cuáles de $MII$. De $MIU$ solo es posible generar $MIUIU$; sin embargo, de $MII$ se pueden generar $MIIU$ y $MIIII$. Si se sigue aplicando este proceso, se tendrá que buscar qué cadenas ahora se pueden formar de $MIUIU$, $MIIU$ y $MIII$, y seguir así secuencialmente hasta que en alguna de esas generaciones se encuentre la cadena $MU$.</p>
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<div class="separator" style="clear: both;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdJeLGnN-_5o1zda1Nh4BOHzTI_pQmJkNQc-PrICKeMMKSdIhKsgFhre605YjlgRKYUfQN_W0SqfyC6I12mH68xEFoGJrWhCmp2HdMKXd0rksXLgikfSoQTv7mr0W6Asnev7akjDCfj9U/s0/treeMIU.png" style="display: block; padding: 1em 0; text-align: center; "><img alt="" border="0" data-original-height="230" data-original-width="439" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdJeLGnN-_5o1zda1Nh4BOHzTI_pQmJkNQc-PrICKeMMKSdIhKsgFhre605YjlgRKYUfQN_W0SqfyC6I12mH68xEFoGJrWhCmp2HdMKXd0rksXLgikfSoQTv7mr0W6Asnev7akjDCfj9U/s0/treeMIU.png"/></a></div>
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<p style="text-align: justify;">De lo anterior se puede deducir que, esta búsqueda nos lleva a la generación de un árbol de teoremas como el mostrado en la <a href="#1">Figura 1</a> , y como puede observarse, cada nodo puede tener una cantidad variada de hijos. En un principio, se podría pensar que cada nodo solo puede tener a lo máximo cuatro hijos, pero si se analiza detenidamente el problema, se puede llegar a la conclusión de que no necesariamente será así, por ejemplo, de la cadena $MIIIIIIIU$ aplicando solamente la regla 3 se pueden obtener las siguientes cadenas:</p>
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<li style="text-align: justify;">$MUIIIIU$</li>
<li style="text-align: justify;">$MIUIIIU$</li>
<li style="text-align: justify;">$MIIUIIU$</li>
<li style="text-align: justify;">$MIIIUIU$</li>
<li style="text-align: justify;">$MIIIIUU$</li>
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<p style="text-align: justify;">De aquí se deduce que el número de hijos de cada nodo es variable y puede ser muy grande.</p>
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<p style="text-align: justify;">Para facilitar el ejercicio se puede hacer uso de algún lenguaje de programación como por ejemplo python y hacer una codificación de las reglas del sistema formal MIU, algo como lo que se muestra a continuación:</p>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="kn">import</span> <span class="nn">re</span></div><span><div style="text-align: justify;"><span class="k">class</span> <span class="nc">MIU</span><span class="p">:</span></div></span><div style="text-align: justify;"> </div><div style="text-align: justify;"> <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span></div><div style="text-align: justify;"> <span class="c1"># Definition of the primary chain.</span></div><div style="text-align: justify;"> <span class="bp">self</span><span class="o">.</span><span class="n">state</span> <span class="o">=</span> <span class="s1">'MI'</span></div><div style="text-align: justify;"> </div><div style="text-align: justify;"> <span class="k">def</span> <span class="nf">get_state</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span></div><div style="text-align: justify;"> <span class="c1"># Check the game status.</span></div><div style="text-align: justify;"> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">state</span></div><div style="text-align: justify;"> </div><div style="text-align: justify;"> <span class="k">def</span> <span class="nf">reset</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span></div><div style="text-align: justify;"> <span class="c1"># Restart the game state. </span></div><div style="text-align: justify;"> <span class="bp">self</span><span class="o">.</span><span class="n">state</span> <span class="o">=</span> <span class="s1">'MI'</span></div><div style="text-align: justify;"> </div><div style="text-align: justify;"> <span class="k">def</span> <span class="nf">rule_one</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span></div><div style="text-align: justify;"> <span class="c1"># Definition of rule one of the MIU system.</span></div><div style="text-align: justify;"> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">state</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">==</span> <span class="s1">'I'</span><span class="p">:</span></div><div style="text-align: justify;"> </div><div style="text-align: justify;"> <span class="bp">self</span><span class="o">.</span><span class="n">state</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">state</span> <span class="o">+</span> <span class="s1">'U'</span></div><div style="text-align: justify;"> </div><div style="text-align: justify;"> <span class="k">else</span><span class="p">:</span></div><div style="text-align: justify;"> </div><div style="text-align: justify;"> <span class="nb">print</span><span class="p">(</span><span class="s1">'Can not use this rule...'</span><span class="p">)</span></div><div style="text-align: justify;"> </div><div style="text-align: justify;"> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">state</span></div><div style="text-align: justify;"> </div><div style="text-align: justify;"> <span class="k">def</span> <span class="nf">rule_two</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span></div><div style="text-align: justify;"> <span class="c1"># Definition of rule two of the MIU system.</span></div><div style="text-align: justify;"> <span class="bp">self</span><span class="o">.</span><span class="n">state</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">state</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">state</span><span class="p">[</span><span class="mi">1</span><span class="p">:]</span></div><div style="text-align: justify;"> </div><div style="text-align: justify;"> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">state</span></div><div style="text-align: justify;"> </div><div style="text-align: justify;"> </div><div style="text-align: justify;"> <span class="k">def</span> <span class="nf">rule_three</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span></div><div style="text-align: justify;"> <span class="c1"># Definition of rule three of the MIU system.</span></div><div style="text-align: justify;"> <span class="n">word</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">state</span></div><div style="text-align: justify;"> <span class="n">result</span> <span class="o">=</span> <span class="n">re</span><span class="o">.</span><span class="n">finditer</span><span class="p">(</span><span class="sa">r</span><span class="s1">'(?=(III))'</span><span class="p">,</span> <span class="n">word</span><span class="p">)</span> </div><div style="text-align: justify;"> </div><div style="text-align: justify;"> <span class="n">words</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">()</span></div><div style="text-align: justify;"> <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">result</span><span class="p">):</span></div><div style="text-align: justify;"> <span class="n">slices</span> <span class="o">=</span> <span class="p">[</span><span class="n">word</span><span class="p">[:</span><span class="n">j</span><span class="o">.</span><span class="n">start</span><span class="p">(</span><span class="mi">1</span><span class="p">)],</span> <span class="n">word</span><span class="p">[</span><span class="n">j</span><span class="o">.</span><span class="n">end</span><span class="p">(</span><span class="mi">1</span><span class="p">):]]</span></div><div style="text-align: justify;"> <span class="n">chain</span> <span class="o">=</span> <span class="s1">'U'</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">slices</span><span class="p">)</span></div><div style="text-align: justify;"> <span class="n">words</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">chain</span></div><div style="text-align: justify;"> <span class="nb">print</span><span class="p">(</span><span class="s1">'Option </span><span class="si">{}</span><span class="s1">:'</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">i</span><span class="p">),</span> <span class="n">new_chain</span><span class="p">)</span></div><div style="text-align: justify;"> </div><div style="text-align: justify;"> <span class="k">if</span> <span class="n">words</span><span class="o">.</span><span class="n">keys</span><span class="p">():</span> </div><div style="text-align: justify;"> </div><div style="text-align: justify;"> <span class="n">option</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="nb">input</span><span class="p">(</span><span class="s1">'Choose an option: '</span><span class="p">))</span></div><div style="text-align: justify;"> <span class="bp">self</span><span class="o">.</span><span class="n">state</span> <span class="o">=</span> <span class="n">words</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">option</span><span class="p">)</span></div><div style="text-align: justify;"> </div><div style="text-align: justify;"> <span class="k">else</span><span class="p">:</span></div><div style="text-align: justify;"> </div><div style="text-align: justify;"> <span class="nb">print</span><span class="p">(</span><span class="s1">'Can not use this rule...'</span><span class="p">)</span></div><div style="text-align: justify;"> </div><div style="text-align: justify;"> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">state</span></div><div style="text-align: justify;"> </div>
<div style="text-align: justify;"> <span class="k">def</span> <span class="nf">rule_four</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span></div><div style="text-align: justify;"> <span class="c1"># Definition of rule four of the MIU system.</span></div><div style="text-align: justify;"> <span class="n">word</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">state</span></div><div style="text-align: justify;"> <span class="n">result</span> <span class="o">=</span> <span class="n">re</span><span class="o">.</span><span class="n">finditer</span><span class="p">(</span><span class="sa">r</span><span class="s1">'(?=(UU))'</span><span class="p">,</span> <span class="n">word</span><span class="p">)</span> </div><div style="text-align: justify;"> </div><div style="text-align: justify;"> <span class="n">words</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">()</span></div><div style="text-align: justify;"> <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">result</span><span class="p">):</span></div><div style="text-align: justify;"> <span class="n">new_chain</span> <span class="o">=</span> <span class="n">word</span><span class="p">[:</span><span class="n">j</span><span class="o">.</span><span class="n">start</span><span class="p">(</span><span class="mi">1</span><span class="p">)]</span> <span class="o">+</span> <span class="n">word</span><span class="p">[</span><span class="n">j</span><span class="o">.</span><span class="n">end</span><span class="p">(</span><span class="mi">1</span><span class="p">):]</span></div><div style="text-align: justify;"> <span class="n">words</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">new_chain</span></div><div style="text-align: justify;"> <span class="nb">print</span><span class="p">(</span><span class="s1">'Option </span><span class="si">{}</span><span class="s1">:'</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">i</span><span class="p">),</span> <span class="n">new_chain</span><span class="p">)</span></div><div style="text-align: justify;"> </div><div style="text-align: justify;"> <span class="k">if</span> <span class="n">words</span><span class="o">.</span><span class="n">keys</span><span class="p">():</span></div><div style="text-align: justify;"> </div><div style="text-align: justify;"> <span class="n">option</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="nb">input</span><span class="p">(</span><span class="s1">'Choose an option: '</span><span class="p">))</span></div><div style="text-align: justify;"> <span class="bp">self</span><span class="o">.</span><span class="n">state</span> <span class="o">=</span> <span class="n">words</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">option</span><span class="p">)</span></div><div style="text-align: justify;"> </div><div style="text-align: justify;"> <span class="k">else</span><span class="p">:</span></div><div style="text-align: justify;"> </div><div style="text-align: justify;"> <span class="nb">print</span><span class="p">(</span><span class="s1">'Can not use this rule...'</span><span class="p">)</span></div><div style="text-align: justify;"> </div><div style="text-align: justify;"> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">state</span> </div></pre></div>
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<p style="text-align: justify;">Para utilizarlo, solo tienes que hacer una instancia del clase MIU:</p>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">game</span> <span class="o">=</span> <span class="n">MIU</span><span class="p">()</span>
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<p style="text-align: justify;">Luego sería usar cada uno de los métodos de la clase:</p>
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<li style="text-align: justify;"><code>rule_one()</code>, <code>rule_two()</code>, <code>rule_three()</code> y <code>rule_four()</code> para hacer uso de cualquiera de las reglas del sistema MIU.</li>
<li style="text-align: justify;"><code>get_state()</code> para ver el estado del juego.</li>
<li style="text-align: justify;"><code>reset()</code> para reiniciar el juego.</li>
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<p style="text-align: justify;">A continuación algunos ejemplos del uso:</p>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">game</span><span class="o">.</span><span class="n">rule_one</span><span class="p">()</span>
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<pre style="text-align: justify;">'MIU'</pre>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">game</span><span class="o">.</span><span class="n">rule_one</span><span class="p">()</span>
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<pre style="text-align: justify;">Can not use this rule...
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<pre style="text-align: justify;">'MIU'</pre>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">game</span><span class="o">.</span><span class="n">rule_four</span><span class="p">()</span>
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<pre style="text-align: justify;">'MIU'</pre>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">game</span><span class="o">.</span><span class="n">rule_two</span><span class="p">()</span>
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<pre style="text-align: justify;">'MIUIU'</pre>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">game</span><span class="o">.</span><span class="n">rule_two</span><span class="p">()</span>
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<pre style="text-align: justify;">'MIUIUIUIU'</pre>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">game</span><span class="o">.</span><span class="n">reset</span><span class="p">()</span>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">game</span><span class="o">.</span><span class="n">get_state</span><span class="p">()</span>
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<pre style="text-align: justify;">'MI'</pre>
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<p style="text-align: justify;">Finalmente, la pregunta es ¿Puedes encontrar MU? ¿Puedes construir un nuevo algoritmo que permita decidir si una cadena $x$ es demostrable dentro del sistema MIU? ¿Qué quiere decir que una cadena es demostrable en MIU? Espero seguir discutiendo estas preguntas en el futuro, por ahora les recomiendo que se pasen por la referencia que motivo esta entrada.</p>
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<h2 id="Referencias" style="text-align: justify;">Referencias<a class="anchor-link" href="#Referencias">¶</a></h2><ul>
<li style="text-align: justify;">Hofstadter. 1979. Godel, Escher, Bach. An Eternal Golden Braid.</li>
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www.asanchezyali.comhttp://www.blogger.com/profile/06396258253910042323noreply@blogger.com0tag:blogger.com,1999:blog-8939855543774830921.post-71591256268062436072020-10-05T00:15:00.039-05:002021-05-02T20:09:22.764-05:00Jugando con el gradiente descendente y Python<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
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<p>Los algoritmos de optimización por gradiente descendente son cada vez más populares, y a menudo son utilizados como cajas negras con explicaciones prácticas de sus fortalezas y sus debilidades. El objetivo de este artículo es proporcionarle al lector una pequeña intuición y los conocimientos mínimos en matemáticas para entender mejor el comportamiento de estos algoritmos y tener criterios sólidos para ponerlos en uso. En el curso de esta descripción general, estudiaremos las diferentes variantes de los gradientes descendentes y sus principales desafíos.</p>
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<p>El aprendizaje mecánico y la estadística comparten importantes características, pero usan una terminología diferente. En estadística, la regresión lineal se utiliza para modelar una relación $\mathcal{R}\subseteq\mathcal{X}\times\mathcal{Y}$ a partir de una muestra de datos $S\subset \mathcal{R}\subseteq\mathcal{X}\times\mathcal{Y}\subseteq\mathbb{R}^{m+1}\times\mathbb{R}$. Usualmente los datos que provienen de $\mathcal{X}$ se denominan <em>variables independientes</em> y los que provienen de $\mathcal{Y}$ se denominan <em>variables dependientes</em>. En el contexto del aprendizaje mecánico, este es llamado un <em>problema de aprendizaje supervisado</em>. El conjunto $S=\{(x_i, y_i)\}_{i=0}^{k}$ se denomina <em>conjunto de entrenamiento</em> y el par de valores $(x_i, y_i)$ es un <em>ejemplo de entrenamiento</em> del conjunto $S$ de $k$ ejemplos de entrenamiento.</p>
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<p>Cada $x_i$ es considerado como un vector columna de la forma $x_i=(1, x_{i,1},\dots,x_{i,m})^{\top}$ de dimensión $m+1$, a menudo es referido como el predictor en la literatura estadística. El proposito de la regresión lineal es identificar el mejor <em>predictor</em> de la clase de predictores de la forma $y =\theta^{\top} x$, donde $\theta \in \mathbb{R}^{m+1}$ y es de la forma $\theta =(\theta_0, \dots, \theta_m)^\top$, el parámetro $\theta_0$ se denomina <em>bias</em>. Para hacer esto, se considera la matriz $X\in M_{k\times m+1}(\mathbb{R})$ donde la $i$ - ésima fila está dada por el $i$ - ésimo vector fila $x_i^{\top}$. De esta manera se obtiene una expresión general para predecir los valores de $\mathcal{Y}$ que viene dada por el modelo:</p>
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\begin{equation}\nonumber
Y=X\theta.
\end{equation}<p></p>
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<p>En Python podemos definir la clase de predictores lineales $y =\theta^{\top} x$ de la siguiente forma:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="k">class</span> <span class="nc">LinearPredictor</span><span class="p">:</span>
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">m</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Input:</span>
<span class="sd"> theta: initial predictor.</span>
<span class="sd"> </span>
<span class="sd"> Output:</span>
<span class="sd"> None.</span>
<span class="sd"> """</span>
<span class="c1"># The coefficient column vector is initialized to zero.</span>
<span class="bp">self</span><span class="o">.</span><span class="n">theta</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">predict</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Input:</span>
<span class="sd"> x: list of float values of the form [1, x_1, ... ,x_m].</span>
<span class="sd"> </span>
<span class="sd"> Output:</span>
<span class="sd"> Returns the dot product (float) between «theta» and «x». </span>
<span class="sd"> """</span>
<span class="c1"># We define theta as self.theta.</span>
<span class="n">theta</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">theta</span>
<span class="c1"># Convert «x list» to a column vector.</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">x</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="c1"># Returns the product of the matrices theta and x.</span>
<span class="k">return</span> <span class="nb">float</span><span class="p">(</span><span class="n">theta</span><span class="o">.</span><span class="n">T</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">x</span><span class="p">))</span>
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<p>Observe que en el código anterior, el vector de coeficientes $\theta$ se puede inicializar a elección del lector, lo importante aquí, es ir actualizandolo hasta encontrar el mejor de ellos. Este problema de encontrar el mejor predictor lineal se resuelve eligiendo algún vector de coeficientes $\theta$ que minimizan la suma residual de cuadrados:</p>
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\begin{equation}\nonumber
E_S(\theta)=(Y-X\theta)^\top (Y-X\theta).
\end{equation}
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<p>En la ecuación anterior, $Y$ es el vector columna donde la $i$ - ésima entrada está dada por cada etiqueta $y_i$ definida en el conjunto de entrenamiento $S$, es decir, $Y = (y_1,\dots, y_k)^\top$. Esto permite definir el problema como un problema de minimización del riesgo empirico (ERM) dado por:</p>
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<p><a id='1'></a>
\begin{equation}\tag{1}
ERM_{\theta}(S)\equiv \operatorname*{argmin\,\,}_{ \theta \in \mathbb{R}^{m+1}} E_{S}(\theta),
\end{equation}</p>
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<p>que es equivalente a escoger un vector $\hat{\theta}\in ERM_{\theta}(S)$<a href="#2"><sup>2</a> para la solución del problema de optimización en la <a href="#1">Ecuación 1</a>. Para estudios de simulación, se puede construir un modelo sintético a partir de la generación de datos con:</p>
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<p><a id='2'></a>
\begin{equation}\tag{2}
Y=X\xi + \epsilon,
\end{equation}</p>
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<p>donde $\epsilon\sim \mathcal{N}(0, \sigma^2I_{k})$. Esto se puede implementar fácilmente en Python de la siguiente forma:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">SyntheticData</span><span class="p">:</span>
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">m</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Input:</span>
<span class="sd"> m: dimension of the space of independent variables.</span>
<span class="sd"> </span>
<span class="sd"> Output:</span>
<span class="sd"> None.</span>
<span class="sd"> """</span>
<span class="c1"># Dimensión of the data.</span>
<span class="bp">self</span><span class="o">.</span><span class="n">m</span> <span class="o">=</span> <span class="n">m</span>
<span class="c1"># The vector of coefficients is chosen at random.</span>
<span class="bp">self</span><span class="o">.</span><span class="n">xi</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">generate</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">k</span><span class="p">,</span> <span class="n">sigma</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Input:</span>
<span class="sd"> k: the amount of data to generate.</span>
<span class="sd"> sigma: standard deviation.</span>
<span class="sd"> </span>
<span class="sd"> Output:</span>
<span class="sd"> Returns a tuple with X, y and xi.</span>
<span class="sd"> """</span>
<span class="c1"># A column vector of ones is constructed.</span>
<span class="n">ones</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="n">k</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="c1"># Random data is generated and added to the ones vector.</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">hstack</span><span class="p">((</span><span class="n">ones</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="n">k</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">m</span><span class="p">)))</span>
<span class="c1"># Random noise is generated.</span>
<span class="n">epsilon</span> <span class="o">=</span> <span class="n">sigma</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">standard_normal</span><span class="p">(</span><span class="n">k</span><span class="p">)</span>
<span class="c1"># Values for y are constructed.</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">X</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">xi</span><span class="p">)</span> <span class="o">+</span> <span class="n">epsilon</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="k">return</span> <span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">xi</span>
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<p>Para entender el comportamiendo del gradiente de descente es conveniente probar con diferentes colecciones de datos o lotes, para eso sea:</p>
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\begin{equation}\nonumber
S_{l}=\{X_{l}, Y_{l}\}_{l\in[r]_{\mathbb{N}_0}},
\end{equation}<p></p>
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<p>una colección de $r$ simulaciones<a href="#2"><sup>2</a>. En Python podemos hacer una implementación sencilla para generar estos lotes de datos, esto sería algo así:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">generate_batches</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="n">k</span><span class="p">,</span> <span class="n">r</span><span class="p">,</span> <span class="n">sigma</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Input:</span>
<span class="sd"> m: dimension of the space of independent variables.</span>
<span class="sd"> k: the amount of data to generate by batch.</span>
<span class="sd"> r: number of batchs.</span>
<span class="sd"> sigma: standard deviation.</span>
<span class="sd"> </span>
<span class="sd"> Output: </span>
<span class="sd"> List with generated batches. </span>
<span class="sd"> """</span>
<span class="c1"># We generate the synthetic data for each batch.</span>
<span class="n">synthetic_data</span> <span class="o">=</span> <span class="n">SyntheticData</span><span class="p">(</span><span class="n">m</span><span class="p">)</span>
<span class="n">batches</span> <span class="o">=</span> <span class="p">[</span><span class="n">synthetic_data</span><span class="o">.</span><span class="n">generate</span><span class="p">(</span><span class="n">k</span><span class="p">,</span> <span class="n">sigma</span><span class="p">)</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">r</span><span class="p">)]</span>
<span class="k">return</span> <span class="n">batches</span>
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<p>El objetivo de la <a href="#1">Ecuación 1</a> es encontrar un vector $\hat{\theta}\in ERM_{\theta}(S)$ , para nuestro ejercicio esto se traduce en estimar el vector $\hat{\theta}$ tan cerca como sea posible al parámetro conocido $\xi$ del modelo simulado en la <a href="#2">Ecuación 2</a>.</p>
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<p>El indicador que se utilizará para comparar la estimación de los coeficientes $\hat{\theta}$ con los coeficientes verdaderos $\xi$ será el error cuadrático medio (RMSE). Esta medición se utilizará para evaluar el rendimiento en cada una de la simulaciones $S_l$. Tenga en cuenta que el RMSE se calculan para un elemento específico en el vector $\theta$. La notación $\operatorname{RMSE}_d$ enfatizará a qué parámetro se refiere. Para los parámetros $d\in [m]_{\mathbb{N_0}}$, considere:</p>
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\begin{equation}
\operatorname{RMSE}_d = \left(\frac{1}{r}\sum_{j=0}^{r}\big(\theta^{(d)}_j-\xi^{(d)}\big)^{2}\right)^{\frac{1}{2}}.
\end{equation}
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<p>Así se obtiene $\operatorname{RMSE} = (\operatorname{RMSE}_0,\dots, \operatorname{RMSE}_{m})$. En Python se tendría algo así:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">RMSE</span><span class="p">(</span><span class="n">matrix_theta</span><span class="p">:</span> <span class="nb">list</span><span class="p">,</span> <span class="n">xi</span><span class="p">:</span> <span class="nb">list</span><span class="p">,</span> <span class="n">r</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-></span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">:</span>
<span class="sd">"""</span>
<span class="sd"> Input:</span>
<span class="sd"> matrix_theta: this a matrix of values theta for each S.</span>
<span class="sd"> xi: synthetic parameters.</span>
<span class="sd"> r: number of simulations. </span>
<span class="sd"> </span>
<span class="sd"> Output:</span>
<span class="sd"> RMSE</span>
<span class="sd"> """</span>
<span class="n">matrix_theta</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">matrix_theta</span><span class="p">)</span>
<span class="n">xi</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">xi</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">arg</span> <span class="o">=</span> <span class="mi">1</span><span class="o">/</span><span class="n">r</span> <span class="o">*</span> <span class="p">(</span><span class="n">matrix_theta</span> <span class="o">-</span> <span class="n">xi</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">arg</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">))</span>
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<p>En el código anterior se espera como parámetro de entrada una matriz $\Theta$ donde cada $l$ - ésima columna es el $l$ - vector de coeficientes aprendido para la $l$ - ésima simulación de datos $X_{l}$, esto se explicará con más detalle a continuación.</p>
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<p>Si se asume que $h_{\theta}$ es un predictor para el conjunto de datos $S_{l}=\{X_{l}, y_{l}\}$, entonces el problema de regresión lineal en la <a href="#1">Ecuación 1</a> se puede reescribir con la siguiente función de costo:</p>
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\begin{equation}\tag{3}
E_{S}(\theta)=\frac{1}{2k}\sum_{i=1}^{k}\big(h_{\theta}(x_i)-y_i\big)^2.
\end{equation}
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<p>Esta función para la costo es facil de implementar en Python como podemos ver a continuación:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">loss</span><span class="p">(</span><span class="n">predictor</span><span class="p">,</span> <span class="n">sample</span><span class="p">:</span> <span class="nb">tuple</span><span class="p">)</span> <span class="o">-></span> <span class="nb">float</span><span class="p">:</span>
<span class="sd">"""</span>
<span class="sd"> Input:</span>
<span class="sd"> predictor: linear predictor. </span>
<span class="sd"> sample: dataset.</span>
<span class="sd"> </span>
<span class="sd"> Output:</span>
<span class="sd"> loss. </span>
<span class="sd"> """</span>
<span class="n">arg</span> <span class="o">=</span> <span class="nb">list</span><span class="p">()</span>
<span class="n">k</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">sample</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">k</span><span class="p">):</span>
<span class="n">x_i</span> <span class="o">=</span> <span class="n">sample</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">i</span><span class="p">]</span>
<span class="n">y_i</span> <span class="o">=</span> <span class="n">sample</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="n">i</span><span class="p">]</span>
<span class="n">k</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">sample</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
<span class="n">arg</span><span class="o">.</span><span class="n">append</span><span class="p">((</span><span class="n">predictor</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">x_i</span><span class="p">)</span> <span class="o">-</span> <span class="n">y_i</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
<span class="k">return</span> <span class="mi">1</span><span class="o">/</span><span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">k</span><span class="p">)</span> <span class="o">*</span> <span class="nb">sum</span><span class="p">(</span><span class="n">arg</span><span class="p">)</span>
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<p>Una forma de resolver este problema es utilizar los métodos del gradiente descente. Estos son algoritmos que hacen uso de las derivadas parciales de funciones diferenciales convexas y, como cualquier algoritmo, su eficiencia puede ser monitoreada. Principalmente, la eficiencia de un algoritmo depende de que tan precisa es la estimación que produce. En segundo lugar, se analiza su capacidad para producir tal estimación dentro de un marco de tiempo factible.</p>
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<p>Los métodos del gradiente descendente produce secuencias finitas de números $\theta$. Para ser eficiente esta secuencia debería converger al valor óptimo. En este ejercicio, para algún $\delta > 0$, la eficacia de un algoritmo se evalúa midiendo la duración para producir una estimación $\hat{\theta}$ con precisión $\delta$ tal que:</p>
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\begin{equation}
||\hat{\theta}-\xi||<\delta
\end{equation}
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<p>En lugar de una respuesta continua $y$, la respuesta podría ser binaria, es decir, $y \in \{0, 1\}$. En estadística, este es un modelo de regresión logística. Dados ciertos predictores, también es un problema de aprendizaje supervisado. Las premisas para resolver un problema de regresión logística son similares a las de un problema continuo. En el caso binario el problema se resuelve para la siguiente función de costo:</p>
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<p><a id='4'></a>
\begin{equation}\tag{4}
E_{S}(\theta) = \frac{1}{m}\bigg(\sum_{i=1}^{m}\Big(y_i\log h_{\theta}\big(x_i\big) + \big(1-y_i\big)\log \big(1 - h_{\theta}\big(x_i\big)\big)\Big)\bigg)
\end{equation}</p>
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<p>donde</p>
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\begin{equation}
h_{\theta}(x) = \frac{1}{1+e^{-\theta^\top x}}
\end{equation}
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<p>Esta es una función convexa y suave. Por lo tanto, el proceso de solución es similar al de la <a href="#1">Ecuación 1</a>. Pero aquí, la variable dependiente $y$ es categórica. Si $y$ tiene más de dos resultados posibles, el modelo se llama regresión logística multinomial.</p>
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<h2 id="Gradiente-descendente-(GD)">Gradiente descendente (GD)<a class="anchor-link" href="#Gradiente-descendente-(GD)">¶</a></h2>
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<p>Para calcular la solución del objetivo de optimización hay que minimizar la función de costo $E_{S}(\theta)$. Su gradiente se representa por $\nabla E_{S}(\theta)$ y revela en cual direción la función decrese más rápido (<a src ='https://alejandrosanchezyali.blogspot.com/2020/10/algoritmo-del-gradiente-descendente.html'>Ver Gradiente Descendente</a>). Utilizando $\nabla E_{S}(\theta)$ es posible dar pasos repetidamente hacia un mínimo local. Esto sugiere el siguiente algoritmo:</p>
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<h4 id="Algoritmo-1.-Gradiente-Descendente-Clásico"><em>Algoritmo 1. Gradiente Descendente Clásico</em><a class="anchor-link" href="#Algoritmo-1.-Gradiente-Descendente-Clásico">¶</a></h4><blockquote>
Input: $\theta$, $X$, $Y$, $t$, $ \alpha$, $\nabla E_{S}$
<br>1. for $k=0$ to $p$ do:
<br>2. $\theta\leftarrow \theta - \alpha \nabla E_{S}(\theta, X, Y)$
<br>3. end
<br>return: $\theta$
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<p>En el seudocódigo anterior se tiene que $t$ es el número máximo de iteraciones y $\alpha$ es la tasa de aprendizaje, hiperparámetros que son ajustados manualmente. Hay métodos que permite aproximar la tasa de aprendizaje para acelerar la convergencia, pero aquí en nuestro caso, el descenso del gradiente se mantendrá en su forma pura. Cuando $\alpha$ se elige lejos de su valor óptimo $\alpha^*$, el algoritmo divergerá si $\alpha > \alpha^*$ y convergerá muy lentamente si $\alpha < \alpha^*$.</p>
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<p>Recordemos la función objetivo $E(\theta)$ en <a href="#1">Ecuación 1</a>. Sea</p>
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\begin{equation}
h_{\theta}(x)= \theta^\top x
\end{equation}
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<p>Si el número de ejemplos de entrenamiento es $k$, el número de parámetros es $m+1$, entonces entonces considerando $j=0, \cdots, m$ y $e_0,\dots,e_m$ la base estandar, entonces el gradiente de $E_{S}(\theta)$ se puede expresar como:</p>
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\begin{equation}
\nabla E_{S}(\theta) = \sum_{i=0}^{m}\frac{\partial E}{\partial \theta_{i}}e_{i}
\end{equation}
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<p>donde</p>
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\begin{equation}
\frac{\partial E_{S}}{\partial \theta_{j}}=\frac{1}{k}\sum_{i=1}^{k}\big(\theta^\top x_i-y_i\big)x_{i,j}.
\end{equation}
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<p>La convergencia del algoritmo del gradiente descendente depende de la elección precisa de la tasa de aprendizaje $\alpha$, así como del número suficiente de iteraciones $t$. Nuestro caso es un problema de optimización convexo y tomando hiperparámetros apropiados, es decir $0<\alpha <1$, el algoritmo debería converger.</p>
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<p>Para la <a href="#4">Ecuación 4</a>, el objetivo es la optimización para la regresión logística, la función de costo es otra, pero nuevamente podemos obtener el gradiente de la siguiente manera:</p>
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\begin{equation}
\frac{\partial E_{S}}{\partial \theta_{j}}=\frac{1}{k}\sum_{i=1}^{k}\big(h_{\theta}(x)-y_i\big)x_{i,j},
\end{equation}
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<p>donde $h_{\theta}(x) = \frac{1}{1+e^{-\theta^\top x}}$. Como la ecuación $E_{S}(\theta)$ para la regresión logistica vuelve a ser una función convexa, entonces se puede usar los algoritmos basados en el gradiente para minimizar la <a href="#4">Ecuación 4</a>.</p>
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<p>A continuación se presenta la implementación del algoritmo del gradiente descendente en python:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">gd</span><span class="p">(</span><span class="n">predictor</span><span class="p">,</span> <span class="n">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="n">alpha</span><span class="p">,</span> <span class="n">gradient</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Input:</span>
<span class="sd"> predictor: it's a predictor function.</span>
<span class="sd"> X: it's a matrix with the independent data.</span>
<span class="sd"> Y: it's a matrix with the dependent data.</span>
<span class="sd"> t: it's the maximum number of iterations. </span>
<span class="sd"> alpha: it's the learning rate.</span>
<span class="sd"> gradient: it's a gradient function of the predictor function.</span>
<span class="sd"> </span>
<span class="sd"> Output:</span>
<span class="sd"> The best predictor.</span>
<span class="sd"> """</span>
<span class="n">theta</span> <span class="o">=</span> <span class="n">predictor</span><span class="o">.</span><span class="n">theta</span>
<span class="n">iterations</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">while</span> <span class="n">iterations</span> <span class="o"><=</span> <span class="n">t</span><span class="p">:</span>
<span class="n">theta</span> <span class="o">=</span> <span class="n">theta</span> <span class="o">-</span> <span class="n">alpha</span> <span class="o">*</span> <span class="n">gradient</span><span class="p">(</span><span class="n">theta</span><span class="p">,</span> <span class="n">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">)</span>
<span class="n">iterations</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="n">predictor</span><span class="o">.</span><span class="n">theta</span> <span class="o">=</span> <span class="n">theta</span>
<span class="k">return</span> <span class="n">predictor</span>
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<p>Para poder hacer el análisis de comportamiento del GD, se harán algunas modificaciones en el algoritmo anterior, que permite obtener información acerca del comportamiento de la función de costo, de la distancia a los parámetros originales de los datos simulados y el tiempo de ejecución. Antes de enseñarte la modificación, vamos a definir una función para medir la distancia euclidiana entre los diferentes parámetros:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">euclidean_distance</span><span class="p">(</span><span class="n">theta</span><span class="p">,</span> <span class="n">xi</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Input:</span>
<span class="sd"> theta: it's an array with predict parameters.</span>
<span class="sd"> xi: it's an array with real parameters</span>
<span class="sd"> </span>
<span class="sd"> Output:</span>
<span class="sd"> This function return the norm of theta - xi.</span>
<span class="sd"> """</span>
<span class="n">arg</span> <span class="o">=</span> <span class="n">theta</span> <span class="o">-</span> <span class="n">xi</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">norm</span><span class="p">(</span><span class="n">arg</span><span class="p">)</span>
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<p>Además también es necesario definir el gradiente para la función de costo, en este caso sólo se hará para la regresión lineal:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">gradient</span><span class="p">(</span><span class="n">theta</span><span class="p">,</span> <span class="n">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Input: </span>
<span class="sd"> theta: it's an array with predict parameters.</span>
<span class="sd"> X: it's a matrix with the independent data.</span>
<span class="sd"> Y: it's a matrix with the dependent data.</span>
<span class="sd"> Output:</span>
<span class="sd"> Return the gradient for the loss function.</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">X</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span><span class="o">==</span><span class="mi">1</span><span class="p">:</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">X</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span>
<span class="k">return</span> <span class="n">X</span><span class="o">.</span><span class="n">T</span><span class="o">.</span><span class="n">dot</span><span class="p">((</span><span class="n">X</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span><span class="o">-</span> <span class="n">Y</span><span class="p">))</span>
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<p>Finalmente, el algoritmo modificado sería el siguiente:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">import</span> <span class="nn">timeit</span>
<span class="k">def</span> <span class="nf">gd</span><span class="p">(</span><span class="n">predictor</span><span class="p">,</span> <span class="n">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="n">alpha</span><span class="p">,</span> <span class="n">gradient</span><span class="p">,</span> <span class="n">loss</span><span class="p">,</span> <span class="n">xi</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Input:</span>
<span class="sd"> predictor: it's a predictor function.</span>
<span class="sd"> X: it's a matrix with the independent data.</span>
<span class="sd"> Y: it's a matrix with the dependent data.</span>
<span class="sd"> t: it's the maximum number of iterations. </span>
<span class="sd"> alpha: it's the learning rate.</span>
<span class="sd"> gradient: it's a gradient function of the predictor function.</span>
<span class="sd"> loss: it's the loss function.</span>
<span class="sd"> xi: it's ana array with real parameters. </span>
<span class="sd"> </span>
<span class="sd"> Output:</span>
<span class="sd"> This function return the best predictor with errors and the delta </span>
<span class="sd"> between real parameters and predict paremeters. </span>
<span class="sd"> """</span>
<span class="n">theta</span> <span class="o">=</span> <span class="n">predictor</span><span class="o">.</span><span class="n">theta</span>
<span class="n">iterations</span> <span class="o">=</span> <span class="mi">0</span>
<span class="n">delta_theta</span> <span class="o">=</span> <span class="nb">list</span><span class="p">()</span>
<span class="n">deltas_thetas</span> <span class="o">=</span> <span class="n">theta</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span> <span class="o">-</span> <span class="n">xi</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">errors</span> <span class="o">=</span> <span class="nb">list</span><span class="p">()</span>
<span class="n">sample</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">([</span><span class="n">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">])</span>
<span class="k">while</span> <span class="n">iterations</span> <span class="o"><=</span> <span class="n">t</span><span class="p">:</span>
<span class="n">gradient_</span> <span class="o">=</span> <span class="n">gradient</span><span class="p">(</span><span class="n">theta</span><span class="p">,</span> <span class="n">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">)</span>
<span class="n">theta</span> <span class="o">=</span> <span class="n">theta</span> <span class="o">-</span> <span class="n">alpha</span> <span class="o">*</span> <span class="n">gradient_</span>
<span class="n">predictor</span><span class="o">.</span><span class="n">theta</span> <span class="o">=</span> <span class="n">theta</span>
<span class="n">delta_theta</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">euclidean_distance</span><span class="p">(</span><span class="n">theta</span><span class="p">,</span> <span class="n">xi</span><span class="p">))</span>
<span class="n">arg</span> <span class="o">=</span> <span class="n">theta</span><span class="o">-</span><span class="n">xi</span>
<span class="n">deltas_thetas</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">hstack</span><span class="p">((</span><span class="n">deltas_thetas</span><span class="p">,</span> <span class="n">arg</span><span class="p">))</span>
<span class="n">errors</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">loss</span><span class="p">(</span><span class="n">predictor</span><span class="o">=</span><span class="n">predictor</span><span class="p">,</span> <span class="n">sample</span><span class="o">=</span><span class="n">sample</span><span class="p">))</span>
<span class="n">iterations</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="k">return</span> <span class="n">predictor</span><span class="p">,</span> <span class="n">errors</span><span class="p">,</span> <span class="n">delta_theta</span><span class="p">,</span> <span class="n">deltas_thetas</span>
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<h3 id="Algunos-código-adicionales-para-analizar-el-comportamiento-del-GD">Algunos código adicionales para analizar el comportamiento del GD<a class="anchor-link" href="#Algunos-código-adicionales-para-analizar-el-comportamiento-del-GD">¶</a></h3>
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<p>Para analizar el comportamiento del GD y sus diferentes variantes la siguiente función nos va a permitir registrar los principales parámetros de comportamiento:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">import</span> <span class="nn">time</span>
<span class="k">def</span> <span class="nf">simulator</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="n">k</span><span class="p">,</span> <span class="n">r</span><span class="p">,</span> <span class="n">sigma</span><span class="p">,</span> <span class="n">gradient_method</span><span class="p">,</span> <span class="n">parameters_grad</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Input:</span>
<span class="sd"> m: dimension of the space of independent variables.</span>
<span class="sd"> k: the amount of data to generate by batch.</span>
<span class="sd"> r: number of batchs.</span>
<span class="sd"> sigma: standard deviation.</span>
<span class="sd"> gradient_method:there are three options (gd, sgd, sdg_mini_batch)</span>
<span class="sd"> parameters_grad: parameter for the gradient method.</span>
<span class="sd"> </span>
<span class="sd"> Output:</span>
<span class="sd"> This function returns the following lists: errors, deltas, deltas_theta, rmse, times. </span>
<span class="sd"> """</span>
<span class="n">batches</span> <span class="o">=</span> <span class="n">generate_batches</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="n">k</span><span class="p">,</span> <span class="n">r</span><span class="p">,</span> <span class="n">sigma</span><span class="p">)</span>
<span class="n">parameters</span><span class="p">[</span><span class="s1">'xi'</span><span class="p">]</span> <span class="o">=</span> <span class="n">batches</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span>
<span class="n">matrix_theta</span> <span class="o">=</span> <span class="nb">list</span><span class="p">()</span>
<span class="n">errors</span> <span class="o">=</span> <span class="nb">list</span><span class="p">()</span>
<span class="n">deltas_theta</span> <span class="o">=</span> <span class="nb">list</span><span class="p">()</span>
<span class="n">deltas</span> <span class="o">=</span> <span class="nb">list</span><span class="p">()</span>
<span class="n">times</span> <span class="o">=</span> <span class="nb">list</span><span class="p">()</span>
<span class="k">for</span> <span class="n">batch</span> <span class="ow">in</span> <span class="n">batches</span><span class="p">:</span>
<span class="n">parameters_grad</span><span class="p">[</span><span class="s1">'X'</span><span class="p">]</span> <span class="o">=</span> <span class="n">batch</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="n">parameters_grad</span><span class="p">[</span><span class="s1">'Y'</span><span class="p">]</span> <span class="o">=</span> <span class="n">batch</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
<span class="n">parameters_grad</span><span class="p">[</span><span class="s1">'predictor'</span><span class="p">]</span> <span class="o">=</span> <span class="n">LinearPredictor</span><span class="p">(</span><span class="n">m</span><span class="p">)</span>
<span class="n">start</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span>
<span class="n">predictor</span><span class="p">,</span> <span class="n">error</span><span class="p">,</span> <span class="n">delta_theta</span><span class="p">,</span> <span class="n">delta</span> <span class="o">=</span> <span class="n">gradient_method</span><span class="p">(</span><span class="o">**</span><span class="n">parameters_grad</span><span class="p">)</span>
<span class="n">end</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span>
<span class="n">delta_time</span> <span class="o">=</span> <span class="n">end</span> <span class="o">-</span> <span class="n">start</span>
<span class="n">errors</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">error</span><span class="p">)</span>
<span class="n">deltas</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">delta</span><span class="p">)</span>
<span class="n">deltas_theta</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">delta_theta</span><span class="p">)</span>
<span class="n">matrix_theta</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">predictor</span><span class="o">.</span><span class="n">theta</span><span class="p">)</span>
<span class="n">times</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">delta_time</span><span class="p">)</span>
<span class="n">matrix_theta</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">matrix_theta</span><span class="p">)</span>
<span class="n">matrix_theta</span> <span class="o">=</span> <span class="n">matrix_theta</span><span class="o">.</span><span class="n">squeeze</span><span class="p">()</span><span class="o">.</span><span class="n">T</span>
<span class="n">xi</span> <span class="o">=</span> <span class="n">parameters</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'xi'</span><span class="p">)</span>
<span class="n">rmse</span> <span class="o">=</span> <span class="n">RMSE</span><span class="p">(</span><span class="n">matrix_theta</span><span class="o">=</span><span class="n">matrix_theta</span><span class="p">,</span> <span class="n">xi</span><span class="o">=</span><span class="n">xi</span><span class="p">,</span> <span class="n">r</span><span class="o">=</span><span class="n">r</span><span class="p">)</span>
<span class="k">return</span> <span class="n">errors</span><span class="p">,</span> <span class="n">deltas</span><span class="p">,</span> <span class="n">deltas_theta</span><span class="p">,</span> <span class="n">rmse</span><span class="p">,</span> <span class="n">times</span>
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<p>Además para hacer varias ejecuciones de la función anterior también vamos a hacer uso de la siguiente función:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">statistics</span> <span class="kn">import</span> <span class="n">mean</span>
<span class="k">def</span> <span class="nf">execute</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="n">k</span><span class="p">,</span> <span class="n">r</span><span class="p">,</span> <span class="n">sigmas</span><span class="p">,</span> <span class="n">gradient_method</span><span class="p">,</span> <span class="n">parameters_grad</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Input:</span>
<span class="sd"> m: dimension of the space of independent variables.</span>
<span class="sd"> k: the amount of data to generate by batch.</span>
<span class="sd"> r: number of batchs.</span>
<span class="sd"> sigma: list with several values for the standard deviation.</span>
<span class="sd"> gradient_method:there are three options (gd, sgd, sdg_mini_batch)</span>
<span class="sd"> parameters_grad: parameter for the gradient method.</span>
<span class="sd"> </span>
<span class="sd"> Ouput:</span>
<span class="sd"> This function returns the following lists: errors, deltas, delta_thetas rmses, times. </span>
<span class="sd"> """</span>
<span class="n">errors</span> <span class="o">=</span> <span class="nb">list</span><span class="p">()</span>
<span class="n">deltas</span> <span class="o">=</span> <span class="nb">list</span><span class="p">()</span>
<span class="n">deltas_theta</span> <span class="o">=</span> <span class="nb">list</span><span class="p">()</span>
<span class="n">rmses</span> <span class="o">=</span> <span class="nb">list</span><span class="p">()</span>
<span class="n">times</span> <span class="o">=</span> <span class="nb">list</span><span class="p">()</span>
<span class="k">for</span> <span class="n">sigma</span> <span class="ow">in</span> <span class="n">sigmas</span><span class="p">:</span>
<span class="n">parameters</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">(</span>
<span class="n">m</span><span class="o">=</span><span class="n">m</span><span class="p">,</span>
<span class="n">k</span><span class="o">=</span><span class="n">k</span><span class="p">,</span>
<span class="n">r</span><span class="o">=</span><span class="n">r</span><span class="p">,</span>
<span class="n">sigma</span><span class="o">=</span><span class="n">sigma</span><span class="p">,</span>
<span class="n">gradient_method</span><span class="o">=</span><span class="n">gradient_method</span><span class="p">,</span>
<span class="n">parameters_grad</span><span class="o">=</span><span class="n">parameters_grad</span>
<span class="p">)</span>
<span class="n">error</span><span class="p">,</span> <span class="n">delta</span><span class="p">,</span> <span class="n">delta_theta</span><span class="p">,</span> <span class="n">rmse</span><span class="p">,</span> <span class="n">time_</span> <span class="o">=</span> <span class="n">simulator</span><span class="p">(</span><span class="o">**</span><span class="n">parameters</span><span class="p">)</span>
<span class="n">errors</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">error</span><span class="p">)</span>
<span class="n">deltas</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">delta</span><span class="p">)</span>
<span class="n">deltas_theta</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">delta_theta</span><span class="p">)</span>
<span class="n">rmses</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">rmse</span><span class="p">)</span>
<span class="n">times</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">mean</span><span class="p">(</span><span class="n">time_</span><span class="p">),</span> <span class="mi">3</span><span class="p">))</span>
<span class="k">return</span> <span class="n">errors</span><span class="p">,</span> <span class="n">deltas</span><span class="p">,</span> <span class="n">deltas_theta</span><span class="p">,</span> <span class="n">rmses</span><span class="p">,</span> <span class="n">times</span>
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<p>Necesitamos además de las siguientes funciones para graficar los resultados:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="k">def</span> <span class="nf">plot_errors</span><span class="p">(</span><span class="n">errors</span><span class="p">,</span> <span class="n">sigmas</span><span class="p">,</span> <span class="n">axis_range</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">200</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]):</span>
<span class="sd">"""</span>
<span class="sd"> Input:</span>
<span class="sd"> errors: array with all errors from each iteration in execute function.</span>
<span class="sd"> sigmas: list with the standard deviations for each iteration in execute function.</span>
<span class="sd"> </span>
<span class="sd"> Output:</span>
<span class="sd"> Figure with error plots.</span>
<span class="sd"> """</span>
<span class="n">fig</span><span class="p">,</span> <span class="n">axs</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">12</span><span class="p">))</span>
<span class="n">j</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">axis</span><span class="p">,</span> <span class="n">error</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">axs</span><span class="o">.</span><span class="n">flat</span><span class="p">,</span> <span class="n">errors</span><span class="p">):</span>
<span class="n">i</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">e</span> <span class="ow">in</span> <span class="n">error</span><span class="p">:</span>
<span class="n">axis</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'batch </span><span class="si">{}</span><span class="s1">'</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">i</span><span class="p">))</span>
<span class="n">axis</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="n">axis_range</span><span class="p">)</span>
<span class="n">axis</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
<span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="n">axis</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="sa">r</span><span class="s1">'$\sigma = </span><span class="si">{}</span><span class="s1">$'</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">sigmas</span><span class="p">[</span><span class="n">j</span><span class="p">]))</span>
<span class="n">j</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="n">plt</span><span class="o">.</span><span class="n">suptitle</span><span class="p">(</span><span class="s1">'Loss vs Iterations'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">setp</span><span class="p">(</span><span class="n">axs</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="p">:],</span> <span class="n">xlabel</span><span class="o">=</span><span class="s1">'N° Iterations'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">setp</span><span class="p">(</span><span class="n">axs</span><span class="p">[:,</span><span class="mi">0</span><span class="p">],</span> <span class="n">ylabel</span><span class="o">=</span><span class="s1">'Loss'</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">plot_deltas</span><span class="p">(</span><span class="n">deltas_theta</span><span class="p">,</span> <span class="n">sigmas</span><span class="p">,</span> <span class="n">axis_range</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">200</span><span class="p">,</span> <span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">]):</span>
<span class="sd">"""</span>
<span class="sd"> Input:</span>
<span class="sd"> deltas_theta: array with deltas for each iteration in execute function.</span>
<span class="sd"> sigmas: list with the standard deviations for each iteration in execute function.</span>
<span class="sd"> </span>
<span class="sd"> Output:</span>
<span class="sd"> Figure with delta plots.</span>
<span class="sd"> """</span>
<span class="n">fig</span><span class="p">,</span> <span class="n">axs</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">12</span><span class="p">))</span>
<span class="n">zeros</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="mi">200</span>
<span class="n">j</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">axis</span><span class="p">,</span> <span class="n">delta</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">axs</span><span class="o">.</span><span class="n">flat</span><span class="p">,</span> <span class="n">deltas_theta</span><span class="p">):</span>
<span class="n">i</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">d</span> <span class="ow">in</span> <span class="n">delta</span><span class="p">:</span>
<span class="n">axis</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">zeros</span><span class="p">,</span> <span class="s1">'k'</span><span class="p">)</span>
<span class="n">axis</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">d</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'batch </span><span class="si">{}</span><span class="s1">'</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">i</span><span class="p">))</span>
<span class="n">axis</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="n">axis_range</span><span class="p">)</span>
<span class="n">axis</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
<span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="n">axis</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="sa">r</span><span class="s1">'$\sigma = </span><span class="si">{}</span><span class="s1">$'</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">sigmas</span><span class="p">[</span><span class="n">j</span><span class="p">]))</span>
<span class="n">j</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="n">plt</span><span class="o">.</span><span class="n">suptitle</span><span class="p">(</span><span class="sa">r</span><span class="s1">'Distance between $\theta$ and $\xi$'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">setp</span><span class="p">(</span><span class="n">axs</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="p">:],</span> <span class="n">xlabel</span><span class="o">=</span><span class="s1">'N° Iterations'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">setp</span><span class="p">(</span><span class="n">axs</span><span class="p">[:,</span><span class="mi">0</span><span class="p">],</span> <span class="n">ylabel</span><span class="o">=</span><span class="s1">'Distance'</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">plot_deltas_parameters</span><span class="p">(</span><span class="n">deltas</span><span class="p">,</span> <span class="n">axis_range</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">200</span><span class="p">,</span> <span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">]):</span>
<span class="sd">"""</span>
<span class="sd"> Input: </span>
<span class="sd"> deltas: array with deltas for each iteration in execute function.</span>
<span class="sd"> </span>
<span class="sd"> Output:</span>
<span class="sd"> Figure with delta plots.</span>
<span class="sd"> </span>
<span class="sd"> """</span>
<span class="n">fig</span><span class="p">,</span> <span class="n">axs</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">8</span><span class="p">,</span> <span class="mi">8</span><span class="p">))</span>
<span class="n">zeros</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="mi">200</span>
<span class="n">batches</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">deltas</span><span class="p">)</span>
<span class="n">m</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">deltas</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
<span class="n">switch</span> <span class="o">=</span> <span class="kc">True</span>
<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
<span class="k">for</span> <span class="n">k</span><span class="p">,</span> <span class="n">axis</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">axs</span><span class="o">.</span><span class="n">flat</span><span class="p">):</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">batches</span><span class="p">):</span>
<span class="k">if</span> <span class="n">j</span> <span class="o">==</span> <span class="n">k</span><span class="p">:</span>
<span class="n">axis</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">zeros</span><span class="p">,</span> <span class="s1">'k'</span><span class="p">)</span>
<span class="n">axis</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">deltas</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">])</span>
<span class="n">axis</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="sa">r</span><span class="s1">'$\theta_</span><span class="si">{}</span><span class="s1">$'</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">j</span><span class="p">))</span>
<span class="n">axis</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="n">axis_range</span><span class="p">)</span>
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<h3 id="Simulaciones-del-GD-en-ambientes-controlados">Simulaciones del GD en ambientes controlados<a class="anchor-link" href="#Simulaciones-del-GD-en-ambientes-controlados">¶</a></h3>
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<p>A continuación se va a ejecutar variables simulaciones con desviación estándar $\sigma = 0.1, 0.2, 0.4, 0.4, 0.6, 0.8$ con $m=3$ y seis lotes de 200 datos. Además vamos a considerar todas las simulaciones con un número máximo de 200 iteraciones y una tasa de aprendizaje de 0.001. El lector puede variar estos parámetros para hacer sus propios análisis. La configuración sería:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">parameters</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">(</span><span class="n">t</span><span class="o">=</span><span class="mi">200</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.001</span><span class="p">,</span> <span class="n">gradient</span><span class="o">=</span><span class="n">gradient</span><span class="p">,</span> <span class="n">loss</span><span class="o">=</span><span class="n">loss</span><span class="p">)</span>
<span class="n">sigmas</span> <span class="o">=</span> <span class="p">[</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.2</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">,</span> <span class="mf">0.6</span><span class="p">,</span> <span class="mf">0.8</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span>
<span class="n">m</span><span class="p">,</span> <span class="n">k</span><span class="p">,</span> <span class="n">r</span> <span class="o">=</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">200</span><span class="p">,</span> <span class="mi">5</span>
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<p>Ejecutamos las simulaciones:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">answers</span> <span class="o">=</span> <span class="n">execute</span><span class="p">(</span><span class="n">m</span><span class="o">=</span><span class="n">m</span><span class="p">,</span> <span class="n">k</span><span class="o">=</span><span class="n">k</span><span class="p">,</span> <span class="n">r</span><span class="o">=</span><span class="n">r</span><span class="p">,</span> <span class="n">sigmas</span><span class="o">=</span><span class="n">sigmas</span><span class="p">,</span> <span class="n">gradient_method</span><span class="o">=</span><span class="n">gd</span><span class="p">,</span> <span class="n">parameters_grad</span><span class="o">=</span><span class="n">parameters</span><span class="p">)</span>
<span class="n">errors</span><span class="p">,</span> <span class="n">deltas</span><span class="p">,</span> <span class="n">deltas_theta</span><span class="p">,</span> <span class="n">rmses</span><span class="p">,</span> <span class="n">times</span> <span class="o">=</span> <span class="n">answers</span>
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<p>Y visualiazamos cada unos de los resultados. A continuación vemos el comportamiento de la función de costo para uno de los valores de sigma:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">plot_errors</span><span class="p">(</span><span class="n">errors</span><span class="p">,</span> <span class="n">sigmas</span><span class="p">,</span> <span class="n">axis_range</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">200</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">])</span>
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<p>El lector puede observar que el comportamiento de la función de costo es peor a medida que los valores de la desviación estándar aumenta. Esto quiere decir que debemos cuidarnos de los datos propensos a un nivel alto de ruido porque las conclusiones que puede arrojar el modelo pueden carecer de sentido.</p>
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<p>Para las distancias entre $\theta$ y $\xi$ obtenidas en cada una de las iteraciones, el lector podrá encontrar que hay una perdida de homogeneidad en la convergencia de las distancias a medida que los valores de $\sigma$ se incrementa. Esto nos sugiere de nuevo que debemos preferir los datos con bajos niveles de desviación estándar. </p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">plot_deltas</span><span class="p">(</span><span class="n">deltas_theta</span><span class="p">,</span> <span class="n">sigmas</span><span class="p">)</span>
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<p>En cuanto a cada uno de los parámetros de $\theta$ hay que tener presente que las simulaciones se ejecutaron con $m=3$, es decir que $\theta$ tiene con cuatro parámetros.</p>
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<p>En los resultados obtenidos, las iteraciones con $\sigma$ igual a $0.1$ y $0.2$ presentan el comportamiento más homogéneo como se puede observar a continuación.</p>
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<h4 id="Resultados-de-los-parámetros-para-la-iteración-0:">Resultados de los parámetros para la iteración 0:<a class="anchor-link" href="#Resultados-de-los-parámetros-para-la-iteración-0:">¶</a></h4>
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<div class="prompt input_prompt">In [17]:</div>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">plot_deltas_parameters</span><span class="p">(</span><span class="n">deltas</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
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<h4 id="Resultados-de-los-parámetros-para-la-iteración-1:">Resultados de los parámetros para la iteración 1:<a class="anchor-link" href="#Resultados-de-los-parámetros-para-la-iteración-1:">¶</a></h4>
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<div class="prompt input_prompt">In [18]:</div>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">plot_deltas_parameters</span><span class="p">(</span><span class="n">deltas</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
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<p>Con respecto a las demás iteraciones con valores de $\sigma$ iguales a $0.4, 0.6, 0.8, 1$ hay una perdida notable en la homogeneidad de los resultados como se puede observar a continuación.</p>
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<h4 id="Resultados-de-los-parámetros-para-la-iteración-2:">Resultados de los parámetros para la iteración 2:<a class="anchor-link" href="#Resultados-de-los-parámetros-para-la-iteración-2:">¶</a></h4>
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<div class="prompt input_prompt">In [19]:</div>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">plot_deltas_parameters</span><span class="p">(</span><span class="n">deltas</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span>
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<h4 id="Resultados-de-los-parámetros-para-la-iteración-3:">Resultados de los parámetros para la iteración 3:<a class="anchor-link" href="#Resultados-de-los-parámetros-para-la-iteración-3:">¶</a></h4>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">plot_deltas_parameters</span><span class="p">(</span><span class="n">deltas</span><span class="p">[</span><span class="mi">3</span><span class="p">])</span>
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<h4 id="Resultados-de-los-parámetros-para-la-iteración-4">Resultados de los parámetros para la iteración 4<a class="anchor-link" href="#Resultados-de-los-parámetros-para-la-iteración-4">¶</a></h4>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">plot_deltas_parameters</span><span class="p">(</span><span class="n">deltas</span><span class="p">[</span><span class="mi">5</span><span class="p">])</span>
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<p>Finalmente, para visualizar el RMSE y los tiempos de ejecución, necesitamos de la siguiente función:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
<span class="k">def</span> <span class="nf">results</span><span class="p">(</span><span class="n">rmses</span><span class="p">,</span> <span class="n">times</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Input:</span>
<span class="sd"> rmses: array with rmses for each iteration of the execution fuction.</span>
<span class="sd"> times: array with times for each iteration of the execution fuction.</span>
<span class="sd"> Output:</span>
<span class="sd"> DataFrame with all results of the simulations. </span>
<span class="sd"> """</span>
<span class="n">columns</span> <span class="o">=</span> <span class="n">columns</span> <span class="o">=</span> <span class="p">[</span><span class="sa">r</span><span class="s1">'RMSE $\theta_0$'</span><span class="p">,</span> <span class="sa">r</span><span class="s1">'RMSE $\theta_1$'</span><span class="p">,</span> <span class="sa">r</span><span class="s1">'RMSE $\theta_2$'</span><span class="p">,</span> <span class="sa">r</span><span class="s1">'RMSE $\theta_3$'</span><span class="p">]</span>
<span class="n">index</span><span class="o">=</span><span class="p">[</span><span class="sa">r</span><span class="s1">'$\sigma=0.1$'</span><span class="p">,</span> <span class="sa">r</span><span class="s1">'$\sigma=0.2$'</span><span class="p">,</span> <span class="sa">r</span><span class="s1">'$\sigma=0.4$'</span><span class="p">,</span> <span class="sa">r</span><span class="s1">'$\sigma=0.6$'</span><span class="p">,</span> <span class="sa">r</span><span class="s1">'$\sigma=0.8$'</span><span class="p">,</span> <span class="sa">r</span><span class="s1">'$\sigma=1.0$'</span><span class="p">]</span>
<span class="n">result</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">(</span><span class="n">rmses</span><span class="p">,</span> <span class="n">columns</span><span class="o">=</span><span class="n">columns</span><span class="p">,</span> <span class="n">index</span><span class="o">=</span><span class="n">index</span><span class="p">)</span>
<span class="n">result</span><span class="p">[</span><span class="s1">'times (seg)'</span><span class="p">]</span> <span class="o">=</span> <span class="n">times</span>
<span class="k">return</span> <span class="n">result</span>
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<p>Antes de presentar los resultado para los RMSE y los tiempos de ejecución, es importante tener presente que los tiempos de ejecución varía de acuerdo a la computadora que se esté usando. La computadora que se usó en estos calculos fue una Asus Zenpro UX410U con procesador Intel CORE i5 7th Gen y 16 GB de RAM, los resultados obtenidos en esta maquina fueron:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">results</span><span class="p">(</span><span class="n">rmses</span><span class="p">,</span> <span class="n">times</span><span class="p">)</span>
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<div class="prompt output_prompt">Out[23]:</div>
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<style scoped>
.dataframe tbody tr th:only-of-type {
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<th></th>
<th>RMSE $\theta_0$</th>
<th>RMSE $\theta_1$</th>
<th>RMSE $\theta_2$</th>
<th>RMSE $\theta_3$</th>
<th>times (seg)</th>
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<th>$\sigma=0.1$</th>
<td>0.075732</td>
<td>0.035154</td>
<td>0.052207</td>
<td>0.068002</td>
<td>0.190</td>
</tr>
<tr>
<th>$\sigma=0.2$</th>
<td>0.028802</td>
<td>0.037847</td>
<td>0.040201</td>
<td>0.052540</td>
<td>0.183</td>
</tr>
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<th>$\sigma=0.4$</th>
<td>0.093742</td>
<td>0.070993</td>
<td>0.091675</td>
<td>0.099229</td>
<td>0.201</td>
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<th>$\sigma=0.6$</th>
<td>0.151054</td>
<td>0.227258</td>
<td>0.090446</td>
<td>0.100349</td>
<td>0.210</td>
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<th>$\sigma=0.8$</th>
<td>0.153092</td>
<td>0.191212</td>
<td>0.176124</td>
<td>0.174510</td>
<td>0.255</td>
</tr>
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<th>$\sigma=1.0$</th>
<td>0.204581</td>
<td>0.142447</td>
<td>0.265922</td>
<td>0.323488</td>
<td>0.275</td>
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<p>El principal problema con GD es que hace uso del todo el conjunto de entrenamiento para computar el gradiente en cada paso, esto lo hace muy lento cuando el conjunto de entrenamiento es muy grande. En el caso opuesto, el gradiente estocástico (SGD) escoge en cada paso escoge aleatoriamente un ejemplo del conjunto de entrenamiento para calcular el gradiente. Obviamente, trabajar con un solo ejemplo a la vez hace que el algoritmo sea mucho más rápido porque está manipulando menos datos en cada iteración. También es útil para grandes cantidades de datos, por que solo necesita un ejemplo en memoria en cada iteración.</p>
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<h2 id="Gradiente-descendente-estocástico-(SGD)">Gradiente descendente estocástico (SGD)<a class="anchor-link" href="#Gradiente-descendente-estocástico-(SGD)">¶</a></h2>
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<p>Como se dijo antes el SGD en lugar de evaluar sobretodo el conjunto de entrenamiento $S$, en cada iteración se selecciona aleatoriamente un solo ejemplo $(x_{i_k}, y_{i_k})$, de manera que el gradiente estocástico sería:</p>
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\begin{equation}
\nabla E_{S}^{sg}(\theta) = \nabla E_{S}(\theta, x_{i_k}, y_{i_k}) = \sum_{i=0}^{m}\frac{\partial E_{S}(\theta, x_{i_k}, y_{i_k})}{\partial \theta_{j}}e_{j},
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<p>en donde:</p>
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\begin{equation}
\frac{\partial E_{S}(\theta, x_{i_k}, y_{i_k})}{\partial \theta_{j}} = (h_{\theta}(x_{i_k}) - y_{i_k})x_{i_k, j}.
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<p>La elección de ${i_k}$ se puede elegir mediante alguna de las siguientes reglas:</p>
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<ol>
<li>Elección aleatoria: escoger $i_k\in \{1,2,\dots, m\}$ asumiendo una distribucción uniforme.</li>
<li>Elección cíclica: seleccionar ${i_k}=1, 2,\dots, m, 1, 2,\dots, m,\dots$.</li>
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<p>La elección aleatoria es la más común en la práctica.</p>
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<p>Por lo tanto, el ciclo se puede inicializar en uno y finalizará cuando se alcance el número máximo de epocas $t$. Este algoritmo tiene la siguiente esquema:</p>
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<h4 id="Algoritmo-2.-Gradiente-Descendente-Estocástico"><em>Algoritmo 2. Gradiente Descendente Estocástico</em><a class="anchor-link" href="#Algoritmo-2.-Gradiente-Descendente-Estocástico">¶</a></h4><blockquote>
Input: $\theta$, $X$, $Y$, $t$, $ \alpha$, $\nabla E_{S}$, $index\_rule$
<br>1. for $k=1$ to $t$ do:
<br>2. for $l=1$ to $m$ do:
<br>3. $i_k = index\_rule(X)$
<br>4. $\theta\leftarrow \theta - \alpha \nabla E_{S}(\theta, x_{i_k}, y_{i_k})$
<br>5. end
<br>return: $\theta$
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<p>Por lo otro lado, por su naturaleza estocástica, este algoritmo es menos regular que el GD, en lugar de disminuir suavemente hasta llegar al mínimo, la función de costo fluctuará, disminuyendo solo en promedio. Con el tiempo acabará muy cerca de
el mínimo, pero una vez allí continuará fluctuando, nunca va a asentuarse. Entonces, una vez que el algoritmo se detiene, el final los valores de los parámetros son buenos, pero no óptimos.</p>
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<p>Este algoritmo tambien se aplica para resolver el problema de la regresión logística. Un implementación rápida de este algoritmo sería:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">itertools</span> <span class="kn">import</span> <span class="n">cycle</span>
<span class="k">def</span> <span class="nf">sdg</span><span class="p">(</span><span class="n">predictor</span><span class="p">,</span> <span class="n">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="n">alpha</span><span class="p">,</span> <span class="n">gradient</span><span class="p">,</span> <span class="n">index_rule</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Input:</span>
<span class="sd"> predictor: it's a predictor function.</span>
<span class="sd"> X: it's a matrix with the independent data.</span>
<span class="sd"> Y: it's a matrix with the dependent data.</span>
<span class="sd"> t: it's the maximum number of iterations. </span>
<span class="sd"> alpha: it's the learning rate.</span>
<span class="sd"> gradient: it's a gradient function of the predictor function.</span>
<span class="sd"> index_rule: there are two options, randomized_rule or cyclic_rule.</span>
<span class="sd"> </span>
<span class="sd"> Output:</span>
<span class="sd"> The best predictor.</span>
<span class="sd"> """</span>
<span class="n">theta</span> <span class="o">=</span> <span class="n">predictor</span><span class="o">.</span><span class="n">theta</span>
<span class="n">epochs</span> <span class="o">=</span> <span class="mi">0</span>
<span class="n">indexes</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">X</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span><span class="o">.</span><span class="n">tolist</span><span class="p">()</span>
<span class="n">m</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="k">if</span> <span class="n">index_rule</span> <span class="o">==</span> <span class="s1">'randomized_rule'</span><span class="p">:</span>
<span class="k">while</span> <span class="n">epochs</span> <span class="o"><=</span> <span class="n">t</span><span class="p">:</span>
<span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">m</span><span class="p">):</span>
<span class="n">i_k</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">choice</span><span class="p">(</span><span class="n">indexes</span><span class="p">)</span>
<span class="n">theta</span> <span class="o">=</span> <span class="n">theta</span> <span class="o">-</span> <span class="n">alpha</span> <span class="o">*</span> <span class="n">gradient</span><span class="p">(</span><span class="n">theta</span><span class="p">,</span> <span class="n">X</span><span class="p">[</span><span class="n">i_k</span><span class="p">],</span> <span class="n">Y</span><span class="p">[</span><span class="n">i_k</span><span class="p">])</span>
<span class="n">epochs</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="k">elif</span> <span class="n">index_rule</span> <span class="o">==</span> <span class="s1">'cyclic_rule'</span><span class="p">:</span>
<span class="n">pool</span> <span class="o">=</span> <span class="n">cycle</span><span class="p">(</span><span class="n">indexes</span><span class="p">)</span>
<span class="k">while</span> <span class="n">epochs</span> <span class="o"><=</span> <span class="n">t</span><span class="p">:</span>
<span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">m</span><span class="p">):</span>
<span class="n">i_k</span> <span class="o">=</span> <span class="nb">next</span><span class="p">(</span><span class="n">pool</span><span class="p">)</span>
<span class="n">theta</span> <span class="o">=</span> <span class="n">theta</span> <span class="o">-</span> <span class="n">alpha</span> <span class="o">*</span> <span class="n">gradient</span><span class="p">(</span><span class="n">theta</span><span class="p">,</span> <span class="n">X</span><span class="p">[</span><span class="n">i_k</span><span class="p">],</span> <span class="n">Y</span><span class="p">[</span><span class="n">i_k</span><span class="p">])</span>
<span class="n">epochs</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'A suitable rule has not been defined'</span><span class="p">)</span>
<span class="n">predictor</span><span class="o">.</span><span class="n">theta</span> <span class="o">=</span> <span class="n">theta</span>
<span class="k">return</span> <span class="n">predictor</span>
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<p>Para nuestros objetivos también se hizo algunas modificaciones para que nos permiten analizar su comportamiento:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">itertools</span> <span class="kn">import</span> <span class="n">cycle</span>
<span class="k">def</span> <span class="nf">sgd</span><span class="p">(</span><span class="n">predictor</span><span class="p">,</span> <span class="n">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="n">alpha</span><span class="p">,</span> <span class="n">gradient</span><span class="p">,</span> <span class="n">index_rule</span><span class="p">,</span> <span class="n">loss</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">xi</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Input:</span>
<span class="sd"> predictor: it's a predictor function.</span>
<span class="sd"> X: it's a matrix with the independent data.</span>
<span class="sd"> Y: it's a matrix with the dependent data.</span>
<span class="sd"> t: it's the maximum number of iterations. </span>
<span class="sd"> alpha: it's the learning rate.</span>
<span class="sd"> gradient: it's a gradient function of the predictor function.</span>
<span class="sd"> index_rule: there are two options, randomized_rule or cyclic_rule.</span>
<span class="sd"> </span>
<span class="sd"> Output:</span>
<span class="sd"> The best predictor.</span>
<span class="sd"> """</span>
<span class="n">theta</span> <span class="o">=</span> <span class="n">predictor</span><span class="o">.</span><span class="n">theta</span>
<span class="n">iterations</span> <span class="o">=</span> <span class="mi">0</span>
<span class="n">epochs</span> <span class="o">=</span> <span class="mi">0</span>
<span class="n">indexes</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">X</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span><span class="o">.</span><span class="n">tolist</span><span class="p">()</span>
<span class="n">m</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="n">delta_theta</span> <span class="o">=</span> <span class="nb">list</span><span class="p">()</span>
<span class="n">deltas_thetas</span> <span class="o">=</span> <span class="n">theta</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span> <span class="o">-</span> <span class="n">xi</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">errors</span> <span class="o">=</span> <span class="nb">list</span><span class="p">()</span>
<span class="n">sample</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">([</span><span class="n">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">])</span>
<span class="k">if</span> <span class="n">index_rule</span> <span class="o">==</span> <span class="s1">'randomized_rule'</span><span class="p">:</span>
<span class="k">while</span> <span class="n">epochs</span> <span class="o"><=</span> <span class="n">t</span><span class="p">:</span>
<span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">m</span><span class="p">):</span>
<span class="n">i_k</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">choice</span><span class="p">(</span><span class="n">indexes</span><span class="p">)</span>
<span class="n">theta</span> <span class="o">=</span> <span class="n">theta</span> <span class="o">-</span> <span class="n">alpha</span> <span class="o">*</span> <span class="n">gradient</span><span class="p">(</span><span class="n">theta</span><span class="p">,</span> <span class="n">X</span><span class="p">[</span><span class="n">i_k</span><span class="p">],</span> <span class="n">Y</span><span class="p">[</span><span class="n">i_k</span><span class="p">])</span>
<span class="n">predictor</span><span class="o">.</span><span class="n">theta</span> <span class="o">=</span> <span class="n">theta</span>
<span class="n">epochs</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="n">errors</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">loss</span><span class="p">(</span><span class="n">predictor</span><span class="o">=</span><span class="n">predictor</span><span class="p">,</span> <span class="n">sample</span><span class="o">=</span><span class="n">sample</span><span class="p">))</span>
<span class="n">delta_theta</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">euclidean_distance</span><span class="p">(</span><span class="n">theta</span><span class="p">,</span> <span class="n">xi</span><span class="p">))</span>
<span class="n">arg</span> <span class="o">=</span> <span class="n">theta</span><span class="o">-</span><span class="n">xi</span>
<span class="n">deltas_thetas</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">hstack</span><span class="p">((</span><span class="n">deltas_thetas</span><span class="p">,</span> <span class="n">arg</span><span class="p">))</span>
<span class="k">elif</span> <span class="n">index_rule</span> <span class="o">==</span> <span class="s1">'cyclic_rule'</span><span class="p">:</span>
<span class="n">pool</span> <span class="o">=</span> <span class="n">cycle</span><span class="p">(</span><span class="n">indexes</span><span class="p">)</span>
<span class="k">while</span> <span class="n">epochs</span> <span class="o"><=</span> <span class="n">t</span><span class="p">:</span>
<span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">m</span><span class="p">):</span>
<span class="n">i_k</span> <span class="o">=</span> <span class="nb">next</span><span class="p">(</span><span class="n">pool</span><span class="p">)</span>
<span class="n">theta</span> <span class="o">=</span> <span class="n">theta</span> <span class="o">-</span> <span class="n">alpha</span> <span class="o">*</span> <span class="n">gradient</span><span class="p">(</span><span class="n">theta</span><span class="p">,</span> <span class="n">X</span><span class="p">[</span><span class="n">i_k</span><span class="p">],</span> <span class="n">Y</span><span class="p">[</span><span class="n">i_k</span><span class="p">])</span>
<span class="n">predictor</span><span class="o">.</span><span class="n">theta</span> <span class="o">=</span> <span class="n">theta</span>
<span class="n">epochs</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="n">errors</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">loss</span><span class="p">(</span><span class="n">predictor</span><span class="o">=</span><span class="n">predictor</span><span class="p">,</span> <span class="n">sample</span><span class="o">=</span><span class="n">sample</span><span class="p">))</span>
<span class="n">delta_theta</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">euclidean_distance</span><span class="p">(</span><span class="n">theta</span><span class="p">,</span> <span class="n">xi</span><span class="p">))</span>
<span class="n">arg</span> <span class="o">=</span> <span class="n">theta</span><span class="o">-</span><span class="n">xi</span>
<span class="n">deltas_thetas</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">hstack</span><span class="p">((</span><span class="n">deltas_thetas</span><span class="p">,</span> <span class="n">arg</span><span class="p">))</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'A suitable rule has not been defined'</span><span class="p">)</span>
<span class="n">predictor</span><span class="o">.</span><span class="n">theta</span> <span class="o">=</span> <span class="n">theta</span>
<span class="k">return</span> <span class="n">predictor</span><span class="p">,</span> <span class="n">errors</span><span class="p">,</span> <span class="n">delta_theta</span><span class="p">,</span> <span class="n">deltas_thetas</span>
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<h3 id="Simulaciones-de-SGC-en-ambientes-controlados">Simulaciones de SGC en ambientes controlados<a class="anchor-link" href="#Simulaciones-de-SGC-en-ambientes-controlados">¶</a></h3>
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<p>A continuación se va a ejecutar variables simulaciones con desviación estándar $\sigma = 0.1, 0.2, 0.4, 0.4, 0.6, 0.8$ con $m=3$ y seis lotes de 200 datos. Además vamos a considerar todas las simulaciones con un número máximo de 200 iteraciones y una tasa de aprendizaje de 0.001. El lector puede variar estos parámetros para hacer sus propios análisis. La configuración sería:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">parameters</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">(</span><span class="n">t</span><span class="o">=</span><span class="mi">200</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.001</span><span class="p">,</span> <span class="n">gradient</span><span class="o">=</span><span class="n">gradient</span><span class="p">,</span> <span class="n">index_rule</span><span class="o">=</span><span class="s1">'randomized_rule'</span><span class="p">,</span> <span class="n">loss</span><span class="o">=</span><span class="n">loss</span><span class="p">)</span>
<span class="n">sigmas</span> <span class="o">=</span> <span class="p">[</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.2</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">,</span> <span class="mf">0.6</span><span class="p">,</span> <span class="mf">0.8</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span>
<span class="n">m</span><span class="p">,</span> <span class="n">k</span><span class="p">,</span> <span class="n">r</span> <span class="o">=</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">200</span><span class="p">,</span> <span class="mi">5</span>
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<p>Ejecutamos las simulaciones:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">answers</span> <span class="o">=</span> <span class="n">execute</span><span class="p">(</span><span class="n">m</span><span class="o">=</span><span class="n">m</span><span class="p">,</span> <span class="n">k</span><span class="o">=</span><span class="n">k</span><span class="p">,</span> <span class="n">r</span><span class="o">=</span><span class="n">r</span><span class="p">,</span> <span class="n">sigmas</span><span class="o">=</span><span class="n">sigmas</span><span class="p">,</span> <span class="n">gradient_method</span><span class="o">=</span><span class="n">sgd</span><span class="p">,</span> <span class="n">parameters_grad</span><span class="o">=</span><span class="n">parameters</span><span class="p">)</span>
<span class="n">errors</span><span class="p">,</span> <span class="n">deltas</span><span class="p">,</span> <span class="n">deltas_theta</span><span class="p">,</span> <span class="n">rmses</span><span class="p">,</span> <span class="n">times</span> <span class="o">=</span> <span class="n">answers</span>
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<p>Y visualizamos cada unos de los resultados. A continuación vemos el comportamiento de la función de costo para uno de los valores de sigma:</p>
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<div class="prompt input_prompt">In [28]:</div>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">plot_errors</span><span class="p">(</span><span class="n">errors</span><span class="p">,</span> <span class="n">sigmas</span><span class="p">)</span>
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<p>De nuevo se puede observar que el comportamiento de la función de costo es peor a medida que los valores de la desviación estándar aumenta. Esto quiere decir que debemos cuidarnos de los datos propensos a un nivel alto de ruido porque las conclusiones que puede arrojar el modelo pueden carecer de sentido.</p>
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<p>Para las distancias entre $\theta$ y $\xi$ obtenidas en cada una de las iteraciones, a diferencia del GD, el SGD tienen a generar resultados más homogeneos en la convergencia de las distancias a medida que los valores de $\sigma$ se incrementa. Esto nos sugiere que el SGD tiene a ser más estable para niveles más altos de desviación estándar.</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">plot_deltas</span><span class="p">(</span><span class="n">deltas_theta</span><span class="p">,</span> <span class="n">sigmas</span><span class="p">)</span>
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<p>Recuerden que $\theta$ tiene con cuatro parámetros y para cada uno se tiene los siguientes resultados:</p>
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<h4 id="Resultados-de-los-parámetros-para-la-iteración-0:">Resultados de los parámetros para la iteración 0:<a class="anchor-link" href="#Resultados-de-los-parámetros-para-la-iteración-0:">¶</a></h4>
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<div class="prompt input_prompt">In [30]:</div>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">plot_deltas_parameters</span><span class="p">(</span><span class="n">deltas</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
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<h4 id="Resultados-de-los-parámetros-para-la-iteración-1:">Resultados de los parámetros para la iteración 1:<a class="anchor-link" href="#Resultados-de-los-parámetros-para-la-iteración-1:">¶</a></h4>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">plot_deltas_parameters</span><span class="p">(</span><span class="n">deltas</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
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<h4 id="Resultados-de-los-parámetros-para-la-iteración-2:">Resultados de los parámetros para la iteración 2:<a class="anchor-link" href="#Resultados-de-los-parámetros-para-la-iteración-2:">¶</a></h4>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">plot_deltas_parameters</span><span class="p">(</span><span class="n">deltas</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span>
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<h4 id="Resultados-de-los-parámetros-para-la-iteración-3:">Resultados de los parámetros para la iteración 3:<a class="anchor-link" href="#Resultados-de-los-parámetros-para-la-iteración-3:">¶</a></h4>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">plot_deltas_parameters</span><span class="p">(</span><span class="n">deltas</span><span class="p">[</span><span class="mi">3</span><span class="p">])</span>
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<h4 id="Resultados-de-los-parámetros-para-la-iteración-4:">Resultados de los parámetros para la iteración 4:<a class="anchor-link" href="#Resultados-de-los-parámetros-para-la-iteración-4:">¶</a></h4>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">plot_deltas_parameters</span><span class="p">(</span><span class="n">deltas</span><span class="p">[</span><span class="mi">4</span><span class="p">])</span>
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<p>Finalmente el RMSE y el tiempos de ejecución son:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">results</span><span class="p">(</span><span class="n">rmses</span><span class="p">,</span> <span class="n">times</span><span class="p">)</span>
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<th>RMSE $\theta_0$</th>
<th>RMSE $\theta_1$</th>
<th>RMSE $\theta_2$</th>
<th>RMSE $\theta_3$</th>
<th>times (seg)</th>
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<th>$\sigma=0.1$</th>
<td>0.026491</td>
<td>0.018543</td>
<td>0.016608</td>
<td>0.040965</td>
<td>2.078</td>
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<th>$\sigma=0.2$</th>
<td>0.052688</td>
<td>0.044309</td>
<td>0.049855</td>
<td>0.046718</td>
<td>2.170</td>
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<th>$\sigma=0.4$</th>
<td>0.079915</td>
<td>0.080375</td>
<td>0.088962</td>
<td>0.085809</td>
<td>1.597</td>
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<th>$\sigma=0.6$</th>
<td>0.087201</td>
<td>0.147681</td>
<td>0.097790</td>
<td>0.055250</td>
<td>1.627</td>
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<th>$\sigma=0.8$</th>
<td>0.172709</td>
<td>0.158146</td>
<td>0.270608</td>
<td>0.239081</td>
<td>1.611</td>
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<th>$\sigma=1.0$</th>
<td>0.154082</td>
<td>0.178732</td>
<td>0.205896</td>
<td>0.191328</td>
<td>1.801</td>
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<p>Hay que señalar que cuando la función de costo es muy irregular, esto puede ayudarr al algoritmo a evitar los mínimos locales, por lo que SGD tiene más posibilidades de encontrar el mínimo gobla que GD.</p>
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<p>Por lo tanto, la aleatoriedad es buena para escapar de los óptimos locales, pero mala porque significa que el algoritmo nunca puede establecerse en el mínimo. Una solución a este dilema es reducir gradualmente la tasa de aprendizaje. Los pasos comienzan siendo grandes (lo que ayuda a avanzar rápidamente y escapar de los mínimos locales), luego se vuelven cada vez más pequeños, lo que permite que el algoritmo se establezca en el mínimo global.</p>
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<p>La función que determina la tasa de aprendizaje en cada iteración se llama programa de aprendizaje, esto se estudiará en otra ocasión. Si la tasa de aprendizaje se reduce demasiado rápido, puede quedarse atascado en un mínimo local, o incluso terminar congelado a la mitad del camino hacía el mínimo global. Si la tasa de aprendizaje se reduce demasiado lentamente, puede saltar alrededor del mínimo durante mucho tiempo y terminar con una solución subóptima si se detiene el entrenamiento demasiado pronto.</p>
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<h2 id="Gradiente-descendente-estocástico-por-minilotes-(Mini-Batch-SGD)">Gradiente descendente estocástico por minilotes (Mini-Batch SGD)<a class="anchor-link" href="#Gradiente-descendente-estocástico-por-minilotes-(Mini-Batch-SGD)">¶</a></h2>
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<p>El último algoritmo de gradiente descendente que veremos se llama el gradiente descente estocástico por mini lotes. Es fácil de entender una vez que se conoce el gradiente descendente clásico y el estocástico: en cada paso, en lugar de calcular los gradientes en función del conjunto de entrenamiento completo (como en GD) o en un ejemplo como en SGD, el Mini-Batch SGD calcula el gradiente en pequeñas partes de los datos, llamadas mini lotes. La principal ventaja de Mini-batch SGD sobre SGD y GD es que puede obtener un aumento del rendimiento mediante la optimización del hardware de las operaciones matriciales, especialmente cuando se utilizan GPU.</p>
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<p>Una parte de los datos se denomina minilote (Mini-batch), mientras que todo el conjunto de entrenamiento $S$ se denomina lote. Estos minilotes se generan seleccionando aleatoriamente los vectores fila de la matriz $X$. El esquema general de este algoritmo sería:</p>
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<h4 id="Algoritmo-3.-Gradiente-Descendente-Estocástico-por-minilotes"><em>Algoritmo 3. Gradiente Descendente Estocástico por minilotes</em><a class="anchor-link" href="#Algoritmo-3.-Gradiente-Descendente-Estocástico-por-minilotes">¶</a></h4><blockquote>
Input: $\theta$, $X$, $Y$, $t$, $ \alpha$, $\nabla E_{S}$, $size\_batch$
<br>1. for $k=1$ to $t$ do:
<br>2. for $l=1$ to $m$ do:
<br>3. $[i_{0, k}, \dots, i_{size\_batch, k}] = choose\_indexes(X)$
<br>4. $\theta\leftarrow \theta - \alpha \nabla E_{S}(\theta, X[i_{0, k}, \dots, i_{size\_batch, k}], Y[i_{0, k}, \dots, i_{size\_batch, k}])$
<br>5. end
<br>return: $\theta$
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<p>Intuitivamente el algoritmo converge si SGD converge. Un implementación rápida de este algoritmo sería:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">sdg_mini_batch</span><span class="p">(</span><span class="n">predictor</span><span class="p">,</span> <span class="n">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="n">alpha</span><span class="p">,</span> <span class="n">gradient</span><span class="p">,</span> <span class="n">size_batch</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Input:</span>
<span class="sd"> predictor: it's a predictor function.</span>
<span class="sd"> X: it's a matrix with the independent data.</span>
<span class="sd"> Y: it's a matrix with the dependent data.</span>
<span class="sd"> t: it's the maximum number of iterations. </span>
<span class="sd"> alpha: it's the learning rate.</span>
<span class="sd"> gradient: it's a gradient function of the predictor function.</span>
<span class="sd"> size_batch: it's a integer number no negative.</span>
<span class="sd"> </span>
<span class="sd"> Output:</span>
<span class="sd"> The best predictor.</span>
<span class="sd"> """</span>
<span class="n">theta</span> <span class="o">=</span> <span class="n">predictor</span><span class="o">.</span><span class="n">theta</span>
<span class="n">epochs</span> <span class="o">=</span> <span class="mi">0</span>
<span class="n">indexes</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">X</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span><span class="o">.</span><span class="n">tolist</span><span class="p">()</span>
<span class="n">m</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="k">while</span> <span class="n">epochs</span> <span class="o"><=</span> <span class="n">t</span><span class="p">:</span>
<span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">m</span><span class="p">):</span>
<span class="n">indexes_batch</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">choice</span><span class="p">(</span><span class="n">indexes</span><span class="p">,</span> <span class="n">size_batch</span><span class="p">)</span>
<span class="n">sgrad</span> <span class="o">=</span> <span class="n">gradient</span><span class="p">(</span><span class="n">theta</span><span class="p">,</span> <span class="n">X</span><span class="p">[</span><span class="n">indexes_batch</span><span class="p">],</span> <span class="n">Y</span><span class="p">[</span><span class="n">indexes_batch</span><span class="p">])</span>
<span class="n">theta</span> <span class="o">=</span> <span class="n">theta</span> <span class="o">-</span> <span class="n">alpha</span> <span class="o">*</span> <span class="n">sgrad</span>
<span class="n">epochss</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="n">predictor</span><span class="o">.</span><span class="n">theta</span> <span class="o">=</span> <span class="n">theta</span>
<span class="k">return</span> <span class="n">predictor</span>
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<p>Para nuestros objetivos también se hizo algunas modificaciones para que nos permiten analizar su comportamiento:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">sdg_mini_batch</span><span class="p">(</span><span class="n">predictor</span><span class="p">,</span> <span class="n">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="n">alpha</span><span class="p">,</span> <span class="n">gradient</span><span class="p">,</span> <span class="n">size_batch</span><span class="p">,</span> <span class="n">loss</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">xi</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Input:</span>
<span class="sd"> predictor: it's a predictor function.</span>
<span class="sd"> X: it's a matrix with the independent data.</span>
<span class="sd"> Y: it's a matrix with the dependent data.</span>
<span class="sd"> t: it's the maximum number of iterations. </span>
<span class="sd"> alpha: it's the learning rate.</span>
<span class="sd"> gradient: it's a gradient function of the predictor function.</span>
<span class="sd"> size_batch: it's a integer number no negative.</span>
<span class="sd"> loss: it's the loss function.</span>
<span class="sd"> xi: it's ana array with real parameters.</span>
<span class="sd"> Output:</span>
<span class="sd"> The best predictor.</span>
<span class="sd"> """</span>
<span class="n">theta</span> <span class="o">=</span> <span class="n">predictor</span><span class="o">.</span><span class="n">theta</span>
<span class="n">epochs</span> <span class="o">=</span> <span class="mi">0</span>
<span class="n">indexes</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">X</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span><span class="o">.</span><span class="n">tolist</span><span class="p">()</span>
<span class="n">m</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="n">delta_theta</span> <span class="o">=</span> <span class="nb">list</span><span class="p">()</span>
<span class="n">deltas_thetas</span> <span class="o">=</span> <span class="n">theta</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span> <span class="o">-</span> <span class="n">xi</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">errors</span> <span class="o">=</span> <span class="nb">list</span><span class="p">()</span>
<span class="n">sample</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">([</span><span class="n">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">])</span>
<span class="k">while</span> <span class="n">epochs</span> <span class="o"><</span> <span class="n">t</span><span class="p">:</span>
<span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">m</span><span class="p">):</span>
<span class="n">indexes_batch</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">choice</span><span class="p">(</span><span class="n">indexes</span><span class="p">,</span> <span class="n">size_batch</span><span class="p">)</span>
<span class="n">sgrad</span> <span class="o">=</span> <span class="n">gradient</span><span class="p">(</span><span class="n">theta</span><span class="p">,</span> <span class="n">X</span><span class="p">[</span><span class="n">indexes_batch</span><span class="p">],</span> <span class="n">Y</span><span class="p">[</span><span class="n">indexes_batch</span><span class="p">])</span>
<span class="n">theta</span> <span class="o">=</span> <span class="n">theta</span> <span class="o">-</span> <span class="n">alpha</span> <span class="o">*</span> <span class="n">sgrad</span>
<span class="n">predictor</span><span class="o">.</span><span class="n">theta</span> <span class="o">=</span> <span class="n">theta</span>
<span class="n">errors</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">loss</span><span class="p">(</span><span class="n">predictor</span><span class="o">=</span><span class="n">predictor</span><span class="p">,</span> <span class="n">sample</span><span class="o">=</span><span class="n">sample</span><span class="p">))</span>
<span class="n">delta_theta</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">euclidean_distance</span><span class="p">(</span><span class="n">theta</span><span class="p">,</span> <span class="n">xi</span><span class="p">))</span>
<span class="n">arg</span> <span class="o">=</span> <span class="n">theta</span><span class="o">-</span><span class="n">xi</span>
<span class="n">deltas_thetas</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">hstack</span><span class="p">((</span><span class="n">deltas_thetas</span><span class="p">,</span> <span class="n">arg</span><span class="p">))</span>
<span class="n">epochs</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="k">return</span> <span class="n">predictor</span><span class="p">,</span> <span class="n">errors</span><span class="p">,</span> <span class="n">delta_theta</span><span class="p">,</span> <span class="n">deltas_thetas</span>
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<h3 id="Simulaciones-de-Mini-Batch-SGD-en-ambientes-controlados">Simulaciones de Mini-Batch SGD en ambientes controlados<a class="anchor-link" href="#Simulaciones-de-Mini-Batch-SGD-en-ambientes-controlados">¶</a></h3>
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<p>A continuación se va a ejecutar variables simulaciones con desviación estándar $\sigma = 0.1, 0.2, 0.4, 0.4, 0.6, 0.8$ con $m=3$ y seis lotes de 200 datos. Además vamos a considerar todas las simulaciones con un número máximo de 200 iteraciones y una tasa de aprendizaje de 0.001. El lector puede variar estos parámetros para hacer sus propios análisis. La configuración sería:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">parameters</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">(</span><span class="n">t</span><span class="o">=</span><span class="mi">200</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.001</span><span class="p">,</span> <span class="n">gradient</span><span class="o">=</span><span class="n">gradient</span><span class="p">,</span> <span class="n">size_batch</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">loss</span><span class="o">=</span><span class="n">loss</span><span class="p">)</span>
<span class="n">sigmas</span> <span class="o">=</span> <span class="p">[</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.2</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">,</span> <span class="mf">0.6</span><span class="p">,</span> <span class="mf">0.8</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span>
<span class="n">m</span><span class="p">,</span> <span class="n">k</span><span class="p">,</span> <span class="n">r</span> <span class="o">=</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">200</span><span class="p">,</span> <span class="mi">5</span>
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<p>Ejecutamos las simulaciones:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">answers</span> <span class="o">=</span> <span class="n">execute</span><span class="p">(</span><span class="n">m</span><span class="o">=</span><span class="n">m</span><span class="p">,</span> <span class="n">k</span><span class="o">=</span><span class="n">k</span><span class="p">,</span> <span class="n">r</span><span class="o">=</span><span class="n">r</span><span class="p">,</span> <span class="n">sigmas</span><span class="o">=</span><span class="n">sigmas</span><span class="p">,</span> <span class="n">gradient_method</span><span class="o">=</span><span class="n">sdg_mini_batch</span><span class="p">,</span> <span class="n">parameters_grad</span><span class="o">=</span><span class="n">parameters</span><span class="p">)</span>
<span class="n">errors</span><span class="p">,</span> <span class="n">deltas</span><span class="p">,</span> <span class="n">deltas_theta</span><span class="p">,</span> <span class="n">rmses</span><span class="p">,</span> <span class="n">times</span> <span class="o">=</span> <span class="n">answers</span>
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<p>Y visualizamos cada unos de los resultados. A continuación vemos el comportamiento de la función de costo para uno de los valores de sigma:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">plot_errors</span><span class="p">(</span><span class="n">errors</span><span class="p">,</span> <span class="n">sigmas</span><span class="p">)</span>
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<p>De nuevo se puede observar que el comportamiento de la función de costo es peor a medida que los valores de la desviación estándar aumenta. Esto quiere decir que debemos cuidarnos de los datos propensos a un nivel alto de ruido porque las conclusiones que puede arrojar el modelo pueden carecer de sentido.</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">plot_deltas</span><span class="p">(</span><span class="n">deltas_theta</span><span class="p">,</span> <span class="n">sigmas</span><span class="p">)</span>
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g3AmjVreOKJJ0gmkyxYsIBbbrmFmTNfOtNVe3s7jY2NeF6clmbMmMGOHXbmK2OqkeWv0c1fNjJnjDnIzJkzWblyJQBXX301Dz30EAAPPvgg5513HkuWLOGBBx5g7dq1L3vu+vXrmTp1KitWrACgvr7+QHK76KKLaGhoIJVKsWjRIrZsOa7zShtjzMuM1/xlI3PGjFFH+gc6Ug7ddV5EyOfz3HTTTbS2tjJz5kw++clPHvWxkpLJ5IHbrusSBMFBjzc3N9PV1UUQBHiex/bt25k+ffqxL4gxpmIsf41u/rKROWPMQbZu3crDDz8MwN13380FF1xwIPFNnDiRvr4+7rnnngPt6+rqDmxXsmDBAnbt2sXq1asB6O3tfVnSG4qI8NrXvvbAvL/xjW/wlre85YQtlzHm5Dde85cVc8aYgyxYsIDbb7+dhQsX0tnZyY033khjYyPvf//7Wbx4MZdccsmB1RAA1157LTfccAPLli0jDENWrVrFLbfcwtKlS7n44ouP6h/wZz/7Wf7lX/6FefPm0d7eznvf+96RWERjzElqvOYvic8DfXJZvny5tra2VjoMY47aunXrWLhwYaXDGNMGe41E5DFVXV6hkE4oy1+mWln+Gp6RyGE2MmeMMcYYU8WsmDPGGGOMqWIVLeZE5GsisldEnhni8deISLeIrClfPj7aMRpjzGAsfxljxopKH5rkLuA24JuHafMbVX3T6IRjjDHDdheWv4wxY0BFR+ZU9ddARyVjMMaYY2H5yxgzVlTDNnOvFJEnReSnIjLkUQhF5HoRaRWR1ra2ttGMzxhjhmL5yxgz4sZ6Mfc4cIqqLgX+L/CjoRqq6h2qulxVl7e0tIxWfMacVDZv3szixYuP6jl33XUXO3fuPGKbm2+++Yjzuu2225g3bx4iwr59+44qjjHI8pcxo2g8568xXcypao+q9pVv3w/4IjKxwmEZYwYYTjIcrpUrV/LLX/6SU0455YTMr5Isfxkz9p0s+WtMF3MiMkXKJ1oTkXOJ422vbFTGnNyCIOCqq65i4cKFXH755WSzWQBuvfVWVqxYweLFi7n++utRVe655x5aW1u56qqrWLZsGblcjtWrV3P++eezdOlSzj333AOnytm5cyeXXnop8+fP50Mf+tCgfZ911lnMnj17tBZ1RFn+Mmb0jdf8VdG9WUXk28BrgIkish34BOADqOqXgcuBG0UkAHLAlXoynrLCmMH89COw++kTO88pS+ANnzlsk/Xr13PnnXeycuVKrrvuOr74xS/ywQ9+kJtvvpmPfzw+usY111zDfffdx+WXX85tt93G5z//eZYvX06xWOSKK65g1apVrFixgp6eHtLpNABr1qzhiSeeIJlMsmDBAm655RZmzpx5YpdvFFn+MuYwLH+NqkrvzfoOVZ2qqr6qzlDVO1X1y+VEiKrepqpnqOpSVX2Fqv6ukvEaMx7MnDmTlStXAnD11Vfz0EMPAfDggw9y3nnnsWTJEh544AHWrl37sueuX7+eqVOnHjj3YX19PZ4X/2e86KKLaGhoIJVKsWjRIrZs2TJKSzQyLH8ZM/aM1/xV6ePMGWOGcoR/oCOlvGbwoPv5fJ6bbrqJ1tZWZs6cySc/+cmjOgE1QDKZPHDbdV2CIDgh8RpjxiDLX6NqTG8zZ4wZfVu3buXhhx8G4O677+aCCy44kPgmTpxIX18f99xzz4H2dXV1B7YrWbBgAbt27WL16tUA9Pb2jrmkZ4w5eY3X/GXFnDHmIAsWLOD2229n4cKFdHZ2cuONN9LY2Mj73/9+Fi9ezCWXXHJgNQTAtddeyw033MCyZcsIw5BVq1Zxyy23sHTpUi6++OKj+gf8hS98gRkzZrB9+3bOPPNM3ve+943EIhpjTlLjNX/Jybg97vLly7W1tbXSYRhz1NatW8fChQsrHcaYNthrJCKPqeryCoV0Qln+MtXK8tfwjEQOs5E5Y4wxxpgqZsWcMcYYY0wVs2LOGGOMMaaKWTFnjDHGGFPFrJgzxhhjjKliVswZY4wxxlQxK+aMMQds3ryZxYsXH9Vz7rrrLnbu3HnENjfffPMR53XVVVexYMECFi9ezHXXXUepVDqqWIwx49d4zl9WzBljjstwkuFwXXXVVTz33HM8/fTT5HI5vvrVr56Q+RpjzGBOlvxlxZwx5iBBEHDVVVexcOFCLr/8crLZLAC33norK1asYPHixVx//fWoKvfccw+tra1cddVVLFu2jFwux+rVqzn//PNZunQp55577oFT5ezcuZNLL72U+fPn86EPfWjQvi+77DJEBBHh3HPPZfv27aO23MaY6jde85c3aj0ZY47KZx/9LM91PHdC53l60+l8+NwPH7bN+vXrufPOO1m5ciXXXXcdX/ziF/ngBz/IzTffzMc//nEArrnmGu677z4uv/xybrvtNj7/+c+zfPlyisUiV1xxBatWrWLFihX09PSQTqcBWLNmDU888QTJZJIFCxZwyy23MHPmzEFjKJVKfOtb3+Lf//3fT+jyG2NGh+Wv0c1fNjJnjDnIzJkzWblyJQBXX301Dz30EAAPPvgg5513HkuWLOGBBx5g7dq1L3vu+vXrmTp16oFzH9bX1+N58X/Giy66iIaGBlKpFIsWLWLLli1DxnDTTTdx4YUX8qpXvepEL54x5iQ2XvNXRUfmRORrwJuAvar6sq0WRUSAfwcuA7LAtar6+OhGaUxlHOkf6EiJv3YH38/n89x00020trYyc+ZMPvnJTx7VCagBksnkgduu6xIEwaDtPvWpT9HW1sZXvvKVow9+FFn+MmZolr9GN39VemTuLuDSwzz+BmB++XI98KVRiMmYcW3r1q08/PDDANx9991ccMEFBxLfxIkT6evr45577jnQvq6u7sB2JQsWLGDXrl2sXr0agN7e3iGT3mC++tWv8rOf/Yxvf/vbOE6l09MR3YXlL2PGlPGavyqaLVX110DHYZq8Bfimxh4BGkVk6pHmW+jtOVEhGjPuLFiwgNtvv52FCxfS2dnJjTfeSGNjI+9///tZvHgxl1xyyYHVEADXXnstN9xwA8uWLSMMQ1atWsUtt9zC0qVLufjii4/qH/ANN9zAnj17eOUrX8myZcu49dZbR2IRT4iRyl/GmGM3XvOXqOqodTZoACKzgfuGWE1xH/AZVX2ofP9/gA+rausgba8n/vfL7AkTz9nU0TaicRszEtatW8fChQsrHcaYNthrJCKPqery0Y5lJPLXrFmzzjnc9jjGjFWWv4ZnJHLYmF+PMVyqeoeqLlfV5UKGYk9vpUMyxphhGZi/WlpaKh2OMabKjPVibgcwcN/fGeVphxW4KX78r98csaCMMWYYjil/GWPM0Rrrxdy9wLsk9gqgW1V3HelJQkT/8x672210zhhTMceUv4wx5mhVtJgTkW8DDwMLRGS7iLxXRG4QkRvKTe4HNgIbgP8AbhrOfCOnk/66+Xzn49+l0tsEGmNOTiOVv4wx5mhV9DhzqvqOIzyuwJ8d7XzrJ6RI9T2FZBbyrR89xbveuvSYYzTGmMGMVP4yxpijNdZXsx6TdO0U9pz+A7wgR899L/Ds9q5Kh2SMMcYYMyJOymIO4E+u/hT50t2I38S3/ulXdOdKlQ7JmDFv8+bNLF78sqNsHNZdd93Fzp07j9jm5ptvPuK83vve97J06VLOPPNMLr/8cvr6+o4qFmPM+DWe89dJW8zNm/1a9l2cZeKeh5iRr+Hvv/IoUWTbzxlzog0nGQ7Xv/7rv/Lkk0/y1FNPMWvWLG677bYTMl9jjBnMyZK/TtpiDuD9b/6//H72D8nk9jLv2W7+9SfrKh2SMWNeEARcddVVLFy4kMsvv5xsNgvArbfeyooVK1i8eDHXX389qso999xDa2srV111FcuWLSOXy7F69WrOP/98li5dyrnnnnvgVDk7d+7k0ksvZf78+XzoQx8atO/6+noAVJVcLvey8ywaY8zhjNf8VdEdIEbazMY5zH3rm/H/6av4U/6GfT/dzKqptVxx7qxKh2bMEe3+//4/CuueO6HzTC48nSkf/ehh26xfv54777yTlStXct111/HFL36RD37wg9x88818/OMfB+Caa67hvvvu4/LLL+e2227j85//PMuXL6dYLHLFFVewatUqVqxYQU9PD+l0GoA1a9bwxBNPkEwmWbBgAbfccgszZ858Wf/vec97uP/++1m0aBH//M//fEKX3xgzOix/jW7+OqlH5gDee/5H+NEb+5m96dtMJsXP/vNZfv28nerLmKHMnDmTlStXAnD11Vfz0EMPAfDggw9y3nnnsWTJEh544AHWrl37sueuX7+eqVOnHjj3YX19PZ4X/2e86KKLaGhoIJVKsWjRIoY6ZdXXv/51du7cycKFC1m1atVILKIx5iQ1XvPXST0yB5D20vzpJbdy97a/4s1PnwrTXsXn73yC5j8/jzOmNVQ6PGOGdKR/oCPl0FUDIkI+n+emm26itbWVmTNn8slPfvKoTkANkEwmD9x2XZcgCIZs67ouV155JZ/73Od4z3vec3QLYIypOMtfo5u/TvqROYDXzX49iZVnszPzfeq7N/K6boe//MpqtnVkKx2aMWPO1q1befjhhwG4++67ueCCCw4kvokTJ9LX18c999xzoH1dXd2B7UoWLFjArl27WL16NQC9vb2HTXoDqSobNmw4cPvee+/l9NNPP2HLZYw5+Y3X/DUuijkR4VOv/ie+d7HPjO3/QbrYyx+0Ke/60iNs3tdf6fCMGVMWLFjA7bffzsKFC+ns7OTGG2+ksbGR97///SxevJhLLrnkwGoIgGuvvZYbbriBZcuWEYYhq1at4pZbbmHp0qVcfPHFw/4HrKq8+93vZsmSJSxZsoRdu3Yd2MbFGGOGY7zmLzkZT3e1fPlybW1tfdn0n2y4l//4/kf5yA9msGbZX7Mr6fDLFuWb15/H/Ml1FYjUmIOtW7eOhQsXVjqMMW2w10hEHlPV5RUK6YQaKn8ZM9ZZ/hqekchh42Jkbr83nfqHnLr8tfz07G0sevYuphThwnbhyq88wjM7uisdnjHGGGPMURtXxZyI8PcrP8VvXtVIV93jnPbCd5mVF17d7fDOOx7h8a2dlQ7RGGOMMeaojKtiDqAp1cQnLvg0n36rS23hf5mz7X5O7Rden/V513/8nkc2tlc6RGOMMcaYYRt3xRzAa2e9lj9Z9i4+fKXPtN0/Ye6unzOnF96UT3LtnY/y4Pq9lQ7RGGOMMWZYxmUxB/DX5/w1Sxa+mo9fkeCUF3/EaR2/ZGavcnkxxfV3tfL1327iZNw5xBgztnXu3FPpEIwxVaaixZyIXCoi60Vkg4h8ZJDHrxWRNhFZU76870T17Toun7vwc3gL5vNvb/OZ8fQPOCP/a6b2Ku+hlk/f+ywf+f7TFILwRHVpjDnJjEQOC4oJin12DExjzPBVrJgTERe4HXgDsAh4h4gsGqTpKlVdVr589UTGUOPXcPtFt/P8GU189/U+kx9ZxdLwVzR0Bvx5spHvr97G5V96mC3tdiw6Mz5s3ryZxYsXH9Vz7rrrLnbu3HnENjfffPOw5/mBD3yA2trao4pjtI1UDlPx+NE/fOEER2vMyW88569KjsydC2xQ1Y2qWgS+A7xltIOYWjuV//sHt/Ff56b56as9mn/zXZb134/bVuCjtc3sbOvnjV94iPueOvybbcx4NZxkeDRaW1vp7KyKPctHJIc5WqR79xwKPfYn0piRdrLkr0oWc9OBbQPuby9PO9TbReQpEblHRGYONTMRuV5EWkWkta2t7agCWdKyhK9c/BW+e2EN37vUp2n1fSxr+x75XVn+XOpZMqGGm+9+go/98GnyJVvtak5uQRBw1VVXsXDhQi6//HKy2XiV36233sqKFStYvHgx119/ParKPffcQ2trK1dddRXLli0jl8uxevVqzj//fJYuXcq555574FQ5O3fu5NJLL2X+/Pl86EMfGrTvMAz5m7/5Gz73uc+N2vIehxOWwwbmr9Dpo5hs4e6P3D4SMRtzUhuv+csb9R6Pzk+Ab6tqQUT+FPgG8AeDNVTVO4A7ID6C+tF2dNaks/iP1/8Hf+r8Kb2ZHNf96EGWZzt5KnEDF/U5nLVsOl/8/VYe39rFF65cZmeMMCPuN999nn3b+k7oPCfOrOVVf3LaYdusX7+eO++8k5UrV3LdddfxxS9+kQ9+8IPcfPPNB05Pc80113Dfffdx+eWXc9ttt/H5z3+e5cuXUywWueKKK1i1ahUrVqygp6eHdDoNwJo1a3jiiSdIJpMsWLCAW265hZkzD65tbrvtNt785jczderUE7rcFTSsHDYwf519zjla2/O/9NW/hv++8+tc+t7ROVG3MSeS5a/RVcmRuR3AwFdiRnnaAararqqF8t2vAueMZEBLWpbwtUu+xiNn1vKFKzPUbX2Cc37/SVJOkbqHO/nns09lT0+eN37hIf79ly+QK9oonTn5zJw5k5UrVwJw9dVX89BDDwHw4IMPct5557FkyRIeeOAB1q5d+7Lnrl+/nqlTpx4492F9fT2eF/9nvOiii2hoaCCVSrFo0SK2bNly0HN37tzJ9773PW655ZaRXLwTaURymCPCnPe+ltrejWz8/VReWP3kCQvYmJPdeM1flRyZWw3MF5E5xAnwSuCdAxuIyFRV3VW++2Zg3UgHdXrT6Xz9kq9zo3cjH3lvxKdX7WLpTz/IC6//GLseUP5x5QzulSz/+svnWbV6Kx9+w+m8eek0RGSkQzPjzJH+gY6UQz/LIkI+n+emm26itbWVmTNn8slPfnLYJ6DeL5lMHrjtui5BEBz0+BNPPMGGDRuYN28eANlslnnz5rFhw4ZjXJIRN2I57MKLXsu6X/2C5JY6fvEfAbWNU5k6f9KJjN2YEWX5a3Tz17BH5kTkFBF5Xfl2WkSOaz2jqgbAzcDPiBPcd1V1rYjcKiJvLjf7gIisFZEngQ8A1x5Pn8M1b8I87r7sblLzF/C+6xL0zilx+v2f4NT8I2z47S7+YCd844/Poqk2wZ9/Zw1v/eLveGxLVWywbcwRbd26lYcffhiAu+++mwsuuOBA4ps4cSJ9fX3cc889B9rX1dUd2K5kwYIF7Nq1i9WrVwPQ29v7sqQ3lDe+8Y3s3r2bzZs3s3nzZjKZzFgu5EY8h139sVsp6XdIFvr54T+vZs+LdnYaY45kvOavYRVzIvJ+4B7gK+VJM4AfHW/nqnq/qp6mqqeq6j+Up31cVe8t3/5bVT1DVZeq6mtV9bnj7XO4WjItfP2Sr3PevNfyp28Xnn59I6f8/pucufnrtG/rZN3Xn+ej06fyubcsZld3jrd/6XfcfPfjbOuw40OZ6rZgwQJuv/12Fi5cSGdnJzfeeCONjY28//3vZ/HixVxyySUHVkMAXHvttdxwww0sW7aMMAxZtWoVt9xyC0uXLuXiiy8+6n/A1WQkc1hN0uM1n/k6te1fIpnr4wf/9Hu2Pml71RtzOOM1f8lwznIgImuId8P/vaqeVZ72tKouGdnwjs3y5cu1tbX1hMwrjEL+7fF/4661d3Hxnibe/+29FKWOHa++jk2500jXJzj7slN4oJjljt9sJFK4buUcbnz1qTRk/BMSgxk/1q1bx8KFCysdxpg22GskIo+p6vIKhXRCHZq/ftr6PPm/fS/dk99Pf+1UXvW2Uzjz9ZVZhWXM4Vj+Gp6RyGHDXc1aKB9HaX+nHjAuznXlOi5/vfyv+eJFX+SJ2Q43vy9FYWLInJ/+Oxfu+hz1iW5++50XmPZoN99961m8aclUvvyrF1n52Qf47H8/R3tf4cidGGPMEN6w/DS23/x5Jm/9AhM61vKbH2znwa89TmCHSTLGlA23mPuViHwUSIvIxcD3iHe5HzdeNeNVfP/N32fxwgt5/zsKPHhpC+6GLSz5yV/yqsS3KHb38Js7nuV1HQ7fv3oFr1nQcqCo+9RP1rKx7cTuom2MGT9ufvO5/P59/x/NO+5k5taf8eyjXXz///yK7jbbrMMYM/xi7iNAG/A08KfA/cDfjVRQY1VTqol/e+2/8alXfZpVrxT+5j0e7RPr8X/+CBc+fiPLG/+H7c+28eiX1nJloo77b1jJG5dM41sPb+EP/vlXXPGVh/nREzvswMPmsIaz6cN4NV5fGxHh41dfzMO3fIF88FPOfPpLdO3p47u3PsTGx3dXOjxjDhiv39HhGqnXZ7jbzNUAeVUNy/ddIKmqY/Jv4YncZm4oPcUevrTmS3x37d38UavLH/2uhJcLSMz12HTGu1nfexap2gTLL5tNy9ImfvT0Llat3saW9iyNGZ+3njWdd5w7i9Ps4MNmgE2bNlFXV0dzc7Md7uYQqkp7ezu9vb3MmTPnoMdO5m3mDnXbLx+h7t/+lCXba1mz4jpy7hyWXVDPK95xNq5byUOHmvHO8tfhjWQOG24x9wjwOlXtK9+vBX6uqucfa8cjaTSKuf02dG7gM6s/wzMbH+GaJ+p4ze96cMIIFjTz3Oxr2ZmbS7LGY8mrZ3DGhdN5al8vdz+6lZ+v3UMxjDh7ViNXnjuLN505lUxirJ+Qw4y0UqnE9u3bq2YPqtGWSqWYMWMGvn/wzkXjqZgD+F7rk7R/+v28an2OJ85+G911r6aprodXXr6YU8491X5ITUVY/jqykcphw96bVVWXHWnaWDGaxRzE1fYDWx/gy099md1b13H1I0kueCyHgxKeNpXNp/whWwpn4noOC14xlWWvm4nW+fzg8e18+9GtvNjWT13S483LpvGGxVM5d04TCc/+YRszXOOtmAN4bNNefvDp93Hlwy+we/JStp32ZnIyhSnNPay4/CxmLptlRZ0xVWK0irnfAreo6uPl++cAt6nqK4+145E02sXcfqrKw7se5mvPfI2N6x7h7as9Xv1kCbcUwdwGts++mBe5kDBymbGgkcWvmcHsJc08tq2b7zy6lf96eheFIKI26XHBvIn8wcJJvHbBJFrqkkfu3JhxbDwWcwBtvQU+fPu/cdkv/x8Ld0SsO/tCeutfS1Yn0jKhl3PefAZzzzsVcayoM2YsG61ibgXwHWAnIMAU4ApVfexYOx5JlSrmBlq7by1fe+ZrtD77S17fWuKyx4VUPiKckKFj/rlsrL2I/qiJmlo4feVMTj1nCpnJKR5+sYMH1u/lgXV72d0TD1UvndHABfMnsmJ2E+ecMoG6lB2/zpiBxmsxBxCEEf/408corvoof/z4diJx2Xjeq+lLnk9vNJUJtb2c/eoJnPq6V+CnEyMYuTHmWI1KMVfuyAcWlO+uV9XSsXY60sZCMbffvtw+frzhx/xk7T1Ma93KxU8Lp28JCcWhb85Cdky9gD3+YhSH+vqQU8+exKnnzaHllFrW7e7lwef28sBze3lyezdhpDgCC6fWc+6cJs6d3cTy2U02cmfGvfFczO33q+fb+Nx3vsNlT/wnr3mum3zCYdP5r6LgvoKuYBauFJk5uYu5r5jH7JVLSFveMGbMGM1i7nxgNnBgK31V/eaxdjySxlIxt5+q0rqnlXuev4dn1vyC857Kc+4G4ZTdEQW/ln1zF9PVvJS9iUUoHjWpHKfMdTjl3PnMWDabksATW7t4dHMHqzd18MS2TvKlCIC5E2tYMbuJhVPrmNtSy9yWGqY1pHFs1YoZJ6yYi+VLIXc+tIl7f/pt3vn0vZy7qY/ujLB95auom7CQ3e3T6AsnIkRMa9rH7NPTTDtnMc2nzcH1bTtdYypltFazfgs4FVgD7D9ImqrqB46145E0Fou5gfqKfTy04yF+v/v3bH76d5yyejvnvBAxdw+Ebpq2ljNpn7qYztqFBE4ahyBOvPM9Zp09h8aFiyk5SZ7Z2c3qTR08uqmD1i2ddOdeGixN+Q6zm2s4taWWORNrmNtSc6DQq7fVtOYkY8Xcwfb1FfjKr15k9X+v4u0v/DfLN/dQcmHneacw5dxXk+9MsWlnMx2lGQA4hExId9AyoZ8pp9Yx47xl1J86z3agqBJhXz9aKuLW1oLnHfZ90yhC83mibJbSzp0EHR1ooQiOII6DRhFOMomTyRD29BL2dEMYgjiI64DjgDhE/f1oUMJtbEREDhw/TcqP4wjsjyOMIArRML4QRmhUvg4DCAI0CNEgQIMSGgRQvk8UIokEkkzhpJLxdTqFJFNIKomTSiGJJOK5iOuC4+Ck0/gzZqBBQJTNEvVniXJZNJslyuXQIAQUoggtldBSCUmmcBsbcRsbcJJJpHw5cNs7+GgTqkrU10dx61ainh4klcJJpYiyWRDBqa3FbWzEa2k58PpoNkvY14fb0ICTSh00v9Eq5tYBi7RKjgY41ou5Q+3p38PqPatZs/G3dDz6Oyatb+OMrcrsPS699XPZ17yYtklnkE9OBSBBH5NqdjGppcCkGSkmnVJHzdQpdPotvFhoZENnxMa2Pjbu62djWx/bOnOE0Utv3cTaJLOa0jTXJmmuSdCQ9mmpSzKrKcPMpgyT61NMyPiWyE3VsGJucHt78nzmp8/x6CP/w9u238drn9tNqgTtTT57XjmPSctfzeSokY4dvbS1p2jrm0gurAeg1utgelMb02cqk2cmaZw5GWf6mdAw86Uf6ZOcFotExRLie0Q9PYTd3YTd3WgpwG2IXycdWKgUSwR7dqPFIjhuXGB4Hk5DA+J6RPkcmi+ghTzRwOt8nqiQRwtFtFAg6u8j2NceFzz7BSFhXy9RT29ckBSLaBAgiQSayx0cuOchvo/sv3bdeFnyebRQBaeYFImLJ8+LC8xiES1VeMsu142Lu0QCRAh7euIi9wgkk0FEiHI5iKJDHowL3tN+/wheff2oFHPfAz6gqruOtaPRVG3F3KF29e1i9Z7VPLNlNYUnnqR+7VbmbyowpbuZ3oYF9NSdQnf9LPprpoO4ADh0k0luZEJqA9MzO5jblGNCcxPUTyPITKIzTLGnkGBH3mdLn8u2rMfOXILtOZ8deZ++4OB/Hb4rtNQmaalP0VKbpD7lkUm61CQ9ahNefJ30qE/7NNUkaMz4uI7gOULad6lP+yQ9xwpCMyqsmDu8Z3Z085Vfb+RXa57ggo5fcNGOF1mwqRdXIe9Dx9xmotedT/OyV9CUnkzvM1vZsTHPjvaJ5MMaADwKNPlbmJjcRc2ENJnGNOn6BInaGkjWk2hoINU8kVRzC4kJTYh34ne2iIpFgr1thF1d5J9+iiibQ/y4YMFx0XyOsL+fqL+fqK+fKJdFfD++3duD+Im4+AnDuEAoFMoFW3zqcRFBo4iwp5uwqxvNjt5x8QeOBDmZDO7EiQeNBonr4NTW4dTV4mRqcJIJcD20UMBtbsJJJuPRslJQHuEK4lGnoARBEC97OoWTSscjW6k0/tQp8chRMgmqaBgijkNUHrlz6xtwG+oRz0OjKC5GoigevUunEc+LixrVlwp81bit6kvFi+PGo3ru/tGz8v0BBe+B4s3z4jaH0DCMC91CAc3lBhTD5SI4DOLiSpWwp5fSzp1IIoGTyZQv6fg6nQYvXjsljsSfHS9+HcOuLsKuboq5PsJCHqcYQLGElEpxv+ViW6MQt6ER6mpgyiScpsb4NcvnkXSaMCpR6u2h1NFOtHUHNX4Gv6YOp6YGp66OoKuLoJADVTx1mPhnN+Emk6NSzD0ILAMeBQ6U9ar65mPteCRVezF3KFVlV/8uNrQ9x+5nVlN67nnczTuo2dZNpnsCkTeLnrpZ9NadQn9mcjzEDQR0UPR3ESTb0HQbpNrwvb3UeXuYrL00hyEJVRIKnuPhuhnUSRNJhpA0pShDLkzTE/j0RQm6wiTdgU8QQXlAnQI+/ZoiS4p+UkQIDopDRMJRMk5I2glIOhG+A56jOIArWh6K93ETSULxCNUhUAhUCCMIVfA8l9qkTybpEyGUIuJLCKFCwvdwXYcgggghUkERXCdOzA6C4wgi8ai/Q3zbdUCQeJojOOVEpKpoeekofzcUELR89+DHODB9YHsFVfqLIWEYUZfyCaOIYhASKTgorhP3nS2GqCoZ3yGKQjQs4RDhCBSdDIGXxhHBlfh5GkWohqiWk6rGqyteuq+gIVGkqEb4jpL2hIzvkPLiof5iGBFF8doSR+JldxzBFcF1oT6VIOEKkcavhEYQoUQKkQpFSVKQJHlJEqqDRiFRFEIUQhTghEWISjjlS6hKST1KuJTUJRSXQDxCPBRBxcF3HRK+j+u6hBGUNF4z47sOaV/ozsYJdP9LHalDvhzHglnTuOUNZ1kxNwzbOrLc+dAmvtu6DbevnUuDh1jY+yKnrt/JpI54lCEU2DvRpWt2M8Wlp5NOzsGpnYsU6yjuDuhqd8kVU4ftxyEg6fST8rKkvAIJP8BzIzwfPO+lz7Oo0JdPUQpcPEIyboFkvp100E+aLH5YQIIQzecp7dhBcedOIjwCL0XopnCiEoliL44GB/WviSROTQZNpdFiCU2nCWvrCIshFAuoI4SeT+D6hL5Pb+TgexFpB3DAaaglqM2Qy6QoOUJYKpBP+RQzKUq1CbyER1MoBIEQhj6hekSRg/oRxUyKSHyiUoSWBC0qkgsRL4/W5YjSEUE6JEhHBCkoJSDwhEiUiIhQQwiF+mACkRsRuAVKWoK8i19KkXCSBMWQMAfJKI2fcvEdn3QySSadJqUZEmkPP+3gug5hKSKr/Ti+kEz4iCPki0WKbgElINCASON+wygk0v2jR3EezgV9pPwk9X4DxcBhU9cO8kVIeRlqvAyqLjUpJZMMAYcoTOK54DgRXbk8+UIJJ1IKhZBUXYTjRZTCgCAICbJCGISUwoAoin89MmEKzbpEAagXELkl8hQpSZE8BfJRCScUQr9Azs1ScgokXKFBJ5LqbcIrpXAQokjxk0qNZEiXavHySTTvEEpA6AaEXolSMkcpkScKlP7+HLl8nmJYIl/KIwglp0jBy+KqS+CVKPo5in6ByAlwAx8NFD9KokQETolUUEPgFMl7/eT9fvJeP5ETIjik3DSBlgii0ku/McS/Q7+58jc0phpHpZh79WDTVfVXx9pxeb6XAv8OuMBXVfUzhzyeBL4JnAO0Ex8OZfOR5nuyFXNHUmzfx761j9P97FP0r99I7/YC+b4a+lIzyGUmkUs1E/g1Bz8pyhLSTt7touB1kvW76Pe76Ev20F7bw976HvpSOQQlpZBUJaERvlIuAOOLj+IruBoXaQ7gqOIOuO0Qv8EDbysQAJEIIfGGmJHIwdMEFCEuz0AUiiJEQhxHBMnIxVUP1EUGXIu6SOTByx7b//jAts6B4lTinkAFFwc3cnDUx4lcIlxCp0ToFImckEjjtuXoCHGIyvcjBE/B03KRWD4Nsq9CQiEot/dU8VQIRYhwiNTDiRI4OIASSLk4JALR8twHFJwocRcDkoM6iMbvRnwNoRMSSohKABK/lvH74yCAM+D+/lciRCjh4GtcBMe9CKqCSryMWi6eo/L9uJBXQpRQIBSNC0HZ/6ooInEbysulKMj+ZVJUXrrePw3R8nK5B1076pJOd/CJv/+3ihRzI5HDRiN/9eZL/HjNTr796FbW7uwBjViZ2sF57nZmdG+lZvs2mja0Udv/0mqkvhR01oJ6LqHjsmtyI31NE2ku1FGTC3GiBJAmIkUkaQJSEKQInAyBmyZyEkSuT+gkiByf0E2AOPjFXrwwT+CmKCWGOL2hRgghinvgz+qBhwgJ3B7AoeSUKHh5Sm6RUAK8KBFfwiTJMEMiTAMQSYiice4oCyWg6OYInYCeZDuOuiTCNMkghaMeOb8XUYdEmMSPUvhhAhn26c2HLyIqf/9HVr/fRc7vI3BKqCiOOhTdPIkwRSgB2UQPXuTTmd5D0c2TDNOkS3WkSjUUvRyBBHHGVEFwiCQgFdRQW2iKX6PyxdOXRmiViJzfRyQhmWLDCVnOUAIiCfCjw//BiIgoellEXbzIP+i9H0mhlCi5OYpujpJboOgUKDol0kEtqTCNo8K1H7+YKS1Nx5XDhrU0x1u0DaZ8ftfbgYuB7cBqEblXVZ8d0Oy9QKeqzhORK4HPAlec6FiqXaJ5ItMufD3TLnz9gWkaRZR27qK0cwfBnr1kd26me1cPPfsK9PYG9OVdclGGQnIC+eQcAr/2pRnuja8kKuEH/bhRHkeL4BTBLQEFlEL8ky0BEQFKSCRFVEpETpGIiMjxiSRBJAmUBOATiRsXNuIieCBefE18X3AR3LjQ2n+tLk4Ul4GiLuz/MR+FhHfg9YzLTYSj33nkQEFy4MKA6yge+ZPyqJ4EQAASD3+KOOWmBxeOMSmXuiD60upslYi4+IsO9CPqQvn1HBjZwJgGjVMENCoXWHGr/VFw4Jq4OkTi0LQcjzjl65eewf7iVl9ahoMv+9sMdtm/TNFBt1O0DfXSj6hqzmF1KZ+rX3EKV7/iFLa2Z/n5s7v5xbMT+fctswj9V8IcSM+Hc7w+ptXkmNe5nklt28j0daJBnjBf4qz1naSze+nPuHRnhKKrhBId+GfgOMKeCdCTjt/SXEJIFZWiJ/SnoD8J/SmHvrTSl4aCDyo+6kygrthEXaGJVFCDE7k46uJGLiohJbdA6OaJnAJ+5FNXmEBtcQJIRG3okwwTpMMERB44OdTvQpN5AjdHye9HxMcliStOXMRIhOdEJII0mZKHlKC50IBLDk/24CdzuBIQhI14UiLh5nAkj7o5Mk4XNdJFndNJWnKUyKDiELgJAhGSUZYEOWqcHEFQTz5oJIhS5LWWgtZR0kR5PYZDSLx2Iiz/XfOdHhSPgmYokcBxCzS6XdRpL2n6SDh9+OQpaYoIJSs+vaTpdaGkKcIoQ5EEoQP1oQIeAT4CuAqF4lQ0TEDJjf+8SkipUIMv3YSaIJedgiMBvZ2nE+HjUCLhdlMjPRS0mVC98vc+/pOGenhOPylvF76bJeHl8CVPQnIkJI9PkWLUQC5sQtWlrmYfNW4HLkVCJ0ng1+BGRdLso07a8MkTaIJAkweuQ00Q4eJKiWKUJh/Vkdc6Ak3Q4O6h0dtJ2ulGiEcXA02SkCxpp5uU04sjL22zVoqS5KJ68lqHS4mEkwMJ2P9KeQQUNUNRMziEFDVDPqqjENUQksCTAp7kSUgeVaGkKVJOL4EmyWtdHFtUW35OHGe+VL6vk8g4ndS6W3ClRK38wXF/p4c7MvcK4P8CC4EE8b/QflWtP+aORV4JfFJVLynf/1sAVf3HAW1+Vm7zsIh4wG6g5Ug7YojIkRfKAHE174qQ8lI01kykMdPEhJqJ1GeaaMg0U5NuJOmnSfgZkokMCT9NwkvjJzK4jodTvhxJFIWEYZEwKhGFAVG0/1IijIJ4mgYHPRaWH48fC4nC0oDp+9uWiKKwPL300nzDAfMuPx7tfzwcMO8oLK+2HLjatLy6EiUsxzNw5Mt1EziOV24ToUq8mhM98DzYP82MtFrX48G+3lEfmRupHFZN+atcux+50YHLENvQqr78f86ht01FOI6Li0MQDb4Dgr1Fx8f3XIqFAuJ6Iz8yB9wGXAl8D1gOvAs47Vg7LZsObBtwfztw3lBtVDUQkW6gGdh36MxE5Hrg+uOMadwJgECVQilHd9c2tnRtO+JzDiUIruPhewkSXgrfS+I6HqUgT7GUpxTkCMPSgHwu5ecdmudlsHEaAPaXRQ4vbesm5fsvtXwprRwuwbw0JgbRIL+pUv5nfGjbQOPxJUcKB/2IqepBv0OH/ibFv1MDt7/b38/+G8IQP3GHxDW8NoMt+2GnDdgWcGA7KW9fGKnilGNUXlreg9u+1F41Hsd0eGl5nf275h9x2WSwq8O0B3+QjaVHyQnLYdWav4b1Q37Qh8V++qtNFIVEHHmvTXNsIgWc489hw15prKobRMRV1RD4uog8AfztcUdwgqjqHcAdMP62mTNmvKv2vaYtfxljjsdwi7msiCSANSLyOWAXHPcGSzuAmQPuzyhPG6zN9vIqigbijYiNMabSLIcZY8aE4RZk15Tb3gz0Eyentx1n36uB+SIyp1woXgnce0ibe4F3l29fDjxQLQcuNsac9CyHGWPGhOEWc3+kqnlV7VHVT6nqXwFvOp6OVTUgLg5/BqwDvquqa0XkVhHZf/y6O4FmEdkA/BXwkePp0xhjThTLYcaYsWK4e7M+rqpnHzLtCVU9a8QiOw62zYkx44udAcIYU82ON4cddps5EXkH8E5gjogMXH1QD3Qca6fGGGOMMebEONIOEL8j3tlhIvDPA6b3Ak+NVFDGGGOMMWZ4DlvMqeoWYIuIvA7IqWokIqcBpwNPj0aAxhhjjDFmaMPdAeLXQEpEpgM/J9679a6RCsoYY4wxxgzPcIs5UdUs8eFIvqiqfwycMXJhGWOMMcaY4Rh2MVc+D+FVwH+Vp1XsHDrGGGOMMSY23GLuL4hP3fXD8nGU5gIPjlhUxhhjjDFmWIZ1Oi9V/RXwqwH3NwIfGKmgjDHGGGPM8BzpOHP/pqp/ISI/AV52dGFVffMgTzPGGGOMMaPkSCNz3ypff36kAzHGGGOMMUfvSMeZe6x8/SsRaSnfbhuNwIwxxhhjzJEdcQcIEfmkiOwD1gPPi0ibiHx85EMzxhhjjDFHcthiTkT+ClgJrFDVJlWdAJwHrBSRvxyNAI0xxhhjzNCONDJ3DfAOVd20f0J5T9argXeNZGDGGGOMMebIjlTM+aq679CJ5e3m/JEJyRhjjDHGDNeRirniMT52WCLSJCK/EJEXytcThmgXisia8uXeY+3PGGNOJMthxpix5EjF3FIR6Rnk0gssOY5+PwL8j6rOB/6nfH8wOVVdVr7YMe2MMWOF5TBjzJhx2GJOVV1VrR/kUqeqx7Oa9S3AN8q3vwH80XHMyxhjRpvlMGPMmDHcc7OeaJNVdVf59m5g8hDtUiLSKiKPiMgfHW6GInJ9uW1rW5sdCs8YM6JOaA6z/GWMOR7DOjfrsRCRXwJTBnnoYwPvqKqKyMtOFVZ2iqruEJG5wAMi8rSqvjhYQ1W9A7gDYPny5UPNzxhjhmU0c5jlL2PM8RixYk5VXzfUYyKyR0SmquouEZkK7B1iHjvK1xtF5H+Bs4BBizljjDmRLIcZY6pFpVaz3gu8u3z73cCPD20gIhNEJFm+PZH44MXPjlqExhgzNMthxpgxo1LF3GeAi0XkBeB15fuIyHIR+Wq5zUKgVUSeBB4EPqOqlgiNMWOB5TBjzJgxYqtZD0dV24GLBpneCryvfPt3HN/hT4wxZkRYDjPGjCWVGpkzxhhjjDEngBVzxhhjjDFVzIo5Y4wxxpgqZsWcMcYYY0wVs2LOGGOMMaaKWTFnjDHGGFPFrJgzxhhjjKliVswZY4wxxlQxK+aMMcYYY6qYFXPGGGOMMVXMijljjDHGmCpmxZwxxhhjTBWzYs4YY4wxpopZMWeMMcYYU8UqUsyJyB+LyFoRiURk+WHaXSoi60Vkg4h8ZDRjNMaYoVgOM8aMJZUamXsGeBvw66EaiIgL3A68AVgEvENEFo1OeMYYc1iWw4wxY4ZXiU5VdR2AiByu2bnABlXdWG77HeAtwLMjHqAxxhyG5TBjzFgylreZmw5sG3B/e3maMcZUA8thxphRMWIjcyLyS2DKIA99TFV/PAL9XQ9cDzBr1qwTPXtjzDgzmjnM8pcx5niMWDGnqq87zlnsAGYOuD+jPG2o/u4A7gBYvny5HmffxphxbjRzmOUvY8zxGMurWVcD80VkjogkgCuBeysckzHGDJflMGPMqKjUoUneKiLbgVcC/yUiPytPnyYi9wOoagDcDPwMWAd8V1XXViJeY4wZyHKYMWYsqdTerD8EfjjI9J3AZQPu3w/cP4qhGWPMEVkOM8aMJWN5NasxxhhjjDkCK+aMMcYYY6qYFXPGGGOMMVXMijljjDHGmCpmxZwxxhhjTBWzYs4YY4wxpopZMWeMMcYYU8WsmDPGGGOMqWJWzBljjDHGVDEr5owxxhhjqpgVc8YYY4wxVcyKOWOMMcaYKmbFnDHGGGNMFbNizhhjjDGmilkxZ4wxxhhTxSpSzInIH4vIWhGJRGT5YdptFpGnRWSNiLSOZozGGDMUy2HGmLHEq1C/zwBvA74yjLavVdV9IxyPMcYcDcthxpgxoyLFnKquAxCRSnRvjDHHxXKYMWYsGevbzCnwcxF5TESur3QwxhhzlCyHGWNG3IiNzInIL4Epgzz0MVX98TBnc4Gq7hCRScAvROQ5Vf31EP1dD1wPMGvWrGOK2Rhj9hvNHGb5yxhzPEasmFPV152AeewoX+8VkR8C5wKDFnOqegdwB8Dy5cv1ePs2xoxvo5nDLH8ZY47HmF3NKiI1IlK3/zbweuKNjo0xZsyzHGaMGS2VOjTJW0VkO/BK4L9E5Gfl6dNE5P5ys8nAQyLyJPAo8F+q+t+ViNcYYwayHGaMGUsqtTfrD4EfDjJ9J3BZ+fZGYOkoh2aMMUdkOcwYM5aM2dWsxhhjjDHmyKyYM8YYY4ypYlbMGWOMMcZUMSvmjDHGGGOqmBVzxhhjjDFVzIo5Y4wxxpgqZsWcMcYYY0wVs2LOGGOMMaaKWTFnjDHGGFPFrJgzxhhjjKliVswZY4wxxlQxK+aMMcYYY6qYFXPGGGOMMVXMijljjDHGmCpmxZwxxhhjTBWrSDEnIv8kIs+JyFMi8kMRaRyi3aUisl5ENojIR0Y5TGOMGZTlMGPMWFKpkblfAItV9UzgeeBvD20gIi5wO/AGYBHwDhFZNKpRGmPM4CyHGWPGjIoUc6r6c1UNyncfAWYM0uxcYIOqblTVIvAd4C2jFaMxxgzFcpgxZiwZC9vMXQf8dJDp04FtA+5vL08zxpixxHKYMaaivJGasYj8EpgyyEMfU9Ufl9t8DAiA/zwB/V0PXF++WxCRZ453nsdoIrCvQn2P9/7H87KP9/4XnOgZjmYOG0P5C+w7PF77H8/LPhb6P64cNmLFnKq+7nCPi8i1wJuAi1RVB2myA5g54P6M8rSh+rsDuKM871ZVXX60MZ8Ilex7vPc/npd9vPcvIq0nep6jmcPGSv6qdP/jedkr3f94Xvax0v/xPL9Se7NeCnwIeLOqZodothqYLyJzRCQBXAncO1oxGmPMUCyHGWPGkkptM3cbUAf8QkTWiMiXAURkmojcD1DeuPhm4GfAOuC7qrq2QvEaY8xAlsOMMWPGiK1mPRxVnTfE9J3AZQPu3w/cfwxd3HGMoZ0Ilex7vPc/npd9vPc/qn2PcA6z99H6H299W//H2b8MvqmHMcYYY4ypBmPh0CTGGGOMMeYYnVTF3GifOkdEZorIgyLyrIisFZE/L0//pIjsKG9Ls0ZELjvSvI6x/80i8nS5j9bytCYR+YWIvFC+njBCfS8YsHxrRKRHRP5iJJddRL4mInsHHrZhqOWV2BfKn4WnROTsEep/0NM6ichsEckNeB2+PAJ9D/lai8jflpd9vYhccjx9H6b/VQP63iwia8rTT+iyl+c51Hdt1N7/kTbe8le5r4rkMMtfB6aNSv46TP+jksPGRf5S1ZPiArjAi8BcIAE8CSwa4T6nAmeXb9cRn9ZnEfBJ4IOjsMybgYmHTPsc8JHy7Y8Anx2l1343cMpILjtwIXA28MyRlpd4u6WfAgK8Avj9CPX/esAr3/7sgP5nD2w3Qn0P+lqXP4NPAklgTvl74Z7o/g95/J+Bj4/EspfnOdR3bdTe/5G8jMf8Ve634jnM8tfI56/D9D8qOWw85K+TaWRu1E+do6q7VPXx8u1e4j3WKn2E97cA3yjf/gbwR6PQ50XAi6q6ZSQ7UdVfAx2HTB5qed8CfFNjjwCNIjL1RPevwzut03EbYtmH8hbgO6paUNVNwAbi78eI9C8iAvwJ8O3j6eMI/Q/1XRu193+EWf56yWjnMMtfsRHLX0P1fxgnNIeNh/x1MhVzFT11jojMBs4Cfl+edHN5ePRrI7GaoEyBn4vIYxIfQR5gsqruKt/eDUweob4HupKDvwijsez7DbW8lfg8HHpapzki8oSI/EpEXjVCfQ72Wo/2sr8K2KOqLwyYNmLLfsh3bSy9/8djPOYvGBs5zPJXrBL5Cyqfw06K/HUyFXMVIyK1wPeBv1DVHuBLwKnAMmAX8RDuSLhAVc8G3gD8mYhcOPBBjcdrR3R3ZYkPhvpm4HvlSaO17C8zGss7FHn5aZ12AbNU9Szgr4C7RaT+BHdbsdf6EO/g4B/DEVv2Qb5rB1Ty/a9mFcxfUOEcZvkrVqH8BWMjh50U+etkKuaO6vRfJ4qI+MRvzn+q6g8AVHWPqoaqGgH/wXGu4hqKqu4oX+8FfljuZ8/+4djy9d6R6HuANwCPq+qeciyjsuwDDLW8o/Z5kJdO63RV+QtJefVAe/n2Y8TbfJx2Ivs9zGs9msvuAW8DVg2Ia0SWfbDvGmPg/T9Bxl3+KvdV6Rxm+atC+as874rmsJMpf51MxdyonzqnvK79TmCdqv7LgOkD122/FTjhJ80WkRoRqdt/m3hD1meIl/nd5WbvBn58ovs+xEH/akZj2Q8x1PLeC7yrvFfQK4DuAcPZJ4wMcVonEWkREbd8ey4wH9h4gvse6rW+F7hSRJIiMqfc96Mnsu8BXgc8p6rbB8R1wpd9qO8aFX7/T6Bxlb/K/YyFHGb5q0L5qzzvSuewkyd/6QjstVOpC/EeIM8TV9IfG4X+LiAeFn0KWFO+XAZ8C3i6PP1eYOoI9D2XeG+fJ4G1+5cXaAb+B3gB+CXQNILLXwO0Aw0Dpo3YshMn3V1AiXgbgvcOtbzEewHdXv4sPA0sH6H+NxBv27D//f9yue3by+/LGuBx4A9HoO8hX2vgY+VlXw+8YSSWvTz9LuCGQ9qe0GUvz3Oo79qovf8jfWEc5a9y/xXNYVj+GrX8dZj+RyWHDdZ3efpdnCT5y84AYYwxxhhTxU6m1azGGGOMMeOOFXPGGGOMMVXMijljjDHGmCpmxZwxxhhjTBWzYs4YY4wxpopZMWeMMcYYU8WsmDPGGGOMqWJWzBljjDHGVDEr5sxJSUSaROSHItIvIltE5J3DeM58EcmLyP8bjRiNMWYwR5u/RORKEVlXbv+iiLxqtGI1Y4NX6QCMGSG3A0VgMrAM+C8ReVJV1x7hOatHITZjjDmcYecvEbkY+CxwBfH5S6ce2sac/GxkzlSUiPgi8g8isllESiKi5ctTxzHPGuLz6/29qvap6kPE5/275jDPuRLoIj5PnjHGHNEYyV+fAm5V1UdUNVLVHaq641j7N9XJijlTaZ8GLgJeBTQSF1M/BP5ofwMRuU9Euoa43DfIPE8DAlV9fsC0J4EzBgtAROqBW4G/OhELZIwZNyqav0TEBZYDLSKyQUS2i8htIpI+UQtoqoOtZjUVIyJ1wAeAM1V1W3na94ErVHXj/naq+qajnHUt0HPItG6gboj2/we4U1W3i8hRdmWMGY/GSP6aDPjA5cQFZQn4MfB3wMeOsl9TxWxkzlTShcBGVX1hwLQJwO7jnG8fUH/ItHqg99CGIrIMeB3wr8fZpzFmfKl4/gJy5ev/q6q7VHUf8C/AZccZg6kyVsyZSmoBOvffkXhY7K3AQaseROSnItI3xOWng8z3ecATkfkDpi0FBtv54TXAbGCriOwGPgi8XUQeP54FM8ac9Cqev1S1E9gO6MDJx75IplqJqr3vpjJEZDnwa+B8YD3wCeAPgJWqWjrOeX+HOKm9j3hvsPuB8w/dG0xEMhz8L/iDxMXdjaradjwxGGNOXmMhf5Xb3gq8AXgj8WrWe4H/VdW/P54YTHWxkTlTMaraCvwDcaLaCEwBLjveRFh2E5AG9gLfJi7O1sKBf8ofLceQVdXd+y/EqzjyVsgZYw5nLOSvsv9DfEil54F1wBPluMw4YiNzxhhjjDFVzEbmjDHGGGOqWMWKORGZKSIPisizIrJWRP58kDYiIl8oHz/nKRE5uxKxGmPMoSyHGWPGikoeZy4A/lpVHy8fr+cxEfmFqj47oM0bgPnly3nAl8rXxhhTaZbDjDFjQsVG5srHxHm8fLuXeMPN6Yc0ewvwTY09AjSKiJ13zhhTcZbDjDFjxZjYZk5EZgNnAb8/5KHpwLYB97fz8mRpjDEVZTnMGFNJFT+dl4jUAt8H/kJVDz2FydHM53rgeoCamppzTj/99BMUoTFmrHvsscf2qWpLJfo+ETnM8pcx49vx5rCKFnMi4hMnwf9U1R8M0mQHMHPA/RnlaS+jqncAdwAsX75cW1tbT3C0xpixSkS2VKjfE5LDLH8ZM74dbw6r5N6sAtwJrFPVfxmi2b3Au8p7hL0C6FbVXaMWpDHGDMFymDFmrKjkyNxK4BrgaRFZU572UWAWgKp+mfjI2pcBG4As8J7RD9MYYwZlOcwYMyZUrJhT1YcAOUIbBf5sdCIyxpjhsxxmjBkrxsTerMYYY4wx5thYMWeMMcYYU8WsmDPGGGOMqWJWzBljjDHGVDEr5owxxhhjqpgVc8YYY4wxVcyKOWOMMcaYKmbFnDHGGGNMFbNizhhjjDGmilkxZ4wxxhhTxayYM8YYY4ypYlbMGWOMMcZUMSvmjDHGGGOqmBVzxhhjjDFVzIo5Y4wxxpgqVtFiTkS+JiJ7ReSZIR5/jYh0i8ia8uXjox2jMcYMxvKXMWas8Crc/13AbcA3D9PmN6r6ptEJxxhjhu0uLH8ZY8aAio7MqeqvgY5KxmCMMcfC8pcxZqyohm3mXikiT4rIT0XkjEoHY4wxR8HylzFmxFV6NeuRPA6coqp9InIZ8CNg/mANReR64HqAWbNmjVqAxhgzBMtfxphRMaZH5lS1R1X7yrfvB3wRmThE2ztUdbmqLm9paRnVOI0x5lCWv4wxo2VMF3MiMkVEpHz7XOJ42ysblTHGHJnlL2PMaKnoalYR+TbwGmCiiGwHPgH4AKr6ZeBy4EYRCYAccKWqaoXCNcaYAyx/GWPGiooWc6r6jiM8fhvxrv/GGDOmWP4yxowVY3o1qzHGGGOMOTwr5owxxhhjqpgVc8YYY4wxVcyKOWOMMcaYKmbFnDHGGGNMFbNizhhjjDGmilkxZ4wxxhhTxayYM8YYY4ypYlbMGWOMMcZUMSvmjDHGGGOqmBVzxhhjjDFVzIo5Y4wxxpgqZsWcMcYYY0wVs2LOGGOMMaaKWTFnjDHGGFPFKlrMicjXRGSviDwzxOMiIl8QkQ0i8pSInD3aMRpjzGAsfxljxopKj8zdBVx6mMffAMwvX64HvjQKMRljzHDcheUvY8wYUNFiTlV/DXQcpslbgG9q7BGgUUSmjk50xhgzNMtfxpixotIjc0cyHdg24P728jRjjBnrLH8ZY0bFWC/mhk1ErheRVhFpbWtrq3Q4xhgzbJa/jDHHY6wXczuAmQPuzyhPexlVvUNVl6vq8paWllEJzhhjDsPylzFmVIz1Yu5e4F3lvcJeAXSr6q5KB2WMMcNg+csYMyq8SnYuIt8GXgNMFJHtwCcAH0BVvwzcD1wGbACywHsqE6kxxhzM8pcxZqyoaDGnqu84wuMK/NkohWOMMcNm+csYM1aM9dWsxhhjjDHmMKyYM8YYY4ypYlbMGWOMMcZUMSvmjDHGGGOqmBVzxhhjjDFVzIo5Y4wxxpgqZsWcMcYYY0wVs2LOGGOMMaaKWTFnjDHGGFPFrJgzxhhjjKliVswZY4wxxlQxK+aMMWYMCTp2VjoEY0yVsWLOGGPGkJ4+D1QrHYYxpopYMWeMMWNIoCkKW56qdBjGmCpixZwxxowpwtM/+Z9KB2GMqSIVLeZE5FIRWS8iG0TkI4M8fq2ItInImvLlfZWI0xhjBjMSOUw05Nmno5EJ2BhzUqpYMSciLnA78AZgEfAOEVk0SNNVqrqsfPnqqAZpjDFDGKkc5kQ5+nURPb/5zgmO2BhzsqrkyNy5wAZV3aiqReA7wFsqGI8xxhyNEclhOb+IKNz7jU6izY8cd5DGmJNfJYu56cC2Afe3l6cd6u0i8pSI3CMiM0cnNGOMOaIRyWFufQtR9h66vQX8/B9+iu5ee6LiNcacpMb6DhA/AWar6pnAL4BvDNVQRK4XkVYRaW1raxu1AI0x5jCGlcMG5i+nmOXOJXNIdf+MF91X8+AnvgWl/KgGbYypLpUs5nYAA/+lzihPO0BV21W1UL77VeCcoWamqneo6nJVXd7S0nLCgzXGmEOcsBw2MH9NbpnIDSvfyT+dqfj9v2OdvJ7Vt/6zHXvOGDOkShZzq4H5IjJHRBLAlcC9AxuIyNQBd98MrBvOjBVLesaYETdiOew9K+ewqOEtfHVRFzU9a3i07ZWsvvXzVtAZYwZVsWJOVQPgZuBnxAnuu6q6VkRuFZE3l5t9QETWisiTwAeAa4cz745s+0iEbIwxB4xkDvNch3+/8ixy+Yv4zrmrqelew6O7zqH1b25Fw3AkFscYU8VEh/lPT0ROAear6i9FJA14qto7otEdoylTJ+vGrZvI+JlKh2KMGQUi8piqLq90HCfC8uXLtbW1FYAfr9nBn69azfK53+N1v7uAyJ/H4t6fs+IT7yV9+ukVjtQYc6Icbw4b1siciLwfuAf4SnnSDOBHx9rpSEsE9fzLb/+NMLJ/sMaY6vWWZdN5+1lzeHzTn/C7Nz5Jr7+BpxvewE8+eh8b3ncThRdeqHSIxpgxwBtmuz8jPqbS7wFU9QURmTRiUR03Ibx3Gh/d+Flu+cNrmdEyrdIBGWPMMfnUW87gsS0dPP/CW1n6zrVs+MVPUC7jf4IFTP2Lr7MgvYUp73kn9ZddhohUOtxxpTPfyZaeLYQa0pBooBAWmFwzmeZU85h6LyKNcGTsHbyiI99Bf6mfMAoJNSSIAhRlVt0sW7N2lIZbzBVUtbj/wykiHozdvQzS+XamZNMEj76CH6x+huTpj/GWt13AlJkTKh2aMcYcldqkx+1Xnc2VX3mEn/zuLL5x4zv52Y//lo0vLqLkvZadYZ6pX3qEKf9yF5Pn1JNauJD0goXUvuoC3IaGUY01W8rSU+wh6SbZ1b+LHX07SLpJ5tTPYUrtFPb072Frz1aebHuSdR3r6C/1M7dhLs3pZgRBRA5c7+eJx6TMJKbWTqUUltjau5X2XDuLJy5GUbKlLBk/Q8rNkHR9+kp9ANQl6niu4zlq/VoWT1zMjLoZAJSiEp54hBqSC3LUJeoA2N2/myfbnuTJtid5rn09RLVMyrTQkHZpy3awt38f/WE3Hfl2+kv9eI5Hf6l/0NdhZt1MVk5byZKWJSxuXszshtkHFVOqGsfheAdNL0UlBMERh7ZsG7kgxy+3/pKn256mGBVpSDYwITmBXJCjt9hLjV9DqCETkhOYN2EedX4d/7v9f3m+83nyQZ5CWKCr0EV/qZ+pNVM5tfFUzmw5kzfNeQsz6qYeeJ2jSNnc3k+kMLUhRU3y4NKgFEaEkZLyXQByQY6dPR1s69nOztyLtOfj7dQ18igWfeqTdTyx+zkmpOtZOWsxpzfPpcavIVvKsrlnM6t3t/KrbQ+xrW/ToK+fIy41Xi2lqEigJWr8GmbVzaIpMZ0gSFCMsqyccQ6phLCnfw8AfaU+Tm08lWk10yhFJRxxmNs4l6ZkE77rUwpL7MnuIeNlyAZZ2nJt9JX6mJKZwtSaqdQmatncs5nW3a3kghzFsEghLFDj13DB9AuY1ziPnmIPrXtaeb7jeRx86pIZavwa0l6ajJ+Jr7342s+GtD30BG37dpPcuxuPgLCljmhSI3UtZ7GvYxN7nHbap2T46/NuHOY3bGjD2mZORD4HdAHvAm4BbgKeVdWPHXcEI2BBbZ3+cM5M8q9r5CeNb6Rhz9n4UZL03JBXX3wmDS0ZahqSpOsSlQ7VmBMmihQBxDkxIwK53iKde7JMmJzBcYWgFJHvK9HfVSCZ8dm7pYfe9jyOJ0yYUsOEKRkaJmVIpj36OgtsW9dBb0eeMIgoZAPyvUUmza6nrjlFvq9EqRjSPK2Wpmk1BMUQxxXqmlIEpYiefXmCUoiIEJYievbl6N6XIyiElIoR+d4iCuT7Skw6pY4L/vi0k3KbuYEe29LJtV97lKTv8Kk/XMSSTf+HuzaspX/f5czoWoBDglT/88zb+AsmdjxHlHBovOhi0qcvxK2rxZ82DX/WLNzaWsK+PsLOTvJPP01p507Crm60VCQx91TE9/EmTyK1cBGkUmhvL6ELWpNCMg38as82Hmv/PdloHzhZuood7O7bTVehl478PpQjn1dWEOY0zMGXDNv6NpINsiPxUh5kRu1Mgmj/D3otpahEMcpT406Ib2tcBBJ5RMUp4PQjbhYQNKxBgxo0rKE+0cQpE5pIJ2BazTReNXshDekUvcVeEm6C7b3b+d2u3/H4nsfJlbIgQq1fS12ijkJYIBfkKIQFIo2o8WuYWjOVvlIfPYUeskEWRxySbpJckDsQ+9yGuaS8FN2FbjryHSScFGm3jog84NBZ6KAUFQHwqGGCNxdfMhC5OFoLUYJs1IaUuihG7fSm9qGlCUgwlYSkCKMsRacbcQuoeviOg+8pabeebJClEBRQFNcNwelHpXTQa6sqCJAu1dKQbyERpghVibwiWb+XnN9LXaEJR10ac5Ooy0/EKUzEKbbgRUlqwyRO5NDp5enw82STe+hPdNPj58k7AUkvIKm94HdSSHSRDGrJKKhEOCSoKdXhS5JCFH+OVJSimydwCtQVmvHDJAUvR9HNUvBy5UsWlaE/q554JNwE+TBPpAe3E/VAS5zSVsepe5tJF0K84i6WbCqRKSXwSkWmdEUkg8N/JgM3xbbJM1h8xz9xyvyFx5XDhlvMOcB7gdcDQrz31ld1uHtPjLKFp5+hX03WUJcoseiSnTzS0MKPosuZsu1s0kHtgXZN02qYMqeedF2CmQubaDmljkRquIOVI0tVKRVCejvyOI7Q25Gntz1PMRdSzAcUcwGu75CpT5BpSJCpT8a36xMkM96Bf1ylYkhfR56+jgLZngK1TSky9QnCQMn1Fcn3lsj2FunY2U/XnixBMcRLuPgpl0TSJShFdOzqJ5HyqGlMkki5qMbxaaR4vksy45HIeKQyPg0tadyEQ1iKSNX69OzLUcyFRKEShRFhEJHtKeInXNJ1CaJQyfeX8BIOqRqfTEOChpYMnu9QzAdke4oUcwFhEBEG8TyKuYBsT4l8XxFEyHYXyPaW8BMOE6bUUDMhSViMyPYWy30qURARhhFRoHFR0l8i31dCHKFxUpqGSRkaJqWJAiXbUyAoRQTFiLAUUszHRcXkOfXUNCZJ1Xikanz8lIeqkkx7uL6DiOB6DrVNSVx3wL/wSOnrKtC1N0v3niz5/hKp2gRRGFEqxNt1pmp8UjU+yRofDZV8tkQxF1DIBhSyJfLZgEJ/fLuQDSjkAkTAT7rk++L3MAoUxxVqJySpa0pROyFFb0eeXG+RhpZ4GRsnpRFHCIoRibRL+85++rsK5PtKhEFEpj5JUAzjWPfmBv1sDuT5DmEYfxYOEA4at3dcwU/Gn5Oefcd+8FsRcBMunueQrk8gAsmMx8yFTZz7prknfTEHsGFvL9d/6zE2tvUzpS7JrWfs4IKt/87abBfram6hd9MiyPpEbgGnsJP6vh7q+9pp6N5EstBFKVFLNj2JXLqFQnICyUInjiM4CRc36CEoeDhRiXxqAqGborHrBUI3hRf0k87tI53fRzLfzs6mgI2TPTa11NFfO526rE+pVKCoHkT1OK5PSTM8V9fC9oYMDdEOZvdsZ2Z7RDE9iWL9XLblUmxJNZOsSXFmKk+jE5Krb2Rr0SVdVNp7CpRUmdeYYnPnHkK3h8YgTX2hkUh96p0+etyIZEOSSTUuqZqI/v4i6ShNX0+J/r48yVIdDUGJpHbhaz9+lCCVz6GlzRSiHRQAcQtM7w5IakCuZTa5M16N29DIgunN7NoXsXdfQCbySYhHLlKy27pIFiIkzOMX+2jqeoFJ3c+RyDgEmUmE2SyRgpYCiCJ2tsymvWkSvk7AoYYooYTpDtL5rWRlI9tSHUzblOXUziSpUpZsxmF3ywS21TXgT2gkN3kpnZnTqY1KFNMZntnYxa6+PKEozQmhZfdm2lN15DN9TCnuYV6hgdqeLtKlPE3FLM3FiNoAOiZdQLYmPlKORCHquCTzu4mcBKVEExIFZLI7qO3bTNELaGtsZk9tkX0T8tQ5DTT3NOEXMnRkCnieT42TxsOnGCZJ4+P2BrjFoygJBMRzSPgOmXoPKNHToYTFgwsndeAwNdcxC4jolRylaB+FZC8d7l6ivjZmtiepLeVprG8g5zXSXlRyiV6ea+lmSm4yp/Y0Mqnkg1dPX+2MwWeuIUKWKO2QbI6gNkOp10F7IqAAUQdO1EiUrwGEd33mfOonpEelmKsB8qoalu+7QFJVR/7v1DFYvny5/s0H/g+L/vGD7Dv9DF79xi7Y/nvum72S/yxMINcv1BeaOLN/JQ35FsKsHPgxStf5ZOqT1DQkDhRKdc1pahuTOK7geA4TZ9SSqvGPKiZVpbc9T8++HF17srRt7yMohISluMBRwE+4FHIB7dv7yPYUh56ZQCLlHXjuYI87ruCUf7SHI5nxaJpWg5/0CIohpUJcNIoIzdNqKBVD+ruLlPIB4pRXhwgEpXjUpZg7wl+QAfxykbj/NXccIYqO7n9BMuORqvVRhXStT21jkmI+oGNXllxPEccTMvUJXM/B9R0c18H15MD9VMYnVesTBRFdbTm692bpac/jiJBpSOAlXFzfwfMdEmmPUj5k79YeomAY3xdH8BJOXNAJFPPBsJ43FMcVkhmPZMY/6FojpVQMSdf6pGsT+CmXoBjS21GgryNPb0eeTH2CmsZkPLK1N0dQOvjz4PkOtU0pUjUejuvEhXbSpb45xcSZdTRPr6FnXx5VxUvEBVlNQ5J8X4mmaTU0Ts4QBhHdbTk6d/XTvS9HMReQzPjMWtRE45TMQYVtrrdItrdIIuXhJ106dvbTsasfP+kSBhH9XQVcz6GuOUWiXCw7rlDfnKauOYXrDb7dz8m6N+tgwkj53/V7uePXG/n9pg5mpQt8Of1FFmVXU3TreLHpT9nUt4i9QR3dfQWkO4EbHZyvAuml4Hbh6gTAxVUXP0pQcgq4kUfR7UeiEkltHiQCxY+ySBBQ9OvgMNtiOWGBVKETNyySyreTzrWTKHbhhiVEA9K5fQRemkKykcDLUEzU0960iFzmyJtku5QIGToPO1ERr5TFD7KouESOhxvkKSYbKPm1g7Qvkcp3IBrhBVl662YROfH8JSqRKPWhjk8y105d3zaCdAP5TDM9iSmHfQ0AkoVO0tk9eMUecJN0NZxKUI4hUewhEpfArwGNEA1Rx8cv9lKT3U3gpigmG4jEI3QTqOMhUUgq346Kg4pDXd926nq34IYlsplJdDQtRMWh5NceWIZaL8+pTR24QYG+vIeERbrCelxHafD6KeHTFdTRWawlUsEv9hB4aSI3CRqRye4hVegkn2nBSSXxXEUENFWD7wc01heZWNdNPXvwi904DQ0Ebh39Hf1kd7eRanuOYjskCz3U0osb9SMEJJozuNJF0BfR35akP5pIjjpKtU0E00+l1DQdt9iPbNtGWAiIGptJ1SjpVERYDAk7u/E6dqK5l3Z4jMQlSqSJ0hn8nn14xSyhl6LkZQi8DIGfIZ9uoi8zjb6aaRSTjS/73EZuctD3UqKQNFlqMhHTZiSZsmgqUaaOro4S+En8pEc+G6/ByPeX2Lu5hygIqE2XqKstkpcmclmhrjnF1HmNTJ3XwLRTG/ES7qgUc48Ar1ONx6FFpBb4uaqef6wdj6T9yfD7H/pHFt37TX593h9y9btaqHnsSxRy7fz67D/huamLuOfFH9GR7yAd1XA+F7NAzySTrydVrMXJJejtzpPvKXHICCsi0Dg5Q11TirrmFBOm1tA8rQbHFbr25Ojck6VrT5ZCf4liIS6MCtkShf6XCp5kjVce0XHx/DgRlAohiZTLhCk11E1M4SdcapuSaAQ1DYkDq7D8pIs4gqqWR6mKZLuL8XVPkXx/KR6RCpVUjR/H2RSvVu5pz1PMxgVZui4uAtJ18ajQ8ayeiyKlkC3RvTdHGES4nkOut0j9xDSpGj8uLsvFsJ9w4xG2fIjjCH7KjZ/fH9DXmadnX7xqLpH2SNfGhYvrO3EhVn6+6w+dPPd/po92A+QwiBAnLoKHmm8xH1LoL5HvL5VH7CiPHOpLo6nteUqFMC7SFRJJl/qWNA2T0jROypCpS5DrK+L6DomkR6R6YJ75/gDHGVC81Xh45VG/46WR0t9dLBdmDoVsQH1zCscdextGH63xVMwNtHpzB9/43WYe39LJhJ51XO3+kje6j1AvOUrq8pR3Bh3peTxfOo1f9Mymze+gO9FJpt5h6oSI+to8XYUOglKCeYlX8pr557Bg8kQm1aVoqklQ7A9IZjwK2YDutlz8p6AtR+++HOIImWRInZ/DbWggn40oFUM8V0mlXcLeLnY9106uNyAQn6xm6OuH8DB/bFxKtESbmRRux831UuzM4nZ3ICj4HslSLzX5NryJdbi5HvrDGkp+HX5K0AmTSCRD3L4enCAgPWs6fksDiQk+iXpwvT6cKIu78Hza+ibRsTtPIRfg1LbgENC57mn6O0uUij65sIbm6EVaSs/SEGyjJmgD9ShlE/j1QuNCBy8lUOgln1d2FU+nXyfiN6WpDdtI9McnAnEIqJ+/EGlahJNKEeT20f/EQyTaN9NXO4ftuQV0FKfjJUJaEpvoC5sJ1SftdNGRn0FnOBOnlCdTasf1faKckKGHYs0EsonJ8ahqymFvdiL9QQ0AvhcyY6aQqEuR9AOmTuwmkfaZvmQWbl0TiAtBDvaug7494CbB8aBrMwRFoqAEUYgGQnavR9fWLvyuF0gn+pGaCfQ9uYncjixhISIqOmg0/NzkNdeRqFO0WECdFBpCsa0PDRRJeGTmTcKvUdzaNMHe3eS2dlPs9XETEemWAonakGKfS6nPIyw4OL7i10R4k1vwm2pINUX4jSlK/Q7ZF9sJ+7N4fh7P7UVccBI+OA7FzhIaCsmGgER9QKGUYocupd+bRLJO6PYXUtuUYsJEh1TKIR80sn2TR9PkBPNfO4dEUxM4fvy69WyHnl2AQqoBdj8NQR72vQDr7oV898tfiKnL4muNYNIiuPQfkZrmUSnm1qjqsiNNGyv2J8Moinj4hr+i6dc/4zsXXs2ff/Ymmh76JDx2F0yYTWHua3i8toGHUwke2fcU6zpeOjj7jNoZbO/bDipM1uksziwjKUl6c/1M7JpFY3Yy6Vw90psgPGRtlOMJmWYPSYfxenu3RFNdA9NOaWLWrCk0Tqyhrjk1pvZ2OipBEXp3gpuAKIg/rMUsJDKQqIVCL/SXz497YBllwP1Db2v8nHw35Lqg1A+JOsh1QCkbH/W+0BM/vv8SlqBuSvz8qBTf1wiS9ZCeEM9bo/h2egKkm8BxwUvCnAuhbhq4Q6xS79kFO5+I+/RS8Rc0LMZfzvQEmL0SJswe+vVRfWm58z3QsRE6N0OyNl6+XCfFyWcgvbvx29bH/TgexXwXnZkmOv0E4rjUehmez7dBfxuFQg9BVGIyPgWUBX49LemJUDMRaidD46w4uRR7IQygpgVqJ8UXr/wPM9cVL4+fOpZ3/eipQvuLkOuMRy78NEw8LX4fVAGFKIR8V9zuxf+B7a2gIUxdCk2nxp+xXGf8+jle/LoG+fgzGAXQfCrMvgCZvXJcFnMDtfUWeGZHN5va+pjJbpqf+08m7FvN5MJWMuQoOGl6mpdSO3ku6aYZ8eeidhL4GejcBHufiz9HM1bEn/MoiN+vuskv76y/HZ74ZvzZDoqw9WFY+IfQtxe2Pxp/H3t2QKox/v4UesBNoHXTKdSdRujUUOraS8/uHpKlXdQ6baScXpzmOfGfyn3Px/2IQ+hPwmlsQYo90LXlpRiSDfHnXaP4sx+VXh7nQG4y/uwP9uMKcY5YcFn8+fMzcT6beBrUT4s/fx2b4s9eFMZtNAK/BqadBelG2PxQfKmfDnNfAzNXwJbfwa8++1KfXhpmLI9f41IuzglTzoyfn6yL897eZ+NLywLo2hp/Zws9sPFX8XQvHefFXMdB4QfqE2iCpPRzXD8t+4uUsBgvJ0DtFKhtid/fiafBhFNg0iKiVAvF59dRipoIsgJ+GnfiFJyaWkq7d0Mxi2TqcBsnkJg7l8Ts2S/73dMoQgsFxPMQ/5CR1lIe7d4VD3zmOuPPZKr8WkH8nqcaIVV/+GXq3R2/Nzsej+cxZQlMPwfQlwqvsBifA7ltXfxdaFsX93msvDSc8db4t6JpLkw+I859z/0XvPDzOB8icd+3PIb4yVEp5n4L3KKqj5fvnwPcpqqvPNaOR9LAZKilEk9dez3uY7/nO6+7jg9+7gM07votPPBpaN8Q/5AgcMr5dM+9kM76qfyyex2t3S+yYtorqfNreaZvKy90vUg+zNOcbqa32Muuvl10FjpBIV2qoyk7FVddCnV97HW3ozL465r20iyfvJyLT7mYUlSiPd9Oe3YfuXwXfhTgRxGJZD3pVAP1eLhhkSd6NuKLw7zMNKbUz2R3mKMuM5GpNVOZUz+bGWEIbevjpFnsg66tZB2P3vqpeGGJhmQDXvOpsOcZQMi7Ps8V9vF431b6NGBespkZkRL17KSrdye/LeyhR0PyRHSHeXqKfXSHOTyNiKKQIhGzSgG1UcRm36PLdTm1WGJesURClaIISVVmBAEvJHwmBSGnFePVxjnH4dRiiUlhSE6ETtehNlLqo4h+R+hwXCKBCAjFwXd8MpGSTtRQStZRSNawL5FmFyEUe5gTudQ7CToch90SEpRyzC3kmBVCDZDJduEXegDocYQX/AT9jpB1HPoyE+lL1VNESPlNTMvtJd2/l7DUT9Zx2OD7hAITw5A5xYBZQYkIYZfnsr5+FtsyTXipOlpcYUJQIp3vQwpdaN9uVDwigS4CXkgkeNH3iYC0Kt2Ow3PJeOcbV5WEgoPS7wx/hExUmRZGJKOItEYsLBTZkIiX7ex8gX7HocNxaHddasTh4iKc1tvO4kKRTLIeaicT1E7Cq50cF+J+Kk46QSG+nrQQJp0RT9/827jAhvgHbdujRBoS9OxFoyBOWoVepNiLV+qNt8fxkmgU4Ra6Dg68vMpm4A9vAOxzXXpdl6hlAQURtnVvppeIggguMFUS7HWEPhHUdYnEJRSHnWE/cxrn8f5rfjnui7khqcLup2D1V2HPs3GB0L/35e3qZ0Df7vjHbqCpS2HGuVDsj4u3UjbOJRrFfxqiEKYshk2/joug+a+PC8WW0+MisZSLf3CDPHRvjwujsBj/CZmyOJ7HpEUw59VxwQDQvy9uUzPp4D9d2Q7o3QUNM+Mf8FI+jkMc2LM2/oMX5OPc3rs77qN+WlxgZZriebRviPNksh5cPy4cHQ+mnX3kouBYReXPvOPFP+gnQqEPsvviP6a5Dmh7Lv7D1jgrvl/sh0RN/L6WsvF7V9hf/Hrxd7x+WvydD4swYc7Bf/SCInRvi/+g107i+CrEKlboha5t8fem1B//UQmL5Ut5UKFhVjwuke2IP/fpxngENDH8w6sc79qF4RZzK4DvADuJQ54CXKGqjx1rxyPp0GQY9ffz9DvfTWL9WtbNPpMLvnYbk6a1xElu7zp49sew7iewd+3gM0zUwSmvjBPVlt+V/0HV0Fbq5QUtMDGCvbXNPCMB+0q9zAkiGvPdTKqdwfSZ55MOA57VHHu7NrEu7ONBp8hueWn9fn0YUhspJYGiCEURcgN+2CcFAQLs8QYfSZpWih+fHgQ0hyFbfI9nky+t709FcfHV5zh0us5B8xZV9JAvaTqKmBiGJFVpCCMacKhx0hTcFIGTAjfDTiegRIlGp5Zap4F2p5ttxb2EGuKLRy4qkdcitU6G/ihX0fPlinq4miSQLAxRZA9K948gDv0cR5XoCEkuESXxi80QQuhEeG6aGYUa9hTS7CNFKIojSsqtp5Dz8QMPlwhx+/EKE+l3JtBU20B9OkEu7KQQCIH/PJG3D9cp4koP/e426qknSQ1t7CEZJaiJfJrFpc/Jss2JN2/11aFePXqlRFGUplCZEgjTg5DTin1MKYFKQLfj0O06tLkeuzyXuigiqYoDBFEaJ3LY6XmkQpc5BdjrubR5QjJIESF0J/I4KPscnyisJZNvpLmUYHqyja01/eSdiAjocvL0uAWio3lfBvCiBhalzuLud95mxdzRUI1/xPv2xNeZZqhpjoujHY/FBZEI7HoS1v93XCh5ybgAcP14VOOMt8HkRS/Ns2NT+Ye/ZWRjN+YkNCrFXLkjH1hQvrteVY8wpl05gyVDLZX4/T9/mcw3vkJHXRPTP/9PzL/wvIOf2NcWr//e/09l3/PxP76da+IEl++GWa+IHwsKceLy03Fi3D/83zgrfk7NRHjxAWh7Pm5TysHEeVDTQhgU2BTlqc0001w7Db92cvzvNNMEqQYKnTvo7OpgtybYXnCY5fk01tcReBEd/TtY4BTp3/S/7I5KPNPQzBOu4qUb2dy3k96wwMTMZM5rOoOWoEhfCC9272BHdjuZ9GR8zSB5l3TOpaU7DX29rJOQHU6avTqBzmgCmp9BQiFJCQV6iPe4OToR4vWhQR04eRw/Xs0g6iLJ3YibRdVDgxrEKSBuDo0SaFgX776kAjggAThFxCmBumjkoWENBBPwXYfA3QlOCQ0zaKkR1MFJ7cLxuqnPhDTXg0qeQPNkvAYWTljCrMaJFEseHmnqUzXUJhN4Xo7NXXvoyhYRESbV1vEHcxcxIZNhX66dHf2baS/sYltHnoZEC6c3z6ElPZmNe/t4dk8bofThuiX29hR5fk8fYST4rkPCyVDjNTKpLsWkuhT5Usiu7jyKMru5htqURxgq/cWQjv4Ck+pS1Ke98rG2yv83evPs6MrRnSuR9v9/9u48Pq6rPvj/58ydfTQz2nfJsrzI8io78pLYCaFZ2RKghgBOSJqWPCF1aOlDWcpTmuZpn19poS1tElpKIIUSMBgCISQkhBgnIZvleN9lWbK175p9u3N+f4yseJNXrfb3/XrppZmrO/ecO6P5znfOPYuBw2aAzsz9lEprkmaaWMqkfSBGKp2mOj8Lq5F5vQ50BukOxlHWQSyOLqxZBzGsUSzpLByGG5t9iKSlF9PowbQMnvQKKq1wmwYulU/KmialU5gaTEuKNHG81jwi5iDxdAQLFnz2PAKJzGWJXHsZSmmchpdgsp/BZMfIca06GyOdi0WlcalCVCqXRDwbu8oix+0AbdDV7yEcdRCOgalTGPYBsqx5qHQWXqeNFVW5WC0GvaEENcVePn/rpQ3rn0omJJkTQkwpE5nMXQNUccJEw1rr711swePpbMFw+3ObCf/VF/DHggQ/+DFWPPR5jBNascaL1hqlFP3hBHvbA3QMRTHTmsbuEM19YXpDicyHctKkuS+CeZbRnTluG3lZDhKpNIORBOGEictmEE6kOJ+XUyko9buoyndTmethUZmf/Cw7NsPCzHwPqbTG57QyGE2ytz1ATzBOoc9BVZ6HvCw7SmVGn/aHE7jtBkopmnpCaMBQCosFLEphGR7xCpn+PM19EdJpTVW+hxx3pm+EYVHkZ2We/4SZJp5MoxQsKvPTHYwzFE1iKEVvKI7daqFtMEp3IEYsmSZhpin0OqjIdVPsc+J1WslyWrFaLHgcBg7rGF3OGAPaNIk3NmIODWHNz8c+YwbJjo7MnF75+ShjfOqqtSaeSmO1KAyLOms/zUgyQluoDZfVRbYjG7fVjSbzuNEkzUxXgXxXPlaLlYSZIK3TOK0n98sLJUK0hdpw29yUZZWd92z0ZloTTqTIsltHHZgCV+4ACCHE5WGiLrN+H5gFbAeOXx/UWuvPXGzB4+lcwbCluYuX/vzLrNr/exJWO5bFS5j1uc/iXrZ0TMpvH4zSH06wpbmfpp4wHUNRXjnUi82wEIqf3B/FYc0kUPlZDhxWCzbDwqxCD3OLvOR67JRluwjEUnQORQnFTRKpNLvaBhmKJrEbFrLddjwOg0jCxOu04bEbmFpjmppUWpPjtlGW4ybXaRBLQ5HPSUWu66REJx2Pg1JY7HZ0MpnJ9iwWUO98+KfDYcxAgETLUeKHGzF8PuKHD6NjcayFhdirqkg0HUbZM32i0pEIFrebZHs76UgUnTZRdjv2ikrSsShmXz/K6cC1YAFYrTiqqzFyclAOJ0ZWZlSWOThI7OBBUj096FiMyLZtWOwOMAwSR46QbG/HWlSITiZJh8IYXi/K7SLZchSdSmErKcExdy6G34dyuVAWAzMQINXZiWPunMwEql4fhs+bmTrm178GrbFXzyIdixLbsQMsBjqRIB0OY2RnY+TkYM3PB50m3niY6K5dJFtbsVdWkPXuP8BeWUH8yBHihw5lngO7HZ1IEtu7l3TkhJl8DAPM4beS1YqttBTXwgU4Fy/GmpcPaHQiQbKzk1RnJ6m+fnQigcXlwuJ2Zc7HakM57Diqq3HMmkU6EsEMhlB2G+lIBNeiRdgqKjAHBjAHBrDPnImyWNCpFKnubnQyiTZNrIWFGFlZI/8LlhO+3OhUCmW1ok2T8GuvkWzvwLW0DmWxkI7GsHg82MrLsNgndgJunU6TPHYM5XRhzc/DYrVKMieEmLYmKpnbB8yfqpMEn+p8gmHKTPPr7z/D4Z8/y1XN28iLBbC++wYq//ef45g9+7zL0loTSZjsahtiy5F+XtzXxY7Wd0ZLZbtt+F02rp2Tj82wkJ/lYGlFNmU5LgyLosjnxDbK1BDpWAyzv5/YgQMk29pBa6z5eZjBIObgELF9e4nvP4AZCuJasBCL2006HM78JBPYSkpJB4aIHTqE2dOLxevFyM0hHQiirFZcV11FbOdOku3tACi7HZ14Z347Iz8/k2wB4ddeyyR6JzIMLA7HyUnKKZTLlUkULBbS0SjpQGYwgsXvR0ciZzymc+EC0qEwiaYmTmxqtPj9YJrodBp71QzsZWUku7tRNhuG10c6GMQMh7GVlWJxuUkeO0a8sZF0OPzOcQwDa24uqZ6e0ytrHR4tOVwnY7jFTNlsWLxezKFBzL5+dDye+XteHq7Fi7FXVhDds4fotu1gmiibDXt1NYbfn3k+lcossbS0Dmt+PsmOTuKHG7FXzgCdJtnRSeLIEaK7dpHq6DitWkZ+Pta8PJTDgY5GSEeipCORzCiwaPSk1+xsrIWFWEuKSTQdIR0Mnvy30hIsLjeJw4exVVRgzcsbSSSV04k2zZHn5YxsNgy3G4vHg5GdnSmrqAhrYQHWwkJ0NEr8yBFsRcXYystRVgNzcJB0OIzF5yNxpJlEUxOp3l50PE46Eceam4fF5cIMBMCwZJJXqxUdi5FobsYcyrzPPNdey4xv/5ckc0KIaWuikrmfAJ/RWp/+STMFXUgwjCRSfG/Tfjr/63Fu3/8SzlQC94oVeG++meyPfmTUFoc97UM8/uoRntnZQWJ44l6lYH6Jjw/WlVGR66K2xMeMPA/pRCKTmChF/FAj4ddeI7ZnD8pux+J2g1KkAwGSPd1YbHbSiQTpQOCcH9LW4mJcixZhcbuI7toNponF48HidqPsNhKtbRh+P47Zs7GVlGAGApj9fViyvJgD/UR37MS1ZAmOeTWZOoTDWDwelFJoM03iaAvxg4fQsRieNWtw1MzFmp+Ps7aWdCiErawMi8tFqreXREsLjtmzMx/6SmHxeEZas4637mmtSQcCmfrZbKTjcRLNzWCaxA4cJB0Jk+rsIrLtbQx/Ns4F83EtXoKtuAhltWKrrBwZUXUh07pordHRKGiNcjhQViupvj5S3d2YgSDpYIB0NIZn1crMRJddXSjDwFpSclo5WutMIqQUhtd70t/SsRip7m5sJSWnD7E/T6meHsxgKDM7us2OtbDgrK1e2jQzSWtTExa3ByPbj04mUTYbkYatmAMDWLxZWDweIq+/jjk4hLW0BNeixVicDrBYSLa1Ez98GDMwhLO2lsThw5nXLjcP+4wZpKNRlGHgXLAAx9w5mf9dw0A5nSMtnSNfIsJhUoODpLq6SXV1YQ68M7Tf4vWelkQep2w27LNmYc3Px+Jyomx2Uj09pONxjGw/mGl0KpVpKbTbsJeX41y0CNJpjLw8/DffLMmcEGLamqhkbhNQB7wFxI9v11rfdrEFDx/3VuAbgEFmebB/OOXvDuB7wFVAH5kRtM3nOu7FBMPm3jBf+M5mql97gVt7dlPY14ZROQPHvX+C/73vJdvnJpow2XywhydeO8IbTf247Qa315VRmeumVoWoTQ1ibWli8Kc/JR0Mjnz4pCMRSL1zedXi9+OqWwJakw5n5lGzZHmwFRWhE0mUw4Hh82Lx+jLJ2JzZ2GfMACDV14fh9WJkZ2cSQSGmsHQigdnTk7mUXFREOhIh2daGTuvM/7DHjTk4iLWg4KTLuxdqsvrMjUcMk2ROiCvPRCVz7zrTdq315osuOLMk2EHgJqAV2AJ8XGu994R9HgAWa63vV0p9DPiQ1vqOcx37YoNhykzzgzeP8u8vNTLj8A7u2/U0laFu2jz5fGfJ7bxVVEtBqBdbURF/5ulm2f7XUYEhLC4n4TffGukD5a6vx1Y1IzMJotWGxe3GUTMXZVixlZXinD9/3Dq8C3ElmoxkbrximCRzQlx5LjWGndeq8peStJ3FCqBRa90EoJT6EXA7sPeEfW4HHhq+vRF4RCmlxqvvntWwcPc1VdyxvILXDy/mSPcHSezbStkP/pO/fu1xEu4s7JHQSN8ys6wMW1kZqb5+ctZ9At/NNw+3pM0Zj+oJIaaWKRfDhBBXpvNK5pRSq4B/B2oBO5lLCmGt9aVMl10GHDvhfiuwcrR9tNYppdQQkAf0nu3AW7duHdOlshSQZxj4DIOQmcZpUcS1puvA/nd2evoX8OUvj1mZQojzY0xeK/e4xLCxjl9CiKnLMAxSqdS5dzyH80rmgEeAjwE/AeqBTwJzL7n0MaSUug+4bzyOrYFe06T3+FQS5ll3F0KICzKe8UsIcfk732QOrXWjUsrQWpvAd5VS24AvXULZbUDFCffLh7edaZ9WpZQV8JPpRHym+n0L+BZInxMhrjST1JI1ZjFM4pcQ4lKc78reEaWUHdiulPpHpdRnL+Cxo9kCzFFKzRw+9seAp0/Z52ng7uHba4GXpK+JEGKKkBgmhJgSzjchu2t43/VAmMw3zQ9fSsFa69Tw8Z4H9gE/1lrvUUo9rJQ6PuXJ40CeUqoR+Avgi5dSphBCjBWJYUKIqeJ8pyb5M631N861baqQyxRCXFlkbVYhxHR2qTHsfFvm7j7DtnsutlAhhBBCCDE2zjoAQin1ceATwEyl1Il9QXxA/3hWTAghhBBCnNu5RrO+BnQA+cDXT9geBHaOV6WEEEIIIcT5OWsyp7VuAVqUUjcCUa11Wik1F5gH7JqICgohhBBCiNGdb5+5lwGnUqoMeIHM6NYnxqtSQgghhBDi/JxvMqe01hEy05E8prX+CLBg/KolhBBCCCHOx3knc0qpq4F1wK+Gt03agohCCCGEECLjfJO5PyezdNdTw5NiVgObxq1WQgghhBDivJzX2qxa683A5hPuNwGfGa9KjYdkMklrayuxWGyyqzIlOZ1OysvLsdlsk10VIcQpJH6dm8QwcSU71zxz/6q1/nOl1C+B05aK0FrfdoaHTUmtra14vV6qqqoma1HuKUtrTV9fH62trcycOXOyqyOEOIXEr7OTGCaudOdqmfv+8O+vjXdFxlssFpNAOAqlFHl5efT09Ex2VYQQZyDx6+wkhokr3bnmmds6/HuzUqpg+Pa0fbdIIBydPDdCTG3yHj07eX7EleycAyCUUg8ppXqBA8BBpVSPUuor41+1y0tzczMLFy68oMc88cQTtLe3n3Of9evXn/NYR44cYeXKlcyePZs77riDRCJxQXURQly5JH4JMbWdNZlTSv0FsBpYrrXO1VrnACuB1Uqpz05EBa9k5xMMz9cXvvAFPvvZz9LY2EhOTg6PP/74mBxXCCHOROKXEBPnXC1zdwEf11ofOb5heCTrncAnx7Nil6NUKsW6deuora1l7dq1RCIRAB5++GGWL1/OwoULue+++9Bas3HjRhoaGli3bh11dXVEo1G2bNnCNddcw5IlS1ixYgXBYBCA9vZ2br31VubMmcPnP//508rVWvPSSy+xdu1aAO6++25+/vOfT9h5CyGmP4lfQkxd5xoAYdNa9566UWvdo5S66PHfSqlcYANQBTQDH9VaD5xhP5N31oA9OlajZ//2l3vY2x4Yi0ONmF/q428+cPZFMQ4cOMDjjz/O6tWruffee3nsscf43Oc+x/r16/nKVzJXru+66y6eeeYZ1q5dyyOPPMLXvvY16uvrSSQS3HHHHWzYsIHly5cTCARwuVwAbN++nW3btuFwOKipqeHBBx+koqJipNy+vj6ys7OxWjMvd3l5OW1tbWN6/kJcSSYzhkn8kvglxKnO1TJ3to4Jl9Jp4YvAb7XWc4DfDt8/k6jWum74Z9pMgzKaiooKVq9eDcCdd97Jq6++CsCmTZtYuXIlixYt4qWXXmLPnj2nPfbAgQOUlJSwfPlyAHw+30hwu+GGG/D7/TidTubPn09LS8sEnZEQV6wrLoZJ/BJi6jpXy9wSpdSZvgIqwHkJ5d4OXD98+7+B3wFfuITjXZBzfQMdL6eOtlJKEYvFeOCBB2hoaKCiooKHHnrogicGdTgcI7cNwyCVSp3097y8PAYHB0mlUlitVlpbWykrK7v4ExFCTFoMk/gl8UuIU521ZU5rbWitfWf48WqtL2Wa7SKtdcfw7U6gaJT9nEqpBqXUG0qpD15CeVPC0aNHef311wF48sknWbNmzUjgy8/PJxQKsXHjxpH9vV7vSL+SmpoaOjo62LJlCwDBYPC0oDcapRTvfve7R4793//939x+++1jdl5CXIGuuBgm8UuIqet812a9YEqpF5VSu8/wc9K7UGutOcPqEsNmaK3rgU8A/6qUmnWW8u4bDpoNU3XiyJqaGh599FFqa2sZGBjg05/+NNnZ2XzqU59i4cKF3HLLLSOXIQDuuece7r//furq6jBNkw0bNvDggw+yZMkSbrrppgv6BvzVr36Vf/7nf2b27Nn09fXxx3/8x+NxikJcNiYyhkn8OjuJX0KcncrEoQkuVKkDwPVa6w6lVAnwO611zTke8wTwjNZ649n2A6ivr9cNDQ0nbdu3bx+1tbWXUOvLnzxHYrpSSm0dTpomqrxxi2ESvy6ePE9iurrUGDZuLXPn8DRw9/Dtu4FfnLqDUipHKeUYvp1PZr67vRNWQyGEGJ3EMCHElDFZydw/ADcppQ4BNw7fRylVr5T69vA+tUCDUmoHsAn4B621BEIhxFQgMUwIMWWcazTruNBa9wE3nGF7A/Anw7dfAxZNcNWEEOKcJIYJIaaSyWqZE0IIIYQQY0CSOSGEEEKIaUySOSGEEEKIaUySuQnS3NzMwoULL+gxTzzxBO3t7efcZ/369ec81iOPPMLs2bNRStHbe9pyu0IIMSqJX0JMbZLMTWHnEwzP1+rVq3nxxReZMWPGmBxPCCHORuKXEBNHkrkJlEqlWLduHbW1taxdu5ZIJALAww8/zPLly1m4cCH33XcfWms2btxIQ0MD69ato66ujmg0ypYtW7jmmmtYsmQJK1asGFkqp729nVtvvZU5c+bw+c9//oxlL126lKqqqok6VSHEZUbilxBT16RMTTLpnvsidO4a22MWL4L3/MNZdzlw4ACPP/44q1ev5t577+Wxxx7jc5/7HOvXr+crX/kKAHfddRfPPPMMa9eu5ZFHHuFrX/sa9fX1JBIJ7rjjDjZs2MDy5csJBAK4XC4Atm/fzrZt23A4HNTU1PDggw9SUVExtucnhJgaJH4JIU4hLXMTqKKigtWrVwNw55138uqrrwKwadMmVq5cyaJFi3jppZfYs2fPaY89cOAAJSUlI2sf+nw+rNZMLn7DDTfg9/txOp3Mnz+flpaWCTojIcSVQuKXEFPXldkyd45voONFKXXa/VgsxgMPPEBDQwMVFRU89NBDF7QANYDD4Ri5bRgGqVRqTOorhJiCJH4JIU4hLXMT6OjRo7z++usAPPnkk6xZs2Yk8OXn5xMKhdi48Z01uL1e70i/kpqaGjo6OtiyZQsAwWBQgp4QYsJI/BJi6pJkbgLV1NTw6KOPUltby8DAAJ/+9KfJzs7mU5/6FAsXLuSWW24ZuQwBcM8993D//fdTV1eHaZps2LCBBx98kCVLlnDTTTdd0Dfgf/u3f6O8vJzW1lYWL17Mn/zJn4zHKQohLlMSv4SYupTWerLrMObq6+t1Q0PDSdv27dtHbW3tJNVoepDnSExXSqmtWuv6ya7HWJD4dfHkeRLT1aXGMGmZE0IIIYSYxiSZE0IIIYSYxiSZE0IIIYSYxiYlmVNKfUQptUcplVZKjXqNWCl1q1LqgFKqUSn1xYmsoxBCjEZimBBiKpmslrndwIeBl0fbQSllAI8C7wHmAx9XSs2fmOoJIcRZSQwTQkwZkzJpsNZ6H5w+CeUpVgCNWuum4X1/BNwO7B33CgohxFlIDBNCTCVTuc9cGXDshPutw9umpebmZhYuXHhBj3niiSdob28/5z7r168/57HWrVtHTU0NCxcu5N577yWZTF5QXYQQF+yyiWESv4SY2sYtmVNKvaiU2n2Gn9vHqbz7lFINSqmGnp6e8Shiwp1PMDxf69atY//+/ezatYtoNMq3v/3tMTmuEJeriYxhEr/OTuKXEGc3bsmc1vpGrfXCM/z84jwP0QZUnHC/fHjbaOV9S2tdr7WuLygouJSqj5tUKsW6deuora1l7dq1RCIRAB5++GGWL1/OwoULue+++9Bas3HjRhoaGli3bh11dXVEo1G2bNnCNddcw5IlS1ixYsXIUjnt7e3ceuutzJkzh89//vNnLPu9730vSimUUqxYsYLW1tYJO28hpqOJjGESvyR+CXEpJqXP3HnaAsxRSs0kEwA/BnxiLA781be+yv7+/WNxqBHzcufxhRVfOOs+Bw4c4PHHH2f16tXce++9PPbYY3zuc59j/fr1fOUrXwHgrrvu4plnnmHt2rU88sgjfO1rX6O+vp5EIsEdd9zBhg0bWL58OYFAAJfLBcD27dvZtm0bDoeDmpoaHnzwQSoqKs5Yh2Qyyfe//32+8Y1vjOn5CyFOMy4xTOKXxC8hTjVZU5N8SCnVClwN/Eop9fzw9lKl1LMAWusUsB54HtgH/FhrvWcy6jtWKioqWL16NQB33nknr776KgCbNm1i5cqVLFq0iJdeeok9e04/zQMHDlBSUjKy9qHP58NqzeTiN9xwA36/H6fTyfz582lpaRm1Dg888ADXXXcd11577VifnhBXjCsxhkn8EmLqmqzRrE8BT51hezvw3hPuPws8O9bln+sb6Hg5deSbUopYLMYDDzxAQ0MDFRUVPPTQQxe0ADWAw+EYuW0YBqlU6oz7/e3f/i09PT3853/+54VXXggxYjJjmMQviV9CnGoqj2a97Bw9epTXX38dgCeffJI1a9aMBL78/HxCoRAbN24c2d/r9Y70K6mpqaGjo4MtW7YAEAwGRw16Z/Ltb3+b559/nh/+8IdYLPKyCyEujMQvIaYueVdMoJqaGh599FFqa2sZGBjg05/+NNnZ2XzqU59i4cKF3HLLLSOXIQDuuece7r//furq6jBNkw0bNvDggw+yZMkSbrrppgv6Bnz//ffT1dXF1VdfTV1dHQ8//PB4nKIQ4jIl8UuIqUtprSe7DmOuvr5eNzQ0nLRt37591NbWTlKNpgd5jsR0pZTaqrUedVmt6UTi18WT50lMV5caw6RlTgghhBBiGpNkTgghhBBiGpNkTgghhBBiGpNkTgghhBBiGpNkTgghhBBiGpNkTgghhBBiGpNkboI0NzezcOHCC3rME088QXt7+zn3Wb9+/TmP9cd//McsWbKExYsXs3btWkKh0AXVRQhx5ZL4JcTUJsncFHY+wfB8/cu//As7duxg586dVFZW8sgjj4zJcYUQ4kwkfgkxcSSZm0CpVIp169ZRW1vL2rVriUQiADz88MMsX76chQsXct9996G1ZuPGjTQ0NLBu3Trq6uqIRqNs2bKFa665hiVLlrBixYqRpXLa29u59dZbmTNnDp///OfPWLbP5wNAa000Gj1tnUUhhDgbiV9CTF3Wya7AZOj8f/+P+L79Y3pMR+08iv/qr866z4EDB3j88cdZvXo19957L4899hif+9znWL9+PV/5ylcAuOuuu3jmmWdYu3YtjzzyCF/72teor68nkUhwxx13sGHDBpYvX04gEMDlcgGwfft2tm3bhsPhoKamhgcffJCKiorTyv+jP/ojnn32WebPn8/Xv/71MT1/IcTEkPgl8UuIU0nL3ASqqKhg9erVANx55528+uqrAGzatImVK1eyaNEiXnrpJfbs2XPaYw8cOEBJScnI2oc+nw+rNZOL33DDDfj9fpxOJ/Pnz6elpeWM5X/3u9+lvb2d2tpaNmzYMB6nKIS4TEn8EmLquiJb5s71DXS8nHppQClFLBbjgQceoKGhgYqKCh566KELWoAawOFwjNw2DINUKjXqvoZh8LGPfYx//Md/5I/+6I8u7ASEEJNO4pfELyFONSktc0qpjyil9iil0kqpUReWVUo1K6V2KaW2K6UaRttvujh69Civv/46AE8++SRr1qwZCXz5+fmEQiE2btw4sr/X6x3pV1JTU0NHRwdbtmwBIBgMnjXonUhrTWNj48jtp59+mnnz5o3ZeQlxpbkSY5jELyGmrslqmdsNfBj4z/PY991a695xrs+EqKmp4dFHH+Xee+9l/vz5fPrTn8btdvOpT32KhQsXUlxcPHIZAuCee+7h/vvvx+Vy8frrr7NhwwYefPBBotEoLpeLF1988bzK1Vpz9913EwgE0FqzZMkSvvnNb47XaQpxJbjiYpjELyGmLqW1nrzClfod8Dmt9Rm/sSqlmoH6Cw2E9fX1uqHh5EPu27eP2trai6zplUGeIzFdKaW2aq1HbSEbx3J/xxjHMIlfF0+eJzFdXWoMm+oDIDTwglJqq1LqvsmujBBCXCCJYUKIcTdul1mVUi8CxWf405e11r84z8Os0Vq3KaUKgd8opfZrrV8epbz7gPsAKisrL6rOQghx3ETGMIlfQohLMW7JnNb6xjE4Rtvw726l1FPACuCMyZzW+lvAtyBzmeJSyxZCXNkmMoZJ/BJCXIope5lVKeVRSnmP3wZuJtPpWAghpjyJYUKIiTJZU5N8SCnVClwN/Eop9fzw9lKl1LPDuxUBryqldgBvAb/SWv96MuorhBAnkhgmhJhKJmVqEq31U8BTZ9jeDrx3+HYTsGSCqyaEEOckMUwIMZVM2cusl5vm5mYWLlx4QY954oknaG9vP+c+69evP+9jfuYznyErK+uC6iGEuLJJ/BJiapNkbgo7n2B4IRoaGhgYGBiz4wkhxGgkfgkxcSSZm0CpVIp169ZRW1vL2rVriUQiADz88MMsX76chQsXct9996G1ZuPGjTQ0NLBu3Trq6uqIRqNs2bKFa665hiVLlrBixYqRpXLa29u59dZbmTNnDp///OfPWLZpmvzlX/4l//iP/zhh5yuEuHxI/BJi6pqs5bwm1Ss/PkjvsdCYHjO/IotrPzr3rPscOHCAxx9/nNWrV3Pvvffy2GOP8bnPfY7169fzla98BYC77rqLZ555hrVr1/LII4/wta99jfr6ehKJBHfccQcbNmxg+fLlBAIBXC4XANu3b2fbtm04HA5qamp48MEHqaioOKnsRx55hNtuu42SkpIxPW8hxMSS+CWEOJW0zE2giooKVq9eDcCdd97Jq6++CsCmTZtYuXIlixYt4qWXXmLPnj2nPfbAgQOUlJSMrH3o8/mwWjO5+A033IDf78fpdDJ//nxaWlpOemx7ezs/+clPePDBB8fz9IQQlzGJX0JMXVdky9y5voGOF6XUafdjsRgPPPAADQ0NVFRU8NBDDxGLxS7ouA6HY+S2YRikUqmT/r5t2zYaGxuZPXs2AJFIhNmzZ9PY2HiRZyKEmCwSvyR+CXEqaZmbQEePHuX1118H4Mknn2TNmjUjgS8/P59QKMTGjRtH9vd6vSP9Smpqaujo6GDLli0ABIPB04LeaN73vvfR2dlJc3Mzzc3NuN1uCYRCiAsi8UuIqUuSuQlUU1PDo48+Sm1tLQMDA3z6058mOzubT33qUyxcuJBbbrll5DIEwD333MP9999PXV0dpmmyYcMGHnzwQZYsWcJNN910wd+AhRDiYkn8EmLqUlpffssA1tfX64aGhpO27du3j9ra2kmq0fQgz5GYrpRSW7XW9ZNdj7Eg8eviyfMkpqtLjWHSMieEEEIIMY1JMieEEEIIMY1JMieEEEIIMY1dUcnc5dg/cKzIcyPE1Cbv0bOT50dcya6YZM7pdNLX1ydv+DPQWtPX14fT6ZzsqgghzkDi19lJDBNXuitm0uDy8nJaW1vp6emZ7KpMSU6nk/Ly8smuhhDiDCR+nZvEMHElm5RkTin1T8AHgARwGPgjrfXgGfa7FfgGYADf1lr/w8WWabPZmDlz5sU+XAghRkx0DJP4JYQ4m8m6zPobYKHWejFwEPjSqTsopQzgUeA9wHzg40qp+RNaSyGEODOJYUKIKWNSkjmt9Qta6+NrubwBnKltfAXQqLVu0longB8Bt09UHYUQYjQSw4QQU8lUGABxL/DcGbaXAcdOuN86vE0IIaYSiWFCiEk1bn3mlFIvAsVn+NOXtda/GN7ny0AK+MEYlHcfcN/w3bhSavelHvMi5QO9k1T2lV7+lXzuV3r5NWN9wImMYVMofoG8h6/U8q/kc58K5V9SDBu3ZE5rfePZ/q6Uugd4P3CDPvN4+zag4oT75cPbRivvW8C3ho/dMFnrNE5m2Vd6+VfyuV/p5SulGs6914WZyBg2VeLXZJd/JZ/7ZJd/JZ/7VCn/Uh4/KZdZh0d4fR64TWsdGWW3LcAcpdRMpZQd+Bjw9ETVUQghRiMxTAgxlUxWn7lHAC/wG6XUdqXUfwAopUqVUs8CDHcuXg88D+wDfqy13jNJ9RVCiBNJDBNCTBmTMs+c1nr2KNvbgfeecP9Z4NmLKOJbF1m1sTCZZV/p5V/J536llz+hZY9zDJPXUcq/0sqW8i+xfCXLwwghhBBCTF9TYWoSIYQQQghxkS6rZE4pdatS6oBSqlEp9cUJKK9CKbVJKbVXKbVHKfVnw9sfUkq1Dfel2a6Ueu+5jnWR5TcrpXYNl9EwvC1XKfUbpdSh4d8541R2zQnnt10pFVBK/fl4nrtS6jtKqe4Tp20Y7XxVxr8N/y/sVEotG6fy/0kptX+4jKeUUtnD26uUUtETnof/GIeyR32ulVJfGj73A0qpWy6l7LOUv+GEspuVUtuHt4/puQ8fc7T32oS9/uPtSotfw2VNSgyT+DWybULi11nKn5AYdkXEL631ZfFDZu3Dw0A1YAd2APPHucwSYNnwbS+ZZX3mAw8Bn5uAc24G8k/Z9o/AF4dvfxH46gQ9953AjPE8d+A6YBmw+1znS6bf0nOAAlYBb45T+TcD1uHbXz2h/KoT9xunss/4XA//D+4AHMDM4feFMdbln/L3rwNfGY9zHz7maO+1CXv9x/PnSoxfw+VOegyT+DX+8ess5U9IDLsS4tfl1DI34UvnaK07tNZvD98OkhmxNtkzvN8O/Pfw7f8GPjgBZd4AHNZat4xnIVrrl4H+UzaPdr63A9/TGW8A2UqpkrEuX5/fsk6XbJRzH83twI+01nGt9RGgkcz7Y1zKV0op4KPADy+ljHOUP9p7bcJe/3Em8esdEx3DJH5ljFv8Gq38sxjTGHYlxK/LKZmb1KVzlFJVwFLgzeFN64ebR78zHpcJhmngBaXUVpWZQR6gSGvdMXy7Eygap7JP9DFOfiNMxLkfN9r5Tsb/w6nLOs1USm1TSm1WSl07TmWe6bme6HO/FujSWh86Ydu4nfsp77Wp9PpfiisxfsHUiGESvzImI37B5MewyyJ+XU7J3KRRSmUBPwX+XGsdAL4JzALqgA4yTbjjYY3WehnwHuBPlVLXnfhHnWmvHdfhyiozGeptwE+GN03UuZ9mIs53NOr0ZZ06gEqt9VLgL4AnlVK+MS520p7rU3yckz8Mx+3cz/BeGzGZr/90NonxCyY5hkn8ypik+AVTI4ZdFvHrckrmLmj5r7GilLKReXF+oLX+GYDWuktrbWqt08B/cYmXuEajtW4b/t0NPDVcTtfx5tjh393jUfYJ3gO8rbXuGq7LhJz7CUY73wn7f1DvLOu0bvgNyfDlgb7h21vJ9PmYO5blnuW5nshztwIfBjacUK9xOfczvdeYAq//GLni4tdwWZMdwyR+TVL8Gj72pMawyyl+XU7J3IQvnTN8rf1xYJ/W+p9P2H7ite0PAWO+aLZSyqOU8h6/TaYj624y53z38G53A78Y67JPcdK3mok491OMdr5PA58cHhW0Chg6oTl7zKhRlnVSShUopYzh29XAHKBpjMse7bl+GviYUsqhlJo5XPZbY1n2CW4E9mutW0+o15if+2jvNSb59R9DV1T8Gi5nKsQwiV+TFL+Gjz3ZMezyiV96HEbtTNYPmREgB8lk0l+egPLWkGkW3QlsH/55L/B9YNfw9qeBknEou5rMaJ8dwJ7j5wvkAb8FDgEvArnjeP4eoA/wn7Bt3M6dTNDtAJJk+hD88WjnS2YU0KPD/wu7gPpxKr+RTN+G46//fwzv+4fDr8t24G3gA+NQ9qjPNfDl4XM/ALxnPM59ePsTwP2n7Dum5z58zNHeaxP2+o/3D1dQ/Bouf1JjGBK/Jix+naX8CYlhZyp7ePsTXCbxS1aAEEIIIYSYxi6ny6xCCCGEEFccSeaEEEIIIaYxSeaEEEIIIaYxSeaEEEIIIaYxSeaEEEIIIaYxSeaEEEIIIaYxSeaEEEIIIaYxSebEZUkplauUekopFVZKtSilPnGWfauUUs8qpQaUUp1KqUeGl3kRQogpQym1XinVoJSKK6WemOz6iKlDkjlxuXoUSABFwDrgm0qpBaPs+xiZNfFKyCz4/C7ggQmooxBCXIh24O+A70x2RcTUIsmcmFRKKZtS6u+VUs1KqaRSSg//7LyEY3rILMny11rrkNb6VTJLxdw1ykNmAj/WWse01p3Ar4HREj8hhDir8YhrAFrrn2mtf05mGTIhRkgyJybb3wE3ANcC2WTWqXsK+ODxHZRSzyilBkf5eeYMx5wLpLTWB0/YtoPRE7R/JbOos1spVQa8h0xCJ4QQF2M84poQo5J+QWLSKKW8wGeAxVrrY8PbfgrcobVuOr6f1vr9F3joLCBwyrYhwDvK/i8D9w0/xgD+G/j5BZYphBDjGdeEGJW0zInJdB3QpLU+dMK2HKDzEo8bAnynbPMBwVN3VEpZyLTC/QzwAPnDdfjqJdZBCHFlGq+4JsSoJJkTk6kAGDh+RymlgA8BJ11iUEo9p5QKjfLz3BmOexCwKqXmnLBtCbDnDPvmApXAI1rruNa6D/gu8N5LOzUhxBVqvOKaEKOSy6xiMu0Gliml6oADwN8AGthw4k5a6/dcyEG11mGl1M+Ah5VSf0JmhOrtwDVn2LdXKXUE+LRS6mtkLtHeDVxSR2UhxBVrXOIawPCUSVYy3UEMpZSTTP/g1KVWWkxv0jInJo3WugH4e+BZoAkoBt6rtU6OweEfAFxkphz5IfBprfUeGPlG/Fcn7Pth4FagB2gEksBnx6AOQogrzDjHtf8DRIEvAncO3/4/Y3BcMc0prfVk10EIIYQQQlwkaZkTQgghhJjGJi2ZU0pVKKU2KaX2KqX2KKX+7Az7KKXUvymlGpVSO5VSyyajrkIIcSqJYUKIqWIyB0CkgP+ttX57eF6erUqp32it956wz3uAOcM/K4FvDv8WQojJJjFMCDElTFrLnNa6Q2v99vDtILAPKDtlt9uB7+mMN4BspVTJBFdVCCFOIzFMCDFVTIk+c0qpKmAp8OYpfyoDjp1wv5XTg6UQQkwqiWFCiMk06fPMKaWygJ8Cf661PnUJpgs5zn1klmTC4/FcNW/evDGqoRBiqtu6dWuv1rpgMsoeixgm8UuIK9ulxrBJTeaUUjYyQfAHWuufnWGXNqDihPvlw9tOo7X+FvAtgPr6et3Q0DDGtRVCTFVKqZZJKndMYpjELyGubJcawyZzNKsCHgf2aa3/eZTdngY+OTwibBUwpLXumLBKCiHEKCSGCSGmislsmVsN3AXsUkptH972V2TWyURr/R9kZtB+L5lZ+SPAH018NYUQ4owkhgkhpoRJS+a01q8C6hz7aOBPJ6ZGQghx/iSGCSGmiikxmlUIIYQQQlwcSeaEEEIIIaYxSeaEEEIIIaYxSeaEEEIIIaYxSeaEEEIIIaYxSeaEEEIIIaYxSeaEEEIIIaYxSeaEEEIIIaYxSeaEEEIIIaYxSeaEEEIIIaYxSeaEEEIIIaYxSeaEEEIIIaYxSeaEEEIIIaYxSeaEEEIIIaYxSeaEEEIIIaaxSU3mlFLfUUp1K6V2j/L365VSQ0qp7cM/X5noOgohxJlI/BJCTBXWSS7/CeAR4Htn2ecVrfX7J6Y6Qghx3p5A4pcQYgqY1JY5rfXLQP9k1kEIIS6GxC8hxFQxHfrMXa2U2qGUek4ptWCyKyOEEBdA4pcQYtxN9mXWc3kbmKG1Diml3gv8HJhzph2VUvcB9wFUVlZOWAWFEGIUEr+EEBNiSrfMaa0DWuvQ8O1nAZtSKn+Ufb+lta7XWtcXFBRMaD2FEOJUEr+EEBNlSidzSqlipZQavr2CTH37JrdWQghxbhK/hBATZVIvsyqlfghcD+QrpVqBvwFsAFrr/wDWAp9WSqWAKPAxrbWepOoKIcQIiV9CiKliUpM5rfXHz/H3R8gM/RdCiClF4pcQYqqY0pdZhRBCCCHE2UkyJ4QQQggxjUkyJ4QQQggxjUkyJ4QQQggxjUkyJ4QQQggxjUkyJ4QQQggxjUkyJ4QQQggxjUkyJ4QQQggxjUkyJ4QQQggxjUkyJ4QQQggxjUkyJ4QQQggxjUkyJ4QQQggxjUkyJ4QQQggxjUkyJ4QQQggxjUkyJ4QQQggxjU1qMqeU+o5SqlsptXuUvyul1L8ppRqVUjuVUssmuo5CCHEmEr+EEFPFZLfMPQHcepa/vweYM/xzH/DNCaiTEEKcjyeQ+CWEmAImNZnTWr8M9J9ll9uB7+mMN4BspVTJxNROCCFGJ/FLCDFVTHbL3LmUAcdOuN86vE0IIaY6iV9CiAkx1ZO586aUuk8p1aCUaujp6Zns6gghxHmT+CWEuBRTPZlrAypOuF8+vO00Wutvaa3rtdb1BQUFE1I5IYQ4C4lfQogJMdWTuaeBTw6PClsFDGmtOya7UkIIcR4kfgkhJoR1MgtXSv0QuB7IV0q1An8D2AC01v8BPAu8F2gEIsAfTU5NhRDiZBK/hBBTxaQmc1rrj5/j7xr40wmqjhBCnDeJX0KIqWKqX2YVQgghhBBnIcmcEEIIIcQ0JsmcEEIIIcQ0dlkmc9F4eLKrIIQQQggxIS7LZK6nt5lnD/2cofjQZFdFCCGEEGJcXZbJXP6Q5mvP/h+u23Adn3zuk2w+tpnMwDIhhBBCiMvLZZnMaYuDf/9RnDtSc+iN9rL+pfV88ZUvEkvFJrtqQgghhBBj6rJM5uLeYvSQnXX//TZ/l/Ux1tet57kjz/GBn3+AH+3/kbTSCSGEEOKycVkmc6kU9N71d0S6HBR966/J2635l+u+SamnlL9/8+/54itflP50QgghhLgsXJbJnNNtZX9bDqkbbiOwx827f/kwu777PZZav8z9izKtdLf+9Fa+uf2bdIQ6SJrJya6yEEIIIcRFuSyTuaxcJ1a7hYMVf0jWDTfSvd3Pbc//lllP/inPPV/Av6z5HqtKVvHYjse4+ac3s+ZHa/jqW1+lNdg62VUXQgghxBiLBBL0d4TR6cuzm5W6HPuP1dfX6/955Jf89ol9rPnoHKoCW+n71/9HvDOIb06UV+fUY/vgXzG31sm+gT1s7drK80eeJ02auoI6qrOryXHkcNOMm6jyV+Gyuib7lIQQZ6GU2qq1rp/seoyF+vp63dDQMNnVmPKC/THsTgNlUQx2RbA7rSTjJg63FbvLiplKYxgWGt/uRilw++wMdkWpWVWM22cnbaZJpzVWmzHZpzImosEEQz1RCmd4sRhnb6fpORpkzyttdDUHyC3xsPTmSmwOK758J0qpMz4mEkjQcXgQT7YDf74LrcFqt2B3TuoS76fpag7QeyzI7PoijmzvIRJMcGR7D51NAQByit1k5TqJR1K4smwsf99Mimb6TjtOIpbCYlFY7WP3/6HTGjOVfueYoW7o3AWzb7jkGHbZJnNbtmzhmUd20N44xMf/egVZPoOuv/kSg089C4B/foRX6q7D/q7PcN1Vi0mqAX5y8Ce80f4GbaE2huJDpHQKgAJXAQvyFrCkcAm3zbqNQnfhZJ6eEOIUksxNPZFAgn2vtRMeTJA20wx0RhjsiuDLd5GMpxjqjlK5MA+LoYhHUqRNjdNjJbc0C6WgYn4uxTP9Jx3z2N5+juzoITyUoGl7DxaLAgukU+f/OWZ3WXG4rYQG4hiGYsG1ZZTM8eMvcJFT5MGwjd0Fq0Qsxe7NbUSDCfyFbmYuzseT7RiTYyfjJqGBGB2Hh+g4NEjj1m5SyTRuv52lN1VSMiubruYh2g8NkkqkCfbHsDkMUgmTvrYwVodBUZWPzqYhzGQaALffTuWCPJIxk2BflLK5ObQ3DpKMmwx1RzFT6ZPqYHcaXPexucy6qhDDauHIjl56W0MUV/toOzhIsC+GN9fBjIX5xCNJDKuF/Aovbp+dSCBBX2uIvvYQziwbvjwXXc0BWvf3Ewsl8WQ7yCl2Ewsl8ea7KKn2k1eehbIoFJBMmAT7Ywx1RQgNxjGsFvo7wux/vROd1igFx9Mbb66The8qw+6ycuCNTtJmGqfHRm9riEggQUGlF6vNQjSU6XKVNtME+mJYDIU/34WZSuNw23B57bi9Nlw+O55sBzUrikFBPJLEmWWndX8/vnwX+WWZegJEQwle+t5+2g8OkIilAIXPOYRH9ZJDE7Wu31L05eewZOVLMneq48Ew2B/jh3/7JkUzfdz2Z3UopUh2d9Pz1b9j6Fe/wV0cp+zqfnbYZvN8/t0UL30ftywqoSzbxWBskM2tm+mJ9tA02MTuvt0cGTqCVVkp8hSR68ylNKuU1aWrubb8WvJd+ZN92kJcsSSZm1zJhEloOFkIDcTZuamVw293kzY1Dnem5San2EN2oYuBrggWQ5Fd6KZ1/wAWq8LhtmEYikgg07oEYDEUy98/k5xiN8G+GMf2DXB0Tx9Wh4HVamH+mhIA0mkonukjlTCxOazEIkkS0RSG1UI8mqKiNherzUIslMThsfH28y0A+PKdBPtjHHqra+RDP7vIzQf/Yike/5kTLq01HYeHCA/GySn2sP3Foxg2C/58F1a7gc1hQSnFgTc7CQ/GMVNpAr0xrDYLqeGEKb8iC1++i4IKLzMW5pFfkTVqa9iIdBod6qb5iMHbz7fQeyw0cjwAhyPFzGpNeXmK/fvttB57pzXJl+/E7rKSleMkEU2hFMysK2DeqmIcbhvB/thwwmfSun+AY/v6sRgKb66T7pYgBZVevLlOPNkO5tQXEoukCPREURY4tKWLzqYAFovC5jKIh1Mj5VoMRVaOg1B/nPQJlzaVAofHRix05r7qOSUevDkOBnuiBPtiONzWUfc9lc1hMLu+kJlLCmjZ3cfsZQUUzvBhcxgjydWJEtEUuza3cnRPP5BJZtVwJbOL3CTjJoGeKIZhEo8pov1DRMNpIhFNOqVxuAxSSRMzk6PB8Gk6PFZ8eS4iQ3ESsRTplElt1is4Ux1YsvLoi5cRI5vuUCHJlMEnH67HV+SXZO5UJwbD3Ztb2fzDg6xeO5u6GytH9hn48Y/p+r//F5xWfIuiFJd2csRSzM/MazlYcht/sGIJDquF6+YWkJ+VeWMfCxzjqcanaA+3MxAboHGgke5oNwBeu5eyrDJqcmqoya1hdvZs5uTMIc+ZR1qnMSyXR1O+EFORJHOTI22m2fFSK2/+oumkVhu702DeNSUselc52UXuCzpmKmmSiqd54fHdHNs3MLLdl++kZlUJy26pHNNLo4loiqHWHnqa+3jl6W7cbs3MeQ7Sdj/xuIW0qbG7rRgWRfPuPoJ978xXanMYIy2LJ3L77eSXZxHrH+KaRYcp9bXS3wdH2nJo680lFHUxGM3O7GsMYrUpPPYwVdmNVPkPYRjgtCdIKztD8Vw6WuHg4BJ6U9X47APMdL6FO92F2xik0NFMjmpGqXc+y7ttK4nkr8abZyev0AbpFKTiYCagZz8MtMBND0PJYrA6ob8Jdm0EfxnalgVDrajBIyTjaWwqCpWrIH8udO+HghpIxSDQTlpbaIkuoavPQywKBWUOqop76N6xm5IyhbOgmLBnId2hfNx+B2bS5Ni+AcJDcfJKs8gr85BbmkV4ME54KE5+uZesnHcSaZ3WKIsiHk3RfnCAQG8MnQij27ZhHdiPxzpETkUBWas+hGlx4ygqR1kMSIQgbYLTn8keL0S4F7b9Dwwehb7GzGXQaD9kFUGoK1MvRza9oWwaQnfgtATItx0hZOZT6dhBqOhGWlN1hGMOslwJjM6t1Np+SWG5G9739cxzefx/L5ai/eAgVYvzp/dlVqXUrcA3AAP4ttb6H075+z3APwFtw5se0Vp/+1zHPTEY6rTm1/+1m6btPbznfy2iuq5gZL/onj10/u3DxHbuxOK0U/A+P7m2HYRw86XEvfwyfTUOq8EfzCvkmtn53La4FL/bNvJ4rTUHBw7yWvtrdIQ7OBo8yv6+/fTF+k6qj8NwcE3pNWTZsuiMdGKmTeblzqMj3EHTUBNpnabSW0ltXi1OI9NnQaHIdebyvur34bQ6L+LZFeLKMVnJ3HjEsKuWLNJbd+wah9pemkQsRcvuPnpagoSH4kQCCXqOBolHUlQtzmf2VYWZFjGbhdlXFV5yXyqtNaGBONFggqwcJ26f/cIPYqZg14+h/wgE2qDl9xAdgPLlkFUMvQch3A0DzQC0JRbwWvCT9CWrMFQSpz2Bxe4kHodkykpJQYSa1ZVkOcJ07TpITX0O7hlzSA12k2p6i+SxnaS6m/G7IxhmMJMEACgD7Flgd4PdAzY3UZXP4chyuoJFmOEgQ8k8uiNlo55KXnaUuuK3mJu7C4u/FCpWZM4jf26m71W4BywGBDrgjccy5xbqyiRwABYrGA7wlWRu9+w/uQDDfvK+2TPA5gKdhu69F/a8KwO0+c79glrwl0FhLZTUZX6yK2CoFXxlYHVkErBgF0R6IXcWdGyHQy9kEtHC+dD8CnTuzryOqRjk14DTB+3bIT3ccuf0Awpig5n77nyYcTUkItC1Bzz5mfPMnwMObyZZS5sQ6c88V8lo5jlIJ8GVCzkzoHhxpq7d+6FkSebx7dugYnnmOq7Dl3ldwz3Q2wjb/wdiJ0x9Vr4Crv8iVL8bLKNfwp+2yZxSygAOAjcBrcAW4ONa670n7HMPUK+1Xn8hxz71m20qYfKzr71NZCjOnf/36pM6NOp0mkhDA11/9/ck29qo/JeHcR74OqqtgVj2HJ7z3M5PeyvZMeQmbs3iPQuLuWVBMWvm5ONz2s5UPL3RXhoHGzk8eJiB2ACD8UFebXuVtE5T4C4gnU5zaPAQ5VnlVGdXY1VWDg8dpnGwkbQ+uU9CobuQ9XXrubb8Wgxl4DAcuG0X9k1XiMvdZCRz4xXDarPdem9/CHWWwD9R0maavvYwnYeHePv5FkIDcSxWhcfvwO2zk1PkZtayQmYsyjv3pcJLpXXmA76/CSpWZT48lcokA54TurlE+uHo69DyGhx8HvoOZbY7s6H6XeDKgcaXMslD0YLMY4sWZJI7px+yCiHSl0kcdvwwk+j5y8Gdlyl/NBbrcKKyGBLhzP3qd2fK9BScVwtRb2uI/vYQZkoTCyUxbJnLnQWVXrJyLuJLvdaZxMewZxK945Ix2PZ9UJbM35UBS+/MJDJmElzZmQTruK69meekZHEmYXF4M0lhKg6dOyHUk0m6IPM8VV+fSYiG2uDwb6HpdxDshJ4DYMZPrqNhzzxXycjp9bdnZeodG8q8btXXZ16nZZ+EovmZfQLt0Phipvz27ZnnObc6c25dezNJoGHL/M/EBjPn27krk7gV1IDFlqlzViHY3GBYoe5OKJh74c/38ec2HoDoYKa8svqzJnHHTedk7mrgIa31LcP3vwSgtf7/TtjnHsYgmQNoOzDAz/9l22mXW49LdnbS/PFPkOruxv+B95M104bX3ITqznxDNq1uXs37CD/oqmBXrIh+az6rZxdQmevOtNzNysN6jhFE52KmTdKkQYNGs6NnB/+y9V/Y1Xvyt3S/w8+NlTdSX1yPBQtOq5MVxSvIsmddUvlCTFeTlMyNSwxb6HTpHz50F4u++K0xrvHoIoEEbQcHGOqJklPkZqArQsuuPnqPBUf6ZuWVZbHmI7MpmZONcYmx7pwCHZnfruxMC1PTZtjxI+jec+b9bZ5MC5LdnUk6INMKVV4PK/8X1N6W2XahCafWmeTGOtwq2N8ErQ2Z7fPem2nZGTyaaZ2pWJFpdROjM5PQvS+TFA+1ZVrr+hoz27OKwFucaRHr3pNJgBd9NJOIDTRn/mYbo5kljuc9w/8Px4LH+M8d/8mRwBHqCuqoL6pnWdEy/A7/WQ5ytsNreqI9DMQGmJMzB4uyEEqE2NO3h4SZIN+Vz+yc2dgs7zQITedkbi1wq9b6T4bv3wWsPDHoDQfC/w/oIfMN+LNa62PnOvZofU5+8a/b6Dka5A8/fxU5xae/6cyhIbr/5V8I/PIZ0uEwtrIyCu78AL5lJaj9v4R9T4/sG7Dl8waL2Rkv5mgqh7izAH9VHfmFJdw0vwibYaEix33SZdmLobXm1bZXaQu1YWqTWCpG01ATLzS/QMw8oe+GxYbdsOO2uqnwVuC0Osl35RM347itbqr91RwJHCHbkU2Ft4JKbyW5zlw6I52EkiE6Qh00DjbSGmwl25FNgbuAQndh5seV+V3gLsBldTEQG6A50EzzUDN+p58qXxXhZJhIMsKC/AX47D56o70kzARlWWXSX3ASDcYGORY8RoG7gDxXHrFUDLthx2GMzYi6qWKSkrlxiWGz/Nn6x1XFbP3gH1J3z/+mriIbu3V8kqdELMXmHx7g4FtdI523jyua6aO42k9hlZfCGT78Ba7zan0z0yZtoTbKveVY1DnqbSahYycc/HXmsl8ymrnM1r7tpN2SwA8q5tFXNI+5hUvJCrRTml3NsfgA6XAP9SnINTID19zZFdirroPSZWC7sNasVDrF4cHDhJIhIskITqsTr92Lx+qhwldxQccSlyZhJhiIDVDkKSJhJmjoamB793a6I93M9M9kpn8mm49tpjXUyoriFXy05qN47V46Qh282v4qRwNHaQu1UeQuwtQmLYEW7BY7n677NHnOPN7qfIvWYCutoVaebXoWw2IwL3ce+/r2kUgnRro65bvyWV68nJUlKynNKuXQwCGeb36eLZ1bKMsqY2H+QhyGg/ZQO9XZ1fjsPp5vfp59/fsAKPGUUOWrYmfvTsLJ8Mj5FXuKWVG8gsH4IN949zewGbbLOpnLA0Ja67hS6n8Bd2it/2CU490H3AdQWVl5VUtLy2n7DPVE+Ok/vY1hKD7ypeWj9sHQqRShl1+m97FvEtu9G2Wz4Zg3D/8t15PubSVrrhdnah+0vJ7pbzEsiZUX01exMbWGfu2jQxViz86MuFpU7qfQ66Aix01dZTZl2S5ePdTLS/u7QcGq6jzml3hZWpGTGW5/DqFEiN5oLxpNX7SPl1tfJplOEkgE6Ah3EE1G6Yn24LQ6GYgNEEgEyHHkEEwGSR1vDj9FobuQCm8FQ/EheqI9F7XkmaEMbBbbSKLpsXl4f/X7+fCcD2Mog8H4IEPxIYo8RfjsPtpD7RS4C5jln3Va0nf8f3PcL9+cImEmeKXtFY4MHSHXmUsgHuDt7rc5OHCQHEcOdsOOy+YaGdySSqfIdebitXuJpWIUugspySqhO9JNIBFgUf4iCt2FzPDNuKAkSms9cu5pnaY/1k9nuHPkR6PJd+XjtrrZ0bODznAnR4NH6Yp0sSBvAWba5PWO14mfelmDzGtd6a3kmtJrSOkUNouNFcUrmJMzB5fVRSQZoS/WR64zF4/tnS8+CTNBT7SHYncx7eF2Dg0cwtQmSwuXcix4jGPBYxzoP0DTUBMWZWFJwRJm+WdR5s0MDhqL13J//35ebn0ZM20yO2c2ywqXke++tGH9F2MsY9iJ8au8sPqqJ2bZKRyCJ9+1hh/6PsiSimz+4cOLmFfsHZPnUGtNy+4+Xv3xIQK9UepurGR2fSHZhW76O8K4vDb8BWfuznHi/yW88z/xvT3fI5VOsadvD3v69lDqKWVJwRLWlKzkfWXXYXiG+yubKdj1E9jxZKaVKxnJXBLLmw32LCJ2F0/lFeOwZ7HI4mG7VfOD/p0cCR3DarGeMX7ZLDZunHEjLx19iXxXPnfW3kmhuxC/w4+ZNmkaamJHzw6aA82Uekq5ccaNtIZa2dq5lQX5C/DYPHRHuvndsd/RFek643mvLl3NA3UPsCh/EY2Djezq3cWasjUjU1W90PwC39r5LUo8JSR1Ep/dxwdnfxA07O3fS9JMUptXy7vK3zXy/J36XF5pzLRJMBHk0OAhtnVvoyXQwqzsWeQ58/jO7u/QNNTEvNx5tARaiKaiWJQFn93HYHwQyLzuM3wzaBxsJNuRTbW/mp09O0npFHaLndKs0pHXc5Z/Fu3hdsLJMKY2R/6P3FY3H5j1Ae5bfB+F7kLiZpxdPbto6GqgK9JFa7CVbd3bToqjha5C1pSvoSvcxa7eXSTTSUo8JRwNHCWlU1R6K7mj5g68di+bjm2iN9pLla+K91W/D4/NQ1uojZ8e+iktgRbynHn8183/RbYze9omc+e8RHHK/gbQr7U+Z7vn2UaD9RwN8tN/2kp5TQ7v+9PFZ30j6XSa4AsvENu9m+Cm35E4fDjzB8Mg693X45w/H1uOl6z6eVgtQTj0IukdP8ISfWcARKe9kre8N/FSsIJF8bc5lCpkg3k9enjxjSJf5sO9K5D5R5lTmMU1s/LIz3IwI9/DLQuKcFgvrWXLTJsMxAdGko+uSBdHg0fpj/ZTklVCli1rJPCdKJaK0RPpoTvaTXck8xM34/jtfmb4Z1Dlq6In0kNnpBOv3YtVWXmt/TWiqSizsmdhKIOGrgZ+1fQrzBM7w56B1+7l6pKrmeGbQWuwleZAMy2BFkxtku/Kp9BdyJzsOZjapDPSSX+0n2Q6SVqnMbWJ1+Zlbu5c8px51BXWsbJk5TkTp3AynEmItSbXlcux4DH29e3j+3u/T9NQ00n7Hh+gEkwESaaThBIhBuIDGMrAarHSE+khmopiN+xnTJ4ArMqK1+7FZrExL28eCkWRu4gcZw6d4U729+9nMD6I3+EnrdMcHjyMzWLDZcskV8njnXxHOXahu5AiTxGF7kL29e3DbthZWriU1WWrGYgN0BvtxWk4iZpR2oJtHBw4yL7+fSgUerhZxqIslGWV0RXuGvl2uqhgEV6bl/ZwO0cDRzG1OeqHKoDdYmdW9iyS6SSNg40j2/Nd+fjtfhxWB2VZZczNmUuWLQvDYvBa+2sk00nqCupwW904DAd2w85gfJDmQDP90X529e46af7H41aVrOLbt3x7Sl5mPWX/84phlQU1+vsb/h/qS/8HBez4o+U83nsHAyHIdtuYW+jljuUVfHhZ2QUnArt7d3N0xwC9LxkE+2L4Cp3M+6CfvFkuvDYvR4aOMBAfIJQI4ba5R5L0PFceB/oPsPHgRt7ueptry6/lXeXv4vftv+c3Lb8BMh+sDsOB0+rkE7P/kJ3tr7Nv6DBdqTB5pkmJ4SIvmaAiEqI8laDEXcSqius5nF/F08ke3ujZTluoDUMZJ111AKjJqeEzyz7DqpJVtIXaCCfDtAZbKfYUY1EWNhzYwNOHn+b68utpC7dxaODQaede7ClmVvYsmoeaaQtlxqNU+6tpDjST1mm8di+LCxbzvpnvy3xJsrmJpqKEE2GOBI7w33v+m8H4IA7DMfIeN5SB2+ombsZJpBPM8s8iTRqn4aQ11EowETytHsuLl/OB6g/w3T3fJZKMcNus25ibO5fX219nMDZIlj2Lcm85Vb4qrq+4ftRJ6yPJCHv79rKkYAk24+xXgMy0iWExCCQCHOg/QDQVJZqKkuPIIU2aznAngXiAOTlzWFa0bNTYGTfjmdYydxGBRICB2ABV/ir6on1sOraJGb4Z1BfV0xvtJd+Vf9L/Z2e4kx09OzCUQdyM81r7a/ym5TdEU9GRffKceSMDCPNd+Xxw9gd5q/MtanNrubbsWpYXL8dtc9Mf6+fw4GFm+GZQ6C5kT98evrv7u/REepiXO4+Pz/s4lb5KLMqCmc589hgWg95oL3/3xt9R5C7iw3M+THV29UmXOkcTN+Ps7NlJf6yfIncRiwsWj7Q6a63R6JGyIqkIHpvn3K3Sp5jOl1mtZC473EBmpNcW4BNa6z0n7FOite4Yvv0h4Ata61VnOt6JzjW0f+emVl7ZcBBPtoPqJfms+eicc86YrdNpku3tKJudvse/TWjT70gey1wtUXY7nmuvxbNyJbbiQnTnHmIHj5Ae6sGaOIrbeghXfiLToVmn6StcxW9m/zUL5i9iYVlm5un2oRhvNvXx36+3cKQnRCA2PGGx18FVlTkcG4gQSZhcNyefT15TxayCLGJJk3gyPeqlXK01O1uHaOwOAeB32ch228h22+kPJ9jVNoTdUCybkcP8Et+4fUM83loDmf5+PruPlkAL4WSYSl8l7aF23up8i9faXqM31kupp5RK3wyKXOV4bE4GE310hDs4OHAQm8VGiaeEfFc+VosVQxkYyqA/1k/jYCOD8UFMbeKyurim9BrqCuo4OHCQYk8xxZ5iwskwcTPOs0ee5cjQkTPWtyyrjL9c/pesKllFf6wfl9V1znkEtdakdRqLshBIBGgPtZPtyMZr97K/fz+90V4ODBwgmAgSToY5OHAQhaI93E4oESLHmUNtXi35znwG4gOY2mR+7nxMbRJJRnDZXBS7i0fOo9hTjKEywSmQCDA3Z+5JLWjnqzfai9vqJpKKsL17OwcHDtI42EiRu4ia3Bpag6282fEmqXQqk1DnzKHQXcjRwFHKveUsyFtASqfY0b2DGb4ZVGdXU+opHflw6Y/10x3pZm/fXho6G4iZsZGuAsc/UCHTUuixec74muQ58zLPT27tSLL63pnvxW1zs7dvL1prlhYtnYxkblxi2IzCGr3hW8+S49tO8k//D/sr4JGPuPFnLyac0IRCfgZiAXLdTqqy5rG0Ok2ZrxC31Y3b5qY8q5xfHfkVvzv2O3qjvRjKwJP2sezozaiAg8rB+fR52mmZ8TZbvZswLWdOys+k0lvJ8uLl/PbobxmMD+I0nHw0ewEFnXu42VFCcTQAfU1Yhlv1NfBi+UJ+5/XRF2qj1+aghSSxU77c2S12rim9hip/FQkzwS1Vt2Cz2DgaPEpNTg2zsmedMz4NxYfwO/wn9Vcaig9hWAzKssoo9hQDmVbutzrfwmP1sKhgEal0irROY7PYzlpGOBlm48GNdEe6qfJXMT9vPpuObiKcDGM37JR6Svnw3A+PJAehRIht3dtwWp3MzZmL2+rmqcaneHT7o/TH+inxlDDTP5M3Ot7IJJM2LyVZJQzFh0Zak4o9xawsXonT6iTPlYdCYWqTY8FjvNz6MsFEkEJ3Ie+peg9rytdQ5inj5baXeebwM7SF2nDb3OQ4ctjbv5cFeQs4MnSEUDJ01ufRY/OwrHAZpVmllGaVMjt7Ng1dDbx87GWahprQaJYVLqM50MxAbID64nq2dW8jlU6hUMzNmcuBgQPMzp7NVUVXEUgE2N69nY5wx2nl3FJ1C7OzZzPDN4MlBUvwO/wMxYfojfZS4im5ogb7TdtkDkAp9V7gX8kM6/+O1vrvlVIPAw1a66eVUv8fcBuQAvqBT2ut9496wGHnSua01ux8qZWOxkEOb+uhemkBt/zJgnMmdKdKJxIkjhxhcONPCf7mN6Q6O9/5o9WKxeEgHc5cI7cW5GCvqEQlBmGgEYtKYTg0ntl+vIvKUC4vlC3LdPKcdQPxrFLeOtLPk28eZX9nkAKvA6/DyquNvcRTaUr8TvrCCcy05ub5Rcwp8jIQTmA1FPNLfLjsBt948RCHus/+xj2uPMfFNbPy8LtsZDls1BR7cdkNOoeiOG0GgWiS/nASl91CodfJ20cHeHdNIStm5nKwK8jhnjArZ+ZSnnN+/WpOFU+ZBKJJ9ncO8vNtXTy3u4NIwsRuWFgxM5frawp497xCqvM9Jx8/1EPItNCfclHsd7KzrYe3OrdwOPwW2/t+T3ekm1xnLkPxoZNaB5cWLuXasmtHAnxvtJeyrDJqc2sp85Zd8Leqi3Xit7rj99E6M3Hl8RFQfYfh8EuZEVvt28FXmhlab7FB74HMqDuAWe+GRWsz2ytWZi5d9ezPdDCODb4zmi+3mkQqzYHOINUFHjyOyVmOJ2kmiaQiRFNRClwFGJbMN/a4GSdhJoibcVTaQTTupDrfQyqtMdOaaMJkMJqkKs/N/s4g0aTJVTNyJ2tqkjGPYXMqF+gvf+JbrHt4FaFf/ZSOL/8NCbtm+6IsfnV7GU3RVgxcxM04aRUDrUCdHMetysZc31VUeqvgSBaFu2bhTDjR2QmMIgvHFmwlbQ9QnlVJIJjN/s4APZEBZvqqWFBUzqLSIgbivbxydCsLC2eT5Y5ixYdfL6I8x4M1dIyjOzdQ0/wUpYEWQjnzcdksGC7/8MjQwsyUDiV14C06qW5pnSYQD3Bg4ABvdLzB7OzZrClbc9GdzaebpJlkZ+9O5ubMxWv3EkgEaBpsojavdqRFLG7G2da9jW9u/ybt4XYiyQiBRGDkGIWuQuqL61lTtoZfHfkVb3W8dVLLfW1uLYvyFzGUGKIn0kNtXi1vd71NubecD8/5MNmObOyGnf5YP4YyKHYX47F72N27mxdbXmRf/z46wh0jXW0MZbCqZBWLCxZjs9h4Ys8TlHhKWFq4lE3HNnFD5Q3cNvs2ntz3JG+0v8Hts2+noauBxsFGXIaLusI6lhYupa6wDqvFikIxK3sWVsvUWgpsMk1YMqeUmgHM0Vq/qJRyAVat9eltyFPAhUy6ueO3x3j1J4eYd00Jf3DXvItundJaY/b1kezsQlkU9upqLE4nqYEBwq/+nsDzvyYdCKITCXQsTHqom9RQlHQkgeExcBcpEn1RUGD3prGWzyLtLEQnEzh8CbIqwJlvEDfc7EiU8Yq6imjOfCypJD/f20t3KIHXaSVlaqLJTNIyM9/D/e+qZsXMPBQwFE0yGE0yGEngtBlcNSOHRCrNK4d6eG53J7vbhgjFU8SS6bOfLGC1KFKjLFjssFpw2gyyrCYfVS9ybbqB8nQbNqVRxYtwVizB0bUNnUqwb+6n+XH/LH72dhvB+HBrpMPkEzWaBdkp/C0vUNjzOqRihHFx1FZNjgozI3mYtqwFLA3/njSwPT2LoHYTxEVIu9itZ/Kr9EoiVpNrq6t51zwfoUSIzkHFzAInZd489nYEGIgkqMrzMDPfQ3mOm5n5ngvrbK51ZvoDqx2qrgXDRjwW4YX9Axzq6CXe30YiFmWeN85b7XEG44qrCjV3zrfis1vg8Eskug7QlzDYZ1vIQF8X16S34lMR9lNNuaWXonSmX+ZRithvraXCHqQ4cRSl03RaS+nyzCMaj3Nt5Ld4dPgcFYY91gVsTc2kxGznCKX484pZ4B4iN9pCyCzkWPoDeBya/KweXAWF5NYtYmjTvzIYCnPEvYjcLDelqhd/di4OXz5mKkU6NkQsbwGDvR30DIU5ZMzBbjOo7fk1FX2v4gsdySSoFctRJUto7ItzrDdAW8qHM6eEWkcvpeG9uALNoBQ/yrqbn0SW0tgdJGlqSv1OesMJEqk0oJmj2ijLUvSEEswqL+Hf16+9bCYNXrJwqb5vzddZcmMFa9bOIfLy8wx8/QsEDsTwLJiB76OfJOvm95L2eXh2326+8fwAOZ4kWqXY0XEMT1Yfof451EX9XBW3kpO20G9ofuWK02l95z1rWBTm8Hs4222jIsdNU0+I/GQb9eogLhWnV/tJYEVZDAZMF3aV4gOW17nD2IRVpdmXruRrqY/w2/Qy8rOcI11EbqzNfNHTZGLFldwvbKwk00kUCkMZpz2fkWSEtzrfoivcxfLi5VRnV49JmUPxIQ70H6DSVznyxRcyyabNYjvjl94z9QM005pXDvWwcmYeruGpwbTW9ITiDEaS/GJ7G8f6o1w3t4Bin5P6qhycNoPndnXwnd8f4WPLK/nQ0jIsFkU6rekMxMhyWkedHmw6mpBkTin1KTKdc3O11rOUUnOA/9Ba33CxBY+nC51B/c1fNtHwq2ZmX1XIu++aN2ELB2vTJPTKKwxu+DHxQ4dwzKoGM0Zi/27MQAhlzSRVqUimPja/gdWt0fEY6ZQiFbVl5kpUYHG7yFpVh23GDAZCFvrW3MiSBTNwF+SDzYbZ20uipYXE0WNY8/NwLbsKI8tDqrcXIzf3pDmt4imT3W1DJFKailwX8VQan9OGd6iR/kP7iIe6qYy8weGYDyPUTmH8KIbTy5aCtRwKziS7bTclgR1UWXdTrFrocM7giGM2AxHFnPQB5lqO0aEKUFpTpnp4Pb0Ae3Yx5ZZ+fPEOXNETWjgtVvTM62kOz8Sa3E/2wA7SWOhw1zAjtJ3fqqtx+vJZZDkC8RBZKoojFcAaH8RUVto8C/j32HuIRsJoFL+3LGMwlRn4YlGQ5bASiKWwkGaxauJW5x7mZYU5RhExdxmzLB10xgxeC5WxSDVyffwV3CpO2mrDxMBhQFk805eyk3z2eFdzbfBXRLUdJwkc6uyXsIIWL2+bs/HrAIstTcQsHtp8dQwaeRRFD9GuC/hNeBb7jUUs8/tQnZ1stpcQcGXhdjlRhoWBcJJivxN7KowteAwzEWa55RD9cThGEYncGqorK3DHe5nX/1tW9D5PVlc/UQqwDAzQ2V3FYLqMIX8VR0tvxIKJxoJWmaBrV2FqXL+lzPkmlbZGbCpB0rSzJfxRjiaWkdIOimwHiaW92C0R/EYn2dYOvEY3MdPD/nQNralKLMAKz8+pNfaDtmAqGy71ztxSh9MlHNTlVKkuai1H2eWsx+LMwW8G2afKSFpmoo0cKsNbKAs1YJCkP1UJZUuo/sw/XzbJXH19vf76X/yA3a+08f4/XcKMhXkQDzH41x+m45dHQSsc+TaqHv8GlrnXnzTdxjM72/nBS03cmHQQOxzEXeamsC6fG26u4sUD3SgUOW4bPaE4BzqDuGwGy2bksKrUinHkd6R7G1Gbv4pKJ0atX1pZaan6COGlf0y7pZx9nSHmFGXx5JtHaR2I0DEUI55Kk+WwDrea5vBfn6zH78p88CbNNJ1DMdx2g7ysM/fNiiZMlALnCSs99IcTdA7FyPXYKfafPkq1NxTnlUM9lPhdrJyZOyYJZCxpZuaFtVp4o6mPHI+d2YVZGEoRjKdGzmkqO9gV5D83N/HR+nJWVudd1DHSac2e9gAt/WFuml9ELJFmd/sQWsPK6lxsJ1zVOtIb5icNx8h222gfzPR9bOwO8WpjLxW5LvyuzHaLgt5Q5v9MKch12+kLZ+6X57go8jnZ2jKA12klGEvhc1rJy3LQORQbabBYMzufz940l/wsO5W5bpRSpMw0ptZn7WseefttzP5+sm64YeT/JGmmCcdTeBxW3mjqo8TvZFZB1sgxm/vClOe4T/qfHEsTlcxtB1YAb2qtlw5v26W1XnSxBY+nC03mtNZse+Eor//8MA63lUXvKqd2dQmuLDs2xyRNq5GMZi6P2T2kzCwCzz1PZOtWzL4+lN2KJdmPVQ1gtQyQDodIhU0CR12k0nZirlwspsmQvxpbOoY30QWRKDFnDvZEAEd8EGWxYPXaiURsuHLBeVUlnc5ldEarSKStpO12rASwJIP0JmeQY+9hIJZHXGfmsssy+sE0cRLCaU0Rj6QpOvJ7XMEu0spK2FNCwFdFacfvMcwEB+d8hIGceaDTWM0oRjqGI9lPSfd2tNUgyzZIeWE3hVcVY5s5D0vJXHDnkXKVs/mnPezfE8PvMVl5FeTZgwy2BbAuX43Z3wdmEltuNq7iAnJnFWU+21obYP8zsPcXMJDphxUyc4mSja/ITbBoOdl92zF69oLFQKdNSCU5Eq9nIF1MreNlPMYgfclyupI1DJkl9CZnciyxGI0VwxLDZgnjtAzS6Uhj8zpYHNmJNzVAOMdBcaGXqjIX9pIasDqI2XOwJcLEDh+jqz3Ic5Fc+rP8RPe1Ux2JMTfbR07gGCFXEd5cF/m5aeJhk0AgRUtLmlg4iSvah3/oMP5AE1YzjnI4cMyahee6a0n29BLft49kStE3990MFC4muzqXgnQ30eY2+vs1rsQAWeF2Eju2MmQvoj93PloZdBVelbkkC5R0vUFF90vYQgESNj9xRzYdZavoya0DFFaS5PXuYshTScyVjy92lFR+LvG4C7sRI42DeNx62jQXDE+GbaTj2FMB4vY8lIIFCwzsuS5iXj8Ri4N4OEk0HMN++AhDQ1aiqcz/m12FSegz9wksn2nwwS9ef1klc6+9+gZPff1tBrsifPCzyyia6YO0idmwkfDvX6btP3+LMyeJZ5af/L/5dyxzVqPTmobnmtnyzBFQiuXvq6L+vVVnT2rMJDR8Fzb/wzvzs825GW76v5k53sI9mX3SZmbiVm1mliNyjn5JNJJI8fLBXl451IPNsPCDN1uYme/hi++Zh8tm5Us/20lzXwSl4A9qCrmhtoi2wQg7W4cIxFLke+z8/nAvsWSaPI8dt8Mg1+NgT9sQqeEF1G+YV0hptotllTlU5Lp4alsbP3rr2MjVgkKvg6tm5HDzgiIKspzMLsw6YwJ4JrGkSetAhM/9ZCfbjw3itFkozXbR1JNp9VYKbBYLCTNNWbaLz940l7VXlTMYSfBGUx/tgzHmFGVhpjVbWwaYVZDF83s6sRoWbppfxPU1BWPWohRPmTisBkPRJMFYkkKvM9O/Om6yvXWQ1xp7+e2+bhJmGqXgEysq+cwNcyjyZZ4LrTVvHx3gcHeYGXlurpqRQ3NfhEAsSUGWg9/s7eKHL+6iJZzGZqYoC/dg9/vYZ2RjDr/HfU4rC0r91Jb46AvHeW53J0kzjdbgGk58zLTm/utn8dL+LmyGhdoSH8lUmtoSH3lZdpaUZ1OZ66axJ0Rzb5h/e+kQsWSadSsrWbdyBi/s7eT3jX0j51id7ybc3MIrm7bRi439OTOoLsiiriKbN4/00x+K85fXz+C6xRXk732bwL4DxLPzqbrtVn779/9G5c+/j0qnca9aRe5dd3K4egl/+eNtHO0J4fJ5GIxkLlmX+J3UGlEGm1rY7q+kNNfDPddUMb/ER50fnm4Ks7sjQDyZpsDrGPm5akYOJf4LmxNvopK5N7XWK5VS27TWS4c7/r6ttV58sQWPp4td27DzyBDbnj9K046ezIeRgoXXlbH6D2djtRtTYhi5mUyza3MrVYvyaT80SNvBAVa9p4jUvhfZvstHY6ONRPLsCaiLAUojb2OPDbE/54PoE5rKHbE+HPEhrGYUXA7SVhfZRhdhexEee5KcRA+RnhCDCS/oNHFnNkmrh7RhJ+oqOKkci9Kkdeb5slpM5ng70ckUsYQiGk0zaBQQt7zzAa3SKbIHD2E1YxguByoZJ2ArJJxVRlHnWwz5q4m58jFSMcxRljizpuMUFlooWlCGryQzuKRr+17aOx0EBjP/63nuborZTnFOPyHXEo62+/E6o7RGKonE3gmyXo9JMJx5Li0WjS/XRlmJgTPbTcJwEw0mCfRG6W45c28Dm11R5gvhiA0wlPLQF3KQtLoxzDh5vbvwBY/SUbyScNboS/gAWHQKlz1NJGUfnusy06fObY2THTlGKKII+mZgKBMTK2llxZYIkrR7z3pcp8sCFgvVdQUsuK4Mi2EhryzTJ1Enk6R6e4nu3s3Ak0/Sf6CNIaOAvqKl9BUsItcTZ25WO87nv4c5MHDygT1ezNp6hpo6sSbDOOJDZFUVk6yczwE9n2RS404NEoooerPnn7FueaVu8vMUbnsKe3EhgYEUxTOzyPanSKQMkmkHybhJTpGbghlebHbrZZXMNTQ0EB6K87N/2koiZvKHf3nVSWucDjz5fQae+DbxY904spN0Lv8gTbbrGQq7mbuiiKs/NPukNS5P0rkbml/NTMD6+29A/+FMF4Hrv5Tps5tbfeGT657F5oM9/NXPdtE2mBm1WORz8OAfzKFjKMrGra10BeIYFkVtiXek1WZVdS4lfhedgRihWIrOQIylFdksrcxmZ+sQP9/WRjCapKyzCXcyxoAnmztK4Jrbrqdr82scOdLO97IX0xrOtOAoBdfNKeB/XVfNquo8Nh/qoWMwRrLxIP7v/SdvXvdhQjPnYm7bhuPIQXpc2UTzirgjL47lWAsdMZizagn2SJDOtJ2Oqvm4C/L4zb4uWg60sEb3keruxp2I8FrpItqyTo6FuZ7MAu594QR2q4U/Wl3Fx5dXsv/gMQb3HeAP734/nYE4//7SIRpaBjDTmpn5Hjx2K7fXlXJjbRF7OwIc7gmR47ZjpjU/2XqM5/d0cXtdKS/u7SIQS6HUO/PhApT6nfxBbSH/67pZPP7qEf7njRYMi+Jdcwt4o6mPcMIcudQOmcvtg+EENx5t4NaWN8mPDlEUHUAP/z+o4YMPlVdju+EmEsqgc/9hAoEIoXCM4tggOVkO5v7ZA9j9XjzZPoyCApJpMI42Y3G7iO3bjzk0iHP+fOzl5QSeew7nggV4VmXGBelUiuCmTaS6urG4nCQ7O4nv34+9aibu5fXEDx6k/wdPkup4Z0BFtKSCxtxKkoEgpdF+coZ6cSRjDNk9+BPvdD1JWqzY0ik2ly0hOKuW9+x8HmNwgCG7B0c6hdWi2L3s3VRWlZCIxlBvvUFRR2Zmg/DMueyzZjMYM/EkY1zduYcmXwl7ymrpyS7iDW8Vx9yZlk/DonjfohI+tKyM5t4wbx8dxGm1UJnr5kBXkGKfk1mFWST7+kn85gX++Ot/icVimZBk7h+BQeCTwIPAA8BerfWXL7bg8XSpC1UPdkVo2dNHf0eYva+043BbycpxMNAVobI2l9n1RVTXFYy02o13kpeMm/QcDRILJznwRidN23uw2i2kEif3bbNYFXPqiyib5cZs3UVRuY14xGQwaCftKSGrpIjIsRbaDvZxpMmGaULV4nwKZ3gxIoOUZvVTmHuUtL2A3qdeJ3qgkXQgSKKlBdLDLSu5ubgWLcK5aBGuRQuxFpdgcbswCgppbwqTjJsYNgtunx1fgYtdm47hcNuoXlqAx3/yh4tOa4L9MewuK8G+GHteOEjHwX5SiRRmLEnaYsXj1sye62D+dRVoh4udmzsJRzTFVVnofduxFRWB20NyKES4rZvO/T0MqHwi7qKRy4QOu6a0Jo/CXJPkwf209LoJmh4S6czla3e4k5gzl+zBQ5S1v4or1kNP/hICvir8Q0cojhwge04J8e3b0dHMB5J91ixy71yXWT+yrZ+BX/wSy0AXqqCIPjOPtNNDv6ea/px5JOxePNFucp1hcueVE7X6OdoYJZZQZHmg/rY5FM7MZqArTG6Jh/72MIMdIdw5Ljx+O6VzsnG4bSRiKbqOBOhsGiKVSNN7LEhfW4isbDuF1dmYCRPDZjB7kQ/3oTcZ7IkS85WSVTuXopoCgn0x+tpDmKk0vnwXJdV+1HnMaQjDAzViMTAMLPZ35mc0g0GiO3aO3E8HA4Q2v0xs3z6y3vUunAsX4FpSh62o8LRjpiMRep7fjD7aRKgvTOxIC+ndWyGZwHbCdAUYBq4lS7CVlmLxZmFxu9HxBLG9e8E0ca9YQdHn/vdll8xBJhb97GtbsdoN/vDzV532Hur71bO8+L3D9OYsIHdwH7Msb1CzPA/fLTegcqsya3YOHcssedX2dmZZpaOvvXOA/Bq4+f9mWuPGMYbFUyavHuolnDBZMzufXE/mf0hrTXNfhFy3/awTrKf6+wlt2kSqtw9baQn2GTPo+OuvED9wYNTHWIuKSNQuJOnx0WTP4edBNx1Jg86iGahgkIV9TTyw8ynyYgFiNgdRm4ucyOBpx1E2GzqVOjlLAixZWRgFBSSam0eSnMwDFKmcPLTNjqekiOD7/5D8g7swrAYdi1fxZDibN17fjS8e5i/e3kBZuJfOnBJez5/LK5XLqFy1DKthobk3TG8oTlcgTkWOk/6uARKGjaSRiVsum8Hq2fm8uK+LxeV+Pukdwmxuxva+9+N2OphblMXMUwaMHe2L8K+/Pcirezv4qL2HQsOkKNvD7GIfRwci7N/dxOJDW8g9sJNIRTXuubMpWLIQnUiAReGsqSHZ2cnAD54k0ZRJcixeL8rpQBlWrAUFpLq7SXWdea6+0Vi8Xqp/8XPih5vofPjhkZkijrNVVJBsbwczk5y7r16F75ZbcMydS6KpicCzzxFvbMTw+7CVV2ArL6PP6iZ4oJHm8hqGVl6Hfd9u4r95nsLb30/8qlX8628P0TsY4aruA/zh4F5WzS/HiIQI/vrXI+U65szB/6EPYcny0PvoY2BRmIkkZijMnqXXM6/7MPZjzehkpiXPWjOPxPU38ZK3mh8cjhKJJQk4PKxM9XDb279kdk8zbXnlPFF7K2Ft4ctvfY+8eJDCjT+ldP7cCUnmLMAfAzcDCniezKLSkzcU9iwuNZk7UfuhQfa82kZkKIG/wEXL7j5CA3G8eU5uvGc+DreVXz26E9NMU1Ltp2J+LvkVXgoqsrAYFsxUmsGuCDklHkIDMQxrJtHp7whz8M0u5q4sIq/0nWW4UkmTfb/vINAbxeW1M9gd4dCWrpMSt+Xvq6Lt4CD+AhdLb67kwJudZGU7mLmkAE/2+U1KGx6K03l4iJl1BeecpDgdjRI/3ISRnY2trHTSWyfPRmtN5K0tRA8eYmh/M6FXf4+t6wgWhyMTkJTC4vViDgWIzVpG1po1lN9UTzoexxwYxFZUiHK7ie3Zg624mHQsRvDXzxNvbMS9fDmeq1eR6u2l//v/8868g4DnmqvxrF5N/OBBbGVlmKEQ9vJyvLfeiiUv/7Tlj7TWhAcTuHy28V8aaRpJR6NEt20j8vY2rEWFWPPziW7fQeSNN0gNDJAOBklHImCx4Jw/H4vDgXPxIoo++9nLMpkD6G4J8NQ/b8PptpJXnsXMxZn5uwK9UZp29DLYFWbFVVaKfv+fhN98G22Cb0aE0pWDnNw/XWUWCp/3flj80cwi8EWLMmtRXgIzGGTo6afR8QShzZtJdnbgWXU1WdeuwbNmDTqZZOjpp4lufZucdZ/AfdVV533sdCJB72OP0f/4d0Y+MI8z8vMp/PM/w1ZWRrKzC1tpKeHXX8NRXY2Rl8fAkz8kfugQ6aEhzKF3JkAPZhfgCQ5gMVOonFwqvv5P9Dz2GIbPj+9978WzahWpnh4Sx45hKy3FOX8+OhYj3tiINTeXZFcX0R07Sba2kuzsxDm/Fs8112ArLQUUgxt/QrK9HZ1IEt22jWRrK8rhAKUyX4hOaD4zs7y0veejBDdtYt7gMYxUEs81V5P3qU/hXrWKwJ69bP67f6N0/9t4YiGwWIi//8NQU0vOwd1YgkPEcwuwHNpPfMcOAFzDz6+ORtHJBGZg+MqB1qRDw7MbWK2kA++Mjj2RtbSE3Ls+Se4n70IZo1/lMUNhdDKBNSfn5NcsEiH08isoh510JEKqpwedSOKYOwcdjWKrqMRWXERs717ih5uwz6yi7S/+N5gmOh7HPnMmhf/7L3AtXUo6GsWal4fF5SLV20vi2DGM7GwcM2ee9//QiU5seIklTRqaBzC15urqvJGBb+l4HJRCWa1nXB9Zaw3p9Mhzo7UmcaSZ8CsvM/SrZ4nt3HnS/kb9Csztb2PxeHBc9y6SDVsyM19ojcrNY8Y3H8W1ZMmEXWb1ADGtM3M7DE9+6dBan2Fl3Mk3lsncqXRa07p/gE0/2E+wL4bFULi8dspqsmk/OEhoIDOZpMNtZWZdAX2tIXqOBrE5DZKx4ckLbRbM4RGjWTkOVq+dQ3gwTtrU7HjpGOHBzGLW6ZTG6jCYfVUhs+oKcPvtGDbLScmfODttmkQathL8zW+weLPIu/tujOxs0okEynb2eaXOddxkaysWjweLz3dSa5WYeJOxnNd4GW1t6befbyHQF2OwKxN2lUXh9tm54Z5aKublAqCTSfr+7R/p+a//wVaUi2/NMpxL6/FdVQ3FC8GVQ7Kzk/Abb+CoribR0kJ023bS4RCOmnm4V67IfOCWl2P4fAz+9GcEnnsOnUxiryjHWlJC4kgzOh4f7mdqEm9sHLnUbistxTF3LpG33iIdiWDx+zMj+KNRlNuNjkTI+cQncC2tI9nWRvZHPoI1L3NpKtHaRvjVV3HMqsZROx9lt9H24GcIbd6M77YPkHfvvdirqojt3k3k7W34P3g7tsLTW3zPJNnZSaLlKMm2NgLP/BL77Nn4bn0Pzvm1WJwXsYD9eUrHYoQ2bcK1dCmG30/o1VeJ7dyFfeZMLG43rsWLsJWWkk5rdCTM4IYN9D3xBGZPL9bSElLtHSi3G9/NN+OYM4f4kSaGNv4UyFwlseblkjjWiqO6Gt8HPoCy2eh99FFslRVYs3PAZsXw+TOjvQDD48nMiRkO473hRmylJWjTfOfKi9+Prbz8jEnMeAq88ALBXz+Pe8XyTEuYY/ouN5g4dozo9u2kevsw+3rpf/KHeK+/nuKH/gbD58MMBun7zncw/H78t98+kgxPVDL3BnCj1jo0fD8LeEFrfc3FFjyexjOZOy4RS7H/9U7aDw2w6oOzyC50o7Ue6UN1dE8fh9/uwWJVXHVL1cglNJ2GcCCOP99FdrGbZ7+5i1T8nfnPSmb5WXFbNWVzs0nGTWyO04ehCyFOdrknc8dprek9FsJqt5Bd5B41NoQ2b6bnkUdHLkXn3nsvrsWLSLQcpf873zmppcridmPxek++NGazYXi9mP39OGprseblEW9sJNXbi2NmFcrtRhmZlgsjN5e8T/0J9ooKLD4fymJBJxKEt2xh6Be/wOJ0kf2Rj+Conkn3N77BwPf/Z6RlSrlcuBYsQDmdRN56K9N6DpnWK6Ugnab4ob8h52MfG5sndxpIx+MM/eIXBH/9a9xXX03ORz+K4X9nwEl0xw50KoVr2TL5bJgGtGmetYXzuAkbzaq1rjvXtqliIpK585FMmFiUwrCN/i2ntzVENJQgrzSLZDyFL//iJt0V4kp2pSRzF0qbJh1/8zcjrTkAzoULKfrSF0n19GKvmoFjzhyUYZDs6iayZQuWLA+hzZtJdXaR96k/wb1sWeZYWoNpoqyXdlk2duAA6WAQIyeH/v/5H+IHDqKTmctwuXffTaqzk+ju3ZBK4VqyhKx3veuSyhNiOpioZO73wINa67eH718FPKK1vvpiCx5PUyWZE0JMDEnmRqfTaaI7dmBxu7GVlGD4fGN2bCHE2LjUGHa+X7H+HPiJUqqdzACIYuCOiy1UCCHExFAWC+6lSye7GkKIcXReyZzWeotSah5QM7zpgNY6ebbHCCGEEEKI8XchnR+WA1XDj1mmlEJr/b1xqZUQQgghhDgv55XMKaW+D8wCtgPHh15qQJI5IYQQQohJdL4tc/XA/Kk6SbAQQgghxJXqfGcG3E1m0IMQQgghhJhCzjeZywf2KqWeV0o9ffznUgtXSt2qlDqglGpUSn3xDH93KKU2DP/9TaVU1aWWKYQQY0VimBBiKjjfy6wPjXXBw0uCPQrcBLQCW5RST2ut956w2x8DA1rr2UqpjwFfRaZEEUJMARLDhBBTxflOTbJ5HMpeATRqrZsAlFI/Am4HTgyEt/NOIrkReEQppaTvnhBiCpAYJoSYEs53NOsq4N+BWsAOGEBYa30pU4mXAcdOuN8KrBxtH611Sik1BOQBvWc78NatW2VJLCGuEMZ5rHs4TsYlhkn8EuLKYRgGqVTqko9zvpdZHwE+BvyEzMjWTwJzL7n0MaSUug+4b7LrIYQQF0rilxDiUpz3pMFa60allKG1NoHvKqW2AV+6hLLbgIoT7pcPbzvTPq1KKSvgB/pGqd+3gG+BrM0qxJVmklqyxiyGSfwSQlyK8x3NGlFK2YHtSql/VEp99gIeO5otwByl1MzhY38MOHWE7NPA3cO31wIvSV8TIcQUITFMCDElnG9CdtfwvuuBMJlvmh++lIK11qnh4z0P7AN+rLXeo5R6WCl12/BujwN5SqlG4C+A04b+CyHEZJAYJoSYKtT5fElUSv2Z1vob59o2VchlCiGuLEqprVrr+smux1iQ+CXEledSY9j5tszdfYZt91xsoUIIIYQQYmycdQCEUurjwCeAmaes+OAD+sezYkIIIYQQ4tzONZr1NaCDzHJeXz9hexDYOV6VEkIIIYQQ5+esyZzWugVoUUrdCES11mml1FxgHrBrIioohBBCCCFGd7595l4GnEqpMuAFMqNbnxivSgkhhBBCiPNzvsmc0lpHyExH8pjW+iPAgvGrlhBCCCGEOB/nncwppa4G1gG/Gt42aQsiCiGEEEKIjPNN5v6czNJdTw1PilkNbBq3WgkhhBBCiPNyXmuzaq03A5tPuN8EfGa8KjUekskkra2txGKxya7KlOR0OikvL8dms012VYQQp5D4dW4Sw8SV7FzzzP2r1vrPlVK/BE5bKkJrfdsZHjYltba24vV6qaqqmqxFuacsrTV9fX20trYyc+bMya6OEOIUEr/OTmKYuNKdq2Xu+8O/vzbeFRlvsVhMAuEolFLk5eXR09Mz2VURQpyBxK+zkxgmrnTnmmdu6/DvzUqpguHb0/bdIoFwdPLcCDG1yXv07OT5EVeycw6AUEo9pJTqBQ4AB5VSPUqpr4x/1S4vzc3NLFy48IIe88QTT9De3n7OfdavX3/OYx05coSVK1cye/Zs7rjjDhKJxAXVRQhx5ZL4JcTUdtZkTin1F8BqYLnWOldrnQOsBFYrpT47ERW8kp1PMDxfX/jCF/jsZz9LY2MjOTk5PP7442NyXCGEOBOJX0JMnHO1zN0FfFxrfeT4huGRrHcCnxzPil2OUqkU69ato7a2lrVr1xKJRAB4+OGHWb58OQsXLuS+++5Da83GjRtpaGhg3bp11NXVEY1G2bJlC9dccw1LlixhxYoVBINBANrb27n11luZM2cOn//8508rV2vNSy+9xNq1awG4++67+fnPfz5h5y2EmP4kfgkxdZ1rAIRNa9176katdY9S6qLHfyulcoH/v737j466vvM9/nw3uEmsCWxNr0YZf3Rhx8kZTPROoBLs0UUWtFtpu9liG7hiLJzATdztPZS66zls5OzZoxb7wxOweqXFekubNrteWaTXloK35V66zdgENca01BsoJv6ieEMuiZj4uX/Ml2kIMwlJ5mfm9Thnjt/55jvf9+czw7z8zPf7nfk0A1cB3cDnnHMnYmw3zB/ngD2aqG/P3v9vHbzS05eIXUWVXVbMP35q7Ekxurq62L59O1VVVdTW1rJt2zY2bNhAfX09mzZFzlyvWrWK3bt3U11dTVNTE1u2bCEUCnH69GlWrFhBc3MzlZWV9PX1UVhYCEB7ezttbW3k5+fj9/tpaGjA5/NF6x4/fpxZs2YxY0bk5Z49ezavv/56QvsvkkvSmWHKL+WXyGjjHZkb68KEqVy0cC/wM+fcXOBn3v1YBpxzFd4ta34GJR6fz0dVVRUAK1eu5MCBAwDs37+fBQsWMG/ePPbt20dHR8c5j+3q6qK0tJTKykoAiouLo+G2ePFiZs6cSUFBAWVlZRw5ciRFPRLJWTmXYcovkcw13pG5cjOL9RHQgIIp1F0O3OQtPwk8D3xlCvubkPE+gSbL6G9bmRmDg4OsX7+ecDiMz+ejsbFxwj8Mmp+fH13Oy8tjaGjorL9ffPHFvPvuuwwNDTFjxgyOHTvG5ZdfPvmOiEjaMkz5pfwSGW3MI3POuTznXHGMW5Fzbio/s32Jc67XW34DuCTOdgVmFjazX5rZp6dQLyMcPXqUgwcPArBz504WLVoUDb6SkhL6+/tpaWmJbl9UVBS9rsTv99Pb20traysAJ0+ePCf04jEzbr755ui+n3zySZYvX56wfonkoJzLMOWXSOY637lZJ8zM9prZyzFuZ70LnXOOGLNLeK50zoWALwDfMLM/G6PeWi80w5n6w5F+v5+tW7cSCAQ4ceIE69atY9asWaxZs4ZgMMjSpUujpyEAVq9eTV1dHRUVFQwPD9Pc3ExDQwPl5eUsWbJkQp+AH3zwQb72ta8xZ84cjh8/zt13352MLopMG6nMMOXX2JRfImOzSA6luKhZF3CTc67XzEqB551z/nEeswPY7ZxrGWs7gFAo5MLh8FnrOjs7CQQCU2j19KfnSLKVmb3gDZpSVS9pGab8mjw9T5KtppphSTsyN45dwJ3e8p3AM6M3MLM/NbN8b7mEyO/dvZKyFoqIxKcME5GMka7B3APAEjP7LXCLdx8zC5nZE942ASBsZoeA/cADzjkFoYhkAmWYiGSM8b7NmhTOuePA4hjrw8AXveX/DcxLcdNERMalDBORTJKuI3MiIiIikgAazImIiIhkMQ3mRERERLKYBnMp0t3dTTAYnNBjduzYQU9Pz7jb1NfXj7uvpqYm5syZg5nxzjvnTLcrIhKX8ksks2kwl8HOJwzPV1VVFXv37uXKK69MyP5ERMai/BJJHQ3mUmhoaIiamhoCgQDV1dWcOnUKgM2bN1NZWUkwGGTt2rU452hpaSEcDlNTU0NFRQUDAwO0traycOFCysvLmT9/fnSqnJ6eHpYtW8bcuXPZuHFjzNrXXXcdV111Vaq6KiLTjPJLJHOl5adJ0u7H98IbLyV2n5fOg1sfGHOTrq4utm/fTlVVFbW1tWzbto0NGzZQX1/Ppk2bAFi1ahW7d++murqapqYmtmzZQigU4vTp06xYsYLm5mYqKyvp6+ujsLAQgPb2dtra2sjPz8fv99PQ0IDP50ts/0QkMyi/RGQUHZlLIZ/PR1VVFQArV67kwIEDAOzfv58FCxYwb9489u3bR0dHxzmP7erqorS0NDr3YXFxMTNmRMbiixcvZubMmRQUFFBWVsaRI0dS1CMRyRXKL5HMlZtH5sb5BJosZnbO/cHBQdavX084HMbn89HY2DihCagB8vPzo8t5eXkMDQ0lpL0ikoGUXyIyio7MpdDRo0c5ePAgADt37mTRokXR4CspKaG/v5+Wlj/OwV1UVBS9rsTv99Pb20traysAJ0+eVOiJSMoov0QylwZzKeT3+9m6dSuBQIATJ06wbt06Zs2axZo1awgGgyxdujR6GgJg9erV1NXVUVFRwfDwMM3NzTQ0NFBeXs6SJUsm9An4kUceYfbs2Rw7doxrr72WL37xi8nooohMU8ovkcxlzrl0tyHhQqGQC4fDZ63r7OwkEAikqUXZQc+RZCsze8E5F0p3OxJB+TV5ep4kW001w3RkTkRERCSLaTAnIiIiksU0mBMRERHJYmkZzJnZ35hZh5l9YGZxzxGb2TIz6zKzw2Z2byrbKCISjzJMRDJJuo7MvQx8Fvh5vA3MLA/YCtwKlAGfN7Oy1DRPRGRMyjARyRhp+dFg51wnnPsjlKPMBw47517ztv0BsBx4JekNFBEZgzJMRDJJJl8zdznw+xH3j3nrslJ3dzfBYHBCj9mxYwc9PT3jblNfXz/uvmpqavD7/QSDQWpra3n//fcn1BYRmbBpk2HKL5HMlrTBnJntNbOXY9yWJ6neWjMLm1n47bffTkaJlDufMDxfNTU1vPrqq7z00ksMDAzwxBNPJGS/ItNVKjNM+TU25ZfI2JI2mHPO3eKcC8a4PXOeu3gd8I24P9tbF6/e4865kHMu9NGPfnQqTU+aoaEhampqCAQCVFdXc+rUKQA2b95MZWUlwWCQtWvX4pyjpaWFcDhMTU0NFRUVDAwM0NraysKFCykvL2f+/PnRqXJ6enpYtmwZc+fOZePGjTFr33bbbZgZZsb8+fM5duxYyvotko1SmWHKL+WXyFSk5Zq589QKzDWzq4kE4B3AFxKx4wd/9SCv/uHVROwq6pqPXMNX5n9lzG26urrYvn07VVVV1NbWsm3bNjZs2EB9fT2bNm0CYNWqVezevZvq6mqamprYsmULoVCI06dPs2LFCpqbm6msrKSvr4/CwkIA2tvbaWtrIz8/H7/fT0NDAz6fL2Yb3n//fZ566im++c1vJrT/InKOpGSY8kv5JTJaun6a5DNmdgy4AXjWzJ7z1l9mZnsAnHNDQD3wHNAJ/NA515GO9iaKz+ejqqoKgJUrV3LgwAEA9u/fz4IFC5g3bx779u2jo+PcbnZ1dVFaWhqd+7C4uJgZMyJj8cWLFzNz5kwKCgooKyvjyJEjcduwfv16PvGJT3DjjTcmunsiOSMXM0z5JZK50vVt1qeBp2Os7wFuG3F/D7An0fXH+wSaLKO/+WZmDA4Osn79esLhMD6fj8bGxglNQA2Qn58fXc7Ly2NoaCjmdvfffz9vv/02jz322MQbLyJR6cww5ZfyS2S0TP4267Rz9OhRDh48CMDOnTtZtGhRNPhKSkro7++npaUlun1RUVH0uhK/309vby+tra0AnDx5Mm7oxfLEE0/w3HPP8f3vf58PfUgvu4hMjPJLJHPpXZFCfr+frVu3EggEOHHiBOvWrWPWrFmsWbOGYDDI0qVLo6chAFavXk1dXR0VFRUMDw/T3NxMQ0MD5eXlLFmyZEKfgOvq6njzzTe54YYbqKioYPPmzcnooohMU8ovkcxlzrl0tyHhQqGQC4fDZ63r7OwkEAikqUXZQc+RZCsze8E5F3darWyi/Jo8PU+SraaaYToyJyIiIpLFNJgTERERyWIazImIiIhkMQ3mRERERLKYBnMiIiIiWUyDOREREZEspsFcinR3dxMMBif0mB07dtDT0zPuNvX19ePu6+6776a8vJxrr72W6upq+vv7J9QWEcldyi+RzKbBXAY7nzA8X1//+tc5dOgQL774IldccQVNTU0J2a+ISCzKL5HU0WAuhYaGhqipqSEQCFBdXc2pU6cA2Lx5M5WVlQSDQdauXYtzjpaWFsLhMDU1NVRUVDAwMEBraysLFy6kvLyc+fPnR6fK6enpYdmyZcydO5eNGzfGrF1cXAyAc46BgYFz5lkUERmL8kskc81IdwPS4Y1//mfe63w1ofvMD1zDpf/wD2Nu09XVxfbt26mqqqK2tpZt27axYcMG6uvr2bRpEwCrVq1i9+7dVFdX09TUxJYtWwiFQpw+fZoVK1bQ3NxMZWUlfX19FBYWAtDe3k5bWxv5+fn4/X4aGhrw+Xzn1L/rrrvYs2cPZWVlPPzwwwntv4ikhvJL+SUymo7MpZDP56OqqgqAlStXcuDAAQD279/PggULmDdvHvv27aOjo+Ocx3Z1dVFaWhqd+7C4uJgZMyJj8cWLFzNz5kwKCgooKyvjyJEjMet/5zvfoaenh0AgQHNzczK6KCLTlPJLJHPl5JG58T6BJsvoUwNmxuDgIOvXryccDuPz+WhsbJzQBNQA+fn50eW8vDyGhobibpuXl8cdd9zBQw89xF133TWxDohI2im/lF8io6XlyJyZ/Y2ZdZjZB2YWd2JZM+s2s5fMrN3MwvG2yxZHjx7l4MGDAOzcuZNFixZFg6+kpIT+/n5aWlqi2xcVFUWvK/H7/fT29tLa2grAyZMnxwy9kZxzHD58OLq8a9currnmmoT1SyTX5GKGKb9EMle6jsy9DHwWeOw8tr3ZOfdOktuTEn6/n61bt1JbW0tZWRnr1q3jwgsvZM2aNQSDQS699NLoaQiA1atXU1dXR2FhIQcPHqS5uZmGhgYGBgYoLCxk796951XXOcedd95JX18fzjnKy8t59NFHk9VNkVyQcxmm/BLJXOacS19xs+eBDc65mJ9YzawbCE00CEOhkAuHz95lZ2cngUBgki3NDXqOJFuZ2QvOubhHyJJY93kSnGHKr8nT8yTZaqoZlulfgHDAT8zsBTNbm+7GiIhMkDJMRJIuaadZzWwvcGmMP93nnHvmPHezyDn3upn9B+CnZvaqc+7nceqtBdYCXHHFFZNqs4jIGanMMOWXiExF0gZzzrlbErCP173/vmVmTwPzgZiDOefc48DjEDlNMdXaIpLbUplhyi8RmYqMPc1qZh82s6Izy8BfErnoWEQk4ynDRCRV0vXTJJ8xs2PADcCzZvact/4yM9vjbXYJcMDMDgG/Ap51zv2PdLRXRGQkZZiIZJK0/DSJc+5p4OkY63uA27zl14DyFDdNRGRcyjARySQZe5p1uunu7iYYDE7oMTt27KCnp2fcberr6897n/fccw8XXXTRhNohIrlN+SWS2TSYy2DnE4YTEQ6HOXHiRML2JyISj/JLJHU0mEuhoaEhampqCAQCVFdXc+rUKQA2b95MZWUlwWCQtWvX4pyjpaWFcDhMTU0NFRUVDAwM0NraysKFCykvL2f+/PnRqXJ6enpYtmwZc+fOZePGjTFrDw8P8+Uvf5mHHnooZf0VkelD+SWSudI1nVda/eKHv+Gd3/cndJ8lvou48XN/PuY2XV1dbN++naqqKmpra9m2bRsbNmygvr6eTZs2AbBq1Sp2795NdXU1TU1NbNmyhVAoxOnTp1mxYgXNzc1UVlbS19dHYWEhAO3t7bS1tZGfn4/f76ehoQGfz3dW7aamJm6//XZKS0sT2m8RSS3ll4iMpiNzKeTz+aiqqgJg5cqVHDhwAID9+/ezYMEC5s2bx759++jo6DjnsV1dXZSWlkbnPiwuLmbGjMhYfPHixcycOZOCggLKyso4cuTIWY/t6enhRz/6EQ0NDcnsnohMY8ovkcyVk0fmxvsEmixmds79wcFB1q9fTzgcxufz0djYyODg4IT2m5+fH13Oy8tjaGjorL+3tbVx+PBh5syZA8CpU6eYM2cOhw8fnmRPRCRdlF/KL5HRdGQuhY4ePcrBgwcB2LlzJ4sWLYoGX0lJCf39/bS0tES3Lyoqil5X4vf76e3tpbW1FYCTJ0+eE3rxfPKTn+SNN96gu7ub7u5uLrzwQgWhiEyI8kskc2kwl0J+v5+tW7cSCAQ4ceIE69atY9asWaxZs4ZgMMjSpUujpyEAVq9eTV1dHRUVFQwPD9Pc3ExDQwPl5eUsWbJkwp+ARUQmS/klkrnMuek3DWAoFHLhcPisdZ2dnQQCgTS1KDvoOZJsZWYvOOdC6W5HIii/Jk/Pk2SrqWaYjsyJiIiIZDEN5kRERESymAZzIiIiIlkspwZz0/H6wETRcyOS2fQeHZueH8llOTOYKygo4Pjx43rDx+Cc4/jx4xQUFKS7KSISg/JrbMowyXU586PBs2fP5tixY7z99tvpbkpGKigoYPbs2eluhojEoPwanzJMcllaBnNm9lXgU8Bp4HfAXc65d2Nstwz4JpAHPOGce2CyNS+44AKuvvrqyT5cRCQq1Rmm/BKRsaTrNOtPgaBz7lrgN8Dfj97AzPKArcCtQBnweTMrS2krRURiU4aJSMZIy2DOOfcT59yZuVx+CcQ6Nj4fOOyce805dxr4AbA8VW0UEYlHGSYimSQTvgBRC/w4xvrLgd+PuH/MWycikkmUYSKSVkm7Zs7M9gKXxvjTfc65Z7xt7gOGgO8loN5aYK139z0ze3mq+5ykEuCdNNXO9fq53Pdcr+9P9A5TmWEZlF+g93Cu1s/lvmdC/SllWNIGc865W8b6u5mtBv4KWOxif9/+dcA34v5sb128eo8Dj3v7DqdrnsZ01s71+rnc91yvb2bh8beamFRmWKbkV7rr53Lf010/l/ueKfWn8vi0nGb1vuG1EbjdOXcqzmatwFwzu9rM/gS4A9iVqjaKiMSjDBORTJKua+aagCLgp2bWbmbfAjCzy8xsD4B3cXE98BzQCfzQOdeRpvaKiIykDBORjJGW35lzzs2Js74HuG3E/T3AnkmUeHySTUuEdNbO9fq53Pdcr5/S2knOML2Oqp9rtVV/ivVN08OIiIiIZK9M+GkSEREREZmkaTWYM7NlZtZlZofN7N4U1POZ2X4ze8XMOszsb731jWb2unctTbuZ3TbeviZZv9vMXvJqhL11HzGzn5rZb73//mmSavtH9K/dzPrM7O+S2Xcz+7aZvTXyZxvi9dciHvH+LbxoZtcnqf5XzexVr8bTZjbLW3+VmQ2MeB6+lYTacZ9rM/t7r+9dZrZ0KrXHqN88ona3mbV76xPad2+f8d5rKXv9ky3X8surlZYMU35F16Ukv8aon5IMy4n8cs5NixuRuQ9/B3wM+BPgEFCW5JqlwPXechGRaX3KgEZgQwr63A2UjFr3EHCvt3wv8GCKnvs3gCuT2XfgE8D1wMvj9ZfIdUs/Bgz4OPDvSar/l8AMb/nBEfWvGrldkmrHfK69f4OHgHzgau99kZfo+qP+/jCwKRl99/YZ772Wstc/mbdczC+vbtozTPmV/Pwao35KMiwX8ms6HZlL+dQ5zrle59yvveWTRL6xlu5feF8OPOktPwl8OgU1FwO/c84dSWYR59zPgT+MWh2vv8uB77qIXwKzzKw00fXd+U3rNGVx+h7PcuAHzrn3nHP/BzhM5P2RlPpmZsDngO9PFsfm0QAABjdJREFUpcY49eO911L2+ieZ8uuPUp1hyq+IpOVXvPpjSGiG5UJ+TafBXFqnzjGzq4DrgH/3VtV7h0e/nYzTBB4H/MTMXrDIL8gDXOKc6/WW3wAuSVLtke7g7DdCKvp+Rrz+puPfw+hpna42szYz+59mdmOSasZ6rlPd9xuBN51zvx2xLml9H/Vey6TXfypyMb8gMzJM+RWRjvyC9GfYtMiv6TSYSxszuwj4F+DvnHN9wKPAnwEVQC+RQ7jJsMg5dz1wK/CfzewTI//oIsdrk/p1ZYv8GOrtwI+8Vanq+zlS0d947NxpnXqBK5xz1wH/BdhpZsUJLpu253qUz3P2/wyT1vcY77WodL7+2SyN+QVpzjDlV0Sa8gsyI8OmRX5Np8HchKb/ShQzu4DIi/M959y/Ajjn3nTODTvnPgD+K1M8xRWPc+51779vAU97dd48czjW++9byag9wq3Ar51zb3ptSUnfR4jX35T9e7A/TutU470h8U4PHPeWXyByzcefJ7LuGM91Kvs+A/gs0DyiXUnpe6z3Ghnw+idIzuWXVyvdGab8SlN+eftOa4ZNp/yaToO5lE+d451r3w50Oue+NmL9yHPbnwESPmm2mX3YzIrOLBO5kPVlIn2+09vsTuCZRNce5axPNano+yjx+rsL+E/et4I+DvzfEYezE8biTOtkZh81szxv+WPAXOC1BNeO91zvAu4ws3wzu9qr/atE1h7hFuBV59yxEe1KeN/jvddI8+ufQDmVX16dTMgw5Vea8svbd7ozbPrkl0vCt3bSdSPyDZDfEBlJ35eCeouIHBZ9EWj3brcBTwEveet3AaVJqP0xIt/2OQR0nOkvcDHwM+C3wF7gI0ns/4eB48DMEeuS1nciodsLvE/kGoK74/WXyLeAtnr/Fl4CQkmqf5jItQ1nXv9vedv+tfe6tAO/Bj6VhNpxn2vgPq/vXcCtyei7t34HUDdq24T23dtnvPdayl7/ZN/Iofzy6qc1w1B+pSy/xqifkgyLVdtbv4Npkl+aAUJEREQki02n06wiIiIiOUeDOREREZEspsGciIiISBbTYE5EREQki2kwJyIiIpLFNJiThDMzZ2YPj7i/wcwaveWLzGyXme0zs8tiPPYmM9s9YnlhAtt1lZl9YcT9kJk9kqj9i0j2U35JNtJgTpLhPeCzZlYS428rgceAvwXuGWc/NwETCkPvF73juQqIhqFzLuycG68NIpJblF+SdTSYk2QYAh4HvhTjb3nAB97N4u3AIpMR1wFfMrN2M7vR+2XufzGzVu9W5W3baGZPmdn/Ap7yPsH+wsx+7d3OBOoDwI3e/r406lP0R8zsv1tkwudfmtm1I/b9bTN73sxeM7N7vPUfNrNnzeyQmb1sZisS8cSJSNopvyTrjPUpQGQqtgIvmtlDo9Z/j8ivcRcAq+I92DnXbWbfAvqdc1sAzGwn8HXn3AEzuwJ4Dgh4DykjMmn3gJldCCxxzg2a2VyvXgi4F9jgnPsrb383jSh5P9DmnPu0mf0F8F0ikz8DXAPcDBQBXWb2KLAM6HHOfdLb18wJPTsiksmUX5JVNJiTpHDO9ZnZd4mcihgYsf5dIpNbT8YtQJlZ9ANxsZld5C3vcs6dqXMB0GRmFcAw5zdJ8iIi07jgnNtnZhebWbH3t2edc+8B75nZW8AlRKZYedjMHgR2O+d+Mck+iUiGUX5JttFgTpLpG0TmtvtOgvb3IeDjzrnBkSu9cPx/I1Z9CXgTKPcec9b2k/DeiOVhYIZz7jdmdj2R+fX+ycx+5pzbPMU6IpI5voHyS7KErpmTpHHO/QH4IZEJlSfjJJFTA2f8BGg4c8f75BrLTKDXOfcBkVMheXH2N9IvgBpvvzcB7zjn+uI1zCLfZDvlnPtvwFeB68fuiohkE+WXZBMN5iTZHgZifSvsfPwb8JkzFxATOeUR8i7yfYXIBcaxbAPuNLNDRK4XOfOp90Vg2Lvod/TFzY3AfzSzF4lcaHznOG2bB/zKzNqBfwT+aWJdE5EsoPySrGDOuXS3QUREREQmSUfmRERERLKYBnMiIiIiWUyDOREREZEspsGciIiISBbTYE5EREQki2kwJyIiIpLFNJgTERERyWIazImIiIhksf8PGO2f+o1ayEwAAAAASUVORK5CYII=
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<p>A continuación se puede notar que este algoritmo en el espacio de parámetros es menos errático que con SGD, especialmente con mini-lotes bastante grandes. Como resultado, el Mini-Batch SGD terminará caminando un poco más cerca del mínimo que el SGD, pero puede ser más difícil para él escapar de los mínimos locales.</p>
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<h4 id="Resultados-de-los-parámetros-para-la-iteración-0:">Resultados de los parámetros para la iteración 0:<a class="anchor-link" href="#Resultados-de-los-parámetros-para-la-iteración-0:">¶</a></h4>
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<div class="prompt input_prompt">In [42]:</div>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">plot_deltas_parameters</span><span class="p">(</span><span class="n">deltas</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
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EykPXmZQSrqIvmR76K+cI0/feCZWesv84y79tzFJ+/9JA8+dTsvesZ504Nl1j1dIaqleBwyse5sdi14GTuLl5BY4y/IDfRVWLyqwOSqlTxRdO5+9jD37xlhpJIwUIoYKMcUooB55ZhXnDPEOYv7WDfUy5qFvQyWtVcvrVFRF8mPnBf11f70gWfnpO8dYzv4xjPf4JZnb+GRAw+zfNskr78fXrqjyOC+SfCQyfIQw4NncXDJhRweOJta0A+AkbFgfg3rSdjRU2LPvAWMFY2dIxXu2XaYqS/5gt4Caxb2sG5hL+cs6eOsoT4GyzGXrplHIQyopRnFSHe8k+mpqMtsc/dpLxZ2d9LMCQM72sbdqSYZ7nB4skYpCuktRtTSjEIYEIeNtvW00aYQnd7RTXenlmZUk4xKPaVabyynrxQRmjHYE1Opp7iDGQRmhEHj0Y7XInNIsowsazzXkoxamhGYEYcBhaixjkHz9Yim9Dv1dazUU8qFaO6LupldDfwvIAT+0t1//5j5ReCzwEuBA8BPuvvTJ1vuXBb1qdydhw48xL8++a98b+f3ODiyh4E946zYn7H2QMhL9/aw4okRhgfOZaR/LVkQMTqwhvH+ZVTiBQAYKfNKwywcHKZnKKa6cD4HSwEPpkM8cShh6/4Ku0eeu/FNIQrIMifJnPWL+1jQW2BRf5FlgyWWDJQoxiEXLO2nEAWsmFdmYV9xrl4emWPtLuozkc8q6qcny5zDk3VGK3XKcchYNWk8JutMTI4zdvgAwyMjWFQgiItgAfWJYZLKKPUUKvWscZfMICQwI8M4MF4nzZyxyUkIYsIwolzdR2hOP2McqoaUg5RD0RBJZZRSscxAVKPXJ6k0j0qmSYWkWiGpV8ksIgtLVC2mmFXAM2qZUfQqE5SYpEhPHOCeUU9SDCcgI8CfNzxBkUmK9IYpQVqjZDUGogxLq0RexzGG6aNKgdjSxoPGc4GEkATLEkJvTichsoSMgAM+QNEmicIylSRjvo1R8QITFJmgSKFQZFVxgkXROJkHVD2i4iGVLKLafK55SJWIikdUs5BJMuKsSq9PUqZKPYsY9xKTlHGMkJSIlJAMIyEkpQAEllH3iAmKUOglyzKCtEJPUMeDkMmghz3VIjf+j/+npXxu+d7vZhYCNwA/CmwH7jSzG939oSnN3gcccvdzzOx64KPAT5586Z1xFMHMuHDoQi4cuvDotB1jO9iyewuPHHyEG3beys59Yyw7uJWhkcdZsxeGJgIueBzmjc5neGAdEz1LGe9dxrbhlVT3LDi6nOXZfpZayBuCEeKoTm9hlGI4SkKFuCchmB+xq15neCJm96GYB8ZLfD3pp+oxBxmgRuPw/VBfgb5ixPBknbMX9bF4oIiZsbC3QDkOobl1ump+DyvmlxkoRQyWYwbKMYPlWFfwCzDT+Zxf7k41rTJWH2OsNsbB0X0cPvQsu/c/S5ImeOZMjowS1SYoJ5MM14cZTidJ04Q0rVH1CdyrRFmKZwG4ETqUPaVMnXlMUrJxdsUhB8KQ0CHCiZrP5jARGGNBwIQZdTPmZxlBc6fNMXoMsgB6ehvfrBngRSMDRoCgH6rAoIdMDDijobErCEgM3EMcB2ssb36WYg6TgdGfZSyow7CVyAjYHRoBGfOyBHDGAxgPGsVuMmh8zxTcSQ1SjKI7Zc84cqPuKnAIw91wjIyA1DIyc9zAMqMnCyh7SjXI2BeGxDhFdwKgakbFjJTGHvCBKKQny5ifZtQN6mbUzEiAgSzjoSwjckgN9oUhBoQOYfP1DXFqzWVWzKgEx/+uDNwJgbAZRwCMNduWsoyA5ypaipEZJMcc7ejNspY+h9CeP+hyGbDV3Z8EMLPPA9cBU78ErgN+tzn8BeDjZmZ+ssME1hlF/XhW9K1gxTkruI7rAEizlOHaME8cfoInDj/BMyPP8LXJAxwe2UN9zx7inQ+xcPcEq/Y5S3eUCWwFRCvxcIgoTagW55GEZfaXh6iUzsaD5iH37YBnlGv7OTtLOS8YI7aDBCT0TtxNUKoTxZOkI05AlflZhfozk9hgSiGs4j7Jsz0wEccsOVhlOO3j6Wgeh4J5HCgMUiMiJcDCGA8ialmIRTH18iIyh74YammGBwVWLOijLzlI3QoQFij5JFmhn8GFS9md9FObOMziBfNZFIwymQYU5q9kRbnKwfE6+8ZqVD1kydAQQWD0FiLqaca8ngKTlUmyyWFKPX30lMsUvML+WoEwGcejHsrj28iKg3h1kh3VAotKKV4ewnGKk/tIRnYzf8EQWb2CFfuYHB+ltGAlC+fNY7xaIw5gvFrn8HiVOIC+QkCWZVTqCZVaQrVWZ9R6oTJM1UpUw17WLOxhqLdAsn8rQX0cK/Swe8yplxYyONBPfPAxrDLM3noPh+mlUOqhrxgyFIwyENQohkacjFOPylSjAWphH0mWYJ5RikLCQpFqCllSx7I6QVrDshp4hoeNoy7RxF68Ns54cQlLB0sMDMznmb2HOFzN6K3uIy7EeFhq90d75vK5wx2sHGS8Nk4tq/HsyLMcrBxkpDbSeFSbz5VDHBjbz+HKYcbTcSa9ijk4jSJ1yqLmwyH0iDgtEqdlCmmROC0RekRGSkBIkAW4QV91Hj3jfZSJMRpFtm4JpVofeEBsIQVi+oMAD1LSxCCNoVnczI0II/CQQr2HQr1MkMUEHmLe6CfIIsKssaOQBQkeZARZiGWN7yO3DA8y3FI8yLAsJEgb//9UOVkjJHPcnMar14gPNwzDPDjm/zgeJlgWPK8vtwzMSUs1yGjMz0IInKxUA3cii8ksJbE6FgRYZgRZgKUBWQpkja0dDzMsOrLh4jiO1UMsiSBoxGzN+JqdN9bDm+syZaOnMduPHm53nKxYhyjFmmlibmCGHblbe+aknnA7bz/l1/J42lHUVwDbpoxvB14+XRt3T8xsGFgI7D/RgsdrSf5u8mLNB3c3PiRmhAYxRmxGZIZZwIK+Ieb3LmFJ31IW9C9jcHAVYPQVByiXFhKGBfoHX4bZkQ/ElD5iYOK50eRwhSSpsiOpkiSV5qNKklTJjo5XqCdVammFWlIhTapkaY3daYJ7SpolPJolkKV4lpA1H/U0oZ7V8SwhyRLqWUKW1fG0Md+zlNQTGgfRjAwnbqZFGBaYdPAswUlxGq9DhlPFCZof9wxI3cFCenCS5pcAPH+7z6yxhR1ZY+8jOZI8zcSr46TeeP2P/rejCzqam0TNz1zmTgaN9wVIgYpnFCwgbL6NAVBrLrdkhgMVd4znlpO4Hx2u09iKN4fAYMpXBBFGbBBgJDhhEDdeS4e6BeApkTVek2oztjU9hdP59J2KGcnnu+66qzNy+cibRvNcZgB25PzmycJzOHpBjD83LQ4LFKISYRCxoG8J83qGKBf66CkO0FscoLc0QF9pkN7SIH2lQYpRCcyIwwLFqEwYtvY1XKmNk2Yp7lnzXDdEYYFaM6e9+XnMPAMc94yRyjATlWdJ0lozj+ukaZ0sS6jWxwktJI6KxGGBelKlnlQAIwgjgiAibB6+T9OEpDm/mlTJPMUsILAAaxYsMyOwEKxxTjmwAJptGkUvAGvE51nWeJ7yyDwjCgsU4jJJWmt8x6R1AguJowJhENJbmkeWJaTN758wiOkrzyfxFHcnsJAgiAiCoNkmoZ7USbI6WVojyTLiKCYOG0c4G9+rRqU+Qa1eIQ4jguZ3U+P19MZ3UuNbA8Pw5uc7aP7fI5/3xutg9JbnEUdF3JsbAH70Q9X8LDlxG3Kk4/70qpltAjYBDPUtnuNoZsCU97Ax6iRAgjM5pdmByk7Yv7MxcnRD4DkGhEFMIYqZ37uIQhBSLvTS2zOfYlSmPy5TiErEUYlCVGx8eURFoqhEMS5RiEoUSgOUokXEzXaNx8ycm298YdTJssYGQhjEFIt9R+fX65PNJLDGBkZ9EveM3t5F1JNJ4qhMGMZUqiOkSY0sq5MkVUqlQaKoTBCEDI9sp79vCWmWUKmMUKuNYRYw0L8cDNLmhkxv7xCTlcNMTBwksIAoKhFFJZJkkizLCKMCUVjALDwak9lzW9WNvAtwT6k3N4CSpEKSNpZvFlAqDlAsDmAWMFk5RK023kj95pddFJUpFvs5skcQBgXiuEy1NkYcl8GhUOhpjDfXr1odo1IdJgwLxFGJMIzxtM73Pv3mGXnPWjU1l+cuCBo1I7RG8T72O9OBrJmQWeMvQx6d7rCgbykL+pcy2LOQgZ4FDJSbzz0LGexZwEDvQsqF3mm7T5IaE5VhKtURJivDHDywlTRpnH/OsoR6fZJ6fZIkmSSpT1KtT1JPJknTWqMQeoZnKYEFjE/so1oZJvOMLMuIgoAwjKnXJ6ftvxVTv6qO8xXUsY6cWpiy/dY1zi+1fuStHUV9B7BqyvjK5rTjtdluZhEwSOMCmx/i7puBzQBrh5b7vtGuPqLXdbLMSWopSS0jqad45mTp8x9pmjWGk4z06PORaU6aNIYbzxlpMuX/Nf9PYEbv/CJUJsksolbNMDIsiqlN1qkOj+MW0LegTL1SJyYhSKvUS8tI6hlpPaVey+jpj4lLjY/xgZ2L6FtUJAoiKuN1xkYniYOIwUU9WGjURsYZHx9nYKBMbWIhk+NrqXuNYiGkVCxQr2YkWUqhp0RQCMjSGkGaEJRKBMUilmX46BhhuYSVS6RpSlJ36mMV6pWEzGKSakpSrxCVnL4F/QQG1cMrSZuHLy1NIDSIoNgfUYzLjS/OwIlLEfXJlGI5xh1KvRFjIxWCooNleGUZ9YmUsBASxUYQONVaBp9u60egbfk8NZdn40K5alrlgf0P8IO9P+DuPXdzz957GK2PAjBUXsS5xTWsHU24aN82XjL2CIuSGuPJcobTRezydexON1BhiIR+6vVesjSinjy/LARep1gfo1A5RKGyn+LeJynUhonSKnhGsXqYcuUAUTJB7LXG+1QsYqUi1twjD+cPEC1eDGGABSUIewjKPQSlEtnEBF6vY1EEUeNUmEURFoUQRVgU4/U6XqkQr1pFUC5hpRJBTw9eqxPOm9f4v0euPA+C5qGqxkaNFQqNR7H43HAYkh4+jIVhY3qxSFAsQhw/7+iKpymeJHi9cfbbjEZMYQhBQLJvP16rYkEAYQgWYGEA7niWQZpCFDXWs1IhKJexQoFsYqJxBMQdsubRhuYyj+WTk6RjY43XpRBjcaH5HDfWJYoa/dO4zsGr1aPL8YkJsmq10TYISMfG8MlJgsFB0gMHCAcHIYzAs0bMaYZPTpBVKoSDg4QLFuKVyUYfcUx9714sjo/2kY1PQJZCEDbW+9i97izD06xxtDPNsCjEiiWCYqFxNKFQgDjmb5YsaSkP2lHU7wTWm9k6Gsl+PfBTx7S5EXg38H3g7cA3u/38W14FgVEoRRTafqpWZsy72rq0rsrnI3eG/IfH/oFbnrmFWlYDYN3AWVw88HKWHqxx4d5necXI/ZSyXWyrXMSTE6/nZt9ExYfwKV+BcTJOsXKIMD1Ib2UrYVqlb2wHvRO7KZehZ6BAaeEA8aIhwoVDRENDRIvOIxoaIly4kLC/v1FgjxTNqOMOhE4rHBg4aRsLw0axLR7/aF685NSPrE7tL5hmecc1fz6nemcPM8Om7vkWCkw98x/Om3d0OF58irH3PXdUprhu3SlGMrta/tQ1z6l9APgajZ/AfMrdHzSz3wO2uPuNwF8Bf2NmW4GDNL4oTq6DL5QTyaMZzec2OlQ5xI1P3MgXHvsCT488TX+hn+vOfgt9hwYYfOxRLn7iDi7wu9g2ehFbxy/jX3kP1XA+AFF9jP6x7SwavZ+B+l56+0L6FpTpX9pPYdky4mVLiRafT7RwIeHQENGCBV1VoOWFrbNvPrNomT+9b9dchyHS0V4oN5+Zulf+jWe+QT2rc8mii3ld6QLWPfIEa/Z8n3ByHk8duoRnk5cyXFgNFhAmkywY3crSgUlWnjPAwhefRXHNauLlywkGBzvjAj6RplbzubM3P5VrIgJ8f+f3+dMf/Cn377+f/kI/b137H3jpznFevOWrTAzv4eHh1/KV4CfIggIEGYPJds4rP8aqDQtYeeWL6LngjdrblheEjv6Uq6aLvLDdu+9e/vTuP+X23beztHcpv3H++7ngrjso3nM3j49cyb+kHyUNysTZKMvH7mP1+n7WvvGlzLviZxvnf0VeYDq6qKuqi7wwPTPyDB/b8jG+ve3bLCgt4IPnvpvL7vo+wR23cMfw9YzZUkqT+1gydh9nXTiPc97+KnouepMOpcsLnoq6iHQMd+cLj3+BP7zzD4ks4hfP/RmuuOsHFO74d34w/GaGo9X0jW3j4rF/5Py3XMa8t32AsL9/rsMW6RgdXdS11S3ywpFkCR/53ke48YkbuWLZ5bx3fDkL//lmbj34PsbDJZRre7gk+Tde9J5X0f+6P9HhdZHj6Oii3jN/cK5DEJFZcKhyiN/47m9w685beffya7jqm4/yyJ5Luavwm5Sre7i8/3ts+C9voXzhO+c6VJGO1tFFvdQz/e0XRSQfdo/v5ue//vPsHNvJT/vlXPFPI3wv/QDF7DAboge5dNNGBl+pYi5yKjq6qItIvj09/DSbbt7E4clhfv6RVxHvfRX3hPNZPPogb/jgqxh82U/MdYgiXUVFXUTmxGOHHuPnv/7zhBNFfunOn2Isu4je8ae4bPWTbPjYLxL29Z18ISLyPCrqIjLrJpNJPvitD7J45zquevitTHiB9Xu+zOW/9mYGrnzVXIcn0rVU1EVk1n3szj+m9/GlvPrJ6ymPb+Ol/fdx/t/+nn6eJtIiFXURmVU3PfENnrp5H6/e+VMsOPQQr77oMMs//EdH/2SmiJw5FXURmTU7R3fxlb++mZfufxOL927hde9cx8Kf+MBchyWSGyrqIjJrPvZnf8z5+69h6Z7beMMHX0n/q1491yGJ5IqKuojMii989d84+8mrGBx+jKt+9UdU0EVmgE5iicis2PEvD1OsjfGyF+1i8MrXzHU4IrnUUlE3swVmdrOZPd58nj9Nu9TM7mk+bmylTxGZGTOZz+4Q11fTP3I/5/6X32pv4CJyVKt76h8CbnH39cAtzfHjmXT3i5uPN7XYp4jMjBnL54mxCTwokfbvxuK4XfGKyDFaLerXAZ9pDn8GeHOLyxORuTNj+VwZHQNg3oX6I00iM6nVor7E3Xc1h3cDS6ZpVzKzLWZ2m5m9+UQLNLNNzbZb9u3b12J4InIa2prPU3M5qzulygFe8jb9YRaRmXTSq9/N7BvA0uPM+vDUEXd3M/NpFrPG3XeY2VnAN83sfnd/4ngN3X0zsBlg48aN0y1PRM7AbObz1FxeO7TaLR1l+bqXtLgGInIiJy3q7n7VdPPMbI+ZLXP3XWa2DNg7zTJ2NJ+fNLNvA5cAxy3qIjJz5i6fA6CKmZ1h5CJyKlo9/H4j8O7m8LuBLx3bwMzmm1mxOTwEvAJ4qMV+RaT9ZjCfDai2K04RmUarRf33gR81s8eBq5rjmNlGM/vLZpsLgC1mdi/wLeD33V1FXaTzzFg+OwFYbYbCFpEjWrqjnLsfAF5/nOlbgPc3h78HXNRKPyIy82Y2n01FXWQW6I5yIjLzzHCrz3UUIrmnoi4iM84JsDCZ6zBEck9FXURmR5jNdQQiuaeiLiKzwmIVdZGZpqIuIrMiKOg36iIzTUVdRGZFWArnOgSR3FNRF5FZEZULcx2CSO6pqIvIrCj2lec6BJHcU1EXkVlRmtc/1yGI5J6KuojMiv6FC+c6BJHcU1EXkVkxb8l0f55dRNpFRV1EZsXilavnOgSR3FNRF5FZ4CxYsnKugxDJPRV1EZlxhhPF8VyHIZJ7KuoiMvNct4gVmQ0tFXUz+wkze9DMMjPbeIJ2V5vZo2a21cw+1EqfIjIzZjKfDW9foCIyrVb31B8A3gp8Z7oGZhYCNwDXABuAd5rZhhb7FZH2m7l8dv3ZVZHZELXyn939YQCzE/6hhsuAre7+ZLPt54HrgIda6VtE2msm83lo3eI2RSkiJzIb59RXANumjG9vThOR7qN8FulgJ91TN7NvAEuPM+vD7v6ldgdkZpuATQCrV+t3rSLtNJv5rFwWmX0nLeruflWLfewAVk0ZX9mcNl1/m4HNABs3btTVNSJtNJv5rFwWmX2zcfj9TmC9ma0zswJwPXDjLPQrIu2nfBbpYK3+pO0tZrYduAL4spl9rTl9uZndBODuCfAB4GvAw8Dfu/uDrYUtIu2mfBbpfq1e/f5F4IvHmb4TuHbK+E3ATa30JSIzS/ks0v10RzkREZGcUFEXERHJCRV1ERGRnFBRFxERyQkVdRERkZxQURcREckJFXUREZGcUFEXERHJCRV1ERGRnFBRFxERyQkVdRERkZxQURcREckJFXUREZGcUFEXERHJCRV1ERGRnFBRFxERyYmWirqZ/YSZPWhmmZltPEG7p83sfjO7x8y2tNKniMwM5bNI94ta/P8PAG8F/vwU2r7W3fe32J+IzBzls0iXa6mou/vDAGbWnmhEZM4on0W632ydU3fg62Z2l5ltmqU+RWRmKJ9FOtRJ99TN7BvA0uPM+rC7f+kU+3mlu+8ws8XAzWb2iLt/Z5r+NgGbAFavXn2KixeRUzGb+axcFpl9Jy3q7n5Vq524+47m814z+yJwGXDcou7um4HNABs3bvRW+xaR58xmPiuXRWbfjB9+N7NeM+s/Mgy8gcYFOSLSZZTPIp2t1Z+0vcXMtgNXAF82s681py83s5uazZYA/25m9wJ3AF9296+20q+ItJ/yWaT7tXr1+xeBLx5n+k7g2ubwk8BLWulHRGae8lmk++mOciIiIjmhoi4iIpITKuoiIiI5oaIuIiKSEyrqIiIiOaGiLiIikhMq6iIiIjmhoi4iIpITKuoiIiI5oaIuIiKSEyrqIiIiOaGiLiIikhMq6iIiIjmhoi4iIpITKuoiIiI5oaIuIiKSEy0VdTP7QzN7xMzuM7Mvmtm8adpdbWaPmtlWM/tQK32KyMxQPot0v1b31G8GXuTuLwYeA37j2AZmFgI3ANcAG4B3mtmGFvsVkfZTPot0uZaKurt/3d2T5uhtwMrjNLsM2OruT7p7Dfg8cF0r/YpI+ymfRbpfO8+pvxf4ynGmrwC2TRnf3pwmIp1L+SzShaKTNTCzbwBLjzPrw+7+pWabDwMJ8LetBmRmm4BNzdGqmT3Q6jI7wBCwf66DaBOtS+c571QbzmY+5zSXIT+fG8jPuuRlPeA08vl4TlrU3f2qE803s/cAPw683t39OE12AKumjK9sTpuuv83A5uayt7j7xpPF2Onysh6gdelEZrblVNvOZj7nMZdB69KJ8rIecHr5fDytXv1+NfDrwJvcfWKaZncC681snZkVgOuBG1vpV0TaT/ks0v1aPaf+caAfuNnM7jGzTwKY2XIzuwmgeeHNB4CvAQ8Df+/uD7bYr4i0n/JZpMud9PD7ibj7OdNM3wlcO2X8JuCmM+hi8xmG1mnysh6gdelEbVmPGc7nvLzWoHXpRHlZD2hxXez4p81ERESk2+g2sSIiIjnRkUW9229DaWZPm9n9zfOSW5rTFpjZzWb2ePN5/lzHeTxm9ikz2zv150fTxW4Nf9J8n+4zs0vnLvLnm2Y9ftfMdjTfl3vM7Nop836juR6Pmtkb5ybq4zOzVWb2LTN7yMweNLNfaU7vivelm/NZudwZ8pLPs5LL7t5RDyAEngDOAgrAvcCGuY7rNNfhaWDomGl/AHyoOfwh4KNzHec0sb8auBR44GSx0zjP+hXAgMuB2+c6/pOsx+8C/+k4bTc0P2dFYF3z8xfO9TpMiW8ZcGlzuJ/GLVw3dMP70u35rFzujEde8nk2crkT99TzehvK64DPNIc/A7x57kKZnrt/Bzh4zOTpYr8O+Kw33AbMM7NlsxLoSUyzHtO5Dvi8u1fd/SlgK43PYUdw913ufndzeJTGVecr6I73JY/5rFyeZXnJ59nI5U4s6nm4DaUDXzezu6xxVy2AJe6+qzm8G1gyN6Gdkeli78b36gPNw1ifmnLYtGvWw8zWApcAt9Md70snxXImlMudrWvzeaZyuROLeh680t0vpfGXrH7JzF49daY3jqt05c8Oujl24BPA2cDFwC7gj+Y0mtNkZn3APwK/6u4jU+d1+fvSyZTLnatr83kmc7kTi/pp3Va2E7n7jubzXuCLNA797Dly2KT5vHfuIjxt08XeVe+Vu+9x99TdM+AveO6QXMevh5nFNL4E/tbd/6k5uRvel06K5bQplztXt+bzTOdyJxb1rr4NpZn1mln/kWHgDcADNNbh3c1m7wa+NDcRnpHpYr8ReFfzCs3LgeEph5A6zjHnot5C432Bxnpcb2ZFM1sHrAfumO34pmNmBvwV8LC7//GUWd3wvnRtPiuXOzeXoTvzeVZyea6vBpzmCsFraVwV+ASNvx415zGdRuxn0bjy8l7gwSPxAwuBW4DHgW8AC+Y61mni/xyNQ1l1Gudv3jdd7DSuyLyh+T7dD2yc6/hPsh5/04zzvmayLJvS/sPN9XgUuGau4z9mXV5J43DcfcA9zce13fK+dGs+K5fnfh1Osi5dl8+zkcu6o5yIiEhOdOLhdxERETkDKuoiIiI5oaIuIiKSEyrqIiIiOaGiLiIikhMq6iIiIjmhoi4iIpITKuoiIiI5oaIuJ2Rml5jZrWY2YWZ3mNnquY5JRM6M8jn/VNRlWma2ErgJ+CiN2xg+CfzWnAYlImdE+fzCoKIuJ/JHwF+4+43uPgl8HnjZHMckImdG+fwCEM11ANKZzGwAuA44d8rkAKjMTUQicqaUzy8cKuoyndcDMXBf468FAlAEvmRmlwH/i8ZfTNoBvMvd63MSpYicihPl8xIafyu+DqTAT3uH/9lVmZ4Ov8t01gI3uvu8Iw/gW8BXgW3A69z91cDTNPYARKRzrWX6fN4PvNLdrwQ+S+PPmkqXUlGX6RSBiSMjZrYO2Ejji2FX85wcQA3I5iA+ETl1J8rn1N2P5HA/jb8dL11KRV2mcydwpZktN7NVwP8BPuzuB480MLM1wBuAf5mjGEXk1Jwwn83sYjO7HfgAcPccxiktMnef6xikA1njxNsngJ8BDgAfdfc/mzJ/APhX4Ofd/dG5iVJETsXJ8nlKu3fQOLX2C7McorSJirqcNjOLgBuBP3L3W+Y6HhE5c2ZWcPdac/iNwBvd/YNzHJacIRV1OW1m9rPA/wTub076hLv/3dxFJCJnqvlrlo/RuPK9ArxXV793r5aLevP8zGeBJYADm939fx3Txmj8BOpaGhdrvMfddd5GpMMon0W6Wzt+p54Av+bud5tZP3CXmd3s7g9NaXMNsL75eDmNczsvb0PfItJeymeRLtby1e/Nnzfd3RweBR4GVhzT7Drgs95wGzDPzJa12reItJfyWaS7tfUnbWa2FrgEuP2YWSto3LDkiO388BeFiHQQ5bNI92nbbWLNrA/4R+BX3X2kheVsAjYB9Pb2vvT8889vU4Qi+XTXXXftd/dF7VxmO/JZuSxy+lrN57YUdTOLaXwB/K27/9NxmuwAVk0ZX9mc9kPcfTOwGWDjxo2+ZcuWdoQokltm9kybl9eWfFYui5y+VvO55cPvzSth/wp42N3/eJpmNwLvsobLgWH9ZEKk8yifRbpbO/bUXwH8LHC/md3TnPabwGoAd/8kcBONn79spfETmJ9rQ78i0n7KZ5Eu1nJRd/d/B+wkbRz4pVb7EpGZpXwW6W76gy4iIiI5oaIuIiKSEyrqIiIiOaGiLiIikhMq6iIiIjmhoi4iIpITKuoiIiI5oaIuIiKSEyrqIiIiOaGiLiIikhMq6iIiIjmhoi4iIpITKuoiIiI5oaIuIiKSEyrqIiIiOaGiLiIikhNtKepm9ikz22tmD0wz/zVmNmxm9zQfv9OOfkWkvZTLIt0tatNyPg18HPjsCdp8191/vE39icjM+DTKZZGu1ZY9dXf/DnCwHcsSkbmjXBbpbrN5Tv0KM7vXzL5iZhfOYr8i0l7KZZEO1a7D7ydzN7DG3cfM7Frgn4H1x2toZpuATQCrV6+epfBE5BQpl0U62Kzsqbv7iLuPNYdvAmIzG5qm7WZ33+juGxctWjQb4YnIKVIui3S2WSnqZrbUzKw5fFmz3wOz0beItI9yWaSzteXwu5l9DngNMGRm24GPADGAu38SeDvwi2aWAJPA9e7u7ehbRNpHuSzS3dpS1N39nSeZ/3EaP5MRkQ6mXBbpbrqjnIiISE6oqIuIiOSEirqIiEhOqKiLiIjkhIq6iIhITqioi4iI5ISKuoiISE6oqIuIiOSEirqIiEhOqKiLiIjkhIq6iIhITqioi4iI5ISKuoiISE6oqIuIiOSEirqIiEhOqKiLiIjkRFuKupl9ysz2mtkD08w3M/sTM9tqZveZ2aXt6FdE2ku5LNLd2rWn/mng6hPMvwZY33xsAj7Rpn5FpL0+jXJZpGu1pai7+3eAgydoch3wWW+4DZhnZsva0beItI9yWaS7zdY59RXAtinj25vTRKS7KJdFOljHXShnZpvMbIuZbdm3b99chyMiZ0i5LDL7Zquo7wBWTRlf2Zz2Q9x9s7tvdPeNixYtmpXgROSUKZdFOthsFfUbgXc1r5y9HBh2912z1LeItI9yWaSDRe1YiJl9DngNMGRm24GPADGAu38SuAm4FtgKTAA/145+RaS9lMsi3a0tRd3d33mS+Q78Ujv6EpGZo1wW6W4dd6GciIiInBkVdRERkZxQURcREckJFXUREZGcUFEXERHJCRV1ERGRnFBRFxERyQkVdRERkZxQURcREckJFXUREZGcUFEXERHJCRV1ERGRnFBRFxERyQkVdRERkZxQURcREckJFXUREZGcaEtRN7OrzexRM9tqZh86zvz3mNk+M7un+Xh/O/oVkfZTPot0r6jVBZhZCNwA/CiwHbjTzG5094eOafp37v6BVvsTkZmjfBbpbu3YU78M2OruT7p7Dfg8cF0blisis0/5LNLF2lHUVwDbpoxvb0471tvM7D4z+4KZrZpuYWa2ycy2mNmWffv2tSE8ETkNbctn5bLI7JutC+X+BVjr7i8GbgY+M11Dd9/s7hvdfeOiRYtmKTwROQ2nlM/KZZHZ146ivgOYuqW+sjntKHc/4O7V5uhfAi9tQ78i0n7KZ5Eu1o6ifiew3szWmVkBuB64cWoDM1s2ZfRNwMNt6FdE2k/5LNLFWr763d0TM/sA8DUgBD7l7g+a2e8BW9z9RuCXzexNQAIcBN7Tar8i0n7KZ5HuZu4+1zFMa+PGjb5ly5a5DkOko5nZXe6+ca7jOBHlssipaTWfdUc5ERGRnFBRFxERyQkVdRERkZxQURcREckJFXUREZGcUFEXERHJCRV1ERGRnFBRFxERyQkVdRERkZxQURcREckJFXUREZGcUFEXERHJCRV1ERGRnFBRFxERyQkVdRERkZxoS1E3s6vN7FEz22pmHzrO/KKZ/V1z/u1mtrYd/YpI+ymfRbpX1OoCzCwEbgB+FNgO3GlmN7r7Q1OavQ845O7nmNn1wEeBn2y1b2lNljlZmpElTpY6aZqRpY1p7hAEhgVGvZIyPlIlqaaN/2iGAY1/IEudejWlXk3xzLHASGopWeYUShFRIQBv9JfWM5JaRlJPSeoZuFPsiSn2RM2+HYCoEBCERnUioVCOjv5/zxptpg67N4bjYsTY4QqeNmIwMyyg+WyYgQVGrZIcXT8csub/98xJk0Z8AEFkhGGABTb9i3gGs8I4oNQbkybN194dTx2sEVOtmjZituYymgM2ZcF2oo5boHwW6W4tF3XgMmCruz8JYGafB64Dpn4JXAf8bnP4C8DHzczc3dvQ/wuCZ87EaI3qeEKtkjB2qApAUk+pTabUKgn1SkKtkgJOvZpRHa9TGU+oV1OSWvNRz0jqGWmSwRy/+maOAZm3r0BFEYSh4YBnNAq+87xHHDcKZuaN/s2ee4ShEYZgOGkGWQqeNV+r51fV54anPDU6OfLSNgfMnjecpEaSHOnTCQIjCBr/NcsgjpvN3RvLaWyZQHPjgyNp05zWZsrnnHB3zBofTE9TLAwbw0mCRdHz2nmthlcqBP39WHDyA7g+NaHSFE9TPM0gTfB6HU+SxqNehyPDSYLXEzypY3FMcvAgaS2B/gEyIMmcJIF63cEy3DOqlayx8Y7jWUZUiCjFAbWxCdK+XgpZimUJtckKERlhFBLHIVEYEsURFkekFtHXV6YexUT1GlQrZJOTJNUaYRyRHjxEODhAsncfViwS9PcR9PTgExMQF8gKJWqTdWoTVSpxEe/pI5sYo17PqCcZQRAQYgRAHBhmjQ10J2vkeeDNdk6aOfWeARICUgtJqzWyNCELIrIwIAnClt/3dhT1FcC2KePbgZdP18bdEzMbBhYC+0+04LvuuuvohzJP+kqDFOMeeuIyA+X5LF+wlt7SAD3FfnqKfZQLfY3nYj+lQh/FQg+BhYRhfMLlpmmden0CzKjXK1Sro9Rqo9Trk9STKllaJU1rpEmNNK2RZSmZJ40PlSeN8azxDI5ZQGAhSVJhYvJQY9nQfE/s6N5i5in1+iRJMol7RmAR9aSCe0Ycl4nCAo7jnpGmNZKkRppWcW/sEUdRiULcS+Yp7inuThQVCYKIWm2cOO7BPcM9JcvSKcPPTQOI4x7q9fEZe9/aySw4uv6tOL9UakM0zzMj+ZzXXD4dIY1tv4IZRQvIcDIgNiNuHv1K3AkwAoOeQh/9PQsoFXoICSiXBojCmEp1lCiIKEYFwiAmDAsEYUwUxsRhgcCMLK3RU55PqTQIFhBYgFlIktbwrE4U9xDHvc3pU4/8NLZuG0eKgsaDKcNTpjeO2AVHx+O4DDhJUiFJqpgFRFGJoFmojmzzRVGROO4hiopADEyewqtnzVfQgRQoAsnRVzbLSqRpDXDc02abanO+T9n2dRwnsIAwLFCrjWIWY1bDbB5ZlpCmY2TZYeK4TByHhGGt+X8Lzf5Hj4lpqqnbtVM3jqa2q/LDaseZdmbaUdTbysw2AZvmOo7TEdB8e83oiQosn7+OhX2LmN+7kIGexqO3ZwH9vYsY6F9KFP3wF7F7Rq023nyMUa2NMXb4WQ7WxqjVx3HPGB/fR7U6SqU2weGJ/dQzJ0kr1OsTVGoT1LI6KU4KxM00zWh8zEKD+pE9v+a0I18q3mx35HDvkXFvfsGYNdYxwI7+nwA7+iWVTlnWkeEjfdTrhwmtsRUbNmOa2t6AsF7DktHG3nUzRq82FuDmePUAR752kuayA4PUIcJwgyJGUD9+Ypxs99GPeW4k/nPS5utBM96jD2fqVyEAWXPn+XmvfXMZNIcDmkcRmvMDGu/PkfGpDwMKGBFGglPHSTjyfsD2ttf09unGXD4dIY2CHJkRY0RGY9iMYlRgXnkhvaUByoUeyoU+CnGZuNBLIe4hLvQQxz0U4l7iuIc4LhHFZcIgJoqKlMvzCcNCS/FlWcpkdaSxIYyTZSlRWCAMY2r1Caq18aMbxI2N7saefWOjOWucFvKMzDM8S45umDce3pjeHHbPqNYbxTmOS8RRiSxLqSUV0ixh6hGtelqnWhun2tzwbxzEaiwnzRLqSZVCXCIMIsYmD2NBc8MCa26E2JQNFSMMIqKoSNR8vaz5rzW/u45sTB7ZcPHm+tbTGsW4p7meKZk7YRARhzFREFNNJqnUxqnWJqjUx8k8BYcAx5sbPwBZmpJkddIsITAjCEICiwiDiMxT4qhIktYpxmUMIznymnjW3MSgsS4Y/aXW3nNoT1HfAayaMr6yOe14bbabWQQMAgeOtzB33wxsBti4caNv2bKlDSG2LpuYoL5jB8m+fdS2baf66KMcfvxZ9u+qMRIOMdq/ionyIqqlBaRh8bn/6BnFbJwS4xQYpZD+gHByP/V4kslChbFwjOHCdvbHYxwoOpOxc7gUMNIDYyUoJFCqQTVuPMwhiYzn3roY6CduDgGYOwGQNj905Syj6ODYc8XKGuNFh97MKGBAgHsIboRkTFqKA31JQJQZSWAkZlhmRB5gHpCQ4QZhFpARE3pGnYgQp0Sd1CMyAswbpTDEKXpKREbqIZUgoBJklNKYxDIqQUY1cAIyJqKE2IEsJnYjdgjJCHAKGaTmpEFGTxoQOpSzgEqQ0p+GZM1lFRyKWUBqUDOnFjg9adB8fRIIEvCQUmb0ZSmxJSSWkZmTmjNOgQoxEQluUCcgIWw+Nw6hQUZMnYiUCKgFGZNBRugBgRuRQ6G5sTIWBiRBndSyoxuD5kZGQIEjp0QM3HACMo8IcCIyIvfG2ntIhhHgmDl/88u3t/Oj3rZ87tRcno67k3hCPa3z1P7HGL/nHnz/AXz7bsJnd2EHDpEdrpBMBHhSoh4PUCsOUi0MUCsMUi0OUisMUikOkEa9J+wrtRqJVchskmpUpRJXmQgnwBPqYZ2x4v2MFUcYL4xQD6s4TiUeJ7OUYlIGS6gFCWmQklnS+EwFCZk1im+UFajE47i1fjToeMLmd0zgTvUUDte3InInOYOjPOaOmzGYplTNqDTjjN0ZTDP6soxxg8SssSPkUHQnxJmw4Oi35WgQkB3ZIDhm4zuDtq7/boD3tLaMdhT1O4H1ZraORrJfD/zUMW1uBN4NfB94O/DNTj3/5llG9fHHqTzwINUnnqD6xFaqW59gfN8YI/2rGe1fzWj/Kkb7L6LW+wo4B8DpZz/lYA+F+DEsvJeD8w6wdXCcJ8uT7IsDxo7zxpccFlnEIiuyOBzi7KiHICywMBrEghLDNWO05lhW4nC1TK1eJkmLVMcjJusRlSRmvB4yVo+YqMckXiAJa9TTAdwLHNlXHAeCIGJRf5EwMKpJRrWeUohCCsWQ3dWUMIAoCBgsxyzsKxCHAQsCIw4DFvYV6CtGHBxv7An3FiPcIQygXIgoxyHze2IW9BbIvHku2p04NMIgIAqMnkLI8nnlxjmlNKOWZiSpYwZLB0qNOta8aA2eO1WcZs54LSE04+B4jTRz9oxWSI/5rjo25Y/9DhgsNzZ5Juspk7W0sfzmkYmBckwtaRxfKEYBhSjgwFiNzJ2BUsxYNWGynjLUW6BcCBmerJNmThw22haOPEcBaeZM1lImailJltHTfH0KUeMwZ5Y5qTtJ2ji/1tiD4uhRijgMiMOAKDTCwEgzf+7/HBnOGhfXJZkTmPE3LD/Tj/vx5Cqfj5VkCdtGt/HYocfYN7GP3eO7efjpOxncuoehrfs5a0fGopECpXQplfJyxnuXM9a7lomeS6gNDuILyj+0TCchCUdI4sMk8S48fpggOkwUHiYORyjZBAST1MIKWThBKazTH0LJIooWUwxjSkFE0SJKQaExbjH1KKYShCwIS8SExFambCElAoK4SBr1UK2NUi30UPWEpNBDb2kBhUIf48kkk/VxwiwhShPwlDEae9HFqJcoLhHEPVhYaBxSxxrDYRGiAlkQ42GBQtxDKS4TjOzC0xrePIxvBmQJZCmT9Qn2ZxWKcS91nP64hyTLqHrSPIUXYMU+zCKCIMbqkwSeYvUJrDpCaDHFqNg41YdTd6dOSpKlFDH6gohDtVFGkgkGw9KRC12ap68aG8uh09hL9sYR04JFEETUg4BiVIQgIrGAxFOKtUksaJa+ZBJ6F0PvEFRHYOIg1CegXmkcTivPg/IC6F0IaQK1UaiOQW0ccJg8TIIzhpNFjdcvKM9vnJqISo31zZLGdQphkSAsYEGMeYolVSypYO7NUxghI8kk87i2pc94y0W9eU7tA8DXaByR+pS7P2hmvwdscfcbgb8C/sbMtgIHaXxRdISsVmPi9tuZ/MEPqDz0MJM/+AHp8DD1qIdDQxsYXv4S9p99NZPrBwEwMgrhTiZ77+dQ3zZ29m1ja/8u9hbS5y03ImBteRFn9S7nit4l9BUW4ywhtCFIB5mY7OXAiLHjcIUdwxUeqdSZqKZU04xa8sNb16sWlJnfU6Ach/SUQ4YKEeVCSE8hbDzHEb3FkLMW9VKMQvqKEaU4JAxgfk+B+T2FxtXeIifQ7fk81a6xXdy7/16eOPwETx5+kieHn+SZ4acZ2l/nvB3OedsDzt+/mI31ZYz1XsZY73JGly/nwNqho8sIqNIbb2d+9BSlcJRyXKWvJ2XBYMzAgjL95SolRrC4AKXB5mMNlF48ZXzKI+754S3OMxQCPc3HsU58nOAMLLnw6GmnY5V5/qGdVkw94jjV/ObjdE05ZkrEzJxvjoB5bVrWYBuWYZ28gT1Th+zSw4cZ+7d/Y/Sb32L8u98lm5ggCyMmz7qEw4vXs7+wmgO+AggIbIKk7yF2DT7NU4M7ebR3G/WwRsFClhfns7x3OcvnncXKwbWs6F1HVhti7+GQZ/Y5uw5XGanUeWzPKPvHfvh871BfgRXze1g+WGKgFFMuNPboFvcXKcUh6xf3cf7SgaPTRY7HzO5y941zHceJzPThd3dn6+Gt3L3nbu7e23jsHt+NubN2n3HF9h4ueKZMeXwdo33nMda7gomepXjzIi4jpT/aS295mMGFsGR5gaXLYhaccw7BwnXQMwRR6+c7RU6m1XzuuAvlZoonCeO33c7wP/0TozffjNfr2NAixjdeyd7SSrbXz6HmfUBK1rudHQv/jR/038euvqcJA2P9/HNZN3gerx58I+sHz2e+XcST+yZ5fO8Yjz42ytf2jLJzeJIjFw6X4oCV83voL0W87vzFnLukn7MX97Gwt7HXvHigSDFq/ecLIi9E7s72se08uP9Bbt15K7fuuJV9k/vAnZeMDPL2Z0qsfWoZwegqhvvWMzKwjh1LFwFQ9GF6SgdZsHQ3y89awJoNa1hwzjmE5Q6+6lDkFOW+qNeefZaDn/4MI1/5CumhQ2SD85m47Er2llezPbmQhBJBOsHwkie4e94PeKL/QbI4YcPQBq5e8hpetvRlrCxv4Ik9dR7cOcJ3bj/A//fsIWpJ4+KkQhRw9qI+XrZuAecu6W8++lg5v4dQh7tF2sbdeejgQ3zr2W9x8zM38+TwkwD0x328YnQer7mjl8WPl9jT+zL2LbqUrYuXwGKIGaM8r8bS82Je9CPnsercRS/4n9dJfuW2qFceeYQDm/+Cka9+FQsCKi++hMdffAV7bT2Nw+rj7FnxCHcMfJ8dA48xv2c+V666kl9Y8S7OHriYe56Z5AfPHub3v3eQB3Z8/+hyNywb4GcvX8PL1s7n3CX9rF7QQxTq0LjITHF37tx9JzfccwN3772bwAJe0n8W/7F+Fi+58ylKz/SzI3gJexe+mKc3LAUyeufXuODly3nJy1ayYHmviri8YOSuqFeffIqDf/0pDn/hH7FCiL9kBY8tvJrtycVExVH2rL6bO4q3sbNvK2sG13DN2jfwqhW/zfjIMr7+4B5+89t72D3SKOK9hZALlg3w61efx8vXLeTsRb3M69F5NZHZUE2rfOWpr/C/H/rfPHroURbEA/xf0YW88fYfkD61m0ftKh4Yei/1tf0YGUtW9/DSK1Zx9qWL6R0snrwDkRzKTVHPajX2f+ITHPjzzXhg7L/4VWxb8AoOpyshqPHIud/mu/P/hSX9i3njujdy1ar/ysFDi/jag7t537/u4cD4NopRwJXnLuIXzj6Li1YOcsmq+bpiXGSWHa4c5vOPfp7PPfI5DlYOsiZawAf3x1x99zYe238Wty/4TwyvOBsjY/W6Aue97lxWv2iIYjk3X2ciZywXWTB5//3s+uAHqGzbx9iGDTyx7D9wMF1FtnCYOwa/yEPzbuOiFRfy38757xRrl/CVB/bwM/+ynZHK0/QWQl53wRKuedFSrjx3Eb3FXLwkIl2nltb4q/v/ir9+8K+ZTCZ5WbiE/7p1hIEn1vJo/c3cOLCeZF0PfT0pV1y1hgtetYpyv46ciUzV1RUsq1bZ/7H/wYH//XdMLFjGw6/9MMO+DPoqfHPFZ9k67we8Yc0beOvQn3H342V++//s5NDE3QyWY350w1KuedFSXrl+iFKsq9BF5tK9++7lI7d+hCeGn+B1wSLe++BeJh+9gMd7fpuRwbMo+Thrz5vHhT92ISvOnadz5CLT6NqiXtu2jW3veSfjeypsf+nbebr/NXhPyvfXfYH7+v6dixdeyY/b/+S7t8M/HNxLKQ740Q1Lecsly3nV+kXEurhNZM5lnnHDPTfwF/f9BUNW5E+eOkTvg+dyV/n3mVy2mHJU55WvX8hFb3oNgXJW5KS6sqhXbv8mz/zHX2HH/Jfx5KveSpUyjy27g+8t/xK9xXXUn/1FvvPIasJgkivOWsivvH49b3zRUvp0aF2kY2wb3cbvfu8j3LH7Tt50uMY7b5/HXcF/Z2zhKnrDCa756XWsvXytrmsROQ3dVeXcGfv0R3jshm/z8Pm/zOH+sxmdv4evrPwTJkq9HHj25xhL1/DmS1bwYxct45LV83SOXKQD7Rnfw3u/8m5GJw7w0bsSqtvfyb8tfiVFqrz2x4c4/9qLVMxFzkD3VLxDzzD6/72X2289i62X/gZJIeDbaz7Powt+QGXftaycuJJfvGodb3vpyqN/vENEOs/24Wd5/5d/hmDfAf7b9y7lyb6fIFncwwUbCrxy02so6Cp2kTPWHdnz2NfY+We/wzf3vI/h9eewu/9Jbl7/acbra3lt/x/yE6++kFecPaQte5EO9/iee/n5m97NxQ/38bJn/yOPzr+AhYURXv+rl7LorAVzHZ5I1+v8or7tDp78s4/y1YnfI+itcceKv+WuJU/y+iW/yO+94R3aKxfpEvX6JP/Pv76b6753CaXgHYwOGK984xAvvu61mDbIRdqis4u6Ozs+81G+Nv6fKVX28E8X/RnB6su45dp/ZclA2/+4oIjMoE/+w3u55tuvgN63sSA8wDW/80YGlgzMdVgiudLRRd0rY3z52fdQrB7m6+s/wctf8TZ+60f+k36jKtKF6t/tp9j7Npb3HeY//I+3Eun+ECJt19FFfWJkgnrQSz35c97/rv+Xq9a+dq5DEpEzkNQr9FVeQ5Q9xZs+/h5C/dlhkRnR0t0czGyBmd1sZo83n+dP0y41s3uajxtPdfm1qhMlE5Tf/HIVdJEZNpP5PDJ8kHpxKb3z96ugi8ygVm/R9CHgFndfD9zSHD+eSXe/uPl406kuPPEi/cOP82NXv6/FMEXkFMxYPqcTKQAv/Q+vaEugInJ8rRb164DPNIc/A7y5xeU9jxOR8gRLBpa3c7Eicnwzls+WFShU9nP2a3+kXYsUkeNotagvcfddzeHdwJJp2pXMbIuZ3WZmbz6dDioL663EJyKnbgbz2QiyUSzQ/dtFZtJJL5Qzs28AS48z68NTR9zdzcynWcwad99hZmcB3zSz+939iWn62wRsAlg1dC6FxUMnC1FETtFs5vPUXF6zcA1QaS14ETmpkxZ1d79qunlmtsfMlrn7LjNbBuydZhk7ms9Pmtm3gUuA4xZ1d98MbAZYveg87xnoO+lKiMipmc18nprLa4fOcqPWhjUQkRNp9VjYjcC7m8PvBr50bAMzm29mxebwEPAK4KFT7aA0TzenEJklM5bPjoFV2xiqiBxPq0X994EfNbPHgaua45jZRjP7y2abC4AtZnYv8C3g9939lIt639DCFkMUkVM0c/lsAQS6PkZkprV08xl3PwC8/jjTtwDvbw5/D7joTPuYt3i6a3VEpJ1mMp8dU1EXmQUdfynqotWr5joEEWmZYVE610GI5F5HF3XDGVqk36iL5IHpDyqKzLiOLup4RqnYM9dRiEgbBCX9ISaRmdbRRd2Y7meyItJtomJH//0okVzo6KIO2VwHICJtEvcW5zoEkdzr7KLu2lMXyYvyPN1ISmSmdXZR1566SG70zJ831yGI5F6HF3XtqYvkxbzFi+Y6BJHcU1EXkVmxcIXuOSEy0zq7qE/7R6JEpNssWbV2rkMQyb3OLuraUxfJBSOj1Ns712GI5F5nF3XtqYvkg37JIjIrOryoz3UAItIOpl+yiMyKji7qpqIukhPaUxeZDR1e1FXVRfJg4ZoFcx2CyAtCRxf1uLc01yGISBtoA11kdrRU1M3sJ8zsQTPLzGzjCdpdbWaPmtlWM/vQqS6/f7627kVmy0zns4jMvFb31B8A3gp8Z7oGZhYCNwDXABuAd5rZhhb7FZH2Uz6LdLmW/haiuz8MJz20dhmw1d2fbLb9PHAd8FArfYtIeymfRbrfbJxTXwFsmzK+vTntuMxsk5ltMbMt+/btm/HgROS0nHI+K5dFZt9J99TN7BvA0uPM+rC7f6ndAbn7ZmAzwMaNG/U7GJE2ms18Vi6LzL6TFnV3v6rFPnYAU/+Sw8rmNBGZZcpnkXybjcPvdwLrzWydmRWA64EbZ6FfEWk/5bNIB2v1J21vMbPtwBXAl83sa83py83sJgB3T4APAF8DHgb+3t0fbC1sEWk35bNI92v16vcvAl88zvSdwLVTxm8CbmqlLxGZWcpnke7X0XeUExERkVOnoi4iIpITKuoiIiI5oaIuIiKSEyrqIiIiOaGiLiIikhMq6iIiIjmhoi4iIpITKuoiIiI5oaIuIiKSEyrqIiIiOaGiLiIikhMq6iIiIjmhoi4iIpITKuoiIiI50VJRN7OfMLMHzSwzs40naPe0md1vZveY2ZZW+hSRmaF8Ful+UYv//wHgrcCfn0Lb17r7/hb7E5GZo3wW6XItFXV3fxjAzNoTjYjMGeWzSPebrXPqDnzdzO4ys02z1KeIzAzls0iHOumeupl9A1h6nFkfdvcvnWI/r3T3HWa2GLjZzB5x9+9M098mYBPA6tWrT3HxInIqZjOflcsis++kRd3dr2q1E3ff0Xzea2ZfBC4DjlvU3X0zsBlg48aN3mrfIvKc2cxn5bLI7Jvxw+9m1mtm/UeGgTfQuCBHRLqM8lmks7X6k7a3mNl24Argy2b2teb05WZ2U7PZEuDfzexe4A7gy+7+1Vb6FZH2Uz6LdL9Wr37/IvDF40zfCVzbHH4SeEkr/YjIzFM+i3Q/3VFOREQkJ1TURUREckJFXUREJCdU1EVERHJCRV1ERCQnVNRFRERyQkVdREQkJ1TURUREckJFXUREJCdU1EVERHJCRV1ERCQnVNRFRERyQkVdREQkJ1TURUREckJFXUREJCdU1EVERHKipaJuZn9oZo+Y2X1m9kUzmzdNu6vN7FEz22pmH2qlTxGZGcpnke7X6p76zcCL3P3FwGPAbxzbwMxC4AbgGmAD8E4z29BivyLSfspnkS7XUlF396+7e9IcvQ1YeZxmlwFb3f1Jd68Bnweua6VfEWk/5bNI92vnOfX3Al85zvQVwLYp49ub00SkcymfRbpQdLIGZvYNYOlxZn3Y3b/UbPNhIAH+ttWAzGwTsKk5WjWzB1pdZgcYAvbPdRBtonXpPOedasPZzOec5jLk53MD+VmXvKwHnEY+H89Ji7q7X3Wi+Wb2HuDHgde7ux+nyQ5g1ZTxlc1p0/W3GdjcXPYWd994shg7XV7WA7QuncjMtpxq29nM5zzmMmhdOlFe1gNOL5+Pp9Wr368Gfh14k7tPTNPsTmC9ma0zswJwPXBjK/2KSPspn0W6X6vn1D8O9AM3m9k9ZvZJADNbbmY3ATQvvPkA8DXgYeDv3f3BFvsVkfZTPot0uZMefj8Rdz9nmuk7gWunjN8E3HQGXWw+w9A6TV7WA7Qunagt6zHD+ZyX1xq0Lp0oL+sBLa6LHf+0mYiIiHQb3SZWREQkJzqyqHf7bSjN7Gkzu795XnJLc9oCM7vZzB5vPs+f6ziPx8w+ZWZ7p/78aLrYreFPmu/TfWZ26dxF/nzTrMfvmtmO5vtyj5ldO2XebzTX41Eze+PcRH18ZrbKzL5lZg+Z2YNm9ivN6V3xvnRzPiuXO0Ne8nlWctndO+oBhMATwFlAAbgX2DDXcZ3mOjwNDB0z7Q+ADzWHPwR8dK7jnCb2VwOXAg+cLHYa51m/AhhwOXD7XMd/kvX4XeA/HafthubnrAisa37+wrlehynxLQMubQ7307iF64ZueF+6PZ+Vy53xyEs+z0Yud+Keel5vQ3kd8Jnm8GeAN89dKNNz9+8AB4+ZPF3s1wGf9YbbgHlmtmxWAj2JadZjOtcBn3f3qrs/BWyl8TnsCO6+y93vbg6P0rjqfAXd8b7kMZ+Vy7MsL/k8G7nciUU9D7ehdODrZnaXNe6qBbDE3Xc1h3cDS+YmtDMyXezd+F59oHkY61NTDpt2zXqY2VrgEuB2uuN96aRYzoRyubN1bT7PVC53YlHPg1e6+6U0/pLVL5nZq6fO9MZxla782UE3xw58AjgbuBjYBfzRnEZzmsysD/hH4FfdfWTqvC5/XzqZcrlzdW0+z2Qud2JRP63bynYid9/RfN4LfJHGoZ89Rw6bNJ/3zl2Ep2262LvqvXL3Pe6eunsG/AXPHZLr+PUws5jGl8Dfuvs/NSd3w/vSSbGcNuVy5+rWfJ7pXO7Eot7Vt6E0s14z6z8yDLwBeIDGOry72ezdwJfmJsIzMl3sNwLval6heTkwPOUQUsc55lzUW2i8L9BYj+vNrGhm64D1wB2zHd90zMyAvwIedvc/njKrG96Xrs1n5XLn5jJ0Zz7PSi7P9dWA01wheC2NqwKfoPHXo+Y8ptOI/SwaV17eCzx4JH5gIXAL8DjwDWDBXMc6Tfyfo3Eoq07j/M37poudxhWZNzTfp/uBjXMd/0nW42+acd7XTJZlU9p/uLkejwLXzHX8x6zLK2kcjrsPuKf5uLZb3pduzWfl8tyvw0nWpevyeTZyWXeUExERyYlOPPwuIiIiZ0BFXUREJCdU1EVERHJCRV1ERCQnVNRFRERyQkVdREQkJ1TURUREckJFXUREJCf+f+yS9q1RyK6fAAAAAElFTkSuQmCC
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<h4 id="Resultados-de-los-parámetros-para-la-iteración-1:">Resultados de los parámetros para la iteración 1:<a class="anchor-link" href="#Resultados-de-los-parámetros-para-la-iteración-1:">¶</a></h4>
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<div class="prompt input_prompt">In [43]:</div>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">plot_deltas_parameters</span><span class="p">(</span><span class="n">deltas</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
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<h4 id="Resultados-de-los-parámetros-para-la-iteración-2:">Resultados de los parámetros para la iteración 2:<a class="anchor-link" href="#Resultados-de-los-parámetros-para-la-iteración-2:">¶</a></h4>
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<div class="prompt input_prompt">In [44]:</div>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">plot_deltas_parameters</span><span class="p">(</span><span class="n">deltas</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span>
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<h4 id="Resultados-de-los-parámetros-para-la-iteración-3:">Resultados de los parámetros para la iteración 3:<a class="anchor-link" href="#Resultados-de-los-parámetros-para-la-iteración-3:">¶</a></h4>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">plot_deltas_parameters</span><span class="p">(</span><span class="n">deltas</span><span class="p">[</span><span class="mi">3</span><span class="p">])</span>
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<h4 id="Resultados-de-los-parámetros-para-la-iteración-4:">Resultados de los parámetros para la iteración 4:<a class="anchor-link" href="#Resultados-de-los-parámetros-para-la-iteración-4:">¶</a></h4>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">plot_deltas_parameters</span><span class="p">(</span><span class="n">deltas</span><span class="p">[</span><span class="mi">4</span><span class="p">])</span>
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QArGlbQHmpnVMYozik6B4/Dw53L7mR102rGZ43n4asefkdif6b2GRp6G7hl0i10RbqoC9SxomEFt02+jcLUwhO+Lz3RHja1bmJhycJT6uApSf0fRLADtv4VDAdU32H//24iveBKha1/gW1/hyt+BPEobHoQxl4MlYugdSfkTQDjLE3Y2bwNDrwJ8YidvP2l4MuBV38AjRvA6bWTtBmBS78H6UXw5i+gYb39+sxRkFYALdsg1m8/5suxE3mwDRxuUA6Ih+ztHH+Fvb78CdCyAxZ+GZwp0LzFLm/LX+GCr9k7C2DvXCgF/Z1Q/xbkjYesCjDj0LAOMkqgcSM8/XkIdUHeRPtzKZwGMz9u179+LcTDkD3arovhhNQ8yJ8Ibt+R96JzPxxcjZr50eRO6ise+g7ll9507BPPfJnAumU82vITnEacsJnKpHNyWPihsfQufZaUmTPo+P199C5bhqnBikZ5Y+H1/N0/ia+uf4iAM4W1H/0CP7ptPsEVb+LMycY7aRIAPcuWoVwu0hcvft/1Xtu0lt9s/g3BWJDPz/w8baE2nq19lrmFc3lgxwP0RHu4afxNOA0nT9Q8QTAWxFAG+b58FpcuZmPrRj5Y9UFeO/QaOzt34lAOclJyqO+tJ9ubTUOfPRaIx+EhxZnCuKxxbG3fSjgeRmN/nuOyxmFaJp3hTgpTCynPKOeFuhcAmF0wm99d8js8Dg8vH3iZDa0bmJo7lT1deyhMLeSGcTcMJpOVDSt5+eDLVPgr6I/1s+zAMgA+WPVBqguq6Qx38pO3fkJDXwOfmPwJNrRu4NvnfZtAJEB9bz2vHXqN787/Lu2hdjrCHeR4c/jL7r/QHmrn9frX6Qx3srh0MTeMv4HJOZPRaJ6tfZY/bPsDneFOKjIqKEkr4c3GNwff3wvKLuD1+textMVnpn+GT075JDc/ezOBSIDeaC+V/kr2dO1hRv4M9gf20xnuBGBe0Tx+f8nv2dO1h0xPJo3BRu544Y5jTrtUZFRw8aiLuW/rfVRkVOB2uNnXvQ9Tm4PL5HhzuLTiUh7Z9QiXjLqEZQeWcXH5xYzNGsvE7InMyp/FY7sf4+5Nd6PRFKcW0x5qx+VwEYwF8Tl9zCqYxcGeg8wpnENHqAOv08sPFvwApRSffvHTrGtZxycmf4LPzvwsOzt2UumvpCPUwc/X/5zRmaO5c9qdpLpSeX7/81wx+gpJ6slIa9CWnSQC9fDn66F9t/1c5SKYdA3Mus1OhvvfACsG5efZCXrlr+GN/4XsSuisBRT4su1Eb0btdWSWQ/dBKJ4JVZfZCSarEmIh+wi56tJjk06oC5Z8HmbfDmMvsh+LR8HhshNb8xY7mS37L/v2qPng8tnryCiFUefBy9+FngYomW0n8HV/tBPu26Xmw3n/Ch17IRqErrojidzlgyt/at/e8xyEeyCzzK5v0xbY9zI0b4Ub7oeDqyDcDaMWwKq77KN5pez3FWDMRfb707X/yLrNKEy61t7h6NoPpXMGWgYGfieyKuyWg1DXkfoWTrU/i+f+A9ILIdhu74i8G18uzPmUXb+uA1DzElgx1Hd6kjepj8obp7e8dB/+6ecf+0T9erjvQsJpE3Bl5vDWzgrWBz/MjIvLmP/hqsHFtGVhBYOsv+HjpNftIWo4cVtxTBQxhxNnRgbOrg6Ux0PKjBnEW1uJ7t+Pcrkou/d3eKdOw5GW2Oaa5mAzqxpXcc2Ya3AYDrTW9g+9y3fc5t7aQC3ffPOb7OjYwQ8X/pBLR13Kjo4dvFj3In/c/kc+OeWTXDn6Sm585kYWFC/gssrL6Iv2ccmoS+iOdHPzszfjNJz0RnsZ7R/N7ZNv579W/hdZniwmZE9gVdMqnIbzmMQ2Lmsc84rmUZVZxXdXfRe3w01/3N4Lnls4l4gZYXPb5ne87jCHso8gvE4vwViQOYVz2NiykbiO43P6iJgRfE4fUSvK1aOv5vG9jw++1qmcxHWcURmjuHXSrdy75V6CsSCfnvZpZhfM5sEdD/J83fPML55PqiuVZQeWke/Lp7W/lV9d+Ctqumv45YZfUphaSFt/G9PzpnNR+UX0RHv43ZbfMS13GlvatwyWNypjFJ+Z/hlK00pxKAejM0eT6krl4Z0Ps7ppNZa2qMqq4sKyCxnlH8WWti3ct/U+1resJ9+Xz3PXP8ddG+/iwZ0PErNiKBR5vjxa+1tZVLqI2kAth3oPMSpjFF3hLn5xwS+4a+Nd7OzcycTsidR015CXkse+wD4+OuGj1HTXsLZ5LdUF1axrWUeWJ4uuSBduw01xWjHNwWaiVpTxWeOZkjuFv+75K9tu3yZJfaTpa7WP3jLLjzy28xnobYK5n7aPXB//FOx/3U66+5fbR50ffQzadsPy/7GPRLMq7Kbf/vZ3llGx0E6Icz4JOVXw4jfsBHXuZ2HHEnjrPhh3Oex5Hjr3vfP1eRNhxkehtxnGXQrLfwp1b9jJ6BPPQeAg/O0OKKmG2tfg8I6v4YRpN9lN3obL3pZo75H1jl4MPY3Qsc8+8r3pYUjNtZdt2mzveFTMB1fKkdeYcTvBW3FIK3z3Jm4zZr83GcXvfE5rO4k2b4U9L9iJvmAqnPc5yK3C9I/G8cq37BaR0jn2TtG+V+2WjUnXQusOqFsBKZkw+gI7eWcU2TtFLq+9TelF9o5R4wZ7B6FwKqRkQ/see4fCsuwdmw33Q83L9ueaXWm/j/M/j8qfkMxJvUrXbnkOR9HYY5/QGrY9DuXn2Ht7r/+EV5/sYlf4Im78bD7ZU6bZy+16FnLHY2WP5rf3LWXhvf/NRn85y8+5lsmbX8cZCdEyajyf6NqC7gngqarCM34cgb89TrytDeXxkHH55Vj9QeKdXRR+8z9x+P1Y4TDOvHzMzg7c5eXvrPh7oLUm1tCAu7T0XZczLRPHUc1tlrZ45eArzC+ZT4ozhc5wJ5mezHfsGHSGO0lzpfHE3ieYUziH0ZmjWdGwgqW1S1nXso7zis/j6/O+zjO1z1DgK2Bn507WNq1lbfNaTG1SlVXF/Zffz9a2rWg080vmY1omX1vxNZr6msj0ZtIT6SEQCbAvsI8rKq5gb/fewfPNVVlV7OzcyXVjryPLm8VbTW/xvQXfY1TGKPqifWR6M2kONtPQ18CWti20hdq4YdwNVPorj/s+xMwYbzS8wYKSBZja5DebfsOuzl3cMukWzi89n5gZ44EdD3BF5RWkudNId6WjlMK0TH6+/ue8Vv8ai0oXkeXNwtIW14y55l2bwk/0ma1rsftkjMsaZ9fLitEf6+f252+nJdjC3Rffzcz8mdQGaqnvrefc4nPpj/Xj9/jRWhOKh/C5jhwF/esr/8prh14jzZXGv8/5d64bex1/2PYHnqx5ktsn387jex9na/tWvnved8n2ZvNfK/+LznAnN46/kW+e+01J6sOdZcK+VyDSYyeCV75v/+CPXmQ3u2oTOmrsZWfdZieSwEEoOweCrTDpOph1C82BHHavbibV72Fc9ja8ex7C7XHaR8+uFKhfZyfV9EKYdB1aKTobg2QXp777qZx4FOIhrLYaWtu8ZKoDmMu+ize4F4cyAW03HS/8Mrz5qyNHob4c6O8gnDEZ10d+R8drf8csmkXewivp6+jH7XNiAAc2N5C+4x6Kx2bAxd+yXxsN0tlmEeyJUTTGj9PtQFuaA9s6iEbijJmRj8N1Gk8LmHE4uIpO1zTWLj1IZ1M/Xc1ByiflMHVRCWnZXnJKUjFjFjvebMKMWUQjcXa+2UThaD9TFpVQXJWJYSi01nQ2BfHnpuB0n+S0yNF6m+1WkZSswYeS+px6Re5Yvf/gepTvJJeLxcKEHvoMD639IB4jxDWfm0J3N+QuvYbU8bPhY38FwOwLUhOI4k9LoaG7n40Hu/nB0p1MKc5AGQajsn2kuBzs2rKHDzvbuFi3EXjiCdAaIyUFs7sbDAPl9eIeNYpoTQ2lv7mbtIULCa5eQ+v//A+R/ftJPe9ccu+8E2d+PpHdu2n75a8wUlMp+PrXiB44QHDNGgr+4z9QTicdf/wjbT/7X4p/8mP811zzvt4ns7cXIy3tmKC1IhFaf/I/pC1eROr8+XT/9W+kTJ1CrKkJz/jxtP/2t3irqsi+7bYjb2NzM12PPkrK9On0zBlHe6idCdkT8Dg8x6xXKYVyHzl/rLVmTfMa9nXv42MTPwZAR6iDxr5GyjPKqemuYXbB7Pe1bYkQa2nFmZONch7pLKkti94Xl5EyYzquwiNJvfeVV3BXVOIZffydiq5HH0WbJmZHBxgOcv/5MyjHkSAOxoKE42FyUnLeUx27w92saV7D/OL5x+3c2BftY0PrBhaULMBQBnErTnuoncLUQjmnfiIt2+Gvt0OoGz72F/uINx6xjzZL54D3XX5XDq6xj57q10HbLvsc6LjL7SPitAI7Ie9YAt4M+zzt4XUFO+CZL0LOGLjoW/aRWct2eOKf7KPDw8rOsV/TthOKptvngLPHYNa+yea9RQRSZlEwYzKxzPFEgjG6mvvJLPCx8cWDKAPiMQs0OFwGUxaV4HQazLxsFJ6UYzsEb3jhAKue2Efl9FwuuGUClqnZv7mdorF+sgtTaazppqc9RKg3hsNpsG15A90t/YOvVwaUVqUzr2Q5be555M2YRsOmfWx9o42cHJOZH5jCthe2UbPPg8fnJBIcaLlTgD7q/wGpmR4y81PIG51BtD/OzhVNaEvjcBqMnplHX1eYppoAYG9b2cRsqqrz6WgM0rwvQHdrP/mjMph2QSllE490MgawTAvDYWDGLbqag4T7YrTU9eDxucjI8VI6MfuYflTxmEl7fR9LfrkJw6EoHO3Hn5vC3vWthHrsUxQFlRnEoxYdDX2Drysc7aejoY9YxMST6kShsCxNNBTHn5/C5AUlHNjWTtWcAiYvtCc47B9YX0q6C62hYVcXPr8bd4oTy9S01vWgDMW+eJTLzylL5qQ+Rte11diBcQpaNu1gyb21xCwPGgel7k1cm/t9+Le99vmk43h8fT2/ea0GS8P+dvtytTkVWbxV18UXL67i+rEZ7GkOUJiRwvY/PESgtYPztr6GIxTEysnF6GjHM24ckdpaXCXFpM47h56lS7H6+uwdAKcTV1ERZm8vZmfnYLm+6mr6N2+272iNcrsp/sH3cebnE3jyKVLnzyf94ovoW76ceGsbyu0mtGUz6RdfTNcDfwaXE3eZ3UrQ+cADeKdMJm3BQsK7duHw+4k1NtK/ejU4naRMnkxo82b7XJtlYWRkYPX0AJD3pS/hnTgB5fXS+JV/I97WhqukhKxbPk5ow0bSzl9IvK2N4KrV9umJgwfxTpxI5g03EGtqIuOySzF7ekg955xj3lezp4dITQ3e8eMxUlMxe3uJNTbiHT/+lD9/sy9IZPcuUmbNOmaHxezro/OBB8i66SaM1FTa/vfnBJ59ltw7P03mhz6E8vlQyt577vjtb2n71a/xjBtH4X9+A+Xz4SoooOEr/0b/mjV4xo0j84Yb8M2ehdnbx8HbbsNTNZb0yy5HRyL4P/hBzM6OwffswMdvOaaOaRddRN4XPk/Hb39L//oNuAoLceTlYvh8+D9wDbHGRszODjzjJ+AqKsTs6sJIzyB64ACR3bsIrlxF4X99k44//BEdDpP3pS9i9ffjmzULrTVWMIgj7d2vYPiHTuq7ltpN0df8CrLH2D2QXT67l/Pz/wE9TYC2OymVzYNdz9jnZ1Oy7cdmfhym32Q3aa/8FUy8Bg6uhjX3YGmDtX03U+lZS4F7LxhOonEn9eYcDoUmkeusxdROfJ4IvrLRZIwqJ7bpKTzBffgc3fR4JmGZJv7YbuLeQsLn/4CapmI62zVxh31VS19XhFjUpKo6n4zcFNYvraWjMYThNLDi1uBmenxOIv1x8sb5uebOaYSDMep3dbJ/czsHd3SCgsx8H+dcOxqtoXFPF/58H6ue3Ic/L4Xu1n6cTgPL1PYOAeBNcxHuix3zduaUpDHtwlL6e6K4vQ56OyPsWdM8mJQOK67KpKOhj0h/HMOpmLq4lN72MNklqeSVpdN2qBdfuptIfwxlKErGZdG0L0B7Qx/tB3vpaAxiKTjkg5oUi8ty/Jg1fRgKSi8qoQuLkhDUrG4mHrUwDEVajpei0X4O7eqkvyfKopvGMfn8EkK9MV75806a9wWYekEpu1Y10df5zvPZWYU+xlYX0H6ol1jEpH5XF06PA1+6i+u+PIv0bLvzsBmzaNjbRXdLP1tercfhNJj3gdGUTsjCjFt401zEoxYHtnVwYFs7DpcDtCazwMe21xsItIUwnArL1KRlelBOg9720ODOjTLsU/qH93ne7nO/uyiJk3pOpa7r2P+eXtNTW8Nb//c04b4odZE5XJ/9VYqmjIZ5/wRjLrCbwVb8L+RPgglXHfPah9YcQKG4eW4Z//bXLTy+oR6XQxEzj7xHZdkpZO/ewieLLb4XH83CPSu4lhYCnlQuvvvHpGT5ibW20r9mLaFNmwht3kzp3XeDtuh94QWchUV0P/YowZWr8Iwbh+HzUfCNr9P8rW8T3rHDLsThANPEU1VFZO/ed2yjkZaGs7CA2KF6dCRC6sKFRA8eIHbgIK6SEqxoBB0Kk/OpTxLZs5fwnt34r7qK8J49ODIz6X7kUTyTJuIZPYaeZ545smKnk+xbbqHzj3+0q+H3YwbsvWbv5Mm4iosx0tMJ/P3vx1bI4SDnk58Ey8SRlYXZ1UXPc88Ta2gAhwPvxInE29qIt7ZS+J1v4500mf51bxGtq6Pga19DOZ3EGhtxFRWhYzGU10vXnx+k7Re/wOrvx3/tNRR+5zuENm7E8Pnoee55Ov/0J1Lnz8fwpdC77CV7x2rPHgCUx0PqOefgzM+j+69/I+3CCwnv3Em8qWlwO7Essj7+MXsHCVBeL8rlAq3tHTKwd4IMA+JxcDpRTifOvDyyb7kFIz0dq6+Plh/+ECwL5XaTftllROvqMHsCmG3tWP39nBLDwEhPR8di6IHXFH772/S9/jrBFSsou+8+UufNxYpE6Pj9ffS98gp5X/wCjqxsvFMmYxjGP15Sb9sNr/8Edj5tNwV7/XYTZlfdUQspuPHPdhPn0n8DhwfK5sLUG+xzwB17B46ejxxWRi0PvWYeGXMvZ0djFSs2V+HLcGEok1BvDNOyW2UchoVpHds0rDDROHB5YXThevYdnEzc8gIWR8+dFXRolNPAqRRpqS5cXgfBhoHvSoqDlZkW64L95DgcXD+3lIaOEPv7w0T74+zpCfHcFxZS4PeS4bXH0tjf1MtzbxwktrodV8hO2IdLTMnxkHppMVNy0zi4uoW6QIhFl1YQONTHmjWNVC8oZdqMfLxpLvp7ouwJhijN8vHAqgMEQjFcDkW6Vux/pYE2n2JeaRadLs3VF1Uyu9jPtjcaOeS0aHdrFlblMb4wHcvSPLGxAcOAyycXkTLQHL23pZc77n+LvnCcQDBGRoqLtBQnWT43WxsCpFngQNHnBNPSGAoyLYPUOHT5FLMqszlndDbdvVGyNwUwG0KYfhepShHti+H1u+nviNCXarArTXOoL0xKsY88n5uLczMJb+4i1B7GSjFIdTkpn5RN28FeLrljErml6XT3R/GnuOzPUimaAiGaAmGWbmni/HF5jMrxsXRrM32RGKVZPva3Bzm/Ko8FVblordnZ1EtXf4R7n9/LqkNdLA65yE9xE+yP0e6wGFWUjhkx6emPURONMi7Fg8/rpDtuUheK4HEZzC3K5Jv/OjeZk3qFruuoe1+vjbUd4s8/qSPVaiKfreQ5djGldJ997qqrDvxl8IUtJ7yUw7Q033t2B609Ee5YUEFjd5i8dA8zyjK54ber2NoQICfVTThmEozaHURumlPGf31gEj63k8buEA+tOYChFP96YRVu55FyIrX76bz/fvK/8mUcGfYeu45G6X31NeLtbfivuoq2u+6m68EHyb7tVrI/8QnMnh6Uw0HbL35Jzqc/Rcq0aXZHwN5eHH676c8KhezkdJKWjb4Vb+IZXYkzP5/9P/4Z7uxsjEN1pEydgv/aa9mzYCHK6WTMC8/T89xzGB4vmR+63q6n1hz65KeINTaSduGFxBoaiNTUEN23z06W8Ti4XDizssj/ypeJ1NURWr8BHYuBZdktBkdJv+Jy4s0thDZutBOnUvjOO5fg68tJXXQ+nrFj6fy/P+DIy8VsO9IZyFVeTuzgQQDy/+M/yL71FnpffJFYQwOxpmZ6X3mFeFMTGdd8gOIf/xgdCtH9xBMot5ueZ57Ff911ZH7wOvrefBPlctH18CMowyD3X/6Z9t/+DndlBVk33kjbr36NMzeXeFcnxE1y7vw07rIjM5P2b9hIZO9eUuefd0y/iHhnJ5GaGlwFBTgLCwm++Sbx1laMtHTi7W14xowl3tpKaPNmAk8+yagH7Z2Lnmefpf+tdfYOnsuFMycHHQqR/7Wv0vf66/Q+9zyOzEz7VBDgqapizDNPJ39S378c1t4LH/iV3Qv6ic/Yvb3HXGR3/Fr5K7vz1fwvQloBvYFOjLyxbOjJYHyej/zGlwnkV/PqxjB1K5tpLnWz9FA7s81N/FNJiJoDs6kLesiKOgADrUBpyCtPp6OhD3emm6yxforzfBSN9hPyOwkc7CM7y8tDy+uIx0zGmRGWH+xjVL+LbMsgZGg2p1n4DQdFeT68Phcq281+K05LT5jatj7a++wjYL+pSNHQ6tDMGJXJ1dOKeX1PG6/vaSPd66QkM4XW3gjRuEXcstAaPjZvFDubetjR1EMgFMPrMJiZkkJDV4is8jTqG/vowAIFhoLizBTqu0KkuByUZqWwt7WPdI+TqaV+esNxfG4Ha/bbrYkOQ5Gd6iYUNemLxJk/NodUt5NlO1swlMJpKD46r5yXdrZwqNPuve40FJdNKaQ5EGb9AbtneLrHyZzKbPLTPTy1qZFUjxOXQzG+MJ3ffnw2SoHbYdDaG6EvEue+N2rpCce57dwK3qxpJ2ZaFPm91LT28ezWZtr7IrgdBrG4xZSYg9kRJz5L8ffUCB0OTY6pcOd5SfW6uHhiPusPdNEUCLO/PYjSUOh20hY3SXE76I3ESfM4KcjwUJyZwht720nzOInGLSpzU9nd0nu8byKGAuuotDkqx4dDKWoHWnr9KS6+dHEVnf0xVu1rZ0JhBiluB/evrMOf4mJKiZ/LpxTykeqy464/qc+pV+aU6/0dB9/36/dvbmPpPUfOY5VnNzC9eDPlhV2w7W9w6xK7o8p7FI6Z7GjqYUxeGg+uPsDfN9QztzKHR9YeJD/dwxcvHscvX95DR1+UuKWZUZZJmsfJ4vF5XD6lkNd2txGMxJlUnMH4gnQeXH2A8YUZpHmdmJbFwqo8nIYismcvnqqxqFO4hnR/e5CtDQHmj8khJ81z0uVX7munvjPEd5/ZQTRuMbkkg2umF3P7eRV0Pf0MvU4vhZdeyMqaDg50BLl0ciF/W19PTWsf543yk+YyuGRmGR6ng3hXF/G2NtxlZVih0OBOxuFzzaal6Q3HyDAs+tesQcdiuEePpuuxv9B1//0Yfj85t9+GGeihf8MGwlu2kHXrLfZRvFJ0/OGPtP7sZ+R98Qu4CgsJrlpN/pe+SPRQPc683GOS7GGWaVK3fhsFUyew9kCAWeVZ+H2uU/p8Dx8lKKVYu78TS2vmVWYP7iy9sL0Zh1JcPKnALsuyLyR0nMK4B2+nLQuzqwtnzpFz8LGmJnqefZaMK65Amyb1X/gikZ327KZ5X/kyWTfcQM+LLxLdX0fnH//IpN27kjupR3rh7nl2j+GBjllkj4aP/Y0WVwkPrKrjnxaNIRwz8bmdfOOJrTy1qRGlIC+myLMMKh0udMRkUtQ+5xwyNE63g65Ug9TOGAoIexT9aQ7ifhct9b14UlzkTstm1Z426kNR4sr+AQ9GTNr7jjTvOg1FqsdJIBSjyO/lR9dNxR+yqCzPwJ/rO8FG2d+ztfs76YvEmVmeSX/ExNSaytwjV9wEI3HcTgOnoTAtzcNrD3LPa/vI8rnZ0dTDxKIMCjM8fPPqSZRl28mlOxQjO9XNoc5+3tjbzuTiDP66/hCPr2/g61dO4M2aDp7f3sz/u2w8u5t7OdTVj8dpsLeljw/PLqUnHOMj1WXMLM/CtDQ7GnsYX5iO22kQCMWIxi2++NhG1tR2MqXEz78sHsPUUj/3vLaPF7Y3k+F1cet5FVTlp/G39fVsb+yhvrOfGeWZ/OTD08hP99qjdTreWye4cMykJxwjy+emKxjF73PR0Rdl7f4OwH5/slJdXDA+/5gDG601SzY38vLOVr525QQaukLcv+oA5dkp9EdNatvs387rZpQQNU0MpdjaEODC8fkUZ6awsCqXVbUd9IRiLB6fT5Hfy4HO/sEdleV72rC05vxxeRT7U5g1Kovs1HcORhWMxHE6FB7nu3ekS/KkXqb3dxwa0jr2vNVMWpaX2k1t7FvfSrgvxvVfmkzeY7PtEYrGXQ6edJh9m9179OAaWP8nKJllX1pyCg7PAvdWXSdf+ctmDnb2U+T38sdPzOHlna385tUaSrJS2NPS947X+lNcBELHntcam5/GpZMKaO2NsGpfBx+eXcoFE/L510c2cPPcciYUpvNmTQdPbGxgRlkmVflp3PtGLVpDXrqHm+eU8ea+DsqyUugOxfjkgkrOHZ2D02Gwcl87S7c28eBqe2epJDOFy6cUsq6uk831AW6eW87Whm62NfSQ7nHSG4kfU0+l7IsPACYVZfCnO+agUKyr6+SxdYfwOh2MK0xnUlE6WxsCXDyxgB89t4sNB7v43AVV/OuFY1myuZEfLN2JS2keuLKM0ZPHgNOJaWlUKET/2jWkLV58zM6MFQ6jPJ5TGoxld3Mv//bXzWxtCOAY+DEsz/bxuQvGcu6YHMqyffSEY6S6nfRH46za10FlbioPrDqAx2mwdGsT2WluLp1UyC9f3otpaRZW5XLLOaNYua+DP62sA6DY72VMfhrd/TH6o3E+Om8UmSkuPjT72CsZesMxXA4Dr8tBzLRwOQwC/TE2HupiYlEG+ekelu9tZ8XeNipyU7mxuuyYHzxtmvSt30BTdz+jL1p4zHO7apuZOKYoeZJ6fyc0bbLjsGE9lFbD5kft1rV5n7GvSz7nX2D2J8Dp5t/+upm/ra8nO9VNsDdKtctLScAiryIDh9PAs8s+2rIMu5G9aHYecxeWsvyh3aRmumnc043K9uBfVMB1iysGR55cWdPOL17ey66mHmaPyuIj1WXELc3v36glL83DlVOLUArqu0LMH5vL9FI/Gw91U5blo9CfuIGdTiQcMznQ0c/4wvRTfo1p6cEdz0AoNtjU/H4dvT6ROEme1Ev1/o76hK2vvyfKX3/4Fu4UJ2NK20nb+2fGuV9CoXGk58K8O+GNn9vXVHoz4f/tA8d7m/MmEIpR09rL1JLMY5rcAd6saWdFTTsfnFlCQYaXe17bx/0r67jrozMpyPASjpk094S5d3ktWxsCpLqdTCrKYG1dJ4ayjwQPn983FFwwPp8tDQHaeiNcPLGA28+r4Ccv7GJLfYDRuam09IQJxy1mlWfS0BUiO83Ntga7g9xHqku5ZnoJY/PTKPTbe87ff3Yn962w+zB8+ZJx7G7uJT/Dw4dmlXL7H9/C6zL462fOJRyz2FLfzRce3YShIMXlIGZq8tI9+NwO9rYeu/PidhicOyaH1/e0Mb0sk6313Uwvy6SuPYg/xcW5Y3JZtqOZnnCcBWNzaekJ88kFlXQGo7xZ0855Y3KZXZHFZx/awMfPGcXq2g4+f1EVcyrszo894Ri/eXUfHz+nnFDU5Nq738TndvKZRaOp7wpRkePj92/sp6HbbibMT/fQ1hchJ9VDTyhG1LTPQx7eXyjL8qHRHOoMMakog+tnlfCDpTuxBgaXunJqEaWZKexrC7Kipg0Aj9MxuHM2tyIbU9tH+939Mfa29pGb5mFaqZ/X97QxrdRPa0+Ehu4QPreDK6cW8bf1R/pvzKnI4o75leRnePGnOAlFLX78/C5W1LSTnepmcnEG37lmMpbWfOr+dbz+7xcmR1Lf8RQs+Vd7YA+wByAJttq91i/8Jq/Ep7BsRwufmF/JpoPd/PTF3XQGo8zJSmPCwRi5MfsDdKY7MfviaA0V03I557rRZBWmogZaX44Wj5k4nIZMzSzO+BTd4XiYVw6+gmEYTMiawMHeg7T2t3LD+BuSOamX6P0dDQldZ836Vl74/bbB+y63wjA05xQsY0rkN0RcRXDeZ/G8/p/wyWV2h5y199qXqFx3z7EDIiRA3LSO2wx19OPPbmnif5ft5r+vm4LbYaAUjCtIJ93rwrI0Lb1hCtK9g5drBPpjpHudKAU/eWE397xmDyzhcijOGZ3DPR+fTZrnnTsrcdPiy3/ZTHm2j3+77Nhe6p3BKJbW5B7VtH/v8n1sOtRNfVeIrv4oSz67gKxUN6/samFnUy+XTCpgT0svM8uzKPZ7uXd5LX9dX8+Msky+e+1kttYH+Orft3Kos5/LphTiMhQrajpI9Tg40GF3HCrNss8DZqe66Qwe6YHrdhhcObWQ7Y09KAV7WvqYUpKBaUFLT5iln194zBGT1pq9rX2s2tfB+gNdlGalcKCzn4J0L4vH57FsRwvnjM5h3uhs0r1O3A6DQ50hijK9uBwGq2s7CMVMzhuTc0zzWV17EFNrMlNcdASjPLmxgeV728jwuohbGrfDYF5lNvevqqO9L8qHZ5eyvbGHcMzkS5eM4xt/30pvJM6HZpXyw+unsmRzIz96bufgudajt/efF4+hoTvEyztb6AnHMS1tX4L5vSQYUW738/DYx6BoBlzwdfs667wJEOpmTQt8a8l2djX3UhEzWBSyjzC126AhBRa5UoiH4ky7sIzc0jTKJ+fQ3dJPzfpWpl9YiucUT7uIoWnsayTLm0WK88hvpKUt6gJ1NPc3U5VZRZ5vaOOiJ0pLsIWna58mx2uf9uoMd/K7Lb/jklGX8B9z/+OUJ+WqDdSS4c4gNyX3hMtEzAhuw41SilA8RCASIBAJ8KXXvjQ4jPjRhjqYVEKSulLqcuCXgAO4T2v9o7c97wEeAGYDHcCNWuu6k623IrdY17U3Drl+R9Na89KfduBLdxMMRLFMi0h/nPpdXVSfZ1BbowiHFdnhdTiUyVWZ3+NgynWEugJMyNkKBZPszjrZlbDmd1D7Onzo96dvooAh2lof4AN3rWBSUQYPf3oe6V5XwpvMLEsTs6yTnis6Hq01MVMf06oRjpmsP9BFSWYKo3J8fOy+Nazc18FNc8oYnZfKxRML+NXLe3l6SxNTijPY3tjDNdOL+fvGBjxOg7s/OmvwfPdwUdcepK4jyOLxx449//y2Jp7Y2MDPb5wx2PQbjVtsbwwQCMXoCcfRWnPemFzy0u0dqgMdQf686gDFmSlcO6OY3HRvQpP66Yjn4yb1rjp72NG2XRDqpj1tMXtKvoW/KJOuXBfL93cwNj+Nu5fsZGbYyfj0FBydUWIORdhnUGg46W7uxzAUV39uOmWTjn/Z6tliDQxFur5lPTErxtzCuTgN+zPWWhO34rgcJ9/haOprYkfnDhaXLh4cgGpT6yaeqX2GSTmT+MDoDwyupzfay+a2zWitebr2aeoCdXRHurmy8ko+OfWTOJQDl8NFKB6iNdjKnq49VBdWD86JYGmLlY0rmVM4Z3B8irgVHxwl8nhHslEzypsNb/KV17/ChOwJ3HPxPSyvX86fd/x5cCAqsOe/+NTUT+FxeHA73Hxw7AdPOAfF6qbVHOo9xHVjrsPlcJ3SUbTWmmUHlrGqaRVuw82G1g0YyiDHm8MdU+4gz5fHuuZ1rGxcybqWdYPDRx82KWcSe7r2MDlnMgtKFqDR3DDuBnJTcmkJtvDY7se4YdwNFKUVYVomP1z7Qx7b/RhgDy997dhrmZQ9CVObTMuzB0B7tvZZ7tp4F5X+SqbkTuGpfU8NzvSZ4c7gRwt/RLo7nUO9h8jz5VGRUUFR2tBOpw05qSulHMAe4BKgHngLuFlrveOoZf4FmKa1/oxS6ibgg1rrG0+27srcIr2/vWlI9TsVlqV59YGd7FrdDIDDaWDGTUAxtWgb29umYsUtPjL3WfJa/jYwNvA1sOUvgLbPyy/+qn3pjL8Mdi+1j+wLpx2ZWegs0Vrz9Se2ceXUQhZWDY+95Pdqd3MvX39iK7++eSbFme9sKYnGLdxOgwMdQfLTvYOX0PyjSOR16qcrngeTejxqj6PduIH+135PKJ6Gu2QctS1FvNVxJZGQCRosNFGg19D4tcLrdODP8RKLmlz3pVn481LQWtPfE8UwFL2Obl479BrXjLlmcErlo0fsA3uAn8MTB+3p2sOuzl2cX3o+Ge6MY0ZrPBmtNS8ceIHKjErGZ49nT9ceGnobKEkvoSvcRX1vPZvaNvH6odfpifYMzhvgdXiZlDOJOYVzWHZgGU3BJhaULGBG3gwWli5kRcMK/r7371RlVvHl6i9japNt7dv4wZof0BnuZEL2BG4cfyMbWzfyYt2LxHWcuBWnNK2U+SXzAXhu/3P0RO1TbNnebCbmTMSpnCyvt6eaDpvhd2yPQzm4vPJyApEAhjJYXr+cD4/7MKZlcrD3IJtaN1GVVUV9bz3XjLmGmBXjrea3qPBXUN9bT22gFktblKSV0NjXODj/xNjMsZxfej4VGRUUpxXz2O7HBueOAMhNyeVfZvwLTuXkyZonMZRBdWE1fdE+Htn1CKY2GZc1jpK0Eur76rn7wrtZun8pf9/7d/pifVxQdgFOw0lNdw03jLuBJ/Y+wZrmNXgcHkzLZE7hHJyGk52dO2kPHblypji1mAp/BV+a/SV8TvtUW1t/GzPzZ7LswDK+seIbRC27pSwvJQ9TmwQiAUxtMj5rPBNzJhKOh3m+7nk+NvFjFPgKWNGwgrXNawfLSHGmEDNjxHWc6XnTOdhzkL5YH4vLFg9OsHVO0TmUpb+zk+9ZP6eulDoX+LbW+rKB+18D0Fr/8KhlXhhYZpVSygk0A3n6JIVX5BXpurbTn9TBPrf2xE834PI6uODjEzC7mnj98QYaD8TJyEshGorjy3Bz+c05ZG3+oT34fv5EGH+lPYHB4ZEFDJd9qQ3Ywype/b/2OMTzv2QPfLHqLrjsh1B21IxmB1fb4ypf9xtIy39H3YR4NwlO6qclnqurq/XK117nqd9+jnVhB85oDnkdC3CYKUScUVLiXoJGjCfK3yS7fz6L0zPJSu2gvrkZbZhMujqHfm+ALW1b2N21m5n5M6kuqKYj3MGLdS9ysPcgwViQiowKgrEgbaE2Pjj2g7gMFxpNc7CZNxreoMBXQMyKDR6lpbvS6Y/3c82Ya/j8rM/zZM2TZLgzONhzkJ5oDxtbN+I0nBSnFZPqSmV35268Ti87OnbgMlxMzpnMprZN79jedFc655edT6GvkFEZo8hwZ7CuZR2bWjexo3MHmZ5MFpYsZG3zWpqCTYNzHkzOmcyerj3ErCOdZ0vTSrlt8m3cs/keOsOdZHuzmZo7le+c9x22d2znzzv+zLb2bcSsGOeXns+1Y64lYkZYVLZo8Gh7S9sWHt/7OMWpxWg0PqePTG8m5enlPFP7DI/veZyC1AIa+hoo8BXQ0t+CUzmZlDOJiTkT2dK2hRRnChtaN+BxeJhbOJfdnbspTS9lbtFcytPLWVy2mF2du9jQsoHx2eM5v/T8dwxbvaVtCy7Dntjork13sb7FnqSlKqsKrTU13TU4DScLShZw1eir+O7K7xKMB3EZLiIDQ9POK5pHtieb1+tfJ2JGSHOnEYgE8Hv8fG7G5/jQuA8Rt+KDpwF6o70sr19O1IwyKWcS47LGvetRf8SMYCiDnR07+em6n1KSVkJRahG5Kbn8cO0P8Tg8RMwI14y5hu/N/97guvZ176Mn2kPUjPJs7bNkebO4tOLSwaN3hTqlncfhkNQ/DFyutf7UwP1bgHla688dtcy2gWXqB+7vG1jmOLMQHJHpy9aBo2fCOc2UsjvMWJa9Z20YDvIzSunobWJs0TRuv+gbxM0Y33n0VrS2SPGk0dNv/ziowXUAGFjawnHU9+btowfpgX8sGFzO0seMqPj2ERbfcV8Ih8OBaZqJTOqnJZ6VUvrfP/QbynPtvhpxM0Zd+04sy6Qws4L7Xv0WDV37iJlR9MBFwMpQaGug2fVw8Gjsx4wjj2nLDiRtaZRTHRm563BgDdzXph4MIj0QbMqpjl32aIeXAxjoZHe47MF1KcAcWLcxUNbhv/dAue3yddRer3LYIyKisX8kDjPedv90UKA8Ch3TYL7tuUSXfzjHvb2co+oyWKeB78Nxyz8T78vh+hxn+NtESUQ8v7eu3WeAUupO4E6AjHcbm/k00Nri6H0cyzJp7j4AwM76dfz2+W/wlet+zc3nf4lReRPITi+gtfsQHrePZRsfYeXu57hm7ieZNXox3/vLHUTjYXscKXXkO2Ad/i1Q9t/h77TmyKAGh78zxlHJnrc9f9jbv8uOgUvOhvL9XjjpGvrCATbWvj6EtRwhOyP/mI6JZV825bnjeWTFz9i6fzW9/V2DzbROh4u4FRscdE057YCxopadMNHv+BINPsbbHj9q9Ed9Ct86HbWX0Ya2E6mpT5iUD6/vhOs9UWI6BYfrMVAAOn6CMs5E4tKgw2eo/JO9Z/rI/4M7WMdzJt6XgXoc8/8wlIik3gAcfWKgdOCx4y1TP9Bc58fuYPMOWut7gXsBKguLdCDUnYAqJs7z924DLiY100PJ+ExK23IARU76l7jj6v8YHCN50+u1jJtXgMNhoGMR2rduI54xhqKxmUdW9uRnYdODcPmP7F6/f/6gPbewxw/RPnuqP6cHNj9iL3/48VufgsqF9jCZr34f5t5J4+j/R+6LH8bduQXQcNXPYNbt0NfMvqeeJj0/g3xzo90XoGIhwS2v4nbGcY2ea08jaMZgyefp8kznkafH4XLGufXDN+OZdxPcM9+eM/lfVtuXG0WDdkfBpi32FIUbH7TrtfDf7MktVv4K+lrsKRXvOc+es/mza+1pFg9r3gar74GqS2DiB2DnEnuWqrn/ZE+SAfYUhWBfr1wy+4Sj/3U1B2mv76NsYjaWqfFlvHPgh1Oi9SnPM/BemKZFLGziVb32ACqFUweK05gx673N6nQcCb4MJ2HxfHQslxSO0nF1kPvnl+Caex3O/HwK/vMbGKknmT1MiCQR2rwZZ2EhroJ378Q71HhIRPO7E7tjzUXYwf4W8FGt9fajlvksMPWojjXXa60/crJ1jykp0fsaEntJ21CZcYv+nig+vxvHwCVnWmsObO1g95pmUNB+qI/ezjBm3CK3NA1futuedAGYfH4JDbu7mHlpOZ2HuphWvof+gsXkV2bSvLuFtX/fwczClZQXB1GL/x3TSOXA80txmr0UL1iA87EPY3XUYaTl2FM4aovN8ZtY0f4Ril3bKJpRRXD/Xuo7CylL30uF8QbPdf07AKM9q5hX8CJG0RT+svYKUo0ursr6Ab6K8bxedwm+/t20xcfQEhtPXLuZnfo3zil+1Z7jGQ0LvgTbn4CuAzDmQjiw0p7feNR59tjbO5fYb9LhGQsKp0HzFkDRP+er9E//HLmh1fY8y4F6u18CQPl5cHClfTt/MnzsL5i7XqT1hUdInXguvRtfouiKGzHK59LX0smbT+wnaOUwdsF48OXyxl/tKSsNZWFpg3MucFPZ9wjp8z+MMWYR3a39ZGZZODb/2Z7LuWDykQ80FrbnM7Zi8H+XUJ/xIdIu/DSZBSceCQyg7WAvW1+rp7u1n9RMD6Xjs+xZm3wuqqrz2fDCAfoaGpjsf5PVW8toC+bz4VG/wB94E3XBV+mb/kVe//0KmhssPvKFSoI1m6npnso5143F6XbQ3xOlbms75ePSSdv3ILH6bXRO+nfyxpdhGIrmrft49ckOpl1QypTzSxPZ/H5a4rksv1L/ZNGXqG55HGduLuHdu8GycJWUkP/lL5E6f/7gSIQicXQ0esyMiu9XvKsL3d9vD3+8ezeRmn34P3jde5qgaTiyolGCb7xBx72/J+ef/on0Cy/AikbpWbr0yA6nUqQuWIDhOXI5rzZNYg0NuIqKiLW04MzPxxh4n2MNDQSefgZnXh7aMnHm5BBc8SZdDz+MIyeH0rt+jXfSJLoeeYTI3r345swh/aKLMHw+lMNx9s+pAyilrgR+gd2a/Aet9feVUt8F1mmtlyilvMCfgZlAJ3CT1rr2ZOsdqXMw73izkbVLahlbXUDd1nZ62kLMu3Y0u9e00NUUPGZUtsPSc7yEeqKYcfsUgNPjIDPf7qDX0273WHWnOCkencrBnV343GG8XpPKyhhvbcwk11lHe3w0hqHw+JzkZIWpP2QAivQsJ+OnONi8Okw8ZuFSEZTLjXI4icdMPPTRH09HY6AwOT/3EZqKPsHebVEuHPsKZtFsdNN2Rnf/Hp+zD2bfRsPWehrN6fSXX01DbZj0HC8lhf3Ubuslqn24+2oZ43iJPcaH8dJNQ6AEjWKR//+YkvIsAPq8LxDZs4qmeouKBTOIj76Ctsd+hEv1s7zj4zTHJgy+P7nOWvJc+2iOTqTXysPvaqEjas9SV1bSz+yK7dRsbKfLHEVDZBIABjG0cqK1oty3gyvTv4XD6UCPuYgtB8eyv6OCqc6/U5m5h97sBazfUcTO0MUYhqYis4bSwiDj5+bTqUdTU5+Ls3kdE2d6ORifyxt/2YvTbZCXD4H2KMH+I0fbqemKYK/GqULEtd1Zx0mEOB4yvAHy2UpNeAEKE4M4ea46esw8+q1sMtIidgdLHaenzwtocpwH6DXziOpUPO442b5OQr1Ruk175Lqhzur0dqcjnkfljdE/WvwpbnzwyxgeD/3r19P32uv0vvIK0X37UCkpZN10E2mLFuGbN9c+f22atN11F30vvYx38mR0NErq+QvxX3klyu2m+4knafv1ryj+wQ/eMUvgcKIti8NB3/aLX9LzzDNY4TCp8+dT9L3/PiZZJIIZCND1yKP0PP880dpaRj30IClTpx55vqfHnkAoFKJ/3Tp88+bR+/zzeKdNw+rrwzthgj1DYF8f4a1b6X3lVbr/9jcwj20rd48aRcXjf8ORlkb04EGcufbshADxjg4Mnw8jxf7+W6EQnX/6E1prsm68kd5lywht2Urq/PNImToVHTexgn2Ed+0iVt+AcjjIuuXjOLOyjryPWhPevBkzGCRt/vzBx6P1DbT/9h4iu3aTutBOvlk33UTf8uUEnnyS7Ds+Sc/TS4geqsddWYF3wkS8EycQ3rmLlp/8BGIxlMeDjkQo+NpX6XtjBcEVK47Z1pTp00mdPx8rHCa8cwfhLVuxgkGU14sOh3Hk5KCjUTxjxhDavh1ix44SimGQ+aHrCa5cRayxESMlBau//5h5HNxjxpB1003k3HrL2U/qp8tITepHM+MWwUCEjJwUOhr62P5GI1MXl3BoZyfZxWnsXtNMfnk6B7Z3kJLqYs7VldTv6qKjsY9Aa4h4zGLK+SW4UxzsWdPCwZ2djJqUjWlq2g720t3ST2ZKNzdcVUvP2NtJy/PjTbWvWW072Mu21+sZf24RxWMzCfVG2fL4G/RFfEy+ZBKpmR5W/b2GeMxi2oVlGAa4Y23klmcRdWbxtx+vp6spOLgtKSkmF14cIeCdzsrHa7AsjcNlUDIui/qdnViWJrcsDV+Gm4Pb7ZaJtCwPThVlTOwJOqIl1EXmUJ7TQHuXD9OTg9uj6O02GTU5i56OCF3N9qAzLmeceeN3w8FVOCZdwbad6YTNNBSaC2+fTGlpnPbnHqCroYvK3j/jMiJQfQfR0gt48/6VZI/KI9jegyPUAmjWBW+ksFhz+fjnaKzp5sVDH8XliGAYBg4VpT+aioHJtOzXiYbi1Mem0xMvINNRT6+ZD0qhtcLnCNBPDqXZbVw69U08e/+KjvbT7Z2BLpzG6k3FdMVLOd9/HwWX3MD20CVoh4fyoh72bQuxfUOUUF+M6enPMX7RODrb4LW1ZWjDyZTMN9nfPRaf0U1HvIILsv9AdzSPZvdC0kqKKGj/C81d2TRGJxEwi1mU8Vvi2s3Mnz407AefGZVXpX9wyc187OHvHvO4jkbp37SJrocepnfZMrAsUs9fSOp559H15weJNTTgmTiReFMTyuWypwYuLSX9ogvpfOhhO1laFr45c3CXl+MqLsY3pxqzuxuH30/04CHSLliMIzOTyK5dBFetJvDE30lbfAH+D15H4Omn8X/gGoy0VBwZGRheL2ZPDz1Ln0O5XMRamlGGgSMzC8OXQt/ry+2Z+m6/DVdh4Tu28/DvqY5GsYJBuh58iK6HH0Z5PLiKiwlt3EjaokU4MjMJPPUUjpwcjLRUnLl5+K++iswbbyTe3m4nRK+XWHMLRqrvmORmRSLEm5pwlZejw2FwOIjsrcE9qpy+5ctp+cEPMTs6SJk5k+ihQxipPrzjxuEqLibW2EjvspdwlZRgBgJYfX24KyqI1tUNrt87aRKRffvQkYHx7V0uMq+/npSpU3BkZeEZM4ZYUxMHP3EHGAYpU6cS2roVd2Ulhd/4OoGnnyHw1FM4c3LI+fSn6d+4geAbK47MfjgwC+XgFNBvP8pxOOxTb0rhmzeXnDs+iXtUOW2/vouep58GIOuWWzC8HiL7aul74w2UUrhHlRPZa7faHZ5m+jAjIwPPuCqitfuPmQI7df580i+7lIwrrqDhC18kuHIlOBwUfvM/8U6eAoYisncvLd/7PlZfH8rlwlNVRcqM6XjGjSO8cxfuslJCm7dg+Hz0b9pIyvTp5H/xi5iBAMrrJd7Sirus1H7P+/ro/MMfMAM9pF98Eb558wg8+RSx+kN0PvQwViAw5LkcJKmPYOFgjNVP1TJ1UQk5Je8+5/b7EYuatB3owZ3iQluaZ3+zhWC3HehFY/1cfudUXF4HLreDui3tdDT2MevSUShDsebpWvZvbueDX55pj+jVsh1z/0pe3XEuNRvaGD0lnbh201rXQ+WMPPasaSYl3c2sy0YNzC9dgM8dtsf9rv6EfU7/uJUM22P1Gw6Y8TFw+6Bluz0aGUDdCgh3szcwnVcePYDTZWDGLLIKfVx02yT+8oO3SMv2MGNKD2Wzq/CXFdqvzxlD3cYGnnu4jVRPmBumPkSXawpPrJiHgygfK/g86a4A+HLhqp/C45+CaB96wVegpBqVWQpF095R3UBbiK6mPiomZw5uUzxqEg2bdl+AYAf0NWMqD45XvmWf4rjzNcgaZa8gHMDs66azvou8Ld+Ccz6LGn/ZsE/q5Xnj9Q+vuI6PPfDjEy5jhUJ0PfYY7b++CysYJGXGDLI/eQcZl1wC2AkzuHw5rb/8JZEdO0m74AIKvvENeyrjN1cSa2nB7HhnVx0jNRX3qFGDUxu7x44hWrNv8PnDR2k4nfiqqwlv2XLCaXMdfj9mfz+OTD+ZH7ye6P79pF1wASkzZ2C2t9P8/R8Qa2xEh0L2zIRA2kUXYfUHMbu68V93Ldm33YZSip4XX6Tv5ZfRcZPI/loiO3biyM62k47TiSMtzT6KMwxchYVo0yT7lo8TWPI0kT17cBYVEW9txZmXR7y5ebCO3ilTKPrv7+KdOJHel1+m/otfwlVcRLzVHtI48/rribe24MjKxurvp+eZZ0i/9FJSZsxAR8K03XU3aYsWkTpvLp7x40mZPn3wiPtowdVrCL75Jr2vvIJ3/DiCb660p2p2uci66SZCmzcT3mInu4yrr8b/gatx5OTS9eCDuIqLyL7tNtp+8xt0KIyRbv9++T/wARwZGcRaW+l9/gW6Hn548EgWIOcz/0R0fx29L7wALheu4iLSFi0i5447cBYUoMNhogcP0fP8czjSM0iZOoXuJ54k7wufx1VQYA/609ZGZOdOzO5uMq64YvD0hNnbS9cjj5J+ycV4KiuP2dbDrS2ns/+HGQhg9vbiKSuTpC7OjHAwRtuhXnzpbrKLT97B6USjQJkxC4frvc3QlAgdjX2s+MtefBlu5l0zmozcFHraQ6Sku3F5jt9ZraOhD2+qi9RMu4l00//8AI/ZzsTb77CHMlUG+LLtznyRXvucfSKdQue9RF6nfrqU543XP7ruA3z09z896bLx9nZiDQ14p0077vfn7VMOv/21/Rs24MrPJ97ZiSMzk+6/PU54507811xD2sIFuMeMIbJnL32vvop38iS6HnkU7+RJWH1Bel95mZRp08m+7TaMVB+u/HxwuTC7u7ECAVxlZcTq66n/7OeIHjxoN592Hbns1khLI/3yy3CkZ+DMz8c7eRKpc+eedJu1ZdH2y18R2rSJ9IsvJtbUhNnRTsrs2cQOHSJaV0e0ocFO/Dk5ZFx2KZF9tbjLy4jU7sd/7TWYgQDu0lLSL710cIZEODYO3x6TOhql57nnSL/4YoxUe1RMs6/vfXVgNHt7Ca5chaeqCs/oSrTWRGtqcGRnHzML4XtaZ08P4e3biezfjzMzk4wrrxyoYxAj1ZeUnSyHxTn100WSuhAnN1KS+v987Fpu/MVPznZVEuJwctTRKM3f+z4Ov98+qp0yGXdFxekp0zSJt7XhzM1FOYfd1cgiQYYaz/LNEEKcEZ6s4Tk/wvtx+AhRud0Uffc7Z6ZMh+O45/GFONqZbwMVQvxDSi8emXMPCDGSSFIXQpwRhWPGnO0qCJH0JKkLIc4ATfmUmWe7EkIkPUnqQojTTmmL9HyZgVCI002SuhDitFNnbMYNIf6xSVIXQpwB4bNdASH+IUhSF0KcdrkVxWe7CkL8Q5CkLoQQQiQJSepCCCFEkpCkLoQQQiQJSepCCCFEkpCkLoQQQiSJISV1pVS2UmqZUmrvwP9ZJ1jOVEptGvhbMpQyhRCnh8SzECPfUI/Uvwq8rLWuAl4euH88Ia31jIG/a4ZYphDi9JB4FmKEG2pSvxa4f+D2/cB1Q1yfEOLskXgWYoQbalIv0Fo3DdxuBgpOsJxXKbVOKbVaKXXdu61QKXXnwLLr2trahlg9IcR7kNB4llgW4sxznmwBpdRLQOFxnvrG0Xe01loppU+wmlFa6wal1GjgFaXUVq31vuMtqLW+F7gXoLq6+kTrE0K8D2cyniWWhTjzTprUtdYXn+g5pVSLUqpIa92klCoCWk+wjoaB/2uVUq8BM4HjJnUhxOkj8SxEchtq8/sS4LaB27cBT719AaVUllLKM3A7F5gP7BhiuUKIxJN4FmKEG2pS/xFwiVJqL3DxwH2UUtVKqfsGlpkIrFNKbQZeBX6ktZYfASGGH4lnIUa4kza/vxutdQdw0XEeXwd8auD2SmDqUMoRQpx+Es9CjHwyopwQQgiRJCSpCyGEEElCkroQQgiRJCSpCyGEEElCkroQQgiRJCSpCyGEEElCkroQQgiRJCSpCyGEEElCkroQQgiRJCSpCyGEEElCkroQQgiRJCSpCyGEEElCkroQQgiRJCSpCyGEEElCkroQQgiRJIaU1JVSNyiltiulLKVU9bssd7lSardSqkYp9dWhlCmEOD0knoUY+YZ6pL4NuB5YfqIFlFIO4G7gCmAScLNSatIQyxVCJJ7EsxAjnHMoL9Za7wRQSr3bYnOBGq117cCyjwLXAjuGUrYQIrEknoUY+c7EOfUS4NBR9+sHHhNCjDwSz0IMYyc9UldKvQQUHuepb2itn0p0hZRSdwJ3ApSXlyd69UL8QzuT8SyxLMSZd9KkrrW+eIhlNABlR90vHXjsROXdC9wLUF1drYdYthDiKGcyniWWhTjzzkTz+1tAlVKqUinlBm4ClpyBcoUQiSfxLMQwNtRL2j6olKoHzgWeVUq9MPB4sVJqKYDWOg58DngB2An8RWu9fWjVFkIkmsSzECPfUHu/PwE8cZzHG4Erj7q/FFg6lLKEEKeXxLMQI5+MKCeEEEIkCUnqQgghRJKQpC6EEEIkCUnqQgghRJKQpC6EEEIkCUnqQgghRJKQpC6EEEIkCUnqQgghRJKQpC6EEEIkCUnqQgghRJKQpC6EEEIkCUnqQgghRJKQpC6EEEIkCUnqQgghRJKQpC6EEEIkCUnqQgghRJIYUlJXSt2glNqulLKUUtXvslydUmqrUmqTUmrdUMoUQpweEs9CjHzOIb5+G3A98LtTWPYCrXX7EMsTQpw+Es9CjHBDSupa650ASqnE1EYIcdZIPAsx8p2pc+oaeFEptV4pdecZKlMIcXpIPAsxTJ30SF0p9RJQeJynvqG1fuoUy1mgtW5QSuUDy5RSu7TWy09Q3p3AnQDl5eWnuHohxKk4k/EssSzEmXfSpK61vniohWitGwb+b1VKPQHMBY6b1LXW9wL3AlRXV+uhli2EOOJMxrPEshBn3mlvfldKpSql0g/fBi7F7pAjhBhhJJ6FGN6GeknbB5VS9cC5wLNKqRcGHi9WSi0dWKwAWKGU2gysBZ7VWj8/lHKFEIkn8SzEyDfU3u9PAE8c5/FG4MqB27XA9KGUI4Q4/SSehRj5ZEQ5IYQQIklIUhdCCCGShCR1IYQQIklIUhdCCCGShCR1IYQQIklIUhdCCCGShCR1IYQQIklIUhdCCCGShCR1IYQQIklIUhdCCCGShCR1IYQQIklIUhdCCCGShCR1IYQQIklIUhdCCCGShCR1IYQQIklIUhdCCCGSxJCSulLqf5RSu5RSW5RSTyilMk+w3OVKqd1KqRql1FeHUqYQ4vSQeBZi5BvqkfoyYIrWehqwB/ja2xdQSjmAu4ErgEnAzUqpSUMsVwiReBLPQoxwQ0rqWusXtdbxgburgdLjLDYXqNFa12qto8CjwLVDKVcIkXgSz0KMfIk8p34H8NxxHi8BDh11v37gMSHE8CXxLMQI5DzZAkqpl4DC4zz1Da31UwPLfAOIAw8NtUJKqTuBOwfuRpRS24a6zmEgF2g/25VIENmW4Wf8qS54JuM5SWMZkud7A8mzLcmyHfAe4vl4TprUtdYXv9vzSqnbgauBi7TW+jiLNABlR90vHXjsROXdC9w7sO51Wuvqk9VxuEuW7QDZluFIKbXuVJc9k/GcjLEMsi3DUbJsB7y3eD6eofZ+vxz4d+AarXX/CRZ7C6hSSlUqpdzATcCSoZQrhEg8iWchRr6hnlO/C0gHlimlNimlfguglCpWSi0FGOh48zngBWAn8Bet9fYhliuESDyJZyFGuJM2v78brfXYEzzeCFx51P2lwNL3UcS977Nqw02ybAfItgxHCdmO0xzPyfJeg2zLcJQs2wFD3BZ1/NNmQgghhBhpZJhYIYQQIkkMy6Q+0oehVErVKaW2DpyXXDfwWLZSaplSau/A/1lnu57Ho5T6g1Kq9ejLj05Ud2X71cDntEUpNevs1fxYJ9iObyulGgY+l01KqSuPeu5rA9uxWyl12dmp9fEppcqUUq8qpXYopbYrpb4w8PiI+FxGcjxLLA8PyRLPZySWtdbD6g9wAPuA0YAb2AxMOtv1eo/bUAfkvu2xnwBfHbj9VeDHZ7ueJ6j7+cAsYNvJ6o59nvU5QAHnAGvOdv1Psh3fBv7tOMtOGvieeYDKge+f42xvw1H1KwJmDdxOxx7CddJI+FxGejxLLA+Pv2SJ5zMRy8PxSD1Zh6G8Frh/4Pb9wHVnryonprVeDnS+7eET1f1a4AFtWw1kKqWKzkhFT+IE23Ei1wKPaq0jWuv9QA3293BY0Fo3aa03DNzuxe51XsLI+FySMZ4lls+wZInnMxHLwzGpJ8MwlBp4USm1XtmjagEUaK2bBm43AwVnp2rvy4nqPhI/q88NNGP94ahm0xGzHUqpCmAmsIaR8bkMp7q8HxLLw9uIjefTFcvDMakngwVa61nYM1l9Vil1/tFPartdZURedjCS6w7cA4wBZgBNwM/Oam3eI6VUGvA48EWtdc/Rz43wz2U4k1gevkZsPJ/OWB6OSf09DSs7HGmtGwb+bwWewG76aTncbDLwf+vZq+F7dqK6j6jPSmvdorU2tdYW8HuONMkN++1QSrmwfwQe0lr/feDhkfC5DKe6vGcSy8PXSI3n0x3LwzGpj+hhKJVSqUqp9MO3gUuBbdjbcNvAYrcBT52dGr4vJ6r7EuDWgR6a5wCBo5qQhp23nYv6IPbnAvZ23KSU8iilKoEqYO2Zrt+JKKUU8H/ATq31/x711Ej4XEZsPEssD99YhpEZz2ckls92b8AT9BC8ErtX4D7s2aPOep3eQ91HY/e83AxsP1x/IAd4GdgLvARkn+26nqD+j2A3ZcWwz9988kR1x+6ReffA57QVqD7b9T/Jdvx5oJ5bBoKl6KjlvzGwHbuBK852/d+2LQuwm+O2AJsG/q4cKZ/LSI1nieWzvw0n2ZYRF89nIpZlRDkhhBAiSQzH5nchhBBCvA+S1IUQQogkIUldCCGESBKS1IUQQogkIUldCCGESBKS1IUQQogkIUldCCGESBKS1IUQQogkIUldvCul1Eyl1JtKqX6l1FqlVPnZrpMQ4v2ReE5+ktTFCSmlSoGlwI+xhzGsBf7zrFZKCPG+SDz/Y5CkLt7Nz4Dfa62XaK1DwKPAnLNcJyHE+yPx/A/AebYrIIYnpVQGcC0w7qiHDSB8dmokhHi/JJ7/cUhSFydyEeACttizBQLgAZ5SSs0Ffok9Y1IDcKvWOnZWaimEOBXvFs8F2HPFxwAT+Jge5tOuihOT5ndxIhXAEq115uE/4FXgeeAQcKHW+nygDvsIQAgxfFVw4nhuBxZorRcBD2BPaypGKEnq4kQ8QP/hO0qpSqAa+4ehaeCcHEAUsM5C/YQQp+7d4tnUWh+O4XTsuePFCCVJXZzIW8AipVSxUqoMeBj4hta68/ACSqlRwKXA02epjkKIU/Ou8ayUmqGUWgN8DthwFusphkhprc92HcQwpOwTb/cAHwc6gB9rrX9z1PMZwDPAp7XWu89OLYUQp+Jk8XzUch/BPrX2mTNcRZEgktTFe6aUcgJLgJ9prV8+2/URQrx/Sim31jo6cPsy4DKt9ZfPcrXE+yRJXbxnSqlbgF8AWwceukdr/djZq5EQ4v0auJrlp9g938PAHdL7feQaclIfOD/zAFAAaOBerfUv37aMwr4E6krszhq3a63lvI0Qw4zEsxAjWyKuU48DX9Fab1BKpQPrlVLLtNY7jlrmCqBq4G8e9rmdeQkoWwiRWBLPQoxgQ+79PnB504aB273ATqDkbYtdCzygbauBTKVU0VDLFkIklsSzECNbQi9pU0pVADOBNW97qgR7wJLD6nnnD4UQYhiReBZi5EnYMLFKqTTgceCLWuueIaznTuBOgNTU1NkTJkxIUA2FSE7r169v11rnJXKdiYhniWUh3ruhxnNCkrpSyoX9A/CQ1vrvx1mkASg76n7pwGPvoLW+F7gXoLq6Wq9bty4RVRQiaSmlDiR4fQmJZ4llId67ocbzkJvfB3rC/h+wU2v9vydYbAlwq7KdAwTkkgkhhh+JZyFGtkQcqc8HbgG2KqU2DTz2daAcQGv9W2Ap9uUvNdiXwHwiAeUKIRJP4lmIEWzISV1rvQJQJ1lGA58dallCiNNL4lmIkU0mdBFCCCGShCR1IYQQIklIUhdCCCGShCR1IYQQIklIUhdCCCGShCR1IYQQIklIUhdCCCGShCR1IYQQIklIUhdCCCGShCR1IYQQIklIUhdCCCGShCR1IYQQIklIUhdCCCGShCR1IYQQIklIUhdCCCGShCR1IYQQIkkkJKkrpf6glGpVSm07wfOLlVIBpdSmgb//SkS5QojEklgWYmRzJmg9fwLuAh54l2Xe0FpfnaDyhBCnx5+QWBZixErIkbrWejnQmYh1CSHOHollIUa2M3lO/Vyl1Gal1HNKqclnsFwhRGJJLAsxTCWq+f1kNgCjtNZ9SqkrgSeBquMtqJS6E7gToLy8/AxVTwhxiiSWhRjGzsiRuta6R2vdN3B7KeBSSuWeYNl7tdbVWuvqvLy8M1E9IcQpklgWYng7I0ldKVWolFIDt+cOlNtxJsoWQiSOxLIQw1tCmt+VUo8Ai4FcpVQ98C3ABaC1/i3wYeCflVJxIATcpLXWiShbCJE4EstCjGwJSepa65tP8vxd2JfJCCGGMYllIUY2GVFOCCGESBKS1IUQQogkIUldCCGESBKS1IUQQogkIUldCCGESBKS1IUQQogkIUldCCGESBKS1IUQQogkIUldCCGESBKS1IUQQogkIUldCCGESBKS1IUQQogkIUldCCGESBKS1IUQQogkIUldCCGESBKS1IUQQogkkZCkrpT6g1KqVSm17QTPK6XUr5RSNUqpLUqpWYkoVwiRWBLLQoxsiTpS/xNw+bs8fwVQNfB3J3BPgsoVQiTWn5BYFmLESkhS11ovBzrfZZFrgQe0bTWQqZQqSkTZQojEkVgWYmQ7U+fUS4BDR92vH3hMCDGySCwLMYwNu45ySqk7lVLrlFLr2traznZ1hBDvk8SyEGfemUrqDUDZUfdLBx57B631vVrraq11dV5e3hmpnBDilEksCzGMnamkvgS4daDn7DlAQGvddIbKFkIkjsSyEMOYMxErUUo9AiwGcpVS9cC3ABeA1vq3wFLgSqAG6Ac+kYhyhRCJJbEsxMiWkKSutb75JM9r4LOJKEsIcfpILAsxsg27jnJCCCGEeH8kqQshhBBJQpK6EEIIkSQkqQshhBBJQpK6EEIIkSQkqQshhBBJQpK6EEIIkSQkqQshhBBJQpK6EEIIkSQkqQshhBBJQpK6EEIIkSQkqQshhBBJQpK6EEIIkSQkqQshhBBJQpK6EEIIkSQkqQshhBBJIiFJXSl1uVJqt1KqRin11eM8f7tSqk0ptWng71OJKFcIkXgSz0KMXM6hrkAp5QDuBi4B6oG3lFJLtNY73rboY1rrzw21PCHE6SPxLMTIlogj9blAjda6VmsdBR4Frk3AeoUQZ57EsxAjWCKSeglw6Kj79QOPvd2HlFJblFJ/U0qVnWhlSqk7lVLrlFLr2traElA9IcR7kLB4llgW4sw7Ux3lngYqtNbTgGXA/SdaUGt9r9a6WmtdnZeXd4aqJ4R4D04pniWWhTjzEpHUG4Cj99RLBx4bpLXu0FpHBu7eB8xOQLlCiMSTeBZiBEtEUn8LqFJKVSql3MBNwJKjF1BKFR119xpgZwLKFUIknsSzECPYkHu/a63jSqnPAS8ADuAPWuvtSqnvAuu01kuAzyulrgHiQCdw+1DLFUIknsSzECOb0lqf7TqcUHV1tV63bt3ZroYQw5pSar3Wuvps1+PdSCwLcWqGGs8yopwQQgiRJCSpCyGEEElCkroQQgiRJCSpCyGE+IcWDcfPdhUSZsi934UQ4h9VPGbicBgoQ73zuagJChwOg5YDPXQ39+NwGqTneFGGwpvqwu110HaoF8vU5Jamk5blSWj9wsEYNetaGH9OES6PI6HrHsn6usI07OkmuyiVl/60g87GIIWj/UxaUMzoGbl4fK5jlteWJhY1cXtPb8o049aQ1yFJXQghTqKjoY/0bC/uFCeNe7vZtaoJh8ugZl0rqZluiquy6OsK43QZ+PN9ZBensvrJfUT64zhcBv2B6HHXaxgKy7KvQHJ7HVx460T6uiM4nAZTzi9Ba01/IIrhUKSku+nvidJU082oKTk43XaSNuMWHQ19+DLcpGV5B9cd7oux5FebaDvYy/YVjVz9uek4HAYOt0E8apKS5n7f70d/TxSPz4nDeaSxV2tNR0OQlHQXLo8Dh8vA4TizjcHa0nQ196MMyCzwodSxO1ttB3tZ/uhuWup60ZZGGYqUNBezLhtF7aY2XnlgJ689pBh/TiGFlX7GVuezZ00zq56sJRqKUzIuE4DyyTmMmZVPRq6Xvq4ILft72P5GA1MWlTBmZj7t9X2kZroH3+NYxKS3I8y25Q3UbW3Hilv4/B7cXgfKUBgORW5ZOvU7O4f8HsglbUKMcHJJ2+nR0x7i5ft3klOSxrbX6/Hn+ygel8mONxpxex3EYxY5JWlE+mOEg3HSsjzEoya9nRG0pXF7HZRPyQENldNzya/IwIxZ9HaGsUxNR0MfsbDJqKk5ALz8p530doYHy5+yqISOhj6aagI4nAaLPz6eHSsaaaoJoBSkpLvJr8igqzlIoDUECsbNKSDUF6OnPUQkGCcajjPrslFsevkQSkEsbA6uf8ysPKZdWEZeeTou97FH8ZalObSjk8LRGXh8LrTW1KxrJRiIsH9zO417u0nN9DDnqgq8aS56O8LsWNFIV3M/KECD0+OganY+3jQXnY1B3F4H3lQXpROyGT3zyLDB0XAcpRQuj4OWuh7qtrTjTXPRfrCXzuZ+xs0pwIxbtB/qpWlfAJfXyYyLy1AKLFPTtC/AgW0dpGd7UQpaD/QCkOp34/Q4iATjuFMcoBSRYAyn28HE84rwprrYtryBi2+fREFlBlprWup62LWqmZ1vNmKZGpfXQSxsUjohi4KKDPasbcHpcdDVFAQgI9dLT0cYtL2DZjgUE84tYtsbDThdBpkFPjLzfRzc3kE0bGI4FBXTcvGkOAkGosSjJpapMeMWbYd6cXud3PmLRUOKZ0nqQoxwktSHzjQtDEMRj1nsXdvCzpVNtNf3YsYstIa0bA+xsEk0bDJpfhELbqgaPMICjjkiNGMW9bu7SM/2kl2cesp1CPVGaT3YS1aBj9VP7mPvulZSMtzMuKiMuq3tNNUEAKi+sgKtNb2dYdoP9eHyOJiyqISmmgB71jaTWeDDn5eCtuxl88rTaarpZvVTtZROyMJwKCL9cba+Wk88Zjf3pmV58Oel4M9LISXdzf4t7XQ2BvGmuvD4nKRleWjY0w1ARl4K4+YW0LCri6Z9gcH655SkMXVxCf09UZSC3o4wu9Y0g4bs4lQiwTjhYIxYxKRiWi6ZBT76OsPUbW3HcBiUjMukbks7AFoDCtIyPfR12SMSe9NclE/KpmV/D4G20GC5hlMxdnY+gdYQfZ1hZl1egeFQNO8LYMYtPKkuoqE4lmkRDZucf9M4MvN97/59iFs07O5izZJaJi0oZtKC4mM+446GPhr2dLF/czsFlRmUT84hPdvL07/eTFdTkNEz8vCmuQaO4gPkj0pn3NxCisZm4s9LOW6ZgbZ+nC4HaVleSepC/COTpH5isah5zFGotuwju4LRGYNNw7tWNfH6w7txeR1EwyZmzCK7OJWScVlMXlhM/a4uyidnk5GTYp8jd56ZJuVIKI7bYzfPmqbF/k3thIMxJi8sfkez8uD2aX3C594uGo5zaEcnXc1Bulr66WkLEWgLEeqNkVuWxqT5xdTv7sKMWRzc3sGkhSXMuaoCX7obZSi0to/mXR4HGXkp+DLc7yg73BdDGQyeozZNizVP1VKzvpX+nigp6S7KJmYT6onS1dxP6YQszr1+LN0t/Zhxi8LRfsJ9MVxeB06XgVIKM2bR3daPy+3AcCicbrsFYLh4+3fuvRpqPEtSF2KEk6Ru01oTaA3R3dpPNBwnHrV47cFdjJqaS19XmJR0N/GoSVNNgDEz80jN9OD0ONjw/AGKqzLJyPXiSXUxenoeRWP9p5wck41pWu84Fx4Jxe3zv/+g78mZNNR4lo5yQogRrac9xOqnagl2R2jc233Mc+k5Xup3dpI3Kp1wX4xQb5RRU3PYt/HI/O4l4zP5wL/OOGNH4MPd8Tq3eVIkVYwU8kkJIUa0FX/dy4FtHaRleznv+rEUjfUTi5jUbGhl7tWV72gWPtxsnFuWTv3uTkZNyZWELpKGJHUhxIhhmhbrnzvAttfrAfv8dl9XhHnXjqb6iopjli2bmH3cdSilKJ9s9zgfN6fwtNZXiDNNkroQYljrbuln56om3F4HW16tpz8QpWJaLqmZHqy4hdPjYMZFZWe7mkIMC5LUhRDD2vLH9nBohz0oR8n4LC66deLgkbYQ4lgJSepKqcuBXwIO4D6t9Y/e9rwHeACYDXQAN2qt6xJRthAisYZTPDfs6eLQjk6qr6pg7Ox8corTTkcxQiSNIfcOUUo5gLuBK4BJwM1KqUlvW+yTQJfWeizwc+DHQy1XiKNFEzBm8nB0pi85HU7x3FwbYOk9W0nP8TLr0lGS0AUA2npnrGutsYLBs1CbY+twWLy9HW2a77L06ZOII/W5QI3WuhZAKfUocC2w46hlrgW+PXD7b8BdSimlh/NF8qdJ3LSo6+inIMNDTzhOSebxRxcC+0vS3hfFYSj8KS5e3tnCtNJMCv3eE74mmbX1Rkj3Olmxt51pZX4Uiue3N9PUHeK+N/bzhYurmFri57+f2UFzT5iJhRnkpXuoae1jYVUu/3pRFf6Ukw9S0RuOoYG4qXl1VyuBUIwLJ+RTkZtK3LT4/tKdxEyLW8+tYFSOD48zMRNlaK0xLY3TYWBZmh+/sIsHVh5gepmfCYUZ7GvrY1JRBjdUlzEmLxWljowbnkDDIp4b93bxzF1bSMlwc+0XZ8hkJCNItL6B0KZNOPx+fHPnYHjsSWp6li5F+XyknXce4b17Ce/YgXfiJMI7tmN2dpL18VswvB5CmzcT7+jAmZdHeMsWtGnhHlWOMyeH1p//gtDGjaQtXkzxj36I8niINTTQ+PWvE962neIf/5iMyy4FBuKpowNnbu5J62x2d+PIzHzf2xxcvZrG//fveMaNw+zuJrx9OynTp1Pyi5/jKioCwAqHUS4XyuHACgZp+H//TvTgAfxXXUXmTTeBaeLw+993HQ4b8uAzSqkPA5drrT81cP8WYJ7W+nNHLbNtYJn6gfv7BpZpP8m6/+GSvhDvhXK40GYsYYPPnK54PtVYzvBlM3/iVVwy/SY6+1r49TP/j0B/x1A26ZQMDFc+yK0Uptac7FjLBcTeY1luFA4FoXf57fUoRbHThdtQtMXjaCDdMGiIxbAG6hc5hd9uz9uWcwL5Tift8TjHn2Lm1OQ5HCgUPZZJTGtKXC4iWuNTihynk8MXEIYsTbsZJ9UwyHbYO2YDI8ACYA3cPvr+uzUfmxo6zTi5TufgawEsDVFt4TMM6mMxmuJxRrlc5DmdHIxGcSuDXstEA4VOJ22miak1uU4nHqVIMwya43HqY/YOvWPgvfMoA6UgZFloIHzUe6lgcHvznU4iWuMAolrTY1kUDLwPDbEYnabJRI8HE+i37Hp6lKLPskg3jmzxOI+Xh7q7kmvwGaXUncCdZ7seQoihea+xnJtRzOev/imZaXnsbdzMH1/6Hn3h7oTXK8MwMLCTi1MpUgyDQqeTXtMipC2yHQ5cA9e1By2L9rg94YgTyHQ4MAFTa9INBw4FXaZJTTSKArIcDkyt6bUsLCDX4SDT4SBoWbiUItPhwDOw7n7L4lAshqk1wYFkYWAnnSKXCw3EtGaM+8hsatkD5XuUoss0cWCXn+d0Etaa5oGkZL/OQ4bDoCUeJ80wcCqFwt4hKHS5CFkWbqVoiMUIa03QsnACcexkFdUahSKKJkUpfIZBijJIdxikDSYi1zuSdEs8Tns8jlcZVLjdlLlcxLSmKR4namncShHUFhHLYrTbg0bTEIuRMlDHuNaELAunUnSbJhYM1j9gmphAj2V/TlGtMbATZxyodLspdbkocDpxKYUFjBp4/4oG0p0G/AM7GDGtiWlNp2lS6HSS63AACucJBs4La40TRVRbeI/6HrXF4xwa2OE6rDUep9TlotTlotjlwtIaU2t8hkHEsjgUj9NtWfgNA69h2M8nYMS+RCT1BuDo60lKBx473jL1Sikn4MfuYPMOWut7gXtheA0Ta1qaP765n4fWHCRuWZRm+lhV24FS9uQDF4zPozsUIxKzKPJ7KfB7+fIl4+gNx2nrjVA9KgvjOHMuH4/WmpaeCAUZnsFBM/oicdI87/y4mgNh/vuZHSyoyiXL5+K3r9fSH42T7nVx4YR8gpE4v3ltHwBOQzE6L5Ub55QzrdTPkk2NjCtI4/pZpbT0hFl/oIsnNjaQ2WtRmuXl7/WdWJbFxb406ht62esy6fMahGL28UtVfho/unQi7pBFbkU6bzUGuHf5PvY09oKC7ChM126qRmdy0eQCXnrtIIc6+umdnM43rp9Cts/F/71Sw1sNAc4Zm0swEiduWtxQXUZrXQ/xljCzzy2iz614eO1B/nnRGDJ973+6SK01K/d1sHZ/J05DMb4wnamlft7Y285Daw5y0YR8Pr1wNN6BMaaP1heJ09ITpizLh/s4A5VYliZmWRzq7Ke1N8LUEj/pXrup/6UdLXz76e00B8JMK/UTMzWjcnzMH5uLx2mwal8HdyyoZGJRxmA99cCsT6ciwUN3Jiye32ssP3v3Zpr2Bbj2izPJK7+YX/GV978V2Oc1O37/e1Jmz8bweFAeD+133U3/ceqRev5Cwjt2YnZ3k3b++aQtXoQZCNDz9DNE9uwZXM47dSoYCh2J4p08CcObQtdDD+GpGkusqRmrr29wWcPnw+rvx1lcRLyxCYD0Sy4hZfo0jIwMWn/0Y6z+fgBcpaV4J04ktG0b8aYm0i+7jMJbL8IRbaCvPZd4v4VnXBXtv7mHeEsLzqw0gm9tQhmg4xbu9DjxsIEVs7+bauA76q6sJLJ3H+7KSrwTJxBvbSPrxg8RXLueSO1+dChEeMfAmRWHA0zzyP8DlNeLDg/MHudy4amoIPuOO0g9Zx69L71MvK2N9Ek54E3DOXE+roKCwdda/f1YkQjOrKzjfkY6HEajMbwnPg35Xmit6X3+eXpfXIZnbCXpV1xF4IknyPrQVYQ2baV/605y/+WzhHfuwmyqI/2CRRgv/QfseoZgi5vuxhIcuQW4pi3EPXoCrr4tqPGXEN74JlZ7E4GVO3Bnuon1xPF4WvEVGfiu+wzOgmLwl0LhNDh6oKNQD53/eSvx/VvJPH8KnlwXGE5Y9P8gNR9W3Q397TDz4zB6sf1+DzGeE9H87gT2ABdhB/tbwEe11tuPWuazwFSt9WeUUjcB12utP3KydQ+HpN7YHWLDwS4eWHWAtfs7mVeZjcNQNAXCfHh2KeMK0nmrrpOvXj7huD/CZsyisymIMhSZBSk4nAbhvhgp6UeSk2laBLsirPz7Phr3djF5YQmzLh/1joko1Cn+yB8tHDP59P1vcdHEAm6eV47b8c6Edcz27u3mqZ9vxLI0WYU+Qn0xwn12A6PhNrj4n6aw8c1GOuv7ONDVT3FMYaAIK802t8kY00FWXGG5FC4UZtwabNdMyXATDcXxprrIzE+h9WAvsbBJSoabzLwUWg/0kpbtISXNTXPtwOxPCiqm5DDz0nL8+T5S/Z4j74nW9PdEqd/VhWVqxs7OP+Vzr/W7OgkH4xRU2ok01e/GcBiDE2KYpkV3cz8ZeSk4XQaHdnYOziT1foIuGrcIxcxTOqf/XiVy7PfTFc8ni+Wu5iAPf3sNc66uZO7VlUPaBm1ZBN9cSdvPf34kYQ0w/H7yv/JlUqZMQZsWRloqzuzsE57L1FoTra3F4ffj8PtRLtc7nm//9a8Jbd2Gq6SY9IsuIt7eQby1lWhtLe4xY8j51Cfpe/kl6K4jffY4KJ4J2iJ6oI5IUzfx5iaCLz5JePsOlFNT/L+/IaXpUdj8sF2Ixw+fWgbphdCyHereRL/+P1jh6P9v787j46rrxf+/PmfWzGSZLJM9aZamadO9TTegLAKVgpZNEBRcEFER/Xp/9171XvRe94uKeL2KKKIIioAgyFb2paVA23Rv0zRJs+97ZjL7cj6/P07oRkpb0iUJn+fjkUdmzpyc8zkz+cz7fHZCQxY8nllkfek6dJ8P32uvoHfX4u9JIHOeB0u6C09fLilLCzGl5YAtCdb9FOZeA+d/G71jNyMNOiLBSXD7diyZGUQ7WrHPmUO8cRvClUuodQD77Nk4FlRgrfszYvGnjWvY+mfY8TdISIW6F4y0Lr8VVv0YhprA6QZ78uFvaMPrRtCrfxk6d0B/HYQ8UH4JrPoRpBQcDIpSGo89HeBph4Kl4GmDts1Q8zR0bIfZV0A0CBkzQMZhuBXCI8bv1ndgyRdhoB7qXzKOabbDR74DLe9A7XOgWYxznPctcKRB1R9hqBkivkMSfWTjzKiUQnCkQtfOg9uKVhrpDAxCYAA6tsJIF5RfCrXPG++HZjHSjIRYGOwpxvOLvw/99YjLfn7mF3QRQlwK/C9GU8SfpJQ/FkL8ANgipXxaCGEH/gIsBAaB697tiPN+zkRQj+uSR6pa2dk2TLLdwmNb2/EEoyTazHxvzWyuXpT3vl/qI4MhfIMhMouT2f16O1uebybsjwHG+sJp2Q56W0eYuSKH4EgER5KVfRu7EZoxO1Z2cTJtNUM4kq24shyE/FH8w2EiwRg50104UqyUzHdTMCuNSChGUrqdaDjOrtfaKV1kLFKx+412bA4LFpsJd2ESa3+7i8yiZBZfMg1dl5gtGnvWdZCS6WDOeXlEAjHWP1JLYCRKT6OHxDQ7c87No61mEKvdRPmKHFKzHTz2ky2E/FGEgKziFAKRGKEkE40WndR6P86QJGe6i/zyVPpaRwh4I1z6lblIXRINx3FlOehu8LD1hRaCIxEypyWT7E6gt8XLUFeA3BkuvP1BhrsDzD43j+J5GdRu7mbPuo4DNxZ55akERyIERyKE/bHDOorllrnIm+HC6bIxMmCULEwWY8axornp2BwWTGaN9tpBNv7z8H+/jIJEUtwJtFQPklmYhLc/iG8ojCvLQWKqjfZ9QwCUVWYy7yMFDPcECPmNNGVOSwKgq8GDEILskhQsNhNmq4bZaqKtZpCQL8rCVYUndEMQjcQZ7g4w2Okj5I9RstBNUtp7O0me7AVdTkV+fr+8PNwb4IXf72a4J8hnfnIWjuQTr42J9vQy/Ogj+N56CySEdu1C2Gzk3vlzIxibTMT6+nGefRampKQTPv64xMLwwBpo22g8t4724o8GjQDQVwvBQUjOh5FOoyQXj8C5/w6zPg5/vRqiIUAeDDYVVxiBub8Ozvo6mMaodG2rgtd/bJQEwyPg7YJ4GHLmQ2+NcQ6ArLlGQAsOGjcN8oje5e5ZcO6/wcZ7oGMLpJXCki/Ai/8JmRUw0ADTLzKOsf0vRgnU3wvmBFj8OZj7CdhyvxHQqv5opAGMdKQUQHKecYMQD0PuIuNc79xtBOWMcuNYgQFILQJvp5Fukw3Sp0PvXrA6D74vFofxo0chbzE0vAbWJFhxq3GTUf1PaNkAJissuRkiflj2Zcg6ZIBHyAM7HwV/HxQug92PQ9kq47MCsCVDe5VxfIsDNt1jpHOoCd64A8JeSEgz3o/0Mlj6RSi9AHr3gTPDSP/9lxrpufo+0Exwz9kQGgaLE/GdrjMf1E+VUxXUo3EdkxCEYnE0IYjpkiF/hFSnla8+tI11dX1kJNrwBqMUZTj4yZVzmZ6ZeFjVbywSZ2QwRHAkirc/SO4MF3ve6GD7K60gjTV+9ZikcHYas87KRUrJ/q29tNcYc0531g9jT7QQ8kUpXeTGnmhl4cWFpLgT6KwfZuerbQR9EexOC4kuG5pFo6N2iKA3gt9zsIvLwosLaakeYLDTj81pxmI1HVh/GIybUCEEEqO0fySb02ysGa1DSmYCqdlOVl5bhtNle8++w70BuvYbawOn5x0+vEjqkmgkjtV+8rtpREIxWvYMMNDho25zD2k5ThJTbdgcFuyJFuMmom2E1/+678ANtaYdvGazVSMWOfyLqmheBksuK6Kzfhg9Ltn+UiuaSVAwK42GHX0kumzMPT+PjU81ommCZWtKCIxE2PJc8we+jjnn5jHvI/mkZhtrbA90+uioHWLmihyEEHTUDWEyG7UB219uZdPTTe/5zBJTbay8dgYZhYlEQ3HScp1omjZpV2nTdcnjd2zBOxDk4ptmM+0EJpXxb9pM789/jjkzE9+bb0Ishn32bOKDg6Tf8kVS1qxBc7z/utknna7DhruML2xHuhGY2jYZQWD1zyCjDHb93QicTjd0boekHJh/HZRcAFvvN0qxK74KJecZx+zeA5vvNTJz+aXgyID8xSeeNn8/7H/VKN162mH3Y0Yp8Z3fGsEmwWUEKmcmBIegYAn01xuBuL/WCNLLboG3fmUcr/Qj8OnHjZsTqxNiIXjwCuNxxRrjpmLn34xrFSajJG1PgYU3GsF8+ZcPpq1/P9SuhfV3QthzcL/GdRALwqLPGjcUidmw8NOQlHswQGoW48ZFaMZ7/m6bqBAQCRgB/N2bnnjUKFmnTzeu92TT44AA7RijxeMxI5i/e5Pfvx8iI5A9H2EyqaB+IkLROGt+swF/OM5wIILFrBGLS3zh2IH/hR9ePpsblk8jrktMmiDgjeDtCxodaywaFpuJtffsZrgn8J7jV5ydQ1ZJCv1tPgpmpVI0L+PwxSR0CQL8w8ZawoNdftwFx19ykLqko26IvlYfbTUDtNUMYbZorLxuBnWbujHbTCy8uBBnio2RoRDrHqplznl5FM3NoLfVi8mkEfRFyS5JwdsfpHl3P2ariVkrcnAXnuYSzEkW8kUxWzV8w2ESU22YzBp6zHi/G7b1Yk0wo8clCYkWskpSDmsueTd4Ck0Q8kexWE0HSvlmq4bdaUFKydbnm4nHJOXLsrGOrlzV2+wFILskhVg0zmCnn1hUJxaJE4voOFNtNO/sZ896o2k6Mc2GxWoi4I0QDsRwJFuxOcwMdQcOpEHqktKFbqZXZo0GbkHTzn5qN3cz0H6wanDG0ixWfWHOpA3q215s4Z0nG1h182zKKrPG+EuDlJLAxo0Etm5DmE2E9tUS3LoVPRJBs1pJWn0JaTfcgLWw8IMnsmMruGcaQelo4lEwjVbBDzUb1bmN60CPGaW5F74Nex4/uL/ZbpQwK79gBMTJKOyDt/8PZl5mlK7rXjQCeNkqsByjLby/3qgVyJlvVJsn50LR2Ufff6Tb+JvsuQeD7rsB+kNCrad+nELROF9/eDv7+3w09vlZPC2V7GQ7MV3HajaxcnoGDX0+ysxW5qclYjJpRMJGr9cNf68/UNUKRjW6xapReWkx1gQTaTlOeltGcCRZKV6QMe6ODscrOBLh1QdqmHt+PtPmqGkzJ7qRwRD1VT30t/uM5oNAjMpLi9jxcisDHT7Ov2EmJrNGd6MHV5aDWSty3tOPIhaJ07Szn0goRk+zl5q3urjt9xdOyqBeu6mbV+7fS8lCN5fcMmfMfBPt7GTklVcI7t6D95lnDmw3u93EfT6KHvor9ooj58Y5Ab4+aFoH+56D6ieMEuTqn0H5aiOQ9FQbJdraF4ySVV8tFCwzSovP/osR3N6lmY3gfuF/G88tDqPqVVNj7JXjp4L6MbQPBfjD+ka2tg6xp8PLtHQHqyqyuP0y44tASknjjj5a9w5id1jY9UY7sfDho1OT3Qks/VgxmknQVjPIcE+Ai2+aPWb7pqKcKCklekxispzYBI9SSoa6AqTnJU66oB4Oxvjrd98hNcvB5d9YOOa1y2iU5uuuJ1Rt9NHL+OpXSfvcZ5GhEGa3GxmJIKzHaH+P+GG4DdzlRim7ab3R2WpgP+z5h9GJCYw22sqboPEN6Ksx2kRLzoO9T2H01jzHCNpJOUbwjwaMdtQ5VxvHTp0GG/4XchfAOf9yUt4z5cNpvEF9wo1TPxl84Rg/enYvHcNBNjYOIBCUZSXywyvmcOPyaQf2k1Ly+l/2UfN2FzaHmXAgRkKShUtumYPFasLutBCP6aTlOg+st/x+VYSK8kEIITBZTrx2RwhBWu77VBVPYFXPNhHyR1n5yRljBvRwYxNd//VdQtXVZP/g+zgWLsRWVma8ONrR7X0Duq7DrkfgmW8YHbCWfNHoMe3rMV4XJqP6ePmtRnVw9jyjWj0ehZ2PQOPrUP0klF4IV/4enIfUhF30PeitNnqA2w/pNX/tA+N7UxTlJJhyQb11IMBXHtrKvu4RyjITuaaygNsumE7u6HSskVCMSDBO8+5+uvYPU7e5h0Ufncayy0sY7glgtmgkZ5ycMZMfFlJKfOvWER8axnXlFUbvUV8fZEw32sf69hm9eE/soEYv0kO/NI8lEjDaMI/VSWWykdIoWfr7jLZG2+Tu+9DV4GHna23MXpl3oB+HlJL+e+7B+/Qz2GbMILB1K8TjZP/g+6Ree8zRr4ccfBes/7kxhCkWMoYYaWao+gO4psGn/m68h073wbbxQ5kssOhG4+eSnxodr478f0p0Q+L5H/wNmMB8ER9/2/c3rph+BQDp9nRMH5LmA0/YgzfsJT8p/7Q1oZ4KUyaotw8F+K+nqllf14fDauK+z1ZyQXkmAHpcp3l3P7Wbumna0W+MncboIT1zeTbLrygxSj05p7jU07vPaJ+btsIoARw6HjM4ZAyBOA5xjwctOfm9/3hSGr1b8xYd97E+qNDevUS7uvCufR7v82uNeRqByKYXsI28iQgNYj9rFdbul4yqylU/ghW3GdfZX4duzyb8+l9JWLAY0kqQ2x8iPGQi4omTeNm1iI2/JrzhSazX3YkmwpBWYvQO1mNGR6TAgDGUZqTb6MDTW4O+6XdolgRY8Clo3wJnfx1mX3l8FyQlbP4DZM6C4pVGL9ZowOgU1L3bOK8lAWasNnoet7xj9AhuWm9U7y74FFR+HmIRI4homlFaNIYfHDxPLHJwyNBwi5H+wUajTffs/2dUFw81w8xLwVVotOU++41DqomtRpvuYCNMO8v4n5pEpJRs+Hsdiak2zrqq9MC2vl/8goH7/kjCggWEamowJSeTf/fd2EqOMmZdSvB2GFXoVX+EC/4TWt6GbQ8aHawW3mB0zpr3SeM93XAXLL3FeE+PV6J7/Bd8iuzp38Pfa//OnIw5VGZXUjdUR4unhSf3P0m2M5tUWyrD4WHWlK6hL9jHVWVXkZFw9DnQRyIjPLj3QV5ufpkGTwNP7X+KtpE2ZqbNZJ57HjdW3EhuYi4W7eTPszAWKSWBWACn5dR+Jw8EB3DZXPxz/z/54cYfEpdxrplxDV9f+HVcdtdJP19cN5p2j3ajVD9UP+5zTOo29bhu9Fp/sbqbHz67Fynh08sL+eS8PDbfvw9bgpncMhe1G7sZGQxhd1ooW5JFaraDjPxEcqa7Ts+FRENGYHjoE8jgMFIHrWg5cu61CHcZvPQdo4Rx1b0wb7RU0vgGvPCfEAsSzfoIum5l6LEnCY4kEWrzYS8vJfnyq5ARH33NjeRfdT1J4Q3w6g8gex7+7NnYii/A7EiDkAdZdC4kugm88w7WkhLiz/8YzVOPddGFxEqvRqRk4nvgDuJRM8nXfh7zrt+jxwVi5deI/fM76BEB53+L4U3PER1ox//Aq+j+IAAtM2M055opa4mR23DwPlFqkpbzUsjKSaQ5XEepyKZoKEDcP0BvtQs5IuhYFKYsOURgjwP6jS+MWGKcnlRBXpsGQuJwR8hdNoypdBbBhHRsTet4JtHJhsRkroiaWDbQzsPJSdydns6nTBnctn8Lbyam4I6G+VPRXEKp09jnbeLGWTfw+elXGeNMNQ38A8ZN1kinUaNQu9aoll3yBSPIekcnUjNZRyeMGK0JmHs1bH8IkGBxQlox9OyBrDnGb9c0KD6X7U0v0aMJLileDRE/cqAJvXkLJqskLGCHzYZX08iKxxHCzJxQAK+msdbpoNts4jOWPFyd9Wh55YhlXyIaTaD5rt+g7+3FnueAoJfkhbmk/Wr9pGlTb97dz3N37+KCG2dScXYuAH13303/r3+D6/rryP7udxFj1bS0bzVK2+WrjV7UPdVGFTkYk7OEPcbN1NIvwXnfPDXDlU6ymB5DExqaOP6aparuKjZ1beLxusfxRDzE9Nhhr1dmVRKXcfqD/UTiEXoCRnNDqi2Vy0ouw2VzYTFZMAsz3oiXV1tfxRf1EY6F8UQ8lKSUUJlVySO1jzAvYx7eiJcufxcumwtvxMtVZVfxzSXfpMPXQY4zB7N24uXCodAQrSOtOM1OCpMLiepR1revJ8uRxaKsRfQH+/nqq19l78BeluUs43/O+R+SbcnYTO8dZnuoaDxKo6eRmB4jJmP0B/upGaghyZrE9TOvx2oymmtCsRAvt7zME/VPsKVnCwKBRHJW7lkUpxTzUM1DaEKjMquS25fdzrTkaYcF4TZvGzmJY197f7Cf3kAv013T0YTGvsF9VHVXsa13Gy6bi7c63mIgNMCKnBUMh4fxR/2ck3cOn6n4DBs6N/DTzT9l641bP5wd5fb3jvCpP2yid8QYk31eRjJfXzmdVJuZHa+00tPkJSndjqc3SEZBIpWXFlE0N+NA2/jJ5Al76Av0YYsJ3AETtmw3ovUdiIWI1L9E17rHsDfaMGcnMViTRqy3j4hLYhmS2F1RIiNWkqbbGMgeYMe0fOav8+MXQZIrHVj22tCrR4wTmcHkihPODiPbbViGR+cvNoE5DjULYvzjPCdmLYDstHDbMzqmpBiWxBi2VhvCZEYPxTG5HMQ9fpACky1OPGzi0GUWrMk6tuQIIx02Aqk6BDUcwcNrBbxOydNnCYZsGm/O1YyMIXUyfSYs4TguzclVL/uZ2zj2khidadCRLlhSb/z/9SfDU8s1YulJXPS6h9JuePpsCzZdcv52STTBRHVWlIgG+2cl4OoMUl2eQCgepnAAUkYkTSsKqQu3cXarjX2pYdrckIAkJy6xmGzUaDE+6R1hFUnk7ysiXluDPsNHultS3Z2MZSALR/0wCbk+Ms9OxVp5DabpS6lyJHHHlp9hReP67mYKhjpwlV7Mfakp7Brez+yM2Vy0ZT2icZisuWczwC4eY4S2YQvnVOtkRnVC6Rpzq8ExIHn9gkSq3TE2FUQx6RA3Ge9tkS0d134POd0Rtk0XfP51yaJaHW+ajR0XFDBvYx8JPR7q5rqYNZJEQkgSbW+nonbfpAjqVVVVPH7HFoK+KJ/+wXI0TTD8+ON0f/e/SLn8cnLu+J+xqz0jAfjd2UbtBBg3WFYHnPU1yJ5vTBDStB7yl0LSqe3zEoqFMGkmqvuryXZmk+3MxhP28GLzi6TaUzELM3sH99LkaUKX+oEv97LUMi4svPDAcZ5tfJY7q+5EIrl1/q2cm38uNrONZk8zpa5SUmwHm532De7jr3v/yvbe7bSOtALgsrn48yV/xhvxsrN3J4uyFqFLnfnu+Qfew0A0wI7eHSTbkrln5z283fE2MXn4TcCS7CXkOHMIxULcWHEjCzIXIKVkZ99OZqXPwmaysa1nGze/dDOZjkw6fB0HguAlRZdwQ8UNhGIh5rnn0eptJduZfVjawSid3rnlTobCQ6TaUnmi/gkCMWP4ZoI5AV3qhONhBIL57vns6d+DSTNxzYxreLT2UaJ6lARzAivzVmI1WRkIDpCbmMt/LPsPNnRs4Jdbf0mPvweLycJIZOSwc7+b1uKUYuwmOzEZozfQiyfsIcuRxdUzriamx8hMyOSKsiuwmWzUDNTwSusrPF73OMFYkEg8QnFKMT2BHoqTi9nVv4uy1DK8YS+z0mZRkVFBw3ADfYE+tvduP3A+b9jLQMiYPbkwqZC+YB/TXdNZnLWYf9T/A5fNRWlKKRs6NhCXcSSSFTkr+MNH//DhC+qD/ghX3P0WgUiMm1eWkD8iaXm29cDrFruJldfOYNZZOcSjOppZnJQ2EhmJoAcCDNli+LrayPIK7o+9zj3Vf2JWq+S2Z+K4vdCfBg3zo3jzY1RHE7j5n5A4OvKlMUejvTCBzA4/7RmC8j4TgZw0Cnb34Qgbn8WwA8y68TcxDTac4yLmcvBYYQ9DSQevI9sbJ2I2sTQcJH+TlVXbJVJAv9uKuzfCQIaZkB7DGYKWQo24ptOYKrh8k05iViLiiut5c9Oj7Hf6mRaxkFVUhGaLUPRAEwBblqcye+sQukXj8bNANwnKZs0m1VXEU+GthJwWrp97M26Hm3A8zP7h/awuWs369vVs7dlKf7CPr2V+Em97I+VaLo+2Pc264E7cMokLV91EWlIORZ0x9tdtJmHlOTQGW9nSs4U1xR9jVdJSGsxD/HrHr7HuaWT1E224tEQcIxGs/rHXlxJWK3osihhtCpBCIFKTYNhLQr6d/UkmBv0BTHFJRRsEHQItIombwBE2bizaMgQLG42/j1tM7Ly0jF+V1JOVkkfUIugcaccZBLcH7DGYWbSE7LVbOW97FE2CLuDlRRpWu4OVVUGEhJgmsYV1wmbwZjlxdxjrPsfTU9BiOr6PLsP6ehXmIS+m2MH8GNcEry6xMqdDI7c9SMgCa788jzezPXT4OlhTsBpLTRPfv+3xSRHUH7//BaOUfsNMZp2dQ+e3voX36WdwVFZScN8f0OxHjCYJeaHqPnjzLmNijivvBYsdpl9sNIUcJU97wh4eq3uMbn83cRmnbqiOjxR8hLLUMiqzKrFoFmOBlhMoZXrCHv5c/WceqnmISDxCXMaxmWzMzZjLnv49hOIHh7ZpQiPXmYvFZKHF24I+2twyI3UGeYl5VGZVctfWu5idMZuYHmPvwF5MwoTVZCUYC+IwO/jM7M/Q4mlh39A+uv3dmDUzlVmVnJV7FmtK12DWzAdKnsdLSklMxojpMaJ6FIEgyXp8/TM8YQ9J1iSea3yOJk8Tg6FB/lH/jwOvZzoy6Qv0kZeYx4/O+REJ5gS29Wyj3ddO/VA9m7s3k2JLIRgNsjx3OdfOuBZf1Mf23u2YNTMXFl7Ik/VPUjtUy8q8lXys5GNMT53Ojt4dbOraROtIK9t6tqFLnVR7KtUD1czLmEfNYA3FKcUszlpMMBZkec5ynBYnJmEiyZpERXoFr7W+xl/2/gWX3YVFs+C0OLli+hUszlr8vrUkLd4Wfrr5p+Qn5dM43EiGI4NdfbtYlLmI7b3bKUguoG6wjr5gHznOHNwON8uyl5GflM9vtv+GkpQSrp5xNUuyl5CRkIEu9QPne/d/QhManb5OHq19lCxHFtfNvA6T9iGbfGYkFOWmP1exs93DQ59fiqgbYfMzTWSXJLPs4yWYLBrp+YmHzZs+Fikl3ufW0nvnnQibFfett2KvqKDvt78l0tKC2ZWKKSOdtOuvw0Innjc30f34a2i9g+wpNpExFCd7GLZMBy3DwoItEaJOnfo5Opn1NjJ7D85gNuxO4HcXxrhMm8++84qo9zfzxXlfxBP28NeavxKOhZmTOovzWhMp2dFL53XnkufMpf9Pf6Trork8o+2mP9DP6uLVpNpTyXZm0+Jt4WdVP+NL877ELWXXcHf1/VwYnUnOjg4CW7fgWFxJ2uc+S9XIHnr8Pfxk00/IcrhZGo7y4kAH+dkzaI30IKXkE+Wf4JmGZ+gPGitnLqnTiVpNxCvncImjkutmfQpvivEFeGi73LvzpB8vKSX9wX7S7Gkn3PkmEo9gNVmJ+3z4N2zAPmcugc2bMaWlYis12mYH7/8zJpcL58pziLS0EGlpIdbTi+Zw4H/rLZCSuDOBWEMDVSvd3F/Rz48eMzOUZsXzyYuYc+6V7OzbScaL2+gYasayp4Hl+3SkEJhSU0m58gqGXnoB2joPT5wQcM1l2Ndcyr6ff4/CXb1oFisJc+aQ/+v/w5SWRl9zDYO6j/KixUQ7OvA+/wKBbVsJ19UT6+rCsWI5CbNnY5k2DWtBIYGqKpIvuwxbSTEyHqe9pop1kWqunX8jAL/Z/hse2PsAiZZE3v7U25MiqP/3Z//IYKePG364gqE//ZG+u+4i49Zbybjtq0aVeyxszMDWXw/Nb44OJwPKLzOaRKZf+J7jNnoaeaLuCYQQ7OjdwTz3PF5peYVOfyfJ1mTiMk5eYh51Q8aiLFbNSkQ3bgptJhufLP8kV5VdRUlKCd6Il9s33M7m7s3oUifBnIDNZCMQDTASHUEguKToErKd2RSlFLG7fzf7h/YzPXU618y4hqHQECbNxMLMhQeqir0RL3E9zn2776N2sJaawRq8ES/lqeU8sPoBEswJNHmaeLL+SUaiI5yffz6P1j7KW51vkWBOYIF7ATazjf9e8d/v2yZ+snmCUZLt5jHz9/bWIcyaYKf3OYTu4LmdfeyPP8yCzNnUDO9kODx8YF+n2UlaQhpXlV3FzXNvPrD9yO8OXzjG5qYBrCYTS4vTxlw06VCP1T3G/XvuJ9uZzS/P/+V7ageklHiDMVIcx98HYMAXZigQxZ1oO6G/e/e76V1D/gg2s4ZjjAW4jseHapx622CALzxQRUOfn/9ZVor/7T4Cngili9xccOMsbAnv/ybKeJyBe+8l2ttLaO9eQjt3YZlVjojEiDQYK5lJswlvrgmzbsY6EMUSjCIxliBsccP2MsEl28ESlayfBwvrBa4Rib3ARcHvfoe5YDrSnEB43z58VVUQDOG64dNEbBoOy8mdsrLN23bcPTV9ER8J5gRMmokn6p/g77V/Jzcxl68u+CqlrlJieoxwPIwv4qMn0EO2M5tMR+ZJTe9EE9fj73tzMRwcIvjHv2AKRwlV78W/cSOW3FxSP/1pLDnZaIlJxAcHsJaUkjBn9gdKQ7S7m+CuXSRdfPEJ1yZF41HMmnlSTBO7eHGl/OKKO5lzbh6LKyI0X3cdyasuJvcXvzCue+Pv0F/+Ln49SpKUNFrtvDXrQnqdqTRokgWZC+jx96Cjs6V7C2n2NDxhDz2BHvxRo+ajJKWEBk8DFekVfGfZd5jrnnvg/B2+DtpG2ljXto5kq9HJtMXbwrONzwJQmlKKpmk0eZr4RNknSDAnEIwFCcVDOC1OXDYXFxRcQHla+bjeh0A0QH+wn5zEnPftdPZSTTONfQE+t6IcbyhKQ68fiaRvJEx+qoPHt7aRbLfwem0vM7OTicR0LqrIYlvrEN/8aPmYqxkGIjHe3j+APxLjgpmZdAwFmZbuwGE9/Hvz+d1dfO3h7UzPTMRi0piW7qBjOEiqw0ogEmNj46Dxfmc46R0JE9clutQRQnB1ZTrb+jZT3+MjHspDRtM4qzSdPFcCdb0+MpNsfGJxPn9Y30iXJ8Ts3GSyU+y8WtNLx7DRR0cTsLQ4jbuuXYDTZuadhn72dnrp9IRwJVg4r9xNfqqDbk+IaekOclLshGM6douJrS2DbGwcZG+Xlxf2dPPFlSWsKE1naVEaPd4Q/9zRwefOKiLRZmZT0yD7e328Wd9HtzfEng7vgfP/66pyKqelEozGeX1fL5G4jq5DXe8InkCUS+fmkJlsozjDiTvJxq52Dy0DfgZ8ER7f2o4Q8PF5uSwpTuON2l5icUlBmoPzyt2cP8NNfa+Pp3YYTRkfmZXJwgIXj1a18eq+Xu777JIPR1BvGfBz1W/fJhrXueujFdQ+WE9GfiLnfKKM3CNWzop2dREfHsb/1lt4nnqaaHc3emkhQ/5+Uut7kFYzsVQnDy+J8dYiO9eXX0fbO6+gd3WzPd1HZ7pxrMSQZPWuOEkxO5HFZSzKcXG2ZwBb8y7iWgqmm+5Hd8/ELExjd+5RphQ9EEDYbAjTxBric7IXdDkV5s5eIL+88i4u/8YCYj/8OtHWVkru/DKm9tfZb4LtjS/wUnoOW0WEyox5bBnYQ1SPYhIm0hPS6Q304jA7iMQjLMtZRiAWwGVzYRIm/rXyX0m1p+K0OAnFQtjNxz8pVKu3lY1dG1nbtJb+YD+3LbiNCwtXYTEdnp+llKyr66Mo3cm0dAcNfX7CsTgzspLes++R9nZ6WV/fR3Wnl/qeEfJTE8hOsROO6nz+7GJaBwO0DvrpHA6xpWWQYCROQ59xo5JsNxOO6YRjB2v+Em1mfGGjbbwiJ5nekRDhmM5I6OC2f7+knPNnuNnf6+Mna2voHA7RNhQgEDH6uGjCGLBi1gRz81NYWpSG2SR4sbqH/b0+KnKSsZo1HFYT+3t9FKY58IVjxHTJlQvzcCfZeGRzK4VpDr52YRmJNjM/fHYvL+zpxp1k4/NnF1GU7qS2e4R71hkFpsXTUmns8x8I3kuL0hgORmgeCJDqsHDH1fOIxnS2tw3z4NvNaEJgs2j0+yKYNEFmko0Bf4TIIe8FQJLNTCgWZ1q6k/29B6dQXjwtla0txkJMVrOG1aThC8fITraT47KzvXUY4EBgPm+GmzxXAi/s6eaF6u4Dx0mwmEi0m5FSUupOxGrWeLO+/z2fs0kTWEyCS+fkkJxg4ZGqVkJRHXeSjXSnldZB4/13WE0EInHMo+tTxHVJSoIFTzBKcYaTN/79gqkf1P3hGFf99m16RkI8dssK6p5oorN+mBt/tAK78+DdbqCqisGHH2Hk+eeNIS+ArzyPLSmDlDYGAcHzlYJXFhjDjDLNTtyxGNWEyY5LFsc1pgVG+PTH7yf8xBewBAZxXfh9Y2jUoT5kcxErE9tkCOrlJXPkv665m+s/5aT9MzeStaaMmvRNPOZK5y2rRkgTmISJ8wvOp3WklQXuBdw05yaSrEkkWhIZCg+Rbk8nHA+fUNA+XrG4zsObW4npkl+8VMfNK4v5xkUzaB0I8MA7zexqH6aq2ah2Tk6wMDjar2NGViK3nj+d8uwkijOc3Lu+kW2tQxSkOnBYTexoG2ZTk1GyzXMlMCMrkS3NQ4RiccyaRjB6sCOpWROsKE0n0WZmXr6L2bnJvFDdjVkTnDM9g3BM59GqNt5u6Of3N1bitJlYUZKOEILO4SDr6vpIdVj5zj930++LsKDARa83RDAaZ0lRGjkpdj46OxtNE7ywp5tZOUk0DwTY1DjArnYPMV2yrDiNC2Zm8qllhSTbT3z4WiASw2rSMB9yozMSiiKEINFmJhSNc8fz+8hJsfOl84xmM384htWsHXZz1Nzv54fP7mXAH+Hbq2eyoMCF3WIiGInzdkM/Pd4whWkOqjs9NA/4SbCYaR4wpv9eMz+XQX+E+QUu+n1harq8vL6vj87hIJcvyOWBd5qp7/HxLxfPYGVZBoVpjsMKhbou2bC//8BaIJVFqe+pzWgbDGDSBA19PoYCUWZmJ1HqTsSkHd6kMOiLkOOyYzFpRGI6z+3uZGebh4I0B5cvyMVm1nh+dzcbmwaYnZvCTWcXjbvmbcIH9c2bq/jKQ1t5ubqH/11WxvCWfkYGQixbU0LlpUU0eZpI8+gEmhsZ/NLXCdoEr86HljwLHelRGjNMLLVl8XGvhxU9DbRbbUTmXIWlcwclXXtJMzsILPoMtoFGTPGQsQxf+WpjzGtw2BgvrCgT2GQI6mWFFfInX3mAZbt+gn9vDbXX+7gj143NmsQ89zy+Mu/LJNtd5Cfln9BxPcEoL1Z3s2Z+Ls0DfsqzkmgfCvJOwwC6lFQ1D+EPx/jMimk4bGZerO5meUk6Z5Wm88/tHfSOhMlPNUpnz+8xSmfvloRnZCVS1+PDatIocTtZsyAXbzCGJxhhdm4KNrPGz1+sPTACx2ISROOSmdlJtAwEiOuSmTlJfGRmJjcun0Z6ou1AmmNxHQm8tq+XBIvRjiyAzOT3v2EJReO0DwWYnnn0Dm7RuM5jW9p58J1mQtE4/3f9Qublu973uHFdEo0bVdjKmTXl29RvuONv/O2F/Xze6ULvCZE5LYmFq6aRPcfB2/Uv0/y977Byj1EdM5AkeO0nayh3ptC052H0aIALR7wsC4Wh+DxjLufZVxoTmeg6dO80lvJLzjnDV6ooH9xkCOql+RXy5zffzaxHbuWhCzSeWq6RYE7giTVPHFcgH/RH2NoyxOzcZHJdCdR0eXnwnWZ6vGFe29d7oPqyPCuJ2p6Dw5oyEq2AoN8XPux47iQbfSOHL1H8b6vKWVGaTkmGk5+9WEuPJ8TCQhfXVBaQdZRgG4npNPX72dftZWvLEAsLXVy5MP9AFfGxOnwpypGmdFCfu2CRTL7ox1zvt2FPMLP0iiKetz1MchCi9z3E4n1RUgJQvyIFPRBi2nRJZWoMvO3Geruf+BO0vm0E8eOdWUxRJpnJENRLcmfJH178FabtvYef3VyKO/lzrCjOZ03FAna2e3huVycJVjPXLSmgbSjAtpZh9nZ5KHUn0tjnp7rTg3e0zXh+fgo93jDdXmMY2fnlbpr7/ZxTlsE7DQOsnpPDFQtz0YSgKN1JKBbn2Z1dmE2Cc2e4eX5PN/e92cgt55Zw5cI8mvr95LkSxuxcpiin2xkN6kKINOBRoAhoBq6VUg6NsV8c2D36tFVKueZ4jl9UPld+8cJfkpuSwMfPDdH0mx9hauvGFgWpQaDETnFRB+5sEyTnGaslWRIgr9KYJtKW+IGvTVEmi5MV1E9lfi7KLpd3LbuRAdcjPFjxv/gj8kC7NBglZ08gSiRulHBNmqA4w0n7UICKHKN0fm1lAXu7vKzd3UVTn5+fXzOPbk+ITy+fdszOaooyWZzpVdq+DbwqpbxDCPHt0effGmO/oJRywYkePOSL4tI18nN20/cvv8KTLuir0FkYC5Ff4CMx3QwX/QCW3AymKTONvaKcKacsP+txHVM8iH/+Daz7hjHefFeHhx2tQzhtZq5YmEdzv5/tbcPMyU0hK9lGeqLtPeOZz53h5svnlaLrEk1TnVUV5UjjjYSXA+ePPn4AeIOxvwQ+EEtUYoo2kPn7X1GXD2+vCfH/5Z5L1qqfQN0LxgpMGWUn63SK8mF3CvOzRsga5KPXffNAMF5Q4GJBgevAHmVZSZRlHd4B7Ghj91VAV5SxjTeoZ0kpR5ePohs42sTLdiHEFiAG3CGl/OfxHFxImFX7Gt1lMT56jovLL7sbSj9ivFh50/hSrijKkU5pfo6bQszKPYGldBVFOWHHDOpCiFeA7DFeuv3QJ1JKKYQ4WgP9NCllhxCiBHhNCLFbStlwlPPdAtwCUJAxA0/6CB+/JBPxxTfGXv9YUZTjdjrz85F5OW6JjjP1iqIcyzGDupTyoqO9JoToEULkSCm7hBA5QO9RjtEx+rtRCPEGsBAYM6hLKe8F7gUodJfLlNx+xJrfqYCuKCfB6czPR+ZlaY0duYuiKCfZeLuMPg18dvTxZ4GnjtxBCJEqhLCNPs4Azgb2Hu8JHKVzIHfBOJOpKMpxOLX52a56qCvKqTbeXHYHcLEQoh64aPQ5QohKIcR9o/vMArYIIXYCr2O0wR13UM+Yu2KcSVQU5Tid0vysJalx4Ipyqo2ro5yUcgB4z3qIUsotwM2jj98G5h65z/EQ6GSXfrDVrxRFOTGnOj/b01QnOUU51SZ0fZiQOvYcNWRNUaaCpNyx+ucpinIyTeigjtQRjrQznQpFUU6CrOkzz3QSFGXKm9hBHV0tcaooU4BAp7hiQk9PryhTwsQP6oqiTH5SkpKacaZToShTngrqiqKcckLlZUU5LSZ2UBfqi0BRpgQRPNMpUJQPhQkd1FVzuqJMDRnT8s50EhTlQ2FCB/UJnjpFURRFmVAmdNgUanlFRVEURTluEzqoO9UMVIqiKIpy3CZ0ULclOM90EhRFURRl0pjQQV1RFEVRlOOngrqiKIqiTBEqqCuKoijKFKGCuqIoiqJMESqoK4qiKMoUMa6gLoS4RghRLYTQhRBHXYJJCHGJEKJWCLFfCPHt8ZxTUZRTQ+VnRZn8xltS3wNcBaw/2g5CCBNwN7AaqACuF0JUjPO8iqKcfCo/K8okZx7PH0spawDE+0/SvhTYL6VsHN33EeByYO94zq0oysml8rOiTH6no009D2g75Hn76LYxCSFuEUJsEUJs6evrO+WJUxTlhBx3flZ5WVFOv2OW1IUQrwDZY7x0u5TyqZOdICnlvcC9AJWVlfJkH19RPsxOZ35WeVlRTr9jBnUp5UXjPEcHUHDI8/zRbYqinGYqPyvK1HY6qt+rgDIhRLEQwgpcBzx9Gs6rKMrJp/Kzokxg4x3SdqUQoh1YATwnhHhxdHuuEGItgJQyBtwGvAjUAH+XUlaPL9mKopxsKj8ryuQ33t7vTwJPjrG9E7j0kOdrgbXjOZeiKKeWys+KMvmpGeUURVEUZYpQQV1RFEVRpggV1BVFURRlilBBXVEURVGmCBXUFUVRFGWKUEFdURRFUaYIFdQVRVEUZYpQQV1RFEVRpggV1BVFURRlilBBXVEURVGmCBXUFUVRFGWKUEFdURRFUaYIFdQVRVEUZYpQQV1RFEVRpggV1BVFURRlihhXUBdCXCOEqBZC6EKIyvfZr1kIsVsIsUMIsWU851QU5dRQ+VlRJj/zOP9+D3AV8Pvj2PcCKWX/OM+nKMqpo/Kzokxy4wrqUsoaACHEyUmNoihnjMrPijL5na42dQm8JITYKoS45TSdU1GUU0PlZ0WZoI5ZUhdCvAJkj/HS7VLKp47zPOdIKTuEEJnAy0KIfVLK9Uc53y3ALQCFhYXHeXhFUY7H6czPKi8ryul3zKAupbxovCeRUnaM/u4VQjwJLAXGDOpSynuBewEqKyvleM+tKMpBpzM/q7ysKKffKa9+F0I4hRBJ7z4GVmF0yFEUZZJR+VlRJrbxDmm7UgjRDqwAnhNCvDi6PVcIsXZ0tyxggxBiJ7AZeE5K+cJ4zqsoysmn8rOiTH7j7f3+JPDkGNs7gUtHHzcC88dzHkVRTj2VnxVl8lMzyimKoijKFKGCuqIoiqJMESqoK4qiKMoUoYK6oiiKokwRKqgriqIoyhShgrqiKIqiTBEqqCuKoijKFKGCuqIoiqJMESqoK4qiKMoUoYK6oiiKokwRKqgriqIoyhShgrqiKIqiTBEqqCuKoijKFKGCuqIoiqJMESqoK4qiKMoUoYK6oiiKokwR4wrqQoifCyH2CSF2CSGeFEK4jrLfJUKIWiHEfiHEt8dzTkVRTg2VnxVl8htvSf1lYI6Uch5QB/zHkTsIIUzA3cBqoAK4XghRMc7zKopy8qn8rCiT3LiCupTyJSllbPTpRiB/jN2WAvullI1SygjwCHD5eM6rKMrJp/Kzokx+J7NN/Sbg+TG25wFthzxvH92mKMrEpfKzokxC5mPtIIR4Bcge46XbpZRPje5zOxADHhpvgoQQtwC3jD4NCyH2jPeYE0AG0H+mE3GSqGuZeMqPd8fTmZ+naF6GqfN/A1PnWqbKdcAJ5OexHDOoSykver/XhRCfAz4GXCillGPs0gEUHPI8f3Tb0c53L3Dv6LG3SCkrj5XGiW6qXAeoa5mIhBBbjnff05mfp2JeBnUtE9FUuQ44sfw8lvH2fr8E+CawRkoZOMpuVUCZEKJYCGEFrgOeHs95FUU5+VR+VpTJb7xt6r8BkoCXhRA7hBC/AxBC5Aoh1gKMdry5DXgRqAH+LqWsHud5FUU5+VR+VpRJ7pjV7+9HSjn9KNs7gUsPeb4WWPsBTnHvB0zaRDNVrgPUtUxEJ+U6TnF+nirvNahrmYimynXAOK9FjN1spiiKoijKZKOmiVUURVGUKWJCBvXJPg2lEKJZCLF7tF1yy+i2NCHEy0KI+tHfqWc6nWMRQvxJCNF76PCjo6VdGP5v9HPaJYRYdOZSfrijXMf3hBAdo5/LDiHEpYe89h+j11ErhPjomUn12IQQBUKI14UQe4UQ1UKI/ze6fVJ8LpM5P6u8PDFMlfx8WvKylHJC/QAmoAEoAazATqDiTKfrBK+hGcg4YtvPgG+PPv428NMznc6jpP1cYBGw51hpx2hnfR4QwHJg05lO/zGu43vAv42xb8Xo/5kNKB79/zOd6Ws4JH05wKLRx0kYU7hWTIbPZbLnZ5WXJ8bPVMnPpyMvT8SS+lSdhvJy4IHRxw8AV5y5pBydlHI9MHjE5qOl/XLgQWnYCLiEEDmnJaHHcJTrOJrLgUeklGEpZROwH+P/cEKQUnZJKbeNPh7B6HWex+T4XKZiflZ5+TSbKvn5dOTliRjUp8I0lBJ4SQixVRizagFkSSm7Rh93A1lnJmkfyNHSPhk/q9tGq7H+dEi16aS5DiFEEbAQ2MTk+FwmUlo+CJWXJ7ZJm59PVV6eiEF9KjhHSrkIYyWrrwohzj30RWnUq0zKYQeTOe3APUApsADoAn5xRlNzgoQQicA/gG9IKb2HvjbJP5eJTOXliWvS5udTmZcnYlA/oWllJyIpZcfo717gSYyqn553q01Gf/eeuRSesKOlfVJ9VlLKHillXEqpA3/gYJXchL8OIYQF40vgISnlE6ObJ8PnMpHScsJUXp64Jmt+PtV5eSIG9Uk9DaUQwimESHr3MbAK2INxDZ8d3e2zwFNnJoUfyNHS/jTwmdEemssBzyFVSBPOEW1RV2J8LmBcx3VCCJsQohgoAzaf7vQdjRBCAH8EaqSUdx3y0mT4XCZtflZ5eeLmZZic+fm05OUz3RvwKD0EL8XoFdiAsXrUGU/TCaS9BKPn5U6g+t30A+nAq0A98AqQdqbTepT0P4xRlRXFaL/5wtHSjtEj8+7Rz2k3UHmm03+M6/jLaDp3jWaWnEP2v330OmqB1Wc6/UdcyzkY1XG7gB2jP5dOls9lsuZnlZfP/DUc41omXX4+HXlZzSinKIqiKFPERKx+VxRFURTlA1BBXVEURVGmCBXUFUVRFGWKUEFdURRFUaYIFdQVRVEUZYpQQV1RFEVRpggV1BVFURRlilBBXVEURVGmiP8fNFGM2/WMXUAAAAAASUVORK5CYII=
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<div class="prompt input_prompt">In [47]:</div>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">results</span><span class="p">(</span><span class="n">rmses</span><span class="p">,</span> <span class="n">times</span><span class="p">)</span>
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<th>RMSE $\theta_0$</th>
<th>RMSE $\theta_1$</th>
<th>RMSE $\theta_2$</th>
<th>RMSE $\theta_3$</th>
<th>times (seg)</th>
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<th>$\sigma=0.1$</th>
<td>0.013715</td>
<td>0.039330</td>
<td>0.024226</td>
<td>0.019937</td>
<td>2.693</td>
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<th>$\sigma=0.2$</th>
<td>0.043813</td>
<td>0.034283</td>
<td>0.038977</td>
<td>0.028324</td>
<td>2.051</td>
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<th>$\sigma=0.4$</th>
<td>0.094143</td>
<td>0.119527</td>
<td>0.057571</td>
<td>0.134192</td>
<td>2.348</td>
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<th>$\sigma=0.6$</th>
<td>0.156373</td>
<td>0.172262</td>
<td>0.113379</td>
<td>0.145197</td>
<td>2.156</td>
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<th>$\sigma=0.8$</th>
<td>0.162770</td>
<td>0.194228</td>
<td>0.199912</td>
<td>0.216657</td>
<td>2.388</td>
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<th>$\sigma=1.0$</th>
<td>0.203166</td>
<td>0.216700</td>
<td>0.255639</td>
<td>0.305202</td>
<td>2.870</td>
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<p>En cuanto al RMSE, parece existir una ligera mejora a medida que se incrementa el ruido, sin embargo no podemos sacar conclusiones aún. Te invito a hacer varias simulaciones con diferentes parámetros y nos compartas tus resultados. Nos vemos en otra ocasión.</p>
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<p>No olvides comentar y suscribirte al blog para que estés enterando de los posts que voy a ir subiendo semana a semana. También sientete en libertad de seguirme en LinkedIn, Twitter, Github e Instagram.</p>
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<h2 id="Bibliografía">Bibliografía<a class="anchor-link" href="#Bibliografía">¶</a></h2><ol>
<li>Sebastián Ruder. 2017. An overview of gradient descent optimization algorithms. Insight Centre for Data Analytics, Nui Galway.</li>
<li>Mustafa Murat. 2019. <a href="https://mmuratarat.github.io/2019-01-07/logistic-regression-in-Tensorflow">Logistic Regression in TensorFlow</a>.</li>
<li>Aurelien Geron. 2019. Hands-on Machine Learning with Scikit-Learn, Keras and TensorFlow.</li>
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<h2 id="Notas">Notas<a class="anchor-link" href="#Notas">¶</a></h2><p><a id="1">[1]</a>. Si $y_{\min}$ es el mínimo global de una función $f(x)$, entonces se define el operador $\operatorname*{argmin\,\,}$ como siguiente conjunto: $$\operatorname*{argmin\,\,}_{ x \in X} f(x) = \{x\in X: f(x) = y_\min\}.$$
<a id="2">[2]</a>. El conjunto $[r]_{\mathbb{N}_0}$ es $\{0, 1, 2,\dots, r\}$.</p>
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<h2 id="Contacto">Contacto<a class="anchor-link" href="#Contacto">¶</a></h2><ul>
<li>Participa de la canal de Nerve a través de <a href="https://discord.gg/edPmghPq8K">Discord</a>.</li>
<li>Se quieres conocer más acerca de este tema me puedes contactar a través de <a href="https://www.classgap.com/me/alejandro-sanchez-yali">Classgap</a>.</li>
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www.asanchezyali.comhttp://www.blogger.com/profile/06396258253910042323noreply@blogger.com0tag:blogger.com,1999:blog-8939855543774830921.post-59891882353021422272020-01-07T23:09:00.009-05:002021-01-29T18:05:00.852-05:00El algoritmo del gradiente descendente<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
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<p style="text-align: justify;">El <strong>gradiente descendente</strong> (GD) es un algoritmo de optimización genérico, capaz de encontrar soluciones óptimas para una amplia gama de problemas. La idea del gradiente descendente es ajustar los parámetros de forma iterativa para minimizar una función.</p>
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<p style="text-align: justify;">Concretamente, se tiene de una función diferenciable convexa<a href="#10"><sup>1</sup></a>, $f:\Omega\subset\mathbb{R}^n \to \mathbb{R}$, el algoritmo GD permite encontrar un $w$ en $\Omega$ tal que $f(w)$ es un mínimo, en otras palabras, GD se utiliza para determinar los elementos del siguiente conjunto<a href="#11"><sup>2</sup></a>:</p>
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<p style="text-align: justify;"><a id="1"></a>
\begin{equation}\tag{1}
w \in \operatorname*{argmin\,\,}_{ w\in \Omega} f(w).
\end{equation}</p>
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<p style="text-align: justify;">Para determinar los valores de $w$ que optimiza la función $f(w)$, GD hace uso de una serie de iteracciones que se hacen de acuerdo con la siguiente regla de actualización:</p>
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<p style="text-align: justify;"><a id="2"></a>
\begin{equation}\tag{2}
w_{t+1} = w_{t} -\eta_{t} \nabla f(w_{t}),
\end{equation}</p>
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<p style="text-align: justify;">que usualmente se inicializa en cero y cada iteración, como se puede observar, se hace en la dirección negativa del gradiente. Recuerde que el gradiente se define como el vector:</p>
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\begin{equation}\nonumber
\nabla f(w)=\left(\frac{\partial f}{\partial x_{1}}(w),\dots, \frac{\partial f}{\partial x_{n}}(w)\right).
\end{equation}
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<p style="text-align: justify;">Un hiperparámetro importante en GD es el $\eta_{t} > 0$, denominado como <strong>tasa de aprendizaje</strong>. Si la tasa de aprendizaje es demasiado pequeña, entonces el algoritmo tendrá que pasar por muchas iteraciones para converger, lo que llevará mucho tiempo. Por otro lado, si la tasa de aprendizaje es demasiado alta, es posible que se salte el mínimo global y termine en otro lado, posiblemente incluso más alto que antes. Esto podría hacer que el algoritmo diverja, con valores cada vez mayores, sin encontrar una buena solución.</p>
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<h2 id="¿Cómo-funciona-este-algoritmo?" style="text-align: justify;">¿Cómo funciona este algoritmo?<a class="anchor-link" href="#¿Cómo-funciona-este-algoritmo?">¶</a></h2>
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<p style="text-align: justify;">Este algoritmo se define a partir de las dos características esenciales que tiene el gradiente, las cuales se mencionan a continuación:</p>
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<li><div style="text-align: justify;">El gradiente es perpendicular a las curvas de nivel de $f$, de manera que para cualquier dirección $v\in \mathbb{R}^{n}$ ortogonal a $\nabla f(p)$, es una dirección de cambio nulo. Esto se observa facilmente al parametrizar la curva $S_{k}=\{p\in \Omega: f(p)=k\}$ mediante una función $\alpha:I\subset \mathbb{R}\to S_{k}$ tal que $\alpha(0)=p$, pues al calcular el producto punto de $\nabla f(p)$ con la velocidad de $\alpha$ en $p$ se obtiene que la tasa de cambio es:</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">\begin{equation}\nonumber|df_{p}(\alpha'(0))|=|\nabla f(p)\cdot \alpha' (0)| = 0, \end{equation}</div><div style="text-align: justify;">es decir, la tasa de cambio en la dirección de $\alpha'(0)$ es cero.</div></li>
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<p><a id="1"></a></p>
<div align="center" style="text-align: justify;"><br /></div><div class="separator" style="clear: both; text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhC_DXZsIrkN4LjV-6NgOQt10226VCLHY4z5csX_iB7rPH32F3Gjonlt9h6yWeiqnxf9Ckh0nmZ7z_nAUNV5yj5r76Jwn9gdsl1NCJ__y2SLYc5U_tVW7BUiWxf6qOW2-paKiIF7903UBw/s487/gd.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="410" data-original-width="487" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhC_DXZsIrkN4LjV-6NgOQt10226VCLHY4z5csX_iB7rPH32F3Gjonlt9h6yWeiqnxf9Ckh0nmZ7z_nAUNV5yj5r76Jwn9gdsl1NCJ__y2SLYc5U_tVW7BUiWxf6qOW2-paKiIF7903UBw/s16000/gd.png" /></a></div><div style="text-align: justify;"><br /></div>
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<li><div style="text-align: justify;">El gradiente indica la dirección ascendente de la tasa de máximo cambio de $f$ en el punto $p$. La tasa máxima se calcula como $||\nabla f(p)||$. La razón de esto, se aprecia cuando se considera un vector $v\in \mathbb{R}$ tal que $||v||=1$, de manera que para este vector la tasa de cambio es:</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">\begin{equation}\nonumber |df_{p}(v)|=||\nabla f(p)||||v|||cos\theta|\leq ||\nabla f(p)|| \end{equation}</div><div style="text-align: justify;">Dicha magnitud es máxima cuando $\theta = 2n\pi$ con $n\in \mathbb{Z}$, es decir, para que $|df_{p}(v)|$ sea máxima, los vectores $\nabla f(p)$ y $v$ deben ser paralelos, de esta manera, la función $f$ crece más rápidamente en la dirección del vector $\nabla f(p)$ y decrece más rápidamente en la dirección de $-\nabla f(p)$, en efecto, si $v=\frac{\nabla f(p)}{||\nabla f(p)||}$, entonces $df_{p}(v)=||\nabla f(p)||$.</div></li>
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<p style="text-align: justify;">La iteración definida en la <a href="#2">Ecuación 2</a> permite construir una sucesión de puntos $\{w_t\}_{t\in [m]_{\mathbb{N}_0}}$ de tal manera que $f(w_{t+1})<f(w_{t})$. Este hecho se puede evidenciar mediante el polinomio de Taylor, en efecto si se considera un punto inicial $w_{0}$, entonces para el primer termino de la expansión de Taylor alrededor de $w_{0}$ se tiene:</p><div style="text-align: justify;">\begin{equation}\nonumber
f(w_{1})-f(w_{0})\approx \langle w_{1}-w_{0}, \nabla f(w_{0})\rangle=-\eta ||\nabla f(w_{o})||^2
\end{equation}</div><p style="text-align: justify;">Por consiguiente:</p><div style="text-align: justify;">\begin{equation}\nonumber
f(w_{1})-f(w_{0}))=-\eta ||\nabla f(w_{o})||^2 + o(\eta)
\end{equation}</div><p style="text-align: justify;">de tal manera que para un $\eta$ adecuado se puede garantizar que $f(w_{1})<f(w_{0})$. El razanomiento se puede repetir para $w_{t+1}$ y $w_{t}$, de tal manera que $w_{t+1}$ es una mejora de $w_{t}$.</p>
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<p style="text-align: justify;">De acuerdo a las consideraciones anteriores, el algoritmo del gradiente descendente se define de la siguiente manera:</p>
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<p style="text-align: justify;"><strong>Algoritmo del gradiente descendente (AGD)</strong></p>
<blockquote><div style="text-align: justify;">Input: $w_0$, $m$, $\eta$, $\nabla f(w)$ </div><div style="text-align: justify;">1. for $k=0$ to $m$ do: </div><div style="text-align: justify;">2. $w\leftarrow w - \eta \nabla f(w)$ </div><div style="text-align: justify;">3. end </div><div style="text-align: justify;">return: $w$</div></blockquote><hr style="text-align: justify;" />
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<p style="text-align: justify;">donde $w_0$ es la condición inicial del algoritmo, $m$ es el número máximo de iteraciones, $\eta$ es la tasa de aprendizaje y $\nabla f(w)$ es la función gradiente de $f$. Observe que la regla de actualización se definió apartir de la <a href="#2">Ecuación 2</a>. Es importante notar que finalmente $w_{t+1}$ es tal que:</p><div style="text-align: justify;">\begin{equation}\nonumber
w_{t+1}\in \operatorname*{argmin\,\,}_{ w\in \Omega} \frac{1}{2\eta_{t}}||w-w_{t}+\eta_{t}\nabla f(w_{t})||.
\end{equation}</div><p style="text-align: justify;">Es fácil comprobar que el problema de optimización anterior se puede reescribir como:</p><div style="text-align: justify;">\begin{equation}
\operatorname*{argmin\,\,}_{ w\in \Omega} \frac{1}{2\eta_{t}}||w-w_{t}+\eta_{t}\nabla f(w_{t})||=\operatorname*{argmin\,\,}_{ w\in \Omega} \left(f(w_{t}) + \langle \nabla f(w_t), w-w_t \rangle + \frac{1}{2\eta_{t}}||w-w_{t}||\right)
\end{equation}</div><p style="text-align: justify;">Por lo tanto, el $w_{t+1}$ es obtenido para minimizar la linealización de la función $f$ alrededor del punto $w_{t}$, manteniendolo lo suficientemente aproximado a este el punto $w_{t}$.</p>
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<h2 id="¿Cuándo-parar-las-iteraciones?" style="text-align: justify;">¿Cuándo parar las iteraciones?<a class="anchor-link" href="#¿Cuándo-parar-las-iteraciones?">¶</a></h2>
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<p style="text-align: justify;">Es importante aclarar, que a pesar de que el algoritmo ejecute el máximo de iteraciones, el resultado arrojado no necesariamente es una buena aproximación a el elemento minimizador de la función $f$. Por lo tanto es necesario definir un criterio que permita decidir si el resultado obteniendo es adecuado o no.</p>
<p style="text-align: justify;">Como primer criterio de parada del algoritmo que se le puede ocurrir al lector es detener las iteraciones cuando $||\nabla f(x_{t})||=0$, pero esto no es práctico debido a diferentes factores que influyen, como el comportamiento de la coma flotante y la elección adecuada de la tasa de aprendizaje. Usualmente en la práctica se suele definir un parametro de tolerancia $\epsilon>0$ que junto con alguno de los siguientes criterios se usan para detener las iteraciones:</p>
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<li><div style="text-align: justify;"><strong>Condición sobre el gradiente:</strong> </div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">\begin{equation}\nonumber ||\nabla f(x_{t})||<\epsilon\end{equation}</div></li>
<li><div style="text-align: justify;"><strong>Condición sobre las diferencias sucesivas relativas de la función objetivo:</strong> </div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">\begin{equation}\nonumber \frac{|f(x_{t+1})-f(x_{t})|}{|f(x_{t})|}<\epsilon,\end{equation}</div><div style="text-align: justify;">si el denominador es muy pequeño, es conveniente remplazarlo por $\max\{1, |f(x)|\}$.</div></li>
<li><div style="text-align: justify;"><strong>Condición sobre las diferencias sucesivas relativas de la variable independiente:</strong> </div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">\begin{equation}\nonumber \frac{||x_{t+1}-x_{t}||}{||x_{t}||}<\epsilon,\end{equation}</div><div style="text-align: justify;">si el denominador es muy pequeño, es conveniente remplazarlo por $\max\{1, ||x_{t}||\}$.</div></li>
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<h2 id="Algunas-consideraciones-sobre-las-tasas-de-aprendizaje." style="text-align: justify;">Algunas consideraciones sobre las tasas de aprendizaje.<a class="anchor-link" href="#Algunas-consideraciones-sobre-las-tasas-de-aprendizaje.">¶</a></h2>
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<li><p style="text-align: justify;">La principal desventaja del AGD se encuentra en el ajuste adecuado de la tasa de aprendizaje $\eta$. Si $\eta$ toma un valor muy pequeño, es necesario un gran número de iteraciones para que el proceso converga; si por otro lado $\eta$ es muy grande, entonces puede ocurrir que el proceso no converga.</p>
</li>
<li><p></p><div style="text-align: justify;">La tasa de aprendizaje $\eta$ es determinada por la minimización exacta de:</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">\begin{equation}\nonumber\eta_{t} \in \operatorname*{argmin\,\,}_{\eta>0}f(x_{t}-\eta\nabla f(x_{t})). \end{equation}</div><div style="text-align: justify;">Esto se usa principalmente para problemas de caracter cuadrático y en donde el cálculo de $\eta$ es económico pero una evaluación de gradiente costosa; de lo contrario, no vale la pena el esfuerzo de resolver este subproblema exactamente.</div><p></p>
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<h2 id="Ejemplo:-Gradiente-descente-para-una-forma-cuadrática" style="text-align: justify;">Ejemplo: Gradiente descente para una forma cuadrática<a class="anchor-link" href="#Ejemplo:-Gradiente-descente-para-una-forma-cuadrática">¶</a></h2><p style="text-align: justify;">Asuma que $Q$ es simétrica y definida positiva ($x^{\top}Q x>0$ para cualquier $x\neq 0$). Considere la forma cuadrática:</p><div style="text-align: justify;">\begin{equation}\nonumber
f(x)=\frac{1}{2}x^{\top}Qx - b^{\top}x
\end{equation}</div><p style="text-align: justify;">el lector puede comprobar que su gradiente es:</p><div style="text-align: justify;">\begin{equation}\nonumber
\nabla f(x)=Qx-b.
\end{equation}</div><p style="text-align: justify;">Así la secuencia de $\{x_{t}\}_{t\in [m]}$ que inicia en cualquier $x_{0}$ viene dada por:</p><div style="text-align: justify;">\begin{equation}\nonumber
x_{t+1}=x_{t}-\eta_{k}(Qx-b)
\end{equation}</div><p style="text-align: justify;">con $g_{t}:=\nabla f(x_t)$ se define:</p><div style="text-align: justify;">\begin{equation}\nonumber
\eta_{t}=\frac{g_{t}^{\top}g_{t}}{g_{t}^{\top}Qg_{t}}.
\end{equation}</div><p style="text-align: justify;">El lector puede validar que con el valor de $\eta_{t}$ definido anteriormente se tiene:</p><div style="text-align: justify;">\begin{equation}\nonumber
\eta_{t}\in \operatorname*{argmin\,\,}_{\eta>0}f(x_{t}-\eta\nabla f(x_{t})).
\end{equation}</div></div>
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<h3 id="¿Cómo-implementarlo-en-python?" style="text-align: justify;">¿Cómo implementarlo en python?<a class="anchor-link" href="#¿Cómo-implementarlo-en-python?">¶</a></h3>
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<p style="text-align: justify;">Para las consideraciones del ejemplo anterior, es fácil definir una clase en Python para todas las formas cuadraticas, junto con tres métodos principales que permiten evaluar la forma cuadrática, calcular $\eta$ y el gradiente en un punto $x$. Esto sería algo así:</p>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span></div><span></span>
<div style="text-align: justify;"><span class="k">class</span> <span class="nc">QuadraticForm</span><span class="p">:</span></div><div style="text-align: justify;"> </div><div style="text-align: justify;"> <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">Q</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span></div><div style="text-align: justify;"> <span class="sd">"""</span></div><span class="sd"><div style="text-align: justify;"> Inputs:</div></span><span class="sd"><div style="text-align: justify;"> Q: Positive definite symmetric matrix.</div></span><span class="sd"><div style="text-align: justify;"> b: Rn vector. </div></span><span class="sd"><div style="text-align: justify;"><span class="sd"> """</span> </div></span><div style="text-align: justify;"> <span class="bp">self</span><span class="o">.</span><span class="n">Q</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">Q</span><span class="p">)</span> </div><div style="text-align: justify;"> <span class="bp">self</span><span class="o">.</span><span class="n">b</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">b</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span></div><div style="text-align: justify;"> </div><div style="text-align: justify;"> <span class="k">def</span> <span class="nf">evaluate</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span></div><div style="text-align: justify;"> <span class="sd">"""</span></div><span class="sd"><div style="text-align: justify;"> Method to evaluate the quadratic form.</div></span><span class="sd"><div style="text-align: justify;"> Inputs:</div></span><span class="sd"><div style="text-align: justify;"> x: Rn vector.</div></span><span class="sd"><div style="text-align: justify;"> Ouput:</div></span><span class="sd"><div style="text-align: justify;"> Value of the quadratic form in x. </div></span><span class="sd"><div style="text-align: justify;"> """</div></span><div style="text-align: justify;"> <span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">x</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span></div><div style="text-align: justify;"> <span class="n">Q</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">Q</span></div><div style="text-align: justify;"> <span class="n">b</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">b</span> </div><div style="text-align: justify;"> <span class="k">return</span> <span class="p">(</span><span class="mi">1</span><span class="o">/</span><span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="n">x</span><span class="o">.</span><span class="n">T</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">Q</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">x</span><span class="p">))</span> <span class="o">-</span> <span class="n">b</span><span class="o">.</span><span class="n">T</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">x</span><span class="p">)</span></div><div style="text-align: justify;"> </div><div style="text-align: justify;"> <span class="k">def</span> <span class="nf">eta</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span> </div><div style="text-align: justify;"> <span class="sd">"""</span></div><span class="sd"><div style="text-align: justify;"> Method to evaluate eta.</div></span><span class="sd"><div style="text-align: justify;"> Inputs:</div></span><span class="sd"><div style="text-align: justify;"> x: Rn vector.</div></span><span class="sd"><div style="text-align: justify;"> Output:</div></span><span class="sd"><div style="text-align: justify;"> Value of eta in x. </div></span><span class="sd"><div style="text-align: justify;"> """</div></span><div style="text-align: justify;"> <span class="n">gradient_x</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">gradient</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> </div><div style="text-align: justify;"> <span class="n">numerator</span> <span class="o">=</span> <span class="n">gradient_x</span><span class="o">.</span><span class="n">T</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">gradient_x</span><span class="p">)</span></div><div style="text-align: justify;"> <span class="n">denominator</span> <span class="o">=</span> <span class="n">gradient_x</span><span class="o">.</span><span class="n">T</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">Q</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">gradient_x</span><span class="p">))</span></div><div style="text-align: justify;"> <span class="k">return</span> <span class="n">numerator</span> <span class="o">/</span> <span class="n">denominator</span></div><div style="text-align: justify;"> </div><div style="text-align: justify;"> <span class="k">def</span> <span class="nf">gradient</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span></div><div style="text-align: justify;"> <span class="sd">"""</span></div><span class="sd"><div style="text-align: justify;"> Method to evaluate the gradient.</div></span><span class="sd"><div style="text-align: justify;"> Inputs:</div></span><span class="sd"><div style="text-align: justify;"> x: Rn vector.</div></span><span class="sd"><div style="text-align: justify;"> Output:</div></span><span class="sd"><div style="text-align: justify;"> Value of the gradient in x.</div></span><span class="sd"><div style="text-align: justify;"> """</div></span><div style="text-align: justify;"> <span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">x</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span></div><div style="text-align: justify;"> <span class="k">return</span> <span class="n">Q</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="o">-</span> <span class="n">b</span> </div></pre></div>
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<p style="text-align: justify;">El AGD se implementaría de la siguiente forma:</p>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="k">def</span> <span class="nf">gradient_descent</span><span class="p">(</span><span class="n">initial_x</span><span class="p">,</span> <span class="n">eta</span><span class="p">,</span> <span class="n">epsilon</span><span class="p">,</span> <span class="n">function</span><span class="p">):</span></div><span><div style="text-align: justify;"> <span class="sd">"""</span></div></span><span class="sd"><div style="text-align: justify;"> Gradient descent Algorithm.</div></span><span class="sd"><div style="text-align: justify;"> Inputs:</div></span><span class="sd"><div style="text-align: justify;"> initial_x: Rn vector.</div></span><span class="sd"><div style="text-align: justify;"> eta: learning rate.</div></span><span class="sd"><div style="text-align: justify;"> epsilon: precision.</div></span><span class="sd"><div style="text-align: justify;"> function: Quadractic Form.</div></span><span class="sd"><div style="text-align: justify;"> Output:</div></span><span class="sd"><div style="text-align: justify;"> Point where the function reaches the minimum.</div></span><span class="sd"><div style="text-align: justify;"> """</div></span>
<div style="text-align: justify;"> <span class="n">k</span> <span class="o">=</span> <span class="mi">0</span></div><div style="text-align: justify;"> <span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">initial_x</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span></div><div style="text-align: justify;"> </div><div style="text-align: justify;"> <span class="k">while</span> <span class="kc">True</span><span class="p">:</span></div><div style="text-align: justify;"> </div><div style="text-align: justify;"> <span class="n">gradient_x</span> <span class="o">=</span> <span class="n">function</span><span class="o">.</span><span class="n">gradient</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> </div>
<div style="text-align: justify;"> <span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">norm</span><span class="p">(</span><span class="n">gradient_x</span><span class="p">)</span> <span class="o"><</span> <span class="n">epsilon</span><span class="p">:</span></div><div style="text-align: justify;"> <span class="nb">print</span><span class="p">(</span><span class="s1">'stop: </span><span class="si">{}</span><span class="s1">'</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">k</span><span class="p">))</span></div><div style="text-align: justify;"> <span class="k">break</span></div>
<div style="text-align: justify;"> <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">eta</span><span class="p">,</span> <span class="p">(</span><span class="nb">int</span><span class="p">,</span> <span class="nb">float</span><span class="p">)):</span></div><div style="text-align: justify;"> <span class="n">x</span> <span class="o">=</span> <span class="n">x</span> <span class="o">-</span> <span class="n">eta</span> <span class="o">*</span> <span class="n">gradient_x</span></div><div style="text-align: justify;"> <span class="k">else</span><span class="p">:</span> </div><div style="text-align: justify;"> <span class="n">x</span> <span class="o">=</span> <span class="n">x</span> <span class="o">-</span> <span class="n">eta</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="o">*</span> <span class="n">gradient_x</span></div><div style="text-align: justify;"> </div><div style="text-align: justify;"> <span class="n">k</span> <span class="o">+=</span> <span class="mi">1</span></div>
<div style="text-align: justify;"> <span class="k">return</span> <span class="n">x</span></div></pre></div>
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<p style="text-align: justify;">Para ejemplicar el funcionamiento del código anterior, se considera la matriz simétrica y positiva definida:</p><div style="text-align: justify;">\begin{equation}\nonumber
Q = \left(\begin{array}{cc} 1 & 0.5 \\ 0.5 & 3 \end{array}\right)
\end{equation}</div><p style="text-align: justify;">y vector $b$ dado por:</p><div style="text-align: justify;">\begin{equation}\nonumber
b = \left(\begin{array}{c} 3 \\ 0.5 \end{array}\right)
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<p style="text-align: justify;">De esta manera la forma cuadrática en Python y usando código anterior quedaría así:</p>
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<div class="highlight hl-ipython3"><pre><div style="text-align: justify;"><span class="n">Q</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">],</span> <span class="p">[</span><span class="mf">0.5</span><span class="p">,</span> <span class="mi">3</span><span class="p">]])</span></div><span><div style="text-align: justify;"><span class="n">b</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">3</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">])</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span></div></span></pre></div>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">quadratic_form</span> <span class="o">=</span> <span class="n">QuadraticForm</span><span class="p">(</span><span class="n">Q</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span>
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<p style="text-align: justify;">Para encontrar el $x$ minimizador de la función se tiene dos opciones, una es definir el parámetro $\eta$ manualmente, y la otra es usar el método <code>eta</code> de la clase <code>QuadracticForm</code>. A continuación se hará uso de los dos casos.</p>
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<p style="text-align: justify;">Para empezar se ejecuta el algoritmo en algún punto $x$:</p>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">initial_x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">105.5</span><span class="p">,</span> <span class="mf">105.8</span><span class="p">])</span>
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<p style="text-align: justify;">Luego ejecuta el AGD con $\eta = 0.0001$ y $\epsilon=0.0000001$:</p>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">gradient_descent</span><span class="p">(</span><span class="n">initial_x</span><span class="p">,</span> <span class="n">eta</span><span class="o">=</span><span class="mf">0.0001</span><span class="p">,</span> <span class="n">epsilon</span><span class="o">=</span><span class="mf">0.0000001</span><span class="p">,</span> <span class="n">function</span><span class="o">=</span><span class="n">quadratic_form</span><span class="p">)</span>
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<pre style="text-align: justify;">stop: 230300
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<pre><div style="text-align: justify;">array([[ 3.18181829],</div><div style="text-align: justify;"> [-0.36363639]])</div></pre>
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<p style="text-align: justify;">Como el lector podrá notar el algoritmo tardó 230300 iteraciones para obtener un candidato al mínimo con la precisión deseada. A continuación se ejecuta usando el método <code>eta</code> de la forma cuadrática:</p>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">gradient_descent</span><span class="p">(</span><span class="n">initial_x</span><span class="p">,</span> <span class="n">eta</span><span class="o">=</span><span class="n">quadratic_form</span><span class="o">.</span><span class="n">eta</span><span class="p">,</span> <span class="n">epsilon</span><span class="o">=</span><span class="mf">0.0000001</span><span class="p">,</span> <span class="n">function</span><span class="o">=</span><span class="n">quadratic_form</span><span class="p">)</span>
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<pre style="text-align: justify;">stop: 15
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<pre><div style="text-align: justify;">array([[ 3.1818182 ],</div><div style="text-align: justify;"> [-0.36363637]])</div></pre>
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<p style="text-align: justify;">En esta ocasión el algoritmo tardó 15 iteraciones. Esto representa una mejora en tiempo de ejecución bastante considerable con respecto a el experimento anterior.</p>
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<p style="text-align: justify;">¿Cómo se puede asegurar que este es el mínimo de la función? Para este caso en particular, el mínimo ocurre cuando $Qx = b$, por lo tanto es suficiente con resolver este sistema lineal. Usando los métodos de la librería numpy se puede resolver rápidamente así:</p>
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<div class="highlight hl-ipython3"><pre style="text-align: justify;"><span></span><span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">solve</span><span class="p">(</span><span class="n">Q</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span>
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<pre><div style="text-align: justify;">array([[ 3.18181818],</div><div style="text-align: justify;"> [-0.36363636]])</div></pre>
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<p style="text-align: justify;">Como se puede observar, el resultado es muy aproximado al valor que se obtuvo al ejecutar AGD, por lo que el algoritmo funciona bastante bien.</p>
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<h2 id="Conclusiones" style="text-align: justify;">Conclusiones<a class="anchor-link" href="#Conclusiones">¶</a></h2><ul>
<li style="text-align: justify;">Se logró aprender que el AGD es un algoritmo iterativo empleado principalmente para resolver problemas de optimización.</li>
<li style="text-align: justify;">La principal desventaja del AGD se encuentra en el ajuste adecuado de la tasa de aprendizaje $\eta$. Si $\eta$ toma un valor muy pequeño, es necesario un gran número de iteraciones para que el proceso converga; si por otro lado $\eta$ es muy grande, entonces puede ocurrir que el proceso no converga.</li>
<li style="text-align: justify;">Finalmente te invito a leer este otro artículo (<a href="https://alejandrosanchezyali.blogspot.com/2020/10/post-2.html" rel="nofollow" src="https://alejandrosanchezyali.blogspot.com/2020/10/post-2.html" target="_blank">Jugando con el gradiente descendente y Python</a>) en donde se análiza el comportamiento general de los algoritmos por gradiente descendente.</li>
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<p style="text-align: justify;">No olvides comentar y suscribirte al blog para que estés enterando de los posts que voy a ir subiendo semana a semana. También sientete en libertad de seguirme en LinkedIn, Twitter, Github e Instagram.</p>
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<h2 id="Notas" style="text-align: justify;">Notas<a class="anchor-link" href="#Notas">¶</a></h2><p style="text-align: justify;"><a id="10">[1]</a>. En el contexto de este artículo, se dira que una función $f:\Omega \subset \mathbb{R}^{m}\to \mathbb{R}$ es diferenciable si tiene derivada continua en $\Omega$ y es convexa, si para todo $w, z\in \Omega$ y $\alpha \in [0, 1]$ se cumple la siguiente condición:</p><div style="text-align: justify;">\begin{equation}\nonumber
f(\alpha w + (1-\alpha)z)\leq \alpha f(w) + (1-\alpha)f(z).
\end{equation}</div><p style="text-align: justify;">Note que la condición es valida para todo $m\geq 1$.</p>
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<p style="text-align: justify;"><a id="11">[2]</a>. Si $y_{\min}$ es el mínimo global de una función $f(x)$, entonces se define el operador $\operatorname*{argmin\,\,}$ como siguiente conjunto: $$\operatorname*{argmin\,\,}_{ x \in X} f(x) = \{x\in X: f(x) = y_\min\}.$$</p>
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<h2 id="Referencias" style="text-align: justify;">Referencias<a class="anchor-link" href="#Referencias">¶</a></h2><ul>
<li style="text-align: justify;">Kris Hauser. <a href="ttp://homes.sice.indiana.edu/classes/spring2012/csci/b553-hauserk/gradient_descent.pdf" rel="nofollow" src="http://homes.sice.indiana.edu/classes/spring2012/csci/b553-hauserk/gradient_descent.pdf" target="_blank">Algorithms for optimization and learning. University of Indiana</a>.</li>
<li style="text-align: justify;"><a href="https://www.andrewng.org/" rel="nofollow" target="_blank">Andrew Ng</a><a href="http://cs229.stanford.edu/materials.html" rel="nofollow" target="_blank">. Machine learning course materials</a>. Technical report, University of Stanford.</li>
<li style="text-align: justify;">Batard, Thomas and Bertalmío, Marcelo. <a href="https://hal.archives-ouvertes.fr/hal-00782496/document" rel="nofollow" scr="https://hal.archives-ouvertes.fr/hal-00782496/document" target="_blank">Generealized gradient on vector bundle - Aplication to image denoising</a>. Department of Information and Communication Technologies, 2013.</li>
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<h2 id="Contacto" style="text-align: justify;">Contacto<a class="anchor-link" href="#Contacto">¶</a></h2><ul>
<li style="text-align: justify;">Participa de la canal de Nerve a través de <a href="https://discord.gg/edPmghPq8K" rel="nofollow" src="https://discord.gg/edPmghPq8K" target="_blank">Discord</a>.</li>
<li style="text-align: justify;">Se quieres conocer más acerca de este tema me puedes contactar a través de <a href="https://www.classgap.com/me/alejandro-sanchez-yali" rel="nofollow" src="https://www.classgap.com/me/alejandro-sanchez-yali" target="_blank">Classgap</a>.</li></ul></div></div></div>
www.asanchezyali.comhttp://www.blogger.com/profile/06396258253910042323noreply@blogger.com0tag:blogger.com,1999:blog-8939855543774830921.post-8250756501813637002018-05-22T08:25:00.000-05:002019-11-17T21:55:19.275-05:00Los cuatro espacios fundamentales de una matriz<p>Cada que se considera una matriz $A\in \mathbb{F}^{n,m}$, donde $\mathbb{F}$ puede ser $\mathbb{R}$ o $\mathbb{C}$, esta induce naturalmente dos aplicaciones lineales: $A:\mathbb{F}^{m}\to \mathbb{F}^{n}$ y $A^{\top}:\mathbb{F}^{n}\to \mathbb{F}^{m}$; las cuales permiten determinar cuatro subespacios vectoriales, dos subespacios vectoriales en $\mathbb{F}^{n}$ y dos subespacios vectoriales en $\mathbb{F}^{m}$, conocidos usualmente como <em>espacio nulo</em>, <em>espacio fila</em>, <em>espacio nulo izquierdo</em> y <em>espacio columna</em> de $A$ respectivamente; por lo tanto, el objetivo en esta ocasión es estudiar estos conjuntos
y las relaciones entre ellos.
</p>
<p>
Para comenzar, veamos la definición de espacio nulo y de rango de una matriz $A$: el <em>espacio nulo</em> de la aplicación $A:\mathbb{F}^m\to \mathbb{F}^n$, es el conjunto $N(A)\subseteq \mathbb{F}^{m}$ dado por
\begin{equation}
N(A)=\{x\in \mathbb{F}^{n}:Ax=0\}
\end{equation};
y el <em>espacio columna</em> o rango, es el conjunto $R(A)\subseteq \mathbb{F}^{n}$ dado por
\begin{equation}
R(A)=\{y\in \mathbb{F}^{n}:y=Ax, \forall\,x\in \mathbb{F}^{m}\}.
\end{equation}
</p>
<p>
En la Figura (1) se muestra el espacio nulo y el espacio columna asociados con la matriz $A$. En este gráfico, se puede apreciar que para la función $A:\mathbb{F}^{m}\to \mathbb{F}^{n}$ el espacio nulo es un subconjunto de $\mathbb{F}^{m}$; mientras que, el espacio columna es un subconjunto de $\mathbb{F}^{n}$. Recuerda que la ecuación homogénea $Ax=0$, siempre tiene como solución trivial $x=0$. Esta propiedad implica que, $O_{_{\mathbb{F}^{m}}}\in \mathbb{F}^{m}$ también pertenece a $N(A)$ y $O_{_{\mathbb{F}^{n}}}\in \mathbb{F}^{n}$ también pertenece a $R(A)$.
</p>
<div class="separator" style="clear: both; text-align: center;"><a imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj38MoEgSZx8DvRAu-9fk5vAcO0VOZJCuBZeNdDwN2QEwzTXeYLiQD_YfU85fV_mlUtM1j4k6ryO424SKqzbU27LELjlbXnFC0KvBrSohsks5a3_yqbq9lR_2sjJ0V1LT_fvvd8Ip5zhRM/s1600/fig2.eps.png" /></a></div>
<h6>
Figura 1. El espacio nulo y el rango de la aplicación $A:\mathbb{F}^m\to \mathbb{F}^n$.
</h6>
<br>
<p>El lector puede observar que, realmente $A$ tiene <em>«cuatro subespacios vectoriales»</em> asociados que son $N(A)$, $R(A)$, $N(A^{\top})$ y $R(A^\top)$. Observe que, el espacio nulo y el espacio columna son subespacios de espacios diferentes; más precisamente, una matriz $A\in \mathbb{F}^{m,n}$ define las aplicaciones $A:\mathbb{F}^{m}\to \mathbb{F}^{n}$, $A^{\top}:\mathbb{F}^{n}\to \mathbb{F}^{m}$ y los conjuntos $N(A)$, $R(A^\top)\subseteq \mathbb{F}^{m}$ y $N(A^\top), R(A)\subseteq \mathbb{F}^{n}$.
</p>
<p>En efecto, para ver que $N(A)$, $R(A)$, $N(A^{\top})$ y $R(A^\top)$ son subespacios vectoriales, recordemos que un subconjunto $U\subset \mathbb{F}^{m}$ es <em>cerrado bajo combinaciones lineales</em>, si para cada par de elementos $x,y\in U$ y todos los escalares $a, b\in \mathbb{F}$ se tiene que $ax+by\in U$.
</p>
<p>Los conjuntos $N(A)$ y $R(A)$ son cerrados bajo combinaciones lineales; dado que, la función inducida por $A$ es una transformación lineal. En efecto, considere dos elementos arbitrarios $x_{_1}, x_{_2}\in N(A)$, entonces $Ax_{_1}=0$ y $Ax_{_2}=0$. Adicionalmente, para cualquier par de elementos $a,b\in \mathbb{F}$ se tiene:
\begin{equation}
A(ax_{_1}+bx_{_2})=aAx_{_1}+bAx_{_2}=0
\end{equation}
de modo que, $(ax_{_1}+bx_{_2})\in N(A)$. Por consiguiente, $N(A)\subseteq \mathbb{F}^m$ es cerrado bajo combinaciones lineales. Análogamente, considere dos elementos $y_{_1}, y_{_2}\in R(A)$; esto es, existe $x_{_1}, x_{_2}\in \mathbb{F}^{m}$ tal que, $y_{_1}=Ax_{_1}$ y $y_{_2}=Ax_{_2}$. Entonces, para cualquier $a, b\in \mathbb{F}$ se tiene:
\begin{equation}
(ay_{_1}+by_{_2})=aAx_{_1}+bAx_{_2}=A(ax_{_1}+bx_{_2}) \Rightarrow (ay_{_1}+by_{_2})\in R(A).
\end{equation}
Por lo tanto, $(A)\subset \mathbb{K}^{n}$ es cerrado bajo combinaciones lineales.
</p>
<p> En consecuencia, si $A=[A_{_{:1}},\dots, A_{_{:n}}]$, cualquier elemento $y\in R(A)$ puede ser expresado como $y=Ax$ para algún $x\in \mathbb{F}^{n}$; esto es,
\begin{equation}
y=Ax =[A_{_{:1}},\dots, A_{_{:n}}]\left[\begin{array}{c}
x_{_1}\\
\vdots \\
x_{_n}
\end{array}\right]=A_{_{:1}}x_{_1}+\cdots + A_{_{:n}}x_{_n}\in gen(\left\{A_{_{:1}}x_{_1},\dots, A_{_{:n}}x_{_n}\right\}).
\end{equation}
Es por esta razón que, el espacio columna y el rango son el mismo espacio. El lector puede verificar que cualquier elemento de la forma $y=A_{_{:1}}x_{_1}+\cdots + A_{_{:n}}x_{_n}$ es también un elemento de $R(A)$; por lo tanto, $y=Ax$.
</p>
<p>El espacio nulo y el rango de una matriz cuadrada, caracterizan si la matriz es invertible o no; esto se establece en el siguiente resultado:
<blockquote>
<b>Teorema 1. </b> Dada una matriz $A\in \mathbb{F}^{n,n}$, entonces las siguientes afirmaciones son equivalentes:
<ul>
<li>La matriz $A^{-1}$ existe;</li>
<li>$N(A)=\{0\}$;</li>
<li>$R(A)=\mathbb{F}^{n}$.</li>
</ul>
</blockquote>
</p>
<p>
Veamos ahora algunas de las relaciones que existen entre los cuatro espacios asociados a un par de matrices $A$ y $B$, tales que, la matriz $B$ se pueda obtener mediante operaciones de fila sobre la matriz $A$. Asumimos entonces la siguiente notación: $A\stackrel{fila}{\longleftrightarrow}B$, para indicar que la matriz $A$ se puede transformar en la matriz $B$ mediante operaciones de Gauss sobre las filas de $A$. En tal caso, se tiene el siguiente teorema:
<blockquote>
<b>Teorema 2. </b>Sean las matrices $A, B \in \mathbb{R}^{m,n}$, entonces:
<ul>
<li>$A\stackrel{fila}{\longleftrightarrow}B\Longleftrightarrow N(A)=N(B)$;</li>
<li>$A\stackrel{fila}{\longleftrightarrow}B\Longleftrightarrow R(A^\top)=R(B^\top)$.</li>
</ul>
</blockquote>
</p>
<p>Es fácil ver que este último resultado es verdadero; dado que, las operaciones de Gauss no cambian las soluciones de sistemas lineales; por lo cual, el sistema lineal $Ax = 0$ tiene exactamente las mismas soluciones de $x$ como el sistema lineal $Bx = 0$; es decir, $N (A) = N (B)$. La segunda propiedad también es cierta; ya que, las operaciones de Gauss en las filas de $A$, son equivalentes a las operaciones de Gauss sobre las columnas de $A^{\top}$. Ahora bien, es fácil ver que cada una de las operaciones de Gauss sobre las columnas de $A^{\top}$ no cambian el $R(A^{\top})$; por lo tanto, $R(A^{\top})=R(B^{\top})$.
</p>
<p>Sin embargo, no podemos pensar que el párrafo anterior es suficiente para hacer una demostración del teorema. Veamos una presentación más detallada de las ideas anteriores. Una forma de hacerlo, es utilizar la multiplicación de matrices para expresar la propiedad en la cual las operaciones de Gauss no cambian las soluciones de sistemas lineales. Con esto, se puede probar lo siguiente: Si se tienen las matrices $A$ y $B$ de orden $n\times m$ relacionadas por las operaciones de Gauss en sus filas, entonces existe una matriz $G$ de orden $m × m$ invertible $GA = B$. La prueba de esta propiedad es simple; debido a que cada una de las operaciones de Gauss se asocia con una matriz invertible, $E$, llamada una matriz de Gauss elemental. Cada matriz de Gauss elemental es invertible, ya que cada operación de Gauss siempre se puede revertir. El resultado de varias operaciones de Gauss sobre una matriz $A$, es el producto de las matrices de Gauss elementales apropiadas en el mismo orden que se realizan las operaciones de Gauss. Si se obtiene la matriz $B$ de la matriz $A$, haciendo operaciones de Gauss dadas por matrices $E_{_i}$, para $i = 1,\dots k$, en ese orden, podemos expresar el resultado del método de Gauss de la siguiente manera:
\begin{equation}
E_{_k}\cdots E_{_1}A=B\hspace{0.5cm} G=E_{_k}\cdots E_{_1} \Longrightarrow GA =B.
\end{equation}
Donde cada matriz elemental de Gauss es una matriz invertible; y por lo tanto, $G$ también es invertible.
</p>
<p>
Considere dos matrices $A$ y $B$ de orden $m\times n$ que están relacionadas por operaciones de Gauss en sus filas; siendo así, existe una matriz $G$ de orden $m\times m$, tal que, $GA = B$. Esta observación es la clave para mostrar que $N(A) = N(B)$, ya que dado cualquier elemento $x \in N(A)$
\begin{equation}
Ax=0\Longleftrightarrow GAx=0,
\end{equation}
donde la equivalencia se sigue del hecho de que $G$ es invertible. Entonces es simple (¡Lo simple es una provocación para que tú lo verifiques!) ver que:
\begin{equation}
0=GAx=Bx \Longleftrightarrow x\in N(B).
\end{equation}
Así pues, se tiene que $N(A)=N(B)$.
Ahora veamos la afirmación opuesta: Si $N(A)=N(B)$, significa que sus formas escalonadas reducidas $E_{_A}, E_{_B}$ son las mismas; es decir, $E_{_A}=E_{_B}$; esto significa que existen operaciones de Gauss en las filas $A$ que la transforman en la matriz $B$
</p>
<p>Ahora mostraremos que $R(A^{\top})= R(B^{\top})$. Considere un elemento $x\in R(A^{\top})$, por lo tanto, existe un elemento $y\in \mathbb{F}^{m}$, tal que:
\begin{equation}
x=A^{\top}y = A^{\top}G^{\top}(G^{\top})^{-1}y=(GA)^{\top}\bar{y}=B^{\top}\bar{y},\hspace{0.5cm} \bar{y}=(G^{\top})^{-1}\bar{y}
\end{equation}
Veamos que dado un $x\in R(A^{\top})$, se puede decir que, $x\in R(B^{\top})$; esto es, $R(A^{\top})\subset R(B^{\top})$. La implicación opuesta se prueba de igual forma: Considere $x\in R(B^{\top})$, por ende existe $\bar{y}\in \mathbb{F}^{m}$, tal que:
\begin{equation}
x=B^{\top}\bar{y}=B^{\top}(G^{\top})^{-1}G^{\top}\bar{y}=(G^{-1}B)^{\top}y=A^{\top}y,\hspace{0.5cm} y=G^{\top}\bar{y}.
\end{equation}
De modo que, se ha mostrado que para cualquier $x\in R(B^{\top})$, por lo cual $x\in R(A^{\top})$; es decir, $R(B^{\top})\subset R(A^{\top})$; y en consecuencia, $R(A^{\top})=R(B^{\top})$. Ahora sí se asume que $R(A^{\top})=R(B^{\top})$; esto quiere decir que, cada fila de $A$ es una combinación lineal de las filas de $B$; que a su vez, significa que existen operaciones de Gauss sobre las filas de $A$ que transforman a $A$ en $B$; y por lo tanto, con eso se establece el resultado final del teorema 2.
</p>
<p>Un argumento similar también dice que, $E_{_A^{\top}}=E_{_{B^{\top}}}$ sí y sólo sí $A^{\top}\stackrel{fila}{\longleftrightarrow} B^{\top}$. También se puede concluir que, $E_{_{A^{\top}}}=E_{_{B^{\top}}}$ es equivalente a $R(A)=R(B)$ y esto también es equivalente a $N(A^{\top})=N(B^{\top})$.
</p>
<p>
Otro resultado con respecto a la transpuesta de $A$ dice:
<blockquote>
<b>Teorema 3.</b>Para cada matriz $A\in \mathbb{F}^{n,m}$ se cumple que $\dim R(A)=\dim R(A^{\top})$.
</blockquote>
Sabiendo que una matriz se dice que es de <em>rango completo</em>, sí y sólo sí, $\dim R(A)=\min(m,n)$. Entonces podemos enunciar el siguiente teorema donde se establecen algunas de las relaciones principales de los cuatro espacios fundamentales:
<blockquote>
<b>Teorema 4. </b>Si una matriz $A\in \mathbb{F}^{n,m}$ es de rango completo, entonces:
<ul>
<li>Si $m=n$, por lo tanto:
\[\dim R(A)=\dim R(A^{\top})=n=m\Leftrightarrow \{0_{_{\mathbb{F}^{m}}}\}=N(A)=N(A^{\top})\subset \mathbb{F}^{m};\]</li>
<li>Si $n < m$, de forma que:
\[\dim R(A)=\dim R(A^{\top})=n < m \Leftrightarrow \left\{\begin{array}{l}
\{0_{_{\mathbb{F}^{m}}}\}\varsubsetneq N(A)\subset \mathbb{F}^{m},\\
\{0_{_{\mathbb{F}^{n}}}\}=N(A^{\top})\subset \mathbb{F}^{n};\end{array}\right.\]</li>
<li>Si $m>n$, siendo así:
\[ \dim R(A)=\dim R(A^{\top})= m < n \Leftrightarrow \left\{\begin{array}{l}
\{0_{_{\mathbb{F}^{m}}}\}= N(A)\subset \mathbb{F}^{m},\\
\{0_{_{\mathbb{F}^{n}}}\}\varsubsetneq N(A^{\top})\subset \mathbb{F}^{n};
\end{array}\right.\]
</ul>
</blockquote>
</p>
<p>Recordemos que, el rango de una matriz $A$ es el número de pivotes columna de la matriz escalonada reducida $E_{_A}$ y que coincide con la dimensión de $R(A)$. Si una matriz $A$ de orden $m\times n$ tiene $rang(A)=n$, esto quiere decir dos cosas: Primero, $n\leq m$; y segundo, que cada columna de $E_{_A}$ tiene un pivote; es decir, que no hay variables libres en la solución de la ecuación $Ax=0$, y así $x=0$ es la única solución. Debido a esto, $N(A)=0$. Por otro lado, al estudiar $N(A^{\top})$ es necesario considerar dos casos: $n=m$ o $n < m$. Si $n=m$, entonces las matrices son cuadradas; debido a esto, se puede decir que no hay variables libres en la ecuación $A^{\top}y=0$; y por lo tanto, se concluye que $N(A^{\top})=0_{_{\mathbb{F}^{n}}}$.
Por otra parte, si $n < m$ entonces hay variables libres en la solución de la ecuación $A^{\top}y=0$; y por ende, $\{0_{_{\mathbb{F}^{n}}}\}\varsubsetneq N(A^{\top})$.
Si se tiene una matriz $A$ de orden $m\times n$ con $rang(A)=m$, note que $rang(A)=rang(A^{\top})$; esto quiere decir dos cosas: Primero que $m \leq n$; y segundo que cada columna de $E_{_A^{\top}}$ tiene un pivote. Esta última afirmación muestra que $A^{\top}$ es de rango completo; es decir, $N(A^{\top})=0$. Ya se han analizado todos los casos en que $n=m$; sólo falta analizar qué pasa cuando $m < n$. En este caso, hay variables libres en la solución de la ecuación $Ax=0$; por lo tanto, $\{0_{_{\mathbb{F}^{m}}}\}\varsubsetneq N(A)$.
</p>
<div class="separator" style="clear: both; text-align: center;"><a imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGR0QKnUE8-KPqAsC-pg-IrYuEuEBDkp1Vogg-LKnF8uMWMpkM87HjTlK1_ksSO23fWwsmdg8ciIOnNETGUx3m0DBxo1ND40egYs1LHju-3AMquYB7WUFPIOm5g7mk-HMreJE2K85rghg/s320/g7228.png" width="320" height="258" /></a></div>
<h6>
Figura 2. Relaciones entre los cuatro espacios fundamentales de $A:\mathbb{F}^m\to\mathbb{F}^n$.
</h6>
<br>
<p>
Para terminar, enunciamos el siguiente resultado que relaciona las dimensiones de los espacios nulos y el rango de una transformación lineal en espacios vectoriales de dimensión finita. Este resultado se suele llamar Teorema de la Nulidad y el Rango, donde la nulidad de una transformación lineal es la dimensión de su espacio nulo, y el rango es la dimensión de su espacio de columna. Este resultado también se le conoce como el Teorema de la Dimensión.
</p>
<blockquote>
<b>Teorema 4. </b>
Para cada transformación lineal $T:V\to W$ entre espacios vectoriales $V$ y $W$ se cumple que:
\begin{equation}
\dim N(T)+\dim R(T) = \dim V.
\end{equation}
</blockquote>
<p>
Si consideramos el producto punto de dos vectores $u, v\in \mathbb{F}^{m}$ como el producto matricial definido por $u\cdot v =u^{\top}v$; podemos observar lo siguiente:
\begin{equation}
Ax=\left[\begin{array}{c}
A_{_{1:}}x\\
\vdots \\
A_{_{m:}}x
\end{array}\right]
\end{equation}
Note que las filas $A$ son las columnas de $A^{\top}$, por lo tanto, $A^{\top}_{_{i:}}\cdot x= A_{_{i*}}x$ Si $x\in N(A)$, y por ende, se puede concluir que: $N(A)$ es el complemento ortogonal de $R(A^{\top})$,y por consiguiente, $N(A)\cap R(A^{\top})=\emptyset$. En otro orden de ideas, si la dimensión de $\dim R(A)=r$, entonces la dimensión del espacio nulo $\dim N(A) = m-r$; y $\dim R(A^{\top})=r$, luego $\dim N(A^{\top})=n-r$. Note que, $\dim N(A)\oplus R(A^{\top}) = m$ y $\dim N(A^{\top})\oplus R(A) = n$; es decir que, $ N(A)\oplus R(A^{\top})\cong \mathbb{F}^{m}$ y $N(A^{\top})\oplus R(A) \cong \mathbb{F}^{n}$. Estas relaciones se resumen en la Figura 2.
</p>
<p>Bueno, ya nos hemos extendido lo suficiente por esta ocasión. Esperamos que aprovechen mucho este post.
</p>
<h5>Referencias</h5>
<ul>
<li><a href="http://meyer.math.ncsu.edu/DefaultPage.html">Carl D. Meyer</a>. <a href="http://www.matrixanalysis.com/"><em>Matrix Analysis and Aplied Linear Algebra</em></a>. SIAM, 2000.
</li>
<li><a href = "http://users.math.msu.edu/users/gnagy/teaching/teaching.html"> Gabriel Nagy </a>. <a href="http://users.math.msu.edu/users/gnagy/teaching/la.pdf"><em>Linear Algebra</em></a>. Mathematics Department,
Michigan State University, 2012.
</li>
<li><a href="http://www-math.mit.edu/~gs/">Gilbert Strang</a>. <a https://ocw.mit.edu/faculty/gilbert-strang/"><em>MIT Open Course Ware | Free Online Course Materials</em></a>.
</li>
</ul>
www.asanchezyali.comhttp://www.blogger.com/profile/06396258253910042323noreply@blogger.com0tag:blogger.com,1999:blog-8939855543774830921.post-57271435739899679962018-05-21T16:33:00.001-05:002020-10-05T00:06:22.976-05:00Números de coma o punto flotante y sistemas lineales<p>
En esta ocasión, estudiaremos algunos aspectos generales de los números de punto flotante y algunas dificultades que se presentan cuando se realizan cálculos elementales en la resolución de sistemas lineales por eliminación Gaussiana y Gauss-Jordan. Esperamos que lo disfruten mucho.
</p>
<p>Los números de coma o punto flotante, son un conjunto finito de números racionales que se emplean para representar números reales empleando computadoras. Existen diferentes tipos de números de punto flotante; todos ellos, se caracterizan porque tienen un número finito de dígitos cuando se escriben en una base particular. La necesidad de estos números es precisamente porque las computadoras sólo pueden representar los números reales con un conjunto finito de dígitos.
</p>
<blockquote>
<b>Definición.</b> Un número racional \(x\) es un <em>número de punto flotante</em> en <em>base</em> $b\in \mathbb{N}$, de <em>precisión</em> $p\in \mathbb{N}$, con <em>rango de exponencial</em> $N\in \mathbb{Z}$, sí y sólo sí, existen enteros $d_{_i}$, para $i=1,\dots, b-1$ y $d_{_1}\neq 0$ tal que, $x$ tiene la forma:
\begin{equation}\label{eq:01}
x=\pm 0.d_{_1}\cdots d_{_p}\times b^{n},\hbox{ con } -N\leq n\leq - N.
\end{equation}
Se denota por $\mathbb{F}_{p, b, N}$ el conjunto de todos los números de punto flotante con precisión $p$, base $b$ y rango exponencial $N$.
</blockquote>
<br>
<p >Lo primero que se puede observar es que el conjunto $\mathbb{F}_{p, b, N}$ es un conjunto finito, y que no hay una distribución homogénea de sus elementos. Por ejemplo, si consideramos el conjunto de números flotantes de precisión $1$, base $10$ y rango exponencial $10$, como el lector podrá notar, es fácil listar los elementos positivos de este conjunto. En efecto sus elementos son:
\[\{0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09\}=\{0.i\times 10^{-1}\}_{i=1}^{9},\]
\[\{0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9\}=\{0.i\times 10^{0}\}_{i=1}^{9},\]
\[\{1, 2, 3, 4, 5, 6, 7, 8, 9\}=\{0.i\times 10^{0}\}_{i=1}^{9}.\]
</p>
<p>
Como se puede observar, los elementos de $\mathbb{F}_{1, 10, 1}$ no se encuentran homogéneamente distribuidos sobre el intervalo $[0,10]$. Esta distribución irregular afecta notablemente la posibilidad de hacer cálculos de adición y multiplicación entre números pequeños y números grandes, o solamente entre números grandes. Observe por ejemplo que, cuando sumamos $0.01$ con $9$ obtenemos $9.01$, que no pertenece a $\mathbb{F}_{1, 10, 1}$; igualmente, se puede verificar que el producto de $8$ por $9$ tampoco pertenece.
</p>
<br>
<div class="separator" style="clear: both; text-align: center;"><a style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXWfotmWPZK69NS2QQ8LARXD2YvDYgwMx_k5-ReAvNKIQkvy_GNGmJpDpoOjHeGgdN0EyVzjHvRMAPQYrxAM9hLZzpZr_WrgFE8qkD_-5BUgTbsl9kN7W-tLZb-T5PRt7GnayZws3Zhzc/s1600/g12700.png" /> </a>
</div>
<h6>
Figura 1. Distribución no homogénea de los elementos de $\mathbb{F}_{1, 10, 1}$.
</h6>
<br>
<p> En general, los conjuntos de números flotantes $\mathbb{F}_{p, b, N}\subset\mathbb{R}$ no son <em>cerrados</em> bajo la suma o la multiplicación. Por lo tanto, al tratar de representar números reales en algún conjunto $\mathbb{F}_{p, b, N}\subset\mathbb{R}$, habrán ciertos cálculos aritméticos que no serán permitidos. Una manera de realizar cálculos con números reales en $\mathbb{F}_{p, b, N}\subset\mathbb{R}$ es, primero proyectar los números reales en los números de punto flotante y luego realizar el cálculo; ya que, el resultado podría no estar en el conjunto $\mathbb{F}_{_{p, b, N}}\subset\mathbb{R}$, uno debe proyectar de nuevo el resultado en $\mathbb{F}_{p, b, N}\subset\mathbb{R}$. La acción de proyectar un número real en el conjunto de números flotantes, es llamada <em>redondear</em> un número real. Existen muchas formas de hacer esto. A continuación, presentamos la forma más común de hacerlo.
</p>
<blockquote>
<b>Definición.</b> Sea $X_{_N}=\max \mathbb{F}_{p, b, N}$; por esto, la función de redondeo se define como una aplicación $fl:\mathbb{R}\cap [-X_{_N},X_{_N}]\to \mathbb{F}_{p, b, N}$ definida como: Dado un número real $x\in \mathbb{R}\cap [-X_{_N},X_{_N}]$, con $x=\pm 0.d_{_1}\cdots d_{_p}d_{_{p+1}}\cdots \times b^{n}$ y $-N\leq n\leq N$, se tiene que:
\begin{equation}
fl(x)=\left\{\begin{array}{cl}
\pm 0.d_{_1}\cdots d_{_p}\times b^n & \hbox{ si }d_{_{p+1}}<\frac{b}{2}, \\ \pm (0.d_{_1}\cdots d_{_p}+b^{-p})\times b^n & \hbox{ si }d_{_{p+1}}\geq \frac{b}{2}.\end{array}\right.
\end{equation}
</blockquote>
<br>
<p>Por ejemplo, si consideramos el conjunto de números flotantes $\mathbb{F}_{3,10,3}$, entonces algunas proyecciones de los números reales serían $fl(0.2103\times 10^{3})=0.210\times 10^3$, $fl(0.21037\times 10^{3})=0.210\times 10^3$, $fl(0.2105\times 10^{3})=0.211\times 10^3$ y $fl(0.2107\times 10^{3})=0.211\times 10^3$. Observe cómo la función $fl$ no es una función inyectiva, y por lo tanto, diferentes números reales pueden ser representados con el mismo número flotante. </p>
<p>Otra consecuencia que cabe mencionar, es que la aritmética de los número reales cambia notablemente; es decir, si $x,y\in \mathbb{R}$, siendo así, la suma de reales sobre un conjunto $\mathbb{F}_{p, b, N}$ queda definida por:
\begin{equation}
x+_{f}y=fl(fl(x)+fl(y))
\end{equation}
y la multiplicación por:
\begin{equation}
x\cdot_{f}y=fl(fl(x)\cdot fl(y))
\end{equation}
Aquí las operaciones $+_{f}$ y $\cdot_{f}$ son la suma y la multiplicación en el conjunto de coma flotante $\mathbb{F}_{p, b, N}$. Éstas operaciones son diferentes de la suma ($+$) y la multiplicación ($\cdot$) usual de números reales. En efecto, se tiene la siguiente proposición:
</p>
<blockquote>
<b>Proposición.</b> Sea $\mathbb{F}_{p, b, N}$, entonces siempre existen $x,y\in \mathbb{R}$ tales que,
\begin{equation} fl(fl(x)+fl(y))\neq fl(x+y),\hspace{0.5cm} fl(fl(x)\cdot fl(y))\neq fl(xy).\end{equation}
</blockquote>
<br>
<p>
Estamos seguros de que el lector puede encontrar algunos ejemplos sencillos que verifican la proposición anterior.
</p>
<p>Como se ha visto, las operaciones aritméticas usuales no son posibles, en general, en los conjuntos $\mathbb{F}_{p, b, N}$; debido a que, estos conjuntos no son cerrados bajo estas operaciones. Por lo que, se han definido de una manera un poco artificial las operaciones $+_{f}$ y $\cdot_{f}$. A continuación, veremos algunos efectos de estas operaciones cuando se trata de resolver sistemas de ecuaciones lineales en algún $\mathbb{F}_{p, b, N}$.
</p>
<p>Considere el conjunto de números flotantes $\mathbb{F}_{3,10,3}$ para resolver el siguiente sistema de ecuaciones lineales:
\[
\begin{array}{rcc}
5x_{_1}+x_{_2} &=& 6,\\
9.34x_{_1}+1.57x_{_2} &=& 11.
\end{array}
\]
Observe que, al resolver este sistema $\mathbb{R}$, sin las limitaciones de $\mathbb{F}_{3,10,3}$, encontramos que las soluciones son $x_{_1}=x_{_2}=1$. Veamos ahora qué ocurre cuando empleamos $\mathbb{F}_{3,10,3}$ con las operaciones $+_{f}$ y $\cdot_{f}$ al realizar Gauss-Jordan sobre este sistema de ecuaciones. Inicialmente tenemos el sistema matricial:
\[\left[\begin{array}{cc|c} 5 & 1 & 6\\ 9.43 & 1.57 & 11\end{array}\right]\];
para cambiar la segunda fila, podemos hacer las siguientes operaciones sobre las filas: empleamos la suma y la multiplicación de redondeo en $\mathbb{F}_{3,10,3}$.
\[\hat{a}_{_{2i}}=fl(a_{_{21}}-fl\left(fl(a_{_{1i}})\cdot fl\left(\frac{9.53}{5}\right)\right)\hbox{ con } i=1,2,3\],
donde $\hat{a}_{_{2i}}$ son las entradas de la nueva fila $2$, y $a_{_{1i}}$ son las entradas de la fila $1$ en el sistema inicial. Al hacer estas operaciones se tiene que:
\[\left[\begin{array}{cc|c} 5 & 1 & 6\\ 9.43 & 1.57 & 11\end{array}\right]\rightarrow \left[\begin{array}{cc|c} 5 & 1 & 6\\ 0.02 & -0.32 & -0.3\end{array}\right].\]
En este caso no es posible continuar con el método de Gauss-Jordan al menos que, $\hat{a}_{_{21}}=0$; lo cual no es posible. Si introducimos la modificación de que $\hat{a}_{_{21}}=0$, se tiene para nuestro ejemplo que,
\[\left[\begin{array}{cc|c} 5 & 1 & 6\\ 9.43 & 1.57 & 11\end{array}\right]\rightarrow \left[\begin{array}{cc|c} 5 & 1 & 6\\ 0 & -0.32 & -0.3\end{array}\right].\]
Es importante notar que, aquí no se ha redondeado el error, pues el valor $0.02$ pertenece a $\mathbb{F}_{3,10,3}$. Lo que se ha hecho es una modificación al sistema para poder continuar con el proceso de Gauss-Jordan. Si completamos el proceso bajo las operaciones $+_{f}$ y $\cdot_{f}$ de $\mathbb{F}_{3,10,3}$, se encuentra
\[\left[\begin{array}{cc|c} 1 & 0 & 1.01\\ 0 & 1 & 0.938\end{array}\right]\rightarrow \begin{array}{l} x_{_1}=0.101\times 10,\\ x_{_2}=0.938.\end{array}\]
Note que la solución bajo $\mathbb{F}_{3,10,3}$, difiere de la solución exacta $x_{_1}=x_{_2}=1$. <em><font color = "green">El error se produce por los redondeos y por la modificación hecha para poder completar el procedimiento de Gauss-Jordan.</font></em>
</p>
<p>En general, los errores por redondeo son muy importantes cuando se hacen sumas entre números pequeños con números grandes o cuando se divide por números muy pequeños. Por ejemplo, considere $x=0.100\times 10^4$ y $y=0.400\times 10$; estos números pertenecen al conjunto $\mathbb{F}_{3,10,4}$; y observe que, $fl(x)=x$ y $fl(y)=y$. Por lo tanto, cuando se hace la suma, se obtiene:
\[fl(x+y)=fl(1000+4)=fl(0.1004\times 10^3)=1\times 10^3=x.\]
Es decir, la información de $y$ se pierde completamente. </p>
<p>
Hay tres estrategias conocidas como el <em>pivoteo parcial</em>, <em>pivoteo parcial escalado</em> y <em>pivoteo completo</em> que buscan evitar la división por números grandes; para así, reducir un poco los errores por redondeo. Considere una matriz $A$ de tamaño $m\times n$ y veamos en qué consisten estos dos métodos:
<ul style="list-style-type:square">
<li><b>Pivoteo Parcial:</b> En cada paso $k$ de la eliminación Gaussiana, se elige en calidad de pivote a la entrada con índice $(k,p)$ tal que:
\begin{equation}
|A_{_{kp}}|=\max_{p\leq i \leq m}|A_{_{ip}}|,
\end{equation};
es decir, la mayor entrada de la $p$ - ésima columna empezando con $(p,p)$ hasta $(m,p)$. Por ejemplo, supongamos que vamos a realizar el paso $p$ de la eliminación Gaussiana, entonces nuestra matriz tendrá una forma parecida a esto:
\[\left[\begin{array}{cccccc|c}
* & * & * & & * & & * \\
0 & * & * & & * & & * \\
0 & 0 & * & & * & & * \\
\vdots & \vdots & \vdots & & \vdots & & \vdots \\
0 & 0 & 0 & & A_{_{pp}} & & * \\
\vdots & \vdots & \vdots & & \vdots & & \vdots \\
0 & 0 & 0 & & A_{_{mp}} & & * \\
\end{array}\right]_{m\times n}\]
Y suponga que nuestro máximo es $|A_{_{kp}}|=\max_{p\leq i \leq m}|A_{_{ip}}|$, luego la entrada $A_{kp}$ se usará como pivote. Esto significa que se aplicará el intercambio de las filas $R_{_p}\leftrightarrow R_{_k}$, y luego se aplican las operaciones elementales para eliminar las entradas desde $(p+1,p)$ hasta $(m,p)$.
</li>
<li><b>Pivoteo Parcial Escalado:</b> Suponga que estamos en el paso $p$. En cada renglón $i$, con $p\leq i \leq m$, se calcula el valor máximo absoluto en la parte principal de la matriz:
\[s_{_i}=\max_{p\leq j\leq m} |A_{_{ij}}|.\]
Suponga que $s_{_i}>0$ para todo $i\in \{k,\dots, m\}$. Si se elige el menor entero $q$ con
\[\frac{|A_{_{qk}}|}{s_{_q}}=\max_{p\leq i\leq m}\frac{|A_{_{ip}}|}{s_{_i}}.\]
En otras palabras, sea $q$ el menor de los índices $i$ en los cuales la expresión $\frac{|A_{_{ip}}|}{s_{_i}}$ alcanza el máximo. Si $q\neq p$, entonces se intercambian los renglones $p$ y $q$, y luego se eliminan las entradas por debajo de $(p,p)$.
</li>
<li><b>Pivoteo Completo:</b> En el $k$ - ésimo paso de la eliminación Gaussina, se buscan los índices $p,q\in \{k,\dots, m\}$ tales que, \[|A_{_{rs}}|=\max_{\substack{p\leq i\leq m \\ p\leq j\leq n}}|A_{_{ij}}|.\]
En otras palabras, se busca el máximo entre los números $|A_{_{ij}}|$ con $p\leq i \leq m$ y $p\leq j \leq m$. En este caso, antes de efectuar el paso $p$ de la eliminación Gaussiana, la matriz tendrá una forma como ésta:
\[\left[\begin{array}{ccccccc|c}
* & * & * & & * & & * & *\\
0 & * & * & & * & & * & * \\
0 & 0 & * & & * & & * & *\\
\vdots & \vdots & \vdots & & \vdots & & \vdots & \vdots\\
0 & 0 & 0 & & A_{_{pp}} & \cdots & A_{_{pn}} & * \\
\vdots & \vdots & \vdots & & \vdots & & \vdots & *\\
0 & 0 & 0 & & A_{_{mp}} & \cdots & A_{_{mn}} & *\\
\end{array}\right]_{m\times n}\]
Si $(r,s)\neq (p,p)$, entonces se intercambian los renglones y las columnas de tal manera que la entrada $A_{_{rs}}$ se pone en la posición $(p,p)$, y luego se aplican las operaciones elementales para anular las entradas por debajo de $(p,p)$.</li>
</ul>
Esperamos que esta entrada haya sido de su agrado, nos vemos en otra ocasión.
</p>
<p>
<h5>Referencias</h5>
<ul>
<li><a href="http://meyer.math.ncsu.edu/DefaultPage.html">Carl D. Meyer</a>. <a href="http://www.matrixanalysis.com/"><em>Matrix Analysis and Aplied Linear Algebra</em></a>. SIAM, 2000.
</li>
<li><a href = "http://users.math.msu.edu/users/gnagy/teaching/teaching.html"> Gabriel Nagy </a>. <a href="http://users.math.msu.edu/users/gnagy/teaching/la.pdf"><em>Linear Algebra</em></a>. Mathematics Department,
Michigan State University, 2012.
</li>
</ul>
</p>
www.asanchezyali.comhttp://www.blogger.com/profile/06396258253910042323noreply@blogger.com0tag:blogger.com,1999:blog-8939855543774830921.post-30667651575560879682017-01-13T12:24:00.000-05:002018-05-24T12:45:12.377-05:00Red neuronal artificial simple
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhY6rXzYAuu7TUr6aajejnpACA4RVjzUeyG2JbO-RNUdpKH2btMuR-pa49PE2cywHWAUurQPuOcrXou3XGiF13FREPR4LY5Sgx09qaA8Y0bc1jMLQaFcxGp0r8Rej7U-k4ndtRlOOzUhi8/s1600/abstract-art-blur-373543.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhY6rXzYAuu7TUr6aajejnpACA4RVjzUeyG2JbO-RNUdpKH2btMuR-pa49PE2cywHWAUurQPuOcrXou3XGiF13FREPR4LY5Sgx09qaA8Y0bc1jMLQaFcxGp0r8Rej7U-k4ndtRlOOzUhi8/s320/abstract-art-blur-373543.jpg" width="320" height="213" data-original-width="1600" data-original-height="1067" /></a><br><br></div>
El objetivo en esta ocasión es introducirnos en el mundo de las redes neuronales. Para empezar comentaremos de una manera general y quizás un poco atrevida el concepto de <b>neurona artificial</b>, para finalmente construir un <b>perceptrón digital simple</b> empleando python 3.
<br>
<br>
<h4>
<b>
¿Qué es un sistema neuronal artificial?
</b></h4>
La idea de los sistemas neuronales artificiales fue inspirada por los sistemas neuronales biológicos. De acuerdo con <a href="https://es.wikipedia.org/wiki/Santiago_Ram%C3%B3n_y_Cajal">Ramón y Cajal (1888)</a>, un sistema neuronal biológico está compuesto por una red de células individuales, ampliamente interconectadas entre sí. Estas células son denominadas neuronas y son como pequeños procesadores de información. Estos procesadores se encuentra compuesto principalmente por:
<ol type="I">
<li>Las <b>dendritas</b>, son el canal receptor de la información.</li>
<li>El <b>soma</b>, es el órgano encargado de procesar la información.</li>
<li>El <b>axón</b>, es el canal de emisión de información a otras neuronas.</li>
</ol>
El cerebro humano tiene cerca 90.000.000.000 neuronas, además cada neurona recibe información de aproximadamente 10.000 neuronas y envía impulsos a cientos de ellas. También hay neuronas que reciben información directamente de exterior. Es importante observar que el cerebro se modela durante el desarrollo del ser vivo, por lo tanto, algunas cualidades no son innatas, sino adquiridas por la influencia de la información que del medio externo recibe.
<br>
<br>
El objetivo de las redes será construir un gran conjunto de neuronas artificiales para simular un comportamiento similar al del cerebro humano.
<br>
<br>
<h4><b>
El modelo estándar de una neurona artificial
</b></h4>
<p>
Según los principios descritos por <a href="https://en.wikipedia.org/wiki/David_Rumelhart">Rumelhart</a> y <a href="https://en.wikipedia.org/wiki/David_McClelland"> McClelland</a> (1986). Una neurona artificial estandar tiene los siguientes componentes:
</p>
<ol type="I">
<li>Las <i>dendritas artificiales</i>. Las dentritas artificiales son un conjunto de parámetros $x_{_i}(t)$ con los cuales se codifica la información de un problema que se quiere resolver. Las variables de entrada y salida pueden ser binarias (digitales) o continuas (analógicas), dependiendo del modelo y la aplicación. Por ejemplo en un perceptrón multicapa (MLP), por lo general las salidas son señales digitales representadas por $1$ y $-1$, en el caso de las salidas analógicas, la señal se da en un cierto intervalo. </li>
<li> Los <i>pesos sinápticos $w_{_{ij}}(t)$</i> de la neurona $i$ son variables relacionadas a la sinapsis o conexión entre neuronas, los cuales representan la intensidad de interacción entre la neurona presináptica $j$ y la postsináptica $i$. Dada una entrada positiva (puede ser una señal proveniente de una neurona), si el peso es positivo tenderá a excitar a la neurona postsináptica, si el peso es negativo tenderá a inhibirla.</li>
<li>La <i>función de potencial</i>, permite obtener a partir de las entradas (dendritas) y los pesos sinápticos, el valor de <i>potencial postsináptico</i> $h_{_i}$ de la neurona $i$ en función de los pesos y entradas
\begin{equation}
h_{_i}(t)=\sigma_{_i}(w_{_{ij}}(t), x_{_j}(t)).
\end{equation}
La función más habitual es de tipo lineal, y se basa en la suma ponderada de las entradas con los pesos sinápticos, es decir,
\begin{equation}
h_{_i}(t) = \sum_{j}w_{_{ij}}(t)x_{_j}(t).
\end{equation}
Habitualmente se agrega al conjunto de pesos de la neurona un parámetro adicional $\theta_{_i}$, que se denomina <i>umbral de excitación</i>, el cual se acostumbra a restar al potencial postsináptico. Es decir:
\begin{equation}
h_{_i}(t) = \sum_{j}w_{_{ij}}(t)x_{_j}(t)-\theta_{_i}.
\end{equation}
Si se tiene un número finito de dendritas y hacemos que los índices $i$ y $j$ comiencen en cero, y denotamos por $w_{_{i0}}=\theta_{_i}$ y $x_{_0}=-1$, la función de potencial lineal se puede expresar como
\begin{equation}
h_{_i}(t) = \sum_{j=0}^{n}w_{_{ij}}(t)x_{_j}(t)=\pmb{w}^{\top}_{_i}(t)\cdot \pmb{x}(t),
\end{equation}
con $\pmb{w}_{_i}(t) = (w_{_{i0}}(t),\dots,w_{_{in}}(t))$ y $\pmb{x}(t)=(x_{_0}(t),\dots,x_{_n}(t))$.
</li>
<li>La <i>función de activación $f_{_i}$</i> de la neurona $i$ proporciona el estado de activación actual $a_{_i}(t)$ a partir del potencial postsináptico $h_{_i}(t)$ y del propio estado de activación anterior, $a_{_{i}}(t-1)$, es decir,
\begin{equation}
a_{_i}(t)=f_{_i}(a_{_i}(t-1), h_{_i}(t)).
\end{equation}
Sin embargo, en muchos modelos de redes artificiales se considera que el estado actual de la neurona no depende de su estado anterior, sino unicamente del actual, por lo tanto,
\begin{equation}
a_{_i}(t)=f_{_i}(h_{_i}(t)).
\end{equation}
</li>
<li> La <i>función de emisión.</i> Esta función proporciona la salida global $y_{_i}(t)$ y es el componente principal del axón artificial de la neurona $i$ en función de su estado de activación actual. Muy frecuentemente la función de emisión es simplemente la identidad $F(x) = x$ de tal modo que el estado de activación de la neurona se considera como la propia señal de la neurona. </li>
</ol>
<p>
Gráficamente, una neuronal artificial se puede representar de la siguiente forma:
</p>
<br>
<br>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmBHmnirPmcTg_4IJ4dEmEU5VGyRP5ZiyVlLqWl1D_rW24b6OrLhBMuf5aNqTbZji3igb6in0zzgJDU1xRFiUwn4yi1rsw0-Id0433MOqCrSO2i7Qhn96KudVrq1nceVNHZJWK9XM_tIo/s1600/g13906.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmBHmnirPmcTg_4IJ4dEmEU5VGyRP5ZiyVlLqWl1D_rW24b6OrLhBMuf5aNqTbZji3igb6in0zzgJDU1xRFiUwn4yi1rsw0-Id0433MOqCrSO2i7Qhn96KudVrq1nceVNHZJWK9XM_tIo/s1600/g13906.png" /></a>
<br>
Figura 1. Esquema de una neurona artificial.
<br>
<br>
</div>
<p>Los pesos sinápticos, la función de potencial y la función de activación son los componentes que definen el soma artificial de la neurona.
</p>
<h4><b>
Ejemplo de una red neuronal simple: el perceptrón
</b></h4>
<p>
En los 50's <a href="https://en.wikipedia.org/wiki/Frank_Rosenblatt">Frank Rosenblatt</a> propuso una red neuronal denominada perceptrón digital simple. Éste consiste de una o varias neuronas, donde la función de activación para cada neurona es
\begin{equation}
y = F\left(\sum_{i=1}^{n}w_{_{i}}x_{_i}+\theta(t)\right).
\end{equation}
Generalmente la función de activación $F$ puede ser lineal, y se dice por lo tanto que la conexión es de lineal, aunque puede ser no lineal. Para los objetivos ilustrativos, vamos a considerar la siguiente función:
\begin{equation}
F(s) = \left\{\begin{array}{cc}
1 & \mbox{ si } s > 0 \\
-1 & \mbox{ si } s \leq 0
\end{array}\right.
\end{equation}
Para simplificar la exposición de las ideas, suponga que las señal emitida por la neurona sera $1$ o $-1$, aunque puede ser cualquier otra cosa. Este tipo de neurona se puede usar para tareas de clasificación, es decir, se puede usar para decir si una patrón de entrada pertenece a alguna de las clases definidas por los valores $1$ o $-1$. Si el potencial de entrada es positivo, entonces el patrón se le asignará la etiqueta $1$, sino por el contrario es cero o menor que cero se le asignará la etiqueta de $-1$. Observe que los patrones de entrada siempre se pueden identificar con algún vector de $\mathbb{R}^{n}$, de manera que esta neurona separa a $\mathbb{R}^{n}$ en dos clases mediante un hiperplano dado por la ecuación:
\begin{equation}
x_{_n} = -\frac{w_{_1}}{w_{_n}}x_{_1}-\frac{w_{_2}}{w_{_n}}x_{_1}-\cdots-\frac{w_{_{n-1}}}{w_{_n}}x_{_1}+\frac{\theta}{w_{_n}}.
\end{equation}
La anterior función se denomina, <em>función discriminante</em>.
</p>
<p>
En el caso en que el espacio de patrones de entrada se pueda identificar con $\mathbb{R}^{2}$, la situación se puede representar gráficamente, en este caso, el hiperplano que define las dos clases es la linea recta dada por
\begin{equation}
w_{_1}x_{_1}+w_{_2}x_{_2}-\theta = 0,
\end{equation}
la cual se puede escribir como
\begin{equation}
x_{_2}=\frac{w_{_1}}{w_{_2}}x_{_1}+\frac{\theta}{w_{_2}} = 0,
\end{equation}
observe que el cociente $\frac{w_{_1}}{w_{_2}}$ determina la pendiente de la recta y $\frac{\theta}{w_{_2}}$ su <em><a href="https://en.wikipedia.org/wiki/Bias_of_an_estimator">bias</a></em>. Note también que el vector $(w_{_1}, w_{_2})$ es siempre perpendicular a recta.
<br>
<br>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgKKXyiSD2d41vBoqZkYvhZ8yXZ6rfkE5q36jyGCgFT7ZC70wvtoBjsiEm5ZLz3rrBsUgHgxAJ-1erc4sIoOVKF9zHU_e6OusVlfAD2oT91MyzwHPMJJKx8Ujg89pgviea1vhhXSgOw_eE/s1600/Perceptron.png" imageanchor="1" ><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgKKXyiSD2d41vBoqZkYvhZ8yXZ6rfkE5q36jyGCgFT7ZC70wvtoBjsiEm5ZLz3rrBsUgHgxAJ-1erc4sIoOVKF9zHU_e6OusVlfAD2oT91MyzwHPMJJKx8Ujg89pgviea1vhhXSgOw_eE/s1600/Perceptron.png" /></a>
<br/>
Figura 2. Función discriminante de un perceptrón simple.
<br>
<br>
</div>
Suponga ahora que se tiene un conjunto de datos $S\subset\mathbb{R}^{2}$, y un vector $\pmb{x}\in S$ para el cual se desea obtener la señal $\hat{y}(x)$. Como se ha dicho anteriormente $\hat{y}(x)$ es usualmente es un vector donde cada entrada es $+1$ o $-1$. ¿Cómo aprende el perceptrón a clasificar adecuadamente? Para eso el perceptrón sigue la siguiente rutina de aprendizaje:
</p>
</p>
<ol type="I">
<li>Iniciar con un conjunto aleatorio de pesos sinápticos.</li>
<li>Seleccionar un patrón de entrada $x\in S$.</li>
<li>Si $y(x) \neq \hat{y}(x)$, entonces los pesos se modifican de acuerdo a la regla:
\begin{equation}
\Delta w_{_i}= \hat{y}(x)x_{_i};
\end{equation}.</li>
<li> Volver al paso 2. </li>
</ol>
<p>
El lector podrá verificar que este procedimiento es muy similar a la <a href="https://es.wikipedia.org/wiki/Teor%C3%ADa_hebbiana">regla de aprendizaje de Hebb</a>, la única diferencia es que cuando la neurona responde correctamente, los pesos sinápticos no son modificados. Por otro otro lado, $\theta$ como es considerado es el peso sináptico $w_{_0}$ que siempre recibe por la dendrita $x_{0}$ el valor de $-1$. Para el caso de $\theta$, la regla de aprendizaje viene dada por:
\begin{equation}
\Delta \theta = \left\{\begin{array}{cc}
0 & \mbox{ si el perceptron responde correctamente} \\
\hat{y}(x) & \mbox{ si el perceptron responde incorrectamente}
\end{array}\right.
\end{equation}
Por ahora no entraremos en más detalles teóricos y vamos a ver como tener nuestro propio perceptrón con Python 3.
<h4><b>
¿Cómo construir un perceptrón con Python?
</b></h4>
<p>
El perceptron que vamos a construir consiste de una capa de $n$ neuronas artificiales, cada una para reconocer un único patrón. El objetivo de la operación del perceptrón es aprender una tranformación dada de la forma $\hat{y}:\{1,-1\}^{m}\to \{1,-1\}^{m}$ usando un conjunto de muestras donde cada elemtento es de la forma $(\pmb{x}, \pmb{y})$ donde $\pmb{x},\pmb{y}\in \{1,-1\}^{m}$ y además se le indican cuales son los vectores $\pmb{x}, \pmb{y}$, para esto se usará la función $tanh\,\theta$, de la siguiente forma:
\begin{equation}
f(t)=tanh(\pmb{w}\cdot \pmb{x}),
\end{equation}
</p>
<p>
Tomaremos como bias para el criterio de desición el valor $\theta = 0.9999999999$ y además vamos a considerar que $\pmb{w}=\pmb{y}$, la razón de esta consideración es debido a que la función $tanh\,\theta$ nos permite decir que tan diferentes son dos vectores, así, si cuando se da un valor de entrada $\pmb{x}$ y la neurona artificial nos entrega el valor correcto de $\pmb{y}$ es porque el patrón $\pmb{x}$ está muy cercado al vector $w$, es decir, que el valor de $tanh,\theta$ es muy cercano a uno. No se preocupen por esto, en otra ocasión explicaré como hacer el entrenamiento de la neurona. Por ahora solo veamos como construir un ejemplo completamente funcional.
</p>
<p>
Lo primero que haremos en importar las librerías necesarias para nuestro algoritmo.
<code><pre class="prettyprint linenums">
import numpy as np
import math
import pickle
from itertools import product
import tkinter as tk
from typing import Callable
</pre></code>
</p>
<p>
Se define la clase Neuron con los siguientes métodos:
<br>
<br>
1. El constructor de la neurona:
<code><pre class="prettyprint linenums">
def __init__(self, dendrite: np.array, sensitivity:
int=2, dilatation: float=0.5) -> object:
sensitivity = '9' * int(sensitivity)
# Attributes of class.
self.sensitivity = 1 - 100 / int(sensitivity)
self.dilatation = 1/dilatation
self.n_weight = len(dendrite)
self.synaptic_weight = np.ones(self.n_weight)
# We define the memory of neuron.
pickle.dump([], open('memory.mem', 'wb'))
self.memory = pickle.load(open('memory.mem', 'rb'))
</pre></code>
</p>
<p>
2. El soma de la neurona:
<code><pre class="prettyprint linenums">
def soma(self, dendrite: np.array, potential_function: Callable=np.dot,
potential = potential_function(dendrite, self.synaptic_weight)
potential = potential / self.dilatation
order = active_function(potential)
return order
</pre></code>
</p>
<p>
3. Toda neurona necesita una método de aprendizaje. Esto se programa a continuación:
<code><pre class="prettyprint linenums">
def learn(self, dendrite: np.array) -> None:
self.memory.append(dendrite)
self.memory.reverse()
print('Signal learned')
</pre></code>
</p>
<p>
3. Y también deba saber olvidar:
<code><pre class="prettyprint linenums">
def forget(self) -> None:
self.memory = []
pickle.dump(self.memory, open("memory.mem", 'wb'))
print('Memory deleted')
</pre></code>
</p>
<p>
4. Y por último se programa el axón o función de activación:
<code><pre class="prettyprint linenums">
def axon(self, dendrite: np.array) -> np.array:
candidate_signals = {}
# Se identifican todas las señales posibles.
for mem in self.memory:
self.synaptic_weight = mem
weight = self.soma(dendrite)
if weight > self.sensitivity:
candidate_signals[weight] = mem
if not candidate_signals:
predict_signal = None
else:
# Se selecciona la mejor señal.
predict_weight = max(candidate_signals.keys())
print(predict_weight)
predict_signal = candidate_signals[predict_weight]
return predict_signal
</pre></code>
</p>
<p>Con la anterior se ha programado el cerebro de nuestro percetrón. Veamos ahora como implementarlo, para esto se debe construir una clase Perceptron con los siguientes métodos:
</p>
<p>
1. El constructor de la clase Perceptrón con una instancia de la clase Neuron. Aquí también se implementa la interfaz gráfica:
<code><pre class="prettyprint linenums">
def __init__(self, sqrt_n_receptors: int=5, sensitivity: int=17, focus:
float=1) -> object:
self.sqrt_n_receptors = sqrt_n_receptors
self.sensitivity = sensitivity
self.focus = focus
# Atributos de la clase.
self.signal = np.array([-1 for _ in range(self.sqrt_n_receptors ** 2)])
self.neuron = Neuron(self.signal, self.sensitivity, self.focus)
# Ventana principal con botones.
main_window = tk.Tk()
main_window.title('Perceptron')
main_window.resizable(width=False, height=False)
# Botones de la ventana principal.
n_row = range(sqrt_n_receptors)
self.buttons = [[None]*sqrt_n_receptors for _ in n_row]
self.buttons = np.array(self.buttons)
self.values = np.zeros((self.sqrt_n_receptors, self.sqrt_n_receptors))
self.coordinates = {}
kwargs = dict(text=' ', bg='gray', relief='flat', width=2, height=2)
for row, col in product(n_row, n_row):
self.buttons[row, col] = tk.Button(main_window, **kwargs)
self.buttons[row, col].grid(row=row, column=col, padx=2, pady=2)
self.coordinates[self.buttons[row, col]] = [row, col]
# Se detectan los eventos de cada uno de los botones.
for button in self.buttons.flat:
button.bind("<Button-1>", self.button_pressed)
# Ventana secundaria.
second_window = tk.Tk()
second_window.title('')
second_window.geometry("110x110")
second_window.resizable(width=False, height=False)
# Botones de la ventana secundaria.
kwargs_memorize = dict(text='learn', command=self.memorize, width=455)
button_memorize = tk.Button(second_window, **kwargs_memorize)
kwargs_analyze = dict(text='Analyze', command=self.id_signal, width=455)
button_analyze = tk.Button(second_window, **kwargs_analyze)
kwargs_reset = dict(text='Reset', command=self.reset, width=455)
button_reset = tk.Button(second_window, **kwargs_reset)
kwargs_forget = dict(text='Forget', command=self.forget, width=455)
button_forget = tk.Button(second_window, **kwargs_forget)
# La ventana secundaria se construye con un pack.
button_memorize.pack()
button_analyze.pack()
button_reset.pack()
button_forget.pack()
main_window.mainloop()
second_window.mainloop()
</pre></code>
</p>
<p>
2. El siguiente método define que ocurre cuando se presiona algún botón de la ventana principal.
<code><pre class="prettyprint linenums">
def button_pressed(self, event: Callable) -> None:
# Se identifican las coordenadas del evento.
row, col = self.coordinates[event.widget]
n = self.sqrt_n_receptors * row + col
if self.signal[n] == -1:
self.signal[n] = 1
self.buttons[row][col]['bg'] = '#5BADFF'
else:
self.signal[n] = -1
self.buttons[row][col]['bg'] = 'gray'
</pre></code>
</p>
<p>
3. Método para reconocer la señal:
<code><pre class="prettyprint linenums">
def id_signal(self) -> None:
signal = self.neuron.axon(self.signal)
try:
n = len(signal)
except TypeError:
print('I do not know is this')
else:
for i in range(n):
if signal[i] == 1:
row = i // self.sqrt_n_receptors
col = i % self.sqrt_n_receptors
self.buttons[row][col]['bg'] = '#01D826'
</pre></code>
</p>
<p>
4. Método para resetear el estado de los botones en la ventana principal.
<code><pre class="prettyprint linenums">
def reset(self) -> None:
self.signal = -1 * np.ones(len(self.signal))
size = range(self.sqrt_n_receptors)
for row, col in product(size, size):
self.buttons[row][col]['bg'] = 'gray'
self.buttons[row][col]['bg'] = '#01D826'
</pre></code>
</p>
<p>
5. Método para aprender nuevas señales.
<code><pre class="prettyprint linenums">
def memorize(self) -> None:
self.neuron.learn(self.signal)
self.reset()
</pre></code>
</p>
<p>
5. Método para olvidar todas las señales.
<code><pre class="prettyprint linenums">
def forget(self) -> None:
self.neuron.forget()
</pre></code>
</p>
<p>
Finalmente instanciamos la clase del perceptrón.
<code><pre class="prettyprint linenums">
if __name__ == "__main__":
Perceptron()
</pre></code>
</p>
<p>El lector debe notar, cuando tenga funcionando el perceptrón, que cada que ingresa un nuevo patrón de aprendizaje, se está entrenando una nueva neurona. En otras palabras, para cada patrón se tiene un vector de pesos que permite caracterizar cada nueva neurona entrenada. Estos pesos, se almacenan en memoria.mem. Así, que el lector, puede imaginar el funcionamiento del perceptrón como se muestra en la siguiente figura:
</p>
<br>
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRVHoBGc_gFwJDRVxokGBOP_3VHTEaRojem-lQ61XUWo9kwAqU1tQxuDJMCr1AxnIrOGVaniUd6cXeGmVw_kmYON10r_SVCEe5PyQhVx09Qjs195MPcMeuh-4i-rgk1V6H41wckMkjsjA/s1600/g8400.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRVHoBGc_gFwJDRVxokGBOP_3VHTEaRojem-lQ61XUWo9kwAqU1tQxuDJMCr1AxnIrOGVaniUd6cXeGmVw_kmYON10r_SVCEe5PyQhVx09Qjs195MPcMeuh-4i-rgk1V6H41wckMkjsjA/s1600/g8400.png" /></a>
<br>
Figura 3. Estructura global del perceptrón.</div>
<br>
<br>
<p>
Otra observación importante, es que el perceptron aprende adecuadamente los pesos sinápticos en un tipo finito. Teóricamente, esto es:
</p>
<blockquote> <b>Teorema. </b> Se tiene un perceptrón con un conjunto adecuado de pesos sinápticos $w^*$ para el resultado $\hat{y}(x) = y$. Entonces el perceptrón converge en un tiempo finito, sin importar quién sea $w^*$ inicial.
</blockquote>
En efecto, si consideramos que $w^*$ es una solución adecuada, entonces $||w^*|| = 1$ (esto si se considera como criterio de desición a la función $sgn$, hacer esta consideración no representa ninguna perdida de generalidad). Ahora si calculamos $|w^*\cdot x|$, entonces tenemos dos posibilidades o que el resultado sea cero, o que existe un $\delta > 0$ tal que $|w^*\cdot x|>0$ para la entrada $x$. Si ahora se considera
\begin{equation}
\cos \alpha = \frac{w\cdot w^*}{||w||},
\end{equation}
entonces de acuerdo a las reglas de aprendizaje del perceptrón se tiene que $\Delta w = \hat{y}x$, y por lo tanto la modificación a los pesos sería $w' = w +\Delta w$. De esto se sigue que:
$$w'\cdot w^* = w\cdot w^*+\hat{y}w^*\cdot x = w\cdot w^*+sgn(w^*\cdot x)w^*\cdot x > w\cdot w^* +\delta$$
por otro lado se tiene:
$$||w'||^2=w^2+2\hat{y}w\cdot x + x^2 < w^2 + x^2 = w^2+ M$$
dado que $\hat{y}=-sgn(w\cdot x)$. Después de estás modificaciones, entonces es puede concluir que:
$$\cos\alpha > \frac{w^*\cdot w + \delta}{\sqrt{w^2+tM}}.$$
De esta última expresión se concluye que el tiempo de convergencia debe ser finito, dado que $cos \alpha \leq 1$. Con algunas modificaciones, se puede considerar como el tiempo máximo a $t_{máx}=\frac{M}{\delta^2}$.
</p>
<h4><b>Conclusiones</b></h4>
<p>
<ol>
<li>Lo que se aprendió hoy fue que una neurona artificial tiene gran parecido a la neurona biológica tanto en su estructura como en su funcionalidad. Así como la unión de las neuronas dan origen al cerebro, las neuronas artificiales dan lugar a arreglos de neuronas llamadas redes neurales, que intentan emular el funcionamiento del cerebro humano, tarea que todavía no se consigue. La neurona
artificial al igual que la neurona biológica, maneja diferentes tipos de señales, como se mencionó con antelación estas pueden ser continuas o digitales.</li>
<li>El codigo completo del perceptron lo encuentras <a href="https://github.com/alejandrosanchezy/ia/blob/master/perceptron.py">aquí</a>.</li>
</ol>
</p>
<h4><b>Referencias</b></h4>
<div style="font-size: 110%; text-align: justify;">
</div>
<ul style="list-style-type: square;">
<li>Michael A. Arbib. <a href="http://izt.ciens.ucv.ve/ecologia/Archivos/References-I-biol/books-biol/Biology/Arbib-The_Handbook_of_Brain_Theory_and_Neural_Networks.pdf">The handbook of brain theory and neural networks</a>. The MIT PRESS, 2002.
</li>
<li>Kröse, Ben and Smagt, Pactrick. <a href="https://www.infor.uva.es/~teodoro/neuro-intro.pdf">Introduction to Neural Networks</a>. University od Amsterdam, 1996.
</li>
</ul>
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