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MA5243 homework 2
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"source": [
"**Name**: Ng Yee Sian\n",
"\n",
"**Matric. No.**: A0073120Y\n",
" \n",
"MA5243 Homework 2\n",
"==="
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"-----\n",
"We will be using the following numerical and plotting libraries to emulate a MATLAB-like environment within python:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from numpy import *\n",
"from numpy.linalg import *\n",
"import matplotlib.pyplot as plt\n",
"\n",
"N_MAX = 10000 # max. no. of iterations\n",
"EPS = 1e-5 # precision"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 13
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Brief remark: in the codes for the algorithms to follow, I'll be returning the entire trace/history of all the iterates, rather than the final solution itself (which can be obtained by taking the last point in the history of iterates) - this is so that we can trace the progress of the algorithm in questions 4 and 5*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"-----\n",
"1) Write the following codes for minimizing a function $f:\\Re^2\\rightarrow \\Re$, where functions for $f(\\cdot)$, $\\nabla f(\\cdot)$, and $\\nabla^2 f(\\cdot)$ are available:\n",
"\n",
" - Steepest descent with backtracking linesearch\n",
" - Newton's method with backtracking linesearch\n",
"\n",
"State clearly in your writeup how the backtracking rules are implemented. For the Newton's method, one may not be able to apply the usual formula $-\\nabla^2 f(x_k)^{-1}\\nabla f(x_k)$ for the Newton step when $\\nabla^2 f(x_k)$ is not positive definite, so state how you continue to minimize $f$ for this case."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def line_search(x, f, p, g, alpha=1 ,rho=0.4, c=0.4, n_max=N_MAX):\n",
" step = c*dot(p,g(x))\n",
" for i in range(n_max):\n",
" if f(x + alpha*p) <= f(x) + alpha*step:\n",
" return alpha\n",
" else:\n",
" alpha *= rho\n",
" return alpha"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 14
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def steepest_descent(f, g, x, alpha=1, rho=0.4, c=0.4, epsilon=EPS, n_max=N_MAX):\n",
" iterates = [x]\n",
" for i in range(n_max):\n",
" if norm(g(x)) <= epsilon:\n",
" return iterates\n",
" else:\n",
" a = line_search(x,f,-g(x),g,alpha,rho,c,n_max)\n",
" x = x - a*g(x)\n",
" iterates.append(x)\n",
" return iterates # even though it hasn't converged after n_max steps"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 24
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def newton_method(f, g, h, x, alpha=1 ,rho=0.4, c=0.4, epsilon=EPS, n_max=N_MAX):\n",
" iterates = [x]\n",
" for i in range(n_max):\n",
" if norm(g(x)) <= epsilon:\n",
" return iterates\n",
" else:\n",
" p = - dot(inv(h(x)),g(x)) # h(x) assumed to be positive definite here (for efficiency)\n",
" a = line_search(x,f,p,g,alpha,rho,c,n_max)\n",
" x = x + a*p\n",
" iterates.append(x)\n",
" return iterates # even though it hasn't converged after n_max steps"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 26
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Remark**: in Newton's method here, the Hessian is assumed to be positive definite - it is easier to condition the Hessian within the (user-specified) function that computes the Hessian - so that users of the function who are certain that their Hessian is always positive definite do not have to pay for the compromise in performance for a more robust algorithm.\n",
"\n",
"The details of how to deal with non-positive definite Hessians will be provided in question 3."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"-----\n",
"2) Write codes for the trust region method for minimizing a function $f:\\Re^2\\rightarrow \\Re$ where $f(\\cdot)$, $\\nabla f(\\cdot)$, and $\\nabla^2 f(\\cdot)$ are easily obtained.\n",
"\n",
"In the writeup, describe the method that you used to solve (approximately or accurately) the trust region subproblem for the cases where $\\nabla^2 f(\\cdot)$ is positive definite and when $\\nabla^2 f(\\cdot)$ is not positive definite. Since this code will be compared to steepest descent and Newton's method, do not take the Cauchy point as the final step when $\\nabla^2 f(\\cdot)$ is positive definite."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def m(f,g,h,p,x): # trust region subproblem\n",
" return f(x)+dot(g(x),p)+0.5*dot(p,dot(h(x),p))\n",
"\n",
"def dogleg(hess,grad,delta):\n",
" pN = - dot(inv(hess),grad) # hess assumed to be positive definite\n",
" if norm(pN) <= delta:\n",
" return pN\n",
" else:\n",
" tau = min(norm(grad)**3/(delta*dot(grad,dot(hess,grad))),1)\n",
" pC = - tau*delta/norm(grad)*grad\n",
" if norm(pC) >= delta:\n",
" return delta / norm(pC) * pC\n",
" else:\n",
" diff = pN - pC\n",
" sq_diff = dot(diff,diff)\n",
" fact = dot(pC,diff)**2 - sq_diff * (dot(pC,pC)-delta**2)\n",
" tau = (sqrt(fact)-dot(pC,diff))/sq_diff\n",
" return pC + tau*diff"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 17
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Remark**: in the Dogleg method here, the Hessian is assumed to be positive definite - it is easier to condition the Hessian within the (user-specified) function that computes the Hessian - so that users of the function who are certain that their Hessian is always positive definite do not have to pay for the compromise in performance for a more robust algorithm.\n",
"\n",
"The details of how to deal with non-positive definite Hessians will be provided in question 3."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def trust_region(f,g,h,x, Delta=1.0, delta=0.7, eta=0.2, epsilon=EPS, n_max=N_MAX):\n",
" zero = zeros(len(x))\n",
" iterates = [x]\n",
" \n",
" for i in range(n_max):\n",
" if norm(g(x)) <= epsilon:\n",
" return iterates\n",
" else:\n",
" p = dogleg(h(x),g(x),delta)\n",
" rho = (f(x)-f(x+p))/(m(f,g,h,zero,x)-m(f,g,h,p,x))\n",
" \n",
" if rho < 0.25:\n",
" delta *= 0.25 # reduce trust region\n",
" elif rho > 0.75 and abs(norm(p)-delta) < epsilon:\n",
" delta = min(2*delta,Delta)\n",
" \n",
" if rho > eta:\n",
" x = x + p\n",
"\n",
" iterates.append(x)\n",
" \n",
" return iterates # even though it has not converged after n_max iterations"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 18
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"-----\n",
"3) Use your codes to minimise the Rosenbrock function\n",
"\n",
"$f(x) = 100(x_2-x_1^2)^2 + (1-x_1)^2$\n",
"\n",
"with the starting points $(-1.2,1)$ and $(0,1/199)$. Choose also 2 other starting points."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def f(x): return 100*(x[1]-x[0]**2)**2 + (1-x[0])**2\n",
"\n",
"# compute the gradient of the (2D) rosenbrock function\n",
"def g(x): return array([400*(x[0]**3-x[0]*x[1])+2*(x[0]-1),200*(x[1]-x[0]**2)])\n",
"\n",
"# compute the hessian of the (2d) rosenbrock function (we deal with the issues of non-positive-definiteness here)\n",
"def h(x):\n",
" epsilon=1e-5\n",
" hes = array([[1200*x[0]**2-400*x[1]+2,-400*x[0]],[-400*x[0],200]])\n",
" e_val,e_vec = eig(hes)\n",
" e_val = sorted(e_val)\n",
" v = e_val[0].real # v = smallest eigenvalue (may be negative)\n",
" if v <= 0:\n",
" return hes+(epsilon-v)*np.eye(len(x))\n",
" else:\n",
" return hes"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 19
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Remark**: when the Hessian $\\nabla^2 f(x)$ is not positive definite for some $x$, we find the smallest eigenvalue $\\lambda_{min}$, and use the matrix\n",
"\n",
"$B(x) = \\nabla^2 f(x) + (\\epsilon - \\lambda_{min})I$, for some $\\epsilon>0$\n",
"\n",
"in place of the original Hessian $\\nabla^2 f(\\cdot)$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"-----\n",
"4) Depict contour maps, and depict iterates and search directions on the contour maps"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def plot_contour(x0,ax):\n",
" ax.set_title('Starting at '+str(x0))\n",
" xs = steepest_descent(f,g,x0)\n",
" xn = newton_method(f,g,h,x0)\n",
" xt = trust_region(f,g,h,x0)\n",
" \n",
" i,j = mgrid[-1.5:1.7:0.025, -0.2:2.5:0.025]\n",
" ax.contourf(i, j, f([i,j]), 10, alpha=.75, cmap=cm.hot)\n",
" C = contour(i, j, f([i,j]), 10, colors='black',linewidth=.5)\n",
" ax.clabel(C, inline=1, fontsize=10)\n",
" \n",
" xs = zip(*xs)\n",
" ax.plot(xs[0],xs[1],'.-',label='steepest descent')\n",
" xn = zip(*xn)\n",
" ax.plot(xn[0],xn[1],'o-',label=\"newton's method\")\n",
" xt = zip(*xt)\n",
" ax.plot(xt[0],xt[1],'^-',label=\"trust region\")\n",
" \n",
" ax.legend(loc='best')"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 46
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig,ax = plt.subplots(2,2,figsize=(18,15))\n",
"for i,x0 in enumerate([array([-1.2,1]),\n",
" array([0,1./199]),\n",
" array([0,1]),\n",
" array([1.5,0.5])]):\n",
" plot_contour(x0,ax[i//2,i%2])"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
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ziAaYR0KHeUQbnGkQJL3PNgC0vb4BoKMuf1OOnXNP3X9XX5748lh3z60jahTo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\nJA2ysrLo2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jSYNWsW/fv3x8fHh7Vr19b7vsTERAYNGsTgwYM599xzXdUdj9LYbTNv3jyS\nk5Pp3bs3zz77rIU9dK9jx44xduxYkpKSuOSSS8iv57mt7W3facz+cPfdd9O7d29SUlJYt26dxT10\nrzNtn4ULF9KhQwcGDx7M4MGD+etf/+qGXrrHrbfeSlxcHAMHDqz3Pe153znT9mnP+463UyzSMMUj\nDVM84pzikYYpHqmf4pGGeXQ8YrrI1q1bze3bt5tpaWnmTz/9VO/7EhMTzdzcXFd1wyM1Zts4HA6z\nZ8+e5t69e83y8nIzJSXF3LJli8U9dY8HHnjAfPbZZ03TNM2//e1v5oMPPuj0fe1p32nM/jBnzhxz\n3Lhxpmma5sqVK81hw4a5o6tu0Zjt85///Me86qqr3NRD91q8eLG5du1ac8CAAU5fb8/7jmmeefu0\n533H2ykWaZjikYYpHjmd4pGGKR5pmOKRhnlyPOKySoPk5GSSkpIam7hwVTc8UmO2zerVq+nVqxeJ\niYn4+fkxceJEZs+ebVEP3eurr75i0qRJAEyaNIkvv/yy3ve2l32nMftD7e02bNgw8vPzyc7Odkd3\nLdfY46W97C+nOv/884mMjKz39fa878CZtw+0333H2ykWaZjikYYpHjmd4pGGKR5pmOKRhnlyPOL2\nOQ0Mw+Diiy9m6NChvPXWW+7ujsfIysqia9euNT8nJCSQlZXlxh5ZJzs7m7i4OADi4uLq/bJoT/tO\nY/YHZ+/JzMy0rI/u1JjtYxgGy5cvJyUlhcsvv5wtW7ZY3U2P1Z73ncbQvtP2tafzSVMpHlE8Upvi\nkYYpHmmZ9rzvNIY79x3flnx47NixHD58+LTfP/3001x11VWNWsayZcvo3LkzR48eZezYsSQnJ3P+\n+ee3pFseoaXbxjAMV3TLY9S3fZ566qk6PxuGUe+2aKv7jjON3R9OzT629f2oWmPW8+yzzyYjI4Pg\n4GDmzp3LNddcw44dOyzonXdor/tOY2jf8WyKRRqmeKRhikeaRvFIwxSPtFx73Xcaw537TouSBt9/\n/32LO9C5c2cAOnbsyC9+8QtWr17dJr5oW7pt4uPjycjIqPk5IyODhISElnbLYzS0feLi4jh8+DCd\nOnXi0KFDxMbGOn1fW913nGnM/nDqezIzM4mPj7esj+7UmO0TFhZW8//jxo3jzjvv5NixY0RFRVnW\nT0/VnvedxtC+49kUizRM8UjDFI80jeKRhikeaZn2vO80hjv3HUuGJ9Q39uL48eMUFRUBUFJSwvz5\n8xucTbMtqm/bDB06lJ07d7Jv3z7Ky8v55JNPGD9+vMW9c4/x48czY8YMAGbMmME111xz2nva277T\nmP1h/PjxvP/++wCsXLmSiIiImrLKtq4x2yc7O7vmeFu9ejWmaeoEfVJ73ncaQ/tO26BYpGGKR06n\neOR0ikcapnikZdrzvtMYbt13XDXD4hdffGEmJCSYgYGBZlxcnHnZZZeZpmmaWVlZ5uWXX26apmnu\n3r3bTElJMVNSUsz+/fubTz/9tKu641Eas21M0zS//fZbMykpyezZs2e72TamaZq5ubnmRRddZPbu\n3dscO3asmZeXZ5qm9h1n+8Prr79uvv766zXvueuuu8yePXuagwYNanCm8LboTNvnlVdeMfv372+m\npKSYw4cPN1esWOHO7lpq4sSJZufOnU0/Pz8zISHBfOedd7Tv1HKm7dOe9x1vp1ikYYpHGqZ4xDnF\nIw1TPFI/xSMN8+R4xDDNdjp9p4iIiIiIiIg0yO1PTxARERERERERz6SkgYiIiIiIiIg4paSBiIiI\niIiIiDilpIGIiIiIiIiIOKWkgYiIiIiIiIg4paSBiIiIiIiIiDilpIGIiIiIiIiIOKWkgYiIiIiI\niIg4paSBiIiIiIiIiDilpIGIiIiIiIiIOKWkgYiIiIiIiIg4paSBiIiIiIiIiDilpIGIiIiIiIiI\nOKWkgYiIiIiIiIg4paSBiIiIiIiIiDilpIGIiIiIiIiIOKWkgYiIiIiIiIg4paSBiIiIiIiIiDil\npIGIiIiIiIiIOKWkgYiIiIiIiIg4paSBiIiIiIiIiDilpIGIiIiIiIiIOKWkgYiIiIiIiIg4paSB\niIiIiIiIiDilpIGIiIiIiIiIOKWkgYiIiIiIiIg4paSBiIiIiIiIiDilpIGIiIiIiIiIOKWkgYiI\niIiIiIg4paSBiIiIiIiIiDilpIGIiIiIiIiIOKWkgYiIiIiIiIg4paSBiIiIiIiIiDilpIGIiIiI\niIiIOKWkgYiIiIiIiIg4paSBiIiIiIiIiDilpIGIiIiIiIiIOKWkgYiIiIiIiIg4paSBiIiIiIiI\niDilpIGIiIiIiIiIOKWkgYiIiIiIiIg4paSBiIiIiIiIiDilpIGIiIiIiIiIOKWkgYiIiIiIiIg4\npaSBiIiIiIiIiDilpIGIiIiIiIiIOKWkgYiIiIiIiIg4paSBiIiIiIiIiDilpIGIF/nwww+59NJL\n3d0NpxITEwkODmbSpEkuWf6FF15IUFAQ559/vkuWLyIi0p6055jCXX744QfCwsLw8fHhxx9/dHd3\nRBpNSQORZlq6dCkjRowgIiKC6OhoRo0axZo1awB47733Wnxxu2/fPmw2G1VVVTW/u+mmm/juu+9a\ntNzmaMz6GIbBN998w4wZM2p+t2/fPsaMGUNISAh9+/Zt8AS5adMmLr30Ujp27IjNdvpX04IFC3j9\n9debvxIiIiIeSjFFXc5iilNNmTKF5ORkfHx8GnwfwC233EJAQABhYWGEhYURHh6OaZqN7vPMmTPp\n3r07oaGh/OIXvyAvL6/e91YnPKrbuuyyy2peu/jiiykqKqJbt24YhtHo9kXcTUkDkWYoLCzkyiuv\n5J577iEvL4+srCz+8pe/EBAQ0CrLdzgcNf/flJOap7nxxhsZMmQIx44d46mnnuK6664jJyfH6Xv9\n/f2ZOHEi77zzTr3L8+ZtISIi4oxiiuZJTU3ltdde4+yzzz7jBbhhGDz44IMUFRVRVFREYWFhoy/a\nN2/ezB133MGHH35IdnY2wcHB3HnnnQ229c0339S0NW/evCatl4gnUtJApBl27NiBYRj88pe/xDAM\nAgMDGTt2LAMHDmTr1q1MnTqVFStWEBYWRlRUFABz5sxh8ODBdOjQgW7duvHEE0/ULK/6DsC7775L\n9+7dueiiixg9ejQAERERhIeHs3LlytOy8zabjTfeeIOkpCQiIyOZNm1azWtVVVXcd999dOzYkR49\nevDKK6+cdpehtr/97W/06tWL8PBw+vfvz5dffglQ7/o0ZhutW7eOJ554goCAAK699loGDRrE559/\n7vT9SUlJ/Pa3v6Vfv36NWr6IiEhboJiiee68804uvPBCAgMDG/X+5iZMPvzwQ8aPH8+oUaMICQnh\nySef5IsvvqCkpKTV2xLxVEoaiDRDnz598PHx4ZZbbmHevHl1ytT69u3L66+/zvDhwykqKuLYsWMA\nhIaG8sEHH1BQUMCcOXP45z//yezZs+ssd/HixWzbto358+ezePFiAAoKCigsLOS8885z2pc5c+aw\nZs0aNmzYwKefflpTavjmm28yb9481q9fz9q1a/nyyy8bzKr36tWLpUuXUlhYyF/+8hduvvlmsrOz\n612fM9m8eTM9evQgJCSk5ncpKSls3ry5UZ8XERFpDxRTWOO1114jOjqaoUOH8sUXXzT6c1u2bCEl\nJaXm5x49ehAQEMCOHTvq/cxNN91EbGwsl156KRs2bGhRv0U8gZIGIs0QFhbG0qVLMQyD2267jdjY\nWK6++mqOHDkCOM8wjx49mv79+wMwcOBAJk6cyKJFi+q85/HHHycoKIiAgIBGZ6kfeughwsPD6dq1\nK2PGjGH9+vUAfPrpp9x777106dKFiIgIHn744QaXed1119GpUycAbrjhBnr37s2qVavqXZ8zKS4u\npkOHDnV+Fx4eTlFRUZOXJSIi0lYppnC9u+++m127dnH06FGefPJJbrnlFpYvX96ozzY1npk5cyb7\n9+9n//79jBkzhksvvZSCgoIWr4OIOylpINJMycnJTJ8+nYyMDDZt2sTBgwe59957633/qlWrGDNm\nDLGxsURERPDGG2+Qm5tb5z1du3Ztcj+qT8oAwcHBFBcXA3Do0KE6y0tISGhwOe+//z6DBw8mMjKS\nyMhINm3adFr/miI0NJTCwsI6v8vPzyc8PLzZyxQREWmLFFO4VnVfbDYb48aN46abbmp0tUFoaOhp\nF/0FBQWEhYU5ff/w4cMJCAggKCiIhx56iIiICJYsWdLidRBxJyUNRFpBnz59mDRpEps2bQJwWrL3\nq1/9imuuuYbMzEzy8/O54447ThsLWPtzLZ1Vt3PnzmRkZNT8XPv/T7V//36mTJnCq6++yrFjx8jL\ny2PAgAE1dwOa05f+/fuzZ8+emoADYP369TV3RkREROR0iik8S//+/WsqLgB2795NeXk5SUlJjfq8\nt62viDNKGog0w/bt2/n73/9OVlYWcOLk+dFHHzF8+HAA4uLiyMzMpKKiouYzxcXFREZG4u/vz+rV\nq5k5c2aDJ5LqRw/u3r270f0yTbPmpHzDDTfw4osvcvDgQfLz83n22Wfrba+kpATDMIiJiaGqqorp\n06fXBCv1rc+ZJCUlkZqayhNPPIHdbueLL75g06ZNTJgwod7P2O12ysvLASgrK6OsrKzO6zrxiohI\nW6OYonkqKiqw2+1UVVVRXl6O3W6vd+jDZ599RnFxMVVVVcyfP79mcsPGuOmmm/j6669ZunQpJSUl\nPProo0yYMKHOnE3VMjIyWLZsWU1/nnvuOXJzcxk5cmSL1lXE3ZQ0EGmGsLAwVq1axbBhwwgNDWX4\n8OEMGjSIF154AYCLLrqI/v3706lTJ2JjY4ETE/A89thjhIeH8+STT/LLX/6yzjJPPfkGBwfzyCOP\nMHLkSKKioli1ahWGYTR456D267fddhuXXHIJgwYNYsiQIVxxxRX4+Phgs51+2Pfr14/77ruP4cOH\n06lTJzZt2sSoUaNqXne2Ps6cerL++OOPWbNmDVFRUTzyyCN8/vnnREdHO/3svn37CA4OZsCAARiG\nQVBQEH379m1w+SIiIt5OMYVzZzrnjx07luDgYFauXMmUKVMIDg6uGQbw4YcfMmDAgJr3vvTSSyQk\nJBAZGcmDDz7I22+/zQUXXNDg8muvz+uvv85NN91EXFwcpaWlvPbaazWvT506lalTpwJQVFTEnXfe\nSVRUFAkJCcyfP5+5c+cSGRnZqLZEPJVhKgoXaRfmzp3L1KlT2bdvn0uWn5yczKFDh7j22muZPn16\nqy9/7NixNUHV999/3+rLFxERkcbx9pjCXX788Ueuu+46ysvL+fbbb2sehSni6ZQ0EGmj7HY7CxYs\n4JJLLiE7O5sJEyYwYsQI/v73v7u7ayIiIuJFFFOItG9KGoi0UaWlpYwePZpt27YRFBTElVdeyYsv\nvkhoaKi7uyYiIiJeRDGFSPumpIGIiIiIiIiIOOVrVUNRoaHklZRY1ZyIiIhXGD16NAsXLnR3N9oN\nxSMiIiKnaygesazSwDAMJqWlWdFUk4WkpwOQnJrq8rY6nWwr4ZS23t67l9+ddVartNEjPZ1wF6+L\nf0U6PhZsr2qPr97L42MKTvyQZF27rapL+um/69w66/L463t5/I4W7j+HnPTvoJdu6x0n16Uk9cS+\nc27rHFsNqTx5bJf7uW6bFZ5sY08rHnu1v3syTy7/sAXH9rb0dEos/A5prvS9e0ltpe/m+sxYuFBP\nBrGQp8YjDoeDD5cupU9EBHdZcGzcvXAhXQyDz06ZiK214pFpixeztqqKA+edR0xgYIuX58z1Gzcy\nJzeXWWP7cl1SnEvaqO3x1XvZU1DKv3Yc4ZxONlb/tXGz73uKnCI7N7+9nf9sz6PcceJ3PjbomRDI\nzVd04oHfJBAY2Pz7iS2JRRwOB2//O5vXPs1i+77jNf3z9YFB8aG8PzmZ/vHeNRTi2lc38e91OYzp\namPB+AssiUdm7znCNXO3cEmED1+mnu+SNtILCxmxdi2XxcbyWL9+rbbc2t89oxYuJMQweMrFE0Ue\nKCzk+bVrGZ6URFKXLi5tq6XcHY9YVmngyUpSU2sSB652ODW1JnHgSoUWJA4q061NHFCSCiHpJy4I\nvTFxcOoFeJf00y/UWymJcEbOEgTgvUmC2molDKzirQkDZ6xIGIjI6Xx9fQkzDLbn51vSXv/oaDbn\n5lJYUUG4n1+rL/8fI0YweulShqxaxX4XBf6zBg6k0+KF3PD9Vgq7RRPaggvexnp/bD9C/X3456ZD\n9H9wEZuf9Z7Z72PCApn3h5San//x/QH+8Z+97M6089g/9/HYP/dhACFBkNglmIuGRXLvrxJIjA9q\n1X7k51fw6mdZfLkgh537iykqhaqT1yk2A2LCDW4+twvPTjgLX1/vvFS54PHFLMms4vIePswZ55qL\n91PZHQ5+MXcLoTZcljAAuHjtWnyhVRMGtb21Zw9VwO2DB7tk+bW9vm4dgMcnDDyBdx6JbUBmevpp\n1QatZU9qKj1cnJgo90vFvyJdiYOWaEwS4VRNSSqcaVltIUFQ245a69vGEgbVXJkwyLQocQonqgxE\n5HRjhgzhqzVrWJqVxaj4eJe2NblvX/64dCm/W76cT11wUe/r68vkxETe3rePL7KzuTbONZUAu0aM\nInbpUrq+t4y8O6y5gH9tdB8i/f14eu0BOt+ziEMvek/ioLZ7x3bj3rHdan7+eFU2L/6YydbDRWzZ\nc5xNu4/z4sysmtd9bBDgB4H+BmGh/kR38CMkyEaAv43gAB92Zhxn5cZCjpdWUlJaRWGJg/wiB6Wl\nDsocUFkJte9hGgaEBMKA+BB+OzKOaWO6eG2SoLbkPy1i+zGTSX3ieO/ivpa1G//OMkxgy7nnuayN\np/bu5Tjw176uW68ZBw4Qahh0Cw93WRtworql2DRJiI52aTtthfcfma1oW3q6JUMUnFUbnB0R0ert\nuLrawMrEQVp8re3TlhIHtZ3pIr6BpELaWRVwqKDpy2wrGqguqLPvuIirEwaFLrzIrv3dY2WVgTcM\nTQDo5ILvZpH6RIaG4gN8sXOny5MGvr6+9IuKYsuxYxQ7HISevFhrzXjk1sREZu7bxy1bt7osaRDq\n68tbffpw2/btXPXNBr6+cpBL2oG655Onhvege1gAty/aSejUheS/PMrrL3gnDotj4rC6f6ecIjuf\n/Pco/9lWwJaDJRwtrqC0wkHR0TIyDpedSAKczASYwLa9pWCAwYkkg78v1OZANwAAIABJREFUBAUY\ndO4QQO/YIC7qG8lNw2LpFOGaISvu1unuRWQfN3l0aDf+d1iPOq+5Mh75xZyNHHOYvJGU5LLhQA6H\ng6f376ejYXChC47nsyMieHvvXqqAKRbECO9s2QLAaBcmQFqTu+MRzWlQS4hFSQOof26D1lRdbdDW\n5jeoEXLyQqotJQ6k6dwwHKGaVVUGhenpllQZWDWXAXhP0sAKmtPAWp4ej6zft4/0fft4bNgwYoJa\ntyz8VA6Hgz8uXUqCYbik2gBgW2Eht65dy7UxMXwwYIBL2gCYkL6EufmVfDg2mV8ldXJZO6f6/kAu\nl3y9EV8bHHrhPGLC2ubFsDTMbncQ84ellFTAG6N7M2WAa5N+tX28I5sbv9/q0nkMAM5ZtIjNpsm8\nkSNdMqQJTsxlEGwYPO3iuQzgxLwuoYbBBAva8hYNxSNKGtRi5YSIcCJx4MqkAVg3KSKgxIFYz6KE\nQdT0FeQdL3NpG9L2BQUEcMPw4af9XkkDa9UXj3y6YgWlZTrOpWXCg/0peGmEu7shFtqVXULy//yX\nShPmXzWQsd2sK3fPt1cQ+c4ywm1w+II0l7VTPfnhmJgYnnJR8u/tvXt5d/9+/jh4MIkdOrikjWor\nDh7kox07uGrIEKLCwlzaljfRRIiNZOWEiNVcObdBtbY0TOE0bXWogpyZhRUGecfLdFEnLWYYhru7\nIA0oLdNxLi1nGAavL8zijjTr7jSL+8zbkMO4lzbhY8Dem4eR2MG11UGn6jp9GQYn5vZwpYvXrsUH\nXJYwAHhv/35CDcPlCQOAz3bswAeUMGgCm7s74ImsmqTLilJgV8+0Xq26PLvSHROcVV807kivOxme\ntF1uHJIgIiLSkKkf7OR37211dzfExZ6YvZdxL20i1A+Kp4yyPGFw7ozFFFfBZwMG1MxJ4gqP7d7N\nceBJFz0tAaiZy+AOC56YkFNaSgUwIDHR5W21JUoanMId42ytmLXclROpVXN74qB28kDaLiUMRETE\ngw3vbOOdpdkMfGiRu7siLpL2xGIe/3o/vSMMiqakEWjxJJhPrN7Lf4ur+G2nToyLiXFZOw6Hg+cz\nMuhsGKTFxrqsneoqA1c/MQHgxdWrAUhV0qBJlDRwMyurDaxMHLiNEgdtV+1KEiUMRETEQy2/9gLu\nT01gU45JyB0LKbY73N0laSUOh4OOv1/EoowqbkqKZcdN1k+i99/sAh7/7356Bhq8mpzs0rZSly0D\nYMbIkS5r49Vdu6gC7jr7bJe1Uc3hcFBgmsRakJxoa5Q0qIfVzxF3dbWBVcMUqrml2qCaEgdtT+1k\ngRIGIiLi4Z4b2Yv5Vw2k1AHh05ayYMsxd3dJWmhDRhGBU5eSU2oyfUwSH4x1Xbl+fewOB+d9tg5/\nAzae59qExfycHPaYJtd27uzS4Q8zMzMJNwziLZhf4MPt2wEYM8h1j2Ztq5Q0cMLqIQpWPhu9zQ9T\nqKZ5DtoOVRdILWlpabzzzjvu7oaIuFBbOc7Hdovm2OSRBPrCRX/foHkOvNhjX+4h5YmfsBmw7VdD\nuaVfF7f0o/Pby6gCNg07z+VtXbdpE4HA/X36uKyNF3bswASmDRnisjZqW3v0KMGGYflwkrZASYMG\ntNVqg3aVOFDVgXdTwqDZHn/8cX7961+7uxsNuuWWW3j00Ueb9BnDMDzyKQT79u3DZrNRVVXl7q5I\nO6Lj3FrNOc4jAv04fnsaQ+NOzHPQ9d5FOBwaruBNUh5axJPfHKBXhEH51DT6RIa6pR/nzFhMfqXJ\nB337khAY6NK2bti4EQfwmouHDHxx8CCRhkGnUNdv0xUHD2ICo1NSXN5WW6SkQT3aarWBlcMUPCJx\nAEoceCMPmr/A7fuveBU9sk+k7WvOcf7f6y7g/847i8xik8CpS1m6M88FPZPWtP1QMQFTFrIhx+Tu\ngV3Y6Yb5C6rdu2Qna4qrmNy5M9fGxbm0rUy7nW9ycznbZiPZhWP/n9y6FRP4/bnnuqyN2qofsxgb\nEWFJe22NkgZn0NaqDapZUW0AHjAxYjUNV/AeHjR/gTckDJ599lkSEhIIDw8nOTmZBQsWMG/ePJ55\n5hk++eQTwsLCGHzyEUYFBQVMnjyZLl26kJCQwKOPPlrnjtm7775Lv379iIqK4rLLLuPAgQM1r9ls\nNl5++WV69uxJx44d+dOf/lQncG7os3/4wx+Ii4ujQ4cODBo0iM2bN/Pmm28yc+ZM/u///o+wsDCu\nvvpqp+v3/fffk5ycTEREBL///e8xTbNF7QKUlpZy3333kZiYSEREBOeffz52ux2AlStXMmLECCIj\nI0lNTWXRop9nP09LS+Oxxx5j1KhRhIeHc+mll5KbmwvABRdcAEBERARhYWGsWrWqiX9JkfrpOG8b\nx/kDQ7qz9+Zh+Nrg/GfXc/1rm5r0ebHOvR/vJPnRNVSasPq6wbx4QZLb+jJ7zxFe3JDFoGCDl104\nVKDakJUrsQGvnNzfXWVudjYxhkFMkOsfVXm0pIQKYKCemNBsSho0QNUGrccjLr40XMGzeVB1Afy8\nz54p8TVlCqSlweWXQ35+89pq7jK2b9/Oq6++ypo1aygsLGT+/PkkJiZy2WWX8ec//5mJEydSVFTE\nunXrgBNlwv7+/uzevZt169Yxf/583n77bQBmz57NM888w7///W9ycnI4//zzufHGG+u09+WXX/LT\nTz+xdu1aZs+ezbvvvnvGz3733XcsWbKEnTt3UlBQwKxZs4iOjmbKlCncdNNNPPjggxQVFTF79uzT\n1i8nJ4cJEybw9NNPk5ubS8+ePVm2bFlN2XJz2gW4//77WbduHStWrODYsWM899xz2Gw2srKyuPLK\nK3nsscfIy8vj+eefZ8KECTUXDAAfffQR7733HkeOHKG8vJznn38egCVLlgAnLtiKiooYNmxY4/+Q\n4vF0nOs4h9Y5zhM7BGG/I43zE2x8tjaHDncuJKfI3uTliGvY7Q4637OIF3/Iol+0gePONM6J6+C2\n/mQW27lm7hbCbLDyXNdXOvzPrl0UAf/j4uTEgxs3AvBHi86VL65ZA0CKkgbNpqSBB2qr1QYekTgA\nJQ48kQdVF0DjEwYAO3bAokUwdy5ERoJhNP3fW2/9vIwpUxrfTx8fH8rKyti8eTMVFRV069aNHj16\nAJx2py47O5u5c+fy//7f/yMoKIiOHTty77338vHHHwPw+uuv8/DDD9OnTx9sNhsPP/ww6enpZGRk\n1CzjwQcfJCIigq5du3Lvvffy0UcfNfjZAwcO4O/vT1FREVu3bqWqqoo+ffrQqVOnmmU2VOb77bff\nMmDAAK699lp8fHy4995763y2Oe1WVVUxffp0XnzxRTp37ozNZuO8887D39+fDz74gMsvv5zLLrsM\ngIsvvpihQ4cyZ84c4MQ469/+9rf06tWLwMBAbrjhBtJP7isaltC26TjXcX6m9WiqxVdfwKyxfSkq\nh45/WMkDn+5qtWVL87zw3QGCpi3lcInJ8yN6sHmi+4YjwInHAybOOHHXf/+IUS5vr9jh4O+ZmSQY\nBpd17uyydhwOB0tyc4k3DEJdPDdDdXuFpklnDUtoESUNGsHKIQpWVxsocaDhCm7lYdUF0LSEAUBw\n8In/Dh0KeXlgmk3/N27cz8t4883G97VXr1784x//4PHHHycuLo4bb7yRQ4cOOX3v/v37qaiooHPn\nzkRGRhIZGckdd9zB0aNHa16/5557al6rvluXlZVVs4yuXbvW/H+3bt04ePBgg589ePAgY8aMYdq0\nadx1113ExcVx++23U1RU1Kj1O3jwIAkJCXV+V7sPzWk3JycHu91Oz549nW6jWbNm1SwvMjKSZcuW\ncfjw4Zr31L6YCQoKori4uFHrIt5Nx7mOc1e4LimO8ttH0aODwfPzM4m8a5GqDtzAbnfQ9d5F3D9r\nD7HBBkWTR3Hf4G7u7hbRby2lElh/zjmWzPY/aNkyAN4fOdKl7dy9YQMA97i4nWrTt20D4MIBAyxp\nr61S0uAMrB6iUM2KagOrhyl4ZOJAVQfu42HVBbU1ZS6OmTPh+uvh+++huUnslizjxhtvZMmSJezf\nvx/DMHjwwQcBTpt5vGvXrgQEBJCbm0teXh55eXkUFBSw8WSJYLdu3XjzzTdrXsvLy6OkpITzzvv5\nsU61xxEfOHCA+Pj4Rn3297//PWvWrGHLli3s2LGD5557zmkfT9WlS5c6d0BN06zzc3Pa7dixI4GB\ngezadfpdvW7duvHrX/+6zvKKior405/+dIa/wpnXRbybjnMd541Zl+bw9fVl982jeTstiYIyk45/\nWMmU97e1ejvi3J8/303QtKVkFps8fk53sn87mtBA9z+Or887iyisgk/69aNnSIjL23srK4vDpsmt\n3bu7NEFhdzhILyykl81m2WMPN+bkEGoY+Ooxiy2ipEEjtcVqg2pWVRuAByYO4OeLVlUdWMMDqwuq\nNWe/jIiATz9t/oVES5axY8cOFixYQFlZGQEBAQQGBuLj4wOcuFO2b9++mnLazp07c8kll/DHP/6R\noqIiqqqq2L17N4sXLwbgjjvu4Omnn2bLli0ANeODa3v++efJz88nIyODl156iV/+8pdn/OyaNWtY\ntWoVFRUVBAcH1+ljXFwce/bsqXf9rrjiCjZv3sy///1vHA4HL730Up27gc1p1zAMbr31Vv74xz9y\n6NAhKisrWbFiBeXl5dx88818/fXXzJ8/n8rKSux2OwsXLqxzF7a+8uSOHTtis9nYvXv3Gf9u4n10\nnOs4B9ce55P7d6H89lH0iTJ4a/FhAm9fqCcsuND2Q8WETV3IM3Mz6Bp2orrgL+ee5e5uAXD1nI3s\nsJs81K0bV8XGurw9h8PBvTt3EmEY/O4s126DW05WM9w5YoRL26n2w/79AFw0ZIgl7bVlSho0Qnuo\nNmj3iQPQkAUreHB1QVOHJXiCsrIyHn74YTp27Ejnzp3JycnhmWeeAeD6668HIDo6mqFDhwLw/vvv\nU15eXjML+fXXX18TnF9zzTU8+OCDTJw4kQ4dOjBw4EC+++67Ou1dffXVDBkyhMGDB3PllVdy6623\nnvGzhYWFTJkyhaioKBITE4mJieGBBx4AYPLkyWzZsoXIyEiuvfba09YvOjqaWbNm8dBDDxETE8Ou\nXbsYNerncZ3Nbff5559n4MCBnHPOOURHR/Pwww9TVVVFQkICs2fP5umnnyY2NpZu3brxwgsv1LmA\nqH2nsfaz5IODg3nkkUcYOXIkkZGRrF69ull/U5FT6ThvP8e5r68v224czY9XD8I0Tzxhod+fFmG3\nO1q1nfbM4XBw7v8sJvnRNZQ64KOxfTnwG8+oLgC4b+lOvtqXyxXR0Tx2cu4SV0tZtgwTmOniSQnz\n7XYOmCZ9IyMtu+s/Z+9efIGI0FBL2mvLDNOi2ZsMw2BSWpoVTblEyMkLimQLEwid0tNJsKi9Hunp\nhFucHPGvSMfHTQmZMwqplTRI8tA+epPaSRgPSxbAmRMGwQsXtvuJ7mw2G7t27aqZgE2arr7z4Azt\nX5bS36F+Os5bzjAMzLvSWmVZt/ywlRnbszmnk43Vf3Xt4+/ag3tm7uDlBQcxgXHdIvn2qhR3d6mO\n1zdmMXXxTgYFG5Y8KQHgw0OHuG37dm6Ij+fe3r1d2tb4RYvIMU1esuh6cHdeHi+uX8/IPn3o5cKJ\nHduShs6DqjRopLZcbVDNymqDah5XbVBN8x20jlOHInhhwkBERMQd3ru4L6W3j2Lxr4LrrYI858k1\nPPXNPus750XeXJiF/5SFvLTgIF3DDPImj/S4hMH3B3KZungnnf2sSxg4HA6mbN9OGLg8YbC/uJgc\n02R4XJxL26ntzQ0bMEAJg1aipIEHq57bQMMU3EhDFprHC5IFoIRBU2iiP5G2T8e55wn09SWwbKjT\neOS5uftZs7+Y//lyH8bvFuI3ZaHb+umJvvjpCEG3L+T2D3YS4AOLrk5h/29GExHo5+6u1bE5t5hL\nvt5IiA12j7TuMY9DTg5L+LDWRKiucttPP2EAN/bt6/K2AIorKig1TXpYmKRo6zxjAI8X2ZaebukQ\nhcOpqXSy6KJ6T2oqPSy+gC/3S8W/Ip3KdA8eqlB9og6pdSGsIQvOefgwhNqUMGiayspKd3dBRFxM\nx7mHOyUeefX7Avx8DMrfGM3MlYdZsO3ExIkXPreO/2wvwADO6xHG8j+3r0ng3l9+iDve306pAwJ9\n4PPL+nFtT9dPKNgcmcV2Bn68Bl8gY8SoM76/tczKzmanaXJt587EBAa6tK3VubkUmyaXJya6tJ3a\n/r5iBQCjLEpStAeqNGgCdw1RgLY9TMErKg7g9CELqjz4mZdUFlRTwkBERLzWyfNsZpFJVZXJrlVr\n+NV5nXj7lr70fGgFS3cVMj4lmu7RAfx0oJhd2SUArN1fyAXPrmXsC+nkF1e4eSVa33Nz9+M/ZSGT\n3t0OJkwfk0TpHWkemzDIt1fQfcZKDODAyJGWPYLQ4XBwy9athAH39+nj8vb+tHEjvsBlFiYNcqqq\niNbkh61KSYNmsPLxi2DtIxjdMUwBvChxAM6TB+01geBlyQJQwkBERNqGLiEBmCb0fquYLvcsgh3p\n7MkpY0CXYGb/fiDrHh2Ko9Lk4c/3AnDBs+ks21XID1vzib1veU0ywZvZ7Q4ufn4dtt8t5E+f7yXI\nF+ZeMYDjd6RxS78u7u5evewOBx3fPTE8YNt55xHhZ92QiYEWDkv4PCuLcuAmC+/4v3/y8awXe2oF\ns5dS0qCJ2kO1wR43raNXJQ7g54vk9lZ9cGqixEuSBaCEgYiItB0HJg2n8q40Phrbl0MlJu+stwPw\nr4sN2JFORKgfVSZclRrNOU+uwe6o4p1JSZhvp1FRafKHT3YDJ+48AzWPdvx4VTYLthxzz0o10ser\nson9/SKCpi3lx20F9Iww2ParoRTclsZliTHu7l6DHA4HkW8uxWHCf4cOJcHFwwNqeyMjg/2myU0J\nCS4flgDw/3buJAgYYuHcAmuOHCHYMCyr3GgvtDWbqS3PbVCt0A2PYfSKOQ6ccTbvAbStuQ+8aL4C\nZ5QwEBGRtsDhcNR5zv3hkjJCfG3ct+DEkIP+wUOBdN7/YiUAv4nJZkpWCX3igrgmtSMABhAa4AOA\nr68vDoeDwEBfpv5rO28tOURl1Yll/9+Es3hgXHfL1q0hm7OK+c0721h3oBgT8LPBr3p3ZMaFfeps\nD0/mcDgIf3MpdhN+SEmhn8Ul9K/v2UNHw+CuXr1c3tY/du6kCpg6eLDL26r2nwMHALjo7LMta7O9\n8I4jzMOUpKYS4qa74Znp6SRYcDFdPSmiEgdNVPtiui0kEE6tnPDCZAEoYSAiIm1L5FtLMQx4ZEg3\nnvrpAJWmSZUJAbaTT8AoSeXxJSuwARuOOKisMukTUkHEwc28nxOHjw3KHD8/j93X1xe73cEbiw7R\nt3MQm58cRuhdi3l76WF+PyaewEBf0p5bx8rdhUSH+jH/D4PoH+/6C94Vu/K5/V872Jx1nCpOJDuS\nowxmXTKE/tHeNWbd4XAQ8dZSSk34dtAgRkRGWtp+YXo6izp0sKyi+NOsLKIMg8QOHSxpD+CrPXvw\nBaLCwixr09UyinLYZs+i0rcKH4eN5MB4uoZZX02j4Qkt0JbnNgD3DVMALxyq4Ex9wxc8eQhD7T6e\nOvxACQNpw2w2G3v27GmVZSUmJvLjjz+2yrJEpPW0lePc19eXc2NDKXVUcv/yPRSXVzJtYDz3D06g\nyoT3tx3i5fUHOFBcxoDoEBbsiMXXMOgUeKLK4F8/7sIGnGUrBKiZFPHGt7ZiApufHAbABb07sPNI\nKYGBvtz05mYWbS8gLtyfwwXlXP3KppphDQAvf3+gVdYtp8jOb97eQuRdizB+t5ARf0tnU9ZxekYY\nzL9qIFV3pbHlxtFemTCIemspJVXw9cCBpEVFuaUfVsX2d5+Mve4fNsyS9gB25uVRCQxPTrasTVfL\nKMphtbGLg9fnkf2LAg5en8dqYxcZRTmW90WVBs3UHqoNqrmj2gC8vOLgVA1VIID7qhCcJTC8NDng\njBIGrcNms7Fr1y569OjR4mW99957LFq0iOnTp7dCz5onLS2NX//610yePNklyzcMQ8+7F6+j47xp\n3H2cf3f1z+e1fHsFEYEnJtJ7bl0Gk37cDkC/yCDeHpNE15AA/rB8Dz3Dg6CkD0szFxHq58t1yf6w\nIx17sQNCfflucz5+Pj+v08asEmycGBbwxbocukYFsP//hjPl/W28tfgwvr6+/HdPAZf9YyPHjju4\n+5M99IoNZOfTjZtgz+Fw8MbiQ8xcfYQN+4soqYDq2odgX7gkIYJXR/emV0RIq2wzd3E4HES+tZTi\nKvh8wAAuio62tG1fX19LJzgvdjhYk59PT5uNUAvna3hzwwYMoEenTpa16Wrb7FkUX2+v87viK+1s\n+yzL8moDJQ1aqK3PbeDOYQrQxhIH1U69KHeWRKjWWsmEhqob2lCSoDYrEgZzvp/DSzNfoswsI8AI\n4O5f3c0VY6+wfBlWME3zzG/yErqgl6bQce6d2tNxXp0wACi9YzQ5x+38PT2Lp0f0rPl9gM3gzyv3\n8taWQ9grTf73nK4Mj+gOJdDJAEqg1LGQ8zobNTFDVl45PToY/OWDEz/fMuLEZHY/7SuuSS788o0t\n5B13YL6dxi9e3shXG3LJL64gIrTu0wBufGMz6zOKOZRnp7jCxFH182sGEOYPF8Z34PFzExnVxdqy\nfVeqnsOg1IQvBwzgkhjXXugNWrmSTv7+dAsM5O1+/fD19eXYmjX4+vpaVmXw62XLALhrxAhL2gPI\nt9spM036xsdb1qYVKn2rnP/ex/nvXUnDE1qgPTxJAdz3GMZqbWKoQkNql/83NKShJf/O1E4bY1XC\n4J5X72F+4nwWnbWI+YnzuefVe5jz/RxLl5GYmMgLL7xASkoKERERTJw4kbKysprXv/nmG1JTU4mM\njGTkyJFs3LgRgOnTpzN+/Pia9/Xu3Zsbbrih5ueuXbuyfv16LrjgAgBSUlIICwtj1qxZALz11lv0\n7t2b6Ohorr76ag4dOlTzWZvNxhtvvEFSUhKRkZFMmzat5rXad+fsdjs333wzMTExREZGcu6553Lk\nyJF61/P5559n0KBBhIWFMXnyZLKzsxk3bhwdOnRg7Nix5Ofn17x/5cqVjBgxgsjISFJTU1m0aBEA\njzzyCEuWLGHatGmEhYVx991313zm+++/d9pn0zT561//SmJiInFxcUyaNInCwsKa1//1r3/RvXt3\nYmJiePrpp8/4NxPvoeNcx3k1bzrOY4ID6yQMAN4ck0SAj8HuAjvTBnThgSHdySy2c/28TeTbTwxP\nsAFRfhFQkkp+bn9M4OHBvVlxsJIQH0gLzoUd6WQcLSHUF17/ZCWZeWUkdjiRaOgbWISvAX96d/Vp\nccgn/z3KjuxSHFUmXUMCuCYxmvlXDcS8K42qu9IouC2NH64Z3KYSBnaHg9CTCYN5KSkuTxiELlzI\nHrudFYWFfHb0KBGLFvH+qlWWJgx2FRWRbZoMi4uzdHLKzE2bGOTvz7m9e1vWphV8HM4v1X0qrb+E\nV9LAC1XPbeCOxIG7tPnEgTP1XeQ39187YdWQhJdmvsTuwbvr/G734N28/NHLli7DMAxmzZrFd999\nx969e9mwYQPvvfceAOvWrWPy5Mm89dZbHDt2jNtvv53x48dTUVHB6NGjWbJkCQAHDx6koqKClStP\nzLS9Z88eSkpKSElJYfHixQBs2LCBoqIirr/+ehYsWMCf//xnZs2axaFDh+jevTsTJ06s0685c+aw\nZs0aNmzYwKeffsp3330HwKRJk3j33XcBmDFjBoWFhWRmZnLs2DHeeOMNgoKC6l3PL774gh9//JHt\n27fzzTffMG7cOP72t79x5MgRqqqqeOmllwDIysriyiuv5LHHHiMvL4/nn3+eCRMmkJuby1NPPcX5\n55/Pq6++SlFRUc1nGurz9OnTmTFjBgsXLmTPnj0UFxfXXGxs2bKFO++8kw8//JCDBw+Sm5tLZmZm\no/9+4tl0nOs4h7ZxnP8muTOFUy6g4s7RvDw6Cf4/e3ceFld99n/8fWYGGDLDlrCHAGHJQhbIolkg\nQG01cW8bl7hE26qPtXVtrHVp1WrVLvqrS61b1bq1ebT2sa7RassQErOQhAhmgUBYwpohbAMM4TDn\n9wcMgUgSIMycc+D7ui6vS7aZGzIHzvmc+3t/gbyaFv57qJn3y3vXR6dOsfBZ1RGe2V1J4ptbMUpw\n3ZxoUHwwYGS+ZR60p9HSBWH+ZirtYfS44KbZ8dCexhRjDD0KIE/5xjmI66fZyD/Jpu1/sim7Zhn/\nd/48zo71Xpu+tzU7uwl4MY8uBXIXLCDTw0MPn6msxAU4srMpWbqUm6dOxVeS+ElnJ7dbvLe848Yd\nOzAAV82e7bXnhN45Hwu82NngLbPMU/H51DjofdYPzMzy835HhQgNxoC3ByKC94ciuqnVbQATNDgQ\nRsSbMwy6lK4h3/9p2adIv5aG9d9nBz8b8jGcLueQ7z+RW2+9lcjISEJCQrjwwgsp6Ps5vPjii9x4\n442cccYZSJLENddcg5+fH1u2bCEhIYGAgAB27dpFbm4uK1euJDo6mv3792Oz2frvPA7lrbfe4rrr\nriMtLQ1fX18ee+wxvvzySyorjw3CuvvuuwkMDGTatGl861vf6q9pIF9fXxobGykpKUGSJBYsWEDA\nSSYe33LLLYSFhREdHc2KFStYtmwZqamp+Pn58b3vfY9du3YB8Oabb3LeeeexatUqAL7zne+wePFi\nPvro2J3dodqwj6959+7d/d/vunXriI+Px2Kx8Nhjj7F+/Xp6enr4xz/+wYUXXkhGRga+vr48/PDD\nGAziT+t4IY5zcZyP5jg3PJvDzobWE35cK9bMiMB+fQbXzIoC4Kfzei9Ebs0rw9njYv13ei/8Ivx9\nsDtlQieZ+cOOCo66FH44M5J2uQcX8PNFvVsy7rI7cCmwLi1Gle/TpQnMAAAgAElEQVRHK8pbOpny\n8iZ6FNi6aBGLvbB7QIrFggSsLSoi0mzmN0lJPObryxRJ4qP6elq7uwcNrvSED2tq6AS+n5h4ys8V\nhicmYArG6QZMnxkI/Mif6H+EcCZJquyeIGYanCY1ByKCd4ciqj3fAMbpjANhTHh76KGf5Dfk+1cm\nrGTDAxuG9Rgry1fyGd+8oDAbRjY4KHLA0B9/f39qamoAqKio4PXXX+eZZ47d0ezu7u7/eFZWFjk5\nORw4cICsrCyCg4Ox2Wx8+eWXZGVlnfD5amtrWbx4cf/bFouFKVOmUF1dTWxs7DdqmjRpEg6H4xuP\ns3btWqqqqlizZg3Nzc1cffXVPPLIIydsaYyIiBj0fQ5822w29z9HRUUF77zzDh988EH/x2VZ5qyz\nzup/e6j1zieq2X2X1S02NhZZlqmvr6e2tpaYmJhBXzfFi0OuBM8Sx7k4zkdznBskcBztOeHHteq6\nOdG9nQXAIYeTGGvva3R1UhgFje0Yns3BIIG/0cDdi+NY9L/5/V+be6iJjTUt+BgkZoboa2eDsbS9\nvoUz/7ELI3Bg6VIivTQI8NtTphDr58e7djvVO3bwntHIpWYznwYF8WF9PbbDh7kwOtqjNfy2uBgz\nkDltmkef53hq3Lz1lsaANnxjTEQFhTD1yGQS69Ub8ihuh4yRidJtoPYyBRAdB8I3qbFLwq1X3kri\nrsFpeuLORG654havPsZQ3CfKsbGx3HfffTQ1NfX/53A4uPzyy4Hei4n//ve/bNy4kezs7P6LC5vN\ndtKLiejoaMrLy/vfbm9vp7GxkakjHEBkMpm4//77+frrr9m8eTMffvghr7/++rC//kRD22JjY1m7\ndu2g77utrY277roLGPmAtOO/38rKSkwmE5GRkURFRVFVVdX/sY6ODhobG0f0+IJ2ieO8vP9tcZwP\n/zhXFNhY1zKi59cad2AAcN/ieD4+fy7Jwf6snDaZsqvPBOCsmGBMEtyUs58f5xZT3d7FRdMnbmj6\nr7IGzvzHLvwkqM3I8Hhg4JRlzty+nZi8PNbX1bFxwQIWWa1sbWtjdksLZWlp3Nu3TGDHgFkgnvDb\nfftwATcvXOix5xjYKXF814Sac+Y8qTzsMPEN4WhhrKsIDcaA2i9Ub842cFNzmQKI4EA4Rq1tFc8/\n+3ye+ulTrKxYSdbBLFZWrOSpm58a0UT0sXiMobhPsm+44Qaef/55tm3bhqIotLe389FHH/XfWXNf\nTDidTqKjo8nIyGDDhg0cOXKEBQsW9D9eREQEpaXH1mRfccUVvPrqq+zevZuuri7uvfdeli5d2n/3\n8UT1HC8nJ4fCwkJ6enoICAjAx8cHo9E45OeOxNVXX80HH3zAZ599Rk9PD06nk5ycHKqrq4f8fk5U\ns7vuK664gj/+8Y+Ul5fjcDi49957WbNmDQaDgdWrV/Phhx+yadMmjh49yv3334/L5f2pxoJniONc\nHOejOc6NBon7FsfzYlE1gS/m4v+8jb8V153296ymVfGh7L9qCR9dOJ/IvkDhD+lJhPv78vzXtexr\n6uTypDDeWTVX5UrV8ettB/nuJ3sINMDh9AysXhgCOCUvj73t7bT29HDdvn1k7NrFmYGBXO7jQ7Oi\nsDwnh+U5ORiAB1NSPFaHLMu8X1dHuCQRGxjosecxmUzU9f1ec3cqFeXnn+xLdE1BoTy8gfjDYWqX\nAojlCWPK29svgve3YARtLFOAwUsVALFcYQJSKzBwO//s80/7xH8sHmOggVPLFy1axEsvvcTNN99M\nSUkJ/v7+rFixov/uYnJyMgEBAaxYsQKAwMBAEhMTCQ8PH3SX7sEHH+Taa6+ls7OTl156iUsuuYSH\nH36Y1atX09TURHp6OuvXrx9Uw4lqGqiuro4f//jHHDp0CKvVypo1a1i7du2IvtehniMmJoZ//etf\n3HXXXVxxxRUYjUaWLFnCc889B8Btt93Gtddey3PPPcc111zDk08+edKf449+9CNqamrIzMzE6XSy\natWq/lbwOXPm8Oyzz3LllVfS3t7Oz372M6Z5uTVT8CxxnIvjfKTHeccN6SS/sYWKti6MBphkMnLV\nv/dhMRm4OCF82N+7HlT/sHf4nL3DSegk77Tia833Py7i/w7aSTZL7F564u6dsfRQWRkAbdnZAJxf\nUEBeSwt/r63lWX9/bk1P57aCAhItFm718I4C1/RtsXhnerrHnuOBL7+k7ehRjJKEC5g3ZQo/mDMH\nk8mk+s1bT7EHtmLqMRLc7r1BlicjKV7alFeSJK7te2GPVxYVQgOgPzTw1mwDt4S+51UzOHDz7RbB\nwUTjzcBgUk7OuNq/XFDHif4OviZeX14l/h0ET5IkiXODjXze4uKMCCubVi8CwPhsDnemxfC79CSV\nKxTG0txXbHzdqXBusJF301Z47XkL29pYsmMH8X5+bDvjDKwmE/dv3swf+y6sc06y9GgsHWpv57Lt\n25kXGsoNcz3TZfLW3r1sra8n2mLBIEk0OZ20yzJGIN1sZvrSpciy7NUtHr1hW+IBfHuMpJVPZ+Os\nvUQ3hXh8psHJ/g6K5QljTM3ZBt5epqCF+QZuYrnCxNFTUKB6h4EgCIIgnMgXLT0k+sHjy3tnWXzn\nvV29uwwsmNi7CownTlkm8Lkcvu5U+FlMjFcDA4B5AQGcERBAfXc31+zZQ2l7O3dOmsRTqakcVRTW\nD9jlxJN+mJ+PBB4LDACKGhvxMRi4+4wz+ElqKjfOm0dmdDQGYFtP78DR8RYYKChUhDcQ36CdziQR\nGowhNdtj1NqCEdSfb+AmgoPxb2BYIAIDQRAEQYt6FPjeFB/OrC/nb8V15Na2Eh/gR+gkMw6nZ7e9\nEzxvZ0MrlhfyaHPB/6ak8Jsk73SPlLa3E5uXR+rWrZy1Ywe2RYuwGgz8p6mJy/LzebGzk4UhIQDY\njx71eD0f1NTQrih8LyHBo8+zYupUul0uHs/Px+rjQ3xQEEmtrcz19cXZ3c0XhYUefX41HA5sxbfb\nh+AObSxNABEaeISaW3+o1W0gggPB00R3gSAIgqAHEvCr5N61/v/zxT78DBJXJPXeMbSaTTgHTH4/\n5HCqUaIwSk/uqmTROzsxSlC2dCkXhnvvTvD87dtpkmVaZJktbW0E2WxUZGSQIkkcVBTu7+pieU4O\nPpLEzV4IMn5XXIw/kH2C4ahj5bzp04nw96fS4eD2nBz+tGsXZpOJ+ct7jzG/cdZlAHBQQwMQ3cbf\nT1ll7WlpWFS6YFVjKCJoZzCimxiQOP6IwEAQBEHQCxlYkZ9PQd+k92tDjTw8qQ04NjDw9X21rNtU\nSlNXb4Cw+/LFzJliVatkYRiyXs8lt81FtI/EviXpXm2J/3lJCQrHBh86ZJmIvDwm5eTwidVK0OLF\nrK+spLyjg7tnzfJ4PfcUFeEC7li82GPPIcsyXzU2kjJlCvctWcLnFRVsqqmhuKWFYkCy2QDI6NtW\ncrxwoVARdpiVBdo65xWdBh4ykboNQJsdB6LrQP/E/AJBEARBb1YEBVHY3s4ko5G9S5fyp5TeqfL1\nW/L7dxi49ov9dMoufjArAh+DxPz1+dSJrgNNcjhlAp7LIbfNxaVhYRxIz/L6Gvrbpk3DV5K4ff9+\nAKwmE+3Z2ZiB8x0OipqbWRMb65XAwCHL2Ox24iSJSKvngq57Nm/mtb17uSsvj3W5ueQ3NLAoIoJr\nrFaiQ0KYGRXFRR4MLdTSENSCuduHoM5JapcyiOg08ICJ2G0AxzoOtGRg14HoONAXERYIgiAIevTp\nggVA77A8s8lEaXs7iZY0Quk9H/Hb3IwEOG7MBMDHYOC1/fVEWifmloVa9s/SBi7ZsAfonV/gzeUI\nA8WYzViNRl6srSXQZOKhxEQa8vP5m8XCZR0dtMnem5VxRd8Wi7d5cIvF3Koqulwufp+RQW51NbZD\nh6jv6KChvZ2Ffn6cPQ7DArdyjQ1AdBOdBuOUGt0GblrpNnAb2HEgug70QQQGgiAIgt6ZTSZym5pY\nlJ/PW7W1HPVJY96OFnoUaFty7A7tvw420t3j6p918LfiukFzDwR1ZL+Ry+oNe7AaoD4jQ7XAQO57\nLRzKyCDcx4fHq6pYZLNxBKhMSEBWFGx2u1dq+dJup1FR+FZMjEe7LUpaWvr//5y4OB5JT+eqmTOR\ngG1dXeQfOOCx51aTe2mC1uYZgAgNPEqtJQpqbcEI2lum4CaWK+iDWI4gCIIgjCeZISH8Mj6eqX5+\n2J1OSrsg1WLBbDLRU1DAvZtLqe04yi8Xx/FhWSMhL+Vx9b/34f9CHj/4fK/a5U9I5S2d+P85B1ur\ni4tDQ6nPzMaq0rA9WZYxmUw0d3f31paezreNRvYqCme2t3N7YSEWo9EryxIA7ioqwgf4nocHLa5O\nSsIoSdy3eTPr9++nzuHAWlfHDcHB+JpMlB8+7NHnV0t9cDOTuvwI1NjSBBChgceouf0iqLsFo1aD\nAxC7K2iZ2E5RADjvvPN444031C5DEAQPmmjH+Z1xcWRPnkyo2YwBCDKZOOqTxvZWmcd2VTE9wI85\nwZO4+ot9dLtcPLMikdQpFt7YXy/mHHjZbbnFTH9zK0cV+Hj+fP4+d64qdeQcOcJbtbX9d/ODfXxw\nyDI1+fm8FRDAXxYs4Mbp07kqJoZ/r1jhlZoe3ruXHuCnXrjGCDabua3vebbV1fFiURH/19pKYVQU\nR2UZH6PR4zWoQatLE0DMNPC4fQUFzFLxAv5QQQExKjy/1nZUGMh9QeordlfQhIEBjl7DAkVRkCRJ\nlceIj4/nlVde4ayzzjqt5x9KeXk5CQkJyLKMweCdjPnjjz/2yvMIwkiJ43zsTOTj3GI0ktvSQlhu\nLk6XC7MEJfP9sX6+lwA/E3elTeOn86fR0e3irsaDHGjtJNRs8vrgvYnG3uEk6fWttPQozDRLbF/s\n3d0RBorJy6NJllGAO0pKWB0Wxt3x8cT5+9NB7zl2tNNJioe3OhzIIct8Ul9PjCSREBzsseexd3ay\ns6GB/Pp6ZgQH80RmJs/s2kVZSwsuoHbvXkwGAxefeabHalCLS3JRGWrnvJ0Lv/ExCVC8X9IgotPA\ngyZytwEc6zjQKjHrQH166C44VceMoij87PrrUZTR/zo/nceQJOmkXyePwbrYkdTV09Nz2s8nCFoj\njvPBxHE+elUZGSwPDMRiNHJpeDhHsrK5YK8BA/DdQImfL4oD4FfbyrGaDGREh7CnqZP1xfU8X1it\nbvHj1G25xYS9uoXWHoWXZs5k11Lv747g9seKCo7IMv9OTeWFGTOQFYW/NzTwgz172Jmfj9lk4umS\nEq7asYNmp/e6UNzDD3/mweGHAI9t386HBw/S6HSSW1PDrTk5WHx8uDE4mGuys1m9dOm4DAwA6oKb\nsTjNBDj91S5lSCI08AI1t18EdYcigjaXKbiJWQfq0MvsguG8dj9991145x0+++c/R/08o32MtWvX\nUllZyYUXXkhAQACPP/445eXlGAwGXnnlFeLi4vjOd76DzWZj2rRpg742Pj6e//znPwBs27aNxYsX\nExQURGRkJHfeeScAmZm9k72Dg4MJCAhg69at36jhwQcf5JJLLmHt2rUEBQXx2muv0dLSwnXXXUd0\ndDQxMTH86le/wuVyAeByuVi3bh1hYWEkJCTwpz/9CYPB0P/x7OxsXn75ZaD3IuY3v/kN8fHxRERE\ncO2119La2grQ/32+/vrrxMXFERYWxqOPPjqin58gDJc4zsVxPpY+X7iQ8vR0XklJAeDL1lZcSDw+\n3Y+eggKSXrahAGtnRbCzoZXUt3ew9vO93JRbwqy3vvnvI4zOV4fbmPTnHJ4urCHJLNGSkcFVUVGq\n1tTWF8gddDpZGx3Nkawspvj4kN/WxjNdXZSlpZEWFMTZ4eEEm72z20ZuQwONisK3PTz8sKy5mW6X\nixvmzuWJzEyezs4mxM+PArud55qbOVhfj9Vsxuql79vbyjU6ANFNhAYeppVuA7WCAy3PNxhIdB14\njx66C+DYa/ZkHTOKovDp44/z/9ra2PCHP4zqDuLpPMYbb7xBbGwsH374IW1tbf0XAQC5ubns27eP\nDRs2DPmYA1ukb7vtNu644w5aWlooKyvj0ksvBWDjxo0AtLS00NbWxpIlS4as4/333+fSSy+lpaWF\nK6+8kh/84Af4+vpSWlrKrl27+Oyzz/jLX/4CwIsvvsiGDRvYvXs3O3fu5L333htUiyRJ/W+/+uqr\nvPbaa+Tk5FBWVobD4eDmm28e9NybNm2iuLiYL774goceeoh9+/YN++cnCMMhjvNe4jj3DKcs09XT\nQ5zZjK//YpZ91UO5U2GWGcKaG1n27i5MEnT/JJu70mIobu7kH8X1apeta7Iss+y1XFLf3kG3Au/O\nnctXKnYXDHR/QgJWg4F7S0t5qbq3s2TXpElMkST+t7ubL+12MsPDuT052Ws13btnD77AxR4efug4\nehQDsHvAkMNfL1vGNVYrBmB/9fjttHFJLirDDmt2ngGI0MBr1Ow20MoyBT0EB6LrwHP00l0AwwsM\noPfO4arCQiRg5datfGYwgCSN6L9PDQZWbd3a+xiFhad1J3OgBx98EH9/f8zDSOR9fX0pKSnBbrcz\nadKk/ouG4V7YLF++nIsuugjovfD45JNP+OMf/4i/vz9hYWHcfvvtrF+/HoC3336b22+/nejoaIKD\ng7nnnntO+DxvvfUW69atIz4+HovFwmOPPcb69ev771YCPPDAA/j5+TF//nxSU1PZvXv3sGoWhOES\nx3kvcZx7htlkIj0oiP2dnUy22dje1kaKxcLvk+fzQn03PS6Ftv/JAKC4uRODBNkxQSpXrV/3bi7F\n94U8tjhcnDt5Mq3Z2ZwbGqp2WbxQVcUbNTXYnU5ujomhuaeHxyoquG3zZgDey8pCAmq6urxa112F\nhbiAOxYt8vhzzQ8PJ8TPj2319Tyen9//fqvJhMXfn/q+DqTxqDakicCOSVi7tNtFIUIDL1C728BN\nzWUKegkOQHQdjLXjw4LxEhi47xye09EBwEpgw5IlKC4XKMqw/lNcLj5dsoRz+h5zZUfHqO9kHu/4\nNuWTefnllykuLmb27NmceeaZfPTRRyN6rpiYmP7/r6iooLu7m6ioKEJCQggJCeHHP/4xh/vuHNTW\n1g6qbeDXHq+2tpa4uLj+t2NjY5Flmfr6Y3fZIiMj+/9/0qRJtLe3j6h2QTgZcZwfI45zz/kgLY1H\npk9naWAg/xMVxdYzzuDvdXXUdyvcE+OLT1ERu/LyKW7pwNdooL7z9GdYTDQbyu2Y/5zDY7uqiPKR\nqFy6lHfnz1e7LKB38OEdpaXcXFJC3JYtTDIaeWz6dI4cPcqbR48S29LCdzZuRAFWT53qtbrqnU7y\nGhtJNhiYGhDgled8YNkyIiZNotLh4NacHH5ls/FuayutnZ1Y/fy8UoMaysMOE3eqpQmSuqMQRWjg\nRVroNhDBwfAc33UgwoOR01tYMNBwhngOvPsIjOoO4lg8xokmsQ98v8VioaPvogd6h5gdHtD+l5SU\nxN/+9jcOHz7ML37xCy655BI6OzuHNeV9YJsx9F7E+Pn50djYSFNTE01NTbS0tFBYWAhAVFQUVVVV\n/Z8/8P+PFx0dTXl5ef/blZWVmEwmIiIiTlmXIIwFcZwfex5xnHvWHXFxfLxgAU/OnAnA3xsaCDGZ\nuDdpOUVdSfy/mi72NXUy3wxzplhVrlY/dja0EvK8jXM/KkICPpg3jwPpWYRqZF387fv3c0SWeWHG\nDP6dmkqkry/3HzzIW+XlfGW1cmZoKCZJQgIe7ZuB4S1X9XVH3dI398TT3ANd7zvzTJ7OzibaYqFF\nUWiUJMw+PqxetswrdXhbj+SiKtSu6XkGILZc9Jr2tDQsKl941qWlEalyDe6tGPWif3vG7mMXwGKL\nxpPT8xaKIwm0cj76CL/Fi/lywIm0oih0ffghK1ev9tpjREREUFpaetKt2GbMmIHT6eTjjz/m7LPP\n5tFHH6VrQIvjm2++ycqVKwkLCyMoKAhJkjAYDISFhWEwGCgtLSX5BOsnj79bGhUVxTnnnMPPfvYz\nHn74YSwWCwcPHqS6uprMzEwuu+wynnrqKc4//3wmTZrE7373uxNetFxxxRX87ne/49xzzyU0NJR7\n772XNWvWnHRbuLG4eysIbuI4P1bvQOI497xgk4mjfd/nDfv3s9shE2AysSnVKs5HhmF/k4Osd3ZQ\n361gBB5LSOA2L25ROFxLg4J4ta6O2RYLsywWSpcvZ21REe/a7WR3d/PPxYuB3i0PrV6cufDX8nI6\nFIXLvDQ7wSnLmOgNDhyyTLDZzHd9fCA4mJa5czUxb8JTakOaCOqYhEXDSxNAhAZet6+ggFkq/5I/\nVFBAjMo1tBYUEKijP3YiPDg1PYcFMPxlCW6/ffXV037OsXiMe+65h1tuuYW77rqLX/3qV3z/+9//\nxsl5UFAQf/7zn7n++uvp6enhrrvuGtQ6/Omnn7Ju3To6OjqIj49n/fr1+PW1Ad53332kp6fT3d3N\np59+ypnHbXV0/B1IgNdff527776blJQU2traSEhI4O677wbghhtuoLi4mPnz5xMUFMQtt9yCzWYb\n8gLhRz/6ETU1NWRmZuJ0Olm1ahXPPPPMoOc+3nDumgrCcInjvJc4zr3vhuhoHqmowJKTgwGI8vNj\nzxlncLTv4sl9PvKLgx1cdMZsMmNC1C1YI/Jqmrj4/a840qNgAG6PieFRDw/wG60PGhoAcCkKFxcW\nUp3RO7viWVnGZTLxwdGjHGpvJ8Zi8WpgIMsyL5aXEyRJZHhhOYQsy5gHfH/BJhPOvq6DqsREutra\niAoZv6/v8vAGTQ9AdJMUL8W1kiRxbXa2N55K0ywaCA0iNRAauLsN9BQcDOTbfewCeaKHB3oPC+DU\ngcHynJwJcWdLDZ988gk33XTToPbk8epEfwdfE68vrxL/Dt430Y7zjjE83720sJBfT59OgtmM2WRC\nluVBd12jN9po7lHwl+DJzGT+Z6731rxryfOF1azLK6HD1XtH9GexsTyYkKB2WScUbLPRrSiYDQYu\nDg1lfUMDRqA6OBjoPR9ZnpPD2mnTuCkx0au1rbbZqFUUHk1Px+rj49HneqWoiL1HjiArClMtFuID\nA0mPjqblwAEA/uJwEBkczLfmzvVoHWrpkVy8vXwzF28/g0lHTzyzIW/mPiJbgkiq8+yWoCf7Oyhm\nGqhAzdkGbmrONgB9zTcYiph5oO+ZBQONtMNAOD3u9mlZlqmurubXv/413//+99UuSxCEMSSO87Hz\nzrx5pFiPzTA4vk27ZkUWL8yYAcCNthKMz+aw8l8F/XdqxzNZlrn4o0KMz+ZwU24JigJPJSfTmp2t\n6cAgcuNGuhWFT1JTcbpc1HR18XlqKj1AVHMzCzo7ybTZALweGOQ2NFCrKGRERXk8MJBlmQK7nclm\nMyaDgUMOB5tra/nL11/jkGXa09JYkpw8bgMDgOrJRwhpt5w0MHBTO9IWyxO8TEuzDdRepuCeb6C3\npQoDDbxQ9i0Y/90Hx4cjeg0K3ERg4H2KovDggw+yZs0a/P39ueCCC3jooYfULksQhDEkjvOxZz5J\ne/ra6GjWRkezx+Hg0sIdfHaoGf8X8ggxSjyansSP542v7oOXv67hro0lHOnpvYyK9ZV4Z95C5nlp\nwv/p+G15Oa09PfwtJYXMkBD8JInclhbO3r2bSEmiWZLoAXwkiT+npnq9vnv37MEPuKxvIKcnvfj1\n1wDc07ccqtbh4NU9e6jr6OAN4LzWVhLG+UDUCp0sTYBTdBpUVVXxrW99izlz5jB37lyefvrpIT/v\n1ltvJTk5mdTUVHbt2uWRQscbtbsN6jRykaT3joOBhuo+GC8dCEN1FYjAQBgNf39/tm3bRmtrK/X1\n9bz88stYrWISuHBy4nxEX8Rxro4Uq5Wvl2XRmpHBmvBw2l0KN+WWID2bw/S/2PhnaYPaJY7aP0sb\niH/JhuHZHK7PKcbhUrgqIoLWjAz2Lc/SRWAAcHd8PB/Mm8d3w8NZV1yMU1F4xmzmbKMROzDVbOa9\nZcv4IjOTuX1LFbzlutxcXMC6vuGLnpbSN6fgl5s3U2i3E2W1cu+ZZ3JV3++KXQcPeqUOtciGHqqm\nNBJnD1W7lGE5aaeBj48Pf/zjH0lLS8PhcLBo0SLOPvtsZs+e3f85H3/8MQcOHKCkpIStW7dy0003\nsWXLFo8Xrmda6DZwU7vbAMZHx8FAg7oPugcHB3rpQBgq7NB7SDCQCAwEQV/E+YggDJ/JZOKVlBRe\nIYVDTidXFhWxy+Fg9YY9wB7CTRI/WRDLfQunaXYqvSzLPLSjkpd2V1HX3dtRYARSrVb+PmcOcf7+\n6hZ4Gr49ZQoAT8yYQWpTE9/182PR0qVU79hBicNBvdPJFJPJq/82+1pb2etykTJ5MpFeCviyY2M5\n1N7OzoYG/re4mO11dQQ7HKSYzShAY1ubV+rwtqo2O/uc1bT7dyF9IWE/2sa0gFMvT1DbSV+NkZGR\nREZGAmC1Wpk9ezY1NTWD/ki///77XHvttQAsWbKE5uZm6uvrJ9z+uqOh9k4KWlmmAOMvOHA7WYAA\n2goRxtvSgxMRgYEg6I84HxGE0Ykxm8ntu3N8yOnkur172dLawoPbK3hwewUmIDnEn+tmR3HbvGjV\nQgRZlnmqsIaX9tRS1tJJX06AjwRLAwJ4NSVF10HBUFoLClhlNPafj+xta8NiMhFh9v7Wezfu3IkR\n+PH8+V57ztyqKq6ePRuz0ciXdXUUNjbiUhRynE4ALvBSx4M3VbXZ2SYdwHGps/992z48AG0wLeDE\nHQda2C9m2L8ZysvL2bVrF0uWLBn0/urq6kFb+sTExHDo0CHxR/oUtNJt4A4OtGC8Bgdux1+Eqxki\nnGjZxHgNCtxEYCAI+ifORwRhdGLMZj5dsADovUh/srqaF6vL2d/UyZ2by7hzcxkSEGCA+BAL50wL\n4bbUGGKsY3sRW+dw8kxhDR9VNFLW1I7DdWzImxGI8JH4YVEX54sAACAASURBVHQsv5im3U6I0+U+\nH6lZvJjW7m4u3LwZBfi0b9tFb7qnqIhu4BYvzVD43fbt1HV04FIU/lFaSrTFwhOZmbz55Ze0uly0\nWCxETZ6MVYXwxNP2OasHBQYAjguc7PtH9UlDAy0Y1pHocDi45JJLeOqpp4Zck3b81gwTYf/csaJ2\nt4GbFroNYPwHBwMNJ0Q43khChVM91ngPCI53OoFBoJ+f+L0mnDZ/P+23H2qdJ89H/MVxLoyBEJ0c\n5yaTiTvj4rgzLq7/fW/V1vJ8dTUlHQ6KGtv5qrGdxwsO9X/cCPgZwGyQCPD3ZYqfDxYfA35GA2aj\nAR+DgfZuGYfcQ2e3i+ajMi2dR+nsUTiqQM9xNRgAq6F3ycH1UVH8aOr4Gth4Isefj1S2txNlNvOU\nCoMPKxwObHY7MwwGkvtmDHhadXs7MVYrZ8XEsLG6moNtbdyak0O4wcC5mZleqUEtPSbX0O83Dv1+\nLTllaNDd3c3q1au5+uqr+e53v/uNj0+dOpWqqqr+tw8dOsTUExz0BQMGWkQGBxPppRenVmmt20AE\nB+o61UX8cEKFkTzeRHK6HQYbli0by3L6tzxVeyCpeyBr+wQ6zrSgrqmJuuZmtcvQHU+fj1w2xse5\nnuwoLaWoqoo7Fy4kNjDQq88tyzImk4m7Nm7E2dNDpCTxdFBQ//lIps1GkI8PHyxf7tW6AJ4uKWF9\ndTXzDAa2jvOLGYCroqK4KmrwPvB2p5N3Dx8mp6WFfe3t2Lu7cbpk2hxdVLV1DdoGTuFYG7UEGCXw\nlcBqNBFkMjHTYuE7wcFcHhlJsIe389Oqovx8Yk2mQecjc4ODWX9c55S3XJufjwG42Uuv7w/LygD4\nXmIiySEhLO5bdvZYbi61LhdbS0pYkpzslVrUYJSH3oPA2HPSvQk8ZiTnIycNDRRF4brrriMlJYXb\nb799yM+56KKL+NOf/sSaNWvYsmULwcHBJ2wFTJs+fVhFTTRa6DbQ0jIFmLjBwcmIEGB0tLokQe3A\nwE0EBt4XGRIyKDTfXVGhYjX6IM5HPGtRYiJfV1Xx9K5dPJ6V5dXnNplM1DocHO3p4fz4eFbGx0NB\nAbubmnjh4EEU4OdJSV6tye3W5GRcwNvV1SzNzWXLBAgOjhdqNnPjtGncOGDpjzA6M202DikKm7Kz\n1S4FgPuKijgK3DRvntee84KEBDbV1PBiYSF/GHA8fS8wkFc7OiiuqWHR9OnjdlnKLPNUWj7soP2C\nrv73WT8wM8tPnS6bkZyPnPRfZNOmTbz55pvMnz+fBX1roB599FEqKysBuPHGGznvvPP4+OOPSUpK\nwmKx8Oqrr47F9zBhaKXbwE0r3QYgggPh9GkxMDikkeNd7W1fBWEkxPmI56XGx1NQXk5pUxOJXu4E\nLW1pwQVkxcRQ1tyMraODL776ihZFIcZs5szJk3HKMmYVLiRuT07uXXtdU8Oy3Fy+nIDBgXD6ZvQF\nBj/VSGBZ4XDwX7udZIOB2X27OXhLRnQ0n1ZWcmtODhaTie/27ZbQ1d2NJEnjNjCA3mGHVb52Dn3S\nSKBzEsYeA7P8pmp+ngGApBy/ANBTTyRJXKuRZE1r3KGB2t0GQH+3gVaCA4CEvppEcCCMhJYDAy10\nGewrKBBdBhrxWk7ON9biC54jzkdO7PWcHEzAEyr8fNbl5tLtciEBBklCURSWmkw8rsJguKE8UVzM\nuzU1pEgS+V7uxhD0bbrNRn1fYHDVgBkSasrKyaEHeNKLx/rv8/O5auZMpgYEAPD8V1+x58gRoPf3\nsqIofGfePKZ6OcTwto8W7iDt4HSmNk0e9tdsmrmP8JYgkuuiTv3Jp+Fk5yPqLKAQBtHSibsWLmaO\n577oaxV3RoVh0mJg4KaFY0x0GQiCMJTFCQl0A3sbG73+3E9kZpIaGsqyyEhSQ0N5Mjub2720X/xw\nrJsxgytjYtijKMyx2dQuR9CJmL7AYF1ysmYCg7sKC+kGbvLi9oqPbtvGIYeD3+3Ywc9zc9nb2MiP\n58/nJ8HBZPj5MSMqisvT08d9YNDi34HD7CSqOVjtUkZMhAYaoqUTea20ULuJ4EAYLq0GBlo7prQU\nVgqCoA0psbEYgJcKC1V5/uvmzmXNrFn8YM4coHdIopZ+d96clMT18fEcVBQSRXAgnIQsy0TabBxR\nFO6fOZPVGtkZYk9LC3mNjcwxGJg5efh3uk9XQ0cHwX5+nD1tGt0uF88VFrIuN5cGWSZx2TJK6+qQ\ne47fX2P8KYuoZ3p9BAZFf5fg+qt4nNLSCbz7TqiW/lCDCA6EU9N6YCC6DARB0LolM2YgA7sbGlR5\nflmW+//fvngxAJvy81WpZSg/io/n9oQEahWFqTbboHoFAcApy4Tl5dGqKPxm9mxWRXm2pXwkbty1\nCyNwo5dnc9yalkbW1KlcmJjIk9nZLIuIQHa5+IfDwWs5OfS4XFjNZq/W5G0KCmUR9STWDz2g92S0\nsBmwCA00Risn9Fq4uBmKCA6EE9FqYOCmpWNKSyGlIAjaMiM6GiPw1z17VHn+44egfRwVxc8dDv5d\nX69KPUO5LDaW+2fNoklRCM/LwymCA6GP3ekkLC+PLuC51FTOOsEOLmr4YW4uPcAdCxd6/bkTgoP5\ndmxs/9tXzJ7NTcHBTA8LA2DpjBler8nbDge2YnQZmOwY3bIrRVJ39pEIDTREiyfyWus2ABEcCN+k\n5cBAS8eQVkJJQRC0LSMlhR4gr7pa7VJYGBGBP/Dg3r2auqu/KjKS51JTcQJheXnUOZ1qlySorNjh\nIG7Llt5tOs84g1Qv70JyMrkNDex3uZgfGkpsYKDa5fSfj9S1tCBJEjOio1WuyPNK+7oMJE30DYyc\nCA00SCsn9lpdpgAiOBCO0UNgILoMBEHQk/jwcHyAd0pK1C4FgF8tXYoCfH/TJrVLGSQ1JIS3zzgD\nF5C4ZQsFra1qlySo5L2GBtLy8zECHy1dSozFonZJ/WRZ5p49ezAD18+dq3Y5/dc57WlpnDN/PudO\ngPOSHslFRXgD00exNEErRGigMVo7odfSxc7xRHAgaDkwcNPKMaSVMFIQBH34dmoqCrChvFztUrCa\nzayKi8OuKLxUVqZ2OYPEWCx8kp6OD7B8507eqKlRuyTByx45eJAr9+whAPhPRgbBGlub//1Nm1CA\ne5cuVbuUfu7rnWCrlbCgIJWr8bzqKY0Et1uwdmnrtTESIjTQKC2d4NelpWmy2wAGBwciPJhYtB4Y\nHCoo0Exg4Ka1UFIQBO2KCAnBT5L4RAOhAcB506cTKkm8WllJvcaWAgT6+PB5RgahksSNxcXcvn+/\n2iUJXrKmqIhHKipIlCQ+zc7+xkwOtf3l4EHsisKquDhNhBkfb92qdgmqKIuoJ+F0ugwU9Zc0iNBA\ng9wn9loKDkCbyxSg96JRdB1MHAMDIi0HBlqitd8lgiDow6pFi1CAtzVyEXxvejoScPmWLWqX8g0m\nk4n3s7JINRh4sbaWrNxctUsSPCzFZuN9u52zjEbeyMpSu5xvsDudvFJRQagkcd706WqXw+H2djZ0\ndpIbEKB2KV511NRNTUgT8YfD1C7ltIjQQKO0dkdQy/MN3ERwMP4NDAu0HhiILgNBEPQu2GrFKknk\n1daqXQrQe2F+49y5HAVu2rhR7XKG9FxmJudHRLDd5SJabMk4LjV3dzM5J4dyReFHcXH8ZsUKtUsa\n0iVbtiDRG7ZpweN9W6cuSkxUuRLvKg87THRTCL6yj9qlnBYRGmiclu4Qau0iaCgiOBi/tN5dMJCW\njpV9BQUiMBAEYdRWLlkCwAuFhSpX0islNJTZISHs7ulhk92udjlDum/2bO6fNYtmRSE4L4/Ctja1\nSxLGSG5TE1M3baIL+FNqKtdr4A7+UG7IzeUocOPcuZpYMlHW3EynojB32jS1S/G6soh6Euoi1S7j\ntInQQMO0eqKv5W4DEMHBeKSXwEBrx4aWQkdBEPTJajYzWZL4urFRM3fNb0pNxQ+4q6gIp0ZqOt6q\nyEjeXbIEA7Bkxw6eqaxUuyThNN1RXMyq3bvxAz5JT2ehhrZUHOjf9fV87XIxLzSUlNBQtcsB4NmC\nAiQmXpeBw89Js6WdqUcmq13KaROhgQ5o6cRfD8sUQAxIHC/0ML/ATSxLEARhvDq3r7350c2bVa7k\nmAf6tmH8rsa2YRwoyt+f/2RkEClJ/KKsjHQx50C3ZttsvFBTQ4ok8Z/sbAJ9tNlq7pRlHti7F3/g\nBg1srwiwo76ebmBJcrLapXjdwYh64hrCMSr6v+TW/3cwzmnxhF9PwYHoOtAvPcwvcNNiYKClsFEQ\nBH0zmUxEh4Rgd7lwaGTnAqvZzCWJibQqCg/v3at2OSdkMpn4Z1YW50dEsMvlYnJODnUa+RkKp1bs\ncBCYk0NF3/yCv2hw4OFAF/WFaL/SyBwDgDf27sUEzJw6Ve1SvEpBoTSinsTT2TVBQ0RooBNauwDQ\n0sXRqYjgQH/00l0wkBaPCS2GjoIg6NPZqakAPKqhLdMyp00jyWDgk/p6djY1qV3OSd03ezZPz59P\nF5CwZYtYrqADPy8pIS0/HwV4fdEizc4vcLuvqAiHonDFjBlYNdIJsaG8HBeQPW+e2qV43RGrgx6D\ni7DWQLVLGRMiNNABLZ/4a73bwE0sV9AHPS1HcNPiMaC1kFEQhPFhZlQUDkWhsrVV7VL63ZqZiQ9w\ny+7dmpm5cCKLJ0/mi4wMwvqWK8wXuytokizLTLfZeLa6mhmSxMbsbJI0vk1gbkMD/7XbmWMwsCw6\nWu1y+n1cXo5Zkpg6ZYrapXhdWUQ9CfURSEhqlzImRGigI1q7ENDLMgU3sVxB2/S0HMFNi8sS3LQc\nNgqCoE9LZ85EAp7auVPtUgb5Zd98gws1PN/AzWwy8a+sLC6bOpUDfbsr5Gq8S2Iieau2lqC8POoV\nhZ8mJPBXjS9HAHDIMnfv2YMZuDEzU+1y+r2+Zw8AqxYvVrkS73NJLg6GN5AwRksTtBA7iNBAJ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D8dFpqu8mliYIE8mK2bORgY/KytQu5ZTuyMwkUpJ4sbycd6uq1C5HGOd+kJvLIUXhnNhYMqdN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PbxWKZjGmc56vGMDDRgU2WlU3tw1nnjx6MCNQ0NHr2OEEIMBlVVadI0JoWFuW3N2TExnJ6Y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\nYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x7a7d9d0>"
]
}
],
"prompt_number": 47
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"-----\n",
"5) Experiment with at least one parameter each of the Wolfe Condition and the trust region method and report the observations. Compare advantages and disadvantages of each method from numerical observations or theoretical properties."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig,ax = plt.subplots(1,2,figsize=(15,6))\n",
"\n",
"x = array([-1.2,1])\n",
"xs = []\n",
"xn = []\n",
"c_values = linspace(0.1,0.4,10)\n",
"for c in c_values:\n",
" xs.append(len(steepest_descent(f,g,x,c=c)))\n",
" xn.append(len(newton_method(f,g,h,x,c=c)))\n",
"\n",
"ax[0].plot(c_values,xs,'o-',label='steepest descent')\n",
"ax[0].legend()\n",
"ax[0].set_title('steepest descent')\n",
"ax[0].set_xlabel('c (wolfe condition)')\n",
"ax[0].set_ylabel('no. of iterations')\n",
"#savefig('steep_performance.png')\n",
"#clf()\n",
"\n",
"ax[1].plot(c_values,xn,'^-',label=\"newton's method\")\n",
"ax[1].legend()\n",
"ax[1].set_title(\"newton's method\")\n",
"ax[1].set_xlabel('c (wolfe condition)')\n",
"ax[1].set_ylabel('no. of iterations')\n",
"#savefig('newton_performance.png')\n",
"#clf()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 49,
"text": [
"<matplotlib.text.Text at 0x64f1a50>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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hOHnypNxhEBGRGbRq1QonTpyQOwyjefjwIQYPHoyRI0diwIABxV4fMWIEevfuXWx7gwYN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\n/1wAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x73bd5f0>"
]
}
],
"prompt_number": 49
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It seems that tweaking the values of $c$ for both steepest descent and newton's method only triggers differences in behavior at discrete thresholds. It is also interesting to observe that the local minima of c for steepest descent appears to the local maxima of c for newton's method in terms of the number of iterations to convergence.\n",
"\n",
"We'll do a trace of the iterates at values of $c = 0.2$ and $0.35$ to observe how they both behave."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig,ax = plt.subplots(1,2,figsize=(15,6))\n",
"\n",
"x0 = array([-1.2,1])\n",
"\n",
"xs2 = steepest_descent(f,g,x0,c=0.2)\n",
"xn2 = newton_method(f,g,h,x0,c=0.2)\n",
"xs35 = steepest_descent(f,g,x0,c=0.35)\n",
"xn35 = newton_method(f,g,h,x0,c=0.35)\n",
"\n",
"i,j = mgrid[-1.5:1.7:0.025, -0.2:2.5:0.025]\n",
"C = contour(i, j, f([i,j]), 10, colors='black',linewidth=.5)\n",
"\n",
"xs2 = zip(*xs2)\n",
"xn2 = zip(*xn2)\n",
"ax[0].contourf(i, j, f([i,j]), 10, alpha=.75, cmap=cm.hot)\n",
"ax[0].clabel(C, inline=1, fontsize=10)\n",
"ax[0].set_title('c = 0.2')\n",
"ax[0].plot(xs2[0],xs2[1],'.-',label='steepest descent')\n",
"ax[0].plot(xn2[0],xn2[1],'o-',label=\"newton's method\")\n",
"ax[0].legend(loc='best')\n",
"\n",
"xs35 = zip(*xs35)\n",
"xn35 = zip(*xn35)\n",
"ax[1].contourf(i, j, f([i,j]), 10, alpha=.75, cmap=cm.hot)\n",
"ax[1].clabel(C, inline=1, fontsize=10)\n",
"ax[1].set_title('c = 0.35')\n",
"ax[1].plot(xs35[0],xs35[1],'.-',label='steepest descent')\n",
"ax[1].plot(xn35[0],xn35[1],'o-',label=\"newton's method\")\n",
"ax[1].legend(loc='best')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 52,
"text": [
"<matplotlib.legend.Legend at 0x7a4a770>"
]
},
{
"metadata": {},
"output_type": "display_data",
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lunSPM4DnduXxwu48CmqbWHX4BGaHg+ONViaF+7SNKd/k2hgWAObsdKoarMQE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bfY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\nBFOMSMwEAoFAIBAIBAKBYIr5/wGFSX8Dd78GJAAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x75fe350>"
]
}
],
"prompt_number": 52
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It appears that steepest descent is best meant for large improvements in the beginning, but that makes very little progress when the gradient is gentle (usually close to the point of convergence). Newton's method, on the other hand, is fairly consistent in the progress it makes in progressing towards optimality.\n",
"\n",
"Perhaps one option will be to do a hybrid algorithm that utilizes steepest descent for large initial improvements, before switching to newton's method for smaller local improvements."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"D_values = linspace(0.1,1.0,19)\n",
"plot(D_values,\n",
" [len(trust_region(f,g,h,x,Delta=D)) for D in D_values],\n",
" '^-',label='Trust region method')\n",
"legend()\n",
"title(\"Trust Region method\")\n",
"xlabel('max. Delta')\n",
"ylabel('no. of iterations')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 50,
"text": [
"<matplotlib.text.Text at 0x63fb9b0>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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mzZqlj9g0RvMEhBCiuzonixUKBeRyOWxsbNC/f39kZGToKy6tUI+AEEJ0V2eP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\n",
"text": [
"<matplotlib.figure.Figure at 0x786eab0>"
]
}
],
"prompt_number": 50
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If we look at the traces of the three algorithms (steepest descent, newton's method and trust region) for the starting points (0,1), and (1.5,0.5), we can see how the trust region method is a compromise between the earlier two, which makes it swing alot less in either extreme.\n",
"\n",
"It is also rather unsurprising to see that the performance in the trust region method is the same for large values of $\\Delta_{max}$, since the algorthm behaves in exactly the same way, as the region boundaries no longer become a constraint in deciding how big the trust region can get.\n",
"\n",
"At smaller values of $\\Delta_{max}$, however, it appears in oscillate in performance, with higher volatility for smaller values of $\\Delta_{max}$, making it difficult to calibre the parameter for good performance at these range of values for the parameter."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
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