From e1c2e8dd5e93c4fe53fc6a45c856887a2394adfb Mon Sep 17 00:00:00 2001 From: Marina von Steinkirch Date: Sun, 21 Aug 2016 12:34:15 -0700 Subject: [PATCH] Add numpy nn example --- Numpy/nn_case_study.py | 25 ++++ Numpy/nn_simple.ipynb | 307 +++++++++++++++++++++++++++++++++++++---- 2 files changed, 308 insertions(+), 24 deletions(-) create mode 100644 Numpy/nn_case_study.py diff --git a/Numpy/nn_case_study.py b/Numpy/nn_case_study.py new file mode 100644 index 0000000..49f6c02 --- /dev/null +++ b/Numpy/nn_case_study.py @@ -0,0 +1,25 @@ +#!/usr/bin/env python +# Adapted from: http://cs231n.github.io/neural-networks-case-study/ + +import numpy as np +import matplotlib.pyplot as plt + +N = 100 # number of points per class +D = 2 # dimensionality +K = 3 # number of classes + +# data matrix (each row = single example) +X = np.zeros((N*K, D)) +# class labels +y = np.zeros(N*K, dtype='uint8') + +for j in range(K): + ix = range(N*j,N*(j+1)) + r = np.linspace(0.0,1,N) # radius + t = np.linspace(j*4,(j+1)*4,N) + np.random.randn(N)*0.2 # theta + X[ix] = np.c_[r*np.sin(t), r*np.cos(t)] + y[ix] = j + + +# visualize the data: +plt.scatter(X[:, 0], X[:, 1], c=y, s=40, cmap=plt.cm.Spectral) \ No newline at end of file diff --git a/Numpy/nn_simple.ipynb b/Numpy/nn_simple.ipynb index 5173aab..338206c 100644 --- a/Numpy/nn_simple.ipynb +++ b/Numpy/nn_simple.ipynb @@ -2,7 +2,112 @@ "cells": [ { "cell_type": "code", - "execution_count": 2, + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "iteration 0: loss 1.100414\n", + "iteration 10: loss 0.908604\n", + "iteration 20: loss 0.836994\n", + "iteration 30: loss 0.804308\n", + "iteration 40: loss 0.787222\n", + "iteration 50: loss 0.777453\n", + "iteration 60: loss 0.771512\n", + "iteration 70: loss 0.767734\n", + "iteration 80: loss 0.765252\n", + "iteration 90: loss 0.763578\n", + "iteration 100: loss 0.762428\n", + "iteration 110: loss 0.761624\n", + "iteration 120: loss 0.761055\n", + "iteration 130: loss 0.760649\n", + "iteration 140: loss 0.760356\n", + "iteration 150: loss 0.760143\n", + "iteration 160: loss 0.759988\n", + "iteration 170: loss 0.759874\n", + "iteration 180: loss 0.759790\n", + "iteration 190: loss 0.759728\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "#Train a Linear Classifier\n", + "\n", + "# initialize parameters randomly\n", + "W = 0.01 * np.random.randn(D,K)\n", + "b = np.zeros((1,K))\n", + "\n", + "# some hyperparameters\n", + "step_size = 1e-0\n", + "reg = 1e-3 # regularization strength\n", + "\n", + "# gradient descent loop\n", + "num_examples = X.shape[0]\n", + "for i in xrange(200):\n", + " \n", + " # evaluate class scores, [N x K]\n", + " scores = np.dot(X, W) + b \n", + " \n", + " # compute the class probabilities\n", + " exp_scores = np.exp(scores)\n", + " probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True) # [N x K]\n", + " \n", + " # compute the loss: average cross-entropy loss and regularization\n", + " corect_logprobs = -np.log(probs[range(num_examples),y])\n", + " data_loss = np.sum(corect_logprobs)/num_examples\n", + " reg_loss = 0.5*reg*np.sum(W*W)\n", + " loss = data_loss + reg_loss\n", + " if i % 10 == 0:\n", + " print \"iteration %d: loss %f\" % (i, loss)\n", + " \n", + " # compute the gradient on scores\n", + " dscores = probs\n", + " dscores[range(num_examples),y] -= 1\n", + " dscores /= num_examples\n", + " \n", + " # backpropate the gradient to the parameters (W,b)\n", + " dW = np.dot(X.T, dscores)\n", + " db = np.sum(dscores, axis=0, keepdims=True)\n", + " \n", + " dW += reg*W # regularization gradient\n", + " \n", + " # perform a parameter update\n", + " W += -step_size * dW\n", + " b += -step_size * db" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "training accuracy: 0.51\n" + ] + } + ], + "source": [ + "# evaluate training set accuracy\n", + "scores = np.dot(X, W) + b\n", + "predicted_class = np.argmax(scores, axis=1)\n", + "print 'training accuracy: %.2f' % (np.mean(predicted_class == y))" + ] + }, + { + "cell_type": "code", + "execution_count": 28, "metadata": { "collapsed": false }, @@ -10,18 +115,18 @@ { "data": { "text/plain": [ - "" + "(-1.8987463970374139, 1.9412536029625895)" ] }, - "execution_count": 2, + "execution_count": 28, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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7AA/esr8czZBbtmwRRoYmooyLt3B3bSfsbUuKqlU8xcuXLzPrREdHC7/mrYSe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\nU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+7616+A8CrT4fuLNx5zKdHkOpDkt7WyRJolRbSMLeI5jKygiIqouduwuTGxpY\n9c6PvPXTKVo2HoOdjRsmUxlxF9ZRmL+L47MeR6G4s1TDu73wLcsyecU6Aj/8kdLSjajVKmJjzzJt\n2iJiYuLJzS1ElmUGDuzAjBnPs2vXCYY/+xFzHm1Bj8igv68A86ZC/lOpRQUEty1kRkb0fU8SSCso\n4sv9J9ibkoFklLlcVMKBmK/x8yvPRPrgg4Xs3xfHU0M78emnyxk0qAOzZi3j/PmfK5ZHBti48RDj\nRs5m5/De97X9QjnRk/+nLmZhe7G8h98u2JVorIEy1iWo0OqzAdUDF+zvpD26omI2fTqXU1uiQZKw\ndXIitGUUx9ZvxtOtJkqlhp2fL6bRgB5MpheL112iTsRT2NmUT3FXKFTUCu3F+r0xDEl1x6/hnX09\nn/yo4V9dgzCaTHy6+xhzD54iI68QBwcbli6NZvDgR2jUqAbLl7/HxYtXqF//ed54oz/z52/g++9/\nJzTUh2BH2zsK8A9KKmRV8bK3YWrna0s4fLH3OHUjn+GRjg3R6wxs2X6Ezp0bo9WWEBbmg4uLA82a\n1awU4AGaNavJ+XRzDWcK5iSC/N+5mEW7q7+2U0BhA38mx3I12ANIZh3GuVfKdHoW/W8CqgJberX/\nCEuNHenZ8USv/owGNfsRHtQRgJIa+WxcMZXg+vUpyMjCOaxy1pIkSTjbB6DLLMZO4/K39Wr1+Uw+\nDLRq87dlb7Tnq59RFBaxZddsIiMD+eKLlYwYMYu0tGy6dIni1KmLjB37LY0a1WDixKE8/3wPwsOf\npv8TbcnacfJvz28a3Zzes6rXxdS79XKLuvSvG8qWc5dRWVgyZdQTtJ23ktGv9WPs2G8ZPrwb+/ef\nxmg0Vgr0+/bFEeohXsMHkRiuuQvlAf/6z8kHL+DLssyen5ay96clYFRiNOrx925MkzpDUassuJR6\niAPHF1AzuDMRwV1QqyyIT9yK1vkiRdl5+GtaEuR7radnkk2s3jGGJz99F++at1xjziyKcvOYO/BZ\nLiUsxNn5Wq/6hx/+YOzYb3F1dcDX1w17exvCwnx4//1nGDZsBmVlRrZuO8z0RWMIrnnzJJ8/rUtQ\nX+2933kqpK5Ey5mDf5B9/gTWLh6Et3gMJ/fbz924lcL8TOIP/E5JTjouQbUIbdCRTIO+yoZr7sS3\nB07x/o5Yatb0p7hEj0Ih0bx5JB9++AJ2dtacOJFArx7jmdS8Hn3rhlZ1c/+TxHDNPWJ7JImPFVRk\n6byZYH+dZ/KFAAAgAElEQVRdD5876unea4d+W82xZVt4tPkk7G090OmLOHTiZ/Ye+Za2US/j4RqB\n0WggO+8iW/d9RKeWY7GxciElPZa2Lw5m1YSZWFrY4ekaiU6v5XD8UlyCfO5pgAfITLxEzcigSgEe\nYNiwRxk1ag4XLiyitFRPePhQMjJy8fLqh1KpQFtUSrvXRxBnUYO4hFuf+3y0GoWkxNf2zodktLnp\nrJ09kjCdFa0MdqQpklm7fz2tBo0luG7bOzrH5fhDbPvhXZrIboSVWXDs2GGOb/yJqBdmAJo7bsv9\nppSgRqgPTZtFsnLlbvR6A8uX72LBgk24ujpQXKxDV1xK14iAqm6qcAsiyJvD1SydjxVZN6RlZnPj\nXin3s6cvyzJ7f1pGq1ovYW9bvjephcaGZvWfZfmm19AWZaItSsfOxp22US+zcc90klJjSL5yBKOt\ngZAmjeg2/hW2fv4DhbHZgExkh7Z0eeO1v67YDOzdXEm4kILBUIZafe1tmpiYhlqt5OOPlzB//gY6\nd27MmjX7mDnzBcaOnYfRCCUpWdiq7JBus5CWQtL94zH3gyu/oE2RA48TWP4nlaGxwZmPf5mBX0RT\n1Jq/zt4xGsuI/vl9XjGEEy45gQQdDbC0LIEz678jssdL/6g999P6C8m8/d5Q+vRpwx9/HOS33yYR\nFRVBTk4BOTlaAgI86N7pLVacuEA9b1f8HO3+8cQs4d4RQd7cbpOWCVzN1rk+8N86H99cjAYDhXk5\nuDoFVzquUmpwsvcjI+csp86tp1ZoVyRJQaBPU06dX09JaT5l6Tp+fX0SfT4YS0TblpQWaFFbWqKy\nuD89Tmc/H9xCgnh77HfMnPE8KpUSrbaYkSNnExHhj1ZbwrJlk9i3Lw6ttpjdu0+gVCp58sk2HD4W\nw4FfrWk2qJ9Z2iLLMgmn9/Ky3LzSZ3agZI+THuaPe5TQyFY06fMKdk4e6Eq0JJ+NQZbBM7A2NvYu\npCUcx8moLg/w1+lm8mPLmX3I8oO78qpCkigrK88+Kigoxt3dEQBnZ3ucne3R6fSkpOfy1qEzBPi4\nkZScRccwX6Z2bkqA03/jAvaDTAT5e8j2SOX1dNpxZ/n45qJUq7F1dCY7LxEXx2uZJkajnqy8BLLz\nEqlToyfBfq0AKCnNAxS4OAVzJfMUJUmlbPzkG3pOeA0rh/v/n7X7xLdZ9950FvkPpEaEP4cPnMLR\n0Za5c18nLMyHlSt3M2XKzwDY2lry6qt9+eyzFURHz6JDl/E0Hdj3nm9RaIWKF6lFUtxl1iaNpHaH\ngcSs/xYnWUOOqYgyZNSSCkmpwK1MfdMmmEokTLKJj/2yKNnz4I3HAzwW5s+cWb/x+OOteOSRhixe\nvI1x465tav7yy3Pw8XNj05aPePfdH0lduYtETLT4ZgWPhgcwp0crbG5YFkG4fx7Md1U1ZnskqeLn\n4+ACegQb6BFcCpRVGs83B0mSaDG0H/tOzqegsHySi05fxK7Dc5GQ6NxiHLXDeiBJEkUl2Zy/tANX\npxBy8y/h7xWFi10Ip7buwFBaesvzl+n1XDgQQ/yufZQWFpm17QA2To48OXsGfWd9iP9j/bBxcqRH\nj+ZMnbqQNm1eZfr0xSiVShQKBYGBXowfP5iCgmJq1w5Cm5tPmU5/120oLS7g6NaF2FrYsVm6XOm+\nS7KWKxRTDxf6SMF4lUgcXf8dDY2OOJmU1MQJL6xxlFW0L3Mnh1JSru2fA0A0Kdip1Pz49uq7buu9\nMqB+GI7Fepo1HIG/vzszZ/7K+PHfcfToeRYv3sKiRVv45ZcJzJjxKzk5BVy8+AtHj31H6pVlKIM9\neWuDWMKjKomefFW6Pj3zaj5++XDOn+4uH1+WZfJSMyjIv8K66AmoVZboDcV4utUiwKcJm/ZNx8+j\nETImktJikGUTpbp8Orccz9Ezy7G0sEOpVFOqLUJtWXnM+cLBWFZOnIGdtTsqlQWrsmfS4aVniOr3\n2L9u7+2U5BcQv2UbZToda9fuY8uWj4iMDKS4uJSPPlrCvHnriIwMYPnynbRsWYvY2LM4ubvc9dBS\nUUE2qz4eTniJht4mD5ZzgWQKaYw7KRSxi1SGEo5aKv8mpjAaaYsH0aTwBCHsJI3hRPI5x+lLKD7Y\n8jFHeUT2xQdbTpDNYTIZYAhj/Oq92Fqq6V7zziZv3U9qpZJF/R9hQ/wlNm47RrdQX06tP8jghVuw\nVCrwdnfC0lLDTz9tIj5+QcWOXDY2Vnw173WC/J5k6iNNcP4Hs44F8xFB/kFxNeC3u/rdKjrQn3UJ\nd5ePf2TtBs5vi6VPp1molRYUlWSTnhXPsbOraBs1k9SM4+jssyhK0dKj3QfY2bihkBTka9NIST9K\niF9LVBZqbJwdK51Xm5XN8vHTaFv/FTxcy5fv1Rals2neh7iHBBLQoO7dvRbXiVm+hsO/LGHcmCcJ\nG9WR6dMXExU1kqAgL7KzCwgN9aF+/RAKC0t58cVPmTPnZQYMnEqDfr3/9VBNVup5Dqz4nPTEEzTH\ng6FSBEhwRs4lhgyuUIwNKsbSEC/JpuJx+ehRIeGNDSfI4RF80aLHA2sUkkQLvFDIEos4SzD2BGLP\nJKJwlCzQGBTM3BT7QAZ5AKVCQfeaQTe1T6vTEzlrMXFxl7CxscTjaq58SUn5UgirVu1BY6Vhzu6j\njG3fGEu1CDn3m3jFH1DtLiZVBPw/8/H/acCPWbqO+qH9sNSUT/ixt/XC3taLhOS9pGacwM0pjIzL\nZzAZTGzcPQV/r8YoJCWJKfsI9W/HnsPf4l4zkDKdHo21VcV5j/+xFT/PRhUBHsDOxoNagd2I+W29\n2YJ8qbaQnfN+5NiRbwgOLl+3vGvXprz77g8cOHCaX36ZwJo1e5k+fTG+vm4YDEbGjPkWHz83jP9y\naeHstATWzXkFjaEMDQo6Ur77kUmWOUwmShTYoCadYnQYKx6XIBeQSTEJlA/hWKFCiYQfdlxCS6Fs\nwFYqH5eOxJmRUu1K9YbjyLdZ92aBuXvJzkLD041r8vorc8jNLeTcuWQCAjzo2nUsNjaWjBnzJLIs\nM2fWMvr9spGVgx9FrRQrVt5PYkz+IfDn+P2fPyCj1Wej1ef85cqYRTm52Nl43nTc3taTktI8cvOT\nMOpkuracSL3w3iQk7yU+cSs6fSGpmSeoU6Mnylxrlrz1fqXHF2ZmY2956/NqM813XeFi7FGaNIus\nCPB/GjWqF9HRR2nS5CX27z/NpElPk5NTgI2NJU2bRvDepKFcPnSI5FOnKc7Lv+P6ZFlm39JPaGiw\nxw0r1CgwUJ5VYkLGiAyYSKUIIzIzOcIk+SAT5QPM5DCN8eCCshA71OgoYyep2KEmCnc+4ShJshZn\nLEggnxsnIV5Ci2Qq36LvYTO5QxR22lL8fN0YMGAKn3yyFFmWWbv2A7p2bUq3bs1Yv3EGBntrVp+6\nzeQF4Z4RPfmHxcVryxJ/rMiisEF5ls5fpWV6R4aTkn6MiOBHKh5rMpWRmnECo7EMlcoChaGkoodv\nZenE0TMr0OsLaV5vGG7OYZjkjqzeMYaUuHh8Ist3ePSpE8He3auIlLtWGhJJyTqGe6NAsy3JrJNK\nKS6++aJvSYketVqFySSzffsR8vML+fzz0Ywe/TnR0cd4/PFWpJ+7wB/vTiG/oIianVrRctTTKK8O\nFZjkW+dw71s+m8yk0zTADw1KHNGwlouMkuugkhTUkB2RkSmhjDSKUSNxhSJ8sOVdovhCOkWtToM5\nseFH8tBhAqYTiztWgMxnHCcXHZYoWU4CveQg1JKCLLmEn4lHg5K2ny1DoZBoF+bDG+0b4udod8u2\nPkhUSgWPhPjh7WxFrXohTJu2iBkzRqC4bp6CUqlk2PPd2PzdBrFS5X0mgvxD6s/0zHZcS8ssD/jX\n0jIbDevBilenoVSqCfRuQlFpDjEnF6M3FKMvK8LTNRK94VpWjK9nA3bFfk29Go8Tn7gNN+cwFJIC\nD5cILsYdwz60fKEy3xa1KPt+MQdP/UTtkJ6olBacS4omPesAe96bjLe3eXqjJTXDqPPJN+zfH0ez\nZpFAeW976tSF2NhY8t13b9KoUQ1On05i5MhPeeWVPsyatZQPPljE/0b3IS+vkF9/3Y511hVMqxYy\nZfpAACYjcz46p9J6NdlpF7hwcCOWKLFGxSEyeIsGvMN+PiCGJrIH9mg4TAZWqLBDjQKJLnhjg4ov\nOYHOxgoXjyA0koq+cjA1cGA3V4ghgyjcKcKAJUoOkM458niDPTjJGjIpRQY8sKK3NggHNBw8nEG7\nU8vZPqov/k4PfqBvE+zDzIW/M/uL/xEXd4m8vMKbyuTmFmIlNhe578wS5CVJehSYTfnwz/eyLM+4\nRZk5QFegCBgmy/JRc9QtVA745Vk65ePnjRt682zwq0x6dyVLNy5AkpS4OoTQrN4zpGef4WLKfh5t\nPaHiPHp9IRIKHO19Sc08UXE8M/MCEWdLmNSgVUXP/bUdY5g0aTkrlr+DXm+gc20/JjR+jOJxiZwn\n0WzP7Z3QtnTr9Db9n2xPjUg/lvy6HZ1ez3vvDWPixB+Ij7+Ml5czzs52ZGTkYjSaKCgo5vjxBJYs\neZfAQE82bozhh++3k78pg+bu/kwb4cj4dl04H53Dn2vXnD+yjaZGZ46RxUaSsELFKhJ4nki+4RSb\nuYwNKiQkDJhQImFEZi9peGGDXqWk8eMvk5+dQm3JlVVyAiE4EIgdNqjZTzomTLxNQ46RTSB2vEAt\nVpOACgU56BhHIyyuZur4y3aUlpbx7K9baB/mg52FhhBXBzqF+T+QuzBFuDvRvYY/Hdu+Su9+bfj8\n85UMG9alYlmKrKx8vp6zgm+6tazilv733PUCZZIkKYCzQEcgFTgEDJBl+cx1ZboCL8uy3F2SpKbA\nZ7IsN7vN+R6aBcoeVMYrSeT8kUJKXuWZrjvTEll28Qw5+hKuFOUTGNSFOjXKUx5lWebA8R8xmUxo\n1FZIkoKGkf2JT9zK6YRNaCSJsbUa0sHn/i9AlV6sZX1yPIeyk7EOdWLD5hlYXJce+edyw7Is4+xs\nx86dn/Hccx/RuXNjRozoiYtLbxzsrXlqaGc2rj2Aq0HDzAaP4v1FbbqNOELepROkxB1CIcvIgEpp\ngdFkBEyAhMlUhkqpwVpW0NLkSjKFJKClPT6oJSW71dk4RzSg3VPvcun0Pk4v+pS3dDU5QDoZlOCF\nNZu5TA46xtKQTziKEolInIgli074osXAU1L5cJhJlvmZeA6QjhMWFKAnHCe0Sj0FGgO/PdONBj5u\nyLLMzoQUdiem4mRtSb+6objf4Sbe94LJJPPz4TMsPHGeizkFGJAZNqwLsgyLf97M0Ho1mNihcZW1\nrzq71wuUNQHOybJ8CUCSpF+BXsCZ68r0An4CkGX5gCRJDpIkeciynH7T2YR7po1XEG28ylPgLmlz\neXHPWpJSY3BxCiY9Ox61yhI/z4YcP7saRztfVm55Cwu1DR2bvUlW7gWWXdpcJUHew9qOZ2s0JiTV\nmd+Kz1cK8ABxcRdRKhX4+3vQtGlNJkyYz6RJTzN06HSeeqoTarWKwqJSSkv1LF31HqNHzeHlPas5\nV2M+zVpF8uSTdVmy5Apn4zMACZNchkIh4WgXgL6sFJPRgJ2NJ9riK2wsScPCypa6HV4gOT8TU5mB\nZvXa4h1SH0mS8I9oyiEbDX8Ykulu8kODgnjyyFPJ2Lj4sy79Inao6UMwp8lFAbhgSQrlw2YX5QLm\ncBwTMl3wJ55c3iWqvIdvgtiSTJ744XeOvDmQIT9v5HxqHnX1LhSoDEzbdIhv+renR2TwzS/ifaBQ\nSDzduCZPN64JwMkr2aw7Vv6tbvWgLkR6VP2Cff9F5gjyPsD1UwGTKQ/8f1Um5eoxEeSrSICdE2s6\nD+b3pHiWJpykqCgTo8mEZVk+gd5NCfJtjkqpwdUpFIVCQXFpDpf0VZv50cIzgFk79vDdt+t5bng3\nJEkiLS2bsWO/Y/bsUcTHX+bgwTPs3HmcMWOeJDMzn1df/RInJ1sKC0tYsGAjixdvZeLEIXxwfDGy\nSmLP3lNsjz4GqDGZZCQJJCQkSUluwWUsLRzQ6bWU6PPxdInA2602SWmxnD24gb6vfY1KXfkirkKp\notvLc9i1aDqbL+5Ho1ChsrSmZZ9x+NZoxPrPX0GfUcTvpiRepS77SccPW5ZynmNyFt8SRyB21MWF\nnaQxjAgSKWCLnEwmJfhgg3WZktfX7CQ3pZSJhsYoJQUYIVEuYMTS7cSN9cHBsuoXCKvt6UItD2fi\nM/Mo1OnRlRmxeACHmqo7cwzX9AW6yLL8wtXbQ4AmsiyPvq7MWmC6LMt7r97eAoyRZfnwLc4nv/tM\nh4rbbRsE0a5B1fRMHla3G675K/LVoYp9Vy4x/sgODEYjRlMZlhZ21KnxGFm5F8jNOMzqzkOwVFbd\n9frEghzePraRUo1MeLgfsbFnef31J5g48Sl0OgM+Pk+Ql1dIixa1MRqNnDp1kdde68fBg2eIjj6K\njY0VtrZWFBQUYWGhxs7OmuzsAvJyS7CxdsNkMmBr7U5OfiKOdv4UFKZhksvw9WxIdu4FtMWZSEgo\nlRosbOxo1GUo+pIikuNj0FjaENG0K37hUSQX5qIvzqdMX4qVvWvFipimMgNpcfspPriQ1ORcXLHC\nIJvogDeLOUcojlijohFuLOYcjxHIHyTRHX9AIolCDnIFOwsNL+hqESJVnhH9tfokzz9Wm4ENwu/5\n3yIlv5C0giLC3Bxv+aFyJiOXF1bvIKtUh5WVBSlp2fSICGB61xa4VeGwUnWwKyGFXYmpFbenb4u5\np8M1KcD1yy36Xj12Yxm/vylTYdKzHc3QLOGfkCQJCdh25SI2Nh60aPA8ttbuZOUmsDPmSwxlpdjb\netJn82I+atKFWs4eVdLOIHtnZjfsztP7fuOtt54kKiocF5fyQGdpqcHR0ZbgYG9iYuL5+OMXWb16\nD2+/PRB//wG0bl2XixevkJmZR8+ezVm//gBpadk4OdmhLdBjKCtBQkKlssDSwh6FQoksl3/YpaYf\nxcrKGZVSg6O9LzWDO5OnTWHP8jm4u9Qg1L8NpboCdvzyMZ71WhHRaTBLJ4BNho4b3+pZH5wlJWoA\nBY2Psv9KDocKSlgWn4imTIkftrhjxWYuY8TEahLpRRBruIg71lcv/UoU6gxY3+K/r7Wsolj/7yaC\n3amc4lJGrd3Fvktp+Pu6kXgpneeb1mJCu8YV+/6uPnWBUWt3M33G85w4kciqVXsY9lxX0tJyaPD5\nUmZ1a0H/evd2T4LqrHWwD62DfSpuT98Wc9uy5gjyh4BQSZICgDRgADDwhjJrgFHAEkmSmgF5Yjz+\nwZNVWsTG5HP06jQLjbp8ur6bcwhtGo9kV+zX1Artxomzqxm1dx2L2vfDx6Zq9rn1sLbFWlke0P8M\n8ACnTiVy5UoOv/46kaFDP2T37pNERPgzZMg0OnVqRGpqNu7ujiQnZzJqVG8MBiNnzlzm/Plk2neo\nw5bNx0GSKS7JQamwwMO1Btn5iQT5NudSygGUCjUatQ0lJXkcPP4ThrJS/Lwa0rrRtWWCA3ya8Meu\nsazsbeL80763eQbl37Dspfo8UzOBl0P8mLrlINHbLxNHDj1pyHIu8Ai+7OIKa7jIaOoSerXXniIX\n8gEx7JWu0JeQirMWyQaOylnMCW1n9tccyjf9vpCdz/RdR6jboQFL93+OlZUFqalZPN7zHZz3n+Dl\nFnWZHh3L/KNnaRQVjqOjLfv3xxEfvwA7O+uKv1Pr5q/QMtAbHwfbe9JW4Zq7nvEqy7IReBnYBJwC\nfpVl+bQkSSMkSXrhapnfgURJks4Dc4EHd4eE/7BEbQ6u9j4VAf5Prk6hlOgKKCsrxcrSkUD/1iw4\ndxSjbKqSdiolBS+GNqFfr3f57bdoUlOzWL16D127jmPcuEGEhHiTnJzJ6tW7WbBgI/7+7jz9dGdO\nn07ixIlEAgM9iYqKID09l8LCYurXD8XNzQFJUYbJZCRfm4q26AquDqHIJiPFxdl4u9clryAZpUKN\nSS5Do7Yt7+1LKk6eW09hcflkNUuNHb6ujZm/IPOOnktKXjBFFy7jptcjqSWsUTGf01ijohme6Cij\nKR4VAR7AR7KlHT7sUKTyq+IcZ+U8DsrpfKI+ylONIwh2Me+Hb6mhjBdX76DpV8sYt+8YJzJymPXZ\nKKyubgzi7e3KN9+9yVcHT5GaX8jX+0/yzPBuREWF89NPmxk7dlBFgAeoVSuIvv3asOz4ebO2U7g1\nswyuyrK8AQi/4djcG26/bI66hLt3oSCbS9pc/G2dCHW4lvHgYWlLVkEKp879jq2NK74eDVAq1WiL\nrqBSWhB/cRvhge2x0Nix7vAutqclMrxGI/oH177n67bfqKtfOHZqC94a9RU5pUXUrh3E7Nkv0aFD\nQwYP/gC1Uom9vTVDhjzCxYvpDBgwFWdnO/R6Az//PI4tW2I5duwCxcWlfPLJSAYN+oCwMB8uJ2Ug\nlckYjLAz9gsUChUlunwMRj1KpYrwoI6cvbgdjcYGbWEaarU1hcWZrIueSONaAwkNaINsMqBU3PkF\nxpS8YB4LMjD1YDyt8OIQGRRRhjtWWKLEi2sBMlkuJJtS3LGmvpcbEf7O/HE2CWcbC95v3pzetc1/\n/Wr85gOUeDpyactSdu8+wezZyyvt1gVQv34oyVn5bDl3mc6dGtG8eSTTpi1GkqjYZOR6Ht6uaC/e\n2QehcHfEjNf/EK1Bx5iDmziTn4ObYyBZ+XsJs3Pi4yadUUgSk45Eo1JZoy1KJyXjGDEnf6F1o5Ec\njluKQqHC2tKRIN8WnDi7hkCfZoQFtmN+7JdIEvQPrnPfn08rz0Cauvsx+8xe/jh+hsnjfuDZlBl0\n8A5lbdunWJ90hiXztpBeWohaoyYtNZt+T7Rl/Pjv2LPnJGVlJjp2bMjgwdNAlnHQKvii3VM4WpRP\nJjucmcxrBzehVKrJyU+ke5vJONr7cvTMckp0eciyiQtJO3B1CqVZvWfZe2QeMiYupcbQPvLGEcu/\nZq9R08nPnS0JV+hJINtIZjsptMWHGDJoJLvzDSfJogQvbDhHHh75NoQU29Mp0p/BjcIJdb05mN6t\nQp2BpUfPcS5xEXZ21kRGBhAbe5bi4lKsr1s6eNeu44R7u2KjUaPN1tK1a1MmTvwBGxtLFi3aQrt2\n9SvK6vUGli3eyqcdoszeXuFmd51dY25iMtTdu112zdhDm7mscKNx3WdQKJSYTEZiTizAu+wKjhoL\nThpsaNrgBcrnt8G5Szs4dGIhlhYONK4zGD+PeqRnn2Xnoc/p3HIcjva+ZOUmcPDQp/zx6FAU97k3\nf718fSmpRQV4WtvhZGF10/2yLHMy5wrrL58hu7QYO7WGEoUJg6GM2g4etPcOIcDO6abHxWYm8/Le\ntVhaudG744cUFF5h7fYJNKn7FIG+zZFkiD70GelZZ3B2CEBblIla1jM0rD7d/CPwtL6zJQkuF+bx\n9NZfeN/YFDtJwxW5mE84ghtWpFGMBUoa4UZfQtBh5GOOANAMT/KVOvZKV5jRqxWDGpo3qyYxp4Ce\nv2zgYspvFceGDJlGSYmOzz9/BW9vV2Ji4hn0xHu81TiSHpFB1P70FzZu+wSFQqJv30lkZOQxZEgn\nnn++O/n5RUyf8jNWuUUs7v/Iff8GWF391WQoEeSroVsF+QJ9Kd02/ESvzrPRqK99/TcYSli16X+Y\nZBM9O87E2uraei6yLLN2yxtoKKNUlv7f3nnHV13d//957sy62ZPsECABJGHIVkABoeLAVRxVq7U/\nba1V67Z1tfZba2tRO9zWqq17KwqyQVYYAUIGZJBJ9l53nd8fN5MMAgkZN+f5eOTBzb2f3PO+J+R1\n3/d93gOrlEgpmJ1wM+EhU9uue//rn7F2+U/x0A99bvbZ4JPMgzx7ZA/urn40NlVhl63ZKwJvj1Bq\nGoox6FwRGi0NjeUE+I5Dp9FTWp7KdWOn8IuJs065xv+OHSDpcCY3ynaRbpY21nCcDboCsEmek/PR\nCQ0fy0zKaeI2JraJZJGs50+6fRx+8IYBHc7RbLUR99d32bH3JWJjHdkcTU1m7rzzed5953vcjAY8\njHrun5/IzS1FUF+nZnPH55vR6PX86q6V3HDDYv7xj8/55JOt1NbUc/u0OO5bME21HB5AznbFq2IE\nUG1uwsXg1kngAfR6V1yN7lTWV+Bi7DzHVQiBydWHO2Ji+G9WCqmVxRgM7uw5/A4lFRmY3ANxdfHC\noNHjqnPOGZ6ljfX8My0Jf+8Y3Nz8KCo5zAXn3ou/TwyFJYfZuHs1k2MvJtBvPJt2v8DSeQ+3zdNt\naq7hs21PMdknsK3SuCf0Gi0WYYcOPlcGVSRTTpPVyhjhjq7lE1YSJdxB53OQEOHORI0v36Yf57oB\nzJE36rTcOXcKP77iMd585xGmTBlLZmYBh/Yf4675Cdw+azK+rka0HTpOXhwfzT2lVewSdh5//CYA\nnnvuFzz33C+465fPY07NVwI/iCiRHyUEu5mw28xU1eTj7dme2lddW4jV2kSc7xiOFyYRHdbeUqi+\nsZyymjxeSq/EO2gW18y+HJ3WQElFBht3rcbfO4by6mzGuLpjlxKtk33yNtus/L/tX1Jvt+Ou1VFw\n4gBGo6nt087R4xtJjLuSSbHLSTn2DVGhszoNTHcxehI37jI+ytl0SpFfEBLDCwe3USwbCBJu7JWl\nvEs61zGeUNz5vUyiFjMmYcCGRNdNYpwODRbbwGc83Ts/AeMODcsW/YbapmY8jAZ+MXsyv56b0JYX\nfzI5NfX86IYLuty/ZNm5/HPb4QG3UdEzamjIKEGv0XLbhBls3/M8J0qPYLOZOVGWyrbdq7l1/HR+\nM3k2+w+9RVrWWmrqisgtTGLTD39iyZixmIUrCfHXoNcZEUIQ5DeBGZOvQ2g0XHXRC0iXYF5L67kY\nY6Ty9yO7adR5M23ij4mNOJ+Vi/9MRPA0tu79FwBFpUeICZsLQFNzLe6uXXuzuLn6UWnufhB6RwJc\n3aK5dtgAACAASURBVLlnynn8SbufDzjKf8ngNiYyQwQSItw5nzG8yCFyZS0J+LPxpAKrStnMQXsZ\nS8dH9LDCmSOE4M65U0i75zrSfnM96fdezz3zE3sUeIBwTzeS9x3tcn/ygWOEqWrXQUV58qOIa2On\nYNLref3wG2yoKyfE3Zc7xydwaZSjV/tL8y7htYw97Mj6mkBXEw9MmkZJYx2ZmuAuB2SBvuM4mP45\nWo2Ocyau4tOdf+KOHmLPZU31aIWm2wPRVuotZvaW5aMVGmYEhGEcwtYJABa7jQ+zDiGFlhNlqTQ1\nV7Mr+d/Mm3Y7adnfk3T4vyAlOw68SX1TGTabBYulAX/fWEL822PlBYW7mOXfdYpWd6yMmcy0gFA+\nyTpMfWYBcbQfBF9DLN+RyzPsoxEbbkJHvcbCdFsgFaKJDfp87lswjRBP915W6B8ajehzT5wbEicw\n56WPWXnV+Sxb5mhltWdPGi/+7WM+v2H5WbNR0RUl8qOMFZHxrIiM7/axeJ9A/jrrok73bTuRQ0Vu\ncpdryyoz8fRwiJe7qy+15sa2x3LrqjhWXUadxcw7mYcpaqjBLu3E+QTxu8TziTopi+Wz7BT+evgH\nArwjsdutVCWt56npizg/ZGh6FlnsNu764WtsUoK0UlF9nCkTLsNus7Jp92q8TKFU1xYikdQ1lCKE\nIC56CVZbMz/se4Ug/3gSJqwkK3czxcV7WbXo6j6vHWny4c5z5vJJ9mFq7Ga8cIiqRgiWyHDW6/LZ\n/qtr8Hd35c1dKaxPy8Ms7dw6fhI/mzP5FM8+eAR7uvP21Yu5/cY/4eHtgcGgo6iwnOeWzWFysOpG\nOZgokVf0ypygCHSHfuBQ+qdMjF2BVqunvCqbfakfMjfxVgByC5OY7BdKs83Ko0nr2VNWQIB3DEVV\nORgNHixf9EdcjJ4czdnAbVs/45Ml12FqycQ5XHGC1al7WHLeE3iZQgAorcjkt7ue5b1F/oxx9+zR\ntrPFU/s2kWd349IL/g8PN39KytPZvv8VdFoXEiasJC5mMR+vvYdJscspKDnERfMeRqNx/CmNj1rE\nZ9/fT3npARaGjOWPC67E36Xv3nVhfQ11lmYuCh3H2wVpJNoD8MJIPN58q8ljfKAP41ry4T2MBvYW\nluArXHij8AirNx/ghZXn8+NBaE7WFxotVuKCfcmqqCHUYOL5VUuZGhY41GaNOpTIK3pFKzS8PO8S\nfrdvI59+9x0arZFmayMTohbjZRpDevb3pKR9zN/n/oin9m5kV3kxer0XFjTMSbyFkvKjbNr9Aovn\n3EdczFIqytP4+ngaq2ITAPgw+wgTYpa1CTw4+uVEhc3li+Op3N6H9MOBpKihls0nsrl0yfOUVmSy\nL/VDGhrKMLkFUVp5jPixF1FSkYGHeyDlVTnERS9uE3gAg96NuOgLmWTL494pfZ+CVFBfze92fUdO\nTSUeQk+VvRm7tGMDKmimlEaCPdz4zcxpfHY4Ey8XA0+s2Ym0QTge+OLCPkq466MtTArxH3Jv+dVd\nKbyw9whP/d/POOecGNatTeKKP/6Xd69ZzNyokFM/gWLAUCKvOCVBbiZemX8ppY111Jib2VuWzwc5\nSazP38wknyD+NW8F24pz+b4oi6jQ2ei0BrILdlJWlU1E8HRq60/w8dp7iBgzA6F1JbmihFUtz13S\n3IhHkOOP3mazUFSagsXWhN7gQ0lTyaC8vmPV5WwszATA2+iCyS2Arzc/Rl29IxQT6DcBX68oSiuP\nUVJxFI1Gh81mQSKhu2IeocFO3+tPLHYbv9j8KXOaAriUUHZTShbV3Eti2zjA/8oMNtcU8vqaFLQI\njjSXIxH8hsS2dsOXy2he4CD3fraFtbev7P/GnCH1Zgt/2JjEzr0vMW6cI5MrMTGWsPAAnnz8P3x3\n84ohs200okRe0WcCXD0IcPVgrJcf14xNaLs/vaqUt48d4vILn2lLL0yIW8k3W57ieNEe3Fx8SYy/\nkgOpHyOlnfymCp7av4lHE88n0SeALcX7MOjd2Zr0D0wewbgYPCgsOYxnYBhSygGtirTabbyZnsTm\nE3loNVrKGmsobWrALm14uPljbq7Farcxf/r/IzxkOlZrIwfTv6CwJJm5U3/G7oP/YcWiP2C21BPs\nHk9GzkYix8xE05LDbrE2kZu3hTunL+yzTVuLchBmOxspYCtF1GDmbhLaBL5YNrCTYh5lOhFmRwXt\nY+zCC0OnfvIaIbhcRvNi0aHulhk09heUMi42tE3gW7n66oXcfNMzNFqsuOqV9AwWKoVS0W++ys1g\nbNQFnapljQYPJo69CDcXX2rriwnyi2NO4k+RSK5Y+jxJNY28ezSZq6MnU3RiP+t3/AU/7xh8PMOJ\ni7mIyy98lpTaujYPeyBIqShm0ddv8FZ2BgVmyZHKImrsWtxcfbhyyd9ImLASNLr2fvJCg0HvzvRJ\nq9BqDQihpba+hPSsdUyZsJKjOVuoqy9lzZanOHZ8C2nZ37N282OcHziGRL++hyQOVZygzN7IT4nj\nj2I2GgQBtFetbqOI+YQQIdpbJATjhkt3/eTR033d4+DhYdBTUVHDydX0VVV16LQa9BolO4OJejtV\n9Jt6mwUXl64HpEaDB3a7FT/vGIwGd7w9w6lvKEOvdyVh0nW8v/dFrh+XgJ+LG3atOwE+Yx3TqQ68\nRljQVOInXMF72d9yQWgshyqK+C4/E5u0sygkmnMDwhBCYLHbKGmsw9vgSr3VzOGKYnyMriT4hXTq\npVNrbua2bZ9jR2DU6KhvKsfTPQSj0YPyyiwOpH3C3Km3YrWZSc/+nuz8HQT5OQ4whRCE+E+kovq4\no+CrZAe5jTXM8A8h1M2d3PpqqnLXMMbdk8enzGRuUORpffrIra1kIaHEC8ebZCxe7KeMhTjaCNRi\nJpLO+3sJUTxNEu/JoxyhEi2CGQTQgIVlcQOfK386JIzxR2+z8/bb67jxxqWAo0XGE797kyunjEOn\nVSI/mCiRV/Sb+YFh/DltCxNiFqMRGsyWBkrKMziS+S11DaWcN8MxVKOoNAUfrwgOH/2azLxt1DfV\nc/u2LyhuNqPRGDl09EtAEBU6k9yivXibQilvbuCZ5C2syc8iOnIBOq0L6w9s5lxff+K9/HkjYx9C\no6feXI8QWsb4jqWhqQKDNLN69jKiTb5IKXlw9xoMLt4smX0/BoM76dnryczbSmNTFVPjr2Z/6ofM\nSriJsKAE9qa8h13aeH/NL5BSEhEyg7qGUox6V6YHRPD3uT8a0P2zWW1E44mUkqNUE4EHH5IJEqYR\ngCdG9lDMItonAfnjihYtNZi5mTis2PmG4xwT1Wxf3PeUzbOBEILXVy7iynv+yXtvr+OcqbF8/+0e\nqG3k0+uXDaltoxHVoMwJOZMZr/3Bardz+/YvOCHd8fQIJSt/O16mUJrNdTSba1k0825sdgs/7H8V\nd1c/dDoXEuJW4mIwkZW3nZTMNei1Lmi1BizWRvQ6VzQaHS4Gd4zWKorqa3Bz9aXZXEtsxAKmjL+M\ntduexGJpYtHcB/A2hdJkrmV38ts0mWtIjLuSyprj5GZ+yd9mL+PRvRvJq6/FxeiJxdKARBLsP5Hw\n4GnkFu2lqPQwIPH1jiYieBr7jnzAuMiFTIxdBgjSstaSnr0eX4Mrby5Y2efOkn3BJu3cs/1LUkuK\nacaKO3pi8CSDKpqxYUPiZ3Sj0WblHJsPy2UkOgRvkIoODXeL9rMRu5Q8o9/H41fN4rLJY3tZdXBo\ntFj5PCWLvKpapoT4s3hceKceN4qBQzUoU5xVdBoN/5i7gmeTt7CmaDcrFv4Bk3sAAAXFyXy/48/o\ntAaiw+aSX5zMZfMfQduSdpgYfyVWu4W6+hIWzrwLm91KauZ3HEz/jIaGMgJ8x7Li3Acw6F2pqi1i\n96H/UNdYxviYi9q8fYDauhOUV2Vhs1vYdfAtGpurcdHquG3LZ5wz8VrmRJxHSUUGaVnrOFF6BG9T\nKLX1J6iqyWVO4k/x9BhDwYkD7D3yPj6e4Zx7zvVtr2/6pFXU1xdzqZ/LgAq8lJLf7fqOkvJqTOiZ\nRzCXE40QAruUvMYRdAGumG1WDlQUso0idnACjdAQaDSwoqnzm7hGCKZbAtmQkT8sRN5Vr2NVoprj\nOtQokVcMCEatjjKzmanxV7UJPEBoUALRIYkEW8vYn7+VsLD5bQLfSnTobLbvewUArUbH5HEXk1uU\nRHllFlqdC19vfrwtxu3jFUFVTT6l5UfbGq01NdewcddqZifeQnjwNIQQlFVm8f2OP+Nm9CQ2aiFJ\nh/9H3om9jI+6kJCASaTnrKe+oYxLFv4RD3d/x3N7hmE0mkjLWtfl9YWFnMvB4k0DumeHK0+wv7iA\nn9viWU0yy4loe50aIbhURvFE6R5+RCTFuGHBTigepMlKzHY7tZi7PGedxkzwaRRfKZwfJfKKAaO4\nsZ5oj65ZJe6mcMZLWDAmmveLq7o83tBUidHQWZiC/OKoqMrB1yuS82f8Ep3WSGHJIbbvf4ULZt1D\nRfVxktM+Q0o7WXnbCQ1KICJketvP+/vEMCn2YnIKdlJWmcXxwt1csugPbfNrx0UuZM3W31NUlsI4\n9wVtPxcdOpudyW92Sd2sqz/BOJeB69MOsLkwG6NNw184gAEtD7GTS2QUFwrHm9d+ykjEnwyqSMCf\nyzp4+c+ZD/CNOM4MGYhJGAAolY1s153gsemze1tWMcpQATLFgHGOTwAnSjr3uZFSUlq8n4k+gSwO\njaWoNIWS8oy2x82WRg6kfkxsxPmdfu5EaQouRi+mxl+FXueCEILQoCmcM/5SjmR+y7jIRWi1enIK\n91DXWI6PV9eMEl/vSMzmOnKLkhgbPh+D3h0pJcXl6aRlryPIbwLHC3d3+pnG5ho0QktVbXuXx6ra\nAjJzvufKlkZuA8Xm/EwiMPEX5rFazOd+EllPPj/IIgBSqSQKE/nUsYKoTl7+z5lEnbTymHYX72jT\n+bcujT/okvjtRTOJD/LtbVnFKKNfnrwQwgd4H4gEcoBrpJTV3VyXA1QDdsAipZzZn3UVw5MbxyXw\nk00fYXTxZWz4eVgsDRzO+BQ32ch5wdHoNBr+NHMpD+9+jgCfsRiNnuSeOIDVbsPN1Q8pJXa7hZRj\n32BpKiUqbH6XNYL84jh6fDNCCHzcA9lz4FV0WiPupjAmju2cuVFSmoLGbqakPINg/4mYLY1s3L2a\npqZqggMmUlmdS2VNHlW1BXibQpHSzqG0Dzk3IIz1235PgLdDWEsqs3lgynzGefn3a39s0k5RQy0e\nOgPlzQ1UNTXyMAloWwqpQoUHP5ETeJd0DFJLNrW4osMbY9vAkFZM6NFpNPxv+UySSitxD/Tj1fgL\nGePl0S8bFc5Hf8M1DwHfSyn/LIR4EHi45b6TsQMLpZSV/VxPMYwJc/filfmXsTplO+8fegejVs9F\n4RP49fxL0bVkVcwNimTNshvZUpRNvcXMuXFXklVTzp+TX2aH1YbVZmayXwh3xM3gfwU5XdYor8rG\n5BaA2VJPeVUW712wijpLM/fu+o6DaZ8QP3Y5Gq2erLzt5ORu4YXZy3kuZScZORtoaKrEw82fpXMf\nbJtjm5GzkbXbniYmbA6lpYcYY9Tz7NyLAdhVkoeUcPPT0zi4bClVwLzNG0n55PQPX9fkpvPiwW1Y\nbXaapJVoDx8ihAfVmNkvy5BIEvEnFk+KaOAbtzzO841hY8ExkI5QTIBob9WcQRU+BlcC9dO4OFQQ\n6p2FuxJ4RTf0K4VSCJEGLJBSFgshgoFNUsq4bq7LBmZIKcv78JwqhbKfDHYKZXecbjsCu5QUNdTg\nqtXj6+KG2WblsnX/JSrmYsZHL0aj0VJelcOGXX9jcuzF5Bf8wHxfLx5KOA+AEw21PHNwOzuKs0FK\nJvqFcv/kOcT7BCKl5Kn9m/gqN5UrljyHm4t3Jzu/+P5efhQSxsIxY5nuH4oQgklX1NJ82UIAnthn\nOKX9K2IsTHr8g273fEfxcR7fuZbbbRMZK7xolja+EDlskHno0DCVADRAEqW4oKUBK3YkE/HFByO7\nKUYg+DkTicREOlW8r83kvmkLWBruyF4J9c4CwH1seJ/3XOE8nLVB3kKICimlb0/fd7g/C6gCbMAr\nUspXe3lOJfL9ZDiI/ECQV1fFI0kbyK2vxqBzob65FqSdQDcvVkVP5JqxUzpVtYJjZJ9Nyi4zZ802\nK/O+eInrVryORtN5vujGbU/ySPwUbntrEfWBjl4w7cIuAC0mgxfJ65p7tLV1uPfdt9R2eezJK59m\nwm4tc0T78JBsWcNzHOBJZuIrXLBLySPsZBaBrKeA+5lKZEsbg2Zp4xmxn1qdhWa7jbEevtwyaSbz\ng6M6rRPqnaVEfpTSrzx5IcQ6IKjjXTjGDf+2m8t7eseYJ6UsEkIEAOuEEKlSym09rfnkG+vbbi+Y\nGs3CqSNbrBRnRriHN28vvIKC+mrqLWaiPX3Ra3ofAG3oYaKUQatjvE8IuUVJRIW2ty+uayijoiaf\nMS/fz/35XpDf+nfiEPZWWgW+t/72+XWVrH6j6+P7DhVzMZ0HtezgBIsJx1c4MnYOU4EeDWlU4YqW\n78njQhlGlPDEKLRcKqPY7FbCGxde0+vrr8/MU0I/CtiaVcDW7MI+XXtKkZdSLunpMSFEsRAiqEO4\nptvesFI60gWklKVCiE+BmUCPIv/4LRee0nDFmSOlJK++GpvdTqTJh31lBbx8aAcp1SX4Gdy4KvYc\nbhg/re1AcKgJdfc69UV94N5Js7h3179paq5hTOBkqmoKSMn8gKk3X8GmMi9Mhu57sPdF4AHCPHy6\nvd83IJys3BoCaI+p12PBgp21MpdwTByijAqamEUk4/EmixpWk8xNMo6pIgBPDNRbuubFd6SgKoZQ\n7ywl9KOA82JCOS+mvc3F/23oecZyfw9evwBuBp4BbgI+P/kCIYQboJFS1gkh3IGlwJP9XFdxhqRW\nlvDE7rVUNDWgR4Nd42gwdoN9HLcyjuLmBj5MSyOvtprfznCuN9vpAWF8eNFUnreksWHvWkwBvsz8\n9SrGL5yNydA17bBjeKY/E6omL72B99/6PcEWNyKFiTxZSzLlBOGKDg1bKKQaM7cxiUThyOAZjzfR\n0sTrpJIg/dmjL2HZvGAmXdE1HAS0HQa3Cr1C0Up/Rf4Z4AMhxC3AceAaACFECPCqlHIFjlDPp0II\n2bLeu1LKtf1cV3EGVDY38qutn3GVNYZZBCGAI7ZKXuIwEZhwFTqi8ORO22Qeyt/JrRPPxWq3szY/\nA7PNxvyQKCb7dB3qPVKYdEUt74T/knggHl2ncMzJ9NV77wuR8bNpuuJOnvviX2gtdhqtDVzNWC5o\nKXoql408zh4S6PxJYjzeSOA1kcZhfSP2KY9zdWb3OfB3P1/LpMc/aPu+PjMPUAexin6KvJSyAljc\nzf1FwIqW29lAYn/WUQwMXx1PZaL06XQAOAlfLpRhbKSA63FkargKHeM13rycsovNBZnMIgijXcOD\nx1KYERzOEzOXdjnwHK4kPBvLZoMjm+bhLMdhbE9hmZMZyPmyIWMT8QsZS37OQUCyk2KipSfRwhMD\nWiQSKxI97ftqR9KAleqp57Byxc/x8Aro9rkL62tY/YYJIm/t+qAV3rm3Fs0LOwbstShGFqqtwSgi\nr6aSKJsJTtLnaDxZT37b91JKTsgGUvMqOJ8xHKECOzDd5s/hoiK+y89gefjwGBbdE6HeWaQ8eQ33\nZ+npmCHTF3rLojkTLM0NfPnCL1nS4MOD9nnoEOymhNUk86icQaBwJVp6spZcLiaq7ee2iCJ8gqNZ\neP2jvT7/qQ6Db3jOROzC83mmZBPNGcPjnEUxeCiRH0XEePuxpSCDC+2d70+jkmDcAIfAbxQFNAkb\nrmgppZHrGI8WwQYKaLCb+TIzZViKfOfc9jmQ1XevHfofoqkqzSN16yfUFufhEz6eCXMvwejqwbH9\nG4g2G7lYRrS9wc4hmHxZxwbyWcU4phHIRyKLVH0jcWZXjhmayNY1cvFPVp+RLa20HgYf21TBlSxT\nXv0oRIn8KOLiyHjeTE3ie3seC2UoGgRJlLBFFKFFUK21UEwDGoOWGDdfyspquYPJbaGZGOnJ8xyk\noKFmiF9JV2Lfms7D+wywD1qVtLvD1J44U4GXUnL8yA+krH+Pstw0xuLJYhnA+sxv+HDje6DRoBUa\n4mwmJJ0LxOLw4WtyWE8+n+nzueDG39NYX032iWx8AyOYmbgIvdHttOzpiTAPX+XVj1KUyI8iTHoj\nLy+8kj8mreez6m1o0TDGzZN/Tl+Jr4sbRyqLCXBxJ8FvDPds+4J5BHeKvQshmCOD2ag9MYSvwkGo\ndxbeFzhi1A+HL20R994PU3sieV3zGXnvUkq2vf9nypN3sNQciJFYtlHER2SBhHF44mN3YTxefEce\n33C8UzgmmxoKdGbsY/24aNm9BEXE97zYAKC8+tGJEvlRRpTJh1cWXUVlcyM2ace/Q+/xsA756BEm\nb6pKu/Sao4omIkze2KR9yPLoE56N5f78OZ3uO52wTEe6i79Lu528jD0UpO/B4Gpi3PQlePqN6XJd\n8fEUCpK38rR5Ki7C8ac0VnrxGLuYhB8zCaSYRj4mi3MJYA25LJHhGISWo7KKdfoSfnTX3/EfE3tG\ntp8pJ3v1fwkvA6Dhf0cG1Q7F4KBEfpTiY3Tt9fEVURP55fFPWGAbg59wwSbtvM8xtlCI/YTkwi9e\n4YroydwxeU6PVaitLTMGKuXy5MPU0wnHVBUVs+udDyncdwh3f18SV11OY4Mj6aujF2+zmvnu5Qew\n5B9nttmbaq2NTzf8j1kr7yJuVufZrjmHtjHf4t8m8ABfkcN0Arme8bxNOgcpx4SezThCYg/oknDV\nGmjUwnk/fmTQBb6Vjl795YS13stnP8lXYu9kKJFXdMsE7wBunTiTJ1N2EYsn6bISb4xMwJtMaphq\n82P7sWN8m5tOoIsHiYFjuG7cVAJdPagxN/Fi8jbW5GdgljZm+oVxV8J8xnt3TgHMqinn8+wUyhsb\nmBYYyvKIOFx1eg6WF/Fp9mGwS667MgTfu29kTa4LcPqHqQBlx/N4+9a7mdvsxyKrL6U5DXyW/CxB\n513KgotvI//oPlI3vE9dRRHC4IJbSRm/tU5xfFKxw4W2EJ765Hki4mfh5tm+tkajxSZkp2YeGVRx\nO5N5lSOY0PMsc3EVOkpkI3/jACHzVhA7bTF+ITFoemjBMJiEebS/UebXVXD522HcfYsXM/+jwjjO\nghrk7YQMZIOy47WV3Lj+fW62T2CacIh0jTTzNElYkdRhIRYvQoQbyboKnpu3gnu3fUW1tQkJxOJF\nDJ78oCvmrQt+jAQ+OnaQ/aUFZNdWMo9gwvAgWVtOmcGMVdqobmpCi6AJG+4aA54TIrj+n39F72Ls\n1dby3HwqCgrxjwzHZ0z7hKpP7nuCuB0l/Eg6BosUywa+Iof9lGMKCKOuooirbVGE4cFhyllHHr8m\ngVjRHr56WZeB4dKrmTz3cizmJrIPbaE0L51jP3zFH23T8RQO234rd3I5MbxLBs8yt1Mf+CxZw989\ncrj2yY/7/Xs5WxTW17Q1W1Ne/chBDfJWnDFHqkqI1XgxTbZ74Z7CwCo5jrXk8Xtm8W9SaZY2zrMG\n86stnzPdHsDlROOKjp0U8wHHmGkN5LkDWzhQXsR8ezALZRAhGNlFMfMI4Xz7GN5qTCODKm5jItWY\nWcNxsENzegF7PvycuT/pvjlXU20dnz30e06kpBOq9yLXXEX0uVO55A8PoXdx4VjSPn5mnwECcmUt\nf+UACwnlLiZzoLSMTVhIoZxE/LlURBMgXfmITB5iWtsaLlKDxWKmNC+dNS/dR5R0Z4zVQBE6HhG7\nWSRDMaGjDivfkks4Hl0GfURjorquHGm3IzTDM7OlNXSlvHrnYXj+T1MMG8qa6gmwd51tGogb1Zhx\nEzp+SjwHKCNB+tFst3ID4zEJAzqhYb4IYTFhVGFmf2kBt9niuYqxzBCBXC/GczWx/BfHOMBlRNCI\nlQThzyyCuJ7x1GKh0t7IkS977oTx9RN/JvhQGX9pnsn99fH81TwTl6Qc1v3lnwDo9QYacHinH5HJ\nSmK4hCi+I4/9lLGIUOxIHmQHX8scpuJPFjU0SxsADdLCXlFG2ISZrHvtEW5qiuA35niutY/l/2zn\nMlkTQFKQlpRzJzD7J49S6+9DJjVYZOeChExq8PYMGLYC35EwD180QsfqN0xcZ12K27UDO/pQMXgM\n//9tiiFlsk8wKaIC20mCdZAyYnB4fa5Chx8uFNOAHm2Xg9aJ+FJAHULCRDp3apxDEPnUUSctCAQS\n+Fbmch/b+ZisllpVQVVpGW/d8Aveu/1+Dq/b2HaoW1dRSXbSAa61xLR5zgah5YbmGA6v24S5sZHg\nSQv5XJeHVdo5QiVzCWY9+Zix8XtmEY8PWdTijwvbKOIhdmDDzrtk8Hu5h0fEboInzKC5vhoPi2SG\nCGyzXyMEV9oiqaksYv6qBxibuJCV97+Od0g0r4lU6qQFgEJZzxuGTKYsvXEgfz1nlTHunm0x+8vf\nDmP3jXOw3+X4UowcVLhG0SuJfiGEe/vwalUql9mi8MLALkr4llweYCoAddJCGU3sphRPuk5RKqSe\neqzoNDgGQXbAjuPcUgDryWMM7mylkN9xLoHCFau08xU5bG4q5OpMd+qw8lX6S+TtPsDyR++hrqwC\nL70bRkvnDB9PYcAgtOz7uoJxi6/nQF46T5UdRGsWNGJjBye4lnFU0cwrHOEOJhMvHG9AB2QZL5NC\ng7CyXEZSQTPfpu8n3eiKSXR9fZ4YaLY0tU3D0ur0XPyrF/nhw+e4/9BmXDUGLBpIXPIT4mevGIDf\nyuAS5uHb3h+nBVVQNXJQIq/oFSEEf513Ca8e2cVfjx+k1tKMGzpuIo5Q4UGFbOI1UnERWswmQUO9\nlT22EmYQgBCCIlnPR2Ry/aqZfLzhKPtKyphOe3x/CwUE4MrrugyOWsvxw4VrGUdgyzxTndBwA08P\n2gAADz9JREFUmYxmH6Vo0TBTBHFOkx+PrNvC9FWX4xs+hiprI+WyCT/RHlbKk3Vg0GL08CHM04fw\ne/5FXtpukr56hc9Kc2i223BHz1aKmEtwm8ADHKGCeQRzAxPa2hCcawnk0eRNSAmVshkf0X4IvIti\nwiPP6fQJRm90ZcENjzKn6W6a6mtw9/JHe9K0qpHEycViqqBq5KBEXnFKXHV67poyn7umzEdKyZtp\nSbx9dB/vygya7DZiPf14JG4u54+JJr2qlId2fMMX1hxcpI4Tso4bH70Gl8WXcOF5Gfz7vj9zyFZN\njNmNVEMtB2UZofET8J8/k6oN2yhMyyCCzoOyhRBESBOlNDEBR3hous2PYzuTmHv91cy67gpe/N8a\nbm6KIRITx6jmNX0mUfNXodE6PHyNRkvkxDkERU7k6xfvwlIO2+1F1GFhPN6d1jtAGXeT0Ok+H2Fk\nsiaA8nFRPHP0MFeZwwjGjWRRwRpDIcsv/1u3e2dwccfQoeDMWVBtEkYOSuQVp4UQglviz+UnE6ZR\n2dyIl8EFY4d874k+QRx95Ure8I6kqaGZHO8J6F1dMBn8mDBtDmM+eI0Dn68hOScf/wlj+eUlF+Hm\n5fASZ193Ja//+OekFVQys8PESbuUZFDFhW1FO9CoteNtdHjT5912I0ZPEy++9QFVVRV4mgKIXnQj\ncxZc1cV+F3cvVt7/Oql71rDls38QZjFipoLzaK9o1SCwnhxXAqxCEj3lPHQzlvLVhg+or8klIHIi\nK5Y+il/I6BtRqdokjAxUnrwTMpSDvGPfmt5hCLZD/E+nn8yxnUl8/dDT/Lx5HHH4UIuF9zhKNWbu\nF44zgEJZz9PGZO74+N94+LUX8ySva0babQiNtk+9aOqry9i39i2O7vqGi2UEiwlDIHiavdRhpg4L\n/riyhDAm4M0fdAe59rEPcBmgcYTORH5dJSCJXdikvPohoLc8eSXyTshginyodxb+jy4F4P781lj7\nmTUKayV1wxY2rX6V2qoqJBKTpxei3szsZl9qdFb2aMpYev8vmXLx0k4/d6aNxmrKC9n50WqOH9uL\n3W7DQxi4VcYxAW9yqeMt0ijXWJh79b1MmLn8jF/XaCC/rgKAu29xjClcaKlWBVWDgBL5UcZgibyj\nUVjnVgVn2ijsZKSUNFbXYHB1RWvQc3z/QbJ27cXo4c7kJYvwCg7sdP1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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -29,25 +134,173 @@ } ], "source": [ - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "%matplotlib inline\n", - "\n", - "N = 100 # number of points per class\n", - "D = 2 # dimensionality\n", - "K = 3 # number of classes\n", - "X = np.zeros((N*K,D)) # data matrix (each row = single example)\n", - "y = np.zeros(N*K, dtype='uint8') # class labels\n", - "for j in xrange(K):\n", - " ix = range(N*j,N*(j+1))\n", - " r = np.linspace(0.0,1,N) # radius\n", - " t = np.linspace(j*4,(j+1)*4,N) + np.random.randn(N)*0.2 # theta\n", - " X[ix] = np.c_[r*np.sin(t), r*np.cos(t)]\n", - " y[ix] = j\n", - "\n", - "# lets visualize the data:\n", + "# plot the resulting classifier\n", + "h = 0.02\n", + "x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1\n", + "y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1\n", + "xx, yy = np.meshgrid(np.arange(x_min, x_max, h),\n", + " np.arange(y_min, y_max, h))\n", + "Z = np.dot(np.c_[xx.ravel(), yy.ravel()], W) + b\n", + "Z = np.argmax(Z, axis=1)\n", + "Z = Z.reshape(xx.shape)\n", + "fig = plt.figure()\n", + "plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral, alpha=0.8)\n", "plt.scatter(X[:, 0], X[:, 1], c=y, s=40, cmap=plt.cm.Spectral)\n", - "\n" + "plt.xlim(xx.min(), xx.max())\n", + "plt.ylim(yy.min(), yy.max())\n", + "#fig.savefig('spiral_linear.png')" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "iteration 0: loss 1.098714\n", + "iteration 1000: loss 0.295563\n", + "iteration 2000: loss 0.257634\n", + "iteration 3000: loss 0.250632\n", + "iteration 4000: loss 0.248781\n", + "iteration 5000: loss 0.247064\n", + "iteration 6000: loss 0.245940\n", + "iteration 7000: loss 0.245230\n", + "iteration 8000: loss 0.244816\n", + "iteration 9000: loss 0.244535\n" + ] + } + ], + "source": [ + "# initialize parameters randomly\n", + "h = 100 # size of hidden layer\n", + "W = 0.01 * np.random.randn(D,h)\n", + "b = np.zeros((1,h))\n", + "W2 = 0.01 * np.random.randn(h,K)\n", + "b2 = np.zeros((1,K))\n", + "\n", + "# some hyperparameters\n", + "step_size = 1e-0\n", + "reg = 1e-3 # regularization strength\n", + "\n", + "# gradient descent loop\n", + "num_examples = X.shape[0]\n", + "for i in xrange(10000):\n", + " \n", + " # evaluate class scores, [N x K]\n", + " hidden_layer = np.maximum(0, np.dot(X, W) + b) # note, ReLU activation\n", + " scores = np.dot(hidden_layer, W2) + b2\n", + " \n", + " # compute the class probabilities\n", + " exp_scores = np.exp(scores)\n", + " probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True) # [N x K]\n", + " \n", + " # compute the loss: average cross-entropy loss and regularization\n", + " corect_logprobs = -np.log(probs[range(num_examples),y])\n", + " data_loss = np.sum(corect_logprobs)/num_examples\n", + " reg_loss = 0.5*reg*np.sum(W*W) + 0.5*reg*np.sum(W2*W2)\n", + " loss = data_loss + reg_loss\n", + " if i % 1000 == 0:\n", + " print \"iteration %d: loss %f\" % (i, loss)\n", + " \n", + " # compute the gradient on scores\n", + " dscores = probs\n", + " dscores[range(num_examples),y] -= 1\n", + " dscores /= num_examples\n", + " \n", + " # backpropate the gradient to the parameters\n", + " # first backprop into parameters W2 and b2\n", + " dW2 = np.dot(hidden_layer.T, dscores)\n", + " db2 = np.sum(dscores, axis=0, keepdims=True)\n", + " # next backprop into hidden layer\n", + " dhidden = np.dot(dscores, W2.T)\n", + " # backprop the ReLU non-linearity\n", + " dhidden[hidden_layer <= 0] = 0\n", + " # finally into W,b\n", + " dW = np.dot(X.T, dhidden)\n", + " db = np.sum(dhidden, axis=0, keepdims=True)\n", + " \n", + " # add regularization gradient contribution\n", + " dW2 += reg * W2\n", + " dW += reg * W\n", + " \n", + " # perform a parameter update\n", + " W += -step_size * dW\n", + " b += -step_size * db\n", + " W2 += -step_size * dW2\n", + " b2 += -step_size * db2" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "training accuracy: 0.99\n" + ] + } + ], + "source": [ + "# evaluate training set accuracy\n", + "hidden_layer = np.maximum(0, np.dot(X, W) + b)\n", + "scores = np.dot(hidden_layer, W2) + b2\n", + "predicted_class = np.argmax(scores, axis=1)\n", + "print 'training accuracy: %.2f' % (np.mean(predicted_class == y))" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(-1.8987463970374139, 1.9412536029625895)" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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5bxd2zfLX0lHVrQapkaAuvCNVcQX/2E/eokHbz8nKyqVLl0ZkZ+dx+3bhu2CT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\n95v6Voiuvz35NJxj7a3DNRuklD0uFS+E+CNgklK+0M3zqif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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# plot the resulting classifier\n", + "h = 0.02\n", + "x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1\n", + "y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1\n", + "xx, yy = np.meshgrid(np.arange(x_min, x_max, h),\n", + " np.arange(y_min, y_max, h))\n", + "Z = np.dot(np.maximum(0, np.dot(np.c_[xx.ravel(), yy.ravel()], W) + b), W2) + b2\n", + "Z = np.argmax(Z, axis=1)\n", + "Z = Z.reshape(xx.shape)\n", + "fig = plt.figure()\n", + "plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral, alpha=0.8)\n", + "plt.scatter(X[:, 0], X[:, 1], c=y, s=40, cmap=plt.cm.Spectral)\n", + "plt.xlim(xx.min(), xx.max())\n", + "plt.ylim(yy.min(), yy.max())" ] }, { @@ -57,7 +310,13 @@ "collapsed": true }, "outputs": [], - "source": [] + "source": [ + "We’ve worked with a toy 2D dataset and trained both a linear network and a 2-layer Neural Network. \n", + "We saw that the change from a linear classifier to a Neural Network involves very few changes in the code. \n", + "The score function changes its form (1 line of code difference), and the backpropagation changes its form \n", + "(we have to perform one more round of backprop through the hidden layer to the first layer of the network).\n", + "\n" + ] } ], "metadata": {