{ "cells": [ { "cell_type": "markdown", "id": "396b2347", "metadata": {}, "source": [ "# Alternating direction algorithms for l1 problems in compressive sensing\n", "\n", "We provide a port of [YALL1 basic](http://yall1.blogs.rice.edu/) package. This is built on top of JAX and can be used to solve the following $\\ell_1$ minimization problems.\n", "\n", "The basis pursuit problem\n", "$$\n", "\\tag{BP}\n", "{\\min}_{x} \\| W x\\|_{w,1} \\; \\text{s.t.} \\, A x = b\n", "$$\n", "\n", "The L1/L2 minimization or basis pursuit denoising problem\n", "$$\n", "\\tag{L1/L2}\n", "{\\min}_{x} \\| W x\\|_{w,1} + \\frac{1}{2\\rho}\\| A x - b \\|_2^2 \n", "$$\n", "\n", "The L1 minimization problem with L2 constraints\n", "$$\n", "\\tag{L1/L2con}\n", "{\\min}_{x} \\| W x\\|_{w,1} \\; \\text{s.t.} \\, \\| A x - b \\|_2 \\leq \\delta\n", "$$\n", "\n", "We also support corresponding non-negative counter-parts.\n", "\n", "The nonnegative basis pursuit problem\n", "$$\n", "\\tag{BP+}\n", "{\\min}_{x} \\| W x\\|_{w,1} \\; \\text{s.t.} \\, A x = b \\, \\, \\text{and} \\, x \\succeq 0\n", "$$\n", "\n", "The nonnegative L1/L2 minimization or basis pursuit denoising problem\n", "$$\n", "\\tag{L1/L2+}\n", "{\\min}_{x} \\| W x\\|_{w,1} + \\frac{1}{2\\rho}\\| A x - b \\|_2^2 \\; \\text{s.t.} \\, x \\succeq 0\n", "$$\n", "\n", "The nonnegative L1 minimization problem with L2 constraints\n", "$$\n", "\\tag{L1/L2con+}\n", "{\\min}_{x} \\| W x\\|_{w,1} \\; \\text{s.t.} \\, \\| A x - b \\|_2 \\leq \\delta \\, \\, \\text{and} \\, x \\succeq 0\n", "$$\n", "\n", "\n", "In the above, $W$ is a sparsifying basis s.t. $Wx = \\alpha$ is a sparse representation of $x$ in $W$ given by \n", "$\\alpha = W^T x$. For simple examples, we can assume $W=I$ is the identity basis.\n", "\n", "The $\\| \\cdot \\|_{w,1}$ is the weighted L1 (semi-) norm defined as\n", "\n", "$$\n", "\\|x \\|_{w,1} = \\sum_{i=1}^n w_i |x_i| \n", "$$\n", "\n", "for a given non-negative weight vector $w$. In the simplest case, we assume $w=1$ reducing it to the famous $\\ell_1$ norm." ] }, { "cell_type": "markdown", "id": "ea3b67b4", "metadata": {}, "source": [ "Import relevant libraries" ] }, { "cell_type": "code", "execution_count": 1, "id": "31fba328", "metadata": {}, "outputs": [], "source": [ "from jax.config import config\n", "config.update(\"jax_enable_x64\", True)\n", "import jax\n", "import jax.numpy as jnp\n", "import numpy as np\n", "from jax import random\n", "from jax import jit, grad, vmap\n", "norm = jnp.linalg.norm" ] }, { "cell_type": "code", "execution_count": 2, "id": "8388b4ab", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "WARNING:absl:No GPU/TPU found, falling back to CPU. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.)\n" ] } ], "source": [ "import cr.nimble as crn\n", "import cr.sparse as crs\n", "import cr.sparse.dict as crdict\n", "import cr.sparse.data as crdata\n", "import cr.sparse.lop as lop\n", "from cr.sparse.cvx.adm import yall1" ] }, { "cell_type": "code", "execution_count": 3, "id": "db11fc41", "metadata": {}, "outputs": [], "source": [ "import matplotlib as mpl\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "id": "43487df4", "metadata": {}, "source": [ "Setup a problem with a random sensing matrix with orthonormal rows" ] }, { "cell_type": "code", "execution_count": 4, "id": "01e91bef", "metadata": {}, "outputs": [], "source": [ "N = 1000\n", "M = 300\n", "K = 50" ] }, { "cell_type": "code", "execution_count": 5, "id": "cd6e376c", "metadata": {}, "outputs": [], "source": [ "key = random.PRNGKey(0)\n", "key1, key2, key3, key4 = random.split(key, 4)" ] }, { "cell_type": "code", "execution_count": 6, "id": "031fcbbd", "metadata": {}, "outputs": [], "source": [ "A = crdict.random_orthonormal_rows(key1, M, N)" ] }, { "cell_type": "code", "execution_count": 7, "id": "1598f000", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "DeviceArray(True, dtype=bool)" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "crn.has_orthogonal_rows(A)" ] }, { "cell_type": "code", "execution_count": 8, "id": "6cf7860f", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig=plt.figure(figsize=(8,6), dpi= 100, facecolor='w', edgecolor='k')\n", "plt.imshow(A, extent=[0, 2, 0, 1])\n", "plt.gray()\n", "plt.colorbar()\n", "plt.title(r'$A$');" ] }, { "cell_type": "code", "execution_count": 9, "id": "b7e7bed5", "metadata": {}, "outputs": [], "source": [ "x, omega = crdata.sparse_normal_representations(key2, N, K, 1)\n", "x = jnp.squeeze(x)" ] }, { "cell_type": "code", "execution_count": 10, "id": "7ffaa82a", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig=plt.figure(figsize=(8,6), dpi= 100, facecolor='w', edgecolor='k')\n", "plt.stem(x, markerfmt='.');" ] }, { "cell_type": "code", "execution_count": 11, "id": "40263464", "metadata": {}, "outputs": [], "source": [ "# Convert A into a linear operator\n", "A = lop.matrix(A)" ] }, { "cell_type": "markdown", "id": "3a3e2478", "metadata": {}, "source": [ "## Standard sparse recovery problems for compressive sensing" ] }, { "cell_type": "markdown", "id": "605599aa", "metadata": {}, "source": [ "### Basis pursuit\n", "\n", "The simple form of basis pursuit problem is:\n", "\n", "$$\n", "{\\min}_{x} \\| x\\|_{1} \\; \\text{s.t.} \\, A x = b\n", "$$" ] }, { "cell_type": "code", "execution_count": 12, "id": "c766e6d2", "metadata": {}, "outputs": [], "source": [ "# Compute the measurements\n", "b0 = A.times(x)" ] }, { "cell_type": "code", "execution_count": 13, "id": "d3bf7d8f", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig=plt.figure(figsize=(8,6), dpi= 100, facecolor='w', edgecolor='k')\n", "plt.stem(b0, markerfmt='.');" ] }, { "cell_type": "code", "execution_count": 14, "id": "2bf9d32b", "metadata": {}, "outputs": [], "source": [ "sol = yall1.solve(A, b0)" ] }, { "cell_type": "code", "execution_count": 15, "id": "fc597a44", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "iterations 30\n", "n_times 61\n", "n_trans 32\n", "r_norm 3.658499e-02\n" ] } ], "source": [ "print(sol)" ] }, { "cell_type": "code", "execution_count": 16, "id": "5e586040", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "DeviceArray(38.35395527, dtype=float64)" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "crn.signal_noise_ratio(x, sol.x)" ] }, { "cell_type": "code", "execution_count": 17, "id": "f8836b56", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig=plt.figure(figsize=(8,6), dpi= 100, facecolor='w', edgecolor='k')\n", "plt.subplot(211)\n", "plt.title('original')\n", "plt.stem(x, markerfmt='.', linefmt='gray');\n", "plt.subplot(212)\n", "plt.stem(sol.x, markerfmt='.');\n", "plt.title('reconstruction');" ] }, { "cell_type": "code", "execution_count": 18, "id": "16270f3f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "5.66 ms ± 702 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n" ] } ], "source": [ "%timeit yall1.solve(A, b0).x.block_until_ready()" ] }, { "cell_type": "markdown", "id": "23974b52", "metadata": {}, "source": [ "### Basis pursuit denoising\n", "\n", "The simple form of L1-L2 unconstrained minimization or basis pursuit denoising is:\n", "$$\n", "{\\min}_{x} \\| x\\|_{1} + \\frac{1}{2\\rho}\\| A x - b \\|_2^2\n", "$$" ] }, { "cell_type": "code", "execution_count": 19, "id": "b1270d4c", "metadata": {}, "outputs": [], "source": [ "sigma = 0.01\n", "noise = sigma * random.normal(key3, (M,))" ] }, { "cell_type": "code", "execution_count": 20, "id": "d2d58557", "metadata": {}, "outputs": [], "source": [ "b = b0 + noise" ] }, { "cell_type": "code", "execution_count": 21, "id": "c3065949", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "DeviceArray(27.34386008, dtype=float64)" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "crn.signal_noise_ratio(b0, b)" ] }, { "cell_type": "code", "execution_count": 22, "id": "8c90be7f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "iterations 28\n", "n_times 57\n", "n_trans 30\n", "r_norm 1.781138e-01\n" ] } ], "source": [ "sol = yall1.solve(A, b, rho=0.01)\n", "print(sol)" ] }, { "cell_type": "code", "execution_count": 23, "id": "7bae3054", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "DeviceArray(23.82452563, dtype=float64)" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "crn.signal_noise_ratio(x, sol.x)" ] }, { "cell_type": "code", "execution_count": 24, "id": "a2e8af4a", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig=plt.figure(figsize=(8,6), dpi= 100, facecolor='w', edgecolor='k')\n", "plt.subplot(211)\n", "plt.title('original')\n", "plt.stem(x, markerfmt='.', linefmt='gray');\n", "plt.subplot(212)\n", "plt.stem(sol.x, markerfmt='.');\n", "plt.title('reconstruction');" ] }, { "cell_type": "code", "execution_count": 25, "id": "6fd039c5", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "6.37 ms ± 604 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n" ] } ], "source": [ "%timeit yall1.solve(A, b, rho=0.01).x.block_until_ready()" ] }, { "cell_type": "markdown", "id": "a2f52a39", "metadata": {}, "source": [ "### Basis pursuit with inequality constraints\n", "\n", "The simple form of L1 minimization with L2 constraints or basis pursuit with inequality constraints is:\n", "$$\n", "{\\min}_{x} \\| x\\|_{1} \\; \\text{s.t.} \\, \\| A x - b \\|_2 \\leq \\delta\n", "$$" ] }, { "cell_type": "code", "execution_count": 26, "id": "2b2e838d", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.16467458902598492" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "delta = float(norm(noise))\n", "delta" ] }, { "cell_type": "code", "execution_count": 27, "id": "cd5079d3", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "iterations 26\n", "n_times 53\n", "n_trans 28\n", "r_norm 1.868910e-01\n" ] } ], "source": [ "sol = yall1.solve(A, b, delta=delta)\n", "print(sol)" ] }, { "cell_type": "code", "execution_count": 28, "id": "c1fd9105", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "DeviceArray(23.58768603, dtype=float64)" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "crn.signal_noise_ratio(x, sol.x)" ] }, { "cell_type": "code", "execution_count": 29, "id": "ab383505", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig=plt.figure(figsize=(8,6), dpi= 100, facecolor='w', edgecolor='k')\n", "plt.subplot(211)\n", "plt.title('original')\n", "plt.stem(x, markerfmt='.', linefmt='gray');\n", "plt.subplot(212)\n", "plt.stem(sol.x, markerfmt='.');\n", "plt.title('reconstruction');" ] }, { "cell_type": "code", "execution_count": 30, "id": "ae5cfd22", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "6.96 ms ± 712 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n" ] } ], "source": [ "%timeit yall1.solve(A, b, delta=delta).x.block_until_ready()" ] }, { "cell_type": "markdown", "id": "f34bb1f0", "metadata": {}, "source": [ "## Non-negative counterparts\n", "\n", "In this case, the signal $x$ with the sparse representation $\\alpha = W x$ has only non-negative entries. i.e. if an entry in $x$ is non-zero, it is positive. This is typical for images.\n", "\n", "Let us construct a sparse representation with non-negative entries." ] }, { "cell_type": "code", "execution_count": 31, "id": "884c67dc", "metadata": {}, "outputs": [], "source": [ "xp = jnp.abs(x)" ] }, { "cell_type": "code", "execution_count": 32, "id": "eba13f67", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig=plt.figure(figsize=(8,6), dpi= 100, facecolor='w', edgecolor='k')\n", "plt.stem(xp, markerfmt='.');" ] }, { "cell_type": "markdown", "id": "688e4b8d", "metadata": {}, "source": [ "### Non-negative basis pursuit\n", "\n", "The simple form of basis pursuit for non-negative $x$ is:\n", "$$\n", "{\\min}_{x} \\| x\\|_{1} \\; \\text{s.t.} \\, A x = b \\, \\, \\text{and} \\, x \\succeq 0\n", "$$" ] }, { "cell_type": "code", "execution_count": 33, "id": "62e8a9c7", "metadata": {}, "outputs": [], "source": [ "b0p = A.times(xp)" ] }, { "cell_type": "code", "execution_count": 34, "id": "92248c67", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig=plt.figure(figsize=(8,6), dpi= 100, facecolor='w', edgecolor='k')\n", "plt.stem(b0p, markerfmt='.');" ] }, { "cell_type": "code", "execution_count": 35, "id": "cd1267e9", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "iterations 36\n", "n_times 73\n", "n_trans 38\n", "r_norm 2.969753e-02\n" ] } ], "source": [ "sol = yall1.solve(A, b0p, nonneg=True)\n", "print(sol)" ] }, { "cell_type": "code", "execution_count": 36, "id": "a3cde3ab", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "DeviceArray(39.20630974, dtype=float64)" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "crn.signal_noise_ratio(xp, sol.x)" ] }, { "cell_type": "code", "execution_count": 37, "id": "4006db0d", "metadata": {}, "outputs": [ { "data": { "image/png": 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tW7fq8ssvd93Py8uTJM2YMUMrV65URUWFysv/fVWc+vp63XfffTpw4IASEhI0ePBgvf7665owYYIfwo9MjDHpPN5DAIhc/phc668kNhL5nHyOGTNGxpg2H1+5cqXb/Tlz5mjOnDk+BwbPKp3H/TZQOlL5c7A5ACA8+WNyLSvEdAzXdg8zew8f4ypEncSVnAAA/sJ6zL4j+Qwz/Xskcs3vTuK66QAABA/JZ5hJd9i5ClEncSUnAACCJyhLLaFzGGPSebyHCCRWUgCAtpF8himuQtR5vIcIBFZSQKTjxxdOh+QTAPyElRQQ6fjxBW8w5hMA/ISVFBDJuNwkvEXyCQB+wkoKiGT8+IK3SD4BwE9YSQGRjB9f8BbJJwD40fU5vXS9/RNdFbdbG/NGMt4NEYMfX/AWE44AwM9YSQGRimXs4A2STwAA4Df8+MLp0O0OAAAAy5B8AgAAwDIknwAAALAMyScAAAAsQ/IJAAAAy5B8AgAAwDIknwAAALAMyScAAAAsQ/IJAAAAy5B8AgAAhIAKZ602f1mlCmdtsEMJKC6vCQAAEGRrPizX3MLtajJSlE3KnzxEUy/qG+ywAoKWTwAAgCCqcNa6Ek9JajLSvMIdXbYFlOQTAAAgiMqqalyJZ7MTxmhv1bHgBBRgJJ8AAABBlJWSpCib+7Zom039UxKDE1CAkXwCAAAEUYYjQY9OOk82nWz+jLJJj0/OVoYjIciRBQYTjgAAAILs+pxe+vhvq1XdZNe8Wberb89uwQ4pYEg+AQAAQkCSrUFJ0Q1Kd9iDHUpA0e2OgImU9coAAID3aPlEQETSemUAAMB7Prd8vvPOO7rmmmuUmZkpm82mtWvXnnafTZs2KScnR3a7XQMGDNCyZcs6EivCRKStVwYAALznc/JZU1Oj888/X08//bRX5cvKyjRhwgSNHDlSJSUlmjdvnu6++24VFBT4HCzCQ6StVwYAALznc7f7+PHjNX78eK/LL1u2TH379tWiRYskSYMGDdLWrVu1cOFCTZkyxdeXRxhoXq+sZQLaldcrAwAA3gv4hKPi4mKNGzfObduVV16prVu3qqGhweM+dXV1qq6udrshfETaemUAAMB7AU8+KysrlZaW5rYtLS1NjY2Nqqqq8rhPfn6+HA6H69anT59Ahwk/uz6nl663f6Kr4nZrY95IJhsBAABJFi21ZLO5XzPKGONxe7O5c+fK6XS6bvv37w94jPC/JFuDMqKPdvn1ygAAgPcCvtRSenq6Kisr3bYdOnRIMTEx6tGjh8d94uPjFR8fH+jQAAAAYLGAt3zm5uaqqKjIbdubb76p4cOHKzY2NtAvDwAAgBDic/L57bffqrS0VKWlpZJOLqVUWlqq8vJySSe7zKdPn+4qP3PmTO3bt095eXn69NNP9dxzz2nFihW67777/HMEAAAACBs+d7tv3bpVl19+uet+Xl6eJGnGjBlauXKlKioqXImoJGVlZWn9+vW699579cwzzygzM1OLFy9mmSUAAIAI5HPyOWbMGNeEIU9WrlzZatvo0aP10Ucf+fpSAAAA6GIsme0eySqctdr8ZRWXlgQAAJAFs90j2ZoPy13XOI+ySfmTh7DeJQAAiGi0fAZIhbPWlXhKJy81Oa9wBy2gAAAgopF8BkhZVY3btc0l6YQx2lt1LDgBAQAAhACSzwDJSklS1CkXcIq22dQ/JTE4AQEAAIQAks8AyXAk6NFJ58mmk82fUTbp8cnZynAkBDkyAACA4GHCUQBdn9NLH/9ttaqb7Jo363b17dkt2CEBAAAEFclngCXZGpQU3aB0hz3YoQAAAAQd3e4AAACwDMknAAAALEPyCQAAAMuQfAIAAMAyJJ8AAACwDMknACBsVDhrtfnLKi5VDIQxlloCAISFNR+Wa27hdjWZkxfuyJ88RFMv6hvssAD4iJZPAEDIq3DWuhJPSWoy0rzCHbSARiBav8MfLZ8AgJBXVlXjSjybnTBGe6uOcdniCHJq6/ejk84LdkjoAFo+AQAhLyslSVE2923RNpv6pyQGJyBYzlPr92/W7VKNiQ1uYPAZyScAIORlOBL06KTzZNPJzCPKJj0+OZtWzwjiqfW7yUjVTVy+OtzQ7Q4ACAvX5/TSx39breomu+bNul19e3br9HNWOGtVVlWjrJQkEtkQ19z63TIBjbJJ3aKOBy8odAgtnwCAsJFka1BG9FGlOzrf2rXmw3JdumCDfv7sB7p0wQat+bDcDxEiUDy1fj866Twl2RqCHBl8RfIJAIg4zJ4PT9fn9NL19k90VdxubcwbqetzegU7JHQAyScAICx1Zsmd9mbPI7T5s/UbwcGYTwBBw3g7dNTL2w7oN+t2dXjBeU/jB5k9D1iDlk8AQcF4O3RUjYl1JZ5Sx7rMmT0PBA/JJwDLMd4OnVHdZPdLl/mp4we5VCdgDZJPAJZjvB06o1vUcb8tOM/4QcB6JJ8ALMfVatAZSbYGPTThHLrMgTBF8okurzMzYhEYjLdDZ00ZlkGXORCmmO2OsHa62dJrPix3jS3syIxYBE4grlaDyJJka1BSdANd5kCY6VDL55IlS5SVlSW73a6cnBy9++67bZbduHGjbDZbq9tnn33W4aDhH+HeIni62dJMagl9jLdDVxbu51ggUHxu+VyzZo1mz56tJUuW6NJLL9Uf//hHjR8/Xrt27VLfvm23KO3evVvduv27ZaNnz54dixh+Ee4tgm0llqPO6elqAW1vUkuPPskWRwwgkoT7ORYIJJ9bPp988knddtttuv322zVo0CAtWrRIffr00dKlS9vdLzU1Venp6a5bdHR0h4NG27z5pd0VWgS9mS3NpBaga6oxsdqy94hqTGywQ/GoK5xjgUDyKfmsr6/Xtm3bNG7cOLft48aN0+bNm9vdd9iwYcrIyNDYsWP19ttv+x4pTsvbRbu7wjI33iSWTGoBup49jSl6+fhQ3brqE718fKj2NKYEO6RWusI5FsFV6TzepYds+JR8VlVV6cSJE0pLS3PbnpaWpsrKSo/7ZGRkaPny5SooKFBhYaEGDhyosWPH6p133mnzderq6lRdXe12Q/t8+aXdFVoEvU0sWUQa6Doqnce1uaGfjE6ewIxs2tzQT5XO40GOzF1XOMciePY0pmjMk+926au/dWjCkc3m/q0yxrTa1mzgwIH6xS9+oQsvvFC5ublasmSJJk6cqIULF7b5/Pn5+XI4HK5bnz59OhJmRPHll3ZXaRH0NrFkUgvQNew9fMyVeDYzsmnfv0KrRbGrnGNhvRoTq80N/br8kA2fks+UlBRFR0e3auU8dOhQq9bQ9lxyySX6/PPP23x87ty5cjqdrtv+/ft9CTMi+fpLu6u0CJJYApGjf49EV0LXzCajft1Dr0Wxq5xjYa3qJnurH1hdcciGT8lnXFyccnJyVFRU5La9qKhII0aM8Pp5SkpKlJGR0ebj8fHx6tatm9sN7evIL20SNwBS+CwJlO6wa0TsPtd5ziajEbH7QvYcxjkWvuoWdbzVD6yuOGTD56WW8vLyNG3aNA0fPly5ublavny5ysvLNXPmTEknWy0PHDigF154QZK0aNEi9e/fX4MHD1Z9fb1WrVqlgoICFRQU+PdIwKLdAHwWbksCnRNTpV7RTlU32dUt6riSbA3BDgnwmyRbg0bE7nONbe6qQzZ8Tj6nTp2qw4cP65FHHlFFRYWys7O1fv169evXT5JUUVGh8vJ/D46tr6/XfffdpwMHDighIUGDBw/W66+/rgkTJvjvKODCFT8AeMub9XJDUfN5DuiKWv7A6qoNSR26vOYdd9yhO+64w+NjK1eudLs/Z84czZkzpyMvAwAIoPYmKoZy8tlVne5ywYgcXb0hiWu7A0CEap6o2DIB7Yrjy8JBuA1/ADqjQ0stAQDCH0sChQauiIRIQ/IJABGMJYGCjysiIdLQ7Q4AEa6rjy8LdQx/QKSh5RMAgCBi+AMiDS2fANAFMXM6vLBOMyIJyScAdDHMnA5PDH9ApKDbHQC6EGZOoz3hcilVdG20fAJAF8LC8WhryAUt4ggVJJ8A0IUwczqytZVghuulVNE10e0OhIFK53G6yuAVZk5HrvaGXLCWKEIJLZ9AiNvTmKIxT75LVxm8Fiozp5lxb632EkyrWsQrncdVcSJZ3aKO+/V5g4XPcGCQfAIhrMbEanNDPzX/vaCrDN4K9sxpxhdar70Es7lF/Nd/3SkjW0BaxP9d5wNlk9H52w7oxtwsvz2/1fgMBw7d7kAIq26yy8jmti2QXWXMhIU/MOM+OE435CKQl1I9tc6NbPrNul1hW+d8hgOLlk8ghHWLOi6bjFsCGqjJI/zKh78w4z54TjfkIlAt4p7qvMkobOucz3Bg0fIJhLAkW4NGxO4L+OQRfuXDn5q7f1tixr11kmwNyog+aumQC091HmVT2NY5n+HAIvkEQtw5MVUB6yprxkxY+BMz7iPPqXVuk9Gjk84L2zrnMxxYdLsDYSDQk0dYGxL+Fioz7mGdlnXeLeq4rs8ZF+yQOoXPcODQ8gmEmOZJP5VO65Yq4Vc+AiEY3b8IruY6T7I1BDsUv+AzHBi0fAIh5NRJP7kxKTonpsqS1+ZXPgDACrR8olNYmsd/PE362dzQTzUm1rIY+JUP+I7zIOAbWj7RYSzN41+eJv0Y2VTdZFdSdNfowgK6Gs6DgO9o+YTPKpy1evXjAyzN42eelvawyXSZy9QBXQ1LlAEdQ/IJn6z5sFyXLtigWatLWZrHzzxN+hkRu6/LDNwHuhqWKAM6huQTXjv1V/6pWJqn81pe/u7NWZdYNtkI6IhIH+vIQuSwSlf7rjHmE17z9Cu/GUvz+I9rTc9u8cEOBWgTYx3/3Vvx67/ulJHN7TxYX18f7PDQRXTF7xotn/Cap1/5ktGY2C8CduUdAKGHsY7/1rK3gvMg/K3SebxLftdIPuE1T2MSL43dp6yYb1iaJ4J0te4f+I6xju5YogyBsvfwMY/ftW17jwQnID8h+YRPGJMY2ZonnP382Q906YINWvNhebBDQhAw1hGwRv8eiR56HKW7XyoJ6/MvySd85vqVz5hES9SYWFWcSHYtNh+slke6WtGMy7ECHePr+TvdYdejk86T5N78Ge7n3w4ln0uWLFFWVpbsdrtycnL07rvvtlt+06ZNysnJkd1u14ABA7Rs2bIOBQtEmj2NKXr5+FC9UT9QLx8fqvsLdwSt5ZGuVrTEWEfANx3tObo+p5fGxH7Zans4n399Tj7XrFmj2bNn68EHH1RJSYlGjhyp8ePHq7zc85tYVlamCRMmaOTIkSopKdG8efN09913q6CgoNPBA11ZZXWdNjf0k9HJPhcjm14prQhayyNdrTgVYx0B73S25yg1usbV09AsnM+/NmNMG4vneHbxxRfrwgsv1NKlS13bBg0apOuuu075+fmtyt9///1at26dPv30U9e2mTNn6uOPP1ZxcbFXr1ldXS2HwyGn06lu3br5Em6HVDhrVbSrUjsOVOtYXaMS42J0ZlKsjhxr0LG6Rklqtc3T/W72aP1f8fuKshkNGpqjqKjodvfx9Lz2GJu+3L5F8WpUnYnW0IsuVWx0lMfnPXz0uEo//ljJUXUaM2qMDlTXnfZ5ZYzOGnpxq+eItzVq+EUXyx4X0+YxDbtwuHaWfOB6juONxvU6vsRyuvtt7ePN+9uyTMvj+ba2Xns+3dEqvo7Wtbf7+PL+Znx/iN7affi0n9erh6QrMT6m0/G29V61LFPhPKZ3vzgsfZcQj/p+itK/Z+/Qe/dtbb3KPvtE3aOO6ayc0fpXTYNX8fu7TlqWafm9OG5iZY9q9Pnzcep3q+X3wt/xnu5z1pFzgbfxnu77F4j3ofkzkxldrZqmODmb4lvVkS/vXXuf+c6eh9qqg858/7x579o7xwT6s9nymOPVqNxRV7R53P74jp419GJJ8vi3zJd6a+v97myZlq9bfrhG75e1niQ05pwUDUxPbvV3qflvfstjPHwiUeWmu+v8O7zf95Tezd7ue1d/wmhASpKuOC/NkmEx3uZrPiWf9fX1SkxM1Msvv6wf//jHru333HOPSktLtWnTplb7jBo1SsOGDdNTTz3l2vbKK6/opz/9qY4dO6bY2Fi/HYw/rNmyT7/9y7aAvgYAAIBV6qLj9PufDA348Bhv8zWfFpmvqqrSiRMnlJaW5rY9LS1NlZWVHveprKz0WL6xsVFVVVXKyMhotU9dXZ3q6urcDsYKFc5a/fYv27T2tQcteT0AAIBAu+7qxzS3cLtGndMzJCYGdmjCkc3mPvDLGNNq2+nKe9reLD8/Xw6Hw3Xr06dPR8L0WVlVjSWvAwAAYKUmo5CZoORTy2dKSoqio6NbtXIeOnSoVetms/T0dI/lY2Ji1KNHD4/7zJ07V3l5ea771dXVliSgWSlJqouO03VXPxbw1wIAALBCXXScomwKmQlKPiWfcXFxysnJUVFRkduYz6KiIl177bUe98nNzdWrr77qtu3NN9/U8OHD2xzvGR8fr/h469eQzHAk6Pc/Gar7C7Zb/toAAACBYNPJa8KHQpe75GPyKUl5eXmaNm2ahg8frtzcXC1fvlzl5eWaOXOmpJOtlgcOHNALL7wg6eTM9qefflp5eXn6xS9+oeLiYq1YsUKrV6/275H4ydSL+mrUOT311q5/ascBp47Vt5ixVtOgY/WnzJ77bltb9+sbjeJibDry3Uze9vZp63n79kiUIyFWztoGHf62XnExtjafV5L69jj5y6b88LHTPm9zuVOf49TYPR1TfaNRjzPi3F6r5ev4EktH3hdv39+W8Z56PKfG15m69nYfX99fR8LJH2nN9d/yPT/1mDsbb1vvlTdlOvLe9Uy2a1BGsj49eFRff3vcq30CUSctyzR/Jk59r339zra3nz/jbe9z1pFzgS/xnu77F4j3oWeyXZd+v4cOfnNcZVU1rerI1/fOH59nX87Hnf3+efPetXeOCfRns/mYm/9mefs6HfmONp8D2/pb5m29deR819HP0KnnvNP9zT/1GD2dl053jAN6JmnsIGtmu3vL5+Rz6tSpOnz4sB555BFVVFQoOztb69evV79+/SRJFRUVbmt+ZmVlaf369br33nv1zDPPKDMzU4sXL9aUKVP8dxR+luFI0LTc/sEOAwAAoMvxeZ3PYLB6nU8AAAD4xtt8jWu7AwAAwDIknwAAALCMz2M+g6F5ZIBVi80DAADAN8152ulGdIZF8nn06FFJsmyxeQAAAHTM0aNH5XA42nw8LCYcNTU16eDBg0pOTm73Skr+0ryo/f79+5ngFKaow/BHHYY/6jC8UX/hz+o6NMbo6NGjyszMVFRU2yM7w6LlMyoqSr1797b8dbt168YXLsxRh+GPOgx/1GF4o/7Cn5V12F6LZzMmHAEAAMAyJJ8AAACwDMmnB/Hx8XrooYeCcn15+Ad1GP6ow/BHHYY36i/8hWodhsWEIwAAAHQNtHwCAADAMiSfAAAAsAzJJwAAACxD8gkAAADLkHyeYsmSJcrKypLdbldOTo7efffdYIeE7+Tn5+uiiy5ScnKyUlNTdd1112n37t1uZYwxevjhh5WZmamEhASNGTNGO3fudCtTV1enWbNmKSUlRUlJSZo0aZK++uorKw8FOlmfNptNs2fPdm2j/kLfgQMHdNNNN6lHjx5KTEzUBRdcoG3btrkepw5DW2Njo379618rKytLCQkJGjBggB555BE1NTW5ylCHoeWdd97RNddco8zMTNlsNq1du9btcX/V15EjRzRt2jQ5HA45HA5NmzZN33zzTWAOysDlpZdeMrGxsebZZ581u3btMvfcc49JSkoy+/btC3ZoMMZceeWV5vnnnzc7duwwpaWlZuLEiaZv377m22+/dZVZsGCBSU5ONgUFBWb79u1m6tSpJiMjw1RXV7vKzJw50/Tq1csUFRWZjz76yFx++eXm/PPPN42NjcE4rIi0ZcsW079/fzN06FBzzz33uLZTf6HtX//6l+nXr5+5+eabzQcffGDKysrMW2+9Zb744gtXGeowtP3ud78zPXr0MK+99popKyszL7/8sjnjjDPMokWLXGWow9Cyfv168+CDD5qCggIjybzyyituj/urvq666iqTnZ1tNm/ebDZv3myys7PN1VdfHZBjIvls4Qc/+IGZOXOm27Zzzz3XPPDAA0GKCO05dOiQkWQ2bdpkjDGmqanJpKenmwULFrjKHD9+3DgcDrNs2TJjjDHffPONiY2NNS+99JKrzIEDB0xUVJR54403rD2ACHX06FFz9tlnm6KiIjN69GhX8kn9hb7777/fXHbZZW0+Th2GvokTJ5pbb73VbdvkyZPNTTfdZIyhDkPdqcmnv+pr165dRpJ5//33XWWKi4uNJPPZZ5/5/Tjodv9OfX29tm3bpnHjxrltHzdunDZv3hykqNAep9MpSerevbskqaysTJWVlW51GB8fr9GjR7vqcNu2bWpoaHArk5mZqezsbOrZInfeeacmTpyoK664wm079Rf61q1bp+HDh+v6669Xamqqhg0bpmeffdb1OHUY+i677DL9/e9/1549eyRJH3/8sd577z1NmDBBEnUYbvxVX8XFxXI4HLr44otdZS655BI5HI6A1GmM358xTFVVVenEiRNKS0tz256WlqbKysogRYW2GGOUl5enyy67TNnZ2ZLkqidPdbhv3z5Xmbi4OJ155pmtylDPgffSSy9p27Zt2rp1a6vHqL/Q949//ENLly5VXl6e5s2bpy1btujuu+9WfHy8pk+fTh2Ggfvvv19Op1PnnnuuoqOjdeLECT322GO64YYbJPE9DDf+qq/Kykqlpqa2ev7U1NSA1CnJ5ylsNpvbfWNMq20IvrvuukuffPKJ3nvvvVaPdaQOqefA279/v+655x69+eabstvtbZaj/kJXU1OThg8frscff1ySNGzYMO3cuVNLly7V9OnTXeWow9C1Zs0arVq1Si+++KIGDx6s0tJSzZ49W5mZmZoxY4arHHUYXvxRX57KB6pO6Xb/TkpKiqKjo1tl+IcOHWr1iwLBNWvWLK1bt05vv/22evfu7dqenp4uSe3WYXp6uurr63XkyJE2yyAwtm3bpkOHDiknJ0cxMTGKiYnRpk2btHjxYsXExLjef+ovdGVkZOi8885z2zZo0CCVl5dL4jsYDn71q1/pgQce0M9+9jMNGTJE06ZN07333qv8/HxJ1GG48Vd9paen65///Ger5//6668DUqckn9+Ji4tTTk6OioqK3LYXFRVpxIgRQYoKLRljdNddd6mwsFAbNmxQVlaW2+NZWVlKT093q8P6+npt2rTJVYc5OTmKjY11K1NRUaEdO3ZQzwE2duxYbd++XaWlpa7b8OHDdeONN6q0tFQDBgyg/kLcpZde2mp5sz179qhfv36S+A6Gg2PHjikqyv1Pf3R0tGupJeowvPirvnJzc+V0OrVlyxZXmQ8++EBOpzMwder3KUxhrHmppRUrVphdu3aZ2bNnm6SkJLN3795ghwZjzC9/+UvjcDjMxo0bTUVFhet27NgxV5kFCxYYh8NhCgsLzfbt280NN9zgccmJ3r17m7feest89NFH5oc//CFLhARJy9nuxlB/oW7Lli0mJibGPPbYY+bzzz83f/7zn01iYqJZtWqVqwx1GNpmzJhhevXq5VpqqbCw0KSkpJg5c+a4ylCHoeXo0aOmpKTElJSUGEnmySefNCUlJa5lIP1VX1dddZUZOnSoKS4uNsXFxWbIkCEstWSVZ555xvTr18/ExcWZCy+80LWMD4JPksfb888/7yrT1NRkHnroIZOenm7i4+PNqFGjzPbt292ep7a21tx1112me/fuJiEhwVx99dWmvLzc4qOBMa2TT+ov9L366qsmOzvbxMfHm3PPPdcsX77c7XHqMLRVV1ebe+65x/Tt29fY7XYzYMAA8+CDD5q6ujpXGeowtLz99tse//bNmDHDGOO/+jp8+LC58cYbTXJysklOTjY33nijOXLkSECOyWaMMf5vTwUAtHTw4EEtX75c1113nS644IKgxHDs2DE98cQTGjNmjMaMGeP22MqVK3XLLbeorKxM/fv3D0p8ACIDYz4BwAIHDx7U/PnzVVpaGrQYjh07pvnz52vjxo2tHps4caKKi4uVkZFhfWAAIgpLLQEIeceOHVNiYmKww7CU1cfcs2dP9ezZ07LXAxC5aPkEEFIefvhh2Ww2ffTRR/rJT36iM888U2eddZaMMVqyZIkuuOACJSQk6Mwzz9RPfvIT/eMf/2j1HG+88YbGjh0rh8OhxMREDRo0yLWUTLN169YpNzdXiYmJSk5O1o9+9CMVFxd7jGXnzp264YYb5HA4lJaWpltvvdV1ha1mL7/8si6++GLXaw4YMEC33nqrJGnjxo266KKLJEm33HKLbDabbDabHn74YUnSzTffrDPOOEPbt2/XuHHjlJycrLFjx0qS+vfvr5tvvrnVMXrqOv/mm2/0X//1XxowYIDi4+OVmpqqCRMm6LPPPtPevXtdyeX8+fNdMTQ/98qVK2Wz2bR3716353zuued0/vnny263q3v37vrxj3+sTz/91K1Mc/xffPGFJkyYoDPOOEN9+vTRf/3Xf6murq5V7AAiG8kngJA0efJkff/739fLL7+sZcuW6T//8z81e/ZsXXHFFVq7dq2WLFminTt3asSIEW7r061YsUITJkxQU1OTli1bpldffVV33323vvrqK1eZF198Uddee626deum1atXa8WKFTpy5IjGjBnj8cIFU6ZM0TnnnKOCggI98MADevHFF3Xvvfe6Hi8uLtbUqVM1YMAAvfTSS3r99df129/+Vo2NjZKkCy+8UM8//7wk6de//rWKi4tVXFys22+/3fUc9fX1mjRpkn74wx/qr3/9q+bPn+/T+3X06FFddtll+uMf/6hbbrlFr776qpYtW6ZzzjlHFRUVysjI0BtvvCFJuu2221wx/OY3v2nzOfPz83Xbbbdp8ODBKiws1FNPPaVPPvlEubm5+vzzz93KNjQ0aNKkSRo7dqz++te/6tZbb9V///d/6/e//71PxwEgAgRkGhMAdNBDDz1kJJnf/va3rm3FxcVGkvnDH/7gVnb//v0mISHBtUzM0aNHTbdu3cxll11mmpqaPD7/iRMnTGZmphkyZIg5ceKEa/vRo0dNamqqGTFiRKtYnnjiCbfnuOOOO4zdbne9xsKFC40k880337R5XB9++GGr1RmazZgxw0gyzz33XKvH+vXr55rV2tLo0aPN6NGjXfcfeeQRI8kUFRW1GcPXX39tJJmHHnqo1WPPP/+8kWTKysqMMcYcOXLEJCQkmAkTJriVKy8vN/Hx8ebnP/95q/j/8pe/uJWdMGGCGThwYJvxAIhMtHwCCElTpkxx/f+1116TzWbTTTfdpMbGRtctPT1d559/vmsCzebNm1VdXa077rijzUvC7d69WwcPHtS0adPcFts+44wzNGXKFL3//vs6duyY2z6TJk1yuz906FAdP35chw4dkiRXl/pPf/pT/eUvf9GBAwc6fcy++t///V+dc845uuKKKzr8HC0VFxertra2VZd/nz599MMf/lB///vf3bbbbDZdc801btuGDh3qur40ADQj+QQQklrOuv7nP/8pY4zS0tIUGxvrdnv//fdVVVUl6eSl4CS5XXb1VIcPH271/M0yMzPV1NTU6jJ0PXr0cLsfHx8vSaqtrZUkjRo1SmvXrlVjY6OmT5+u3r17Kzs7W6tXr/b6eBMTE9WtWzevy5/q66+/bve4fXW696n58WaJiYmy2+1u2+Lj43X8+HG/xQSga2C2O4CQ1LLlMiUlRTabTe+++64r8WupeVvzhJqW4ztP1ZxIVlRUtHrs4MGDioqK0plnnulzvNdee62uvfZa1dXV6f3331d+fr5+/vOfq3///srNzT3t/m211Nrtdo+TdqqqqpSSkuK637Nnz3aP21ene59avjYA+IKWTwAh7+qrr5YxRgcOHNDw4cNb3YYMGSJJGjFihBwOh5YtWybTxvUzBg4cqF69eunFF190K1NTU6OCggLXDPiOio+P1+jRo10TbUpKSlzbpX+3lnqrf//++uSTT9y27dmzp9U11sePH689e/Zow4YN7cbmbQy5ublKSEjQqlWr3LZ/9dVX2rBhg2s2PgD4ipZPACHv0ksv1X/8x3/olltu0datWzVq1CglJSWpoqJC7733noYMGaJf/vKXOuOMM/SHP/xBt99+u6644gr94he/UFpamr744gt9/PHHevrppxUVFaUnnnhCN954o66++mr953/+p+rq6vT//t//0zfffKMFCxb4HN9vf/tbffXVVxo7dqx69+6tb775Rk899ZRiY2M1evRoSdJZZ52lhIQE/fnPf9agQYN0xhlnKDMzU5mZme0+97Rp03TTTTfpjjvu0JQpU7Rv3z498cQTrdbknD17ttasWaNrr71WDzzwgH7wgx+otrZWmzZt0tVXX63LL79cycnJ6tevn/76179q7Nix6t69u1JSUjxe0eh73/uefvOb32jevHmaPn26brjhBh0+fFjz58+X3W7XQw895PP7BACSmO0OILQ0zzD/+uuvWz323HPPmYsvvtgkJSWZhIQEc9ZZZ5np06ebrVu3upVbv369GT16tElKSjKJiYnmvPPOM7///e/dyqxdu9ZcfPHFxm63m6SkJDN27Fjzf//3f17FcurM8Ndee82MHz/e9OrVy8TFxZnU1FQzYcIE8+6777rtt3r1anPuueea2NhYt1nnM2bMMElJSR7fj6amJvPEE0+YAQMGGLvdboYPH242bNjQara7MSdnqDdftzs2NtakpqaaiRMnms8++8xV5q233jLDhg0z8fHxbteHPvWYmv3P//yPGTp0qImLizMOh8Nce+21ZufOnW5l2oq/+f0DgJa4tjsAAAAsw5hPAAAAWIbkEwAAAJYh+QQAAIBlSD4BAABgGZJPAAAAWIbkEwAAAJYJi0Xmm5qadPDgQSUnJ7d5CToAAAAEjzFGR48eVWZmpqKi2m7fDIvk8+DBg+rTp0+wwwAAAMBp7N+/X717927z8bBIPpOTkyWdPJhu3boFORoAAACcqrq6Wn369HHlbW0Ji+Szuau9W7duJJ8AAAAh7HRDJJlwBAAAAMuQfAIAAMAyJJ8AAACwDMknAAAALBMWE44AwCoVzlqVVdUoKS5aNfUnlJWSpAxHQrDDAoAug+QTAL6z5sNyzS3cribz721RNil/8hBNvahv8AIDgC6EbncA0MkWz1MTT0lqMtK8wh2qcNYGJzAA6GJIPgFAUllVTavEs9kJY7S36pi1AQFAF0XyCQCSslKSFNXGusjRNpv6pyRaGxAAdFEknwAgKcORoPmTBrfaHmWTHp+czaQjAPATkk8A+M6UnN6ttr2VN5rJRgDgRySfANCOdIc92CEAQJdC8gkAAADLkHwCAADAMiSfAAAAsAzJJwAAACxD8gkAAADLkHwCAADAMiSfAAAgbFU4a7X5yypVOGuDHQq8FBPsAAAAADpizYflmlu4XU3m5NXI8icP4aIQYYCWTwAAEHYqnLWuxFOSmow0r3AHLaBhgOQTAACEnbKqGlfi2eyEMdpbdSw4AcFrJJ8AACDsZKUkKcrmvi3aZlP/lMTgBASvkXwCAICwk+FI0PxJg133o2zS45OzleFICGJU8IZPyWd+fr4uuugiJScnKzU1Vdddd51279592v02bdqknJwc2e12DRgwQMuWLetwwAAAAJI0Jae36/9v5Y1mslGY8Cn53LRpk+688069//77KioqUmNjo8aNG6eampo29ykrK9OECRM0cuRIlZSUaN68ebr77rtVUFDQ6eABAAAkKd1hD3YI8JJPSy298cYbbveff/55paamatu2bRo1apTHfZYtW6a+fftq0aJFkqRBgwZp69atWrhwoaZMmdKxqAEAABCWOjXm0+l0SpK6d+/eZpni4mKNGzfObduVV16prVu3qqGhweM+dXV1qq6udrsBAAAg/HU4+TTGKC8vT5dddpmys7PbLFdZWam0tDS3bWlpaWpsbFRVVZXHffLz8+VwOFy3Pn36dDRMAAAAhJAOJ5933XWXPvnkE61evfq0ZW0297UQjDEetzebO3eunE6n67Z///6OhgkAAIAQ0qHLa86aNUvr1q3TO++8o969e7dbNj09XZWVlW7bDh06pJiYGPXo0cPjPvHx8YqPj+9IaAAAAAhhPrV8GmN01113qbCwUBs2bFBWVtZp98nNzVVRUZHbtjfffFPDhw9XbGysb9ECAAAgrPmUfN55551atWqVXnzxRSUnJ6uyslKVlZWqrf33dVTnzp2r6dOnu+7PnDlT+/btU15enj799FM999xzWrFihe677z7/HQUAAADCgk/J59KlS+V0OjVmzBhlZGS4bmvWrHGVqaioUHl5uet+VlaW1q9fr40bN+qCCy7Qo48+qsWLF7PMEgAAQATyacxn80Sh9qxcubLVttGjR+ujjz7y5aUAAADQBXFtdwAAAFiG5BMAAACWIfkEAACAZUg+AQAAYBmSTwAAAFiG5BMAAACWIfkEAACAZUg+AQAAYBmSTwAAAFiG5BMAAACWIfkEAACAZUg+AQAAYBmSTwAAAFiG5BMAAACWIfkEAACAZUg+AQAAYBmSTwAAAFiG5BMAAACWIfkEAACAZUg+AQAAYBmSTwAAAFiG5BMAAACWIfkMAxXOWm3+skoVztpghwIAANApMcEOAO1b82G55hZuV5ORomxS/uQhmnpR32CHBQAA0CG0fIawCmetK/GUpCYjzSvcQQsoAAAIWySfIaysqsaVeDY7YYz2Vh0LTkDwC4ZRAAAiGd3uISwrJUlRNrkloFGS+qckBi0mdA7DKAAAkY6WzxCW4UjQ/EmD3bYZSe/s+To4AaFTGEYBAADJZ8i79PspbveNAp+w0C0cGB0ZRkFdAAC6GrrdQ9y+wzWttjUnLBmOBL+/Ht3CgeNpGEW0zdbmMArqAgDQFfnc8vnOO+/ommuuUWZmpmw2m9auXdtu+Y0bN8pms7W6ffbZZx2NOaL065HUalt7CUtn0C0cWKcOo4iySY9Pzvb4I4K6AAB0VT4nnzU1NTr//PP19NNP+7Tf7t27VVFR4bqdffbZvr50REp32N3ut5ewdBaz6wNvSk5v1//fyhvdZksmdQEA6Kp87nYfP368xo8f7/MLpaam6nvf+57P+8HdW3mjNaDnGQF5bl+7hdE5p/6waIm6AAB0VZZNOBo2bJgyMjI0duxYvf3221a9bJfTXsLSWb50CyOwqAsACA9MDPVdwCccZWRkaPny5crJyVFdXZ3+9Kc/aezYsdq4caNGjRrlcZ+6ujrV1dW57ldXVwc6THxnSk5v/eavOyUFtpUVp0ddAEDgVDhrVVZVo6yUpA7/sGdiaMcEPPkcOHCgBg4c6Lqfm5ur/fv3a+HChW0mn/n5+Zo/f36gQ8NpBLKVFb6hLgDAf/yRNLY1MXTUOT3ppTqNoKzzeckll+jzzz9v8/G5c+fK6XS6bvv377cwOgAA0FX5azURJoZ2XFDW+SwpKVFGRkabj8fHxys+Pt7CiBCJ/NHlAgAIL+0ljb78LWBiaMf5nHx+++23+uKLL1z3y8rKVFpaqu7du6tv376aO3euDhw4oBdeeEGStGjRIvXv31+DBw9WfX29Vq1apYKCAhUUFPjvKCIQiVPnME4HACKTv5LG5omhzWPzmRjqPZ+Tz61bt+ryyy933c/Ly5MkzZgxQytXrlRFRYXKy8tdj9fX1+u+++7TgQMHlJCQoMGDB+v111/XhAkT/BB+ZCJx6hzG6QBA5PJn0sjE0I7xOfkcM2aMjDFtPr5y5Uq3+3PmzNGcOXN8DgyeVTqPkzh1kr+6XAAA4SkQSSMTQ70XlAlH6Lh9hxng3FnNXS4tMU4HACITSaP1SD7DTL8eJE6dxQLuAAAED8lnmEl32Emc/MDba6wDAAD/IvkMQyRO/kWXC/yNy+0hkvH5x+kEZZ1P+A+JExBaWI0CkYzPP7xByycA+Im/rpwChCM+//AWyScA+AmX20Mk4/MPb5F8AoCfsIwXIhmff3iL5BMA/IRlvBDJ+PzDWySfAOBHrEaBSMbnH94g+QSAAGE1CkQyPv9oC8knAAAALEPyCQAAAMuQfAIAAMAyJJ8AAACwDMknAAAALEPyCQAAAMuQfAIAAMAyJJ8AAACwDMknAAAALEPyCQAAAMuQfAIAAMAyJJ8AAACwDMknAABACKhw1mrzl1WqcNYGO5SAigl2AAAAAJFuzYflmlu4XU1GirJJ+ZOHaOpFfYMdVkDQ8gkAABBEFc5aV+IpSU1Gmle4o8u2gJJ8AgAABFFZVY0r8Wx2whjtrToWnIACjOQTAAAgiLJSkhRlc98WbbOpf0picAIKMJJPAACAIMpwJGj+pMGu+1E26fHJ2cpwJAQxqsAh+UTARMqsPQAAOmtKTm/X/9/KG91lJxtJzHZHgETSrD0AAPwp3WEPdggB5XPL5zvvvKNrrrlGmZmZstlsWrt27Wn32bRpk3JycmS32zVgwAAtW7asI7EiTETarD0AAOA9n5PPmpoanX/++Xr66ae9Kl9WVqYJEyZo5MiRKikp0bx583T33XeroKDA52ARHiJt1h4AAPCez93u48eP1/jx470uv2zZMvXt21eLFi2SJA0aNEhbt27VwoULNWXKFF9fHmGgedZeywS0K8/aAwAA3gv4hKPi4mKNGzfObduVV16prVu3qqGhweM+dXV1qq6udrshfETarD0AAOC9gCeflZWVSktLc9uWlpamxsZGVVVVedwnPz9fDofDdevTp0+gw4SfRdKsPQAA4D1Lllqy2dxXTjXGeNzebO7cuXI6na7b/v37Ax4jAqerz9oDAADeC/hSS+np6aqsrHTbdujQIcXExKhHjx4e94mPj1d8fHygQwMAAIDFAt7ymZubq6KiIrdtb775poYPH67Y2NhAvzwAAABCiM/J57fffqvS0lKVlpZKOrmUUmlpqcrLyyWd7DKfPn26q/zMmTO1b98+5eXl6dNPP9Vzzz2nFStW6L777vPPEQAAACBs+NztvnXrVl1++eWu+3l5eZKkGTNmaOXKlaqoqHAlopKUlZWl9evX695779UzzzyjzMxMLV68mGWWAAAAIpDPyeeYMWNcE4Y8WblyZatto0eP1kcffeTrSwEAAKCLsWS2OwAAACCRfAZchbNWm7+s4rrmAAAAsmCppUi25sNyzS3criZz8io/+ZOHsNg6AACIaLR8BkiFs9aVeEonr3M+r3AHLaAAACCikXwGSFlVjSvxbHbCGO2tOhacgAAAAEIAyWeAZKUkKeqUq4dG22zqn5IYnIAAAABCAMlngGQ4EjR/0mDX/Sib9PjkbGU4EoIYFQAAQHCRfAbQlJzerv+/lTeayUYAACDikXxaJN1hD3YIAAAAQUfyCQAAAMuQfAIAAMAyJJ8AAACwDMknAAAALEPyCQAIGxXOWm3+soqrxQFhjGu7AwDCwpoPy12XLY6ySfmTh7CEHRCGaPkEAIS8CmetK/GUpCYjzSvcQQsoEIZIPgEAIa+sqsaVeDY7YYz2Vh0LTkAIGoZehD+63QEAIS8rJUlRNrkloNE2m/qnJAYvKFju1KEXLS9jjfBByycAIORlOBLcEo0om/T45GxlOBKCGBWs5GnoxUPrdgY3KHQIyScAICxMyent+v9beaOZbBRhPA29OPU+wgPJJwAg7KQ77H55HsYPho/moRctnXof4YHkEwAQkdZ8WK5LF2zQz5/9QJcu2KA1H5YHOyS0w9PQC8Z8hieSTwBAxGHppvB06tCLlvcRPkg+AQBhqTNd5izdFP78NfQC1mOpJQBA2CnY9pUeWrezw1c7YukmIHho+QQQNEz2QEc1J55Sx7rMWboJCB5aPgEEBdfpRme01WXuS/I4Jae3fvPXk+tEvpU3WgN6nuHPEAG0gZZPAJZjsgc669QldjrbZc74QcA6JJ8Ia95029K1G3qY7IHOmjdhkOv/dJkD4YVud4Qtb7pt6doNTUz2QGddNyxTv3v9U0l0mQPhpkMtn0uWLFFWVpbsdrtycnL07rvvtll248aNstlsrW6fffZZh4MGvOm2pWs3dDHZA/4Uql3m9LoAnvmcfK5Zs0azZ8/Wgw8+qJKSEo0cOVLjx49XeXn7V4bYvXu3KioqXLezzz67w0HDP8L5xOhNty1du6GN63SjM7bu/VewQ2gXV08C2uZz8vnkk0/qtttu0+23365BgwZp0aJF6tOnj5YuXdrufqmpqUpPT3fdoqOjOxw02uZtQhnuJ0ZP1/g9tdvWmzIIDaHacoXQNXNVSbBDaBO9LkD7fEo+6+vrtW3bNo0bN85t+7hx47R58+Z29x02bJgyMjI0duxYvf32275HitPyNqHsCidGb7pt6doFupZK53GftgcLvS7orErn8bDtmfSGT8lnVVWVTpw4obS0NLftaWlpqqys9LhPRkaGli9froKCAhUWFmrgwIEaO3as3nnnnTZfp66uTtXV1W43tM+XhLKrnBi96balaxfoOvYdrvG4vfxfoXXuotcFnXXFk5vCtmfSGx2a7W6zuX+rjDGttjUbOHCgBg4c6Lqfm5ur/fv3a+HChRo1apTHffLz8zV//vyOhBax2ksoT23p64ozjb3ptqVrFwhv/Xokedzet3tonbuae12aF7Cn1wW+OrUhadQ5PbvU58enls+UlBRFR0e3auU8dOhQq9bQ9lxyySX6/PPP23x87ty5cjqdrtv+/ft9CTMi+fJLm+5oAOGorR+QofjDkl4X+Es49kyejk/JZ1xcnHJyclRUVOS2vaioSCNGjPD6eUpKSpSRkdHm4/Hx8erWrZvbDe3zNaHkxAgA1gjF5BjhI9x7Jj3xuds9Ly9P06ZN0/Dhw5Wbm6vly5ervLxcM2fOlHSy1fLAgQN64YUXJEmLFi1S//79NXjwYNXX12vVqlUqKChQQUGBf48EHb5OMSdGILJVOGtVVlWjrJQkekCAENJVeyZ9Tj6nTp2qw4cP65FHHlFFRYWys7O1fv169evXT5JUUVHhtuZnfX297rvvPh04cEAJCQkaPHiwXn/9dU2YMMF/R4FWSCgBeIOrgAGhq6tevatDE47uuOMO3XHHHR4fW7lypdv9OXPmaM6cOR15GQBAALW1SkZXm9wAhKuu2pDUoctrAgDCX1dZdq2rCOerzgG+6FDLJwAg/HXFZdfCFcMfEElo+QSACMWya6GhK1x1DvAFyScARDCWXQs+hj8g0pB8AgAkdd3JDaGOy3Ei0pB8AkAXxOSV8MHwB0QaJhwBQBfD5JXw09GLhPiKCwogFJB8AkAXwtqd4S9Qwx/4UYJQQbc7AHQhTF6BpyEXzKhHKKHlEwC6ENbujGxttW6296OEFnFYjZZPIAxUOo8zeQReYfJK5GqvdZMZ9QglJJ9AGLjiyU36+bMf6NIFG7Tmw/Jgh4MQFyprdzLj3lqna93kR4nv+AwHBt3uQBiwavIIM2G7nmCt3cnkFuudbsiFFTPqK53H/f6cwcJnOHBo+QTCTKAmj6z5sFyXLthACys6jcktweFL62YgfpSs+bBcVzy5yXW/YNtXfn8Nq/AZDiySTyDMBGKcFida+BMz7oMnWEMuTj2HSNJD63aG7TmEz3BgkXwCYSRQ47Q40cKfmNwSGqwccuHpHNJkFLbnED7DgUXyCYSRQLVkcKKFPzG5JfJ4OodE2RS25xA+w4FF8gmEkUC1ZHCihb+Fyox7WOPUc4gkzZ80OKzPIXyGA4fkEwgxzUt7WD1rlBMtAiVYM+5hrZbnEE/3wxmfYf9iqSUghJy6tEewcKIFAAQKLZ9AiPA04xxA6GMhcsA3tHyiU1iU3H88zRYFENpYiBzwHcknfNaccG4/4NTv//czTrp+4unqJABCV1vr4446p6ccCbHBDQ4IYSSf8EnLX/ktBfqyj5GgebZo8+XvSESB0Nbe+rjn93EEJyh0SV2tl5Exn/CapytYtMSi5J3Xcnboq7MuDWIkAE6H9XFhha546WOST3jtdGMSOen6V1o3ZpwjtEX6RBvWx0WgVTqPd8lLH5N8wmuefuU346QLRJau2BrTEayPi0Dad9jz0I5te48EJyA/IfmE1zz9ym/GSTdyRHprF9qeaBPpnwnWx4W/9evhudHn7pdKwvoHH8knfNLWmEROupGB1i5I7U+0AeA/6Q57q8uWSuH/g4/kEx3GmMTgCFbLI61daMZEG8A6bV2mNJx/8HUo+VyyZImysrJkt9uVk5Ojd999t93ymzZtUk5Ojux2uwYMGKBly5Z1KFgg0s0r3B60lkdau9CMiTZA8IXzDz6fk881a9Zo9uzZevDBB1VSUqKRI0dq/PjxKi/3/EewrKxMEyZM0MiRI1VSUqJ58+bp7rvvVkFBQaeDB7qyf1Yfb7VtbenBoLU80tqFlphoAwRPuP/g83mR+SeffFK33Xabbr/9dknSokWL9Le//U1Lly5Vfn5+q/LLli1T3759tWjRIknSoEGDtHXrVi1cuFBTpkzpXPQBUuGsVdGuSu04UK1jdY1KjIvRmUmxOnKsQcfqGiWp1TZP98+w//vt/fUr2xUTFdXuPp6eNy7G/fdB/vpPFRsd5fF5vz5a59r+x41fqKK6zqvnbes58td/qsS46DaPaeHfdrs9R31jk+t1fInldPfb2seb97dlmZbHU13b4DG+jta1t/t09P1tywlj9Nhru5QYH9PpeNt6r1qWGXFWD733xWFXuUvP6qH/LtrTofeuZR3kr9+lIzUNXsXv7zppWebU71tHPh+nfrdafi/8Ha83nzNfzwXextvy8/L0hs9bff8C8T60/My0VUe+vHftfeY7ex5qqw468/3z5r1r7xwT6M9my9c+3XH74zv661e2u72ep78D3tRbW+93Z8t05pzY1jE2u3lEf23bd0Tv7vm63eetP2E0ICVJV5yXFlKJqs0Y4/U1VOrr65WYmKiXX35ZP/7xj13b77nnHpWWlmrTpk2t9hk1apSGDRump556yrXtlVde0U9/+lMdO3ZMsbGnvwRZdXW1HA6HnE6nunXr5m24HbJmyz799i/bAvoaAAAAVqmLjtPvfzI04D0U3uZrPrV8VlVV6cSJE0pLS3PbnpaWpsrKSo/7VFZWeizf2NioqqoqZWRktNqnrq5OdXX//gVVXV3tS5gdVuGs1W//sk1rX3vQktcDAAAItOuufkxzC7eHzCWwOzThyGZzH/hljGm17XTlPW1vlp+fL4fD4br16dOnI2H6rKyqxpLXAQAAsFKTUchMEPWp5TMlJUXR0dGtWjkPHTrUqnWzWXp6usfyMTEx6tGjh8d95s6dq7y8PNf96upqSxLQrJQk1UXH6bqrHwv4awEAAFihLjpOUTaFzARRn5LPuLg45eTkqKioyG3MZ1FRka699lqP++Tm5urVV1912/bmm29q+PDhbY73jI+PV3x8vC+h+UWGI0G//8lQ3V/geYAvAABAuLFJyp88JCS63KUOzHbPy8vTtGnTNHz4cOXm5mr58uUqLy/XzJkzJZ1stTxw4IBeeOEFSdLMmTP19NNPKy8vT7/4xS9UXFysFStWaPXq1f49Ej+ZelFfjTqnp97a9U/tOODUsfoWs9FqGnSs/pQZa99ta+t+faNRXIzNNZO3vX3aet6+PRLlSIiVs7ZBh7+tV1yMrc3nlaS+PU7+sik/fOy0z9tc7tTnODV2T8dU32jU44w4t9dq+Tq+xNKR98Xb97dlvKcez6nxdaauvd3H1/fXkXDyR1pz/bd8z0895s7G29Z75U2Zjrx3PZPtGpSRrE8PHtXX3x73ap9A1EnLMs2fiVPfa1+/s+3t58942/ucdeRc4Eu8p/v+BeJ96Jls16Xf76GD3xxXWVVNqzry9b3zx+fZl/NxZ79/3rx37Z1jAv3ZbD7m5r9Z3r5OR76jzefAtv6WeVtvHTnfBeqceOrf/FOP0dN56XTHOKBnksYOCq3Z7j4nn1OnTtXhw4f1yCOPqKKiQtnZ2Vq/fr369esnSaqoqHBb8zMrK0vr16/Xvffeq2eeeUaZmZlavHhxyC6zJJ1sAZ2W2z/YYQAAAHQ5Pi21FCxWLrUEAAAA33mbr3FtdwAAAFiG5BMAAACW8XnMZzA0jwywarF5AAAA+KY5TzvdiM6wSD6PHj0qSZYtNg8AAICOOXr0qBwOR5uPh8WEo6amJh08eFDJycntXknJX5oXtd+/fz8TnMIUdRj+qMPwRx2GN+ov/Fldh8YYHT16VJmZmYqKantkZ1i0fEZFRal3796Wv263bt34woU56jD8UYfhjzoMb9Rf+LOyDttr8WzGhCMAAABYhuQTAAAAliH59CA+Pl4PPfRQUK4vD/+gDsMfdRj+qMPwRv2Fv1Ctw7CYcAQAAICugZZPAAAAWIbkEwAAAJYh+QQAAIBlSD4BAABgGZLPUyxZskRZWVmy2+3KycnRu+++G+yQ8J38/HxddNFFSk5OVmpqqq677jrt3r3brYwxRg8//LAyMzOVkJCgMWPGaOfOnW5l6urqNGvWLKWkpCgpKUmTJk3SV199ZeWhQCfr02azafbs2a5t1F/oO3DggG666Sb16NFDiYmJuuCCC7Rt2zbX49RhaGtsbNSvf/1rZWVlKSEhQQMGDNAjjzyipqYmVxnqMLS88847uuaaa5SZmSmbzaa1a9e6Pe6v+jpy5IimTZsmh8Mhh8OhadOm6ZtvvgnMQRm4vPTSSyY2NtY8++yzZteuXeaee+4xSUlJZt++fcEODcaYK6+80jz//PNmx44dprS01EycONH07dvXfPvtt64yCxYsMMnJyaagoMBs377dTJ061WRkZJjq6mpXmZkzZ5pevXqZoqIi89FHH5nLL7/cnH/++aaxsTEYhxWRtmzZYvr372+GDh1q7rnnHtd26i+0/etf/zL9+vUzN998s/nggw9MWVmZeeutt8wXX3zhKkMdhrbf/e53pkePHua1114zZWVl5uWXXzZnnHGGWbRokasMdRha1q9fbx588EFTUFBgJJlXXnnF7XF/1ddVV11lsrOzzebNm83mzZtNdna2ufrqqwNyTCSfLfzgBz8wM2fOdNt27rnnmgceeCBIEaE9hw4dMpLMpk2bjDHGNDU1mfT0dLNgwQJXmePHjxuHw2GWLVtmjDHmm2++MbGxseall15ylTlw4ICJiooyb7zxhrUHEKGOHj1qzj77bFNUVGRGjx7tSj6pv9B3//33m8suu6zNx6nD0Ddx4kRz6623um2bPHmyuemmm4wx1GGoOzX59Fd97dq1y0gy77//vqtMcXGxkWQ+++wzvx8H3e7fqa+v17Zt2zRu3Di37ePGjdPmzZuDFBXa43Q6JUndu3eXJJWVlamystKtDuPj4zV69GhXHW7btk0NDQ1uZTIzM5WdnU09W+TOO+/UxIkTdcUVV7htp/5C37p16zR8+HBdf/31Sk1N1bBhw/Tss8+6HqcOQ99ll12mv//979qzZ48k6eOPP9Z7772nCRMmSKIOw42/6qu4uFgOh0MXX3yxq8wll1wih8MRkDqN8fszhqmqqiqdOHFCaWlpbtvT0tJUWVkZpKjQFmOM8vLydNlllyk7O1uSXPXkqQ737dvnKhMXF6czzzyzVRnqOfBeeuklbdu2TVu3bm31GPUX+v7xj39o6dKlysvL07x587Rlyxbdfffdio+P1/Tp06nDMHD//ffL6XTq3HPPVXR0tE6cOKHHHntMN9xwgyS+h+HGX/VVWVmp1NTUVs+fmpoakDol+TyFzWZzu2+MabUNwXfXXXfpk08+0XvvvdfqsY7UIfUcePv379c999yjN998U3a7vc1y1F/oampq0vDhw/X4449LkoYNG6adO3dq6dKlmj59uqscdRi61qxZo1WrVunFF1/U4MGDVVpaqtmzZyszM1MzZsxwlaMOw4s/6stT+UDVKd3u30lJSVF0dHSrDP/QoUOtflEguGbNmqV169bp7bffVu/evV3b09PTJandOkxPT1d9fb2OHDnSZhkExrZt23To0CHl5OQoJiZGMTEx2rRpkxYvXqyYmBjX+0/9ha6MjAydd955btsGDRqk8vJySXwHw8GvfvUrPfDAA/rZz36mIUOGaNq0abr33nuVn58viToMN/6qr/T0dP3zn/9s9fxff/11QOqU5PM7cXFxysnJUVFRkdv2oqIijRgxIkhRoSVjjO666y4VFhZqw4YNysrKcns8KytL6enpbnVYX1+vTZs2ueowJydHsbGxbmUqKiq0Y8cO6jnAxo4dq+3bt6u0tNR1Gz58uG688UaVlpZqwIAB1F+Iu/TSS1stb7Znzx7169dPEt/BcHDs2DFFRbn/6Y+OjnYttUQdhhd/1Vdubq6cTqe2bNniKvPBBx/I6XQGpk79PoUpjDUvtbRixQqza9cuM3v2bJOUlGT27t0b7NBgjPnlL39pHA6H2bhxo6moqHDdjh075iqzYMEC43A4TGFhodm+fbu54YYbPC450bt3b/PWW2+Zjz76yPzwhz9kiZAgaTnb3RjqL9Rt2bLFxMTEmMcee8x8/vnn5s9//rNJTEw0q1atcpWhDkPbjBkzTK9evVxLLRUWFpqUlBQzZ84cVxnqMLQcPXrUlJSUmJKSEiPJPPnkk6akpMS1DKS/6uuqq64yQ4cONcXFxaa4uNgMGTKEpZas8swzz5h+/fqZuLg4c+GFF7qW8UHwSfJ4e/75511lmpqazEMPPWTS09NNfHy8GTVqlNm+fbvb89TW1pq77rrLdO/e3SQkJJirr77alJeXW3w0MKZ18kn9hb5XX33VZGdnm/j4eHPuueea5cuXuz1OHYa26upqc88995i+ffsau91uBgwYYB588EFTV1fnKkMdhpa3337b49++GTNmGGP8V1+HDx82N954o0lOTjbJycnmxhtvNEeOHAnIMdmMMcb/7akAAABAa4z5BAAAgGVIPgEAAGAZkk8AAABYhuQTAAAAliH5BAAAgGVIPgEAAGAZkk8AAABYhuQTAAAAliH5BAAAgGVIPgEAAGAZkk8AAABYhuQTAAAAlvn/N4xk8T3j9VkAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig=plt.figure(figsize=(8,6), dpi= 100, facecolor='w', edgecolor='k')\n", "plt.subplot(211)\n", "plt.title('original')\n", "plt.stem(xp, markerfmt='.', linefmt='gray');\n", "plt.subplot(212)\n", "plt.stem(sol.x, markerfmt='.');\n", "plt.title('reconstruction');" ] }, { "cell_type": "code", "execution_count": 38, "id": "d9250905", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "8.3 ms ± 511 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n" ] } ], "source": [ "%timeit yall1.solve(A, b0p, nonneg=True).x.block_until_ready()" ] }, { "cell_type": "markdown", "id": "eca778f8", "metadata": {}, "source": [ "### Non-negative basis pursuit denoising\n", "\n", "The simple form of L1-L2 unconstrained minimization with non-negative $x$ is:\n", "$$\n", "{\\min}_{x} \\| x\\|_{1} + \\frac{1}{2\\rho}\\| A x - b \\|_2^2 \\; \\text{s.t.} \\, x \\succeq 0\n", "$$" ] }, { "cell_type": "code", "execution_count": 39, "id": "9e8bbd6a", "metadata": {}, "outputs": [], "source": [ "bp = b0p + noise" ] }, { "cell_type": "code", "execution_count": 40, "id": "750c4934", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "DeviceArray(27.43652935, dtype=float64)" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "crs.signal_noise_ratio(b0p, bp)" ] }, { "cell_type": "code", "execution_count": 41, "id": "0246ec43", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "iterations 28\n", "n_times 57\n", "n_trans 30\n", "r_norm 1.898381e-01\n" ] } ], "source": [ "sol = yall1.solve(A, bp, nonneg=True, rho=0.01)\n", "print(sol)" ] }, { "cell_type": "code", "execution_count": 42, "id": "11d9a1e8", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "DeviceArray(27.55570803, dtype=float64)" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "crs.signal_noise_ratio(xp, sol.x)" ] }, { "cell_type": "code", "execution_count": 43, "id": "06d3342b", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig=plt.figure(figsize=(8,6), dpi= 100, facecolor='w', edgecolor='k')\n", "plt.subplot(211)\n", "plt.title('original')\n", "plt.stem(xp, markerfmt='.', linefmt='gray');\n", "plt.subplot(212)\n", "plt.stem(sol.x, markerfmt='.');\n", "plt.title('reconstruction');" ] }, { "cell_type": "code", "execution_count": 44, "id": "360e9861", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "6.48 ms ± 793 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n" ] } ], "source": [ "%timeit yall1.solve(A, bp, nonneg=True, rho=0.01).x.block_until_ready()" ] }, { "cell_type": "markdown", "id": "6e229a3b", "metadata": {}, "source": [ "### Non-negative basis pursuit with inequality constraints\n", "\n", "$$\n", "{\\min}_{x} \\| x\\|_{1} \\; \\text{s.t.} \\, \\| A x - b \\|_2 \\leq \\delta \\, \\, \\text{and} \\, x \\succeq 0\n", "$$" ] }, { "cell_type": "code", "execution_count": 45, "id": "9ef19b83", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "iterations 24\n", "n_times 49\n", "n_trans 26\n", "r_norm 1.915944e-01\n" ] } ], "source": [ "sol = yall1.solve(A, bp, delta=delta)\n", "print(sol)" ] }, { "cell_type": "code", "execution_count": 46, "id": "36e568ec", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "DeviceArray(25.37898646, dtype=float64)" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "crs.signal_noise_ratio(xp, sol.x)" ] }, { "cell_type": "code", "execution_count": 47, "id": "a4e11f7a", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig=plt.figure(figsize=(8,6), dpi= 100, facecolor='w', edgecolor='k')\n", "plt.subplot(211)\n", "plt.title('original')\n", "plt.stem(xp, markerfmt='.', linefmt='gray');\n", "plt.subplot(212)\n", "plt.stem(sol.x, markerfmt='.');\n", "plt.title('reconstruction');" ] }, { "cell_type": "code", "execution_count": 48, "id": "62c8f30f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "6.37 ms ± 334 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n" ] } ], "source": [ "%timeit yall1.solve(A, bp, delta=delta).x.block_until_ready()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.8.13" } }, "nbformat": 4, "nbformat_minor": 5 }