{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Using optimization routines from `scipy` and `statsmodels`\n", "====" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import scipy.linalg as la" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finding roots\n", "----\n", "\n", "For root finding, we generally need to proivde a starting point in the vicinitiy of the root. For iD root finding, this is often provided as a bracket (a, b) where a and b have opposite signs." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Univariate roots and fixed points" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def f(x):\n", " return x**3-3*x+1" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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adhyoZebEMdy6oCig8RQUZIW9fsESy3UD1S/axUP9/BH0G8PGmL82xtQYYxKH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\nAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(-3,3,100)\n", "plt.axhline(0, c='red')\n", "plt.plot(x, f(x));" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from scipy.optimize import brentq, newton" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### `brentq` is the recommended method" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(-1.8793852415718166, 0.3472963553337031, 1.532088886237956)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "brentq(f, -3, 0), brentq(f, 0, 1), brentq(f, 1,3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Secant method" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(-1.8793852415718169, 0.34729635533385395, 1.5320888862379578)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "newton(f, -3), newton(f, 0), newton(f, 3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Newton-Raphson method" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(-1.8793852415718166, 0.34729635533386066, 1.532088886237956)" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fprime = lambda x: 3*x**2 - 3\n", "newton(f, -3, fprime), newton(f, 0, fprime), newton(f, 3, fprime)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Analytical solution using `sympy` to find roots of a polynomial" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from sympy import symbols, N, real_roots" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[-1.87938524157182, 0.347296355333861, 1.53208888623796]" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x = symbols('x', real=True)\n", "sol = real_roots(x**3 - 3*x + 1)\n", "list(map(N, sol))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Finding fixed points\n", "\n", "Finding the fixed points of a function $g(x) = x$ is the same as finding the roots of $g(x) - x$. However, specialized algorihtms also exist - e.g. using `scipy.optimize.fixedpoint`." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from scipy.optimize import fixed_point" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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HqPzdb0mOqKLugflZmWdWRKS/cj4J/PT0x9a6vtveMl1P7lnqChl8cyGDjv01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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(-3,3,100)\n", "plt.plot(x, f(x), color='red')\n", "plt.plot(x, x)\n", "pass" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(0.2541016883650524, -2.114907541476756, 1.8608058531117035)" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fixed_point(f, 0), fixed_point(f, -3), fixed_point(f, 3)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(0.2541016883650524, -2.114907541476814, 1.8608058531117062)" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "newton(lambda x: f(x) - x, 0), newton(lambda x: f(x) - x, -3), newton(lambda x: f(x) - x, 3)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def f(x, r):\n", " \"\"\"Discrete logistic equation.\"\"\"\n", " return r*x*(1-x)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n = 100\n", "fps = np.zeros(n)\n", "for i, r in enumerate(np.linspace(0, 4, n)):\n", " fps[i] = fixed_point(f, 0.5, args=(r, ))\n", "\n", "plt.plot(np.linspace(0, 4, n), fps)\n", "plt.axis([0,4,-0.1, 1.1])\n", "pass" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Note that we don't know anything about the **stability** of the fixed point\n", "\n", "Beyond $r = 3$, the fixed point is unstable, even chaotic, but we would never know that just from the plot above." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Qnb2R8nLO2M6ir/RoGSilRqNv4g9qmrZD07S/ArcCVyulrgxwyu3AeUCupml7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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "xs = []\n", "for i, r in enumerate(np.linspace(0, 4, 400)):\n", " x = 0.5\n", " for j in range(10000):\n", " x = f(x, r)\n", " for j in range(50):\n", " x = f(x, r)\n", " xs.append((r, x))\n", "xs = np.array(xs)\n", "plt.scatter(xs[:,0], xs[:,1], s=1)\n", "plt.axis([0,4,-0.1, 1.1])\n", "pass" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Mutlivariate roots and fixed points\n", "\n", "Use `root` to solve polynomial euqations. Use `fsolve` for non-polynomial equations." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from scipy.optimize import root, fsolve" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Suppose we want to solve a sysetm of $m$ equations with $n$ unknowns\n", "\n", "\\begin{align}\n", "f(x_0, x_1) &= x_1 - 3x_0(x_0+1)(x_0-1) \\\\\n", "g(x_0, x_1) &= 0.25 x_0^2 + x_1^2 - 1\n", "\\end{align}" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def f(x):\n", " return [x[1] - 3*x[0]*(x[0]+1)*(x[0]-1),\n", " .25*x[0]**2 + x[1]**2 - 1]" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ 1.11694147, 0.82952422])" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sol = root(f, (0.5, 0.5))\n", "sol.x" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ 1.11694147, 0.82952422])" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fsolve(f, (0.5, 0.5))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### We can also give the jacobian" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def jac(x):\n", " return [[-6*x[0], 1], [0.5*x[0], 2*x[1]]]" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(array([ 1.11694147, 0.82952422]),\n", " array([ -4.23383550e-12, -3.31612515e-12]))" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sol = root(f, (0.5, 0.5), jac=jac)\n", "sol.x, sol.fun" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Check that values found are really roots" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.allclose(f(sol.x), 0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Starting from other initial conditions, different roots may be found" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ 0.77801314, -0.92123498])" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sol = root(f, (12,12))\n", "sol.x" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.allclose(f(sol.x), 0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Optimization Primer\n", "----\n", "\n", "We will assume that our optimization problem is to minimize some univariate or multivariate function $f(x)$. This is without loss of generality, since to find the maximum, we can simply minime $-f(x)$. We will also assume that we are dealing with multivariate or real-valued smooth functions - non-smooth or discrete functions (e.g. integer-valued) are outside the scope of this course.\n", "\n", "To find the minimum of a function, we first need to be able to express the function as a mathemtical expresssion. For example, in lesst squares regression, the function that we are optimizing is of the form $y_i - f(x_i, \\theta)$ for some parameter(s) $\\theta$. To choose an appropirate optimization algorihtm, we should at least answr these two questions if possible:\n", "\n", "1. Is the function convex?\n", "2. Are there any constraints that the solution must meet?\n", "\n", "Finally, we need to realize that optimization mehthods are nearly always designed to find local optima. For convex problems, there is only one minimum and so this is not a problem. However, if there are multiple local minima, often heuristics such as multiple random starts must be adopted to find a \"good\" enouhg solution. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Is the function convex?\n", "\n", "Convex functions are very nice because they have a **single global minimum**, and there are very efficient algorithms for solving large convex systems. \n", "\n", "Intuitively, a function is convex if every chord joining two points on the function lies above the function. More formally, a function is convex if \n", "$$\n", "f(ta + (1-t)b) \\lt tf(a) + (1-t)f(b)\n", "$$ \n", "for some $t$ between 0 and 1 - this is shown in the figure below." ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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196YPSK+P1+tEVRU+//xz/vOf/2Czmfmvr+D3Jm63nawsM50ffvghO3fuxOHQ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\nImkNVi0xh66gvvwS3HorfP65eNJuFxUXLrqI+B57EgrFCHv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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def f(x):\n", " return (x-4)**2 + x + 1\n", "\n", "with plt.xkcd():\n", " x = np.linspace(0, 10, 100)\n", "\n", " plt.plot(x, f(x))\n", " ymin, ymax = plt.ylim()\n", " plt.axvline(2, ymin, f(2)/ymax, c='red')\n", " plt.axvline(8, ymin, f(8)/ymax, c='red')\n", " plt.scatter([4, 4], [f(4), f(2) + ((4-2)/(8-2.))*(f(8)-f(2))], \n", " edgecolor=['blue', 'red'], facecolor='none', s=100, linewidth=2)\n", " plt.plot([2,8], [f(2), f(8)])\n", " plt.xticks([2,4,8], ('a', 'ta + (1-t)b', 'b'), fontsize=20)\n", " plt.text(0.2, 40, 'f(ta + (1-t)b) < tf(a) + (1-t)f(b)', fontsize=20)\n", " plt.xlim([0,10])\n", " plt.yticks([])\n", " plt.suptitle('Convex function', fontsize=20)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Warm up exercise\n", "\n", "Show that $f(x) = -\\log(x)$ is a convex function." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Checking if a function is convex using the Hessian\n", "\n", "The formal definition is only useful for checking if a function is convex if you can find a counter-example. More practically, a twice differentiable function is convex if its Hessian is positive semi-definite, and strictly convex if the Hessian is positive definite.\n", "\n", "For example, suppose we want to minimize the scalar-valued function\n", "\n", "$$\n", "f(x_1, x_2, x_3) = x_1^2 + 2x_2^2 + 3x_3^2 + 2x_1x_2 + 2x_1x_3\n", "$$" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from sympy import symbols, hessian, Function, init_printing, expand, Matrix, diff\n", "x, y, z = symbols('x y z')\n", "f = symbols('f', cls=Function)\n", "init_printing()" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPgAAAAYBAMAAAAluy26AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nDevrFZti/gKYu+d7e+zGkgAAAABJRU5ErkJggg==\n", "text/latex": [ "$$x^{2} + 2 x y + 2 x z + 2 y^{2} + 3 z^{2}$$" ], "text/plain": [ " 2 2 2\n", "x + 2⋅x⋅y + 2⋅x⋅z + 2⋅y + 3⋅z " ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f = x**2 + 2*y**2 + 3*z**2 + 2*x*y + 2*x*z\n", "f" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAFgAAABLCAMAAADDCbAzAAAAPFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAo1xBWAAAAE3RSTlMA\nMquZdlQQQOkwRCK7ie/dzWZsTaT2EwAAAAlwSFlzAAAOxAAADsQBlSsOGwAAAtNJREFUWAntmeuS\npCAMhVGQnVVRWd7/XVdu6USCqdrunaqp0h/TkdN8nYlcjqqGkI5RfejYM0+pIWhzHtOHuMpH2hgi\nePgU88XxGLxova43PyLoRMZgG6vswvz6WRoJOpUxeLQRtG0U9zoTdCpj8LZHyNituKBTGYOPEFPu\ngwWdyhic/+k94XPM/RX0KjfgOTgOB22CDnID3oUJKOggX8FaQ25sIOgv+QI2AlfQkUzBU+QuC5tr\nbBR0LBPwkPI1XbCgExmDl905p8c0TbikBZ3KGHzkdbQLFnQqYzCX5T+3PWAo3VOKpxRQAQi+Z1QQ\nxwG/TYO8hNG2cma18676HZwxdRxsX6X2tSModZzuz+5l0cVg6jj4/mbrgn1yOu7IHTGYOg4WvPij\nC17TNjwV94DB1HGwYKf64JDAc8h2GIMzqjoODuyXPtiGtLHNwaSeDRgcBwO2Z59uxkt2OkMxPA0Y\nHAcDjh7pBpwy7oFfjqMFT3GMdsFMKX59/a4U5DhqE3zaZOq6YJUv3lQu3p8vfA+CHQcAazCN8Qjb\nmK9ObYbPNQ1Ezww3RRwHdKCBNEE0M0Go46A8OAvdCaL2OKW3sljgUUEdB6Bw4NYQRo9bUGzdeXvH\nLULoO++HOOP3aYjwgKEYTymeUkAFICCjQjIsxJEAAgXOmepYMFg0LMSRIF4J7XE+nOGWTcmwUEfS\ngte46eXlXimcsWRYqCNpwHPAt7QYLBkW6kga8EoeJmFw/mrXsFy24QYcjsEZXZ+BNeC+Ybk4kivY\nhiNuLVt54NiA+4ZlyR6qOpIWnPZnvaWHbOTixa/eGBaxFOnu3pcHgpeM7wzLxZFcM1Z72vh9yHst\nBd8aljJEqyNpwGMaFWzGgmHJE6ROrQY8lBpnAWcsGhbiSBqwGk9zZ7lRIRoW4khasHJaP4alrQu+\neK36RstPBf+nFyw2vhAxpq6kbxQ2d00vWIxRfwHfnSnjyjAnFAAAAABJRU5ErkJggg==\n", "text/latex": [ "$$\\left[\\begin{matrix}2 & 2 & 2\\\\2 & 4 & 0\\\\2 & 0 & 6\\end{matrix}\\right]$$" ], "text/plain": [ "⎡2 2 2⎤\n", "⎢ ⎥\n", "⎢2 4 0⎥\n", "⎢ ⎥\n", "⎣2 0 6⎦" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "H = hessian(f, (x, y, z))\n", "H" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ 0.24122952, 7.06417777, 4.69459271])" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.real_if_close(la.eigvals(np.array(H).astype('float')))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since the matrix is symmetric and all eigenvalues are positive, the Hessian is positive defintie and the function is convex." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Combining convex functions\n", "\n", "The following rules may be useful to determine if more complex functions are covex:\n", "\n", "1. The intersection of convex functions is convex\n", "2. If the functions $f$ and $g$ are convex and $a \\ge 0$ and $b \\ge 0$ then the function $af + bg$ is convex.\n", "3. If the function $U$ is convex and the function $g$ is nondecreasing and convex then the function f defined by $f (x) = g(U(x))$ is convex.\n", "\n", "Many more technical deetails about convexity and convex optimization can be found in this [book](http://web.stanford.edu/~boyd/cvxbook/)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Are there any constraints that the solution must meet?\n", "\n", "In general, optimizaiton without constraints is easier to solve than optimization in the presence of constraints. In any case, the solutions may be very different in the prsence or absence of constraints, so it is important to know if there are any constraints.\n", "\n", "We will see some examples of two general strategies - convert a problme with constraints into one without constraints, or use an algorithm that can optimize with constraints." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using `scipy.optimize`\n", "----\n", "\n", "One of the most convenient libraries to use is `scipy.optimize`, since it is already part of the Anaconda installation and it has a fairly intuitive interface." ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from scipy import optimize as opt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Minimizing a univariate function $f: \\mathbb{R} \\rightarrow \\mathbb{R}$" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def f(x):\n", " return x**4 + 3*(x-2)**3 - 15*(x)**2 + 1" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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5fwB+A3BGwHXPwV5vMuoyUhIozk+ntKpZt5UPM0+8so+ymhaWzi3gtHmhTfJK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\nWHotONxylIaWo1TWtdHc1ml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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(-8, 5, 100)\n", "plt.plot(x, f(x));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The [`minimize_scalar`](http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize_scalar.html#scipy.optimize.minimize_scalar) function will find the minimum, and can also be told to search within given bounds. By default, it uses the Brent algorithm, which combines a bracketing strategy with a parabolic approximation." ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ " nit: 11\n", " nfev: 12\n", " x: -5.5288011252196627\n", " fun: -803.39553088258845" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "opt.minimize_scalar(f, method='Brent')" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ " nfev: 12\n", " success: True\n", " fun: -54.210039377127622\n", " status: 0\n", " message: 'Solution found.'\n", " x: 2.6688651040396532" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "opt.minimize_scalar(f, method='bounded', bounds=[0, 6])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Local and global minima" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def f(x, offset):\n", " return -np.sinc(x-offset)" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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JZrdZmaeKWbG5Gn24kenjOi889Y3t7DhwnMmjCxhdFLvNHYyRT6HPvHRR1xpY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\nKVaNQhKFMEEShRBprrMzu3uikBqFMEM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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(-20, 20, 100)\n", "plt.plot(x, f(x, 5));" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ " nit: 10\n", " nfev: 11\n", " x: -1.4843871263953001\n", " fun: -0.049029624014074166" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# note how additional function arguments are passed in\n", "sol = opt.minimize_scalar(f, args=(5,))\n", "sol" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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jvPTvIyyeWRosXe092sTWffVMryjo1eslnN1mZaEqYfW2GvTRJmZN7Lnx1Dd1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\nIiZJFEIIIWKSRCGEECKm/w+XE0npBuW51AAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(x, f(x, 5))\n", "plt.axvline(sol.x, c='red')\n", "pass" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### We can try multiple ranodm starts to find the global minimum" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": false }, "outputs": [], "source": [ "lower = np.random.uniform(-20, 20, 100)\n", "upper = lower + 1\n", "sols = [opt.minimize_scalar(f, args=(5,), bracket=(l, u)) for (l, u) in zip(lower, upper)]" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "collapsed": false }, "outputs": [], "source": [ "idx = np.argmin([sol.fun for sol in sols])\n", "sol = sols[idx]" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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KQ6WrXYea2LS7gSkVBd16vURy2G3MUyWs2FyLPtTE9PFdN56Gpnbe3X+cyWMK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\nkkQhhBAiLkkUQggh4pJEIYQQIq7/D9rDLPET9zG/AAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(x, f(x, 5))\n", "plt.axvline(sol.x, c='red');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Using a stochastic algorithm\n", "\n", "See documentation for the [`basinhopping`](http://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.optimize.basinhopping.html) algorithm, which also works with multivariate scalar optimization. Note that this is heuristic and not guaranteed to find a global minimum." ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ " nfev: 1812\n", " njev: 604\n", " fun: -1.0\n", " nit: 100\n", " message: ['requested number of basinhopping iterations completed successfully']\n", " x: array([ 5.])\n", " minimization_failures: 0" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from scipy.optimize import basinhopping\n", "\n", "x0 = 0\n", "sol = basinhopping(f, x0, stepsize=1, minimizer_kwargs={'args': (5,)})\n", "sol" ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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KQ6WrXYea2LS7gSkVBd16vURy2G3MUyWs2FyLPtTE9PFdN56Gpnbe3X+cyWMK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\ne6gw1ypRNLd1JYpQrycpUYgkyKSAQqS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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(x, f(x, 5))\n", "plt.axvline(sol.x, c='red');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Minimizing a multivariate function $f: \\mathbb{R}^n \\rightarrow \\mathbb{R}$\n", "\n", "We will next move on to optimization of multivariate scalar functions, where the scalar may (say) be the norm of a vector. Minimizing a multivariable set of equations $f: \\mathbb{R}^n \\rightarrow \\mathbb{R}$^n$ is not well-defined, but we will later see how to solve the closely related problme of finding roots or fixed points of such a set of equations.\n", "\n", "We will use the [Rosenbrock \"banana\" function](http://en.wikipedia.org/wiki/Rosenbrock_function) to illustrate unconstrained multivariate optimization. In 2D, this is\n", "\n", "\\begin{align}\n", "f(x, y) = b(y - x^2)^2 + (a - x)^2\n", "\\end{align}\n", "\n", "The function has a global minimum at (1,1) and the standard expression takes $a = 1$ and $b = 100$. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Conditioning of optimization problem\n", "\n", "With these values fr $a$ and $b$, the problem is ill-conditioned. As we shall see, one of the factors affecting the ease of optimization is the condition number of the curvature (Hessian). When the condition number is high, the gradient may not point in the direction of the minimum, and simple gradient descent methods may be inefficient since they may be forced to take many sharp turns." ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$$\\left ( \\left[\\begin{matrix}802 & -400\\\\-400 & 200\\end{matrix}\\right], \\quad 2508.00960127744\\right )$$" ], "text/plain": [ "⎛⎡802 -400⎤, 2508.00960127744⎞\n", "⎜⎢ ⎥ ⎟\n", "⎝⎣-400 200 ⎦ ⎠" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sympy import symbols, hessian, Function, N\n", "\n", "x, y = symbols('x y')\n", "f = symbols('f', cls=Function)\n", "\n", "f = 100*(y - x**2)**2 + (1 - x)**2\n", "\n", "H = hessian(f, [x, y]).subs([(x,1), (y,1)])\n", "H, N(H.condition_number())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### As pointed out in the previous lecture, the condition number is basically the ratio of largest to smallest eigenvalue of the Hessian" ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array(2508.009601277337)" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import scipy.linalg as la\n", "\n", "mu = la.eigvals(np.array([802, -400, -400, 200]).reshape((2,2)))\n", "np.real_if_close(mu[0]/mu[1])" ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def rosen(x):\n", " \"\"\"Generalized n-dimensional version of the Rosenbrock function\"\"\"\n", " return sum(100*(x[1:]-x[:-1]**2.0)**2.0 +(1-x[:-1])**2.0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Why is the condition number so large?" ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "collapsed": false }, "outputs": [], "source": [ "x = np.linspace(-5, 5, 100)\n", "y = np.linspace(-5, 5, 100)\n", "X, Y = np.meshgrid(x, y)\n", "Z = rosen(np.vstack([X.ravel(), Y.ravel()])).reshape((100,100))" ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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IiFVrTL1Jsrar1Nq3dHMEIT4W3ARRcQWMmxv06WPm2DENFS46ssk3pqtSvI6o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\no0yxChiAi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BoBTdNM7AvauZC92BdyGXCzrusfhmtv4UDTtGjgY2A4ME7X9ROi\n8kXTtH7AcqCdrus7672fDbym6/pzYdtcmNA07S/AE8BLuq7fE+79hANN074CzgQcDWIF+6muEnhX\n1/XbwrW3g3GieOpHIuuA/x+FXZ/bCzih6pODpWyfAIOxE2WLwrsjV1mLfSMfBHwAoGlaJpAJNLh6\nZGk0TXsAu7x3oq7rT4Z7P2HkD9h1+g4Z2HXqNwIN7vqIeOoHQdO0PwDTdF1vWFMLXEDTtNuBl7FP\n2DkH/HG+rusujewID5qmPYWdDLseyMMOQVXouj4krBtzmWC/xhrsXNPEA/64VNf1Ctc31UAIxtS3\nA4MjzUcRGgPXYidRp2BXfewCdgd/9g/jvtxiIvA+doPJYuyk8pVh3VF4uArbPtxA3XngvE7IMMwB\nNFhvOOKpR4gQIUITIuKpR4gQIUITImLUI0SIEKEJETHqESJEiNCEiBj1CBEiRGhCRIx6hAgRIjQh\nIkY9QoQIEZoQEaMeIUKECE2IiFGPECFChCZExKhHiBAhQhPi/wGfAHgpB8vXywAAAABJRU5ErkJg\ngg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Note: the global minimum is at (1,1) in a tiny contour island\n", "plt.contour(X, Y, Z, np.arange(10)**5, cmap='jet')\n", "plt.text(1, 1, 'x', va='center', ha='center', color='red', fontsize=20);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Zooming in to the global minimum at (1,1)" ] }, { "cell_type": "code", "execution_count": 50, "metadata": { "collapsed": false }, "outputs": [], "source": [ "x = np.linspace(0, 2, 100)\n", "y = np.linspace(0, 2, 100)\n", "X, Y = np.meshgrid(x, y)\n", "Z = rosen(np.vstack([X.ravel(), Y.ravel()])).reshape((100,100))" ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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1msKfCUmehVtfmeKExb632Ztc117mvPEQUa5Ympa2C5pLFTBHSJRDMC3APAQw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\nLPrYQcmUFAN9+27lwIF4oqJCiIl5hXLlXEVkz55bjBmzl6tX0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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.contour(X, Y, Z, [rosen(np.array([k, k])) for k in np.linspace(1, 1.5, 10)], cmap='jet')\n", "plt.text(1, 1, 'x', va='center', ha='center', color='red', fontsize=20);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Gradient descent\n", "----\n", "\n", "The gradient (or Jacobian) at a point indicates the direction of steepest ascent. Since we are looking for a minimum, one obvious possibility is to take a step in the opposite direction to the gradient. We weight the size of the step by a factor $\\alpha$ known in the machine learning literature as the learning rate. If $\\alpha$ is small, the algorithm will eventually converge towards a local minimum, but it may take long time. If $\\alpha$ is large, the algorithm may converge faster, but it may also overshoot and never find the minimum. Gradient descent is also known as a first order method because it requires calculation of the first derivative at each iteration.\n", "\n", "Some algorithms also determine the appropriate value of $\\alpha$ at each stage by using a line search, i.e.,\n", "$$\n", "\\alpha^* = \\arg\\min_\\alpha f(x_k - \\alpha \\nabla{f(x_k)})\n", "$$\n", "which is a 1D optimization problem.\n", "\n", "As suggested above, the problem is that the gradient may not point towards the global minimum especially when the condition number is large, and we are forced to use a small $\\alpha$ for convergence. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Simple gradient descent\n", "\n", "Let's warm up by minimizing a trivial function $f(x, y) = x^2 + y^2$ to illustrate the basic idea of gradient descent." ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Start [ 1. 1.]\n", "0 [ 0.8 0.8]\n", "5 [ 0.262144 0.262144]\n", "10 [ 0.08589935 0.08589935]\n", "15 [ 0.0281475 0.0281475]\n", "20 [ 0.00922337 0.00922337]\n", "25 [ 0.00302231 0.00302231]\n", "30 [ 0.00099035 0.00099035]\n", "35 [ 0.00032452 0.00032452]\n", "40 [ 0.00010634 0.00010634]\n" ] } ], "source": [ "def f(x):\n", " return x[0]**2 + x[1]**2\n", "\n", "def grad(x):\n", " return np.array([2*x[0], 2*x[1]])\n", "\n", "a = 0.1 # learning rate\n", "x0 = np.array([1.0,1.0])\n", "print('Start', x0)\n", "for i in range(41):\n", " x0 -= a * grad(x0)\n", " if i%5 == 0:\n", " print(i, x0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Gradient descent for least squares minimization\n", "\n", "Usually, when we optimize, we are not just finding the minimum, but also want to know the parameters that give us the minimum. As a simple example, suppose we want to find parameters that minimize the least squares difference between a linear model and some data. Suppose we have some data $(0,1), (1,2), (2,3), (3,3.5), (4,6), (5,9), (6,8)$ and want to find a line $y = \\beta_0 +\\beta_1 x$ that is the best least squares fit. One way to do this is to solve $X^TX\\hat{\\beta} = X^Ty$, but we want to show how this can be formulated as a gradient descent problem.\n", "\n", "We want to find $\\beta = (\\beta_0, \\beta_1)$ that minimize the squared differences\n", "\n", "\\begin{align}\n", "r = \\sum(\\beta_0 + \\beta_1 x - y)^2\n", "\\end{align}\n", "\n", "We calculate the gradient with respect to $\\beta$ as \n", "\n", "$$\\nabla r = \\pmatrix{ \\frac{\\delta r}{\\delta \\beta_0} \\\\ \\frac{\\delta r}{\\delta \\beta_0}}$$\n", "\n", "and apply gradient descent." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def f(x, y, b):\n", " \"\"\"Helper function.\"\"\"\n", " return (b[0] + b[1]*x - y)\n", "\n", "def grad(x, y, b):\n", " \"\"\"Gradient of objective function with respect to parameters b.\"\"\"\n", " n = len(x)\n", " return np.array([\n", " sum(f(x, y, b)),\n", " sum(x*f(x, y, b))\n", " ])" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "x, y = map(np.array, zip((0,1), (1,2), (2,3), (3,3.5), (4,6), (5,9), (6,8)))" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [], "source": [ "a = 0.001 # learning rate\n", "b0 = np.zeros(2)\n", "for i in range(10000):\n", " b0 -= a * grad(x, y, b0)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.scatter(x, y, s=30)\n", "plt.plot(x, b0[0] + b0[1]*x, color='red')\n", "pass" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Gradient descent to minimize the Rosen function using `scipy.optimize`\n", "\n", "Because gradient descent is unreliable in practice, it is not part of the `scipy` optimize suite of functions, but we will write a custom function below to illustrate how to use gradient descent while maintaining the `scipy.optimize` interface." ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def rosen_der(x):\n", " \"\"\"Derivative of generalized Rosen function.\"\"\"\n", " xm = x[1:-1]\n", " xm_m1 = x[:-2]\n", " xm_p1 = x[2:]\n", " der = np.zeros_like(x)\n", " der[1:-1] = 200*(xm-xm_m1**2) - 400*(xm_p1 - xm**2)*xm - 2*(1-xm)\n", " der[0] = -400*x[0]*(x[1]-x[0]**2) - 2*(1-x[0])\n", " der[-1] = 200*(x[-1]-x[-2]**2)\n", " return der" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Warning** One of the most common causes of failure of optimization is because the gradient or Hessian function is specified incorrectly. You can check for this using `check_grad` which compares the analytical gradient with one calculated using finite differences." ] }, { "cell_type": "code", "execution_count": 53, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 0.84795961 0.8841431 ] 4.12099762158e-06\n", "[ 0.25702089 1.12043717] 2.22491327726e-06\n", "[ 1.06226702 -1.80970275] 3.12407324679e-05\n", "[ 1.5334192 -1.5059954] 1.13208298556e-05\n", "[-0.15930274 1.80868951] 3.71611303963e-06\n", "[ 1.32643444 -1.18424149] 3.25553261955e-05\n", "[ 0.49184844 -0.00341954] 2.67781137655e-06\n", "[ 0.85557139 1.12996825] 3.31235322885e-06\n", "[-1.00825153 -1.85587153] 1.62466187316e-05\n", "[ 0.41514196 0.6850504 ] 1.7634932791e-06\n" ] } ], "source": [ "from scipy.optimize import check_grad\n", "\n", "for x in np.random.uniform(-2,2,(10,2)):\n", " x0 = np.array(x)\n", " print(x0, check_grad(rosen, rosen_der, x0))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Writing a custom function for the `scipy.optimize` interface." ] }, { "cell_type": "code", "execution_count": 55, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def custmin(fun, x0, args=(), maxfev=None, alpha=0.0002,\n", " maxiter=100000, tol=1e-10, callback=None, **options):\n", " \"\"\"Implements simple gradient descent for the Rosen function.\"\"\"\n", " bestx = x0\n", " besty = fun(x0)\n", " funcalls = 1\n", " niter = 0\n", " improved = True\n", " stop = False\n", "\n", " while improved and not stop and niter < maxiter:\n", " niter += 1\n", " # the next 2 lines are gradient descent\n", " step = alpha * rosen_der(bestx)\n", " bestx = bestx - step\n", "\n", " besty = fun(bestx)\n", " funcalls += 1\n", " \n", " if la.norm(step) < tol:\n", " improved = False\n", " if callback is not None:\n", " callback(bestx)\n", " if maxfev is not None and funcalls >= maxfev:\n", " stop = True\n", " break\n", "\n", " return opt.OptimizeResult(fun=besty, x=bestx, nit=niter,\n", " nfev=funcalls, success=(niter > 1))" ] }, { "cell_type": "code", "execution_count": 56, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def reporter(p):\n", " \"\"\"Reporter function to capture intermediate states of optimization.\"\"\"\n", " global ps\n", " ps.append(p)" ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Initial starting position\n", "x0 = np.array([4,-4.1])" ] }, { "cell_type": "code", "execution_count": 58, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ " nit: 100000\n", " success: True\n", " nfev: 100001\n", " x: array([ 0.9998971 , 0.99979381])\n", " fun: 1.0604663473448339e-08" ] }, "execution_count": 58, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ps = [x0]\n", "opt.minimize(rosen, x0, method=custmin, callback=reporter)" ] }, { "cell_type": "code", "execution_count": 59, "metadata": { "collapsed": true }, "outputs": [], "source": [ "x = np.linspace(-5, 5, 100)\n", "y = np.linspace(-5, 5, 100)\n", "X, Y = np.meshgrid(x, y)\n", "Z = rosen(np.vstack([X.ravel(), Y.ravel()])).reshape((100,100))" ] }, { "cell_type": "code", "execution_count": 60, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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ZanbYbjFokPYj3ry5lGuvtc/jOnFid9LSTvLttweZMaN1EZeY2JvPP8/h88+z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\nblcmZOdUO/PhALrs3njrctR+IYQN/TprNPbje0xnY3j93++fWQdzwvMad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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ps = np.array(ps)\n", "plt.figure(figsize=(12,4))\n", "plt.subplot(121)\n", "plt.contour(X, Y, Z, np.arange(10)**5, cmap='jet')\n", "plt.plot(ps[:, 0], ps[:, 1], '-ro')\n", "plt.subplot(122)\n", "plt.semilogy(range(len(ps)), rosen(ps.T));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Newton's method and variants\n", "\n", "Recall Newton's method for finding roots of a univariate function\n", "\n", "$$x_{K+1} = x_k - \\frac{f(x_k)}{f'(x_k)}$$\n", "\n", "When we are looking for a minimum, we are looking for the roots of the *derivative* $f'(x)$, so\n", "\n", "$$x_{K+1} = x_k - \\frac{f'(x_k}{f''(x_k)}$$\n", "\n", "Newotn's method can also be seen as a Taylor series approximation\n", "\n", "$$f(x+h) = f(x) + h f'(x) + \\frac{h^2}{2}f''(x)$$\n", "\n", "At the function minimum, the derivtive is 0, so\n", "\\begin{align}\n", "\\frac{f(x+h) - f(x)}{h} &= f'(x) + \\frac{h}{2}f''(x) \\\\\n", "0 &= f'(x) + \\frac{h}{2}f''(x) \n", "\\end{align}\n", "\n", "and letting $\\Delta x = \\frac{h}{2}$, we get that the Newton stpe is\n", "\n", "$$\\Delta x = - \\frac{f'(x)}{f''(x)}$$\n", "\n", "The multivariate analog replaces $f'$ with the Jacobian and $f''$ with the Hessian, so the Newton step is\n", "\n", "$$\\Delta x = -H^{-1}(x) \\nabla f(x)$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Second order methods\n", "\n", "Second order methods solve for $H^{-1}$ and so require calculation of the Hessian (either provided or approximated using finite differences). For efficiency reasons, the Hessian is not directly inverted, but solved for using a variety of methods such as conjugate gradient. An example of a second order method in the `optimize` package is `Newton-GC`." ] }, { "cell_type": "code", "execution_count": 61, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from scipy.optimize import rosen, rosen_der, rosen_hess" ] }, { "cell_type": "code", "execution_count": 62, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ " success: True\n", " nfev: 38\n", " fun: 1.3642782750354208e-13\n", " nit: 26\n", " njev: 63\n", " nhev: 26\n", " status: 0\n", " message: 'Optimization terminated successfully.'\n", " x: array([ 0.99999963, 0.99999926])\n", " jac: array([ 1.21204353e-04, -6.08502470e-05])" ] }, "execution_count": 62, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ps = [x0]\n", "opt.minimize(rosen, x0, method='Newton-CG', jac=rosen_der, hess=rosen_hess, callback=reporter)" ] }, { "cell_type": "code", "execution_count": 63, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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R2GgkLc1SC56QEM7AgQF8//1hzp5tPzj18DDw6KNjqatr5pVX9tp1\nDs4QHx/C5s03kJQUzoYNhUyfvvqSSDRUVWXlyjymT1/N7t1lzJs3gI0b53WqddyF7/evf+0C4Ikn\nEm1u+9Zbmsb53nt/LvY7cOB+ysoe46GH4gHYuvU4BoOOqVMtLePWrtWC6euvty3HMOuXR4zoZbd+\nuaHBRGZmLcOHe+Pp6fh369AhPcHBJkJDncsOH6mCZlUiytc1/XK9vgwktdtbyl3JRIa1FP4VCVmG\nQCC4tHSLgLmzCv/MOmZXZBnDhxk5fUbHyZOOp7LGjNGWq/ftsz87cs01mnXZxo22A8aQEG9Gj+5N\nSkoxFRWWQa/ZRuyrr7ItxiRJ4he/GE59vZHlyw/ZfJ/Fi2Po39+fTz7J4OTJi5flCQnx4osvZvLk\nk6M5daqO22/fwJIlGy6ai0Z2dgU33fQjv/71NmpqmnjhhUTee28qPTqpq5g1kpML2bWrmJkzI2xm\nl3NzK1iz5igjR4Yyfrx1K7vKynr27y9l/Pi++PlZHvO6dXl4e7sxebJtOca2bcU0NZmYNs1+/+WM\njBoaG1VGj3ZcjlFZCScKdQyLcX6JPbNC+6/scktsbSVHZJi7LoP6aAGzKPwTCASXmm4RMHu1ejG7\npmM2W06ZLaicwbxsbF5GdgRnAubp0/sAsHlzcYfbzpo1EJNJbfXaPZ9p0yKQ5V6sWJFNaanl+y9Z\nEouvrzuvvbaHmpr2uyq6u+t57LGxNDZqvsEXE51O4uGHR7Bx43wmTuzN+vWFTJ68ij//eXeneTZn\nZ1fwyCPJTJ++muTkEmbN6su2bQu4++4oh90eHEFVVV58cTcAjz+eYHPb11/fg8mk8vDDY9s9pu3b\nCzCZVGbMiLQYy82tIDe3kqSkfnh52W7hvXGj1jXZ/KBmD2b9svn6doRDWeaCP+ezw4daZPtRLhf8\nmQNm4ZDRVQnt6Y2Xh0EU/gkEgktO9wiYm80ZZledMrSbsrNezPBzx78DBx0Pus0ZOEc6/vXp44Ms\nB5CcfJL6ettSjmuu0ZbiN2w4ZjGm00k8/vh4mppMVhuV9Ozpxf33x1FeXsuHH9puZLJwYRT9+/uz\ndGkmxcUXv798TEwg33wzm3feSSIkxIv33stm/PhvuPPOjaxbV2AzwLfGuXONfPttPrfeup6kpG9Z\nvvwIERF+LFt2DZ9+OoOBA/0v0pn8zPbt9mWX6+qaWL36MH37+nH99ZaNSMyYP9MFCyy7//300zFA\ne6CyhaqqbN5cRECAO3FxQXachYY5YHYmw5x+QPsujoh1Ptg91GIN7rIHc8sKlpBkdF10kkRkmB+l\nZ2qptlKPIRAIBBeLbhEwe5qCkVS9ywFzoDuEeJg47ELAPGqUdlM+cMDxgLlXLzeGDPFkz54qmpvt\n12tOnRpOXZ2R1FTbramHDw8mONibLVsKrDY7WbJkBH5+7qxYkW11/IEHxuDlZWD58kybzVLc3PQ8\n/ngCDQ1G/vOfS9NlV5IkFiwYyO7dN/POO0nExQWxbt0J7rxzE1FRn7Fo0U+8/PIBVq3K5+DB0xQW\nVlNYWM3x4+c4cKCcb77J44UX9nPzzT8SFfUZ9923lS1bihk/PpRPPplOcvKNzJxpW67QWaiqynPP\naQV7f/yjbe3yunW5VFU1ctNNUeh01rPLhw6dYufOQqZOHcCIEZaFeps3Hwc6boedm3uOwsIaJk8O\nw2Cw7zuiqiopKVUEBRkYONBx+Yr5ezRqlAsZ5kroYVAJ9XDVIaMUVEmzshR0WSJb/JjzRZZZIBBc\nQmyvz3YRdOjxNAa7XPQHms5x+2kD1U4mJ4KDVPqEm0g/qBX+Obpqn5joz9KlZWRk1BAXZ19GburU\ncN5+O4utW4uZMqV9balOJ5GU1I8VKxQOHSpn+PDgNuNeXm7MmTOYL7/MYs+ekyQktJ2rRw9PZs2K\n5NtvD5OZecqiU9z5LFwYxRtvpLF8eRYPPDCawYMvTmHchbi56ViwYCA33BDBvn3lrF1bwE8/FbJp\nUxGbNhXZNcfIkb2YNasfc+b0Z/jw9n2PLxbff3+U/ftLueGGIYwcaTs4++KLLABuu20YALt2FbJ0\naQYvvjgDHx+tKO+jjw4AWO3+V1fXzK5dRURH9yIszPb1tmWLJvuZNq2P3edy7FgDJSVNzJvX0ykJ\nS/pBPYGBKgP6OxfsNhjhaBWMCTC65JAB2gqWh6kneqy3HBd0DVo7/hWdJTay12U+GoFAcLXQLQJm\n0HTMZwzpNEk1uKmOW1eZifI1sf00ZJ0FZ111R440smatGydPSoSHO3ajT0z0Y+nSMlJSquwOmBMT\nQ3F317FtW8dFj7NmDWTFCoXvvjtqETAD3HDDUL78Mot1645aBMygtdL+9tvDfP75IZsBs8Gg489/\nnsDdd//As88m8/HHc+06l85CkiTGjAlmzJhgnnxyDMXFNWRlVZCXd468vHNUVWlPRJ6eBtzdJQYP\n7kFkpD8xMYGEhnpf0mM9n6YmI//4x04MBh3/8z/jbW6bl1fB5s3HiI8PY8gQLbC//faV1NQ0MWfO\nIObNG0pjo5FVqxTCwnyZOdPyit6x4wT19UamTu3f4bFt3aoFzFOn2l/wl5KiSXLGj3e8YUllJRw7\npiNpSrPTwW5urQ6j6nrBn5F6GvUVBDQOc2me7oosy2HANkVR2tf9dBHMAbPQMQsEgktJtwqYQcsC\nuTU735p4aMuNNasSBvZwbo6RI0ysWavpmMPDHTN1TkzUAovdu6t44AH7iot8fNyIjw9m165SKioa\nCAxsf+l71qyB+Pi48fXXCn/6U6JF1m/SpH54eurZuDGfv/51isX+M2cOJDjYm6++yuLJJyfh5dW+\ntdicOZEkJISxdm0eu3cXM26c/YFWZxMe7kN4uOWDVHCwH6dOXXydtb0sXXqI/Pyz3HNPLJGRATa3\nfeedfagq/PrXP7fLNuu1m5q063jbtuOcPdvAokXD0OstZRRff30YgHnzLDv/nU9zs4nk5BIiI/3p\n29d+LbI5YB43zvGA+WBGixxjpPNyDLO8ytWA2bx6dTXql2VZngy8BdhvvH0Z8fN2JyTAi/zic6iq\nelGLcwUCgcBMt9AwA3gbtd9y1wv/tBuruVDIGUaOMBf+Of7n69fPgz593ElNrbKpE76QKVPCUVXY\nscN2ltnb243rrhtEQcE50tIs/1ZeXm5MnNiP7OzTFBVZBpJubnpuv304lZUNrXKA9pAkib/+dRIA\nTz+9w6HzuRqpqmrgpZd24+3txuOPj7O5bWlpNZ99dsii2C8iQnvKCw/XAtTvv9faXc+fb9kuu7a2\niXXr8oiI6MGYMbYDwfT0cqqrm5g82TGHiN27q/Dz0xMT43jWPr1FvzxihPPBrrmAd4hP5wTMXsZu\nETN2NncDiy/3QThCZB9/auqbKa1wrZmVQCAQ2Eu3CZjPzzC7wtAWp4xsyw7SdmO+wTvjlAFaNq68\nvJm8PPs72E2cqJ1/cnLH53/DDVqA9d13R62OT50aAcCWLcesjt97bxyennpeeSWVxkbb2b+EhDDm\nzh1EWloJq1cf6fDYrmZefTWN8vI6fve7MYSE2A4w//vfVOrqmnn00XFtCvBSU39FWdljJCb2wWRS\n2bDhGEFBXowZYxnobtx4jNraJhYsGNJhFm7HDu26mjLF/oC5rKyJvLx6EhJ80esdz/IdzNDOqzMy\nzK5ayl0JHsyyLL8ly/I7F7ymk2X5eVmWi2VZrpJl+StZlttorRRF+ZWiKAcv7dG6hrmBSV6xCz/k\nAoFA4ADdKGDWbuS1LjYv6ekOwe6mVu9WZwjqpdK3j4kDBx3v+AeQkPCzLMNe4uKC8PY2dJhhBkhK\n6oefnzs//JBrNes7a1YkOp3E+++nWx0PDfXhrrtGUlRUxdKlHd9Hn3pqIm5uOp59did1dU72Hb/C\nOX78LG+9tZ+wMB8eeCDO5rY1NU188UUW4eG+LFrUvqY2M7OMsrIapk2LsOqgsXq19sA0f37HstTt\n27XrasIE+wPG1FTt+jVfz45y4KCenoEm+vZxfmVCqdLh7wa9XXTIqDOYLeW6pwezLMt/B+63MvQM\ncAewBJgM9AVWXMJDuyiYnTJyRQMTgUBwieg2AbOnqRc61c3lgBm0bNSxaqh2IbYbMcJIebmOkhLH\nM2sJCZpGNDXVfj9md3c948aFcPjwWU6erLG5rYeHgRkzIigoOMehQ+UW4wMHBjBv3hAyM0+xffsJ\nq3M8/HAC3t4G/u//9mEy2Q5GBg4M4P77R1FQcI7XX7+4zUy6K3/963YaGow89dREvL1tt5xevVqh\nurqRxYuH4+bW/iqGWY5xzTWWxX719c1s2HCMgQN7MGyYbU/l+vpm9uwpIyYmkF69PO04Gw1XAubK\nSjh+XMeIESanC/4ajJBXqyOmh+NuNRdSqy9GUvXdzlJOluWBsixvAn4NHL9gzA14GPgfRVE2KYqS\nDiwCJsmybNvPsIvTP9QXg14nOv4JBIJLRrcJmCV0eBl7U2s4iYpr2aToFh1ztgstss2NFpzRMUdH\ne+Prq2sNOOzF3H3tp59st8kGuPZarePbunV5VscfeGAMAG+9ZT3ADQ72Zt68oRQUnGXXro7f7/HH\nEwgN9eG11/Zy/LhYJj2fzZuPs3ZtHuPGhXPzzXKH23/ySQaSBLffPrzdbaqrG/nggwP06uXF7NmW\nRbDbt59oddPoSI6RnFxCfb2RpCTHijb37KnGYJCIi3PctSYjs0W/HOu8HONIjY5mVWKki86AKiq1\n+pN4GkPQdZ86aDMTgAIgFjh2wdgowBfYan5BUZTjLdtNtjJXt6meM+h1DAj1pbCsmsYm568hgUAg\nsJduEzCDtlxqkhpo0J1xaZ5oP3PA7HyLbHPhn/nG7wh6vcSYMb4cPVrPmTP2G0LPnKkFzBs2dBzA\nXnPNAAwGHRs3HrM6Pnp0GKNH92bTpmOUlVnPWP/iF1rAZvb5tYWvrzt/+9tE6uuNPPXUtg63v1po\naGjmz3/eik4n8c9/JnUYvO7eXURa2klmzoykXz9Np7liRTaLF3/TRk/+5ZdZnDvXwL33xrX6MZ/P\njz/mA3DttR2bJ5ofwGbNsr8ddn29iYMHaxg+3Btvb8e/A2b9sisd/rJaHnhjbZuNdEiTVEWzrqZb\nyjEURVmmKMrdiqJY62pk/kAvNCgvBqx16elWVbuR4T0wmlSOl3YdFxyBQHDl0r0C5mYtA1bnoiwj\nxk8LPHJc6Pg3fLh2o8/IcG6O+HhtGdvcVtgeBg70Z/Bgf7Zt67hNtr+/BwkJYezbV8qpU7VWt7n5\n5ihMJpVvv1Wsjo8b14fo6CB++OEoJ092fFO6+WaZ8ePDWbcu32p77quRt97aT25uJb/85QhiYy19\nsS/k9df3APDb38a3vvbgg2vZuPEYmZlaTKSqKh99dAA3Nx1LlsRazKGqWjFgYKAn8fG2g0BVVfnp\npxP4+7uRkGC/Q8SBAzU0NalO65czWizlYl3IMJsfeEe42DOnVt+99cs28AZMiqJc+EduACy0N4qi\nXPye8J3Izw1MhCxDIBBcfLrV+uP5hX+BTe0vV3eE7GdC4ucMlTOEhqiEhppavWQdZexYTce8Z081\nM2faf8e/5pq+vP12FikpZR02mJgxI4KdO4v46ad8br/dsnjshhtknnxyC99/f4T77httMS5JEvfd\nF8djj/3Ea6/t4Z//nG7z/SRJ4vnnpzJjxuc88cRmtm79Bb6+V2/XtLy8Sv7zn1SCgrx44omOJaN7\n9xbz4495jB0bzrhxlt32zO3UDx4sIyfnNPPnDyU01FIOcehQOcXF1dx0k9xhi+sjR85y4kQNN9wQ\ngZub/d+HPXu0B6j4ePs9m8/nYIYOPz/nO/zBz5Kq4QHQ7ELMZC7487ryAuY6QCfLsk5RlPNT+R6A\n7UKIDggOdu5BqTOJH67j7dWHKDpT6/TxdIXz6CzEuXQ9rpTzgCvrXJylWwXM3q0Bs2vWct56GOSn\nZaicaW9tJna4iQ0bDZw+LdGrl2M3/jFjzAGz4zrmt9/OYtOmog4D5vnzh/D3vyfz5Zc5VgPmkBAf\nRo8OIzW1mIqKOgIDvSy2ufXWGF55JZWPPz7Ib34zhv79bXd7iYkJ4qGHRvPKK3v5979TePZZy+Yo\nVwOqqvKHP2ymvt7Iq68m0aNH+81mzDz/fDIATz01uY104/7749i48RgDBmgZtZUrcwBthcAa336r\nFQPaI8fYuFFbrb/mGvvbYQPs3autjDgTMFfXQG6ejvGJRnQurHFlV+kI9zQR6KHjlPPTXMkZZnNF\nbxhtZRnhWMo0HKIrNAPSqSr+3m7k5J926ni6WlMjVxDn0vW4Us4DrrxzcZbuJclouaHVGYpdnmt4\nAFQ0SZQ2OF/nEjvcrGN2/M/Yo4eBmBhv0tKqaWiwX8c5fnwo3t4GNm/u+H7Xv78/Eyf2YefOIk6c\nsJ6Cmz07EqNRZdOmY1bH3d31PPHEBJqaTK0BXUc89lgCkZEBvPvuAavNU64Gli/PYvv2E8yaFdHq\ni22L7Oxytm8/weTJ/UlMbBu8/uMf09i16x5CQ31RVZXvvz+Cn58706dHWMxjMqmsWJGDn587s2dH\ndvi+mzZp19G0afYHzCaTyu7dVfTp406fPo6vIGRl6VBVidjhzuuXK5vgZIOOKBc7/MF5AXPzFRcw\nHwCqgSTzC7IsRwARQLcvNJAkicjwHpw+10BldcPlPhyBQHCF060CZoPqjZvJ3+UMM0BsiwrCFaeM\n2FjXGphMmuRPfb3K/v3265g9PPSMHx+KolRSXNzxqqrZlWHlysNWx2fN0oKq5csPtTvHTTdFER0d\nxKpVCiUlHR+rl5eBl1+ejsmk8sgjG2houLq8mU+erOavf92On587L7wwza7Wve+9tx+Ae+8dZXO7\nnJzTFBSc45prBuLhYblAtH17AUVF1cybNxgvL9sLSLW1zaSklBATE0hoqP2d+hSljtOnm5k40d+p\ntsQHD7quX85p0S9Hu9iwBLSaCL3JGze1W0l4O0RRlEbgTeAlWZZny7I8GvgM2KwoSurlPbrOwaxj\nFvZyAoHgYtOtAmbQskD1ulOYsN9dwhrDWyrrs10o/Bs9Srvhp+1zbo4JE7SlgR07HPuxN0sxtm7t\nONM+d+5g3Nx07QbMMTHBTJ06gO3bC0hJsZ611ukk7rlnJEajyscf29cQbMKEvtxzTyyKcoYXX9xt\n1z5XAqqq8thjG6mqauTppye1trC2xalTtaxYkU3//v6tDzDtsWaN1oykve2WLcsEsMu+LiWllIYG\nk0PZZYCdO7Xr1Xz9Osq+dC3YjRvpfLBrftCN8nPNUsyEkTp9Kd7GMKTu46rWHtZ0YU8Cy4ClwEYg\nHxLeOW4AACAASURBVFh4KQ/qYtJa+Cc6/gkEgotM9wuYjWEgqdTpS12ax2xFpbhgLRcWphX+pR9w\nbo7ERC3g2LXLMW2Q2S9369aO3UICAjyZOrU/hw6Vc/SodTu+Rx8dB8C77+5rd56FC2MIDPTkww/T\nqamx72HlqacmMmCAP6+/vo+UFNdlNN2Bjz7KYOPG4yQl9WPJkva79J3PG2/soa6umQceiEev176S\nS5ce5MEH17ZpGlNb28T776fj6+vOzJmW+uSmJiPffKMQEuLNhAkdB8HmB66OtPAXkpxsDpidy8ju\n36/Hz09l0CDnA2azw02Mi5KMBl05qmS8IvTLiqJMVxTl/gteMyqK8gdFUUIURQlUFOV2RVFc8+Xs\nQgwM80cC8kWGWSAQXGS6XcDcWS2yB/uDu6S6lGGWJIgbZaSkRMfJk45np3r2dCM62ou9e6tpbLT/\nxi/LAYSEeLFtW7HV1tYXMnfuYAC+/jrH6nhiYh+GDw9mzZqjFBdbD959fNy4556RnDlTz6efZth1\nnL6+7rzxxmwAfvvb9Zw7d2XrDI8cOcPTT+8gIMCDV1+daZdcoaSkmg8/PEB4uC9Llvzs/PL44xtY\nsSK7zUPO0qUZlJfXct99cfToYdmRLzm5iNOn65g7d3Br4G2LbduK8fDQkZBgf3c7VVVJSakiLMyN\nAQM6LmS8kLNntYK/USNdL/jToTLYxYC5ttUhw/6W4IKug5eHgfAgH/JPVnXYkVQgEAhcodsFzN4t\nN7Y6F3XMbjoY7GvicLUOV35n40ZpN+z96c5nmevqtCYQ9iJJElOmhFFeXk9mZsfJotmzB6LXS6xa\nZV2WIUkSd92lSS6++cZ6UA1w332j8fNz5z//2cXp03V2HWtCQhiPPBJPQcE5fv/7TXYF+N2R+vpm\n7rtvHXV1zfznP9MJC7PPPeK553ZQV9fM738/3qomua5O03+rqsqHH6bj4aHn17+2tAAEWLMmF4B5\n8wZ3+L5lZXUcOlRBQkJoh1rn8zl6tJ7y8mbGj3dOv2xejYkb5byUQlUhp1pPhLeKl/MLRMDPvyPe\nImDutgwM96ehyUhRuUtOeQKBQGCTbhcwe3WStRxoBUO1RokTdc5rF0eN1G78zrTIBhg/XlvWdlSW\nMXu21qhrzZqCDrft2dOLxMRwdu8uorTU+k1l3rwhGAw6Vq603sQEoFcvL/74xwlUVjbwr3/Z55gB\nWtvssWPDWLXqCJ9+2n5xYXfm6ad3kJVVzp13DmfevI5dMQCOHz/LV19lEx0dxOLF1uUbQUFaMd6O\nHSfIy6tk/vyh9Oxpaf9nMqmsW5dHr15ejBvXscTip580x7Hp0x3TL5uvU7OcyFHMAfOoUc5nhssa\nJCqbJJf1y/DzSpXXleeQcdUwqLXwT+iYBQLBxaMbBswhoEqtzQZcwWxJ5YpThjlgdiXDDJCS4ljA\nPH16H9zcdPz444mONwauvTYSVYW1a/Osjvfs6cW0aQPIyCjj2LHKduf55S9HMnhwIMuWZbYr37gQ\nNzc9b701m4AAD/78561kZFjr4tt9WbnyMB98cJDo6F4O+U6/8cZeTCaV3/1urIWE4u67R/KXv0wi\nOFgLmL/8MguAO+6w7OwHsH9/KSUlNcydO6TDZiUA69Zp182cOf3tPl6AlBRNK+pswLw/XTu2uJEu\ndPhrkVF1hqWcOcMsJBndl8hwzRs+V+iYBQLBRaTbBcw63PA0BXdKhln21W7aSrXz67qBgTBggIkD\nB7UmKI7Su7c7AwZ4sGePYxo8Pz93Jk7sTWbmGYqKOl6KnD9/CDqdxOefZ7W7zZw52lL+unW57W7j\n5qbnwQfjaW42tVqh2UO/fv688cYsGhqM3HPPGioq6u3etyuTk3OaRx/diI+PG++/f53d8oaSkmqW\nL89kwIAeLFhg6WjxwgvX8P/+XwLu7nrq65tZs+Yoffv6kZBgPSNsltvceOPQDt+7traZbduKkeUA\nIiMdK9zbvbuKnj0NyLJlltseDhzQExxsIjzceWlOTssDbmdYytXqT+JuDMRg2Sla0E3oE+SDh5te\nFP4JBIKLSqcEzLIsh8iy/LEsy8WyLFfIsrxOlmX7LAKcwNvYmybdWZqlWpfmkVsyVDkuFP6Bli2r\nqJA4XuCctCMx0Y/KSiM5Ofbpgs2YZRnr13ecZQ4L82XOnEHs21dKdvZpq9vMmhWJwaDj448P0tzc\nfjByyy3RBAV589FHB+3WMgPMnDmQxx4bS0HBOX71qzU0Nbm+pH45KS+vZcmS76itbeKVV2YweLD9\nLc5feimFxkYjDz88tjUjXFfXRHV1o8W2W7Ycp6qqkfnzh6LTWV5jjY1Gvvoqh6Agr9aHHlts336S\nujojs2b1tft4AYqLGzhxopGEBF+n9MunyiWKinWMGmlyursmgNLyfZVdzDAbaaRBf1rol7s5Op3E\nwDA/istrqLvKPN8FAsGlw+WAWZZlCVgFDAbmAeOBs8BGWZbtjyAcwKvZXPjnmrXcAG8VL52K4oIk\nA2Bky/LyQScbmCQkaMvbqamOyTJmzNACno0bC+3a/u67RwDw1VfWC/tCQnxYvHgYubkVrFiR3e48\nnp4G/t//S6C6upFXXnGs/8Ef/5jInDmR7NhRyJ/+tLXbFgE2NDRzzz1rKCg4x+OPJzB/vn26ZYCM\njLL/z955h0Vxrv/7nt2lLV26ShHQEVQUe+8aNbHHaDzRJJ5UY3oxzeSY5OR8zy/GNHPSNXaTaBJ7\n7x0rCspaAEFRQEG6lN35/TEsNsru7BpL5r4uLtrMyzvs7Mwzz/t5Pg9z5x5BFH0YM+bqc+WoUUuI\nivoGo/H6QNAsxxg8uPrs8fr1qeTkXOHBB5vi6Fj3OWjWL/frF2zxnAH27pWb1pjPV2uJj5ffZ61s\nkGOAXPCnEyTCXW0LmK/KMVT98t1Oo/oeSEDKeTXLrKKicmuwR4a5JdABeNxgMBwwGAxJwDjADbjf\nDuPfxNXCP9u8fTUCNHEzcbJIQy0J1TppVdmA4XC8sn9nhw7KAubQUHeaNPGszBjWnVl54IHGeHo6\nsXhxUo3yj1de6Yijo5bPPttbq0TkscdiCA72YObMwyQn51o8Z41G4Ouv+9O8uS9z5ybwzTeWyzru\nFCRJ4tVXN7F3bwZDhzbm9dc7WLXvO+9sRpLgo4964uAgB7gmk0RcXAalpcbrVgCOHctmxYqTtGoV\nQOvW1WdCf/lFDqhHj46y6O9v3HgOLy9H2rb1s3jecPX8VBowmwv+WsbY5pBxolBDhKsJRxuvXqp+\n+d4holLHrHb8U1FRuVXYI2BOAx4wGAzXepaZw89bkmG2l7UcyDrIUpNAcrENLbKbm50ylGWYIyOd\nqVdPx549BVZnXPv0aUhJiZE9e+rOtjs76xg8OJILF4pq7OrXoIE7I0Y0JSXlMtu21ezA4eSk4/33\nu1NWZuSNNzZaNW83N0fmzRtMYKArU6fuYMmSmp057jQkSeLDD3fx669JtG4dwBdf9K1WJlETmzef\nYc+ecwwYEEGPHqHVbuPgcPVcnDFjPwCvv96pWhlEbu4VNm48Q3S0L82a+db595OSLnPuXBG9ezew\nqDjwWvbuLcDJSaBlS1er9jNzpNJJpqUNHf7SSwQKKgQ76ZdVS7l7BbVFtoqKyq3G5oDZYDDkGAyG\n1Tf8+EXAGVhn6/jVYa/mJQDRldZUifnK/xUeHhAebuLIUWWFfxqNQOfO7pw9W0ZqqnXNPfr0kYvA\nNm2qPgC+kWHD5GX9P/44WeM248fLTgxz59beBnvw4Mb06hXKtm1pbN9umVuHmfr13Zk/fwju7o5M\nmrSO5ctPWbX/7WL69H3MmHGAiAgv5swZjF7vYPG+kiTxySe7ATkAvpZrg+7AQDkgPXs2nz/+SCIq\nyoe+fW/u7AewYsUpystNjBhRd7EfwIYNsnynd2/r9Ms5OeUkJBTTrp07Tk7K3iuHj2gJDDQR4K9c\nhpNY2ZmzmR0CZlWSce/g5eaEj4cTyRl5d63MS0VF5c7G7i4ZoigOAT4GPjUYDLckdehs8kEjOdgl\nYG7mId94j9mqY25hJC9PIPWMsmqmrl3lJUVz22FL6dAhAL1eZ3HA3KVLA3x9XVi58tRNWlkzbdoE\nIYo+rFuXTEFBzQG8IAi8/XZXAD7+eIfVN6oWLfxYuHAozs46nn56DatX1+zOcSfw5Zf7+e9/9xAS\n4sHixcPx99dbtf+yZSc4cOA8998fSYsWN3fXmzSpLbNmDcbDQ+6gt3BhIkajxFNPta6xyG7ZMvnB\nx/wgVBdbtihthy3LMbp0UdYOOzNL4MIFDS1b2Bbomt+n0fbwYNadQ5C0slXl3xxRFINEUaz5Kfou\noFF9T/KLy7mYd2848KioqNxZ2DVgFkXxMWAxsNBgMEy259jXIqDBxRhEse48ErbdgKPczAGzbS3D\nYip1mUePKhuna1c5ENmxw7qA2clJS5cugZw8mUd6emGd22u1GgYODOfixRLi4qp/4BAEgeHDRUpL\njVXd42qiZcsAhgxpwsGDF1ixwvr7bbt2QSxcOBRHRy1PPLGa5cvvvHu2JEl8+mkcH320iwYN3Fiy\nZDgNGlin4y0pKeeDD7bj4KDhvfeq92p+773u3H9/YwRBwGSSWLQoEVdXB4YOvdl2DiAnp4QdO84S\nGxtASEjdgWxRUTl792bSokU9/P2ts4XbsUNuCtGtm7KA+ehR+VITY4N+Ga6uBNmaYZaQKNZm4GIM\nQIPlnQ7vRURR7AZsAAJu91xsIUKVZaioqNxC7HanEEXxHeBD4EuDwfCSJft4e+vR6ZQFmPUIJZ00\n3PzK0GNd8ZIZPz93/IAgFzhepMPPT1kxE0DPHjD1Q0gyuPDPCdbv7+vrRmCgIzt3FuDra51t1/Dh\nkaxff5adO7N4/vnal5f9/Nx55JEY5s5NZOXKZIYMaVrtdhMmtOb//m8Xv/12nOeea1/rfP7f/+vH\nqlWneP/9bTz4YPOqDKmlDB4ssmrVaB544FeeeGI106dX8NJL7a0aozZseV0rKkxMnLiaH344TGio\nJxs2jCUysp7V47z55gbS0/N5/fXOtG9/1Z1i/Pg/KC83sXDhyOu237btDOnp+Tz+eCsaNfKpdsxl\ny05jNEqMGdPsumOs6Xh37jxNWZmJBx5oZPX/ZPfuQlxdtfTvH3idxtpSTlQ+B3Xv5oSfn3Xnx7UY\nisHbEWKC3a6zprP2eK5wmQqK8dfE2HR+3CM8BjwM7LjN87AJs475dEYeHaLv6thfRUXlDsQuAbMo\nim8AHwDvGgyGjy3dLzdXuY+yRu8HrpB++ST1yq1vOuDn5052trzMHOXqwqaLOk5mFOBluST1OkJD\nQKNxY8dOI9nZ1vkpm+nUyZ0//rjE7t3ZNG5seQawWzd/BAEWLTIwZkx4jduZjzkmxoeGDd2ZNy+B\nyZPb4+5+cwDj5eVI376N2LAhhV9+OUqfPtVraAHq1XPipZfaM23aHp5/fhXTpvW1eO5moqPrsXTp\nCMaOXc7LL68nKSmbqVO7WVVQVx3Xvs7WUlhYxjPPrGHdulRatPBjwYIheHo6WD3eqVM5TJu2i5AQ\nDyZObFO1f1FReZVO/OOPe+Lm5li1z48/HgBg0KCIGv/eN98cQBCgb9+Qqm1qO97582U7wV69gqw6\nhszMMpKSiund25PLl+tuklMd23e4ADrCwwvJzlamMS02wqkCNzrVM3Lx4tX3mJLX+LLDCfACXbEf\n2UXKzg/z376diKL4LaAxGAxPXfMzDfBv4FHAHVgDPGcwGKptsWkwGP5Zud+tn/AtJDTAHa1GIDkj\nH0mSFHmFq6ioqNSEPXyYY5AvzjOBn0RRDLjmwzqRpxXozYV/Osu0u7Vh1kMey1cuy3BzA1E0ER+v\npbxc2Rhmfai1OuaAAD1t2/qzZ08WFy/Wrd/TajWMG9ec4uJyfv/9RI3bvftuVwQB/u//dtWpT37p\npQ5ERfkwZ84RDh9W5l7SooU/q1aNokkTb7777jBjxiwlK8u25jRKOXbsIvfd9wvr1qXSq1cIS5eO\nJCBAmTvE++9vxWiUmDq1B66uV5/IrrXju/br9PR8Fi1KJCTEky5dqvdKTky8yIEDF+jTJ4zg4Lpl\nEmVlRtatS6dhQ1datqw+Y10Tu3bJAWXnzsrkGJIEBw9pCQkx4eervCDLUKBBwl4OGbIcyaXi7i34\nE0XxA+Cpan41Fdna8xGgG9AQWSp3T+PooKWhvxvJGfm8PGMnX/wWz7KdKRxNvkRhicKLsoqKikol\n9tAwj64cZwKQccOHRdIMJeiNctGSPQr/zDfg4zZ2/GsTa6TkikBSkrJxOneWs1W7d1uf8Ro0KAST\nSapqSlEXY8ZE1dkqOzraj4EDI4mPz6zRhs6Mo6OWjz7qBcC//rVNcaV6cLAHK1aMom/fMLZsSaNX\nrwVs2VKzvZ29kSSJuXMTGDDgF06ezOWpp1oxb97g67K/1rB+fTLr16fQrVswgwZd34UvMNCt6uug\noKuZyunT91BebmLy5E41Wr8tWJAIwCOPWNZQc9euTPLzyxk0KMTqzNuuXfIDnNKCv5QUgdxcgTax\ntumXzXUG0XYJmOXiR/N15G5CFMVGoihuAp4GztzwOwfgBeAtg8GwyWAwHAbGAF1FUexYuc1UURQP\niaJ4UBTF1n/1/G8lY3pH0lb0w0ErEH/6En9uT+GzX+N54YvtTP52F98uTWBtXBon0i9TWFJOeYUJ\nk+qqoaKiYgE2SzIMBsM7wDt2mItV6Cu7/dnHWs4+ThmtY03MWwAHDmlpocANICLCGX9/B3butH5J\nceDAEKZO3c/q1Wk8/HDdXeeCgtzo1SuEjRvPYDBcQhSrzzo++2wbVq06xXffHaRTp9qtyLp1C6F/\n/3DWrUtm6dITDBumbInXy8uZefMG8/33h/nww52MHv0njz8ew+TJHfH2tl5+YykpKZd5991trF+f\nipeXE999N4CBAyMUj1dYWMbbb29GqxX497973fR6+vq63PS1ObvcpEk9RoyoXl9eWlrBb78l4een\np1+/MIvmsnq1/NAxcGCI1cexa1c+er2GmBhlC0YHD8uBbuvWtgXMxyvfn1FudnDIqLxu3I0BM9AZ\n2f9+DPDLDb9rhdw0aqv5BwaD4YwoiqnI2eY9BoPhfeD9asa96zUMYog3Yohs/59XVEbK+XxSMvLl\nz+fziTueRdzxm5UpggBajQadVkCrEdBqNfJnjYCTo5ZgPzfCgjxoFOROSIA7Tg62FYmrqKjcfdy1\n5eFanHEy+tjc7Q+gsZsJnSDZ7JRhDggOHdLy2HjrlwAFQaBTJ3eWLs0hJaWU8HDLg8PwcA+aNPFk\n69YMSkoqcHGp+6UdPTqKjRvPsGSJgbff7lztNu3b16dZMz/WrUsmO7sYP7/ag6YPPujB9u1pvPnm\nRjp3boi/vzIZg0Yj8MwzsXTsWJ+JE9cxc+YR/vzzBG++2Ylx45qh1drP4KW4uJyvvjrAjBkHKC01\n0rVrQ774oq9FUofamDp1G2fO5DFpUluaNr3aVOTSpRKcnXW4ujqwceMjNG/uVxVM//xzPEajxKRJ\n7Wo8xvXrU7l8uZRnn42t6hRYG5IksXZtGl5ejnToYF0xVHZ2OSdPXqFnT09FxX4ABw9WBsw2Z5jl\nv9/UHhlmXQYOJg8cJGXn5+3EYDDMB+ZDtbpj81PtjUtCGUBdvdDvqVSrp6sjrSJ9aRUpv/ckSSL7\ncgkp5wtIOZ9PTmEZJSVlGE0SFUYJo8mE0SjJ35skjEYTRpPExbwrnMsuYs8xuTmURhBo4OdKoyB3\nOYgO9KCBnys6O16TVFRU7jzu2oAZZB1zrmMCFUIJOsk6m6xrcdRApKuJpAINJkluma0EsYkJvV7i\n4CHlF85OnTxYujSHXbvyrQqYAfr3D2bGjAS2bz9P//513Ruhf/9GuLo6sGSJgbfeqr6TnCAIjBnT\njClTtrBkyXGeeaZNrWOGh3vzzjtdeffdLbz22gZmzx5iU/FNq1YBbNkylh9+iGfatL288cZmvv76\nAE8+2YqxY6MVSyUAMjOLmDnzCD//fJTc3CsEBbkydWo3hg5tbHPB0M6d6cyefYSoKB8mT776MFJe\nbqRv33mUlRmJi/vndX7MV65UMH/+UXx8XGrNzv/2m1y8N2pU9RnoG0lIyCEjo5gHHwy3urvfnj1m\n/bLy4rZDh7U4OEi0aK480JUkOcMcpjfhZuNVy0Q5VzTZeJZb5l19l6EHTAaD4cank1LkZlI1YjAY\nbHtCvMMRBAF/bz3+3no6RAdYXCxqkiSyckuqstSp5wtIyywgPauQbfHySoWDTkNDP1f0Tjo0Gjk7\nranMUJu/vvZ7X08XGvq50sDPDS83R7VAUUXlLuCuDphdjEHkkkCJ9gLuFTW7OFhClLuJpEIt6SUC\noXpliRatFlq1NLJ7j5bCQrkQ0Fo6dpQDkz17CnjkEesaKpgD5vXrz1oUMOv1Dtx/fwS//prE/v0X\naNeu+gKokSObMnXqNmbPPsI//9mqzqzmE0/Esnr1KdasOW2TNMOMo6OW555rzYMPinzyyV5+/fU4\n7767jf/+dw9DhzamT58wundvWK3bx41kZxezceMZ1q1LZt26FMrKTNSr58xrr7Vn4sTWNgXgZq5c\nqeDVV9ej0Qh8/vl9ODldfZslJV3i3Dn5Jp2aeplmza5aIq5de5qcnCs891xbnJ2rf2vm5ZWycWMq\nUVE+NG9umZ3iunVyd7/77qv7nLiRPXtk/XLHjspiqbIyOJqgITrKhLMNapqsMoFL5RraedtevFWs\nvQCCVFU4fI9RAmhEUdQYDIZrn1CcAGUWJ9Vwu91B7IWlxxHg70EL8erqjNFoIi2zgBNplzmZnsvJ\n9MucOZ+P0WT9vcPNxYHQIA/CgjwIDXQnNMiD0EAPXF2ss2y6V14TuHeO5V45Dri3jkUpd3XArK8w\nt8jOsEvA/Md5OYsVqle+dNyqpYldu3XEH9HSpbP14zRt6oKXl5bdu63XMbdt64eXlyMbNpy1eN/h\nw5vw669J/PZbUo0Bs6+vnn/8ozmzZx/h55/jefLJ2uuENBqB6dP706PHbN55ZzM9e4bi5WW79jgg\nwJVp03rz1ludmD37KDNnHmHevETmzUtEp9PQtGk9GjXyIjzci3r1nDGZwNXVkdTUyyQn53L69GVO\nncqtal8eGenNk0+2ZPToKKtaXNfF9Ol7SE6+zNNPtyY2NvC63x09elU/eaNsZs4c2WJuzJiaC/lW\nr5a9lIcPtzw7un59OlqtYHV3P5ALUJ2cBGJjlUkXjh3XUFYmEGurHCPf3OHPHi2x72r9cl2Yq36D\nuF6WUZ+bZRqKUWrVeCdhi+UkgJuDhtYR9WgdIfuymyQJk0mqknWYpMrPpkq5R+XX5RUmsnJLOJtd\nyLnsIs5mF3Is+RKJyZeuG7+ehxPuLo4gyOJyQRAQrvm66ueAn48rDerpCa8vB913s8ba1tflTuFe\nOQ64945FKXd3wGy2lrOHU0ZlIdHxAi0DApTf3M06zYOHlAXMGo1A584erFqVa7WOWafT0KtXA/74\nI4Vjx3Jp1qzuBhs9eoRQv74bv/2WxJQpnWvM0k6e3Jnff0/i88/jeOSRFrjUkf1o1MiLV17pyMcf\n7+S11zbwww/3223Z0cfHhVdeac+LL7bl4MFMNm48w+bNZ0hKukRCwsUa9/P0dKJz5wb07duI/v3D\niIz0tvtS6K5d6Xz55T6Cgz2uk2KYKbnG3uraAsYtW86wfXs63buH1FiACTB3biKCYHkr7OzsEg4d\nukinTgF4elrXMOTSpXISE4vp3NkdJyeF+uVD8o07tqVtAXNSpYONXSzldJWWcvdmhjkeKAR6AAsA\nRFEMA8KAbbdtVn8DNIKARitgSS+ukAB32ja9uoJYWm7k/KUizmbJAfS5i0Wcyy7kQk4xEhJIICev\npaoHfpMk/1wCTpzNu24eDf1dCa/vSUR9D8LrexBQT49GlX2oqNiEGjBXYr4RJ9loLdeqlRwYHI5X\nPk6PHp6sWpXLtm15VuuYBwwI5o8/Uli58oxFAbNOp+HRR1vwn//s5tdfk/jnP1tWu52vr54JE1rx\nxRdxLFiQwD//GVvn2JMmtWPjxlSWLTtB9+4hjB8fY9Wx1IVWq6FduyDatQvizTc7IkkSFy4UkZx8\nmYKCMgQBvLz0SJKJyEgvfHxcbqlWMCenhGefXY0gwDffDKpW3jFyZBQffbSD7t1D8PaWdfcmk8QH\nH2xDEOD996tvmw1w+HAm+/adp1+/MMLCPC2a09q16UgS9O1rvRxj+/Z8JEk+H5VyqNIhIzbWtkD3\neGVBrj09mO/FDLPBYCgTRfF/wDRRFC8B2cDXwGaDwRB3e2enUhNODlrCAj0IC7Re+iRJEpJOx/6E\nDJIz8jmdkceZC4WkZRay5ZC8qODipCM8yJ0gH1c0mspMdWXGWlP5GQQ0lT93cdLRIrweQT53X1Gs\nisqt4q4OmJ1MPmgkx6olVlto6CLhqpWqrKuUEtxQwtfHxOHDypfEzAHK1q15PPaYda4G/foF4+ys\nZenSVN54o+6gFmQv308/3cvPPx9lwoSYGoPKp59uzfffH+Sbbw7w+OOt6uzCp9Np+PbbQfTqNYd3\n391Mu3b1iYryrXUfWxAEgaAgN4KCrorH/6qlJEmSeOWV9Zw/X8jbb3ehffv61/3uww+306yZHyNH\nRpGS8vx1+65adYqEhGwefDDquiLAG5k5U5Zs1PRQUx1Ll6YCMHhwqBVHI7Ntm5y1siVgPnxYg14v\n0TjStkA3qVCDoyARrrePB7MgaXE2WqYBv8OpTjT7LvK1fS7gAKwGJv2Vk1L56xAEAf96etpHBdA+\nSr5fVBhNpGcVkpyRT3JGHskZ+SSm5pKYmlvHaFdZtBEC6+lp3cSP2Ca+NAryULPUKn9r7uqAWUCD\nizGQYt0FJCQEG2xENQI0dTMRn6+hzCQ7ZyiakwAtW5rYuEnHxUsCvj7WF4E0auREcLAjO3fm1jTM\nmgAAIABJREFUYzRKaLWWH5ebmwN9+jRk5cozJCXl0rSpd537+PnpGTQogj//PMm+fRdo375mLfOI\nEU2ZPz+BLVtS6d27bt14gwbufPnlAMaPX8ozz6xi7dqxNRa03c3MnXuUVatO0blzQ55/vt11vzt2\n7CIzZuwHYNgw8Sa7uG++kdtgv/xyhxrHz8srZenSk4SGetCzp2VeypcuXWHHjvPExvoSGmq9bmvb\ntnw8PbXExCjLMhUWwomTGjp2MKK1QVJplOQuf03cTFhp8nETEhIl2vO4GAPQcPfqPM0YDIbe1fzM\nCLxe+aHyN0Sn1dAoyINGQR70aSM7DRaWlHMp7wpSpayjStJR+bUkyT+XgJz8Kxw6eZGE5Eus2nOG\nVXvO4OXmSGxjP1o38UMM8VJt9FT+dtz1Z7y+IgiTUEqpJsfmsaI9jFRIAidslWVU6jXjFcoyBEGg\ne3dPLl82kpBgfWtoczZx2bJUi/f5xz/kQrP58xNr3e7RR2VZxaxZ8RaPPWBABOPHx3D8+EWmTNli\n8X53CwkJ2UyZsgUvLye+/nrgTQHxhg0pVV/Hx2de97sDB86zb18G/fuH07hxzRKaJUsMlJRUMG5c\n8zoz+2bWrEnDaJQYPDjM8oOpJDX1CmlppXTp4mHVA9u1HE3QIkkCrVralhU+UyxQYhLs4r9cLuRT\noSm+V/XLKio14ubiQGigO2GBciAdUd+TiAaeRDb0pEmwF2KIN01DvYkK9aZLiyAmjWjBFy924/kR\nLejSIpDyChObD53j018O8+KXO/h+WSJ7Ei+QkHyJpDO5nDqbR+qFfM5mydrri3klXC4spbCknLJy\n25sNqajcbu76VJ9Zx1yivYCzqeZiKUswV+AnFmho7qH85hxbqWM+dFhLn97KLhTdunkwf34227fn\n0bKldRm+/v2DcXTUsGpVmsWyjG7dggkOdmfZspN8/HEPXF2rL+pr1SqQtm2DWLs2mV270unc2TJt\n7NSpPdi3L4PZs48QHe3H449bLiu4k8nJKeGxx5ZSUlLBt98OokGDmzO52dlX3bw8Pa/XpM+ceRiA\nJ5+s/XVatOgYWq3A6NFRFs9t5Uq5u58SOcaOHbKdXPfuNsgxKh8YW9lY8JeQL2eCm3vYo8PfBYB7\n1VJORcWuODloiW3iR2wTP4wmEyfT8zh4IptDJ7PZcyyzqpmLJTT0c6NlpA8xET6E1/dAq7nr83Uq\nfzPu+oDZxXi1RbZ3ec12XJZgDpIT8rWMblCheBxzgdOBg8qXfLt0kYs/tm/PZ9Ik64qT3Nwc6NGj\nPuvXnyU5OZ/w8LoLSTQagVGjmjJ9+j5WrTpda1OMjz7qycCBC3nrrU1s2jTOoq57rq4OzJ07lPvu\nW8A772ymSZN6dOlifSHanUR5uZEnn1xJWlo+r73WkYEDI6vdrrj4qjNGeLhX1deJidksWZJE48b1\n6NatZplFUtIlDh/Ool+/MAICLHt4ys8vY+vWDJo3r6dIjrF9uxwwd+umvJeF+fw3F8IqJbGyrqC5\nPSzldOaCPzVgVlGxBq1GQ9NQOQv9cN/GpGUWYki/TFm5kQqjiQqjVPnZdMP3EsVXyjl1Lp+zuwtZ\nufsMrs46mof7EBPuQ/Pwerjrbfe/V1G51dz1AbO50t0eThnN3OUb+zEbC//8fCVCQ00cOKjFZAIl\nD9IBAY40aeLM3r0FlJebrG5LPGhQCOvXn2XNmjQmTmxu0T4PPRTF9On7mDcvodaAuXXrIMaMacbC\nhYksXXqCESMs6zgXEuLJrFmDGTFiMf/853LWrBlLWJhX3TvegUiSxJtvbmL79jQGDIjgtdc6Xfd7\no9HE1Knb6dYtmE6dGnLgwAXefrtLVUGlJEm8997WSoeMHrXKLBYtOg5gVXZ548azlJebGDTIMr3z\njce2Y0c+/v4OREYq98/ev1+Ln5+JsFDbOi6bM8zNbFj1MWO+TpgftFVUVKxHEAS5yUqg5Q/jpWVG\njp/J5cjpi8SfvsTeY5nsPZaJAITX9yAmwoeYCF8cXRwpLCmvcuwwu3jc6OqhdkdU+au5BwLmSms5\nXYbNY7npIExvIiFfiySBLe/Htm2MLPndgVOnNTRprOxG36WLB7NmZXHoUBHt21uXJezXLxhBgDVr\n0i0OmMPDvejVK4TNm9M4dCiT2NiaHTpefrkDv/56jOnT9zB0aBOLsswAHTs25L//7c2rr25g/Pil\nrFw5xqIOfXca33xzgLlzj9K8uR//+9/AmwLe9etT+PbbA3z77QH27fsnW7ZEXXeB37Qple3b0+jV\nK5Q+fWouniwsLGP+/ER8fV3o39/y5jyrV8tyjEGDrJdjnDhRQnZ2OSNG+Ci+KZ07J5BxXsPAAeU2\nvY8AEvI1BDqZ8HG0LfCGayzlKtQMs4rKX4mTo5ZWjX1p1dgXSZI4l13EkeRLHDl1kVPn8jmdkc8f\n21PqHqiSYH83esU2oGOzAJwd7/pQRuUu4K4XEekkPY5GL4q19mli1czdSG65wPkrtt3l27aRs9X7\n9yv/F3ftKi+H79yZb/W+/v4utGvnT1xcFpcuXbF4v2eflbv4ff/94Vq3Cwvz4qGHojlxIof16y2/\nyAGMGxfDE0+0IinpEuPHL+XKFeXyl9vB778n8a9/bSMw0JV584ZV67f822/Hqr6Oizt3XeApSRKf\nfLK7Tt9lkLPLeXmlTJgQY7G7SGmpkQ0bzhES4kZUlPUZfLN+2SwLUoJZjtG2jW1Z4ZwyOF+qsUt2\nGaBYew6dyQ0HSfmxqaio2IYgCDT0d2NQx1DefKQNX7zYlWeGNqNbTBCdY4Jo3cSPVpG+tIyQNc/N\nw+vRLEwuSGwa4kVkA0/OZRcxZ62BV7/eyYL1Jzh/yW6d31VUquWeeCzTGxtw2TGRCq6gw7YWzM3c\nTazMlHWT9V2Uay/bVQbMBw5pGfuwsoCwY0f5pr5rVz4vv9zA6v3vuy+YuLgs1q5NZ+zYxhbt06NH\nMKJYj2XLTvKvf3WtVTP7zDNtWLgwkW++2c9994VblY388MOenD9fyMqVp3jyyRXMnDkYh7ugnevG\njSlMmrQGDw8nFiwYQf3612f+vXp2QncskaWV38fjT2HMo9dts3NnOgcPXmDQoEiio2v2AjaZJH74\n4TBOTloee6yFxXPcufMChYXl/OMfjRVliHftkn2rbQmY91cGzO3a2qpfrpRjuNte8GeinBJtJh4V\njW2yoFRRUbEvrs4OVT7Slnrn5xaUsvXwObYezmDDgbNsOHCW6DBverduSMtIH7WoUMXu3BNnVJVT\nhs4OOmYPs1OGbcFbVJQJF2eJ/QeUj+Pn50DTpi7ExRVSWmp9hm3o0DAAlixJtngfQRCYMCGG8nIT\nc+cm1LptVJQvffqEsXv3OVasOGnV3LRaualJjx6hrF2bzJNPrqSs7M62Htqy5QyPP74MBwcN8+YN\no3nz64Ndn0ZBOBxLRICqj1Zk0eGpB67b7quv9gHc5Nd8I5s3nyElJY8RI0R8ffUWz/PPP+WM//33\nWy/HMJkkdu/OJyjIgUaNlEtlDhzQotVKxLSwMWDOly9RzexR8KfNBEHCteLe6/CnovJ3w9vdiWHd\nwvlkYmeeGdqMJsFeHEvNZcbvR3nz292s2JVKflHZ7Z6myj3EvZFhrpCzr8XaDNwrLNd5Voe9Cv8c\nHKBlSyNx+7QUFoKbW937VEePHp58990F9u4tsNriKyTEnbZt/di58wKZmcX4+Vmmgx41qikffLCT\nBQuO8fLL7WrVJ3/0US+2b5/DlClb6NUrrFp5Qk04Oen4+echjB//J6tWnWLChOX8+OMDd2Rjk40b\nU3j88WVIEvz88xA6drw+4+/VsxOaouqXBHXHr3pbr159is2bz9C1azBt2tSuo509+ygAEyZY3lL8\nypUKVq48Q8OGrrRvX3PXwJpITCzm4sUKHnrIV7F+uawMjhzV0CzahN7yOL9ajhXYr+CvqFK2pTda\nv1qjoqJyZ6LTaqqy02ezCtl06By7Ey7w+7Zklu1MoVGQBw46DTqtBq1GQKvVoNMIaLUCWo0GXeVn\nN70DTRp6El7fAwfdnb/aqfLXc09kmF0rnTKK7KBjDnaR8NBJVZktW2jT2oTJJHDIhjbZvXrJQfKm\nTXmK9h8xIhyTSbKqiYmbmyMjRoicPVvA5s1ptW4bEeHNpEltycgo5Isv4qyen2w3N4yePUNZty6Z\nhx5aQk5OidXj3EoWLkxg3DhZZDF79lB69w677vdOfyzG4VjtDV9Atpd7661NODpq+c9/bmrQdh0Z\nGQWsW5dKq1b+tGxpeeC7alUqBQXlDB/eyOIGJ9eyadNlAHr3Vu6/nHhMQ2mpQOvWtq8YJBZocNbY\nqSV2ZWGw2VlHRUXl3qKhvxvj7xP59LkujO3bGD8vF06ezeNYai5HTl/i0MmL7E/KYs+xTHYevcC2\n+Aw2HTzH+v3p/LEtmf8uOMRzn23n/+Yf5PdtySSm5lB6h698qvx13HmpPAWYM0b2cMoQBIhyN7Iv\nV0uJEVxseNA0BwwHD2np1lXZm65TJw+cnAS2bFEWMA8eHMo77+xl6dJU3n675tbLNzJ+fHPmzk1g\n9uyj9O0bVuu2L77YnvnzE/jhh0M8/XRrq+QDAHq9A3PmDOW551azfPlJ7r9/EQsWDKdRo9trOWcu\nzps2bQ9eXk7MnTuMDh1uzk66vfmaReN9++0BMjIKefHF9ohi7U12Fiw4hskkMX68ZQ4nZn75RZbG\nDBumbKVl8+Y8BEFe2VDKgUoZUhsbA+YKk9wSO9rD9pbYIK9AAehVSQaiKGqAb4DOQBnwqsFg2HJb\nJ6WiYif0zjr6tg2mb9tgJEnCaJIwGiUqTCb5s9GE0XT1s9EocTHvCifSL2NIz+Vk+mVOpF9mxS7Q\nagTCgtzlbojB3jRu6ImL0z0ROqlYyT2RYXY0eaE1OVfdEG2lmbsJEwIGG1tkt4mtLPw7qHwcFxcN\nHTu6c+xYMZmZ1uuxAgL0dO4cSFxcFmfPFlq8X0yMH23aBLJ2bQrHj1+qY44OvPBCO4qLy/nf//Zb\nPUcAZ2cdP/zwAJMmteX06VwGDVrIjh21Z7dvJfn5pTz55EqmTdtDSIgHq1Y9XG2w7Pr26wi5tbdl\nr4huRnZ2MV99tQ9fXxdeeKF27XJJSQWzZh3F3d2RYcOaWDznoqJyVqxIJSLCg+bNa26zXROFhUb2\n7SukZUtXfHyq7/RoCQcOVQbMsbYFzKeKNJRJgl0K/kAOmDWSA84mX7uMd5fzEOBmMBhaAGOAH27z\nfFRUbgmCIKDTanBy1OLq7ICHqyP1PJzx83IhyMeVhn5uhAa600b04+G+jfnX4+356qVuvPhgDAM6\nhBAS4E5KRgGr96Tx+W/xvDxjB7sSbK+XUrn7uCcCZgEBvbEBJdoLmLD95mpukX3cRh1z/foSgYEm\nDh6SfZ2V0rOnnGndulVZlnnIkDAAliw5ZfE+giDw4ottAfj66wN1bj9uXAwBAa7MnBlPWpqyeWo0\nAu+9151p0/qSl1fKyJGL+fe/d1Be/tcuicXHZ9KnzzyWLTtBhw4NWLXqYSIjbw5AvXp2Qv/jd7X6\nLZhcXbm8ZTdff72PoqJyXn21Y52+07/8cpzs7GIef7yFVZrwjRvPUVxcwZAhYQrdMfIpL5fo2VN5\ndhnkFRVPT4nwcNt8k811BFF2KPiTMFGsO4+LMQjh3rjs2YTBYFgEjKv8Ngyo/alYReVvhN7ZgZaR\nvjzUK5Ipj7ZlxsvdeGV0S+7vFIpWo+HHFcdZsOEEFUb72F2q3B3cM3cOvbE+kmDkijbb5rGiqwr/\nbBf+t441kpWlISNDuY1Vjx6yvdfWrdb7MYPc9U8QYPFiywNmgP79G9GkiTe//36Cc+dqt/lxdtbx\n7rvdKC4u56WX1mEyKQ+Wxo+PYfny0YSEePLFF3EMHvwLJ07c+vt5aWkFn322l/vvX0RaWh4vvdSe\nP/4Yhb//zdZ6rm+/XqduWQIupZwnOTmXWbPiCQpy45FHareHq6gw8fXXB3By0vLUU7FWzX/58lQA\nBg8Os2o/M+YHMlsC5pwcSEnRENvKqKjD5bWYA2Z7OGSUanIwCaX3jBxDFMVvRVH8/oafaURR/I8o\nihmiKBaIovibKIo1CuANBoNJFMX5wApg+q2es4rK3Yqzo47mjXwY2SOC9x5tS31fVzbsP8uniw6r\nThx/I+6dgLmyc5c9Gpg0rbxB26Pwr3WsPNbBQ8qD7+hoPb6+OrZty0NSkKoOCNDToUMAO3eeJzOz\n2OL9NBqBiRNbU1FhYubMI3Vu/9BDUQwYEMGOHeksXnzc6nleS5s2QWza9AgPPRTNwYMX6NlzLlOm\nbCEvz/ImLNawdesZevacy3/+sxNPTycWLRrB2293RVeDeNZl1o91jlnyxNOYTBKvvLKekpIK3n+/\nO051aN9Wrz7NmTP5jB4dhb+/5VrwkpIK1q8/S0SEJ82aeVu837Vs25aPXq+hbVuFli7A4Xj5PG9t\noxwDrj6wRtlBklGlX74HCv5EUfwAeKqaX01Fzho/AnQDGgKLaxvLYDD8AwgHpomiaH0fdRWVvxkB\n9fS8M64NbZr4YUi/zAez95FyXlkyS+Xu4rYGzJtenMil48fq3tACzDdCc+tbWzC3yD5WoLFJSgFX\nAwdbAmaNRqB7d08yM8s5cUKZg8QDD4QiSbBixRmr9pM9gF2YNy+R4uLyWrcVBIF//7sXLi46Pvhg\nO4WFtj15u7s7MWPGAObMGUqDBu58991BOnWaxYwZ+8jNtd1JQ5IkNm9OZcyY3xk1agkpKZd54olW\n7N79OL16hdW4n8NrryAYaw7iJKD4iacp+vgT5s8/yq5dZxkwIILhw8U65/Tdd3KHxWeesS67vGVL\nBsXFFYwcGaFIjnHhQhkGQwmdOrnj6Kj8smB2hLFPwCy3xK5nuSqlRswFwa52CpjzUpLZ/dG/7DKW\npYii2EgUxU3A08CZG37nALwAvGUwGDYZDIbDyNrkrqIodqzcZqooiodEUTwoimI3URQjAQwGwzlg\nDxD1Vx6PisrdiouTjonDmzOiezi5+aX8Z95Bdh5Vdc33Orc1YE5aOI+LR+PtMtbVgNk+hX9R7kZy\nyjVkldrWEaxVSyMajcT+A7b9q7t3l2UZ27Ype5IdMiQMjUZg8eLTVu3n7Kxj/Pjm5OZe4fffDXVu\nHxzswfPPtyMrq4gvv7TeZq465Kz1o7z7bldKSir44IPttGr1A6+/voGDB89jtFJHduFCIbNnH6Fv\n3/mMHv07mzal0qlTA9atG8vHH/fGw6NmjbHrW6/hOaf27HJJZbCcm1vCBx9sx93dkf/+t3edgWx8\nfBZxcefp2zeMyEjrssTm1/Whhyzr6Hgj27bJcoxu3WzTL+/bLwfMsbG2ySgul0PGFY1d9Mtw9UHa\npaJ272tLyT5ymENf/uUqhs5AGtACSL3hd60AN2Cr+QcGg+FM5XbdKr9/32AwxBoMhtZABPAfgErZ\nRixw+NZOX0Xl3kEQBB7oHMaLo1riqNPw08rjzF+n6prvZW67N0peaopdxnExBoCksYu1HMi6ydWZ\nkFCgIcBZebbMzQ2io0wcjtdSWgpOCpunmQOZ7dvzefLJQKv3DwzU069fMGvXpnHqVB6RkZYHRo8+\n2oIvvtjP998fZuzYZnX6+06c2JY5c47w3XcHGT26GRERyiQC1+LkpOOFF9ozfnwMCxcm8uOPh5g9\n+wizZx/B29uZ7t1DaNUqkJAQD0JCPHF3d8RkksjKKuHkyYucOpXLqVM5xMWd49ChTEDO3A8bJjJx\nYhtatar7f+r69uvof/q+1m3Ko5tR9PEnAHz2WRx5eaVMndqDoKC6m8b8+KP88PjEEy3r3PZaLl8u\nZe3adJo29aJ1az8uXrTcDcWM+UHM/GCmBKMR9h/QEh5uws/XtqWZxHz7tcSGygdpSajqCmoreSmW\nd8+0FwaDYT4wH0AUb1qtaFj5+UZNWgYQXM1ws4H2oigeRbaVe9lgMGTab7YqKn8PYiJ8mPJYW2b8\nfpSNB8+SnlXAs8Nb4OdX974qdxe3P2BOti7jWRMadLgYAyjWZiAhIdTqXVA3LSo7ix3N19LHz7ab\ndof2RhIStRw5qqFdW2VPn8HBToSFObFrVz4VFRI6nfXHN25cU9auTWPx4tO8+WZri/cLCnJj5EiR\nX39NYvnykwwdWrvVmV7vwAcf9OSpp1byzDOrWLVqDA4O9umc5OXlzLPPtuHJJ2NZty6Z9euT2bw5\nlaVLT7B06Yk699fpNHTrFsKAAeEMGBBJcLDlAaLzzNqdtySNlstbdgOQmJjNzJmHCQnxYMKEugPg\n1NQ8liwx0LixNz17WiclXbo0lbIyE6NGKZNjSJLEjh35+PjoiI5W3prPcEJDfr7AoAEViscwc7Sy\nfqCFHTr8gRwwO5l80KK83fe13I6AuQ70gMlgMNx4sSoFnG/c2GAwSMDEv2JiKir3OgHesq555qok\n9idl8cHP+3h3Qge8XW57iKViR27rq6lxcCD/jH0yzAB6YxCXdOcpFwpwlJRnygBaeMj3naN2KPxr\n387IT7Pk5WqlATNA9+6ezJmTxYEDhXToYFmb62sZNiwcvV7HkiUpTJ4ca1Vw9eqr7VmyxMD06fsY\nPLhxnVnmYcNENm5M4ZdfjjFjxn5eftnypimWoNNpGDQokkGDIpEkidOnczlxIof09HzS0vIoLi5H\noxFwc3PC0VFDRIQ3kZHeiKJPnbZu1ZE69DH8TLW/diUTngBkP+SnnlpJWZmRjz/uXWehH8Dnn++j\nosLEa691sLpD3+LFpxEEGDky3Kr9zJw4UUJGRhlDh9ZT1B3QTNw++aGofTvbs8JHKzPM5vehLVQI\nxZRpL+NdZnmL8brIS0lGsNUGxL6UABpRFDUGg+HaE9UJqL5nuw34+Vl//bkTuVeOA9RjuRN474mO\n/L75FHNWHeONr7bTwN+NIB9XAnz0BNZzJdBHT6CPK/719DjZKYn0V3G3vib25LYGzO7BIXbN1OiN\nQVxCLvBxLLctYG7gLOHtIFXduG2hXVv5ph+3T8vEZ2ovnKuNvn29mDMniw0bLisKmF1dHRg4MIQl\nS5LZvz+bdu0sb7ncqJFXVZZ51arTPPBAZJ37fPhhT7ZuPcO0absZODCCpk1vTcMIQRCIjKxXrVey\nn5872dm1W+LVhutbr+E4+2d8K2ouYJS4qlsGeO+9LZw8mcNTT8XSv3/dQWxqah6//HKcJk28GTKk\n7v/rtaSnF7J3bxZduwZSv/7N9neWsGGDrF/u29e2zopm/XI7OwTMCfka9FqJcFcbq265ql/W20m/\nDJCfmoJbw+qUDreN9MrPQVwvy6jPzTINm7HlPXWnYOu14U5CPZY7h+4tAqnn5sDyXWc4m1VA2oXq\nj8XLzRE/Lxf8vV1o3siHVo1979gg+m5/Ta7FlsD/tqZIPBuFcyUnh9J8ZY0ubsSeThmCAM09jKQW\nayhQHuMC0KCBRFCQiX37bWtg0q2bB46OAhs3XlY8xoMPygHcn39an9l/6aV2CAJ89dUBi+ztvLyc\n+eSTvpSXm5g8eaMiS7zbicvk19D/9D26irJaBT7XBst79pxj7tyjREX5MmVKN4v+ztdfH8RolHj5\n5fZotda9Jf/4Q34dlWaXgarzqXdv2wNmLy+JxpG2ySiuGOFEkYZodxM2JLyruGopZ5+AubyoiKIL\n5/EMVdZ+/BYRDxQCPcw/EEUxDLkpybbbMyUVlb8nzRv5MP2lHsx4qTtfvtiNKY+25ZmhzRjZI5zu\nLYOICvVGp9Vw6lweO49e4Ltlibz81Q5+WnmMY6k5NvUxULl13NYMs2cj+Safn5qCX0wrm8czZ5BK\n7BAwAzT3MLH9EiQWaOlYT3nWTBDkLPOy5Q6kpQuEhih7M7i6aunUyZ2tW/PJzCwjIMB6v63u3evj\n7e3E0qWpfPBBO6sCtMhIbwYOjGDVqtPs2nWOLl0a1rnPffdFMGBABGvWnOarr/bxwgvtrZ7z7aB4\n5jx8ZtVe4AeybtkcLJeWVjB58gYApk3ra5EUIyurmEWLjhES4sHQodY7XPz5ZwoODhruvz/U6n0B\nCgoq2LOngFatXPHzU94OOytbIDVVQ98+FTY3LDEUajBKgl3kGHBNhtlOlnL5Z1IB8Gik/CHF3hgM\nhjJRFP+H7Kd8CcgGvgY2GwwG+9jVqKioWIUgCLi5OODm4kCjoJtXvSuMJjIuFrEvKYs9iRfYeVT+\n8HZ3okN0AJ2aBRLsr9wXX8W+3NYMs0eYnKGxlyzDxc7Wci0qK/QT7KBjbttGHsu8bK2UPn3kLOCm\nTcqy8g4OGh54IJSsrBJ277a+KH7SJLlYcMaMuttlm5k2rS9BQW58/PFO9uyx++qw3Un5z7eEvjnR\nojeHWbcM8Pbbmzl+/BLjxrWgXTvLgrOffoqntNTIxImta2ySUhOnTuWRkJBDr1718fJSVsy2fbtc\nRGprdnl/5XltPs9twSyDam6vgj+dfTPM5uuVZ9htzTBX99T9LrKLxlxgI5ACjPorJ6WiomI5Oq2G\nkAB3RvaI4L/Pdmby2Fi6t6zPlTIja/am8f7MON77aS+r95whJ//WNO1SsRy7BczWtmWFqxlme1nL\nOUruOJjcKbKTtZz5hp1YYL+Aeb+NAbM5sNm0SbksY/hw+Ub/22/WO5S0bRtEp0712bjxDHv2WPZ/\n9vd35bvv7gfgmWdW2qXpyK2gsLCMqVO34fzZp7VuJwGSk3NVcxKAOXOOMHfuUZo39+PDD3ta9Pdy\nckr46ad4fHycGTPG+p4RS5bIgduwYcoDN/ODV58+tvkvm33G7REwJ1Q5ZNjPUk5rcsHRZLu9IVy9\nXnnexgyzwWDobTAYnrrhZ0aDwfC6wWDwNxgM3gaDYazBYMi5XXNUUVGxHI0gIIZ489jApnz+fBee\nG96c2Ma+nL9UzG9bTvP6/3axNi7tdk/zb409M8xWt2X1DKsMmO1Z+FfRkCuaLIzY3t8TnrLUAAAg\nAElEQVQ90tWEk8Y+hX8tmptwcpLYf8C2sRo3dqZhQ0e2bMnDaFQm7ejcOZCQEDeWLk2lsNB6gfaU\nKV0A+PDDnRbrkjt2bMAbb3QiI6OQ117bcMfpmePjM+nTZx5ff72faLJr3bbkiae5mJ5VFSwnJmbz\n9tubqVfPmZ9/HoJeb5m04fPP95OfX8aLL7azeB8zRqOJRYtO4eYmF3IqQe50eBlPTy2xsbYt++0/\noEUQJLt0+Eso0KAVJEQ32zPMJioo0V5Ab6xvs9WkmfzKgNnj9maYVVRU7lEcdFraiP48PzKGz57v\nyvj7RNz1DvyxLZncgtLbPb2/LXYJmC1py1odHiGhIAhVNyB74GpsAIJkF1mGTgNR7iYMhRrKbbx3\nOznJQXPiMQ3FxcrHEQSBXr08ycszcviwMrcojUZgzJhIiosrWLrU+v9927ZBDBgQzr5959m40fJW\n2y++2J6OHRuwfPlJfvjhkNV/91aQlHSRd97ZzKBBC0lJuczEiW0ob1x9C2tJEK7LKgOUlJQzceJq\nysqMfPXVAEJCLMvUnjtXwKxZRwgOdufxx1tYPe+tW89z7lwRw4c3wtVVmfb49OkrpKeX0aOHpyJf\nbzPl5RAfr6VpUxNuNsrtTJLctKSxqwkXOxSMl2gzkQQjrhV16+0tJS/1jpBkqKio/A1wc3GgZ2wD\nhncPp6zCxPKd9ouXVKzDXhnmOtuyVofWyQm3Bg3tnGGu1DHr7KOVbe5upNQkcLLIDrKMtkaMRoH4\nI7ZFAj17ykHZ5s3KZRljxkQiCLBgwSlF+7/5ZkcEAf7v/3ZbnC3WajX8738D8fd3ZcqULaxbd/ua\nP5SXG5k8eSPdu8/hhx8O4eur55dfRtC9eyivXmxT7T4F3/50XbBsMklMmrSG48cv8uijMfTrZ/kS\n/fTpcZSWGnn99Y4WFQfeyIIFJwEYO1ZZK2yALVtkOYb5fFLK8eMaSq4IdpFjpBYLFBkFou3WEtus\nX25gl/EA8lNS0PsH4OCqzMZPRUVFxVq6xgQRWE/PtvjzZObYkHVTUYy9AmZr27JW4RnWiKLzGVSU\n2EfX6lp5Y7RX4V8zs47ZHoV/reWA4sBB28bq1s0TjQa2bs1XPEbDhm506xbEvn1ZJCdbP050tC9D\nhzbmyJFs1q9PteLverBgwTCcnLQ8++wqTp/OtfpvK6W0tIJt29KYPHkjbdr8yKxZ8URF+TBz5mCW\nLn2IuXOPMmbM73yf35jNHUYDIGk0VEQ3J/+7mZQOf/C68f797x0sX36Szp0b8tFHPS2eR1paPgsX\nHicy0ptRo6rPZtdGbm4pa9ak0aSJJ61bK/e2tlfAvP9gZcFfa9sD5sSqgj/76JeLdGeBq9cFWzGW\nl1NwLl2VY6ioqPylaDUaRnQPxyRJ/L7tjus0+rfAXgGzVW1Zr8V848lPs3xpv9aJVN4Yi+yUYW5W\nmelKKLB9fbhNa/s4ZXh56YiNdWX//gLy85W3IR49Wm6S8euvyrLML73UDoBPP42zSpMcExPAp5/2\no6CgjMceW0bBLdZkbdiQjL//dIKDv+TBBxcza1Y8RUXldOsWzNixLVi79jQ9e85lxYqTtG9fn/Xr\nHyH2ZTlgLnprCrlbdt0ULC9YkMBXX+0jIsKbWbMGW5Ul/uKL/VRUmHjlFets/cz8+WcKZWUmRo+O\nVNQKG6CszMSOHfmVmnjb2kWbdflt2tieFTYX2NrNIUMrXwf0FfYJmAvT05CMRlWOoaKi8pfTRvSj\nUZA7+5KySL2gPGGmogx7BcxVbVlv+HmdbVnNNx576ZgdTV5oTfqqG6WtRFday9kjw9yggUSD+ibi\n4mxrYALQq5cXRiNs3aq86cugQSG4uupYvDhZURFedLQvQ4ZEcuhQJosXG6zad9SoaJ56KhaD4RJj\nx/5JYaHtRZo1kZl58ylYUFDG9u3pTJmyhV9+OYarqwNffnkfy5aNpnlzv1rH2749jTfe2Ii3tzPz\n5w/D29vF4rmcOJHDwoXHiIjwYvjwJlYfC8juJhqNUNWERgl79hRQXGyyObsMEBenxdtbIjLC9iA3\noTLD3MyOkgyN5Iizyccu4+WpBX8qKiq3CUEQeLBHBACLt1jvcqViG/ZqXKKoLau3t56GMdEAGC9m\n2K1XuSfB5GpO4ePngqaWQ7Tk7/kBYW5wvEiHr687ChN6VfToDgsWwaVL7kRZ7yRWxcMPN2DatHNs\n2VLIhAlhFu937TH7+cHIkZHMmZPEiROFdO1qfWOHL764j3XrUvnoo12MGxeDu7vl2cqvv36AvLwy\nfvklkQkTVrBq1VhcXJQ3z6iJl17qTNeuYcyYEUdiYjbFxeX4+ekJDvakS5dgunYNITraD821beW8\n9AC4uTrhds3/bOPGZP7xjz8B+O23UXToYLlDhSRJjB27nIoKE5991o/AQOuD1VOnLrN/fzb9+gUT\nExNY7TaWnNfbtsmSpYceqm/T+y49HdLSYchgCAiw/f17vAgCXSC6oXXVg9Udg4SRYs7jQUP8/Wx/\nMABIvSQ3QWkYE22365WKioqKpUSF1aNZo3okpuSQmJpDs7B6t3tKfxvsFTBf25Z1AVjWljU3txih\nnnzTz0g4brde5Y5ugUguBtJyTtWoXbSmN3pTvTNrshxIPFtIgLNtqeFWrRxYsMiZVWuu4OurvOd2\nw4YQFOTAihUXuXAhH6227ki+umMePDiEOXOS+OabI4ii9QGAq6uW555rzaefxjF16jYmT67RFKVa\npk/vS1FRGStWnGT48EXMmjXE6gYetWE+5tBQdz75pE+N2126VHjd9w6Xi/ECCotKKan8n+3bl8Go\nUYsxmSR+/nkwMTF+Vp2za9cms2FDCr17h9KhQ6Ci8/27744AMGRIaLX7W3JeS5LEn39m4e6uJSpK\nZ9P7btVqHeBCbKsrZGfb1kP+cjmkF7vTy7eC7GzLaxpqOuYSTRYmnzIcrwSSXWCfa8u5o8cBEOrJ\nr58aNKuoqPzVPNgjgsSUHJZsOU30o96KpXkq1mGXyMRgMJQB5ras94mi2BpYiAVtWau6/VW2m7UH\nejsX/pn1lAl2aGDSsYMs8YjbZ5uOWRAE+vXzJje3gv37C+veoQa6dpU9mf/4I5m8PGVa4ueea42/\nv55vvjnIhQvWzcXBQcu33w6ie/cQ1q5NZsKE5RQX2xZ43Qri4zP5xz/+oLTUyA8/3E/fvtbJIcrL\njUyduhONRmDq1K6KLnDl5SbmzTuJm5uD4lbYACdOlJCWVkrv3p44Otp2Tu+Nk89j83ltC8eq5Bh2\nalhSWcdgr4I/uNoW2+whr6KiovJXExroTvsof1IvFLDfUHvfABX7Yc/GJYrasjp5eOLk7W1nL2b7\nWsvFVFbsH8mzvfCvSWMT3t4Se/baPla/fnLXv/XrlTtNaLUaxo8XKSkx8ttvyipv3dwceeONjhQX\nV/DJJ7U+H1WLo6OWn38eQvfuIaxZc5qHHlpCXt6d0wZ006YUhg79lby8Uj7//D4GDoy0eoz5849x\n6lQujzzSDFFUpqddty6dCxeKeeihCNzclEtX1q2T7Qj79rWtHTbAnjgtLs4SLZrbrjmOr+rwZx/9\ncpHZUs5OBX8ga5gdXN1w9rGPJlpFRUVFCcO7h6PVCPy+9TQVRvtcM1Vqx24Bsy1tWT3DGpGfdgaT\n0T6ZJfMNsshOGeaYyhv4ETsU/mk00K6NkbQ0DZmZti2jdO3qgZOTwIYNygv/AB5+OBIHBw1z5hgU\nd+AbOzaayEhvFixI5OjRLKv3d3NzZMGC4QwfLhIXl8Hw4b+Rmak8c24vjh7J4pFHlmIymZg5czCj\nR0dbPUZ+fimffLIXvV7H6693UDyXOXPkwspHH7Xeiu5aNmy4jCBAnz62Bcx5eZCUpKF1ayOOjjYN\nBcCRygxzS097tcSudMgwWq/Nrw5Jksg/k4pHWKN7YglUFMVVoigeEUXxYOWHco9CFRWVv5QAbz3d\nW9YnM7eEHUfP3+7p/C2wZ4ZZMR5hjTCVlVF03j4BrrPJF43kYDenjCBnCV9HU9UN3Vbat5MDAvNy\ntlJcXbV06eLBsWPFnDun3JrNz8+FQYNCSEq6zL59ypZ3dDoNH3/cA6NR4pVXNmFU8MTr6Kjlf/8b\nyPjxMSQkZNOnz3x27Uqve8dbgHn+y5afwNXVgV9/fZD771fWJOSjj3aRnV3MCy+0JSBAWbOLM2cK\n2LIlg3bt/ImK8lY0BkBeXgVxcQW0bu2Gr69tBZb7D2iRJIEO7e0T4B7N0+CukwjT26dterEuA0HS\n4mIMsMt4JVlZVBQX3UuWco2BlgaDoXXlx8XbPSEVFRXLGdwlDEcHDUt3pFBabp/rsErN3BkBc2il\ntZyddMwCGlyMQRTrziNh+1KFIMjLxOklGnLt4H7Wvr19dMxwdVl90ybbssyPPCJbnJk7yCmhZ88Q\nRo4UiY/PYvbsBEVjaLUaPvmkD1On9iAnp4QRIxbzxRdxmEz2CaIsIT09n3/9S65V9fZyZvny0XTs\nqGxZ/8CBC8yefRRRrMekSdV3ELSEhQtPIkkwbpzyzn4g2xAajfaRY5gf+MwPgLZQVAEnizQ0dzei\nsUPyVkKiWHsOF2NArU451lBlKRcaZpfxbieiKDYEXIB1oigeEEVx5O2ek4qKinV4uTnRr20weYVl\nbNh/e5JLfyfuiIDZs5FcQJOXbD9fQX1FfUxCKf+fvfOOb+I+//j77iQPWbblCcYGbDOOZfbeG0IG\nCVmEzGa3JashTdO0SdM065c0q22aPUjIJCEBSghhm03YEDiwzcZ44L0t6X5/nOQ4bKyvsAz3fr38\nMpzkR3fS6e655z7P56mWjwmJ59UxbxNQZe7ezUVQkO5zhRlg5Egj8Vm4sOFjsgGGDEmgVSs73367\nl7Kyhjfd/e1vg4mICOLZZ1eRm9uw8Z2SJPHb3/Zi1qxradYsjGeeWcFVV33Jrl3+LYC53Tqff76D\nkSM/ZvceQ010553d6dChYXeqnU4306YtRtfhxRdHEBTUsM/b5XLz+ecZhIdbufzy5AbF8OLdT0aN\nEuC/vF5BknQhI7F3lMroSHSNFKPFq5VKcMoVwuQYAMV7jeOT93jVmKiq+qaqqm8ft0xWVfU5VVWP\nqKpaqqrqV6qqxp8iRCxGr8nlwESMhu1k/661iYmJaC7p15qwEAvz1hygrDLwGuYvJAIiYXakGEbc\nxXvFjXv0nigrFDHaHq+OeZsAHXNICHRNc7N9h0y5jyPhU1NDSEkJZvnyYmpqGp5syLLE5Mltqahw\nMnv2vgbHadYsjMceG0BJSQ3PPruqwXEA+vVLZNGimxg/vg2rVx9m5MhPePLJZX6ZDLhu3RHGj/+U\n++//gdpaF/fe0xOAoHOY4Hc8H320jR078rnhhk4NrlADLFt2hCNHKrjqqhTCwhouo3C7dRYvLiY2\n1kLXrg2ThniprYVNmxQ6dHATEeFTKOCXC9E0YSOxxeqXAYr3Gcenxk6YVVX9O3D3SR56CrgZuAkY\nAiQBM08WQ9O0zZqm3appWpWmaYeAb4ERflplExMTP2ELsXDpgGQqq518v0bMxGSTkxMQCXNdhVlg\nwvyLU4YoazlxFWaAPr1duFwSmzeLkWWUl7tZvdo3r9nJk9siSfDhh7sa3PwHcOutaXTqFMunn/7M\nihW+3SaKjbUxffpEPvnkSlq0COe//91Az57v8vzzK8nNPe0QyTOi6zrp6Qe4+eZvueyyz9m8OYdJ\nkzqwcuVvGDEi2afYOTnlPP/8GiIigvjLXwb6FGv69N0ATJnimxxj+/YKcnNrGTHC8eshLQ2JtUOm\nskoSIseAXxxougobie11yBBZYfYkzKlthMU8F1RVTVFVdTFwD7D/uMeswP3AY5qmLdY0bTMwGRis\nqmp/z3OeUlV1k6fBr5eqqqPrhZAA5/nZEhMTE5GM6pVIVHgwCzccoqAkcBymLjQCImEOjY/Hag+n\nSLAkA6BcUONfsk0nwqILccoA6NNHnI553DijCez77xtuLweQlGRn/PhWbN58jJ9+ari3o8Ui88or\no1AUiQceWCikIjx2bCrp6bfw+OODsVhkXn55LT17vsudd87lm292UVJydq+h6zo7duTx+uvrGDLk\nI66+eiY//JBFnz4tmDt3Mm++OYHExHCg4RcMuq7z4IMLKS6u5vHHBxIXZ2twrP37S5k//yDdusXQ\no4dvJgbz5hn7x/jxvuuX1/9k7Lci5BhgONCEyjptw0QlzMadJaEV5qwslJAQ7C3E2dSdIwOBA0Aa\nsO+4x7oDdmCZd4Gmafs9zxvi+f+Tmqb10DStJ2AD/k9V1SBVVeOAS4Ef/b0BJiYm4rFaFK4cnEKt\n083sleIsek1+jahJfz4hSRKRKakUZexG13Uhlk2hrgTQJWHDSyTJqDKvLlAoc4Ldx3eujyfR8CYe\nvjBgQDgOh8L8+YU891xrn96/u+/uyPffH+Ddd3fSp8+p5I9npkePZjzwQB9efnkdTz65gpdfPvWU\nvbMlNNTKAw/05c47e/DFFzt4991NzJ69m9mzd2O1ynTt2oxOnWLp0CGG5s3tWCwyMTFh7NtXSFZW\nIVlZRaxff4TDh41KvNUqc/XVHbj99u706XOKxKoB7+X06dtZtGg/I0a04rbb0nzZZN5/fxdut85d\nd3Xy+Xvx/fcFBAdLjBghIGFeL67hr9oFWplMtwg3ooY8VtRJMhKExNN1neKsTCKTU5DkxqkzaJo2\nA8PrHlU9wVowyfP7+ArBEaDlSWKlq6r6DbAJo7r8mKZpR4WusImJyXljYFpz5q87QPrWbMb1bUVC\njG+yO5MTCYiEGQxZRv62LZQfzcae4HtVSCGIEHecMEkGGE4Zqwos/Fwq0zfKt0pYs2Y6KSlu1q5T\ncLlA8SFvtlplxoyJ4quv8tm8uZwePewNjjVwYHM6doxizpx9PPVUH5o3b3h19A9/6MOCBVl88skO\nLr+8LSNGNHw6XX3Cwqzcfnt3fvObbuzadYx58zKYPz+TLVty2LDh9Jr1qKgQJk3qwOjRKYwcmUx0\ndKiQdfJy4EAJTz65gsjIYF59dbRPSW55eS2ffrqHuLgQJk5M9mm9srKq2LmzkrFjHdjtvl2k6box\nsCQ+3k1ya9/dS7QyGacu1cmeRFChHCbIFYVFb/j+W5+qY8eoKS0hMnmIkHh+wAa4NU07/k2sBkJO\n9geapv0D+Ie/V8zExMT/KLLMpKFt+M+sbXyzLIvfT/KtWGNyIgGVMIOhExSRMAOEOZM4FryRGqmE\nIN33zqT6OmZfE2aAgf2dzPgsiB07ZLp29S3eJZcYCfMPPxT6lDBLksQdd3Rg2rTVfPzxbh55pHuD\nYwUFKbz++hjGjv2CadMWs3TpFMLDgxsc72Tr2rFjLB07xvLww/2pqXGRkVHAzp35FBZW4XS6CQ0N\nQtfdtGkTRWpqFAkJdp/1u6dC13UefngRFRW1/OtfY0hIaPjnAPDNN3spLq7h4Ye7ERzsW5L7ww+G\nHOOSSxru4ewlK0siJ0fmyitqG1KAP4FfGv7EyDGcUgXVSgFRNeJOGHUOGY2kXz4LKgFZVVVZ07T6\nb2Qw4JvY/yTExYWLDtkoXCjbAea2BCLnezvGxdpZuPEQG3bnkV9WS8eUaGGxL5TPxBcCL2HOyiRx\n4GAhMcNciRxjI+WWQwTVnvuEtuPxntC3C9IxDxjgYsZnsGqN4nPCPHx4JMHBEt9/X8if/nTCHdhz\nYtKkVJ566ic+/ng3Dz7YFau14dvbpUsc99/fm5dfXseDDy7i3Xcv8duUtKAghU6d4ujUKa5uWVxc\nOHl5vjVDni1vvrmJZcsOMmpUa667roNPsXRd54MPdqEoErfc0t7ndZs/vxBJgjFjfE+YV642DhsD\nB4qpCG8v9Y7EFuSQ4elbCHMmneGZZ4+34S8icIeWeLtrE/i1LKMFJ8o0fOZ8faf8yfk8Nvgbc1sC\nj8bajklDUnhufyFvz9rKYzf1FHK+vVA+E/At8Q+Ipj+olzDvEydYt3lOmKIm/rULcxMs62wX5JQx\nsL+RIKxe43s8u11hyJBIdu6s5MAB35rs7HYr11/flqNHK1iwwHcz9GnT+tK/fwvmzMnggw+2+Rwv\nEFm3Lpunn15FfLzNZykGwIYNeWzfXsD48a1ISPBNi1ZQUMvataX06mUnPt636X7wy/46oL+gCX8l\nMoqk0yFcTIW53HIIgDCXwITZ05DsCNwK8xagDBjmXeDxVU4GljfOKpmYmJxv2iU56Nk+jozDxWzc\n3fDmfZMTCZyE2XMiEjm8xHvC9J5AfcUqQwe7m11lMrUCzu1JSTotk9ysWWvBLSDeuHFGM9eCBb65\nZQB1Vc3339/lcyyLReatt8YTExPCE08sZ+vWXJ9jBhLHjlVy113zcLt13nprfIPHX9fngw80AG67\n7YTmrnNm4cIi3G4YP9736rKuw+rVCjHRbtq3832ndeuwo0ShXZibUDHXoVQoxvfd5hTnZhEoHsyn\nQtO0GuANjAEk41RV7Ql8BizRNG1d466diYnJ+eTqYanIksTMpZk4XWIKESYBlDDb4pthsdkoEVph\nbgG6JMxaDgwdc7VbYk+5mLeuf38XhYUS2m7f440dayREXr2qL3ToEMXQoQmkp2ezZYvvE/YSEuz8\n5z9jqalxc/fd8ykrEzBjPADQdZ0HHviR7Oxy/vSn/gwa5HtV88iRcmbNyqJdu0iGDPHd5WHBAmO6\n39ixvrtjHDgocSRbpl8/lxD98r4KiXKXRGdB+mX4ZWhJmEtgwrw3CzkoiLDGs5Q7npN1W/4Fw0Xj\nY4wpfnuBa8/nSpmYmDQ+CTFhDOvRgpzCSpZtFmd8cLETMAmzJElEJqdSvDfLp6EZ9TGcMuLrLKZE\n0MVzYt9aLEjH3M+4rb1mre/ltYSEINLSbKxaVUpZme+3y6dONZqm/vOf7T7HAhg5Mpnf/a4nWVlF\n3H33fJzOpn/l++KLa1mwYB9Dh7bk/vt7C4n51ls/43TqTJ3axecGxZoaN0uWFNOqVTCq6rsjiHc/\nHThAkH7ZI2/qHC7WISPYFS3MIQOMhDmidTKyL3Y2AtE0baSmaXcft8yladojmqbFa5oWpWnaFE3T\nChprHU1MTBqPiYNSCA5SmL1yL5XV5kwiEQRMwgzG7c7a8jIqc8Xdsg9zJlIrl1AjlQiJ183TmLRV\nkI65fz9jR14jQMcMRlNXba3O4sVFPscaNiyBLl2imT17PwcOiBH8/+UvAxk5sjULF+7jqadWCInZ\nWHz9tcZLL62jVasI/vvfcULcN0pKavj44900b25j0iTfb/+vXl1KaamLsWMdQpo/1noS5v59xSS4\nmzwT/rpFinXIEDmwpKqwgOqiIiIDt+HPxMTE5FdEhAUxoV8rSitqmWeOzBZCwCXMILjxz3NbVlSV\nuXOEG0XS2VIsJsFt00YnNtbNmnUKIgrrl11myDLmzvW9sCRJEr/9bWfcbp133tnpczww9Mxvvz2e\n9u2jeOutzXz66Q4hcc8369dn8+CDCwkPD+LTT6/waZpffT7+eDdlZbXceWdHn63kAObMMfaDCRN8\n1y+DUWG223U6dxaT4HonZ3ZrAg4ZAWwpZ2JiYnICY/u2wmEPYsH6g+bIbAEEZsK8V2Djn6fxR5SO\nOVQxGv+2l8iIUBRIEvTr6yI7W+bAQd8rgJ0720hJCWbBgiIqK31fwYkTk2ne3MaMGXsoLRWjO46I\nCGb69MuJigrhkUeWsGzZASFxzxf79xdz661zqa118847l9C+vRivS6fTzbvv7sRmswixknO5dObN\nKyA21sKAAb77kOflS2RkKvTp7fJp0I4XXYctxQqpNjcRvpt3APUn/InVLwNmhdnExKRJEWxVuHJI\nKrVON9+mmyOzfSWgEmavx6m3I10EXqcMkTrm7pEuKt0Su0U1/nl0zGvX+Z6FSJLE5ZdHU1HhZskS\n32UZQUEKt9/egbKyWj77LMPneF5SUx28//4EZFnillvmsnq1cKtYv3DoUCmTJn1Dfn4lzzwzlJEj\nxUwvBJg37wCHD5czeXJbHA7fB7ysXVtKfr6TCROiURQBcgzP/undX31lb4VEiVOie6Q4/bI/Ksze\nRuRAdcgwMTExORWD0xJIjAtj5bZsDuWWNfbqNGkCKmGuP+1PFDan4TJQroixlgPo6mn82yKo8a+f\nRw+6VkDjH8BllxkVTxGyDICbb25PSIjCW2/toFaEn56HQYOSeO+9CTidbqZMmc2GDUeFxfYHR4+W\nMWnSNxw8WMpjjw3gjju6CYut6zr//a/RXHnXXR2FxPTKMbz7g694E+Z+gvTLW+r0y2Ib/sA/FeYA\nHlpiYmJiclJkWeLa4W3RgS+Xiit6XYwEVMIcltACOShIqLWcQgghrjgqFHHWKt4TvCgdc5fObmw2\nXYhTBkC3bmEkJQWxYEERNTW+J7gxMSHcdFN7Dh4sZ+ZMcXIZgLFjU3jrrfFUVTm54Ybv2LIlMD2a\nc3MruOaaWezbV8wf/tCXhx7qIzT+0qVH2LAhn0suaUWbNpE+x3O7DTmGw6EwaJCYkaZr1ypYrTrd\nuwlKmD2Ns90EW8oFuRxYdd+9sL0U79uLpCiEtxR3N8HExMTkfJGWGk3H1lFszypgxz7TOKehBFTC\nLCsKEa2ThVaYwfBjrlGKqJXKhcTrFO5p/BPklGGxGFW7PRkKObm+3zqXJIlLL42mpMTFihVi3EHu\nu68LQUEyr7yyVbgd3GWXteW110ZTXFzNxIlfs3hxYHX0ZmYWcumlX7J7dyH33tuDRx/tJzS+ruu8\n9NIWAKZNE1O13rSpnOzsWsaNi/JptLmXkhLYuk2mZw8XNkFubV5rRlEjsV1UUa3kC60ug1FhDk9q\niWIVJLQ2MTExOY9IksR1I9oC8NXiDNyCrHsvNgIqYQajsaa6qIiqIt+Hb3ipc8oQ1PgXooBqd/Oz\noMY/gEEDjaRh1SoxSbjXFWHePDHvY0JCGFOmtGPfvlK+/VZ888B113Xkvfcm4ANcVMgAACAASURB\nVHK5uemmOcyc6fuEQV+QPAeUw4dLueyyr9i/v4SHH+7LU08NFmLPVp+VK4+yfn0u48a1JC0tRkjM\nefPEumOsXqPgdkt1+6mv6LphzdgmzE24sIa/bAChlnK1ZWVU5uWacgwTE5MmTevm4fTv3IwDuWWs\n2RHY8sdAJfASZo+OWaQswzvxq1xg41+3CDeVAif+DRls+DGvEJQw9+kTTkyMhfnzC3G7xVxNTp3a\nBUWReO21bcJi1ueyy9ry1VdXEhZm5Xe/W8ALL6zB1chjPT/5ZAeFhdX8858jefTR/sKTZYBXXtkK\nwIMPdhUW8/vvC7HZZIYP9326H8CKVRYABg8S2/Anyk4OfulTEGopZzb8mZiYXCBMGpqKRZH5ZnkW\ntU5xx96LhYBLmOucMoQ2/hkVJ1EVZoCudTpmMW9hWhc34eE6K1ZahMSzWCTGjo0iN7eWDRvEdMa2\nahXOpEmpaFoRP/xwUEjM4+nfP5HZs6+hZctw/vnPdVx77bfk5IiR0pwtlZVO3nlni+d/Eh9+eCk3\n39zFL6+1aVM+6enZDBmSQK9ecUJi7tlTSUZGFcOHRxIaKmb/XLlSIShIp3cvMQfZbR45kyg5BkCF\nxehTEFlhrkuYky+shFlV1QdVVd2kqupGz2+nqqojG3u9TExM/EdsZCijeydRUFLNwp/EGSFcLARc\nwuzwDAcozhLXXCZ6eAlAV8+JfrtAHXP/fi727pXJzhZTxbz0UuN2/OzZ4kT+991nJI6vv75V2Ajz\n4+nYMYZFi25g/PhUVqw4xIgRnzJ/vlhd+6nYvj2P8eO/YJFHR33nnV0ZP95/ydLrr28DxFaXvZ+3\nKDlGYSHs+Fmmdy8XISFCQv4ysETQhD+obykn0CEjy+gqv9CGlmia9qqmaT00TesJvATM1jRtcWOv\nl4mJiX+5dEBrwkIszF29n7LK2sZenSZFwCXMkSnGiakoU5z9iVUPI8jlEDa8BIyJfzI6W0rEvYWD\nBhqyjJWrxSThw4dH4nAofPfdMWESig4dopgwoRUbNuT7rcoM4HCE8NFHl/KPfwyluLiaW26Zy403\nziYry3dv6ZNRUFDJo48uYfToz9m58xhjxyQDEBMjqMPtJGzdeoz//W8/PXvGMnhwcyExdV1n1qx8\ngoMlLrlE1HQ/C7ouMXCAuGrwVo/DTBeRFWblCBZ3GFbd9yEtXoo8F+4XWsLsRVVVG/AUMLWx18XE\nxMT/hIVYuXxgMpXVTmavNIeZnAsBlzCHt2yFbLUKnfYHxgCTauUYTqlCSDybAu3tbraXKIiS83ob\nqlYLSpiDgmQuvTSao0drWbu2VEhMgMce64ksSzz33Ca/aJm9SJLE3Xd3Z8mSKQwZksSPP+5j6NBP\nePzxZRw4IMb9o6ioin/9awMDBnzMBx9sIzXVweefT+T228VVfE/FM89sAIz3U5Q2evv2cnbvrmL0\naAfh4WLkPas8+6Mo/bKuw7YSmdahbhyCGv5c1FCpHCXMmYSEOJ15cVYmkiwT2TpZWEwRqKr6pqqq\nbx+3TFZV9TlVVY+oqlqqqupXqqrGnyHUHRjVZXG+myYmJgHNiJ5JRIUHk74123TMOAcCLmGWLRYi\nWifXVXZE4W0EElllTotwU+6SyCoXc4Lu0tmjY14lJtEBmDjRcF349ttjwmKqqoNrr01l585CZs3y\n/xVq+/bRzJx5Fe++ewnx8WG8884W+vX7iLvu+p6lSw9QU3NuiZzbrbNlSy6PPbaU7t0/4OmnV1Jb\n6+JvfxvM0qVThE7vOxWrVh1lyZIjDBmSwLBh4jS3n39udD9fdZUYtw2AlasUgoN1evYQkzAfrpIo\nqJXr+gBEUGE5ApJOmKulsJhgJMzhSa1Qgn2fvCgKVVX/Dtx9koeeAm4GbgKGAEnAzDOEuxP4t9AV\nNDExCWisFhm1lYPqGhd5RZWNvTpNBnGZmUAiU9tQlLGHqoJjhESLOfF7T6TllkNEOtsJiZkW4eKr\nI1a2lSi0tTt9jqcohh/zwkUWjh6VaN7c9yu/wYMjiI21MGdOgVD/5GnTuvP111m8+OJmJk5MxmLx\n77WXJElccUU7LrkklW+/3cMbb2zku+/28N13e7DbrYwc2ZoBAxJp0yaKdu2iiI0NRZIknE43ubkV\nZGUVkplZxPr12SxcuI/cXONOQ4sWdqZN68vNN3chMvL8JEW6rvP885sA+POfewqN++WXOdhsMqNH\ni3HHKCoy9MsD+ovTL3sb/rqKHFiiGPIgkQ4ZNWWlVOTm0HJ4YPTCqaqaArwHdAb2H/eYFbgfmOrV\nIquqOhnYq6pqf03T1qiq+hRwBaBjJMr5gEvTtPPTIGBiYhIwtIyzs4YcDuaU0SzKf9LDC4mATJgd\nKW3Yj6EfbC4qYa6rMIvrDPU2LG0qVriqhe8JM8CA/kbCvGq1wqSrfI9psRhDTD76KJdly4ro2lXM\nPfDWrcOZMqUd06fvZubMTCZPFnMRciasVoVrr+3ANdeorFlzhP/9L5Mffshi9uwMZs8+O917bGwo\n113XgfHjUxk3LgWrVYwE5mxZtiybNWtyGDs2SZgzBsD27RVkZFRy5ZXR2GxitmntOgVdlxjQX1w1\neLPHWaarSEs5i8dSziXQUi7w9MsDgQPAZOCL4x7rDtiBZd4FmqbtV1V1H0a1eY2maU8CT3ofV1X1\nWmCVf1fZxMQkEGkZbwfgUF4ZvTucSbllAgGaMEfWc8po3ruvkJi2Oi9mcY1qaREuZPS6BEAEAwc4\ngWBWrxWTMANMnGgkzDNn5tC1q7iE4qGHuvH55xm89NIWrroqleDg85d4SpLEgAGJDBiQyNNPD2HP\nnkK2b89jz55CMjIKKSqqQteNBDs4WCE11UGbNg46dYqlW7d4ZFm8n/LZoOs6L7ywEYBHH+0hNPZ3\n3xmym8svFyfHWLXaOESIbPjb5Gn46y5QkuEPD+ZAa/jTNG0GMANAVdXjH/Zu+PGasyPAqXQqySd5\nvomJyUVAkidhPpgrxnb2YiCwE2aBXswWPZRgV6xQL2a7xZj4t7VEwekGEaqErmlubDZdWOMfQP/+\nhizjm2/yePLJRBRFTLKYmBjGbbepvP32Tt55ZydTp/rHq/hMSJJE+/bRtG8ffcJjcXHh5OWJa3j0\nlVmz9rJhQz6XX95a2FQ/MBLx2bMLsNlkRo2KFBZ3zVoFq1WnV09xDX+bihRSbG6igoSEBIwKc5DL\ngVUPFxbTe/xxBEjCfAZsgFvTtOM/qGrgpGIaTdNe9PtamZiYBCSRYUHYQ61mwnwOBGTCXOfFLNop\nw5lEQfBmaqVSQMyJtXukm51lCrvLZTqF+67JtFoNHfOSpRZyciSaNfNdx2yxSEyYEM306bmsWVPK\noEHibLemTevOV19l8corW5g8uS2xsYKErhcglZVOnn56A0FBMn/9a2+hsbdvr2Dfvmquu66ZMDlG\ncTFs2Wr4L9sESdz2VkgUOyVGxYm5ewJQSwXVSj6Oms7CYkJASjJORyUgq6oqa5pW/0AUDAif/BMX\nJ+7CpDG5ULYDzG0JRAJ9O9okRbJlTz5h4SHYQk4v1wz0bTkfCEmYVVXtCbwA9AYqgHnAHzVNK2xI\nPHtiEkpwsHinDFcSBWz26B3FOBN0j3Tx2WErW4rFJMwAQ4c4WbLUQvpKhWsmiUksrrjCSJi/+eaY\n0ITZ4QjmkUe68+c/r+XFFzfzwgv9hcW+0HjrrZ85fLic++7rQnKy2IOP1wXl2mvFadFWrrLgdksM\nHSJSvyxejlGCt+FPvEOGpCiEt/S/a4oAvFqzBH4ts2iBH2QXgXTXpqEE2t0nXzC3JfBoCtvRzBEK\nwOadR2mXdOpG8aawLWeLL4m/zyICVVUTgB+BTKA/cA3QlxObUs4aSZaJSE6hOCtL6DQ5fzT+9XAY\nJ36vLlME3gRl2XJxNwAGDYogMTGY2bOPUVUlzp0A4NZbVdq0iWD6dI3du/0zWKSpk5tbyWuvbSU2\nNkToVD8wbPK+/voY4eEKl14aKyzu8nRjnxaZMP+iXxa3D5ZwAIAwl7gJf2Dc4Ypo1RrFKsgs2r9s\nAcqAYd4FqqomY+iUlzfOKpmYmAQydY1/pizjrBDRrXY9xu3A32oGq4HfA6NUVW1wB44jpQ01JcVU\nHRPnH+ztoPd21IugU7ibIEmvq5yJoHMnNzHRbtLTFURdLyiKxJQpzSkudrFwodik1mqVeeKJ3rhc\nOv/4xwahsS8UXnxxM+XlTh55pDvh4QLFu8CqVSUcOVLDxInRhIaK2w+XpyvYbOL8lwG2FMvI6KQJ\ndMgo9ibMAhv+qkuKqczPbypyDDRNqwHeAF5SVXWc567fZ8ASTdPWNe7amZiYBCJJcZ7Gvzzhqq0L\nEhEJ83fA9Zqm1U/tvP9u8GzeiJRUAKGyDJuzBeiS0OElQbIxJntHiUy1oBxAlmHQIBdHsmWyssS5\nOdx0kzF+eebMfGExvYwf35L+/Zsxf/5BFi0Sd0FyIbBt2zE++WQ3bdtGcNNN7YXHnznTuKi85hpx\n1eXsbImMTIWBA1wECcrvXTpsLVFQ7W7CBHZPeCvMNoEVZm/DXwAnzCe7lP4LhovGx8AiYC9w7flc\nKRMTk6ZDi1gbsiRxMPfCkFv4G59PW5qm7cU4MNfnUQzd3PaGxo30JMzFezNJ6NuvwetXH4VgQtxx\nVFjESvq6RbrYVKywq0yu82b2lSGDXcyeYyV9pYU2bWqFxOzaNZyOHUNZuLCI4mInkZHishZJknj+\n+f6MGjWbRx9dw/LlV2KzBWRP6dkhqLTvcrmZNm01LpfOs8/2x2oVO+ClqsrNnDkFtGgRRP/+4nTR\n6Su947DFNeftKZOpcEl0FSjHACNhDnJFYdXDhMWsa/jzHIcCDU3TTpim4nHIeMTzY2JiYnJarBaF\nhBgbh/LKces6stQ4dqtNhTOevVVVba2qqltVVZfnd/2fipM8/3lgAoZEo8FZh9cpo0SgtRwYt21r\n5RKqKRYWs3uEeB3zEE+ikr5CrLfxpEkx1NTozJ1bIDQuQKdOUdx7b2cOHCjjlVe2CI/fKPh4APnw\nQ41Nm/KZNCmV4cPFjcD28uOPRZSWupg0KUaot/SKFcbFzpDB4geWiGz4q5XKqeSY0IEl0OQs5UxM\nTEwaRFK8neoaF/nFVY29KgHP2ZS7DgMdgI6e3/V/6rqXVFWVVVX9LzANuFfTtP/5smLeW6FFgq3l\nvLdtvbpHEXirylsFDjBJSdFJbOFm1SoFt8CC3FVXGbftv/lGnDa8PtOmdSMpKYw33thBRoa4i5Km\nSG5uJc89t5GICCt//3sfv7zGN98Y8ppJk0R6OsOKlQpRUTqdO4nb+bZ4RmJ3E6hfrlCOAGL1y1BP\nkpEcmBVmExMTExF4G/8O5piNf2fijPfMNU1zArtP9xxVVYOBr4CxwI2app2VQ0ZUlA2L5eQV1NiY\nDijBwVQc3C/U/6+CthzEsKJqG5cmJObgGAhZAzsqgoiLE9fQNWokTP8EcnLC6SrIWKFXr1gGDIhk\nxYpinM4gEhKCxQT2EBcHr78+jEmT5vHkkz/xww8TkRr5Nk+D9p9Iw3jYbg/G3sD975FH1lBSUsu/\n/z2Mzp3Fjx4tLnaycGExnTqFMXx4s7r32dfvS2YmHDoMV0+CZs3Effd+rgCLBMNTwwgVpNYpxbhg\naG5rQ5xN4HHi4D5ki4XUXl2QLU1YWmRiYmJyGryNf4fyyuilxjXy2gQ2Pp8JVFWVgJnAcOAyTdMW\nnu3fFhaeoOj4FRHJKeTv3kNubomwpMtliYEoQ/co0lewc7iNLYUyB4+WESJIRdG7l4Xpn4Qy539V\nJCT4rmP2eilefrmD1auLee+9/dxzT4KANf01gwbFMXJkIj/+eJB//3sTkye3E/4aZ0tD/SODiiuI\nBMrKqqlswN8vWXKYjz7aRVpaNFdf3dovHpZffJFHdbWbK66IIj/fqA6I8MucPccKhNC7VxV5eWL0\n8043bD5mR7W7KSusQFQtIycsE2zgKowlzynuPc7fvQd7UkuOFVae9nmmmb+JiUlTpqU5IvusEaEh\n+B1wKXA/sE1V1Wb1fnxKyCNTUqkpKaa6UJze1uuUUVLn8y+GbhEunLrEzlJxsoxBg4xb1ytWitUx\nT5wYg8Ui8cUX4t0ywGgAfPHFAdjtVh5/fB2HDl1cX8SiomoefHAlFovEq68OQlHENvp58X5+V10l\nTo4BsGKVt+FPnHRid7lMpVuim0D9MkC5p4FXpAdzTWkJlfl5pn7ZxMTkgsdhN0Zkm17MZ0bEmXwK\nhsXRu8ARz0+253dfXwJ79YMireW8ThklAjXM8Esjk0g/5pZJOq1auVm12oJLYJ4RF2dl7FgH27dX\nsG2bf/wXW7a088wzfSktreWBB1YKHUAT6Dz++DqysyuYNq07aWlik1kv+/ZVsWJFCQMHhpOSIm4c\nua7DylUKsbFu2rcTqF/26Pu7Roh1yKhQDhFCNBZd0Oxu6umXA9Qhw8TExEQUkiSRFBdGblElVTXi\nXJEuRHxOmDVNG6RpmnLcj+z5vcqX2HXWcqJHZDuTqKaYGklcU5q38U+kUwbAsKFOSkokNm0WW6W8\n4QZDq/TZZ3lC49Zn8uS2jBmTRHp6Nh9/fFoZ/AXDDz8c5KuvMunePYb77xejkT8Z3uqy93MUxS5N\nJidHZuhgl68GIb9iY5Hxvegh2CGjWikgErGjq70X6BFmwmxiYnIR0DLekJYdMgeYnBb/3CsWhNcp\nQ3zC3BKAMos4WUZ7u5swRWdDkdi3dPgwI8FYslRs49HIkZHExlr4+utjVFeLrfp5kSSJl14aQESE\nlb/97Sf27buwzdELCqqYNm0VQUEyr78+GIvFP18vt1vnyy/zsNtlLrssWmjsJUuNxHb4cLGVho3F\nCsGyTmeBFWbviPtIkoXFhMD3YDYxMTERSVK84WFvyjJOT0AnzI42bQHx1nJ2l5EwlwtMmBXJqJ7t\nKVcoEdMnBRh+zLKss2y52Mq11SpzzTWxFBY6WbBA7Kjs+iQkhPHss/0pK6vlrruWUi1qHGKA4Xbr\n/P736eTkVPLHP3anQ4cGD7k8IytXlnDwYA1XXBFDWJjY/WLpMuPCbMQwgdZvLvi5VKZLhJsggUcc\n7/dXdIXZmzBHtWm8ZlUTExOT80Vd41+emTCfjoBOmO0tErGEhlKc6Z8Kc7kitvGvp0P8ABOHA3r0\ncLNho0JJibCwAFx/vXE7/8sv/SfLALjuujZMmdKOLVuO8cQT6/36Wo3F669vY9Giw4wY0YKpU/0n\nxYBf5BjXXy9uFDZAZSWsWavQsaOLZs3Eac63lSi4dIneDtENf/5JmIsyM5CtVsJbiY1rYmJiEogk\nxoYhSaZTxpkI6IRZkmUiU9pQmLFHaNNYqCsBGYvQCjNAT4d/dMzDhzpxuSRWrBQry+jc2UaXLjYW\nLSoWZh92Kp59th8dOzr44INdzJmzz6+vdb5ZsyaH55/fREKCjTfeGCp04t7xlJW5mDu3gFatgunX\nT6yl2dp1ClVVEsOGik1sN3pkSiL1y+BJmHWJCFoKi6nrOkWZe4honXxB+y+rqmpRVfV9VVV/VlV1\niaqqHRt7nUxMTBoHq0WhebSNQ7llF1WD/rkS0AkzGDpmZ0U5FTlHhcWUUQgniXLLYXTEaSp7ehKC\njYJ1zN4ERrQsA+C662JxOnVmzfLP5D8vNpuFd94Zjs1m4aGHVpKVJbhc3kjk51dx773LkCR4661h\nxMSIc6w4GfPmFVBR4ea662KFJ+bLlhsJ4vBhYvXL3gvIngIrzDo6ZcpBQl3NURA3LKiqoIDqoiIc\nbS94OcZdQJimaZ2AW4A3G3l9TExMGpGW8XaqzBHZpyXgE+Y6HXPGHqFxI2mNW6qmUs4VFrN5iE6L\nEDcbixVEXqT16ukiLExnWbr4itekSbFYLBIzZuT6/cqyfXsHzz/fn5KSWm66aSFFRdV+fT1/U1Xl\n5NZbF3PkSAWPPtqD/v2b+f01P/3UkM9ce61YOQbA8nSFoCCd/n1FV5gVoq1uWoeK27+q5QJcckVd\nP4IoijIzAIhMueA9mDsDcwA0TTsIhKiqKn4cpYmJSZPAq2M2G/9OTdNJmAU7ZXg76yssh4TG7RHp\nIrdaJrtKXPXPaoVBA1xkZckcOiS2qhgfb2XChCh27qzkp5/8/0WZPLktv/99FzIySrjjjqXU1vrH\nocPf6LrOgw+uYv36XCZNSuGBB/yrWwbQtApWrSpl6NAIod7LAPnHJLZtV+jbx4VNnKUx+dUSBypl\nejjcQm3qvA4Z3n4EURRnGQlzVIBXmFVVfVNV1bePWyarqvqcqqpHVFUtVVX1q9MkwZuBKzzSjPZA\nR8BMmE1MLlK8I7LNxr9TE/AJc2SqJ2H2VH6ExaUVINZaDqCHx495gx/8mOGX2+YiueUW4zz50Ufi\nqu2n4y9/6cn48S1JT8/mscfWNEnN1Msvb+Wbb7Lo3TuOV18dJGx0++n4+GOjunzrreIr2StWGPvr\n0CFiq8ubPQNLuvtDv4z4hNl7YR4ZwFP+VFX9O3D3SR56CrgZuAkYAiQBM08R5gOM4VIbgEeBdKBG\n+MqamJg0CcwR2Wcm4BNm73jaYsHWchGeznpvpUoUPRzeiX9i39qhHh1z+grxOubBgyNISQlm9uxj\nFBX5f9KPosi88cZQOneOYvr03bz22ja/v6ZIPv88gxde2ETLlmF89NFIQkL83xxWWenmyy/ziIuz\nMn68Q3j85enGfuW9MBPFRs+FYy/hCbOnwuxKEhq32HNh7r2zFUioqpqiqupi4B5g/3GPWYH7gcc0\nTVusadpmYDIwWFXV/p7nPKWq6iZVVTcC3YBnNU3rpmnaHUACIPZgaGJi0mSICg8mLMRiSjJOQ8An\nzCExMQRHOoRXmG3EobhDhDtldIvwWMsViU1s27dz06yZm+UrxOqjAWRZ4sYb46mq0vn663yxwU+B\n3W7lk09Gk5QUxrPPbuTNN3ecl9c9a7xv8nGV42++yeKBB1bgcATxySejiYsLPS+rM3duAUVFLm64\nIRarVfzXdnm6hchIna5pYiUy3lHx3SPFxi1XDiLpVkJdYqvtRZkZWGxh2Jo1FxpXEAOBA0AasO+4\nx7oDdmCZd4Gmafs9zxvi+f+Tmqb10DStJ9AKeAVAVdXhQK6maRX+XX0TE5NARZIkWsbbyS2spLrm\nwpyX4CsBnzBLkkRkaiol+/bidon7ECUkwlxJVCpHcSOuqhZhhbZhLraUKLgFJraSZNwuz8+X2b5D\n/Mc2eXIcFovExx/nnTeJRGJiGF9/PY7mzW088cR6pk/XzsvrNpR58/bz+9+nY7db+fLLsXTs6L/h\nJMczY4Yhl7nxRvEy06wsiQMHZQYNdKIIvM7TddhUJNMy1E1ssLh9SsdNheUwYc4WSAIPYbrbTfG+\nLBypbc6LxOZc0TRthqZpt2madjLtlLfUfvi45UfgpL573wFOVVW3A3/DcM0wMTG5iEmKs6MDh/LN\nKvPJCPiEGQwds7u2ltKDB4TGDXMmoUsuKpRsoXG7R7opdUpklot9e0eNMBL7RYvFSwDi462MG+fg\n558r2LLl/M2TT0mJYObMscTGhvDII6v56KPATJq///4Ad9+9jOBghc8+G0P37uJdKk5FVlYVq1aV\nMmSI+GY/+GV/GjVSbFXhUJXEsVpZuH65UsnFLdUSJtgho/xoNs6KioDWL58GG+DWNO34N7saOGGn\n0TRN1zTtVk3TumiaNtzjlGFiYnIRk2Q6ZZyWJuHM79UTFmdlEpmcIixuWL0R2SLtqXpEuph5xMqm\nYpl2dnG3oocPM8ZkL1qs8OD9wsLWceON8fzvf4V8/HEe3bvbxb/AKWjf3sEXX4zh+ut/5JFHVpOd\nXcGjj3YPmCrfBx/s4rHH1hISovDJJ6Po2/f8mgl4q8tTpsT5Jf6iJcZhYORwsfrlzUX+k2OAccEr\nkjpLuaaZMFcCsqqqsqZp9d/wYED4FXBcnNihOY3FhbIdYG5LINLUtqOrGg/f7yK/tOaEdW9q2+IP\nmkbC/KvGv9HC4npPuMIb/yJ/GZF9XaK4JCQ62hiT/dMGheJiiIwUFhqAESMiadkyiK+/zuevf22J\nw3H+do+0tBjmzp3A9df/yMsvb+Ho0QpefHGAX/S658KixYd4dMUaYmND+PTT0ee1sgxGs9+MGXlE\nR1u49NJo4fErKmDlKmMcdmKiWCmOt+FP/IQ/b8OfaEs5o7E4EBv+zgJvhTiBX8syWnCiTMNn8vJK\nRYc878TFhV8Q2wHmtgQiTXE7bIqEJMGe/QW/WvemuC2nwpfEv4lIMoyEWXTjn9eSqlywF3NahJsg\nSWeD4MY/MGQZLpfkF3s5RZG4/fbmVFQYSdr5JjU1gv/9bwLdusXw6ad7uPrqHzhy5PzJQ+pTVmaM\nCl+x4iipqRHMm3fpeU+WAWbNyqegwMnNN8cTEiL+67p6jUJ1tVQn9xHJT0UyMrp4S7m6CnOi0Lhe\nSzlH06wwbwHKgGHeBaqqJgPJwPLGWSUTE5OmRJDVGJF9MK+8Sdq9+psmlTAXCx5eYtUjsLjtVAiu\nMAcrkBbpZnuJTKXgZtNRI43EZslS8ck4GLf9Q0NlPvwwB5fr/H9h4uNDmTVrPJdf3po1a3IYOXI2\nCxeeX7ertWtzeOzPawFISQ5n7twJJCef/9tRuq7z7rs5KAr85jf+kYEsXuIf/XKtG7YUK3QMd2MX\nfG1XbjmM4g4h2C32AsY7tMTr/d6U0DStBngDeElV1XGqqvYEPgOWaJq2rnHXzsTEpKmQFGenstrJ\nsRJzRPbxNImEOTgiktDYOOHT/iQkwpxJVCq5uBA7prm3w4VTl9gieIBJt65uYqLdLF5qEW4vBxAV\nZeHqq2PYv7+aRYuKxL/AWWC3W3n33eG88EJ/ystrmTJlIdOmraKgwL9f4LKyWp55ZgNXXjmfwgJj\nf7jp5vbExopvtDsb1q0rY/v2CiZMiKZFi2C/vMbiJRZsNp0+vcUmzDtKTy+pnQAAIABJREFUZarc\nEr0cYuO6cVKpZBPmSkJCrMa9KCuT4EgHIdHipS9+4GTf/r8AM4CPgUXAXuDa87lSJiYmTZtfGv8a\n5+5uINMkEmYwqsylBw/gqq0VGtfuagWSLlyW0duTKPxUJPYtlmUYNtRFdraMtts/H99vfmN4237w\nQY5f4p8NkiTxm990YN68S1FVB9On72bAgFlMn67hcoltItN1nVmzshg0aBavvbaN5s1tPP54TwDk\nRmw89L7/t98ufrIfwIGDEplZMkMGuQgKEhvbK0fqLThhrlCOoEsuwpythMZ1u1yU7N9HZGpqwDSb\nng5N00Zqmnb3cctcmqY9omlavKZpUZqmTdE0raCx1tHExKTp8cvEvwtDsyySJpMwO1LboLtclB7Y\nJzSuV8dcZhFrWderLmEWL50Y7nEzWLzEP7KMtLQw+vSxs3hxMXv3Nu5tmbS0GBYvvoK//a03NTUu\npk1bzeDB3/LBB7uoqPBNd1tT4+LLLzMZM2Yu99yznIKCKv7wh26sXHnVefVYPhm5ubXMmVOAqoYy\ncKB/5CBLlhpaiRF+0S8b+2afKLEJs/d7ahc8Ervs8CHcNTVEpjRJ/bKJiYmJEFrGeRLmPLPCfDxN\nJmGua/wTLMuwO70jssXakCaG6DQLdrOhSPxkvhHDjCRk6TL/uVj85jfN0HX48MPGqzJ7sVplfve7\nLqxePYkbb2zHwYNlPProGnr0+IrHHlvDkiWHqa4+u8TM6XSzevVRnnrqJ3r2nMnUqels317AFVck\ns3z5lfzpTz2w2RrfPGbGjFxqa3Vuuy3ebxVPrw5++DDxCfOGIgWHVSfVJnbnL/ckzP5yyGiilnIm\nJiYmQoiOCMYWbI7IPhmNnxmcJXWNf5kZMEZc3DBnIuiS8AqzJBlV5nk5Vo5USSSGikscmjXT6djR\nxZq1CpWVEOqH6cyXXx7NE0/sZ8aMPKZNSyQ8vPF3lebNbbzyyiD+9KcefPCBxkcf7eK994yfsDAL\nPXvG0bZtJG3aRBAdHWxMiYwMZf/+IrKySsjKKuGnn/IoLq4BIDzcyr33duaOOzrQunXgeExWV7t5\n//0c7HaZ667zjzOH0wnpKyy0bu0mNUVsUptfLbGvQmZkrPP4yeI+4/2eipZkFDdthwwTExMTIUiS\nRFK8nT2HiqiudRFs9c+d7KZI42dBZ4nD07lelCm2wqwQQqirGeWWA+joQhuJejnczMsxqm2JoWKr\neCOHu/jPToWVqxRGjxI/9z04WObOO5vz/POHmDEjj3vvTRD+Gg2lWTMbf/pTDx5+uBtr1uSwYMFB\nFiw4SHp6Nunpp5/amJQUxlVXpTB2bEsGDWpOaGjgfQVmzTpGTk4t997b3G8XKut/Uigtlbh6ktie\nAICNxcaNq56C9ctg3AkKdsVg1cOExi3M3ANAZNP0YDYxMTERRss4O7sPFnEkv5yUhIjGXp2AIfCy\nhVPwixfzHuGxw1wtybesp0YuJNgtrkO+l8d/dkOxwhUJYhPmsWOc/Oe/QSxYaPFLwgxw223xvP76\nEd5++yh33NGs0YeIHI/VKjNkSAJDhiTw9NN9KSurZe/eEjIzSygpqUHXITw8BF13kZoaQWpqOJGR\n/nGbEIWu67zxRjYWi8Q99zT32+ss+NH46o8dLV6OsdFPDX81Ugk1ShEx1T2ExgUoyjCOK1Ft2wmP\nbWJiYtKUaNnM2/hXZibM9WgyCbPVZsOe1LLuxCYSu7Ml+cHrKbMcILhGXMLcLdKFjM4GwU4ZAH16\nu3A4dBYssPDCs9XCb30DREdbueGGON57L4c5cwqYNOn8D+44F+x2K2lpMaSlxdQta+iEIuvqlQCE\nPf0kIV99TsWDD1N91TXC1vVULFlSzK5dlVx9dQyJif5L7hf8qGAL1Rk8SPzFltchQ/yEP8/AEsH6\nZTCGItnimxEUbp4cTExMLm6S4n5JmE1+IbBKhmfA0aYt5UezqS0T+yF69ZCiG//CLNAh3M3WYoVa\nsU5oWCwwcoSTI9kyP+/038d4993NkSR4882jF83kn+BZM7H9+zUAJN2NZecOIu65neBZM/3+2m+8\nYUhKfvc7/0lg9u6T2JOhMHSokxDBFtNu3RiJnWpzEyXYqs5f+mVnVRWlBw/gMKvLJiYmJiTGhSGB\n2fh3HE0uYQYoyvLPiOwyi9iEGYzGvyq3xM5S8W+193b6jwv9d6MgJSWESy6JYvPmctasuTh8GW2v\n/vOky8OeexqqxQ64qc+OHRUsX17C4MERpKWJ1ejWZ6FnfxkzWnx1ObNcptQp+U2/DOIt5Yr3ZoGu\n1x1fTExMTC5mgq0K8dE2DuaWXTSFsrOhaSXMngqQaFlGqDseWQ+uu+Urkh6RRml5o+CJfwAjhjuR\nZd2vCTPAvfcaWto33zzq19cJFJTdu06+fN9eYtXWRNxwNaFv/htl105Eega+/bbx/vpTuwywwJsw\nj/KHnZxxSBE94Q8MSYakWwh1iX1/vMcTRxuzwmxiYmIC0DIujIpqJ4Wl/isSNTWaVsLsOaEVCk6Y\nJWTCnIlUKIdxIzaJ8FbaNvhhgElUlKFl3rBR5tgx/00n69cvnF69wvj++0J27qzw2+sECq72HU66\n3B0dg6tlK4IX/Yj9iT8TPbQf0d06ED71HoK/+hwpp+Ge1YcOVTNzZj5t24YwZoyjwXHORFk5rF6j\n0KWzi+bNxVcOvBeGPQXrl3XclFsOYXO1QBbceuFtJHa0NSvMJiYmJlB/4p8py/DSxBJm44RWLFiS\nAYYuUpdcVCpiq6iq3U24RWd9oX+8DEePcuF2Syxd5j+vREmSeOihRABee+2I314nUKh48OGTLi97\n7kUK09dxbPNOSl7/L1WTrkVyOgn58jMifn83sWntiBo2gLAnH8e6eCFUnP3Fxb/+dYTaWp0HHmiB\nLPvv4ic93UJNjcRoP1SXAdYVKoTIOp0jxIr2K5Vc3FKNcDkG1KswXwQaZlVVE1RVPaHicKrlJiYm\nFydJZsJ8Ak0qYQ5PaokSHCzcixnA7vKPjlmRDHutrAqZ/GrxidCokR4d8yL/yjLGjHHQubONb789\nRmZmpV9fq7GpvuoaSt56H2enLugWC85OXSh56/06lwx3i0SqJ99I6ZvvcWz7HgoWr6TsiaepGTYC\nZW8mtv/+C8fkScS2b0Xk1ZcT+vrLWLZuBvevk8jgWTOJGjaA2IQoHvrwSqbGruDqq/3rRLJwsXFh\n5Y+EubQWdpbK9Ih0EST4yOLVL4f5I2HOzEC2WIholSw8diChquoQYCHQ7GyWm5iYXLx4R2QfyjMT\nZi9NxlYOQJJlIlPbUJSxB13XhY4M9p6Iyy0HoHqAsLgAfRwuluRbWF+kcEkzsYlK505umjd3s3Sp\ngssFip8KzZIk8Yc/tOCOOzL417+yefXVVP+8UIBQfdU1Z2cjJ8u4uqRR2SWNyqkPQGUl1nVrCFq2\nBOvSxQSlLyMofRn842+4Y2KoGTKM2mEjoaqS8MceqQuTxl7+lf8UJXNa+82+Ttdh0SILDodOr56C\nbVuAn4oUdCT6RPlHvwziLeV0Xacocw8RySnIliZ1OGwItwE3ACvOcrmJiclFSkxkCKHBillhrkeT\nqjCDoWOuLS+jIkesdKIuYVYOCY0L0NeTQPzkBz9mSYLRI50UFMps3OTfj3PChGjatg3hyy/zOXTI\nbAQ4KaGh1A4bQfkTf6do8Qryd2RS8uZ7VN5wE3pQMCHffkP4Q1N/lSzXx/bay35btZ27ZI5ky4wY\n5vTLhdV6j06/rz8TZsEV5qqCAqqLigJejqGq6puqqr593DJZVdXnVFU9oqpqqaqqX6mqGn+qGJqm\n3aFp2tazXW5iYnLxIkkSSXF2jhZUUF3rn+FoTY2mlzD7ySkjSI/A6o70i1NGT4cxwGSdn3TMY8cY\nVevv5/u3QqYoEvff3wKnU6/zCzY5PXpcHNWTrqXstTco2LyTghXrKXvmBfRT3B1Rft6OY8Jowu+7\nF9urLxE05zuUn3dApe8ymPk/GPvHuLH+0S97dfqiJ/wBlCkHsbhtQidxgiHHAIhMaSM0rkhUVf07\ncPdJHnoKuBm4CRgCJAH+Nws3MTG5KGgZb0fX4eDRi8NS9kwIz7BUVX0EeEHTNL8k4w7viOysTBIH\nDxUaO8yZRFHQDpxSJRY9VFhcuwU6hrvZUqxQ40a4vnPYUBe2UJ35P1h44i81YoMfx9VXx/B//3eI\nTz7J5b77WpCQIHg6xYWMJOFqr1LZXiXkk+lYdu448TlBQVg2b8T607oTHnIltcSV2hZXmza42rTF\n1aYtztS2uFu1PistzvfzLVitul/0yy7dcIJpG+YiWvAu4aKGSuUokbXtkRDbB+BtIA7EkdiqqqYA\n7wGdgf3HPWYF7gemapq22LNsMrBXVdX+mqatUVX1KeAKQAfu1DRt43ndABMTkyaNt/Fv75FiuqeK\nLVY0RYQmzKqqdgX+jnGA9gt1w0v8MiK7FUVBOyhXDhDpVIXG7hPlYkepwvYSmZ4OsfrR0FAYPtzJ\nvO+t7Nkj066deH2qF6tV5uGHE3noob289NJh/vnPFL+91oVMxYMPE3HP7ScsL/3Xm1RfNhHl4H6U\nzAzPTyZK5h6UzAyCli+B5Ut+9Td6UBCu5BRcqW0hrRMhCa3qkmk9Ph4kicOHJbZsVRg21ElEvenP\nwbNmYnv1nyi7d+Fq36HBI8B3lcqUuSR6C963Acoth0DS/TYSGyAyNSArzAOBA8Bk4IvjHusO2IFl\n3gWapu1XVXUfRrV5jaZpTwJPniTuqa46/GfPYmJi0uTwNv7tyy4xE2YEJsyeisd0YBUwXFTc46mz\nltvrB6cMz8jdMov4hLm3w8WHB4zGKNEJM8D4cUbC/P0PFtq182+V+frr4/j3v7P57LM8pk5NICVF\n8Hzli4ADA6/g/6yP86j+OZ3YbySrD/yhLll1pbY1EuAxx/1hWRnK3iwsWRm/JNRZGSgZGVh2azD/\nf4TXe7rbHo6rTVtypfY84e5Iz2bJWLak4EptQ9DCBb9K2r0jwEvgnJPmnzz6Zf80/Bkjse3O1sJj\nexPmQNQwa5o2A5gBoKonHI+SPL8PH7f8CHCmK4tTFTTMkV4mJiZ1eEdk7z1S0tirEhCIrDA/AxwC\nPsOPCXNIdAzBUVF+qjAbJ+Qyy/4zPPPc6ePwNv4p3E2t8PhjRrmQZUOWcf9U/ybMFovEH/+YxD33\nZPDii4d44w1z4MO58tprR/i4djhp/3cb8bedg5uX3Y4rrSuutK6/Xq7rSMeOEVtwhJINW7HUS6Yt\nu36mc/UmngLj2/mZ50+Uk3/9bS88S83gYejR0Wdtu1KXMPtDv+z5PvorYbaG2bHFNzlHNRvg1jTt\n+De8GjjtFaymaRHnstzExOTiJCTIQlxUKPuyi4U7kzVFhCTMqqoOBW4FugKjRcQ8HY7UtuRt2YTb\n6RRqBWVzJSLpCmWeipZIkm06sUFufvJT419MjE7fPi7WrlPIy5eIi/VvsWjixGhee83G118f48EH\nE2nfXpzm+0Ln8OFqpk/PpVWrYKZMiRMTVJLQY2OhYwrV7btS38OkpNDFuK5FjErcyUt37UDJzMCS\nmYF1yaKThrJkZRDbuQ26LOOOjUOPi8cdH487Lh53fDPjd1zcL/+Ob8aGgiTCLTrt7eLvnpQp+0GX\nCHMmnfnJ54DudlO8N5Po9h2a4omgEpBVVZU1Tav/pgcD5f5+8bi48DM/qQlwoWwHmNsSiFwI26G2\njiZ982GKqly0bxXV2KvTqJwx21RVtTWwF+N23fFnlSoMs/sPgfs0Tcs5ya1D4TjatCVnw3pKD+wX\nqj2UsWBzJVJuOYiOG0mgiYgkQS+Hmx9yLWRXSSSEiE9ox411smathYULFW6Y7B8nBC+yLPHHPyZy\n2217ePHFQ7zzTuDd0g5UXnnlCDU1OtOmJRIkugP0JCxJDybTlcykaxOoumNw3fKoYQNO2njojoqm\ndtAQ5NwcpLxc5H17sezYdtrX+FmxUBQZjyMxDnd8vJFknyzRjo9Hd0QZX4izQEenzHIQmysBheBz\n2/AzUHb4EK6qqqY6Ettr55PAr2UZLThRpiGcvLym3zUfFxd+QWwHmNsSiFwo29G3Qxzpmw/zxYJd\n3DuxS2Ovjs/4chFzNuXZw0CHUzzmBl4H1mua9qVn2VmXaqKibFgs515xbdG1M9qX4M4/TFy/7uf8\n915O9sbF0ob9HCA0rpRwxFa0hiXCD7mw222nq6DCYn1uuB6eehqWLAvl/vtO/hyRV7y33GLn3//O\n4bvvCvjzn9307RspLLZIAukqf9eucj79NI/27W389rfJWCziE+bjt3fZcuP35OuCiYurl3Q+8Re4\n4YYT/l5+4z8ET57864UVFZCTA0ePnvD76L4csjKO0qEqB2vmHti25fQraLVCs2bGT/PmJ/673u/y\nyCpcUgUxcq8TP8fPP4dnn4WffyauUyf485/h+PU+DSWbjTHvCV06BdQ+cpZsAcqAYcCnAKqqJgPJ\nwPJGWysTE5MLik6to0hOiOCnXXkcG15FTOTF27N0xoRZ0zQnsPtUj6uqeitQqaqq91LKAkiqqpYA\n92ia9tmp/rawsOIcV9fA2tzoaTmwaRtRfRtmLXeqqz9LaALY4UDJTuKrxSaAHa0KYGPJgRqG2cQP\n/oiOhjapYSxYIHHwYBkhx+3X/rji/etfE5k4sYSpU3cyd26ngLu1HWhX+ffdp+F06jz+eCKFheLv\nnB+/vU4nzJ1nJyFBJympnLy8ek8edSnBb72P7bWXf3HJeOAPVI+6FE72ntljoW0stP11leHF3UG8\nnBnM570rGBnngrIy5Lxc5Nz/b+/Oo6So7gWOf6u7h4HZhx0ckdWfGhBcUFRwRURAJZpFk3g08Tzj\nc9c8YxKXJ3n4FPH5IO8YISH6fAazaFQUXImKJi4MCAaRXGTfF2FWZpiZ7q73R1XDOAwzw9jV1dXz\n+5wzZ5iapuvW3K7qX9/63d/d5X7f+dWfd+8ktHs3oZUrsZYubfF4unTKYkLvCPRYSV23t92R6h6E\ntm+nyx/nHnzgihVw1VVUVta2ecLipk+cUfNOvY9u92vEr0DbGFMvIr8GHhWRPcBu4HHgHWPMoTUJ\nlVKqHSzLYvI5g5jxx2X8dekWvnN+IO/IJUUyEoCb/vUmA9OB4cCuJDz/IYoGuqXl3BnuyZSbmPgX\n3kRPRiX1uUcUxghb3i1gAs4iJk/M7sTf/h5m7AXer85zxhkFTJpUzPz5Zcybt5fJk7t5vs+geued\nchYuLGfMmALGj09NLtji0jDl5RaXXdrQbBZEm5cAb0Fihb+TCt3XW14e8bw84gNaWT7dtrGqqw4E\n01YzwXXDHoO1aztdPttCqG5dq23JmflYm4+nfF1al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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ps = np.array(ps)\n", "plt.figure(figsize=(12,4))\n", "plt.subplot(121)\n", "plt.contour(X, Y, Z, np.arange(10)**5, cmap='jet')\n", "plt.plot(ps[:, 0], ps[:, 1], '-ro')\n", "plt.subplot(122)\n", "plt.semilogy(range(len(ps)), rosen(ps.T));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Frist order methods\n", "\n", "As calculating the Hessian is computationally expensive, first order methods only use the first derivatives. Quasi-Newton methods use functions of the first derivatives to approximate the inverse Hessian. A well know example of the Quasi-Newoton class of algorithjms is BFGS, named after the initials of the creators. As usual, the first derivatives can either be provided via the `jac=` argument or approximated by finite difference methods." ] }, { "cell_type": "code", "execution_count": 64, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ " nfev: 280\n", " hess_inv: array([[ 0.49982388, 0.99958969],\n", " [ 0.99958969, 2.00405492]])\n", " fun: 1.2055799758407391e-11\n", " nit: 44\n", " njev: 67\n", " success: False\n", " status: 2\n", " message: 'Desired error not necessarily achieved due to precision loss.'\n", " x: array([ 0.99999659, 0.99999311])\n", " jac: array([ 2.46198954e-05, -1.12454678e-05])" ] }, "execution_count": 64, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ps = [x0]\n", "opt.minimize(rosen, x0, method='BFGS', callback=reporter)" ] }, { "cell_type": "code", "execution_count": 65, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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p0eM5O8OV99lVVFXlkUe2s39/OXfeOYz58/t1yXO98souVBXuvXdkh/N9/nkO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\nFHK49dYKZs9+j/nzt/LTn2b8knZg/OAH22lvd/nGN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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ps = np.array(ps)\n", "plt.figure(figsize=(12,4))\n", "plt.subplot(121)\n", "plt.contour(X, Y, Z, np.arange(10)**5, cmap='jet')\n", "plt.plot(ps[:, 0], ps[:, 1], '-ro')\n", "plt.subplot(122)\n", "plt.semilogy(range(len(ps)), rosen(ps.T));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Zeroth order methods\n", "\n", "Finally, there are some optimization algorithms not based on the Newton method, but on other heuristic search strategies that do not require any derivatives, only function evaluations. One well-known example is the Nelder-Mead simplex algorithm." ] }, { "cell_type": "code", "execution_count": 66, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ " nfev: 162\n", " success: True\n", " status: 0\n", " fun: 5.262756878429089e-10\n", " nit: 85\n", " message: 'Optimization terminated successfully.'\n", " x: array([ 0.99998846, 0.99997494])" ] }, "execution_count": 66, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ps = [x0]\n", "opt.minimize(rosen, x0, method='nelder-mead', callback=reporter)" ] }, { "cell_type": "code", "execution_count": 67, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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++kgqKztq6LduLebcuSYWLTLfdjE5OWcoL69n0aKhNve7mC1blKcWw4e7OfxZ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\nHvTsGcz27SkcPpxO27bVO3S89FJHliw5waxZBxg2rJlFWWaATp0C+c9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T6ToDfYAIoAPw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\n442jZGeXMWFCc3r0iLekT78fVqx0kpISYNB/mfOE9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MpzajQaTT2nwRvMqZ06s//T1RTs\nzqFF74sjeu6EKoPZnIp/fVN9OGwB1uU7iXgqgBCGXuYjMTHAO+/aePhBS5JFhOWXv0zns8+KWLEi\nnyefzOXZZzOiI6Q2nE68vS/G2/tiuGMKBALY83KNMI51xC5eGPbXdtOSWwe/x5uLM/GbnG+6LpYt\nd+J2qxWFs+VssnGsy3dgI0CWyR7m4MbbSFKwZzcEAlX7H+orQoj2wN+A7lTz+AohXMC9wN1Syk+M\ntgnAd0KILCnlOiHEDOBqlEF8m5TyyzDdHCAkptn4/4GI/zEajUbTCGjwWftDM2VEGre/GU5/XNUX\neKRJcELvJD9bC+2UmOOsA06GZeTmwpat0bvkNpuNWbM60LVrE+bOPcy8eYejpuWMsNnwt8ug4oYJ\nFP/hJfCGv0htOcorr3YxvThLXeyQdnbucjBmNCQkmNdPpR825TvomugnxaS4+2JnLvaAmya+9NMf\nfJYU7lHhWw0gfnkgkIfajLe32nsXAQnAp8EGI+54LzDY+Pm3UsqLpZR9qhnLoTfpR8B1RuxyT8Ap\npQxfj12j0WjOcxq+wdzRPIPZho14bzvKHIfwYU6J56w0H96AjS8LTc6W8ROVNeG9902ycs6QpCQn\nCxYImjVz8vjje/n008Ko6jkbatsEV9lR0KxZdMd16ftqseiG68ztZ2uhnTK/jYEmeZf9eCh1fE+C\n90JsJnw85Qc3/NXzHMxSyoVSysm1xCS3MV6/r9Z+ADhdGpqqEAwp5efAJ8BXwALgth8pV6PRaBo9\nDd9g7tSZ5A4dccWb41ZL9nYmyduRSvsJU84/INVL53gfpSZ6mAEuH+qjTRvwmdzPmdC2rZvXXlMe\n2fXrzRlXMyi974Gw7b6HH7RYSU28Xmje3M81V5vbT7HXhkjwMSCC+ZdD8dhPkOjtQJLHnBzJrvh4\nUjp1bug5mOMAv5Sy+kWoAGLr+kUpZVK1n38vpewhpewtpdwQYZ0ajUbTaLAFAuaUZdZoGiU22wTg\nUVTu2u3AcwQCb0ZXlKYxI4RYDewKZskQQlwLvA24pJT+kOM+AzZKKe+PjlKNRqNpvDT4TX8ajaUo\n41gbyJposs94bcWpYRmtqRmmodFoNJoI0OBDMjQajeY84yugGLgs2CCEyAAygH9HR5JGo9E0brSH\nWaPRaBoQUspKIcRfgT8IIY4DR4HZwGodh6zRaDTmoA1mjUajqd+E22jyG9Tn93zABawE7rZSlEaj\n0ZxP6E1/Go1Go9FoNBpNHegYZo1Go9FoNBqNpg50SIaBEOIhYKaUslE/RAgh+gAzgUuBUuBD4GEp\nZX5UhUUQIYQdeAa4GUgEVgFTaykC0SgQQrQAXgRGAk2A9cADUsptURVmAUKILOA/wHAppd70ZgL1\nYU4JIeYA9mB6PaNtFOrzTAA7gV9LKVdFuN8655YVGox+LgBeAoahnF2rgOlSyoNW6qimqcbcs3A8\nugHbUCFLwQqWAWCwlPILK8dDCHEb8BCqcNB24CEp5WrjPSvu0cuA1Zw6FkE+kVKOsEhHnNHHtah8\n8WtRcyXbeN+qeyMRNWd/ArhRIWvTpZRHz0VHozYOzxQhRC/gKcLHCjYahBCtUOVwdwNZwPVAP2Bx\nNHWZwAxgEvALVKngNsA7UVVkIkIIG7AU6IT6gBgAFAIfCyFSo6nNbIwP6PnozzKzieqcEkI8BdxR\nrS0TeB/1+XURsAxYahhSkeq3zrllhYYQVgDJqOwoQ1BpBZcZOq3UgdFnjblnsY6eqA2vLUP+tQLW\nW6lDCHEz8N/As0APVMn6ZUKIthbq+JyTf39wLG4CfMDzRn9W6HgZ9UB3HcrGKAdWCiFiLL433gGu\nQD3gDwYSgNVCCNe56DjvY5iFEC5gI3AcGCqlNLdGdRQRQtwHPAhcKKUMGG2DUBO8nZRyfzT1RQLj\neh4D7pZSzjfa2gHfAQOllOuiqc8MhBAXAZuBblLKnUZbDPADcJeUckE09ZmJEOJVlDEzFLhce5gj\nTzTnlBCiPfA3oDtqReyjkAIuc4AuUsphIcd/AuyUUt4Vof7rnFvAILM1GOdMB/6M8oTlGW1XA+8B\nacALQGezdVTTVGPuGW2W6DAeogZLKS8P857p90bIeb8DXpdSzjB+tqHumRdQY2OJjmqakoAdwGtS\nysetui5CiKPA76SUs42fuwHfApeg5osVc6U3sAW16hH08scDecB9wH/9WB3aK6OWGfcD86ItxALe\nB24MGssGwf83Fk/kRainyU+DDVLKXGAv6kmzMZIHXBX8QjcIVoBrLNe1BkKIK4ExwL3UXIbURI5o\nzqmBqPu7p9FfKIOBNdXa1kRY0+nmlhUakFIellL+PMRYboMyQDZIKQtRhrvpOoLUMfes1NEDyK7l\nPUuuixBCAO2At4JtUsqAlLKPlPJNq3SE4UmUd/f3xs9WXZejwI1CiObGg+VtqIfLPVg3Fp1Rds3n\nwQYpZQmQg3qA+dE6zusYZiHEEJTLvhcwIspyTEdK+R3KKxTKI6jqYN9ar8gU2hiv1SueHUDFlzU6\npJQ/oGK0QpkGxAL/sl6R+QghmgFzUfO3IMpyGjtRm1NSyoXAQgBlm9TQZaqmM5hbT5utoTpCiPeA\na1CGSNC7avpYhPRf19yzTAfKYI4VQqxFFe35FnhMSrnRQh1dUMZZqhDiY0PTDtRKwFoLdVQhhGgO\nTAXulFKWG81W6bgDWAAcRoWDlACjpJRFxkOeFRoOGK9tUIZ6cA9GG+AIcMGP1dFoDeaQJcNwQfDl\nQDrwOnCPlPJwmA/jBsfp/mYpZVy1458HrgSuqeZ1bsjEAX4ppa9aewXqS67RYyzVPgv8UUopo63H\nJOYAS6WUHxmboTTmUV/nVBzqszwUUzVVn1tGHK+lGlA5uJ8BngA+MjZyW6kj3NwLfn9YokMIEQt0\nQBlmDxp93AOsEUJcYpUOIAn1Xfs66npI4HZUjLvV1yXIFNS4LAxps0pHZ+AgcCfqge5B4B0hxAAL\nNWxEXYc5QoibUHsOZgDNgJhz0dFoDWbUE0TXWt7zo4LTN0opg0spjWFJ93R/M1D1tDUbNbHvklKu\nsECbVZQBdiGEXUrpD2l3o552GzVCiMnA/wBvSCkfibIcUzA22VyEWhmCxjF36zP1dU6VGRpCMU1T\nLXPLUg0AIdk5JqBCRm5GxXebrqOOuRd8tWQ8pJTlQogUoEJK6TG0TQb6oAxGS8YD8BivT0spg5vn\npxp7g35loY5QJgLzqj3gmn5dhBAZqPkx0PDyI4SYiMoacj8WjYWU0iOEGIfydB9AGcMLURnBPJzD\nWDRag1lK6UWlCwmLMfHLhBAnjCYnYBNCFKGWMhZZIDOinO5vBhBCuIG3gVHAxJBJ3ljYZ7y24tRl\nl9bUXIZpVAghHkfFrL0spbwv2npM5GbU8lpwZSj4Zb1SCPF3KeWUqClrnNTXObUPpSkUUzTVMbcs\n0SBUarvLQz+vpZRlQog9Rn9WjUVdc+8fKAPekmsipSyu9nNACLEdtbRu1Xh8j/KuVw9p3AG0t1AH\nUJWlpCM1M19ZoeNS1L64zcEGKaVXCLEVtTnUsrEw9hz0M7JEVUopS4QQm4F/Apk/Vsf5vOmvE2oj\nSW/j3+OoG783Rqqexoaxe/cdVNzbVY3QWAb4CihGpV4Cqp58M4BGm0FBCPEwKjXibxq5sQzKg5LJ\nybl7hdF+K2qziyay1Nc59RkhmgwuJ8KaTjO3LNGA2li2yFjmD+pKRuWR3Y7a4GSFjrrm3hNW6RBC\n9BFCFAohLg5ps6O839+irstQs3UAX6I8p32rtWeiNplZpSPIYOBgmFA8K+7TYJatXtXaM1GOPEvG\nQgiRKIRYI4ToLqXMN4zlDNT9+i/O4R4979PKBTGWDv7RyNPKTQX+gvpw+7Da28cND3WDRwjxHMoT\ncgtq1+5soFRKOTyqwkxCqDzim1FxdL+p9vYJKWWp5aIsxIij3IdKC9loH4qiSX2YU0KI1cCukLRy\nPYBNwPPAIpQx9wDQJ1Kx+6ebW6g4WlM1GDpsqMIUSaj4UK/RZwZwsVU6wug6Ze5ZcU2Mfh2o61IJ\n3I1aTn8EtSenKyoPsSXjYaS3m4IKcfwGteHuDpSBFmuVDkPLHCBDSjm6WrsVc8WOMorjUGNwDBWK\n8TPUZshkszWEaPkPKvRiGqrQ0t+A/VLKMecyFuezh/l85OcoL/pcVGzPAVSA/gFUAZPGwm9QMUvz\ngY9RGyFviKoic7kRNZd/ycnrGvzX2L3NQfSTv7nUhzl1yjWWUn4LjEcVSdgCXIVaOYvkl2+dc8si\nDRibsq8FtgLLUcZzPspQLbVKRy1UXRcLx8OHSmsnUSvC64AWwBAp5TErx0NK+SSqqtyfga+B/sBI\nKWVOFK5LK9Rmu+oaTddh7G+4ClUJcxGqyl8HYJCUcp/FY3EjalXsC1ThodVGv+c0FtrDrNFoNBqN\nRqPR1IH2MGs0Go1Go9FoNHWgDWaNRqPRaDQajaYOtMGs0Wg0Go1Go9HUgTaYNRqNRqPRaDSaOtAG\ns0aj0Wg0Go1GUwfaYNZoNBqNRqPRaOpAG8wajUaj0Wg0Gk0daINZo9FoNBqNRqOpA20wazQajUaj\n0Wg0dfD/++/jt9YTmwUAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ps = np.array(ps)\n", "plt.figure(figsize=(12,4))\n", "plt.subplot(121)\n", "plt.contour(X, Y, Z, np.arange(10)**5, cmap='jet')\n", "plt.plot(ps[:, 0], ps[:, 1], '-ro')\n", "plt.subplot(122)\n", "plt.semilogy(range(len(ps)), rosen(ps.T));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Lagrange multipliers and constrained optimization\n", "\n", "Recall why Lagrange multipliers are useful for constrained optimization - a stationary point must be where the constraint surface $g$ touches a level set of the function $f$ (since the value of $f$ does not change on a level set). At that point, $f$ and $g$ are parallel, and hence their gradients are also parallel (since the gradient is normal to the level set). So we want to solve\n", "\n", "$$\\nabla f = -\\lambda \\nabla g$$\n", "\n", "or equivalently,\n", "\n", "$$\\nabla f + \\lambda \\nabla g = 0$$\n", "\n", "![Lagrange multipliers](https://upload.wikimedia.org/wikipedia/commons/thumb/b/bf/LagrangeMultipliers2D.svg/300px-LagrangeMultipliers2D.svg.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Numerical example of using Lagrange multipliers" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Maximize $f (x, y, z) = xy + yz$ subject to the constraints $x + 2y = 6$ and $x − 3z = 0$.\n", "\n", "We set up the equations\n", "\n", "$$\n", "F (x, y, z, λ, μ) = xy + yz − λ(x + 2y − 6) − μ(x − 3z)\n", "$$\n", "\n", "Now set partial derivatives to zero and solve the following set of equations\n", "\n", "\\begin{align}\n", "y - \\lambda - \\mu &= 0 \\\\\n", "x + z - 2\\lambda &= 0 \\\\\n", "y +3\\mu &= 0 \\\\\n", "x + 2y - 6 &= 0 \\\\\n", "x - 3z &= 0\n", "\\end{align}\n", "\n", "which is a linear equation in $x, y, z, \\lambda, \\mu$\n", "\n", "\\begin{align}\n", "\\begin{pmatrix}\n", "0 & 1 & 0 & -1 & -1 \\\\\n", "1 & 0 & 1 & -2 & 0 \\\\\n", "0 & 1 & 0 & 0 & 3 \\\\\n", "1 & 2 & 0 & 0 & 0 \\\\\n", "1 & 0 & -3 & 0 & 0 \\\\\n", "\\end{pmatrix}\\pmatrix{x \\\\ y \\\\ z \\\\ \\lambda \\\\ \\mu} = \\pmatrix{0 \\\\ 0 \\\\ 0 \\\\ 6 \\\\ 0}\n", "\\end{align}" ] }, { "cell_type": "code", "execution_count": 68, "metadata": { "collapsed": false }, "outputs": [], "source": [ "A = np.array([\n", " [0, 1, 0, -1, -1],\n", " [1, 0, 1, -2, 0],\n", " [0, 1, 0, 0, 3],\n", " [1, 2, 0, 0, 0],\n", " [1, 0,-3, 0, 0]])\n", "\n", "b = np.array([0,0,0,6,0])\n", "\n", "sol = la.solve(A, b)" ] }, { "cell_type": "code", "execution_count": 69, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ 3. , 1.5, 1. , 2. , -0.5])" ] }, "execution_count": 69, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sol" ] }, { "cell_type": "code", "execution_count": 70, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def f(x, y, z):\n", " return x*y + y*z" ] }, { "cell_type": "code", "execution_count": 71, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAABoAAAAOBAMAAADDIxFwAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAiXYyEM1Embsi72ZU\n3au6f2Q3AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAp0lEQVQIHT3OPQrCQBCG4TdEksWNxp/SSk/g\nFSxECEgCllrkCKm0tbP1Bm7hQXIEDyASyQmUKIgpnFVwi4GHb2ZngO5wjLzZoC91mvqJ1Yr5Hnao\nrUAbnATvZQNQBUGFMl8QFng14aK3to4zvDvxkmYuOnRwb8QV/tEqswpP6Oe/s5Wg3yL5Jahpm18m\nS3WFK3NGMtlub7oS5Y0HnInkXmdTwgUmo5IPjXwowTkCLxwAAAAASUVORK5CYII=\n", "text/latex": [ "$$6.0$$" ], "text/plain": [ "6.0" ] }, "execution_count": 71, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(*sol[:3])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Check using `scipy.optimize`" ] }, { "cell_type": "code", "execution_count": 72, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Convert to minimization problem by negating function\n", "def f(x):\n", " return -(x[0]*x[1] + x[1]*x[2])" ] }, { "cell_type": "code", "execution_count": 73, "metadata": { "collapsed": false }, "outputs": [], "source": [ "cons = ({'type': 'eq',\n", " 'fun' : lambda x: np.array([x[0] + 2*x[1] - 6, x[0] - 3*x[2]])})" ] }, { "cell_type": "code", "execution_count": 74, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ " nfev: 15\n", " fun: -5.9999999999999689\n", " nit: 3\n", " njev: 3\n", " success: True\n", " status: 0\n", " message: 'Optimization terminated successfully.'\n", " x: array([ 2.99999979, 1.50000011, 0.99999993])\n", " jac: array([-1.50000012, -3.9999997 , -1.50000012, 0. ])" ] }, "execution_count": 74, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x0 = np.array([2,2,0.67])\n", "cx = opt.minimize(f, x0, constraints=cons)\n", "cx" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Another example of constrained optimization\n", "\n", "Many real-world optimization problems have constraints - for example, a set of parameters may have to sum to 1.0 (equality constraint), or some parameters may have to be non-negative (inequality constraint). Sometimes, the constraints can be incorporated into the function to be minimized, for example, the non-negativity constraint $p \\gt 0$ can be removed by substituting $p = e^q$ and optimizing for $q$. Using such workarounds, it may be possible to convert a constrained optimization problem into an unconstrained one, and use the methods discussed above to solve the problem.\n", "\n", "Alternatively, we can use optimization methods that allow the specification of constraints directly in the problem statement as shown in this section. Internally, constraint violation penalties, barriers and Lagrange multipliers are some of the methods used used to handle these constraints. We use the example provided in the Scipy [tutorial](http://docs.scipy.org/doc/scipy/reference/tutorial/optimize.html) to illustrate how to set constraints.\n", "\n", "$$f(x) = -(2xy + 2x - x^2 -2y^2)$$\n", "\n", "subject to the constraint\n", "\n", "\\begin{align}\n", "x^3 - y = 0 \\\\\n", "y - (x-1)^4 - 2 \\ge 0\n", "\\end{align}\n", "\n", "and the bounds\n", "\n", "\\begin{align}\n", "0.5 \\le x \\le 1.5 \\\\\n", "1.5 \\le y \\le 2.5\n", "\\end{align}" ] }, { "cell_type": "code", "execution_count": 75, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def f(x):\n", " return -(2*x[0]*x[1] + 2*x[0] - x[0]**2 - 2*x[1]**2)" ] }, { "cell_type": "code", "execution_count": 76, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAIsAAAAUBAMAAABPB9NaAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nSUVORK5CYII=\n", "text/latex": [ "$$\\left [ 0, \\quad 3, \\quad 0, \\quad 3\\right ]$$" ], "text/plain": [ "[0, 3, 0, 3]" ] }, "execution_count": 76, "metadata": {}, "output_type": "execute_result" }, { "data": { 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TyqJXKPO6J3l1BDqCKgmuHEDcdjq1MviXf/nVzRYhRhQEamvwrlxG0eIF1B07CkBabw/9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Nb2JbOsX2/Sr1+APXtsKlQQmDjxQ1q3zkt8/AUSEkLdu+CT3jP1UODzGQwd+jOzZv1Bnjxepkxp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\nmTGjKDNmGDz5pGsw/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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(0, 3, 100)\n", "y = np.linspace(0, 3, 100)\n", "X, Y = np.meshgrid(x, y)\n", "Z = f(np.vstack([X.ravel(), Y.ravel()])).reshape((100,100))\n", "plt.contour(X, Y, Z, np.arange(-1.99,10, 1), cmap='jet');\n", "plt.plot(x, x**3, 'k:', linewidth=1)\n", "plt.plot(x, (x-1)**4+2, 'k:', linewidth=1)\n", "plt.fill([0.5,0.5,1.5,1.5], [2.5,1.5,1.5,2.5], alpha=0.3)\n", "plt.axis([0,3,0,3])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To set constraints, we pass in a dictionary with keys `ty;pe`, `fun` and `jac`. Note that the inequality constraint assumes a $C_j x \\ge 0$ form. As usual, the `jac` is optional and will be numerically estimate if not provided." ] }, { "cell_type": "code", "execution_count": 77, "metadata": { "collapsed": false }, "outputs": [], "source": [ "cons = ({'type': 'eq',\n", " 'fun' : lambda x: np.array([x[0]**3 - x[1]]),\n", " 'jac' : lambda x: np.array([3.0*(x[0]**2.0), -1.0])},\n", " {'type': 'ineq',\n", " 'fun' : lambda x: np.array([x[1] - (x[0]-1)**4 - 2])})\n", "\n", "bnds = ((0.5, 1.5), (1.5, 2.5))" ] }, { "cell_type": "code", "execution_count": 78, "metadata": { "collapsed": false }, "outputs": [], "source": [ "x0 = [0, 2.5]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Unconstrained optimization" ] }, { "cell_type": "code", "execution_count": 79, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ " nfev: 20\n", " hess_inv: array([[ 0.99999996, 0.49999996],\n", " [ 0.49999996, 0.49999997]])\n", " fun: -1.9999999999999987\n", " nit: 3\n", " njev: 5\n", " success: True\n", " status: 0\n", " message: 'Optimization terminated successfully.'\n", " x: array([ 1.99999996, 0.99999996])\n", " jac: array([ 0., 0.])" ] }, "execution_count": 79, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ux = opt.minimize(f, x0, constraints=None)\n", "ux" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Constrained optimization" ] }, { "cell_type": "code", "execution_count": 80, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ " nfev: 21\n", " fun: 2.0499154720925521\n", " nit: 5\n", " njev: 5\n", " success: True\n", " status: 0\n", " message: 'Optimization terminated successfully.'\n", " x: array([ 1.26089314, 2.00463288])\n", " jac: array([-3.48747873, 5.49674428, 0. ])" ] }, "execution_count": 80, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cx = opt.minimize(f, x0, bounds=bnds, constraints=cons)\n", "cx" ] }, { "cell_type": "code", "execution_count": 81, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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MmY4URfXRloigb19H3bMOyQgh7HEdcwoIt4qMK12IWvkOkum3cgIyJhDInk0w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\nk+xUz6LJOpIAT9DF6EA3Bmu5ODq4LlB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IsjUfAJA99iJG3fsT8idNaZuEdG2tRQDPPGXV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v9wAX3vPQ8dOkTy0ktuEhJAluHDDz1cr0T13r1n6dt3MTt2xFO7dhFmzLiPEiVCJLDFIUtkx20v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\nJbrd5aNq2eCrZk5w2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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(0, 3, 100)\n", "y = np.linspace(0, 3, 100)\n", "X, Y = np.meshgrid(x, y)\n", "Z = f(np.vstack([X.ravel(), Y.ravel()])).reshape((100,100))\n", "plt.contour(X, Y, Z, np.arange(-1.99,10, 1), cmap='jet');\n", "plt.plot(x, x**3, 'k:', linewidth=1)\n", "plt.plot(x, (x-1)**4+2, 'k:', linewidth=1)\n", "plt.text(ux['x'][0], ux['x'][1], 'x', va='center', ha='center', size=20, color='blue')\n", "plt.text(cx['x'][0], cx['x'][1], 'x', va='center', ha='center', size=20, color='red')\n", "plt.fill([0.5,0.5,1.5,1.5], [2.5,1.5,1.5,2.5], alpha=0.3)\n", "plt.axis([0,3,0,3]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Some applications of optimization" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Curve fitting\n", "\n", "Sometimes, we simply want to use non-linear least squares to fit a function to data, perhaps to estimate parameters for a mechanistic or phenomenological model. The `curve_fit` function uses the quasi-Newton Levenberg-Marquadt algorithm to perform such fits. Behind the scenes, `curve_fit` is just a wrapper around the `leastsq` function that does nonlinear least squares fitting." ] }, { "cell_type": "code", "execution_count": 82, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from scipy.optimize import curve_fit " ] }, { "cell_type": "code", "execution_count": 83, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def logistic4(x, a, b, c, d):\n", " \"\"\"The four paramter logistic function is often used to fit dose-response relationships.\"\"\"\n", " return ((a-d)/(1.0+((x/c)**b))) + d" ] }, { "cell_type": "code", "execution_count": 84, "metadata": { "collapsed": false }, "outputs": [], "source": [ "nobs = 24\n", "xdata = np.linspace(0.5, 3.5, nobs)\n", "ptrue = [10, 3, 1.5, 12]\n", "ydata = logistic4(xdata, *ptrue) + 0.5*np.random.random(nobs)" ] }, { "cell_type": "code", "execution_count": 85, "metadata": { "collapsed": false }, "outputs": [], "source": [ "popt, pcov = curve_fit(logistic4, xdata, ydata) " ] }, { "cell_type": "code", "execution_count": 86, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Param\tTrue\tEstim (+/- 1 SD)\n", "a\t10.00\t10.38 (+/- 0.09)\n", "b\t 3.00\t 4.04 (+/- 0.77)\n", "c\t 1.50\t 1.47 (+/- 0.07)\n", "d\t12.00\t12.08 (+/- 0.08)\n" ] } ], "source": [ "perr = yerr=np.sqrt(np.diag(pcov))\n", "print('Param\\tTrue\\tEstim (+/- 1 SD)')\n", "for p, pt, po, pe in zip('abcd', ptrue, popt, perr):\n", " print('%s\\t%5.2f\\t%5.2f (+/-%5.2f)' % (p, pt, po, pe))" ] }, { "cell_type": "code", "execution_count": 87, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(0, 4, 100)\n", "y = logistic4(x, *popt)\n", "plt.plot(xdata, ydata, 'o')\n", "plt.plot(x, y);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Finding paraemeters for ODE models\n", "\n", "This is a specialized application of `curve_fit`, in which the curve to be fitted is defined implicitly by an ordinary differential equation \n", "$$\n", "\\frac{dx}{dt} = -kx\n", "$$\n", "and we want to use observed data to estimate the parameters $k$ and the initial value $x_0$. Of course this can be explicitly solved but the same approach can be used to find multiple parameters for $n$-dimensional systems of ODEs.\n", "\n", "[A more elaborate example for fitting a system of ODEs to model the zombie apocalypse](http://adventuresinpython.blogspot.com/2012/08/fitting-differential-equation-system-to.html)" ] }, { "cell_type": "code", "execution_count": 88, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from scipy.integrate import odeint\n", "\n", "def f(x, t, k):\n", " \"\"\"Simple exponential decay.\"\"\"\n", " return -k*x\n", "\n", "def x(t, k, x0):\n", " \"\"\"\n", " Solution to the ODE x'(t) = f(t,x,k) with initial condition x(0) = x0\n", " \"\"\"\n", " x = odeint(f, x0, t, args=(k,))\n", " return x.ravel()" ] }, { "cell_type": "code", "execution_count": 89, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "k = 0.313004\n", "x0 = 9.88547\n" ] } ], "source": [ "# True parameter values\n", "x0_ = 10\n", "k_ = 0.1*np.pi\n", "\n", "# Some random data genererated from closed form soltuion plus Gaussian noise\n", "ts = np.sort(np.random.uniform(0, 10, 200))\n", "xs = x0_*np.exp(-k_*ts) + np.random.normal(0,0.1,200)\n", "\n", "popt, cov = curve_fit(x, ts, xs)\n", "k_opt, x0_opt = popt\n", "\n", "print(\"k = %g\" % k_opt)\n", "print(\"x0 = %g\" % x0_opt)" ] }, { "cell_type": "code", "execution_count": 90, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "t = np.linspace(0, 10, 100)\n", "plt.plot(ts, xs, 'r.', t, x(t, k_opt, x0_opt), '-');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Another example of fitting a system of ODEs using the `lmfit` package\n", "\n", "You may have to install the [`lmfit`](http://cars9.uchicago.edu/software/python/lmfit/index.html) package using `pip` and restart your kernel. The `lmfit` algorithm is another wrapper around `scipy.optimize.leastsq` but allows for richer model specification and more diagnostics." ] }, { "cell_type": "code", "execution_count": 91, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from lmfit import minimize, Parameters, Parameter, report_fit\n", "import warnings" ] }, { "cell_type": "code", "execution_count": 92, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[Fit Statistics]]\n", " # function evals = 169\n", " # data points = 200\n", " # variables = 6\n", " chi-square = 212.716\n", " reduced chi-square = 1.096\n", "[[Variables]]\n", " x0: 1.02052198 +/- 0.181683 (17.80%) (init= 0)\n", " y0: 1.07046508 +/- 0.110177 (10.29%) (init= 1.997345)\n", " a: 3.54341848 +/- 0.454160 (12.82%) (init= 2)\n", " b: 1.21280681 +/- 0.148475 (12.24%) (init= 2)\n", " c: 0.84529664 +/- 0.079478 (9.40%) (init= 2)\n", " d: 0.85715536 +/- 0.085627 (9.99%) (init= 2)\n", "[[Correlations]] (unreported correlations are < 0.100)\n", " C(a, b) = 0.960 \n", " C(a, d) = -0.956 \n", " C(b, d) = -0.878 \n", " C(x0, b) = -0.759 \n", " C(x0, a) = -0.745 \n", " C(y0, c) = -0.717 \n", " C(y0, d) = -0.683 \n", " C(c, d) = 0.667 \n", " C(x0, d) = 0.578 \n", " C(a, c) = -0.532 \n", " C(y0, a) = 0.475 \n", " C(b, c) = -0.433 \n", " C(y0, b) = 0.271 \n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/Users/cliburn/anaconda/envs/py35/lib/python3.5/site-packages/ipykernel/__main__.py:4: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n" ] }, { "data": { "image/png": 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Wq7UPSGp9YO/UJMPfkzT8gk9/lpwnjwDge/mjuP7lOCJaRMGNN02aGN7+hVyy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\nWp79GwA5191A1lVXj/r7SG12431bAo4xEXt0LMPyxmjAOh3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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def f(xs, t, ps):\n", " \"\"\"Lotka-Volterra predator-prey model.\"\"\"\n", " try:\n", " a = ps['a'].value\n", " b = ps['b'].value\n", " c = ps['c'].value\n", " d = ps['d'].value\n", " except:\n", " a, b, c, d = ps\n", " \n", " x, y = xs\n", " return [a*x - b*x*y, c*x*y - d*y]\n", "\n", "def g(t, x0, ps):\n", " \"\"\"\n", " Solution to the ODE x'(t) = f(t,x,k) with initial condition x(0) = x0\n", " \"\"\"\n", " x = odeint(f, x0, t, args=(ps,))\n", " return x\n", "\n", "def residual(ps, ts, data):\n", " x0 = ps['x0'].value, ps['y0'].value\n", " model = g(ts, x0, ps)\n", " return (model - data).ravel()\n", "\n", "t = np.linspace(0, 10, 100)\n", "x0 = np.array([1,1])\n", "\n", "a, b, c, d = 3,1,1,1\n", "true_params = np.array((a, b, c, d))\n", "\n", "np.random.seed(123)\n", "data = g(t, x0, true_params)\n", "data += np.random.normal(size=data.shape)\n", "\n", "# set parameters incluing bounds\n", "params = Parameters()\n", "params.add('x0', value= float(data[0, 0]), min=0, max=10) \n", "params.add('y0', value=float(data[0, 1]), min=0, max=10) \n", "params.add('a', value=2.0, min=0, max=10)\n", "params.add('b', value=2.0, min=0, max=10)\n", "params.add('c', value=2.0, min=0, max=10)\n", "params.add('d', value=2.0, min=0, max=10)\n", "\n", "# fit model and find predicted values\n", "result = minimize(residual, params, args=(t, data), method='leastsq')\n", "final = data + result.residual.reshape(data.shape)\n", "\n", "# plot data and fitted curves\n", "plt.plot(t, data, 'o')\n", "plt.plot(t, final, '-', linewidth=2);\n", "\n", "# display fitted statistics\n", "report_fit(result)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Optimization of graph node placement\n", "\n", "To show the many different applications of optimization, here is an example using optimization to change the layout of nodes of a graph. We use a physical analogy - nodes are connected by springs, and the springs resist deformation from their natural length $l_{ij}$. Some nodes are pinned to their initial locations while others are free to move. Because the initial configuration of nodes does not have springs at their natural length, there is tension resulting in a high potential energy $U$, given by the physics formula shown below. Optimization finds the configuration of lowest potential energy given that some nodes are fixed (set up as boundary constraints on the positions of the nodes).\n", "\n", "$$U = \\frac{1}{2}\\sum_{i,j=1}^n ka_{ij}\\left(||p_i - p_j||-l_{ij}\\right)^2$$\n", "\n", "Note that the ordination algorithm Multi-Dimensional Scaling (MDS) works on a very similar idea - take a high dimensional data set in $\\mathbb{R}^n$, and project down to a lower dimension ($\\mathbb{R}^k$) such that the sum of distances $d_n(x_i, x_j) - d_k(x_i, x_j)$, where $d_n$ and $d_k$ are some measure of distance between two points $x_i$ and $x_j$ in $n$ and $d$ dimension respectively, is minimized. MDS is often used in exploratory analysis of high-dimensional data to get some intuitive understanding of its \"structure\"." ] }, { "cell_type": "code", "execution_count": 93, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from scipy.spatial.distance import pdist, squareform" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- P0 is the initial location of nodes\n", "- P is the minimal energy location of nodes given constraints\n", "- A is a connectivity matrix - there is a spring between $i$ and $j$ if $A_{ij} = 1$\n", "- $L_{ij}$ is the resting length of the spring connecting $i$ and $j$\n", "- In addition, there are a number of `fixed` nodes whose positions are pinned." ] }, { "cell_type": "code", "execution_count": 94, "metadata": { "collapsed": false }, "outputs": [], "source": [ "n = 20\n", "k = 1 # spring stiffness\n", "P0 = np.random.uniform(0, 5, (n,2)) \n", "A = np.ones((n, n))\n", "A[np.tril_indices_from(A)] = 0\n", "L = A.copy()" ] }, { "cell_type": "code", "execution_count": 95, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def energy(P):\n", " P = P.reshape((-1, 2))\n", " D = squareform(pdist(P))\n", " return 0.5*(k * A * (D - L)**2).sum()" ] }, { "cell_type": "code", "execution_count": 96, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$$479.136508399$$" ], "text/plain": [ "479.136508399" ] }, "execution_count": 96, "metadata": {}, "output_type": "execute_result" } ], "source": [ "energy(P0.ravel())" ] }, { "cell_type": "code", "execution_count": 97, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[[1.191249528562059, 1.191249528562059],\n", " [4.0389554314507805, 4.0389554314507805],\n", " [4.474891439430058, 4.474891439430058],\n", " [0.216114460398234, 0.216114460398234],\n", " [1.5097341813135952, 1.5097341813135952],\n", " [4.902910992971438, 4.902910992971438],\n", " [2.6975241127686767, 2.6975241127686767],\n", " [3.1315468085492815, 3.1315468085492815],\n", " [None, None],\n", " [None, None],\n", " [None, None],\n", " [None, None]]" ] }, "execution_count": 97, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# fix the position of the first few nodes just to show constraints\n", "fixed = 4\n", "bounds = (np.repeat(P0[:fixed,:].ravel(), 2).reshape((-1,2)).tolist() + \n", " [[None, None]] * (2*(n-fixed)))\n", "bounds[:fixed*2+4]" ] }, { "cell_type": "code", "execution_count": 98, "metadata": { "collapsed": true }, "outputs": [], "source": [ "sol = opt.minimize(energy, P0.ravel(), bounds=bounds)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Visualization\n", "\n", "Original placement is BLUE\n", "Optimized arrangement is RED." ] }, { "cell_type": "code", "execution_count": 99, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.scatter(P0[:, 0], P0[:, 1], s=25)\n", "P = sol.x.reshape((-1,2))\n", "plt.scatter(P[:, 0], P[:, 1], edgecolors='red', facecolors='none', s=30, linewidth=2);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Optimization of standard statistical models\n", "---\n", "\n", "When we solve standard statistical problems, an optimization procedure similar to the ones discussed here is performed. For example, consider multivariate logistic regression - typically, a Newton-like algorithm known as iteratively reweighted least squares (IRLS) is used to find the maximum likelihood estimate for the generalized linear model family. However, using one of the multivariate scalar minimization methods shown above will also work, for example, the BFGS minimization algorithm. \n", "\n", "The take home message is that there is nothing magic going on when Python or R fits a statistical model using a formula - all that is happening is that the objective function is set to be the negative of the log likelihood, and the minimum found using some first or second order optimization algorithm." ] }, { "cell_type": "code", "execution_count": 100, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import statsmodels.api as sm" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Logistic regression as optimization\n", "\n", "Suppose we have a binary outcome measure $Y \\in {0,1}$ that is conditinal on some input variable (vector) $x \\in (-\\infty, +\\infty)$. Let the conditioanl probability be $p(x) = P(Y=y | X=x)$. Given some data, one simple probability model is $p(x) = \\beta_0 + x\\cdot\\beta$ - i.e. linear regression. This doesn't really work for the obvious reason that $p(x)$ must be between 0 and 1 as $x$ ranges across the real line. One simple way to fix this is to use the transformation $g(x) = \\frac{p(x)}{1 - p(x)} = \\beta_0 + x.\\beta$. Solving for $p$, we get\n", "\n", "$$p(x) = \\frac{1}{1 + e^{-(\\beta_0 + x\\cdot\\beta)}}$$\n", "\n", "As you all know very well, this is logistic regression.\n", "\n", "Suppose we have $n$ data points $(x_i, y_i)$ where $x_i$ is a vector of features and $y_i$ is an observed class (0 or 1). For each event, we either have \"success\" ($y = 1$) or \"failure\" ($Y = 0$), so the likelihood looks like the product of Bernoulli random variables. According to the logistic model, the probability of success is $p(x_i)$ if $y_i = 1$ and $1-p(x_i)$ if $y_i = 0$. So the likelihood is\n", "\n", "$$L(\\beta_0, \\beta) = \\prod_{i=1}^n p(x_i)^y(1-p(x_i))^{1-y}$$\n", "\n", "and the log-likelihood is \n", "\n", "\\begin{align}\n", "l(\\beta_0, \\beta) &= \\sum_{i=1}^{n} y_i \\log{p(x_i)} + (1-y_i)\\log{1-p(x_i)} \\\\\n", "&= \\sum_{i=1}^{n} \\log{1-p(x_i)} + \\sum_{i=1}^{n} y_i \\log{\\frac{p(x_i)}{1-p(x_i)}} \\\\\n", "&= \\sum_{i=1}^{n} -\\log 1 + e^{\\beta_0 + x_i\\cdot\\beta} + \\sum_{i=1}^{n} y_i(\\beta_0 + x_i\\cdot\\beta)\n", "\\end{align}\n", "\n", "Using the standard 'trick', if we augment the matrix $X$ with a column of 1s, we can write $\\beta_0 + x_i\\cdot\\beta$ as just $X\\beta$." ] }, { "cell_type": "code", "execution_count": 101, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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admitgregparank
003803.613
116603.673
218004.001
316403.194
405202.934
\n", "
" ], "text/plain": [ " admit gre gpa rank\n", "0 0 380 3.61 3\n", "1 1 660 3.67 3\n", "2 1 800 4.00 1\n", "3 1 640 3.19 4\n", "4 0 520 2.93 4" ] }, "execution_count": 101, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df_ = pd.read_csv(\"http://www.ats.ucla.edu/stat/data/binary.csv\")\n", "df_.head()" ] }, { "cell_type": "code", "execution_count": 102, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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admitdummygregpa
0013803.61
1116603.67
2118004.00
3116403.19
4015202.93
\n", "
" ], "text/plain": [ " admit dummy gre gpa\n", "0 0 1 380 3.61\n", "1 1 1 660 3.67\n", "2 1 1 800 4.00\n", "3 1 1 640 3.19\n", "4 0 1 520 2.93" ] }, "execution_count": 102, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# We will ignore the rank categorical value\n", "\n", "cols_to_keep = ['admit', 'gre', 'gpa']\n", "df = df_[cols_to_keep]\n", "df.insert(1, 'dummy', 1)\n", "df.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Solving as a GLM with IRLS\n", "\n", "This is very similar to what you would do in R, only using Python's `statsmodels` package. The GLM solver uses a special variant of Newton's method known as iteratively reweighted least squares (IRLS), which will be further desribed in the lecture on multivarite and constrained optimizaiton." ] }, { "cell_type": "code", "execution_count": 103, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
Generalized Linear Model Regression Results
Dep. Variable: admit No. Observations: 400
Model: GLM Df Residuals: 397
Model Family: Binomial Df Model: 2
Link Function: logit Scale: 1.0
Method: IRLS Log-Likelihood: -240.17
Date: Thu, 18 Feb 2016 Deviance: 480.34
Time: 15:23:26 Pearson chi2: 398.
No. Iterations: 6
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coef std err z P>|z| [95.0% Conf. Int.]
Intercept -4.9494 1.075 -4.604 0.000 -7.057 -2.842
gre 0.0027 0.001 2.544 0.011 0.001 0.005
gpa 0.7547 0.320 2.361 0.018 0.128 1.381
" ], "text/plain": [ "\n", "\"\"\"\n", " Generalized Linear Model Regression Results \n", "==============================================================================\n", "Dep. Variable: admit No. Observations: 400\n", "Model: GLM Df Residuals: 397\n", "Model Family: Binomial Df Model: 2\n", "Link Function: logit Scale: 1.0\n", "Method: IRLS Log-Likelihood: -240.17\n", "Date: Thu, 18 Feb 2016 Deviance: 480.34\n", "Time: 15:23:26 Pearson chi2: 398.\n", "No. Iterations: 6 \n", "==============================================================================\n", " coef std err z P>|z| [95.0% Conf. Int.]\n", "------------------------------------------------------------------------------\n", "Intercept -4.9494 1.075 -4.604 0.000 -7.057 -2.842\n", "gre 0.0027 0.001 2.544 0.011 0.001 0.005\n", "gpa 0.7547 0.320 2.361 0.018 0.128 1.381\n", "==============================================================================\n", "\"\"\"" ] }, "execution_count": 103, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model = sm.GLM.from_formula('admit ~ gre + gpa', \n", " data=df, family=sm.families.Binomial())\n", "fit = model.fit()\n", "fit.summary()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Solving as logistic model with bfgs\n", "\n", "Note that you can choose any of the scipy.optimize algotihms to fit the maximum likelihood model. This knows about higher order derivatives, so will be more accurate than homebrew version." ] }, { "cell_type": "code", "execution_count": 104, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully.\n", " Current function value: 0.600430\n", " Iterations: 23\n", " Function evaluations: 65\n", " Gradient evaluations: 54\n" ] }, { "data": { "text/html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
Logit Regression Results
Dep. Variable: admit No. Observations: 400
Model: Logit Df Residuals: 397
Method: MLE Df Model: 2
Date: Thu, 18 Feb 2016 Pseudo R-squ.: 0.03927
Time: 15:23:26 Log-Likelihood: -240.17
converged: True LL-Null: -249.99
LLR p-value: 5.456e-05
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
coef std err z P>|z| [95.0% Conf. Int.]
Intercept -4.9494 1.075 -4.604 0.000 -7.057 -2.842
gre 0.0027 0.001 2.544 0.011 0.001 0.005
gpa 0.7547 0.320 2.361 0.018 0.128 1.381
" ], "text/plain": [ "\n", "\"\"\"\n", " Logit Regression Results \n", "==============================================================================\n", "Dep. Variable: admit No. Observations: 400\n", "Model: Logit Df Residuals: 397\n", "Method: MLE Df Model: 2\n", "Date: Thu, 18 Feb 2016 Pseudo R-squ.: 0.03927\n", "Time: 15:23:26 Log-Likelihood: -240.17\n", "converged: True LL-Null: -249.99\n", " LLR p-value: 5.456e-05\n", "==============================================================================\n", " coef std err z P>|z| [95.0% Conf. Int.]\n", "------------------------------------------------------------------------------\n", "Intercept -4.9494 1.075 -4.604 0.000 -7.057 -2.842\n", "gre 0.0027 0.001 2.544 0.011 0.001 0.005\n", "gpa 0.7547 0.320 2.361 0.018 0.128 1.381\n", "==============================================================================\n", "\"\"\"" ] }, "execution_count": 104, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model2 = sm.Logit.from_formula('admit ~ %s' % '+'.join(df.columns[2:]), data=df)\n", "fit2 = model2.fit(method='bfgs', maxiter=100)\n", "fit2.summary()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Home-brew logistic regression using a generic minimization function\n", "\n", "This is to show that there is no magic going on - you can write the function to minimize directly from the log-likelihood equation and run a minimizer. It will be more accurate if you also provide the derivative (+/- the Hessian for second order methods), but using just the function and numerical approximations to the derivative will also work. As usual, this is for illustration so you understand what is going on - when there is a library function available, youu should probably use that instead." ] }, { "cell_type": "code", "execution_count": 105, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def f(beta, y, x):\n", " \"\"\"Minus log likelihood function for logistic regression.\"\"\"\n", " return -((-np.log(1 + np.exp(np.dot(x, beta)))).sum() + (y*(np.dot(x, beta))).sum())" ] }, { "cell_type": "code", "execution_count": 106, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ " nfev: 80\n", " hess_inv: array([[ 1.15242936e+00, -2.77649429e-04, -2.81644777e-01],\n", " [ -2.77649429e-04, 1.16649722e-06, -1.22069519e-04],\n", " [ -2.81644777e-01, -1.22069519e-04, 1.02628000e-01]])\n", " fun: 240.17199089493948\n", " nit: 8\n", " njev: 16\n", " success: True\n", " status: 0\n", " message: 'Optimization terminated successfully.'\n", " x: array([ -4.94933570e+00, 2.69034401e-03, 7.54734491e-01])\n", " jac: array([ 9.15527344e-05, -1.96456909e-03, 4.59671021e-04])" ] }, "execution_count": 106, "metadata": {}, "output_type": "execute_result" } ], "source": [ "beta0 = np.zeros(3)\n", "opt.minimize(f, beta0, args=(df['admit'], df.ix[:, 'dummy':]), method='BFGS', options={'gtol':1e-2})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Optimization with `sklearn`\n", "\n", "There are also many optimization routines in the `scikit-learn` package, as you already know from the previous lectures. Many machine learning problems essentially boil down to the minimization of some appropriate loss function." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Resources\n", "\n", "- [Scipy Optimize refernce](http://docs.scipy.org/doc/scipy/reference/optimize.html)\n", "- [Scipy Optimize tutorial](http://docs.scipy.org/doc/scipy/reference/tutorial/optimize.html)\n", "- [LMFit - a modeling interface for nonlinear least squares problems](http://cars9.uchicago.edu/software/python/lmfit/index.html)\n", "- [CVXpy- a modeling interface for convex optimization problems](https://github.com/cvxgrp/cvxpy)\n", "- [Quasi-Newton methods](http://en.wikipedia.org/wiki/Quasi-Newton_method)\n", "- [Convex optimization book by Boyd & Vandenberghe](http://stanford.edu/~boyd/cvxbook/)\n", "- [Nocedal and Wright textbook](http://www.springer.com/us/book/9780387303031)" ] }, { "cell_type": "code", "execution_count": 107, "metadata": { "collapsed": false }, "outputs": [ { "data": { "application/json": { "Software versions": [ { "module": "Python", "version": "3.5.1 64bit [GCC 4.2.1 (Apple Inc. build 5577)]" }, { "module": "IPython", "version": "4.0.1" }, { "module": "OS", "version": "Darwin 15.3.0 x86_64 i386 64bit" }, { "module": "scipy", "version": "0.16.1" }, { "module": "statsmodels", "version": "0.6.1" }, { "module": "sympy", "version": "0.7.6.1" }, { "module": "lmfit", "version": "0.9.2" } ] }, "text/html": [ "
SoftwareVersion
Python3.5.1 64bit [GCC 4.2.1 (Apple Inc. build 5577)]
IPython4.0.1
OSDarwin 15.3.0 x86_64 i386 64bit
scipy0.16.1
statsmodels0.6.1
sympy0.7.6.1
lmfit0.9.2
Thu Feb 18 15:23:26 2016 EST
" ], "text/latex": [ "\\begin{tabular}{|l|l|}\\hline\n", "{\\bf Software} & {\\bf Version} \\\\ \\hline\\hline\n", "Python & 3.5.1 64bit [GCC 4.2.1 (Apple Inc. build 5577)] \\\\ \\hline\n", "IPython & 4.0.1 \\\\ \\hline\n", "OS & Darwin 15.3.0 x86\\_64 i386 64bit \\\\ \\hline\n", "scipy & 0.16.1 \\\\ \\hline\n", "statsmodels & 0.6.1 \\\\ \\hline\n", "sympy & 0.7.6.1 \\\\ \\hline\n", "lmfit & 0.9.2 \\\\ \\hline\n", "\\hline \\multicolumn{2}{|l|}{Thu Feb 18 15:23:26 2016 EST} \\\\ \\hline\n", "\\end{tabular}\n" ], "text/plain": [ "Software versions\n", "Python 3.5.1 64bit [GCC 4.2.1 (Apple Inc. build 5577)]\n", "IPython 4.0.1\n", "OS Darwin 15.3.0 x86_64 i386 64bit\n", "scipy 0.16.1\n", "statsmodels 0.6.1\n", "sympy 0.7.6.1\n", "lmfit 0.9.2\n", "Thu Feb 18 15:23:26 2016 EST" ] }, "execution_count": 107, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%load_ext version_information\n", "%version_information scipy, statsmodels, sympy, lmfit" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 0 }