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atcemgilatcemgil
committedFeb 27, 2018
Logistic Regression minor update
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‎LogisticRegression.ipynb

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"source": [
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"# Logistic Regression\n",
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"\n",
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"Logistic regression is a classification method. The main goal is learning a function that returns a yes or no answer\n",
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"when presented as input a so-called feature vector. \n",
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"Logistic regression is a classification method. Its main goal is learning a function that __returns a yes or no answer__\n",
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"when presented as input a so-called __feature__ vector. \n",
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"\n",
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"As an example, suppose we are given a dataset, such as the one below:\n",
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"\n",
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"\\end{eqnarray}"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {
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"collapsed": true,
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"scrolled": true
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},
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"outputs": [],
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"source": [
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"%matplotlib inline\n",
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"import numpy as np\n",
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"import matplotlib as mpl\n",
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"import matplotlib.pylab as plt\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 153,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"%matplotlib inline\n",
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"import numpy as np\n",
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"import matplotlib as mpl\n",
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"import matplotlib.pylab as plt\n",
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"\n",
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"from ipywidgets import interact, interactive, fixed\n",
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"import ipywidgets as widgets\n",
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"from IPython.display import clear_output, display, HTML\n",
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"from matplotlib import rc\n",
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"\n",
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"import scipy as sc\n",
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"import scipy.optimize as opt\n",
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"\n",
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"mpl.rc('font',**{'size': 26, 'family':'sans-serif','sans-serif':['Helvetica']})\n",
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"mpl.rc('text', usetex=True)\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 155,
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"metadata": {},
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"outputs": [],
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"source": [
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"\n",
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"def sigmoid(x):\n",
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" return 1/(1+np.exp(-x))\n",
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"\n",
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"def dsigmoid(x):\n",
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" s = sigmoid(x)\n",
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" return s*(1-s)\n",
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"\n",
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"def inv_sigmoid(p=0.5):\n",
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" xs = opt.bisect(lambda x: sigmoid(x)-p, a=-100, b=100)\n",
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" return xs\n",
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"\n",
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"def inv_sigmoid1D(w, b, p=0.5):\n",
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" xs = opt.bisect(lambda x: sigmoid(w*x+b)-p, a=-100, b=100)\n",
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" return xs\n",
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" "
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Plotting the Sigmoid"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 158,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"application/vnd.jupyter.widget-view+json": {
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"model_id": "60ca092bd27947bb9d636bedf46d5c61",
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"version_major": 2,
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"version_minor": 0
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},
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"text/html": [
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"<p>Failed to display Jupyter Widget of type <code>interactive</code>.</p>\n",
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"<p>\n",
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" If you're reading this message in Jupyter Notebook or JupyterLab, it may mean\n",
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" that the widgets JavaScript is still loading. If this message persists, it\n",
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" likely means that the widgets JavaScript library is either not installed or\n",
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" not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
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" Widgets Documentation</a> for setup instructions.\n",
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"</p>\n",
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"<p>\n",
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" If you're reading this message in another notebook frontend (for example, a static\n",
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" rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
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" it may mean that your frontend doesn't currently support widgets.\n",
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"</p>\n"
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],
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"text/plain": [
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"interactive(children=(FloatSlider(value=0.0, description='w', max=3.0, min=-3.0), FloatSlider(value=0.0, description='b', max=10.0, min=-10.0), Output()), _dom_classes=('widget-interact',))"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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" \n",
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"fig = plt.figure(figsize=(10,6))\n",
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"ax = fig.gca()\n",
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"ax.set_ylim([-0.1,1.1])\n",
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"x = np.linspace(-10,10,100)\n",
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"ax.set_xlim([-10,10])\n",
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"\n",
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"ln = plt.Line2D(x, sigmoid(x))\n",
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"ln2 = plt.axvline([0], ls= ':', color='k')\n",
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"ln_left = plt.axvline([0], ls= ':', color='b')\n",
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"ln_right = plt.axvline([0], ls= ':', color='r')\n",
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"\n",
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"ax.add_line(ln)\n",
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"plt.close(fig)\n",
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"ax.set_xlabel('$x$')\n",
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"ax.set_ylabel('$\\sigma(wx + b)$')\n",
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"\n",
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"def plot_fun(w, b):\n",
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" ln.set_ydata(sigmoid(w*x+b))\n",
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" if np.abs(w)>0.00001:\n",
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" ln2.set_xdata(inv_sigmoid1D(w,b,0.5))\n",
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" ln_left.set_xdata(inv_sigmoid1D(w,b,0.25))\n",
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" ln_right.set_xdata(inv_sigmoid1D(w,b,0.75))\n",
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" display(fig)\n",
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" \n",
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"res = interact(plot_fun, w=(-3, 3, 0.1), b=(-10.0,10.0,0.1)) "
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]
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},
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{
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"cell_type": "code",
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"execution_count": 157,
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"metadata": {
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"scrolled": true
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},
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"outputs": [
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{
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"data": {
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"application/vnd.jupyter.widget-view+json": {
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"model_id": "338bb9459a3a4a5993f8821def86ef1e",
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"version_major": 2,
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"version_minor": 0
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},
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"text/html": [
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"<p>Failed to display Jupyter Widget of type <code>interactive</code>.</p>\n",
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"<p>\n",
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" If you're reading this message in Jupyter Notebook or JupyterLab, it may mean\n",
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" that the widgets JavaScript is still loading. If this message persists, it\n",
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" likely means that the widgets JavaScript library is either not installed or\n",
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" not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
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" Widgets Documentation</a> for setup instructions.\n",
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"</p>\n",
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"<p>\n",
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" If you're reading this message in another notebook frontend (for example, a static\n",
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" rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
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" it may mean that your frontend doesn't currently support widgets.\n",
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"</p>\n"
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],
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"text/plain": [
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"interactive(children=(FloatSlider(value=-0.2999999999999998, description='w0', max=3.0, min=-3.5), FloatSlider(value=0.5, description='w1', max=4.0, min=-3.0), FloatSlider(value=0.5, description='w2', max=4.0, min=-3.0), Output()), _dom_classes=('widget-interact',))"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"xl = -5.\n",
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"xr = 5.\n",
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"yl = -5.\n",
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"yr = 5.\n",
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"\n",
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"w = np.array([0.5, 2, 3])\n",
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"\n",
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"fig = plt.figure(figsize=(5,5))\n",
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"ax = fig.gca()\n",
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"ax.set_ylim([yl, yr])\n",
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"ax.set_xlim([xl, xr])\n",
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"ln = plt.Line2D([],[],color='k')\n",
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"ln_left = plt.Line2D([],[],ls= ':', color='b')\n",
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"ln_right = plt.Line2D([],[],ls= ':', color='r')\n",
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"\n",
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"ax.add_line(ln)\n",
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"ax.add_line(ln_left)\n",
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"ax.add_line(ln_right)\n",
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"plt.close(fig)\n",
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"ax.set_xlabel('$x_1$')\n",
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"#ax.grid(xdata=np.linspace(xl,xr,0.1))\n",
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"#ax.grid(ydata=np.linspace(yl,yr,0.1))\n",
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"ax.set_ylabel('$x_2$')\n",
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"\n",
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"ax.grid(True)\n",
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"def plot_boundry(w0,w1,w2):\n",
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" if w1 != 0:\n",
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" xa = -(w0+w2*yl)/w1\n",
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" xb = -(w0+w2*yr)/w1\n",
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" ln.set_xdata([xa, xb])\n",
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" ln.set_ydata([yl, yr])\n",
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"\n",
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" xa = -(-inv_sigmoid(0.25) + w0+w2*yl)/w1\n",
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" xb = -(-inv_sigmoid(0.25) + w0+w2*yr)/w1\n",
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" ln_left.set_xdata([xa, xb])\n",
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" ln_left.set_ydata([yl, yr])\n",
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"\n",
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" xa = -(-inv_sigmoid(0.75) + w0+w2*yl)/w1\n",
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" xb = -(-inv_sigmoid(0.75) + w0+w2*yr)/w1\n",
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" ln_right.set_xdata([xa, xb])\n",
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" ln_right.set_ydata([yl, yr])\n",
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" \n",
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" \n",
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" elif w2!=0:\n",
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" ya = -(w0+w1*xl)/w2\n",
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" yb = -(w0+w1*xr)/w2\n",
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" ln.set_xdata([xl, xr])\n",
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" ln.set_ydata([ya, yb])\n",
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"\n",
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" ya = -(-inv_sigmoid(0.25) + w0+w1*xl)/w2\n",
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" yb = -(-inv_sigmoid(0.25) + w0+w1*xr)/w2\n",
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" ln_left.set_xdata([xl, xr])\n",
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" ln_left.set_ydata([ya, yb])\n",
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"\n",
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" ya = -(-inv_sigmoid(0.75) + w0+w1*xl)/w2\n",
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" yb = -(-inv_sigmoid(0.75) + w0+w1*xr)/w2\n",
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" ln_right.set_xdata([xl, xr])\n",
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" ln_right.set_ydata([ya, yb]) \n",
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" \n",
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" else:\n",
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" ln.set_xdata([])\n",
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" ln.set_ydata([])\n",
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" \n",
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" display(fig)\n",
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"\n",
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"res = interact(plot_boundry, w0=(-3.5, 3, 0.1), w1=(-3.,4,0.1), w2=(-3.,4,0.1)) "
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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},
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{
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"cell_type": "code",
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"execution_count": 52,
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"execution_count": 165,
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"metadata": {
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"collapsed": true
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},
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"def sigmoid(t):\n",
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" return np.exp(t)/(1+np.exp(t))\n",
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"\n",
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"D = 5\n",
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"N = 200\n",
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"D = 3\n",
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"N = 100\n",
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"\n",
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"# Some random features\n",
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"X = np.random.randn(N,D)\n",
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"X[:,0] = 1\n",
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"\n",
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"# Generate a random paramater vector\n",
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"w_true = np.random.randn(D,1)\n",
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"\n",
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"# Generate class labels\n",
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"pi = sigmoid(np.dot(X, w_true))\n",
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"y = np.array([1 if u else 0 for u in np.random.rand(N,1) < pi]).reshape((N,1))\n"
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"y = np.array([1 if u else 0 for u in np.random.rand(N,1) < pi]).reshape((N))\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 168,
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"metadata": {
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"scrolled": true
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},
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"outputs": [
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{
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"data": {
732+
"image/png": 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k2AwvYnwwrYRk2ExJZZA0nV22+sv3Fr9zRrmCoUjMOYchHgQHZCfhhrBuw9sv36f7O4di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\nxBbhUivRL14AAAAASUVORK5CYII=\n",
733+
"text/plain": [
734+
"<matplotlib.figure.Figure at 0x11d3cf518>"
735+
]
736+
},
737+
"metadata": {},
738+
"output_type": "display_data"
739+
}
740+
],
741+
"source": [
742+
"plt.plot(X[y==1,1],X[y==1,2],'xb')\n",
743+
"plt.plot(X[y==0,1],X[y==0,2],'or')\n",
744+
"plt.show()\n",
745+
"\n"
509746
]
510747
},
511748
{
@@ -573,6 +810,8 @@
573810
}
574811
],
575812
"source": [
813+
"\n",
814+
"\n",
576815
"# Implement Gradient Descent\n",
577816
"w = np.random.randn(D,1)\n",
578817
"\n",
@@ -588,45 +827,6 @@
588827
"print(w_true.T)\n"
589828
]
590829
},
591-
{
592-
"cell_type": "code",
593-
"execution_count": 34,
594-
"metadata": {},
595-
"outputs": [
596-
{
597-
"data": {
598-
"text/plain": [
599-
"array([[1],\n",
600-
" [1],\n",
601-
" [0],\n",
602-
" [1],\n",
603-
" [1],\n",
604-
" [1],\n",
605-
" [1],\n",
606-
" [0],\n",
607-
" [1],\n",
608-
" [0],\n",
609-
" [1],\n",
610-
" [1],\n",
611-
" [0],\n",
612-
" [0],\n",
613-
" [0],\n",
614-
" [1],\n",
615-
" [1],\n",
616-
" [1],\n",
617-
" [0],\n",
618-
" [0]])"
619-
]
620-
},
621-
"execution_count": 34,
622-
"metadata": {},
623-
"output_type": "execute_result"
624-
}
625-
],
626-
"source": [
627-
"y.reshape((N,1))"
628-
]
629-
},
630830
{
631831
"cell_type": "markdown",
632832
"metadata": {},
@@ -656,15 +856,18 @@
656856
},
657857
{
658858
"cell_type": "code",
659-
"execution_count": 1,
859+
"execution_count": 152,
660860
"metadata": {},
661861
"outputs": [
662862
{
663-
"name": "stderr",
664-
"output_type": "stream",
665-
"text": [
666-
"/Users/cemgil/anaconda/lib/python2.7/site-packages/matplotlib/font_manager.py:273: UserWarning: Matplotlib is building the font cache using fc-list. This may take a moment.\n",
667-
" warnings.warn('Matplotlib is building the font cache using fc-list. This may take a moment.')\n"
863+
"ename": "ModuleNotFoundError",
864+
"evalue": "No module named 'cvxpy'",
865+
"output_type": "error",
866+
"traceback": [
867+
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
868+
"\u001b[0;31mModuleNotFoundError\u001b[0m Traceback (most recent call last)",
869+
"\u001b[0;32m<ipython-input-152-53c98774130d>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0mget_ipython\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmagic\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'matplotlib inline'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0;32mfrom\u001b[0m \u001b[0mcvxpy\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 3\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mnumpy\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mmatplotlib\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mmpl\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mmatplotlib\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpylab\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
870+
"\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'cvxpy'"
668871
]
669872
}
670873
],
@@ -1486,21 +1689,31 @@
14861689
],
14871690
"metadata": {
14881691
"kernelspec": {
1489-
"display_name": "Python 2",
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"display_name": "Python [conda root]",
14901693
"language": "python",
1491-
"name": "python2"
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"name": "conda-root-py"
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},
14931696
"language_info": {
14941697
"codemirror_mode": {
14951698
"name": "ipython",
1496-
"version": 2
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"version": 3
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},
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"file_extension": ".py",
14991702
"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
1502-
"pygments_lexer": "ipython2",
1503-
"version": "2.7.13"
1705+
"pygments_lexer": "ipython3",
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"version": "3.6.1"
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},
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"toc": {
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"nav_menu": {},
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"number_sections": true,
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"sideBar": true,
1712+
"skip_h1_title": false,
1713+
"toc_cell": false,
1714+
"toc_position": {},
1715+
"toc_section_display": "block",
1716+
"toc_window_display": false
15041717
}
15051718
},
15061719
"nbformat": 4,

‎Regression.ipynb

+3-1
Original file line numberDiff line numberDiff line change
@@ -1649,7 +1649,9 @@
16491649
{
16501650
"cell_type": "code",
16511651
"execution_count": 54,
1652-
"metadata": {},
1652+
"metadata": {
1653+
"collapsed": true
1654+
},
16531655
"outputs": [],
16541656
"source": [
16551657
"sg = np.argsort(x)\n"

‎Visualizations.ipynb

+54,772-54
Large diffs are not rendered by default.

‎bouncing_ball_animation_01.py

+81
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,81 @@
1+
# -*- coding: utf-8 -*-
2+
"""
3+
Created on Sun Feb 7 01:30:34 2016
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5+
@author: cemgil
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7+
Bouncing Ball with x and y coordinates
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9+
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"""
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import numpy as np
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import matplotlib.pyplot as plt
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from matplotlib.animation import FuncAnimation
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# Create new Figure and an Axes which fills it.
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fig = plt.figure(figsize=(7, 7))
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ax = fig.add_axes([0.1, 0.1, 0.8, 0.8], frameon=True)
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ax.set_xlim(0, 1), ax.set_xticks([])
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ax.set_ylim(0, 1), ax.set_yticks([])
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global x
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global y
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global N
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# Number of particles to simulate
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N = 1
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x = np.zeros((2,N))
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x[0,:] = np.random.rand(1,N)
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x[1,:] = np.random.randn(1,N)/10
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y = np.zeros((2,N))
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y[0,:] = 0.9
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y[1,:] = 0
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ln, = plt.plot(x[0,:], y[0,:], 'go')
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ln2, = plt.plot([x[0,0], 0], [y[0,0], 0], '--')
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lnx, = plt.plot([x[0,0], x[0,0]], [y[0,0], 0], 'b--')
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lny, = plt.plot([x[0,0], 0], [y[0,0], y[0,0]], 'r--')
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global A
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A = np.matrix('[1,0.05;0,1]')
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def update(frame_number):
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global A
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global x
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global y
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global N
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#e = np.matrix('[0;1]')*0.002*np.random.randn(1,N)
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#e = 0
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x = A*x
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y = A*y + np.matrix('[0;-1]')*0.005
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for i in range(N):
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if x[0,i]<0:
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x[0,i]=0
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x[1,i]=-1.0*x[1,i]
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if x[0,i]>1:
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x[0,i] = 1
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x[1,i]=-1.0*x[1,i]
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if y[0,i]<0:
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y[0,i]=0
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y[1,i]=-1.05*y[1,i]
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if y[0,i]>1:
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y[0,i] = 1
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y[1,i]=-0.2*y[1,i]
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ln.set_xdata(x[0,:].tolist()[0])
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ln2.set_xdata([x[0,0], 0])
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lnx.set_xdata([x[0,0], x[0,0]])
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lny.set_xdata([0, x[0,0]])
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# ln.set_ydata(y[0,:])
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ln.set_ydata(y[0,:].tolist()[0])
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ln2.set_ydata([y[0,0], 0])
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lnx.set_ydata([0, y[0,0]])
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lny.set_ydata([y[0,0], y[0,0]])
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fig.gca().set_title(frame_number)
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return ln
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animation = FuncAnimation(fig, update, interval=5)
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plt.show()

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