{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## ISTA\n", "\n", "The **Iterative Soft Thresholding Algorithm (ISTA)** is used for solving inverse problems where the solution is known to be sparse. For such problems it is common to use $\\Vert \\cdot \\Vert _1$ as the regularization term in the Tikhonov functional: \n", "$$\n", "J(x)= \\frac{1}{2} \\| A x - y^\\delta\\|^2 + \\alpha \\Vert x \\Vert _1.\n", "$$\n", "\n", "However for this case there is no closed formula as for $\\Vert \\cdot \\Vert _2$. The necessary first order condition for $x$ to be a minimizer is given by\n", "\n", "$$ \n", "0 \\in \\partial J(x)\n", "$$\n", "\n", "which is equivalent to\n", "\n", "$$\n", "0 \\in A^T(Ax-y^\\delta) + \\alpha \\partial \\Vert x \\Vert _1\n", "$$\n", "\n", "where $\\partial$ represents the [subgradient](https://en.wikipedia.org/wiki/Subderivative). For $\\lambda > 0$ this yields\n", "\n", "$$\n", "x - \\lambda A^T(Ax-y^\\delta) \\in x + \\lambda \\alpha \\partial \\Vert x \\Vert _1.\n", "$$\n", "\n", "The above equation is equivalent to\n", "$$\n", "S_{\\lambda \\alpha} \\left(x - \\lambda A^T(Ax-y^\\delta) \\right) = x. \n", "$$\n", "\n", "where $S_\\varepsilon$ is the proximal operator of $\\Vert \\cdot \\Vert _1$, which is the soft-thresholding function \n", "\n", "$$S_\\varepsilon(x) = \\text{sign}(x)\\text{max}(0, |x|-\\varepsilon)$$\n", "\n", "Turning the fixed point condition into an iteration scheme and reorganizing the operands yields the ISTA iteration\n", "\n", "$$\n", "x^{k+1} = S_{\\lambda \\alpha} \\left( (I - \\lambda A^TA)x^k + \\lambda A^Ty^\\delta \\right).\n", "$$\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 1\n", "\n", "Recall the integration operator $A:L^2\\left(\\left[0,1\\right]\\right)\\rightarrow L^2\\left(\\left[0,1\\right]\\right)$\n", "\n", "$$ (Ax)(t) = \\int_0^{t}x(s) ds $$\n", "\n", "discretized by the matrix\n", "\n", "$$\\tilde{A}=h \\begin{bmatrix}\n", " \\frac{1}{2} & 0 & 0 & \\cdots & 0 & 0 \\\\\n", " 1 & \\frac{1}{2} & 0 & \\cdots & 0 & 0 \\\\\n", " \\vdots & \\vdots & \\vdots & & \\vdots & \\vdots \\\\ \n", " 1 & 1 & 1 & \\cdots & \\frac{1}{2} & 0 \\\\ \n", " 1 & 1 & 1 & \\cdots & 1 & \\frac{1}{2}\\\\\n", "\\end{bmatrix}\n", "$$\n", "\n", "\n", "**a)** Create a sparse vector $x$. Create two plots one containing $x$ and the other one containing $y^\\delta = Ax + \\sigma\\eta$ with $\\eta \\sim \\mathcal{N}(0, 1)$ and $\\sigma=10^{-3}$." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x288 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "\n", "def plot_solution(x_true, x_delta=None): \n", " plt.scatter(s, x_true, marker='o', s=15, color='black')\n", " for i in range(len(s)):\n", " plt.plot([s[i], s[i]], [0, x_true[i]], linestyle=':', linewidth=1, color='black')\n", " \n", " if x_delta is not None:\n", " plt.scatter(s, x_delta, marker='o', s=15, color='red', facecolors='none', zorder=100)\n", " \n", " \n", "N = 100\n", "h = 1 / N\n", "s = np.arange(h / 2, 1, h)\n", "\n", "A = h * (np.tril(np.ones(N)) - (1 / 2) * np.diag(np.ones(N)))\n", "\n", "x_true = np.zeros(N).reshape(-1, 1)\n", "x_true[30] = 40\n", "x_true[50] = -80\n", "x_true[65] = 50\n", "x_true[85] = -20\n", "\n", "\n", "plt.figure(figsize=(10, 4))\n", "plot_solution(x_true)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[<matplotlib.lines.Line2D at 0x2e161898240>]" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x288 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "sigma = 0.001\n", "y_delta = np.dot(A, x_true) + sigma*np.random.normal(size=x_true.shape)\n", "\n", "plt.figure(figsize=(10, 4))\n", "plt.plot(y_delta)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**b)** Try to reconstruct $x$ from $y^\\delta$ using Tikhonov with $\\Vert \\cdot \\Vert^2$ for different values of $\\alpha$." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x288 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": 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c10/eli71R/q/5ZYaCDKGSkuB+fOBtWur/RXVbsfFxf6dFXburPa840ZxMXDyyUDz5v7FHitWRP6dI0YAffoAAwYAkydH/n0SkagnW2Z2gpnNM7OFZnZjtOdXJatX+7dWqezE19JSYMkSoKTkh7Ldu4Hly/0bse6xa5e/Uym/gSxeDNxxB/D3vwPr1h14PqT/KD+P998HRo8G1q+v8mKVWbcO+OKLvWNcudL/zuXLK/98SYm/THts3QpMmQLMnftD2ebNwNixwMSJfrx7rF//4yvCior2XtelpcC4ccCrr1bv6rGNG/0bOe+5/Q0ArFoFfPwxsGbN3vNZvfrHO/vy8VaE9G8s3bevf4L0N9/89BgBDB069Kd/6Kuv/NHm27QBLr1072Xc1+rV/iGv8sv85Zf+TvbTT/eedt9l3rLFr9OFC38o27nTX9bKdvRbt/pt8/XX/fOb9lizxq+Hys4D/e47f9ry023f7reTPXHu3Onfc/Kyy4BRow78nWZAamrN3tMvNRWoLMlYvdo/Mf+66/ztfw/yx+ub/HFdLlsGTJ2693ZK+ut3389u3Lj3Oli40D9XbcaM/ce3fj1w1FHA//0f0KUL8OSTB16e/ahWO376aSArCzj1VODww/263Z/du/1Yyy/fpk3+PmzDhh/Ktm8H5s3be31VZNcuf/9bft9JAoWFe38f6U9XlcRm8WI/qS+/X5w929/+tm37oezrr/2rWfed944dB/7+yy7z62jOHD/ZOuecymM6kHfe8X97Hn3U7/E9/XR/26xIaSnw3nv+Z777bv/fSfr72Ndfrzx5373br8Pydbp1q/8bUn59Af48y09XUuJf9FLZhRm7d/vbQXHxD2W7dvn1VH6/VleQjNoDgAtgEYBOABIAfAXg0P1N37dvX0bb+pdf5gbP4xTX5QbP4/pRo8i1a/n9kCHc4roscBye3bcv13z5JXd27cqihASuB/iX7t1ZNHcutx9+ONeGQtwI8J6uXVm0cCG35+RwVYMGXAfwufbtueazz1jasiVHtW3L5z2Py5KSWLRwITfddx/XJCSw0IzDO3dmOBzmxoce4gbP4xaA/23XjuHCQm47/XQuatiQ/3NdhhMTueaLL7juzTe5PCmJmwGOb9WK4WXLuPZ//+OypCR+D3BKaiqL5s/n+hdf5EbP49eOw7WhENe+/z757rvclZrKGU2acK0Zbzj0UBYtWMDvTjuNa0MhfuK6PDMnh0Vz5nD7UUfxO8fhWjP+qWdPrvnqK+7s2JGzk5MZNuOz7duz6JtvuLNjR37etClnOQ7fb9mS4VWruO2ss7jFdVkCcGRGBsOrV3PrhRdys+dx3Z64V6zg90OGcHZyMt91Xa5o0IBF337L9S+/zFUNGnADwNfbtGF41SquGzOGhYmJ/B7ghy1aMLxkCTf8+9/c5HlcYMZVDRqweNo0bhg5khs8j1ODOl331lvk7Nkszcjg+lCIq8x4cXY2i2bN4vcDB7IU4EIzXtSnD8PLl3Pr+edzTUICCxyHv+3Thxsffpg7unXj73v14lWJiVyTkMCihQsZDoc5aNAgpqSkcNCgQQyHwxWWVaRKn12xgqXp6bw7K4vdGzXi1GbNWHLNNVxTUMD8Zs240IxvtW7N8JIlXP/CC9zgeZzmOP4yjxlDvvoqS1u25Li0NC4z44OdOrFozhx+f8wx3AlwUbAe1nz+OUszMjg7OZlrzPhox44smjePO3r14oqgHT/VoQPD4TA333knVzRowG8ch9f26MGihQu5o0cPft60KSe7LmelpDC8eDG3XHYZN7su15r5dbVyJYsnTuTk5s050XV5xyGH+O39sce4xXW5HuCMJk1YtHAh1z//fFkbmZOczKJvvuG2X/+anzdtymsTE7k0KYmb7rprv+s66vVSQVnR/Pnc2b49R6en896EBK4PhVg8dSo3jBjBDZ7H7wG/rlat4vrnn+dGz+P2YDsNL17MjQ88wA2exwLHYVFCAos//ZRr33uPqxMT+R3AeY0acc2MGeTs2dyZmcmtrsvFZjzv8MO5/tVXuSs1lR+2aMGVZnywc2eGCwu5+aabOLNxY77iefzFkUdyy6WXcut553HQwIHs2agRN3sei775Jurrq2juXO5KSeGvc3KYkpzMV9LTufWCC1g8dSq/aNKEy804Li2N4SVLuPbdd1mUkMBNAJcmJbF4+nQyP5+lLVpwQaNGLDbjlYcdxuKpU1makVHWPq/r0YPhJUu47YwzuNnz+I3j+Nv4/Pnc3rcvixISuBHgPzt3ZnjZMn5/3HHc4HncBPDJzEyGV67kdyef7O8jzfhGmzYMr17NTffcw02ex417pguHueXSS7k+FOJiM37ZuLHf3q+8ksUJCZzhOFyalMSib77h5ptu4pqEBE50Xa7ZU6fjx3N1YiJ3ApzZuDGLvv2W4eXLOaJDB77meXykUyeGV60iO3Zk8dSpHDRoENslJ3Or40RUL1v++EeWXH99Wdn0pk25/oUXuOlvf+PaYJ94b9eu/v74mGM4NzmZU12Xc5OTWbRoETc8+2zZOnyxXTt/X37BBVyWlMQJruu32enTWTxxIr9u3JjL96zD5cu57u23uTYUYsmedvzll1w3dizXhUJcaMbihASuffddctky7ujZkzvMuNiMv+3Th8WffMLS9HTOa9SI6wDeecghDC9dym1nnMFtjsNFZry8Vy8WLVrE7UceyaKEBG4A+FjHjgwvWcLtAwZwZYMGDJvxtaBOow1AAauSD1Vlouo+APQH8G651zcBuGl/09dGsrU0KYknOA4B8ETH4ZKkJPLss/lGmzZs4bq8EuBMgBNateJ/MjLoeR4PB7gR4Kj0dL6dlkbPddkV4AaA/8nI4PstWzLkumwOsBDgy23b8o02beh5HgHwAzM+0aEDixISmO26PBTgUoB3ZmVxXSjE3q7LtGC+j2dmsjAxkY1clwD4gBlHpadzfSjEUx2HqQDHmfHZjAwWJSTwbMdhEsCRZhzTujWLEhI4OPjsRY7DLxs3Jnv25LU9etDzPOYCXABwbOvWnNCqFTu4Lq8L5j2mdWu+2bo1Q67LgQDXAnytTRuOatuWnuexeVD2ctu2fLN1a3qexwSA8wE+3aEDZ6WksHGwHhYBfKRjRy5u2JBNXZdJAD8H+ExGBhc2bMiEIMZnzTgyI4MbPI/HOQ7TAH4M8JHMTK4PhTjUcdgI4OtmfL5dO252XR4ZfPYmx+Gk5s1ZlJDAQUHZmY7DWSkpZG4uh3fuTM/z+GuA3wR1+nqbNmzgujwL4GKAz2VkML9ZM3Z2XV4AcHmQFP6jS5ey+vsK4EV9+nDQoEFlZZ7ncdCgQRWW7XHbbbeVPa/KZ3/Vrx/XhkJlZb9wHE5t1oxzk5N5m+OwW7AeRqenc2WDBjw2aMe/chzOa9SI7NWLVx52GD3PY1eAxQDHpaXxzdatmeS6PCNYvrfT0vjvoG2nA9wE8KW2bflO0LZbASwC+I8uXbg8KYk5rsvjAa4B+ERmJqekppbF+GGQgK9o0IDNXZeJAD8JfuTWhkK8ynE4FOAygLcecgg3ex57ui4dgC+a8b/t2nGz5/HooP4eNuPYtDTuMGOToOyY4EfgmIEDeY3j8N8Ar3Qc5g4cWOV1W75eyqvqZ0866ihe7ji8FGAL1+VN3btzetOmZdM9bMYX2rblBs9jP9dl46AdP5qZyU3B8oUAvhos81bHYbdg+f7sOPyoRQsuT0riOUGd3mHGT1JTyf79+c+gHV8CcDrArxs35l+6d6fneewIcHNQL9+mpHCI4/BegF8CfLdlS97btWtZjAsBntu3b9Tb8ZlHHME1CQn0guU7z3E4MTWVS5OSeK3jsCPAN8w4qm1bLk1K4tnBMt/oOJzWrBnZty9v7daNnufxBIBzgyT1sY4d6Xkejw7a4gvt2vHj5s3ZxnX5a4ArAb5Qrh1nAlwH8JkOHTi1WTM2CPazqwD+q0MHzmzcmEmuy0YAZwN8oHNnFiUksJvrMgPgvKCsMDGRqa5LA/hmsL9aHwqxZbB8jwXb5FbXZXq5fdOEli1ZlJDAMxyHDsBHzDihVSuOS0vjBDOeDXBKsBw880y+2bo1O7ku7wI40SyidnxXVhZnJyczzXXZI9ie78rK4qoGDdjDddkrWF+PdOzIb1NSyvbHY8z4VIcO3BC02TbBfvvxzEyuC4XKtsm7zPhG69YsTEzkZY7DTgAnmPHf7dqxKCGBpwV1ercZP2rRgosbNuSvgrLz9+yjTzqJz7RvT891eV6wj/64eXM+GtRzt6Btj8zI4JTUVLZwXZ4cLMvIcr+7bYL28Gz79pySmsoE12Vy8Dt3We/eEWQLVVNXkq0zADxT7vV5AB7bZ5o8AAUACtq3bx/VlUKSq8zYGSAAdgG40ozs2ZNHN2xIAAwB3AnwI9fl6UlJBEALfpDe9Dxe2qABEXx+EcAXPY9/TUgoK5sO8LFQiGOChu8GO77HQyGODIXKpnsS4HOex/FB4wXAO4OyeY5DC8puBfhfz+Nis7LpzgQ4LuhB2lP2M4BTXJffAWwSlB0OcJbjkB06MCdYvo4AwwC/dBweE5Q5AEsBfuC6HBYsM+D/WI/2PF6TmFi2HhYB/Lfn8f5yyzwD4DOex0fLLd9ogM96Hl8J1gMA/gvgU6EQPw82OgB8KFjmL8qVXRrMd0W5Zf4VwPGuy++Ddbpnmae6LjcCTAvKsgHOcxyyY0f2adSIANgcfrJc4DgcEiwzAO4A+K7r8tfl6nQVwH+GQnw3SBBz4CeYmY0aMSU5mS0AJgfTpqSkMCUlpeyze8r2KP8jVdF0+5Y1S07mSjOeB7AtwLcB3h8KcWe5aY4EOCPoeWwblPUAuNiMPOwwnhjUX+cg7nzH4c/L1ek2gGNdl5cEy+wAXA3wZc/jDUE970kwn/c83l2unt8B+GQoxNfK1enbQdnYcmXDgzqdUq5t/znYVuaVq+ffAnwj6OXaU3YSwA8ch+sA9gnKLoK/PT4eCvFjgL8D+CnAB0OhKq/bSOqlXXIyF5jxZYCj4P/4n9mgAWc7DhOD7eJN+Nt9frnluwrgKM/jonLt+ByAbwbbbigoGwrwQ8fhToCJQVlvgN86DtmmDbsF7Tgd/rZb4Dg8JajTlkGdfuS6/GW5el4PMC8xkcvNeD7AR+D/Q9UsOTnq66tJcjI/dxw+DfBCgEuCWLaUm+YYgJ+6LrcBbFSuHc8L9leHB9tpOvz90AzH4XHB8iXA33bf32d/FQb4uufxj+Xa8Wz4+887yrXjifD3Tf8qt796Df4+7OVy7fhhgM+FQpy8zz565D7t+GqAL3ke15qV1el58Lez7eWWeQDA6Y7DjQBbBGXd4fc4c906jvE8rgQ4HmCbCOulcXIyHwuFuA3+fuBcgDcmJu61zM/D3x+/V275ngH4dCjESeXKbgjW4TKzsn3vn4K2XVSubZ8M8P2gHTtBWb+g7tYBbI0ffneXmZFZWTwiqOdGQTueXK4dh4Kyt12X55fbRy8G+Mo++6sZQb0ML1fP7wEclpRUA1nDgaGKyVa0z9mq6Bps7vWCHEEyh2ROy5YtoxwO8H67dngVwDUAXg1e48gjcVujRjjEdXEz/MxvZmYm7jPDWY6Dp+Ef//yyc2fcCuAcx8E/AWwDMK1bN1xN4oqgrBmA9w4/HIcmJiIfwEwAy8wws0cPnGyGXNfFUQCGAljQtSv6m+FXjoMB8DPRWYccgi0pKRhvhkcAXA5gYs+eaBQK4RLHQXcAfwSwLCMDaxo2xM2Og54AbjDD4vR0fJiWhtFmuAjAMwA+zcgA8vLwCoAbHQevA3jGDKtatsQNycnIcF1cDWAWgLnt2+MO18VxjoN7ABQCmNKtG27ZvRs3Og5eBFAE4KNevXARiYfM8BqAXQCm9+iB3wC4wHFwGYBcAJ/16IHjAVwTlJ0OYGrPnmjUsCHGmuEpAGcC+Piww9DBdXF2sCyXAliSmQk3IQFXOQ56A/gTgCXt2+OLZs3wkhnOBfAIgM87dMB76ekYA+BqAP8F8FH79sDJJ+PJUAinOA6eAjDeDAvatMFdiYk4wnVxN4AvAaxOT8eVDRuiveviHPiN892cHFhqKjYBmAAgz3GQmZ2NtxMTsQDAagDXOw6ys7ORnZ3OYeK8AAAcgklEQVQNz/NvMep5HrKzs8va2u233172vKLp8tq3xzIAWwE8a4bevXvjr9nZuCpog0VmmNCvH1YnJeESx0EKgIvMEG7ZEu+np+N1AFcCeBHAh+3bAzffjP+WlmKEGd4HcK/jYFF6Ou5o0ABHuC7uADAXwKeHHIJ7du/GdY6DVwDMNkN+t2748+7duMJx8Aj84/9LO3fGWZ6HLq6LfgByABT06IGjPA8vmWEUgC4APu7VCwPMcJ3j4JKgHc/NysKhjoOurotEAMebYV1GBhomJOBvZjgVwF8AfN25M8LJyXjUDEMB3APg28xMPNitG94DMB3A3wD8t1cvnA3gt66L5wBcFLSX/a3bA9VLeVX57B/atEFhairO8zycBWCuGXpnZGB5ixaYDX/f0BLAR9nZyHJdXOA46A/gMgDzOnVCUkICrnccDAJwPYAFHTviy+bN8YYZrgTwKICpXbrgi6ZN8agZBgK41wyzW7cGjj8e/2rQAMc5Dh4E8IEZxnXtimd37cI/zfAhgIfNUNKyJc5v0gQh18UxwTY5PycHT3XrhhPNsBvACa6Lnn36YFCPHjjbcXAigATXjbgd71vWq08f3NqvHzaZ4dhgW5lzxBHY1KAB8hwHLQBcaoZwq1YoaN4cT5phCIDhZvi6dWvgnHPwvOsiz3HwEoBXzPBZ+/Z43HFwbrAfescMK9q2xXWJiejmurgU/v74i65dcTP8/dD9QcwF3brhchIXOA5uCtrs9B49cBaJaxwHNwIYAOCr7t3xczOc6DjIhb+/+vqQQ9DF83CfGa4K6nRqz57Y1bAhXjTDjfAP10zp3h2zU1Mxzgy3ArgPwMfdumFhSgruN8ORAG4zw/z0dGxOSkL/oO32dxxsTUkBUlPxQP/+yPQ8nASgOMJ23LtPH7xy1FFo7LpoAWCU56HkkEPwS8dBf9fFQAD/B+CLQw/FIQkJ+K8ZngBwAoCpPXqgd/C71AfAbwHM79IFhU2b4n9mGA7gRgATe/SAhUI4z3GQBuBiM4TT0/FVkyZ4wgw/A/APM8xq2xZTWrfG82Y4G8CzAPLT04EhQ/BggwbIdV08AGCiGaZ26oRHgt/T1wC8a4bl7dvjTwkJ6O26yIN/Q+fPDzkE15G4yHHwdwApAD7t0QO/C/Zr9wLIArCld+8K11dMVCUjq+4DdfAwYnj1at6dlcUnQiHenZXlH9PdvJnbzjiDhYmJfNd1+at+/fzj9/ffz4+bN+djoRBP7N/fP+fkiSf4cfPmfCYU4mlHHslwOMx1r73Gd9LS+HgoxF8EZeGlS/mnnj15QlISjxk40P/s449zaVIS55vxrqwshsNhrh89mrNSUvi14/DvXbuWffa+Ll14S0ICz87JYTgc5tqPPuLMxo250Mw/hr5qFdd89hmnNmvGOY7DV9PTGV6+nOEVK/h4x478r+f537d6Nbl7Nzc8+SRfbtuWFzdowEEDB/rnbJ16KteFQpziuvx1To5/3sfNN3Nm48Yc5Xn8Rb9+/vK9+SZfTU/nnQkJPD5YD8VTp3JEhw78c2Iijz/66LJl+SQ1lWM8zz8fKhzm2g8+4HstW/I1z+OlvXv7y7doEe/v0oU3Jib66zoc5rp33uGslBQuDA5LhVevZvEnn/Czpk0523H4fEYGw6tWMbxoEUdmZHB0ueULFxbyH1268F+hkH9u0OrV5PbtLPnTnzitWTM+GArxuKOPZnjZMm655BIubNiQb+5ZvmXLuO3ss7k+FOKXjlMWdzgc5jEDBzIlOZmDBg3ipnvu4ffHHMOfDRjAro0asTghgcUTJ1b7nIqi2bO5KzWVfzzsMLZPTuZnTZty8623Vvh9xRMnckGjRtwKcGqzZiyaO7dsmZ8Khfy2FJybsHbCBD7QuTNPSEryP798ObdceikXNmzIscGhynA4zPWvvMLX2rThbQkJ/roJh7n+1Vc5Li2ND4dCHHrkkQyvXs2S667jhuC/2r9268ZwOMyiWbP4QOfOvCYxkScedVRZjBNateJrnsfLe/ViOBzmpvvu4zbH4VaAH7RowfCKFVwzYwYntGrF912X9wTtvejbb/lW69Z833X5YKdOfp2Gw/xFv34c0rBh2ba3MyuLNxx6KFNSUnhLt27ccdhhFa7bmj4HaeMjj/D7Y4/loKA95Ddrxo2PPsrw6tX8XZ8+HNKwIQcPGOC39wkT+EWTJpzpOHyoUyd/3eTn85PUVH7mOHy8Y0d/+ZYt4+MdO3JEKMQbDz3UXw9z5/LttDROcxx/G1+2jNy6lVsuvZRfNm7Mx/e043CY6956i09mZvKsPdvz7NncfuSR/N5xWGzGq3r2rHBZ1sycydK2bTklNZUzHYcTmzdnuLAwovVVPGkSp6Sm8lPX5T+6dNnv+i+eOJFzk5O5Hv45mEWLFrFowQK+3qYNJ7uuv40vX07u2sVN997Ld9LSeENior//XL2am/7+d37YogXv29Nmly/n1gsvZGFiIj91XZ57+OEMh8Pc8Mwz/LBFCz5dbn+8/oUXOKl5c77oeTxrzz51/HhOaNWKI0Mh/qZvX/+zI0dybnIyv3Ic/3yhcJhrvviCr6an89+hEC8L9mFFCxbw6Q4d+Fi5svDy5Xygc2fen5DA3wfbwJqvv+YHLVpwxp46Xb6c68aM4frg/KU1CQlc+8EHtdKOw+EwNz7wAJclJXGO4/DWPdvz7Nl8rGNH3pqQ8MP++PXXOTs5mfMcxz+vLFi+f3TpwtsSEnhesK7Xvvce5wfnV01o1YrhJUtYNGcOx7ZuzU9cl8+1b8/wypUMr1jBJzMz+Zrn+dvAqlXkd99xy6WX8tuUFP4nFCrbl2wYMYJvtW7N2xISOGTAAIZXreKWK67gsqQkTnZdnh/Me/0LL/D9li35dCjEXwZxrx0/nm+1bs3HQyGefsQR+11fNQlV7NmK6gjyZuYBmA9gCIBVAD4HcA7JWRVNrxHkpc668UagUSPgr3/1Xw8ZAvz5z8AJJ1Tv+774wr8tzJ577z3zjH8F4b//XTPx1hU7dviP5OTIv2vyZP+qqtat/asZ33wT6N//J39NVlYW5s+fX/UPbN0KDBrkX5a/e7d/ZeDkyX57qGu2bAEaNtz/lZm33OJf7fXww3699OgBvPRS9YfM2LwZ6N7d3z66dfPvT3nvvcAZZ1R/GeLBli3+VZAdOvj1VQ0/uR1LVFR1BHkvmkGQLDWzKwC8C//IxHP7S7RE6rSTTgJ+/Wv/8uzCQv8S7UjGdOrSxU8YRo4EevcGnngC+P3vayzcOiMhwX/UhNxcYMECfziWTp2AJk2q9TXjxo37aR9o1MgfJmPcOH+YiZNPrvYPZNRVltTu3PnDNJ4HNGgQ2ThYs2YB6enAH//ov77qKuDDD5VsVSY52U9SI/CT27HEVFSTLQAgOR7A+GjPRySqcnP98aueftr/8f3wQ7+no7oaN/bHtbnqKn9ctLPPBi6+uObiPVg1beoP1BiBkvLj5lVVw4bAmWdGNN864aKL/F66dev8cb5SUyP7p6F9e38Mqtmzgc6dgfHj/XGiJHJbt/r/gH34of/P2bPP+n8DZe14926/x/3FF/36fPRRfyBTqVN0I2oRiSt9+/bFjAMNBnqwW7IEGDPGT/jPPdfv3YrECy/4ScGOHcBpp/mva6o3M55dcYU/YOd99wFvvOGfajDrhwNDZe34qaeA554Dnn/eH9Dz97/3B39t1iyGwcePqh5GVLIlIiKR2bXLT7aSkmIdycHjqKOA4cP9XioSSEz0R2Xfdx1ffLHfO3nppf7rww/3E7BIb10lVVLVZEv3RhSRuHLttdfGOoSDj+sq0appffr453KuXu3/7dRpr3Vc1o579/Z7E1euBP73P//E+06dYhS07E/Uz9kSEalL0tPTYx2CSOXuuw+45BKgVy//fLi33trr7bJ2/Ic/AIsW+clZairwyiuRnU8qUaHDiCIiIiLVoMOIIiIVUM+WHAzUjusXJVsiElfUey4HA7Xj+kXJlojEFY26LQcDteP6RcmWiMSV8jdWFqmv1I7rFyVbIhJXJk2aFOsQRCKmdly/KNkSkbiSl5cX6xBEqu/zz4E77sDzublAaWmso5EqUrIlInElJ6fSq7RF6qYPPgCGDgW2b8eQNWuAs87yR5eXOk/jbImIiNQHZ5zhJ1u//S2wfTuQnu7fD7FNm1hHFrc0zpaISAVSUlJiHYJI9TRoAKxdCwDIbN4c2LnTv2ei1Hm6XY+IxJXCwsJYhyBSPX/5C3DsscDEiVicmur3cKWmxjoqqQL1bIlIXNFVXFJvHXoo8NVXQF4eplx9NXDnnbGOSKpIyZaIxJURI0bEOgSR6ktLA047DfdPnBjrSOQn0AnyIiIiItWgE+RFRCpwzjnnxDoEkYipHdcvSrZEJK4MHTo01iGIREztuH7RYUQROfjMmQN8/DHQsSNw/PGAWcXTLVgAjBkDNGkCXHCBf2m9iEgV6TCiiMSniROB3FygoAC45hrgxhv3etv2JF6zZgEDBgArVwJjxwInnKDbn0i9Yfv7B0LqpIiSLTO738zmmtnXZjbGzJqWe+8mM1toZvPM7OeRhyoiUgX33Qc89BDwzDPAp58CjzwCbNtW9nZZb/6zzwJ/+IP//ttvA2vWAF9+GaOgRX6aunRUSioXac/W+wB6kuwFYD6AmwDAzA4FcBaAHgBOAPCEmbkRzktE5Kep4AfppZde8p8kJACbN/vPd+zwE7KEhFoMTuSnKyoqQm5uLpKSkpCbm4uioqJYhyRVEFGyRfI9knv63acBaBc8Pw3AKJLbSS4BsBBAv0jmJSJSJddfD1x9NXDxxf5hwiuvBBo2LHt73Lhx/pMrrgBefx04+WTgiCOAgQOBXr1iFLRI1QwbNgz5+fn4/vvvkZ+fj2HDhsU6JKmCGjtB3szeBvAKyRfM7DEA00i+ELz3LIAJJF+r4HN5APIAoH379n2XLVtWI/GISByr6gny69f753g1aeLfBsXRaaxStzVu3BglJSVlr1NSUrB5Tw+t1LqqniBf6b0RzewDAK0reOtmkm8F09wMoBTAi3s+VsH0FWZ1JEcAGAH4VyNWFo+ISKW6d/cfFTjllFPw9ttv+y9SU4HTT6/FwEQik52djfz8fJSWlsLzPGRnZ8c6JKmCSpMtkscd6H0zuwDAUABD+EM32UoAGeUmawdAd38VkZjLy8uLdQgi1TZ69GgMGzYMM2fORHZ2NkaPHh3rkKQKIjqMaGYnAHgAwDEki8uV9wDwEvzztNIBfAigK8ldB/o+jbMlItFWUlKClJSUWIchIgeBGjuMWInHACQCeD8Y82MayctIzjKzVwHMhn948fLKEi0RkdqQnp6+1zkvIiLRFlGyRbLLAd67G8DdkXy/iEhNU6IlIrVNl96ISFwZMWJErEMQkTijZEtE4orOCxWR2qZkS0Tiinq2RKS2KdkSkbgyePDgWIcgInFGyZaIxJXbb7891iGISJxRsiUicSUrKyvWIYhInFGyJSJxJSen0vEHRURqlJItEYkrhYW6c5iI1C4lWyISV4YPHx7rEEQkzijZEpG4op4tEaltSrZEJK6oZ0tEapuSLRGJK3379o11CCISZ5RsiUhc0QjyIlLblGyJSFxJSUmJdQgiEmeUbIlIXBk6dGisQxCROKNkS0Tiyvz582MdgojEGSVbIhJXdG9EEaltSrZEREREokjJlojEFfVsiUhtU7IlInElKysr1iGISJxRsiUicWXcuHGxDkFE4kyNJFtmdp2Z0cxaBK/NzB4xs4Vm9rWZHV4T8xERiVRJSUmsQxCROBNxsmVmGQD+D8DycsUnAugaPPIA/CvS+YiI1IS8vLxYhyAicaYmerYeBHA9AJYrOw3A8/RNA9DUzNrUwLxERCIyY8aMWIcgInEmomTLzE4FsIrkV/u81RbAinKvVwZlFX1HnpkVmFlBcXFxJOGIiFTq2muvjXUIIhJnvMomMLMPALSu4K2bAfwFwPEVfayCMlZQBpIjAIwAgJycnAqnERGpKenp6bEOQUTiTKXJFsnjKio3s8MAdATwlZkBQDsAX5hZP/g9WRnlJm8HoDDiaEVEIqSeLRGpbdU+jEjyG5KtSGaSzISfYB1OMgxgLIDzg6sSjwKwieTqmglZRKT61LMlIrWt0p6tahoP4CQACwFsA3BhlOYjIvKTFBQUxDoEEYkzNZZsBb1be54TwOU19d0iIjVl/vz56t0SkVqlEeRFJK7o3ogiUtuUbIlIXJk0aVKsQxCROKNkS0TiikaQF5HapmRLROJKTk5OrEMQkTijZEtE4op6tkSktinZEpH48NVXwN134/IGDYCdO2MdjYjEESVbInLw+/RT4LjjgI0b8fCRRwJnnglQdwcTkdqhZEtEDn7/+hdw553A/ffjf1ddBeTnA0uXxjoqEYkTSrZE5OCXmAhs3AgAeGHECGDHDr9MRKQWROt2PSIidcf11wODBwNTp2LUggXA734HaBR5Eakl6tkSkYPfIYf4J8hfeCFu79QJ+Oc/Yx2RiMQR9WyJSHxo1Qr41a+Q9f33sY5EROKMerZEJK6cc845sQ5BROKMki0RiStmFusQRCTOKNkSkbhCja8lIrVMyZaIxJWXXnop1iGISJxRsiUicWXcuHGxDkFE4oySLRGJK+rZEpHapmRLROLKKaecEusQRCTOKNkSkbiSl5cX6xBEJM4o2RKRuDJ48OBYhyAicSbiZMvM/mhm88xslpndV678JjNbGLz380jnIyJSE9J1T0QRqWUR3a7HzH4G4DQAvUhuN7NWQfmhAM4C0ANAOoAPzCyL5K5IAxYRiURJSUmsQxCROBNpz9bvAfyd5HYAILkmKD8NwCiS20kuAbAQQL8I5yUiErERI0bEOgQRiTORJltZAAaZ2XQz+9jMjgjK2wJYUW66lUHZj5hZnpkVmFlBcXFxhOGIiBxYQUFBrEMQkThT6WFEM/sAQOsK3ro5+HwzAEcBOALAq2bWCUBFNx+r8B4ZJEcAGAEAOTk5uo+GiESVerZEpLZVmmyRPG5/75nZ7wG8Qf9mY5+Z2W4ALeD3ZGWUm7QdgMIIYxURidjgwYMxadKkWIchInEk0sOIbwI4FgDMLAtAAoC1AMYCOMvMEs2sI4CuAD6LcF4iIhG7/fbbYx2CiMSZiK5GBPAcgOfM7FsAOwBcEPRyzTKzVwHMBlAK4HJdiSgidUFWVlasQxCROGN+blQ35OTkUCevikg0paeno7BQZzWISOTMbAbJnMqm0wjyIhJXlGiJSG1TsiUicWX48OGxDkFE4oySLRGJK+rZEpHapmRLROKKerZEpLYp2RKRuNK3b99YhyAicUbJlojEFY0gLyK1TcmWiMSVlJSUWIcgInFGyZaIxJWhQ4fGOgQRiTNKtkQkrsyfPz/WIYhInFGyJSJxRfdGFJHapmRLREREJIqUbIlIXFHPlojUNiVbIhJXsrKyYh2CiMQZJVsiElfGjRsX6xBEJM4o2RKRuFJSUhLrEEQkzijZEpG4kpeXF+sQRCTOKNkSkbgyY8aMWIcgInFGyZaIxJVrr7021iGISJxRsiUicSU9PT3WIYhInFGyJSJxRT1bIlLblGyJSFxRz5aI1DYlWyISVwoKCmIdgojEmYiSLTPLNrNpZjbTzArMrF9Qbmb2iJktNLOvzezwmglXRCQy8+fPj3UIIhJnIu3Zug/AHSSzAdwavAaAEwF0DR55AP4V4XxERCJSVFSE3NxcHHfcccjNzUVRUVGsQxKROBFpskUAjYPnTQAUBs9PA/A8fdMANDWzNhHOS0Sk2oYNG4b8/Hzs2rUL+fn5GDZsWKxDEpE44UX4+asBvGtm/4SfuB0dlLcFsKLcdCuDstX7foGZ5cHv/UL79u0jDEdEpGIzZ85EaWkpAKC0tBQzZ86McUQiEi8q7dkysw/M7NsKHqcB+D2Aa0hmALgGwLN7PlbBV7Gi7yc5gmQOyZyWLVtWdzlERA4oOzsbnuf/f+l5HrKzs2MckYjEi0p7tkget7/3zOx5AFcFL0cDeCZ4vhJARrlJ2+GHQ4wiIrVu9OjRGDZsGGbOnIns7GyMHj061iGJSJyI9DBiIYBjAEwCcCyABUH5WABXmNkoAEcC2ETyR4cQRURqS1paGiZPnhzrMEQkDkWabF0C4GEz8wB8j+DcKwDjAZwEYCGAbQAujHA+IiIiIvVSRMkWySkA+lZQTgCXR/LdIiIiIgcDjSAvIiIiEkVKtkRERESiSMmWiIiISBQp2RIRERGJIvPPZa8bzKwYwLIoz6YFgLVRnof8dKqXukd1UjepXuom1UvdUxt10oFkpSOy16lkqzaYWQHJnFjHIXtTvdQ9qpO6SfVSN6le6p66VCc6jCgiIiISRUq2RERERKIoHpOtEbEOQCqkeql7VCd1k+qlblK91D11pk7i7pwtERERkdoUjz1bIiIiIrVGyZaIiIhIFB20yZaZnWBm88xsoZndWMH7iWb2SvD+dDPLrP0o40sV6uRPZjbbzL42sw/NrEMs4ow3ldVLuenOMDOaWZ24lPpgV5V6MbMzg21mlpm9VNsxxpsq7MPam9lEM/sy2I+dFIs4442ZPWdma8zs2/28b2b2SFBvX5vZ4bUd40GZbJmZC+BxACcCOBTA2WZ26D6TXQRgA8kuAB4E8I/ajTK+VLFOvgSQQ7IXgNcA3Fe7UcafKtYLzCwFwJUAptduhPGpKvViZl0B3ARgAMkeAK6u9UDjSBW3lVsAvEqyD4CzADxRu1HGrZEATjjA+ycC6Bo88gD8qxZi2stBmWwB6AdgIcnFJHcAGAXgtH2mOQ3Af4LnrwEYYmZWizHGm0rrhOREktuCl9MAtKvlGONRVbYVAPgb/OT3+9oMLo5VpV4uAfA4yQ0AQHJNLccYb6pSJwTQOHjeBEBhLcYXt0hOBrD+AJOcBuB5+qYBaGpmbWonOt/Bmmy1BbCi3OuVQVmF05AsBbAJQPNaiS4+VaVOyrsIwISoRiRAFerFzPoAyCA5rjYDi3NV2V6yAGSZ2admNs3MDvSfvUSuKnVyO4BzzWwlgPEA/lg7oUklfurvT43zanNmtaiiHqp9x7ioyjRSc6q8vs3sXAA5AI6JakQCVFIvZubAP8z+29oKSABUbXvx4B8WGQy/F/gTM+tJcmOUY4tXVamTswGMJDnczPoD+G9QJ7ujH54cQMx/7w/Wnq2VADLKvW6HH3fnlk1jZh78Lt8DdUNKZKpSJzCz4wDcDOBUkttrKbZ4Vlm9pADoCWCSmS0FcBSAsTpJPuqqug97i+ROkksAzIOffEl0VKVOLgLwKgCQzAfQAP7NkCW2qvT7E00Ha7L1OYCuZtbRzBLgn6g4dp9pxgK4IHh+BoCPqBFeo6nSOgkOVz0FP9HS+Se144D1QnITyRYkM0lmwj+X7lSSBbEJN25UZR/2JoCfAYCZtYB/WHFxrUYZX6pSJ8sBDAEAM+sOP9kqrtUopSJjAZwfXJV4FIBNJFfXZgAH5WFEkqVmdgWAdwG4AJ4jOcvM7gRQQHIsgGfhd/EuhN+jdVbsIj74VbFO7geQDGB0cK3CcpKnxizoOFDFepFaVsV6eRfA8WY2G8AuAH8muS52UR/cqlgn1wJ42syugX+Y6rf6Jz76zOxl+IfTWwTny90GIAQAJJ+Ef/7cSQAWAtgG4MJaj1HtQERERCR6DtbDiCIiIiJ1gpItERERkShSsiUiIiISRUq2RERERKJIyZaIiIhIFCnZEhEREYkiJVsiIiIiUfT/uLxp2DGI0bgAAAAASUVORK5CYII=\n", "text/plain": [ "<Figure size 720x288 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x288 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x288 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Your code goes here !!!\n", "\n", "def tikhonov(A, y, alpha):\n", " return np.linalg.solve(np.dot(A.T, A) + alpha * np.eye(len(y)), np.dot(A.T, y)) \n", "\n", "\n", "alphas = [1e-7, 1e-5, 1e-4, 1e-3]\n", " \n", "for i in range(len(alphas)):\n", " alpha = alphas[i] \n", " x_delta = tikhonov(A, y_delta, alpha)\n", " \n", " plt.figure(figsize=(10, 4))\n", " plt.title(r'$\\alpha={}$'.format(alpha))\n", " plot_solution(x_true, x_delta)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 2\n", "\n", "Implement the ISTA algorithm to solve the problem and use $\\alpha=10^{-4},10^{-3},10^{-2}$." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x288 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": 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oyDmUksKKOXPI5csZzspqyPmyY49l+aJF3DNgAEMpKdwC8Jrhw1m+ciV3DxvWkPNNRx3Fsk8+Ye2oUaxITmYVwMmDBjG0bh13nXJKQ86P5uRw2wMPsHbUKH77pJOY2aUL13bqxK3Tpu076PbsYe1JJ3FJt2583nFYlpzM8iVLWHXHHdweDLLEjCu6dmXZJ5+w8uGHG3L+pHNnlq9cya3PPcdtbs4bOnRgxaJF3PLvf3Ozm3NZcjI3v/02+cEHDPfpw9KUFJab8ZcjRrB88WLuGTSIoZQUbgX4u2HDWPbBB9x9zDEsc/v0lqOOYtnataw94YSGcfy3gQMZWr+eO7/7XW51c348O5uhkhLuOOccbnPH8cu9ezNUUsLtl13G6mCQm804Oz2doY0bWX399dweDLLMjIu6d2fo889Z9de/ssbN+YPUVJatXs3KRx9ldTDIDWZc26kTy4uKuPWFF1jpOFxnxk0dOrDivfe4+bXXGnIuT07m5v/8h/zwQ4b79o2OdTP++phjGAqFGAqFOHr0aKampnL06NEMhUJNrgehUIhjv/lNpnbpEj1uwwbuPP10VjoOtwF8ul+/6Nz98Y8b5u6MXr0YKi3l9l//mtXu3J2TlhbN+cYbG+ZuYbduDH36Kbfdc0/D3P2wSxeWffQRK594gtWOww1m/KxjR5YvXcotL73UkHNJSgor5s8nCwsZzsxkaUoKS83487w8Vrz7buP16uijWV5UxD1HHdWwXl3vrle1xx/fMHfvGDyYoc8+464xYxr6+cH+/aPr1RlnNF6v9vP7qrn66oa5+079enXLLQ1zd2m3bixbu5bb/v73hpw/7tKFZatWcevTTzfM3XUdO7K8sJBb/vnPxnN33jxy2TKGe/dumLu/OPZYVixc2LBebQH426OPZvmKFdw9dGjD3L1xyBCWFRezNj+/Ye7e1cR69UhODkObNnHHD37QkPPzWVnR9epnP9t3vbr22oac361fr/78Z9a4ORfVr1cPPdQwd4s7d2bZypXc+uyzDTlv6NCB5YsWccsrr3BL7NydM4dcsaJhvSoz4+X169XAgQ3r1bXDhzfdL9XVrP3617nZze+eQYMYWr+eu/7nfxrm7pT6ufujHzXM3Rfr5+6ECQ1z9z8ZGQxt2sTqiRNZ487dBUccEZ27d97ZMHdXpqayrLiYlY880pDzmk6dWL5iBbdOm8Zt7jje2KEDKxYu5OZXX228Xs2eTa5a1Wi9umLECJYXFjZar34/bBjLVq3i7hEjGv7u3pqby9Dataw98cSGcXzvwIHRuXvaaQ05P9mv337HcUsCUMjm1EPNOehQvwB8A8AbMbcnApi4v+Nbo9ha3bkzfxwIEAAvDAT4cZcu5He/y3sHDqTjODwV4Hp3oj3Vrx8dx+HxALe5E3JGr150gkEeCbAS4OP9+nFeWhqTg0H2Bhhyi4+l3bqxUzDI7gDXuEXYJ507s1swyE4Al7ptJSkpzAgGmQRwthkfzsnh1qQkZgeDDAB8wYxP9uvH6mCQw4JBAuBDZnyxd29WOw5PcNtuMeObGRksSUnh6W5+vwkEuLh7d3LUKN6am0vHcTge4AqA83v04AMDBtBxHJ4MsBTgrJ49+WzfvnSCQY5wc36uTx/OysykEwxyAMCtAB/Lzub8Hj2YEgwyE2AJwAdzcri8a1d2DgbZDeBqgPcPGMBPO3Vi92CQHQC+D/CB/v0ZSklhZjBIB+AbZizIzmal43BAMEgDONWMz/Tty5pgkMe4+f3djC/36sUqx+FJbtuNgQDfTk/n+o4deZab8+WBAJd17UqedBLvGDyYjuPwbIAfApyXlsaH+/en4zg8CWC5+4dzWp8+dIJBDndz/kffvny9Z08mBYPMAbgZ4KPZ2VxwxBHsEAwyA+AGgBcfdxznpKVxE8AygI+acfQ3v9kw1m666aboN/Pm8ZPOnZnkxn2vGZ/LymKV43CQm/MzZvxHnz6sCQaZ5x53txlnZGay0nF4sts2MRDgO2lp/LRTJ/7IzfnngQBXpqaSJ5/Mu448ko7jcBzAYoCz09P5aE4OHcfh1wFuAfhS7958sXdvOsEgh7g5P9W3L/+TkcGkYJB9AVYALMjJ4fvdu7NDMMg0gOvcMfthly5MDQbZBeBKgPf3788NHTowLRhkCsD/AnwoJ4ebk5LYJxhkEOAMM07Jzma14zDXzeUJMz7n5jzSbbvTjP/OzGRFcjJPcfO7NhDge0ccwU86d+Z5bttPAwF+2KULeeqpvGfQIDqOw+8C/Azg6NGj+YNRo/jDQIDHAXQch6NHj953Mdizh//OzGStO67PCwR4x+DBXNKtGzsGgzwC4Kdufqs7d2ZXd+4WueN4U4cOTHfn7hx37m5JSmI/d+6+ZMYn3Lk7xM2vwIzPZ2WxOhjkKLftNjO+kZHBUEoKT3PzuzoQ4KLu3cmRI3nLUUfRcRyeC3AZwAVHHMH73PXq2wA3Any1Z08+07cvHcdhnrs2TcvK4ivu3B3k5jglZr3q5c77h/r3Z1HXruzkzt1PAP5yxIh9x/HixSxNSWFPN+f/mPGRnBxWOg5z3JynuetVTTDI4W5+D5rxxV69WO04PNFtu9mMb6Wnc2OHDhzn5vyrQIBLunUjTziBt7nr1Q/dMfbfHj34oDt3R7vr7CuZmXzOnbvHuOP42T59+Ko7d/u74/2x7Gy+665XPQFucnNe4a5XXQF+7PZz7Hq1CNFitCw5mb3c9eo1s+h/tByHA2PXK3ccj4iZ4//MzOQ2x+Fot+2PgQDnpqXx844d+QM3518EAizq2pUcPZp/cefumQA/Ajg3LY0F7tz9hrsOxa4vDW68kW+6cze7fr3KyeFCd71Kd/+mPdi/P1elprKLO3dXuTmv69iRPdy5+677u6lITmaWO3dnmfGx7GxWOQ6PdHN+yozPujkf5+Y32Yyv9OzJLUlJHOu2/T4Q4PwePbi2Uyee4+b8s/r16lvf4mR37p6O6N/Jt9LTOSU7m47j8GvumH2xd2++7K5XR7n9/HS/fpydns7kYJB93LX8EXe96hgMsgfAzwH+PC+v5YqH/WhusZXolxH7ANgQc3uj29bAzCaYWaGZFVa0wtZftx078I67BTqvrg5dv/gCKCnBS6EQwuEw5gPoBSBlyxbM3LwZ4XAYywAYgJTycry6bRvCkQjWANgKIKW0FG9u347dkQhKAXwGIGXjRryzYwd2RCLYBmAVgOQNG7CothZVkQh2AFgCIGXDBqwMh1ERiWAPgEUkUjZtwmeRCNZHIqgD8B6JlNJSbKurw4fu1vR/SSSVlyMQDuN9t+0dEh22bkWP2tpG+XWurgZKSvDCpk2N8uu0bRteLitDOBzGAgBpbs4ztmxBOBLBSgARAMllZXjNzfkzAOUAOpSU4K3t21EbiaAMwBoAHTZtwn937sQXkQiqAKwE0GHDBizevRvbIhHsqs9540asCodRFokgDGAhiZSSEmyoq8NnkQgI4F0SyaEQaurqsDImv5SKCiSHw1hQ31ZXhw6VlThi585GOXepqdkn594AOlVWNuS8CEA3ACkVFXjFzXkVgF0AUkIhvF5VhT2RCNYBKAWQUlKC2V98gV2RCCoAFAOo/PhjnFlbi9EARgG4lETR8uX7Djoz7Nq5E5H6lxZI7Cgvx6a6Oqx1c/4viZRQCDvr6lAU08/JFRXoHA7j3ZicO1ZWovte47jL9u1ASQmml5Q0yrljZSX+VV6OcDiMxQA6ueN4VmUlwpEIPgawHUCHUAhvVFdjTySCjYhO2pRNmzBnxw7sikSwBcDHbv8tqK1FTSSC7QCK3OOWhcPYEomgFsD7bltxXR02RSKI1I/jkhKURSIojs0vFMKeSARLY/o5uaIC3Xfvxn/d/N6pq0PHqip037ED82JyTnXn7oulpY1ytsJCPLJ4MS6qq8NMAFeFwygqKmrojoYPVn7wQXTevBk9AIwFcF9dHTp+/jnm7tyJnZEIKgF8CKDDxo1YVFuLanfuLnV/D8v37MHmvebup5EINuw1d7fU1eHjmJxTysqASASLY3PesgU9amsb5dfJnbvPb9zYeO5WVeFld716F0DP2LkbDqN+BKaUleHfVVUIRyJYC2ALgA6lpXirpga7IxGEAHzq5vLOzp3Y4c7dDwDUFBfvO45LSvBBOIzyvXL+vK4O62Jy7lBaiqq6Oqzaa+464TAWxrZVVqLHrl2N1yt37k7fe+5u24aX3HG8EEAPACmbNzdar/a4Ob/mzt3PAZTBnbvuelUO4BM35/nuelUNYAWia9iSmPWq0D3uw0gEoZj1KnnTJmysq8OnsXO3rAxf1NVhRezY3rwZHcNhvHeQ9Sq1fr2KmbtZ7tx92c35fQCpAD5qahyXlOB1d+6uB7AJ0fn3trtebQaw2m17b9cubHfn7nK3bemePdjqzt3FAJI3bcLqSAQle83d0ro6rHFznu+uV7V1dVgWO443b0bqnj2N16tt2/aZu13r16u95m6Hykr8q6IC4XA4+vcCjder1QCqEf27+4Y7jjcBWO/239wdO7AzEsFWAB8BqFq9et9x7JFEF1vWRFujC3uRLCCZTzI/IyMjweEACzMz8ZgZfgjgUTMsyswEzj4bDwSDOCcQwNMAXjHD8v79cacZzg0E8CiiA3PpoEG4icSPAwHcDUSLpqOOwlUkfhoIYBKii+H7w4bhJwB+EQjgWkT/EC8ePhzfB3BlIIBfAjjLbRsZCOC6QAA/A3AJgMVDh6JXcjJuNcMFAK51n2NXp064zwz/B+AWAMuPPBKru3XDE2b4EYDJAIpycvBuejqedvN7AEBhnz7A2WdjSlISzgkE8Jib35J+/fD3QAD/FwjgKQCvmaFowAD8BcC5gQAeRnSCLj3ySFwP4IJAAHciWoAtHjIEvyJxcSCAGwDkuDn/mMRlgQCuBvBNAIuGD8d3AFwdCOAyAD90cz4mGMQfAgFcDOAXbs5HJCfjdjP8GMB1AJbk5qKqc2c84OZ8K4CiQYOwsnt3PO3mfDeAZdnZeC8jA0+6OT8EYHFWFnD22XjUzflxADPNsCQ7G/cFg/i/QABPAphthqKBA3GbGc4LBPAgopN2yeDBuA7AhYEAbgeQ5MZ4OYlLAgH8AUAugNpjj0XeccdhveNgHQDHcZCXl9cw1hoWw298Azu7dsVcANMA/ADAm3l56JSSgjvNcD6A6wEszc1FRZcueNgM5wD4M4Dlgwah8IgjGnK+F8DSfv2wIDMTj7s5P2KG93v3Bn7wAxQ4Ds4JBPCE28/LsrNxt9vPTwCYb4aiQYPwJwDnBwK4D9ECujA3F/+PxE8CAdyK6MK+eOhQXEri54EArgNwNIDFw4bhf0n8KhDArwF8x207yQzXBgK4FMCFbtsAx8GkQAA/AXAlgMVHHQWnQwdMNsN5AG4AsGzwYGzs2hWPmmE8gDsALB8wAAvS0vCMm9/fASzp2xfvZWZiittWYIb3e/UCzj4bD7k5P+X28587dsQTgwbhfx0HowDcDGDUiBH7LgarV2N5Tg5qHQcrED3f4YucHFxMYkIggP8H4HgA7w8fjjMA/CYQwK8AjHPbRgUC+F0ggEsAXOzm3CcpCbeY4UIAv3VzjnTsiL+Z4VwAkwAsGzQIa7t2xeNuzn8FUNS/P+anpzfkfD+AJe7cfcIdx4/Wz92+fXF/zHr1bzMU9e+Pv7jrVQGiBdPSwYNxI4kLAgH8FUAtgMKjjsKV7ty9CdH/+b4/bBguQHS9ugbRlyNqjj22yXGcFwxiorteXeqOkYzkZNzmrle/c8fSF5064e/u3P0TgGVHHolV3bvjydj1Kjsb72Zk4Ck35wcBFLpz9zG3T6eg6fXqDTMsGzAAd7hz92G3/5YMHow/uHP3L4j+ASocMgS/JPGzQAB/RPSclveHD8d5JC5316sxABYNG4ZTzPDbQAC/ADDePW54MIjrAwH8FMDlAAqHDkXXlBTc4c7die7zbu3cGQ+5c/dWAMsHDsSymLl7D9z1qmdPPOHm/DD2Xa+ewJfr1b1uzk8CmGOGoccdt+84Pvts/J7EhYEA/gygI4D3hw7FL9z1aiKAoW4//4jEFYEArgRwits2xp27EwCc7+Y3OBjEjYEALgLwa/d32CElBXe5c/d6N+dQly6Fnxk2AAAV0ElEQVQocHO+3c35/R49DrheFcSsVw+7/fykm/Oy7GxMdnN+HMBCMyw78kjcjC/Xq63uvLqWxEWBAP4EoLs7Fn9O4tJAAL8HMALAzqbmvVeas/11qF9ogy8jhtav56M5OZzpOHw0J4ehDRvISITVkyZxXloa70pO5qknnshQaSmr7rqL89LSeH9SEr/3jW8wFApx20MPcW5aGh9NSuKZX/86Q6EQtz79NN9OT+eTSUkc/7WvMRQKccvLL3N2ejqnOg4vOP54hkIhbn7jDb6ZkcEXHIeX5uUxFAqxYv58vtazJ190HP7GPd+kvLCQr2Rm8mXH4XXDhjEUCrFs5Uq+3Ls3/+U4vOWoo6JtxcWc1qcPZzhO9NyE0lKGPvuMT/Xrx5mOEz1/bNMmcvdu1lx3HeelpfG25GR+66STGCopYdWf/sR5aWmcnJzM/3Fz3nb33ZyXlsYHkpL4vRNOYCgUYuUjj3BOWhofS0ri2fU5P/ss305P59OOw3Py86M5z5jBt9LT+Zzj8Cf1Ob/1Ft/IyOB0x+Evjj02mvO77/LVnj35kuPwqqOPjua8dCln9OrFfzoO/zB0aDS/Vav4opvzrbm50bY1azjVzfnuQYOiOX/+OZ9wc37IPQeFe/aw+vrrOS8tjbcnJ/Pb9TnfeivnpaXxnqQkfqc+53vu4by0ND6UlMTv1+f82GOck5bGKUlJ/MGoUdGcp03j7PR0PuM4PNfNudnnBm3YwBuHDOHlHTrwDPd3WF5U1JDzH4cMieb30UecnpXFGY7DPw8ezFBpKcvWruWzfftypuNEz6UqKWFo3To+np3NmY4TPWdu40YyHGb1H//IeWlp/EtyMk856aToOL79ds5LS+O9SUn8bv04vu8+zk1L4yNJSRxXn/MTT3BOWhofT0ri/9bnPH06Z6en8x+Ow/NGjoz26auv8s2MDD7vOPzZccdF+3TOnIZxfMWIEdH8Fi3iLHcc159vUr5iBf/Zqxf/5Ti8qT7njz/mC27Od7g5h9au5T/69uUMx+F99TmvX8/H3JwL6uduOMzqm27ivLQ03pmczFNOPJG7Tj6ZlVOmcPTo0czs0oU7AwGWrV27b6c8/zz3DBrEX40YwV+mpHBzUhLLPv6YW158kbPT0/ms4/CC+pxfe60h50vq5+477zTkXH+uWPnixQ1z93fu3C2Pmbs3NzF372xi7t4fO3d//3vOS0vjrTFzt/rmmzkvLY1/jV2v/vrXL+eu28+VDz/csF6dVT93n3mGb6en86mkJJ5Tv1798598y12vLnTnblMq5s/nq27OV9bnvGQJZ/bqxZcdhxPr16sPPuBLe69Xn3zSkPNf6+duU+vVnj2snjiR89LS+Ocm5u7dTaxXDyYl8fT6cVxQ8OV6VT+Op07l7L3Xq5kzG9ari5pYry6rX6/ee4//zszkS47Dq+vXq2XLGubu9fXr1YcfNqxXt+XmRuduzHp1T8x6VT93m1qv7oidu7fdxnlpafxbUhK/4/ZpUyqnTGmYuw3r1fPPN6xX59XnPGsW/5ORwWmOw4vdubt5zhy+7vbpL925WxEzd6+pn7vLl/Nfbs43NLFe3R4zd5915+69MevVFDfnR3Jyvlyvbrih0dwNlZay6o47OC8tjffFrlf33//leuWO48onn+SctDQ+kZTEH7o518/dfzgOz3fnbqKhmS8jJvQK8mbmIPqKyymI7m4uBnA+yVVNHa8ryItI3GbMAC67DLj4YmDuXGDoUGDKlIa7c3NzUVz/MtmDDwJPPAF07w7ceSfQ1M6BSBvUaByLZ5p7BfmEf1yPmZ0O4G+IvjPxcZK37e9YFVsi0iLefReYPRvo3x+44AIg8OUZE8XFxcjNzfUuNpEWoHHcNjS32HISHQjJVwG8mujnERFpcNJJ0a8m1MRek0mkndI4bl90BXkR8ZUJEyZ4HYJI3DSO2xcVWyLiK0uWLPE6BJG4aRy3Lyq2RMRXrrnmGq9DEImbxnH7omJLRHwlKyvL6xBE4qZx3L4k/N2IX4XejSgiIiLtRXPfjaidLRHxFe0IyOFA47h9UbElIr6i3XM5HGgcty8qtkTEV3TVbTkcaBy3Lyq2RMRXGj5YWaQd0zhuX1RsiYivzJ071+sQROKmcdy+qNgSEV/RlbflcKBx3L6o2BIRX8nPP+i7tEXaPI3j9kXX2RIRERE5BLrOlohIE1JTU70OQSRuGsfti4otEfGVkpISr0MQiZvGcfuiYktEfEXv4pLDgcZx+6JiS0R8paCgwOsQROKmcdy+6AR5ERERkUOgE+RFRJpw/vnnex2CSNw0jtsXx+sARERa07hx47wOQeTQrV4NvPUWLuvVCyABM68jkmbQzpaI+Ip2BKTdWrgQ+OY3geXLMWbuXEBXkW83VGyJiK+YdgKkvbrnHuDWW4GCAnRetgx48UWgvNzrqKQZ4iq2zOwuM/vYzFaY2T/NrHvMfRPNbI2ZrTaz78YfqohI/NrSm4JEvhIzIBIBAHxRXQ3U1ellxHYi3p2t/wA4muQIAMUAJgKAmQ0DcC6A4QBOA/CgmQXjfC4RkbhNnTrV6xBEDs2116LuhhvwemYmVnXrhpc7d0ZZXZ3XUUkzxFVskXyTZNi9uRBAX/f7swBMI1lL8jMAawCMiue5RERawqxZs7wOQeTQ5OfjvIED8fLmzbiWxP+Vl2P8+PFeRyXN0JLvRvwZgOfd7/sgWnzV2+i27cPMJgCYAADZ2dktGI6IyL60syXt2WurV6OmfjcrEkFRUZG3AUmzHHRny8zeMrMPmvg6K+aY6wGEATxb39TEQzV5ogTJApL5JPMzMjIOJQcRkWY744wzvA5B5JDl5eXBcaL7JI7jIC8vz+OIpDkOurNF8tQD3W9mFwEYB+AUfnnm6UYA/WIO6wtAn5opIp6boLfLSzs2ffp0jB8/HkVFRcjLy8P06dO9DkmaIa6P6zGz0wDcDeBkkhUx7cMBTEX0PK0sALMBDCYZOdDj6eN6RCTRampqkJqa6nUYInIYaO7H9cR7ztb9AFIA/Me9ds1CkpeRXGVmLwD4ENGXF684WKElItIasrKyUFNT43UYIuIjcRVbJI88wH23AbgtnscXEWlpKrREpLXpCvIi4isFBQVehyAiPqNiS0R8ReeFikhrU7ElIr6inS0RaW0qtkTEV8aOHet1CCLiMyq2RMRXJk2a5HUIIuIzKrZExFdyc3O9DkFEfEbFloj4Sn7+Qa8/KCLSolRsiYivlJTok8NEpHWp2BIRX5k8ebLXIYiIz6jYEhFf0c6WiLQ2FVsi4iva2RKR1qZiS0R8ZeTIkV6HICI+o2JLRHxFV5AXkdamYktEfCU1NdXrEETEZ1RsiYivjBs3zusQRMRnVGyJiK8UFxd7HYKI+IyKLRHxFX02ooi0NhVbIiIiIgmkYktEfEU7WyLS2lRsiYiv5Obmeh2CiPiMii0R8ZVZs2Z5HYKI+EyLFFtmdq2Z0czS3dtmZveZ2RozW2Fmx7fE84iIxKumpsbrEETEZ+IutsysH4D/AbA+pvl7AAa7XxMAPBTv84iItIQJEyZ4HYKI+ExL7GzdA+B3ABjTdhaApxm1EEB3M+vdAs8lIhKXJUuWeB2CiPhMXMWWmZ0JYBPJ5Xvd1QfAhpjbG922ph5jgpkVmllhRUVFPOGIiBzUNddc43UIIuIzzsEOMLO3APRq4q7rAfwBwHea+rEm2thEG0gWACgAgPz8/CaPERFpKVlZWV6HICI+c9Bii+SpTbWb2TEABgBYbmYA0BfAUjMbhehOVr+Yw/sCKIk7WhGROGlnS0Ra2yG/jEhyJcmeJPuT7I9ogXU8yRCAmQB+4r4r8QQAVSRLWyZkEZFDp50tEWltB93ZOkSvAjgdwBoAOwBcnKDnERH5SgoLC70OQUR8psWKLXd3q/57AriipR5bRKSlFBcXa3dLRFqVriAvIr6iz0YUkdamYktEfGXu3LlehyAiPqNiS0R8RVeQF5HWpmJLRHwlPz/f6xBExGdUbImIr2hnS0Ram4otEfGV1NRUr0MQEZ9RsSUivlJSog+zEJHWpWJLRHxF70YUkdamYktEfKWgoMDrEETEZ1RsiYivvPLKK16HICI+o2JLRHzl/PPP9zoEEfEZFVsi4ivjxo3zOgQR8RkVWyLiK9rZEpHWpmJLRHzFzLwOQUR8RsWWiPgKSa9DEBGfUbElIr4ydepUr0MQEZ9RsSUivjJr1iyvQxARn1GxJSK+op0tEWltKrZExFfOOOMMr0MQEZ9RsSUivjJhwgSvQxARn1GxJSK+MnbsWK9DEBGfibvYMrNfm9lqM1tlZnfGtE80szXufd+N93lERFpCVlaW1yGIiM848fywmX0LwFkARpCsNbOebvswAOcCGA4gC8BbZpZLMhJvwCIi8aipqfE6BBHxmXh3ti4HcAfJWgAgWe62nwVgGslakp8BWANgVJzPJSISt4KCAq9DEBGfibfYygUw2swWmdk8M/ua294HwIaY4za6bfswswlmVmhmhRUVFXGGIyJyYIWFhV6HICI+c9CXEc3sLQC9mrjrevfnjwBwAoCvAXjBzAYCaOrDx5r8jAySBQAKACA/P1+foyEiCaWdLRFpbQcttkieur/7zOxyAC8z+mFj75tZHYB0RHey+sUc2hdASZyxiojEbezYsZg7d67XYYiIj8T7MuK/AHwbAMwsF0AygM0AZgI418xSzGwAgMEA3o/zuURE4jZp0iSvQxARn4nr3YgAHgfwuJl9AGA3gIvcXa5VZvYCgA8BhAFcoXciikhbkJub63UIIuIzFq2N2ob8/Hzq5FURSaSsrCyUlOisBhGJn5ktIZl/sON0BXkR8RUVWiLS2lRsiYivTJ482esQRMRnVGyJiK9oZ0tEWpuKLRHxFe1siUhrU7ElIr4ycuRIr0MQEZ9RsSUivqIryItIa1OxJSK+kpqa6nUIIuIzKrZExFfGjRvndQgi4jMqtkTEV4qLi70OQUR8RsWWiPiKPhtRRFqbii0RERGRBFKxJSK+op0tEWltKrZExFdyc3O9DkFEfEbFloj4yqxZs7wOQUR8RsWWiPhKTU2N1yGIiM+o2BIRfygtBaZNQ8F55wGk19GIiI+o2BKRw99HHwHHHQdMn45HAgHgqqu8jkhEfETFlogc/u66C7j6auCll/CHU08F/vEPYNMmr6MSEZ9QsSUih789e4AuXQAAPfv1Axwn2iYi0gocrwMQEUm4K64AzjgDKC7GVUuXAiefDOTkeB2ViPiEdrZE5PB3wgnA3LlA37749cqVwNSpgJnXUYmIT2hnS0T8YfhwYPhwTPzxj6MvI4qItJK4drbMLM/MFppZkZkVmtkot93M7D4zW2NmK8zs+JYJV0QkPsXFxV6HICI+E+/LiHcCuJlkHoAb3dsA8D0Ag92vCQAeivN5RETiUlZWhjFjxuDUU0/FmDFjUFZW5nVIIuIT8RZbBNDV/b4bgBL3+7MAPM2ohQC6m1nvOJ9LROSQjR8/HgsWLEAkEsGCBQswfvx4r0MSEZ+I98SFqwC8YWZ/RbRwO9Ft7wNgQ8xxG9220r0fwMwmILr7hezs7DjDERFpWlFREcLhMAAgHA6jqKjI44hExC8OurNlZm+Z2QdNfJ0F4HIAV5PsB+BqAFPqf6yJh2ry8zFIFpDMJ5mfkZFxqHmIiBxQXl4eHPfEeMdxkJeX53FEIuIXB93ZInnq/u4zs6cBXOnenA7gMff7jQD6xRzaF1++xCgi0uqmT5+O8ePHo6ioCHl5eZg+fbrXIYmIT8T7MmIJgJMBzAXwbQCfuO0zAfzKzKYB+DqAKpL7vIQoItJaMjMz8c4773gdhoj4ULzF1qUA7jUzB8AuuOdeAXgVwOkA1gDYAeDiOJ9HREREpF2Kq9giOR/AyCbaCeCKeB5bRERE5HCgj+sRERERSSAVWyIiIiIJpGJLREREJIFUbImIiIgkkEXPZW8bzKwCwLoEP006gM0Jfg756tQvbY/6pG1Sv7RN6pe2pzX6JIfkQa/I3qaKrdZgZoUk872OQxpTv7Q96pO2Sf3SNqlf2p621Cd6GVFEREQkgVRsiYiIiCSQH4utAq8DkCapX9oe9UnbpH5pm9QvbU+b6RPfnbMlIiIi0pr8uLMlIiIi0mpUbImIiIgk0GFbbJnZaWa22szWmNl1TdyfYmbPu/cvMrP+rR+lvzSjT35rZh+a2Qozm21mOV7E6TcH65eY435kZjSzNvFW6sNdc/rFzM5x58wqM5va2jH6TTPWsGwzm2Nmy9x17HQv4vQbM3vczMrN7IP93G9mdp/bbyvM7PjWjvGwLLbMLAjgAQDfAzAMwHlmNmyvwy4BUEnySAD3APhL60bpL83sk2UA8kmOAPAigDtbN0r/aWa/wMxSAfwGwKLWjdCfmtMvZjYYwEQAJ5EcDuCqVg/UR5o5V/4I4AWSxwE4F8CDrRulbz0J4LQD3P89AIPdrwkAHmqFmBo5LIstAKMArCH5KcndAKYBOGuvY84C8JT7/YsATjEza8UY/eagfUJyDskd7s2FAPq2cox+1Jy5AgB/QrT43dWawflYc/rlUgAPkKwEAJLlrRyj3zSnTwigq/t9NwAlrRifb5F8B8DWAxxyFoCnGbUQQHcz69060UUdrsVWHwAbYm5vdNuaPIZkGEAVgLRWic6fmtMnsS4B8FpCIxKgGf1iZscB6EdyVmsG5nPNmS+5AHLN7F0zW2hmB/qfvcSvOX0yCcAFZrYRwKsAft06oclBfNW/Py3Oac0na0VN7VDtfY2L5hwjLafZv28zuwBAPoCTExqRAAfpFzMLIPoy+09bKyAB0Lz54iD6sshYRHeB/2tmR5PcluDY/Ko5fXIegCdJTjazbwB4xu2TusSHJwfg+d/7w3VnayOAfjG3+2Lf7dyGY8zMQXTL90DbkBKf5vQJzOxUANcDOJNkbSvF5mcH65dUAEcDmGtmnwM4AcBMnSSfcM1dw2aQ3EPyMwCrES2+JDGa0yeXAHgBAEguANAB0Q9DFm816+9PIh2uxdZiAIPNbICZJSN6ouLMvY6ZCeAi9/sfAXibusJrIh20T9yXqx5BtNDS+Set44D9QrKKZDrJ/iT7I3ou3ZkkC70J1zeas4b9C8C3AMDM0hF9WfHTVo3SX5rTJ+sBnAIAZjYU0WKrolWjlKbMBPAT912JJwCoIlnamgEcli8jkgyb2a8AvAEgCOBxkqvM7BYAhSRnApiC6BbvGkR3tM71LuLDXzP75C4AXQBMd9+rsJ7kmZ4F7QPN7BdpZc3slzcAfMfMPgQQAfD/SG7xLurDWzP75BoAj5rZ1Yi+TPVT/Sc+8czsOURfTk93z5e7CUASAJB8GNHz504HsAbADgAXt3qMGgciIiIiiXO4vowoIiIi0iao2BIRERFJIBVbIiIiIgmkYktEREQkgVRsiYiIiCSQii0RERGRBFKxJSIiIpJA/x8uaQMVWds6oQAAAABJRU5ErkJggg==\n", "text/plain": [ "<Figure size 720x288 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x288 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def ista(A, y, x0, alpha):\n", " tol = 1e-6\n", " lam = 1/(2*np.linalg.norm(A, 2)**2)\n", " \n", " W = np.eye(N) - lam * np.matmul(A.T, A)\n", " b = lam * np.dot(A.T, y_delta)\n", "\n", " def prox(x, eps):\n", " return np.sign(x) * np.maximum(np.abs(x) - eps, 0.)\n", " \n", " x = x0 \n", " for i in range(200000):\n", " x0 = x\n", " x = prox(np.dot(W, x0) + b, alpha * lam)\n", " if np.linalg.norm(x-x0, 1) < tol:\n", " print('Stopped after {} iterations'.format(i))\n", " break\n", " return x\n", " \n", "alphas = [1e-4, 1e-3, 1e-2]\n", "\n", "for i in range(len(alphas)):\n", " plt.figure(figsize=(10, 4))\n", " \n", " alpha = alphas[i] \n", " x_delta = ista(A, y_delta, np.zeros(shape=x_true.shape), alpha)\n", " \n", " plt.title(r'$\\alpha={}$'.format(alpha))\n", " plot_solution(x_true, x_delta)" ] } ], "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": "3.7.1" } }, "nbformat": 4, "nbformat_minor": 2 }