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   "source": [
    "<center><h1>Introduction to Artificial Neural Networks</h1>\n",
    "<h3>Part 1:  Feedforward Networks for Regression<br /><br /> Elliott Forney, 2018</h3></center>\n"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thank you for finding your way to my tutorial series on Artificial Neural Networks (ANNs).  These guides are intended to be an introduction to Machine Learning (ML) applications of neural nets for people who have at least a moderate level of experience with Python, NumPy, data analysis, linear algebra and some calculus.  It is my hope that these tutorials will help to demystify the inner workings of neural networks and give the reader a strong starting point for designing and engineering neural nets to solve your own unique problems."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Preliminaries\n",
    "\n",
    "This tutorial is written in a Jupyter Notebook in Python3 so that you can actually run the experiments as you read!  I will also assume that you have some experience with array-based programming in NumPy and a basic knowledge of linear algebra and calculus.  If you don't have prior experience with Python and NumPy, it is probably a good idea to brush up on those tools first.  If you don't have a strong background in mathematics, you can probably continue and skim over some of the details of the derivations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "matplotlib.rcParams['figure.figsize'] = (10.0,6.0)"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regression\n",
    "\n",
    "In machine learning and data science we frequently think in terms of data and models.  If we know the model that generated a given data set, then things are generally made quite easy.  It is generally the case, however, that we have some dataset and wish to derive a model that could have potentially generated it.  If we can find a good model, then we can make predictions about new data once we encounter it.\n",
    "\n",
    "Another useful way to think about models is in terms of inputs and outputs.  For a given observation (the model inputs) the model generates some type of predictions (the model outputs).  Statisticians like to call model inputs \"predictors\" and model output \"response variables\" but this always seems less descriptive to me.\n",
    "\n",
    "Regression is the act of finding an approximate model that maps input variables to outputs variables."
   ]
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   "metadata": {},
   "source": [
    "# Linear Least-Squares Regression\n",
    "\n",
    "Linear Least-Squares Regression, often simply called Linear Regression, is straight forward and yet incredibly powerful tool for performing regression.  Linear Regression assumes that out model outputs can be described as a linear combination of our model inputs.  Suppose that a single observation to be fed into our model is a row vector\n",
    "\\begin{equation}\n",
    "  \\textbf{x} = [x_1, x_2, \\ldots, x_F]\n",
    "\\end{equation}\n",
    "where $F$ is the number of input dimensions to out model, also called the number of features.  The the predictions of a linear regression model can be described as\n",
    "\\begin{equation}\n",
    "  y_j = \\sum\\limits_{i=0}^{F} x_i \\cdot w_{i,j} + b\n",
    "\\end{equation}\n",
    "where $b$ is a constant bias value, $w_{i,j}$ is the model weight associated with the $i$'th input dimensions and the $j$'th output dimensions and $y_j$ is the predicted value along the $j$'th output dimension.\n",
    "\n",
    "Linear regression can also conveniently be written entirely in matrix notation.  Let $\\mathbf{X} \\in \\mathbb{R}^{N \\times F}$ be a matrix where the columns represent input dimensions and the rows represent observations and $\\mathbf{W} \\in \\mathbb{R}^{F \\times K}$ be a matrix of weights.  A linear regression model can then be written as\n",
    "\\begin{equation}\n",
    "  \\mathbf{Y} = \\mathbf{\\tilde{X}} \\mathbf{W} \n",
    "\\end{equation}\n",
    "where where $K$ is the number of output dimensions and where the tilde above $\\mathbf{X}$ denotes that a column of ones has been added in order to incorporates our bias terms and where $\\mathbf{Y} \\in \\mathbb{R}^{N \\times K}$ is our matrix of predictions."
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   "source": [
    "A linear regression model can also be visualized as network graph, which illustrates how information flows through the model.\n",
    "\n",
    "![linreg.svg](attachment:linreg.svg)"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Parameter estimation for Linear Regression\n",
    "\n",
    "Now that we have established how information flows through an LR model, we need to determine the values of $\\mathbf{W}$ that allow the model to actually fit a given dataset.\n",
    "\n",
    "First need a target dataset $\\mathbf{G} \\in \\mathbb{R}^{N \\times K}$.\n",
    "\n",
    "Then we wish to minimize squared error\n",
    "\\begin{align}\n",
    "  E(\\mathbf{W}) = (\\mathbf{Y} - \\mathbf{G})^2 = (\\mathbf{\\tilde{X}}\\mathbf{W} - \\mathbf{G})^2\n",
    "\\end{align}\n",
    "\n",
    "From calculus, recall that the derivative of a continuous function must be zero at it's minimum.  The gradient of our error function is the matrix of it's derivatives,\n",
    "\\begin{align}\n",
    "  \\nabla E(\\mathbf{W}) = & 2 \\mathbf{\\tilde{X}}^T (\\mathbf{\\tilde{X}}\\mathbf{W} - \\mathbf{G}) \\\\\n",
    "  = & 2 \\mathbf{\\tilde{X}}^T \\mathbf{\\tilde{X}}\\mathbf{W} - 2 \\mathbf{\\tilde{X}}^T \\mathbf{G}. \\\\\n",
    "\\end{align}\n",
    "\n",
    "We can then set the gradient to zero in order to find the local minimum\n",
    "\\begin{align}\n",
    "  & \\nabla E(\\mathbf{W}) = 0 \\\\\n",
    "  \\Rightarrow & 2 \\mathbf{\\tilde{X}}^T \\mathbf{\\tilde{X}}\\mathbf{W} = 2 \\mathbf{\\tilde{X}}^T \\mathbf{G} \\\\\n",
    "  \\Rightarrow & \\mathbf{W} = (\\mathbf{\\tilde{X}}^T \\mathbf{\\tilde{X}})^{-1} \\mathbf{\\tilde{X}}^T \\mathbf{G} \\\\\n",
    "\\end{align}\n",
    "As it turns out, linear regression is convex, meaning that there is only one minimum on the error surface.  We can verify this by finding the second-order gradient, left as an exercise for the reader"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear regression example\n",
    "\n",
    "Let's implement linear regression in python..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 1.],\n",
       "       [1., 1.],\n",
       "       [2., 1.],\n",
       "       [3., 1.],\n",
       "       [4., 1.]])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def bias(v):\n",
    "    \"\"\"Add a column of ones for the bias term.\n",
    "    \"\"\"\n",
    "    ns = v.shape[0]\n",
    "    return np.hstack((v, np.ones(ns).reshape((ns,-1))))\n",
    "\n",
    "# example\n",
    "a = np.arange(5)[:,None]\n",
    "bias(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "class LinearRegression(object):\n",
    "    \"\"\"Linear least squares regression\n",
    "    \"\"\"\n",
    "    def __init__(self, x, g, **kwargs):\n",
    "        self.train(x, g, **kwargs)\n",
    "        \n",
    "    def train(self, x, g):\n",
    "        # analytical solution, fails for underdetermined problems\n",
    "        x1 = bias(x)\n",
    "        self.w = np.linalg.solve(x1.T @ x1, x1.T @ g)\n",
    "\n",
    "    def predict(self, x):\n",
    "        return x @ self.w[:-1] + self.w[-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's consider a simple example of a linear function with normally distributed noise..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "ns = 100\n",
    "x = np.linspace(0, 1, ns)[:,None]\n",
    "x -= x.mean(axis=0)\n",
    "x /= x.std(axis=0)\n",
    "\n",
    "g = 20.0*x + np.random.normal(size=(ns,1))\n",
    "g -= g.mean(axis=0)\n",
    "g /= g.std(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "lm = LinearRegression(x, g)\n",
    "y = lm.predict(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
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4MXz7LYwcCZs3MzC5YXpAS5Nt1k1ESi1PS3A8k+Hn8kB3IKnghyMiUrxFhDU+\nsyfNWm7auoLnF00h+Oi/cOedMHYs1KkD5DLrJiKlnkchzVobm+WuFcaY3wphPCIixVraMuXMT77n\nidnjaLNrPUcaNmXZmxMYcuA84t5fT3DQNiLCGrtsAQWuZ+NEpPTxtE7aeRm+qhpjwoAqhTw2EZHi\n5+BBwie/yqfjH6PNcQe8/z6Lp39P752VcMQnYDmz96xDk2rpLaDSBAb4ExHW2DtjFxGf4umetFgg\nJvX7L8Ag4OHCGpSISLGTlOSscdaoEXz4ITzxBPz5J/Tpw+sLt7s88bloy35Gd2tJSFAgBggJCmR0\nt5Y6NCAigOfLnfULeyAiIr4kao2DsfO3EhefQHBQIBFhjd2Hp8WLoV8/Z9eA66+Hd9+FFi3SH85p\n71l4qxCFMhFxydPlzvLGmKeNMbOMMTONMQOMMeULe3AiIt6QVpA26/JkthpmO3fCHXc4uwMcPQrf\nfAMLFmQKaOB+j5n2nolITjxd7pwGNMfZCuq91J8/Pds3N8Z0NsZsNcZsM8YMcfF4OWPMl6mPrzTG\n1Dvb9xQRyU2uBWlPnIARI6BJE5g3z9kpYPNmZ99NY7K9XkRYY+09E5E887QERwtrbbMMtxcZYzad\nzRsbY/yBCcANwB5glTHmW2ttxtd9GDhsrb3IGHM38Bpw19m8r4hIbtwuTx4+AV9+6SxIu3s33H03\nvP461K6d4+ulLWd6vHwqIoLnIW21MeYqa+2vAMaYK3EeJDgbVwDbrLV/pb7mF0BXIGNI6wqMTP35\nG+A9Y4yx1tqzfG8REbdclcZo9s9fvLJkMry+Di65BD77DK691uPX1N4zEckrT5c7LwN+NsbsMMbs\nwHnC83JjzHpjzLp8vncIsDvD7T2p97m8xlqbBBwB1H1YRApVxuXJc08cYdT8Ccz9ZADNDu+GiRMh\nNjZPAU1EJD88nUnrXKijKADGmN5Ab4A6qdW8RUTyI7xVCCYpie0vv8nDP06hYmICO+5+kAYT3oBz\nz/X28ESklPA0pI2y1t6f8Q5jzKdZ78sjB5BxI0et1PtcXbPHGFMGZwHdg65ezFobCUQChIaGajlU\nRPIvOpqu/fvDhg3QsSO8+y4Nmjd3eWmeSnWIiOSBpyEt079OqYHpsrN871VAQ2NMfZxh7G7gnizX\nfAs8gHN59XYgWvvRRKSgpQUtvx1/8/LyT2i/cRnUrw+zZkF4uMsTm2nPS+/TyZlSHYCCmoictRz3\npBljhhpjjgEXG2OOGmOOpd7+B5hzNm+cusesLzAf2Ax8Za3daIx5yRjTJfWyj4DzjTHbgKeBbGU6\nRETORtQaBy99sYq7vo1kwTob+9sAACAASURBVOQ+XPHHb7zTviffzvgJbrvNbUADD0p1iIichRxn\n0qy1o4HRxpjR1tqhBf3m1trvgO+y3PdChp9PAncU9PuKiABgLWte+4D/++5Dgo8dYE7T6xjdvhf7\nzqlKyOKddLmqQY5Pz6mTgIjI2fJ0ufN7Y0y2o0zW2qUFPB4RkaKxZg3068eLy5ezvkYDnuoymNha\nZ8pBugpaWfefBVUI4PCJxGzXqZOAiBQET0NaRIafy+OscRYLXF/gIxIRKSAuN/XXKgvPPw+TJkHV\nqozp9jSRDa4jxS9zR4CsQcvV/rMAP0OAvyEx+cxWWXUSEJGC4mmD9Vsz3jbG1AbeKZQRiYgUgKyh\n6p+Dx9g4ZBQ3/fI5ZRP+g/79YcQImvz9H+UyXAeug5ar/WeJKZagwAAqliuj050iUuA8nUnLag/Q\ntCAHIiJSkDKGqrY71jJiQSSNDu5iZcNQrpwzDZo6/wkLbxWUfn1OQcvdPrMjCYmsHfG/QvyTiEhp\n5VFIM8aMB9Lm8/2AVsDqwhqUiMjZiotPoHb8Pp6PnkzYn7+yI6gmj3QbzsKLruDvppn/H9OTlk2u\nWkWl3S8iUhg8nUnbBKRt2IgHPrfWriicIYmIuOdR8djjxxm5cgZ3L/uaJD9/Xr+2J5Mvv43TZQII\nyWeoighrnGn5FLT/TEQKV44hLbVo7avAQ8Cu1LvrAFOMMb9Za7MfaxIRKSBZA1mHJtWYGetwXzzW\nWpgxAwYP5oG4OOa07Mgr7Xryb2Vny9+zCVVpQVDdBUSkqJicCvgbY94GKgMDrbXHUu87B3gDSLDW\n9i+SUeZRaGiojYmJ8fYwROQsZN34D2A4s+8io5CgQFbcUAX69YOff4bQUBg3jqjydbKFKlDQEhHf\nYoyJtdaGZr0/t+XOW4BGGVsxWWuPGmP6AFsAnwxpIlL8uTpN6Sqgnf9fPP2+HwfP/QTVqsFHH8GD\nD4KfH+Fkbs+kNk4iUpzkFtKsq16Z1tpkY4x6aIpIocmtan+Z5CQeWP1/9F8+gwpJp+Dpp2H4cKhS\nxe1zcmrjpJAmIr4mt5C2yRjT01o7LeOdxpj7cM6kiYgUCnenKQ3Q7q9YXlg4iYsO7WFpg1BOv/4G\nnbpdl+trqo2TiBQnuYW0J4FZxpiHcHYYAAgFAoHbCnNgIlK65HZIAKDxsX94Z9U0mq5awt/n1iSi\n5yja9n+A8Na1PDr1qTIaIlKc5NZg3QFcaYy5Hmieevd31tqFhT4yESk1XO0VmxnroPtlISzasp8j\n/xzk2TWzuOfnWfiXKwuvvUb9/v0ZW66c2+e72mumMhoiUpx42hYqGogu5LGISCnlbq/Y4k3/sKL2\nXhj3LOzdCz17wpgxULOmR8/PutdMZTREpDjJb1soEZFsPCo064KrPWEX7/2DkZ9+CHFb4fLLYfZs\nuPJKj5/v7n5PuguIiPgChTQRKRDulhxjdh5i0Zb9Hu8Vq/rfYQYv+YQ71y/gYKVz4eOPnTNofn5u\n31t7zUSkJHL/r56ISB64W3Kc/usuHPEJWM4Et6g1jkzXRYQ15hy/FB75bRbRkY8RvnExH13VnV++\n+zm95llOIsIaExjgn+k+7TUTkeJOM2kiUiDcLTlmLajocq/YvnV0nDGAyjv/YtGFl/Fh+FPcfV8n\nbvFwWVJ7zUSkJFJIE5EC4W7J0ZX0QPfnnzBwIMybR+WGDWHePDrcdBMd8vH+2msmIiWNljtFpEC4\nWnI0bq69KNDCs89C8+awdCmMHQsbNsBNNxX+QEVEignNpIlIgXC15Ji1IK2xKdy1eTHDlk+Dwwf4\nukUnpnV5jIc7tiG8bFlvDl9ExOcopIlIgXG15Bha9zzGzt9KtU1reWXxZJrv3szvIY154Zah/B7c\nGJJRk3MRERcU0kSkUIXX9Cd866fw6VS44AJevuNZptRvizVndluoybmISHbakyYiheP0aedes0aN\nYPp0GDwY/viDKRe2yxTQ0qjJuYhIZgppIlLw5s2DFi2cwey662DjRnjtNahc2W2BWRWeFRHJTCFN\nRArO1q3OE5q33OIsQPv99zB3LjRsmH6JCs+KiHhGe9JE5OwdPQovvwzvvgvly8Mbb8BTT4GLE5sq\nPCsi4hmFNBHJv5QU+OQTGDoU/v0XevWCV1+FGjVyfJoKz4qI5E4hTUTyZ+VK52zZqlXQpg383/9B\naKi3RyUiUmIopImUYlFrHHlfdty7F4YMgWnToGZN5/d77821CbqIiOSNQppIKRW1xsHQWevTuwE4\n4hPcFpWNWuPgnXnr6bzgS/r98iXlbDL+Q4fCc89BpUpFPnYRkdJA/+srUkqNnb81PaClSSsqm1HU\n6j3MHzOJj996iCFLprK87iXc+OgHRN3xpAKaiEgh0kyaSCnlrnhspvu3bOGCu3vywZ+r+PP82tx/\n50ssq98aQB0CREQKmUKaSCkVHBSIw0VQCw4KhPh4eOklGD+eZv7leOn6R5nW+maS/M/8k6EOASIi\nhcsrIc0Ycx7wJVAP2AHcaa097OK6ZGB96s1d1touRTVGkZIuIqxxpj1pABX94b0TsdDobjhwAB55\nhB7Vw9iYVD7b89UhQESkcHlrT9oQYKG1tiGwMPW2KwnW2ktTvxTQRApQeKsQRndrSUhQIAboHL+d\nFbOG0urlwc5+mzExEBnJo92vUocAEREvMNbaon9TY7YC7a21e40xNYHF1tps/+IbY45ba/O8Mzk0\nNNTGxMQUxFBFSj6HA5591tkEPSSEmCeG0N80Je7IyfSyHJC9Q4Cr+7RHTUQk74wxsdbabIUmvRXS\n4q21Qak/G+Bw2u0s1yUBa4EkYIy1NsqT11dIE/HAyZPw1lvODgFJSfDMM8y9sSeDf/gr0xJoYIA/\no7u1zBTAspbvcHediIjkzl1IK7TlTmPMAmPMBhdfXTNeZ50p0V1SrJs66HuAd4wxDXJ4v97GmBhj\nTMz+/fsL7g8iUtJYC1FR0Lw5DBsGN9wAmzbBqFGMWbbHo7IcnpbvEBGR/Cu0gwPW2k7uHjPG/GOM\nqZlhufNfN6/hSP3+lzFmMdAK2O7m2kggEpwzaWc5fJFiK8cuAps2wYAB8NNP0KyZ83unM39VPSrL\nkYfrREQk/7x1cOBb4IHUnx8A5mS9wBhzrjGmXOrPVYG2wKYiG6FIMZS2DOmIT8BypovAvKWp4ezi\ni529Nt99F9auzRTQwP2Jzaz3e3qdiIjkn7dC2hjgBmPMn0Cn1NsYY0KNMZNTr2kKxBhjfgcW4dyT\nppAmkoOsy5B+KcmEr5pHmxuvJmXcOGa0uIGbn/yIqHbdISAg2/Mjwhp7dJLT0+tERCT/vFInzVp7\nEOjo4v4Y4JHUn38GWhbx0ESKtYzLjaF7NjJyQSQt/tnOb7Wa8WKnl9hYowEk4bZHZ9rt3E5tenqd\niIjkn1dOdxY2ne6U0qrtmGiSd+1m6OKP6bp5CXGVqzK6fS/mNr0WjMl0bUhQICuGXO+lkYqISBp3\npzvVFkqkGMt4SKBeRX9e3DKPq7+ehH9KCuPa3MUHV91BQtns3QJAm/xFRHydQppIMZVeq+x0EmF/\n/sLz0R9R+8g/bGjTiRHterHaVCE4KJATp5M4fCIx2/O1yV9ExLcppIn4IFdlNCDzHrATp5OoFfcX\nIxZGcs3O39lStS497n6FXZdclWkZ013hWW3yFxHxbQppIj4ma6hyxCcQ8fXvYCAx2bmH9Ni+/Qxc\nPp37V8/jeLkKvNDpMaa3uolkP39MlmVMbfIXESmeFNJEfIyrav6JKc5w5peSzN3rfuSZpZ9S5eRx\nZlzambeuuZfDFaqkX+tqGTO8VYhCmYhIMaOQJuJj3G3ov3z3BkYuiKT5v3+xsnYLRnbqzebqF2a6\nRsuYIiIlh0KaiJdl3X8WVCEg00b/mkf389yiKdy6ZRmOytXo22Uw/9ekHRhDUGAAFcuV0TKmiEgJ\npJAm4kWu9p8F+BkC/A1+J0/y2G+z6PPrNxgs46/pwYQrunMywFlSIzDAn5FdmiuUiYiUUAppIl7k\ncv9Zcgrdd6xk0E+TCT68j+gW15I45nVqB9fifG3+FxEpNRTSRLwo6/6zxvt3MGJBJFfvWgctW8LM\nGVzfoUP64wplIiKlh0KaiBcFBwXiiE+gSsIxnl7+Gfet+Z6j5SryRpd+PDPzTSijv6IiIqWV/gsg\n4kURnS7i9xdep9+iaZxz6j+mX3ojH3ToybP3tVVAExEp5fRfARFvWbKE8H79CF+3jtUXXsKw6x7h\naKNmPKu9ZiIigkKaSNHbuRMiIuDrr6FuXfj6a1p37873xnh7ZCIi4kP8vD0AkVLjxAk2Pz6IUxc1\nImH2t0zu9ADffr4Abr8dFNBERCQLzaSJFJL0IrWHT3DvnlU889Mkmu7fy9wm7RjdoRdx51Qn8Ltt\npJQP1PKmiIhko5AmUgjSitTWdWxjxsJI2uxaz6bq9el9zxh+q90i/bqExGTGzt+qkCYiItkopIkU\ngg9n/cZz8yZzz9ofOFK+EsP+9wSfXxJGip9/tmvd9eoUEZHSTSFNpCAlJcHEiXz+xlAqnTrBtNY3\n807bezgSWNntU4KDAotwgCIiUlwopIkUlOho6N8fNmzgzwatGXbdQ/xRrV6mSwxgM9wODPAnIqxx\nUY5SRESKCZ3uFDlbO3ZA9+7QsSMcPw6zZuH4ag67gxtkuiwwwJ97r6pDSFAgBggJCmR0t5bajyYi\nIi5pJk0kD9JPbMYncGEFmLDnJ5pMm0iS8WPKDb14q+UtnL+1ChH1DKO7tUy/Vg3RRUQkrxTSRDyU\ndmIz4XQSt25eytDFHxN87AC/t7uR/q16sCPwPAAc8QkMnbWe0d1asmLI9V4etYiIFFcKaVJiZJzl\nKoyZq7Hzt3Lhnj94YUEkV+7ZyMbqF9L/1mdYXaclydZmulalNURE5GwppEmJkD7LlZgMnJnNAgom\nKB04wBNfjqXH2vkcDqzM0LC+fHnxDc6SGlkCWhqV1hARkbOhgwNSIoydvzU9oKVJm806K0lJMG4c\nNGzIXet+ZOplt9KhdySfX9o5veaZv5uWTiqtISIiZ0MzaVIiuJu18nQ2y+VS6cHNzpIamzbBDTew\n5LGhjF17KlMYDAzwp/tlIcyMdWS7X6U1RETkbGgmTUoEd7NWnsxmpS2VOuITsIDfjr+p1OMOuOEG\nSEiA2bNh/nw6du/A6G4ts5XQGBXe0uX92o8mIiJnw1g3+2mKs9DQUBsTE+PtYUgRyronDZyzWZ6E\npbZjonHEJxB4+iRP/Po1vX+bRbKfHx+168Gs9nex479kldAQEZFCY4yJtdaGZr1fy51SIqSFJ09O\nd2Zd2nQcPkGXzUsZumgKNY8fZHaz9oxp/yD/VK4K/xXSQQQREZFcKKRJiRHeKiTXAJV1xi1oy3re\nWRDJ5Y5NrK/RgL5dnyW2VjOXz1VZDRERKUoKaVKqpJ0CPe/EEZ5ZOo27f/+RQxXOYUjnp/iqZaf0\nE5vuqKyGiIgUFYU0KVX+PXiMh1bPY8CKGQQmnmRKaBfGte3B0fKVCAkKTF8CPXE6icMnErM9X2U1\nRESkqHglpBlj7gBGAk2BK6y1Lnf5G2M6A+8C/sBka+2YIhuklDw//siP0/pR/99dLK3Xihc79mZ7\n1dqA80RmxhZO7g4iqKyGiIgUFW/NpG0AugEfurvAGOMPTABuAPYAq4wx31prNxXNEKXE2L4dBg2C\nOXOoVqsufe4cwff1QiG1CK2r8JWXgwgiIiKFwSshzVq7GcC4qdSe6gpgm7X2r9RrvwC6Agpp4pnj\nx+HVV+HNNyEgAEaPptLAgYRtOsA6D8KXJwcRRERECosv70kLAXZnuL0HuNJLY5HixFqYPh2efRbi\n4uD++2HMGAgOBhS+RESkeCi0kGaMWQBc4OKhYdbaOYXwfr2B3gB16tQp6JeX4iI2Fvr1g59/htBQ\n+OYbaNPG26MSERHJs0ILadbaTmf5Eg6gdobbtVLvc/d+kUAkODsOnOV7i4/LWpB22OXnc9Pn42HK\nFKhWDT76CB58EPzU+UxERIonX17uXAU0NMbUxxnO7gbu8e6QxBdkPHlZJjmJzj99TruRM0hJPo3f\n00/D8OFQpUr6tdr8LyIixZG3SnDcBowHqgHzjDFrrbVhxphgnKU2brLWJhlj+gLzcZbgmGKt3eiN\n8crZOduglPX5J04nkZCYzLV/xfLCwklcdGgPiy68jMjwp/j8jQcyPS9jGQ21dhIRkeLEW6c7ZwOz\nXdwfB9yU4fZ3wHdFODQpYGcblFw9v+7hOF6PnswN237jr3OD6XX7CBY1uJysZ4XTugtkpNZOIiJS\nXPjycqeUAHkNSu5mzQAqnjpB31++4qGYKBL9A3i1fS+mXtaF02UCgOzdANy1cFJrJxERKQ4U0qRQ\n5SUouZo1AzA2hfCNixmyZCo1jh/i6xadeP26B9hf6dz057oqSBscFJj+GlnvFxER8XUKaVKo8hKU\nXM26Xbz3D0Yu+JDWcVtZW7MRj902jLXBjQkKDCCkXJkc97lFhDVWaycRESm2FNKkUOUlKGWcXat2\n/DCDl3zCHRsW8G/Fcxl000BmteiANX4EBvgzskvzXPeVqbWTiIgUZwppUqjyEpSCgwL59+BResV8\ny1M/f0G5pEQmXtmdTzvc6yypEZ9ASB6DlroLiIhIcaWQJoXO06D0RsU91Bz7HPUOOVjY4HJGXf8I\n+2rUYXS3lgpaIiJS6iikSYHKV020P/6AgQNp8913HKt7IYO6vMqsGhcTHBTIaC1PiohIKaWQJgUm\nzzXRjh6FUaPgnXegfHl44w0qP/UUb5Yty5tFOXAREREfpMaGUmByqomWSUoKTJ0KjRrB2LFw333O\n2bRBg6Bs2aIbsIiIiA9TSJMC41FNtJUroU0b6NWLDWXPo2vPt2jb6D6i9ia7fK6IiEhppeVOKTA5\n1kTbuxeGDIFp00ioWoORXZ7hqybXYo0fqKemiIhINgppUmBc1UQ7xyQTuXcBNOoKp0/DkCF0Kd+W\nPxMyd9pUT00REZHMFNKkwGSqiXb4BLfv+50RiyZTafcOuPVWeOstuOgitg2Z5/L56qkpIiJyhkKa\nFKjwViGEVzgOAwbADz9A48bO72Fh6deop6aIiEjuFNIk37LWRBt6dU1umTMZxo2DChXgzTehb99s\nJzbVU1NERCR3CmmSLxlrohmbwtVL53DVqGnYE0cwDz0Er7wCNWq4fK56aoqIiOROIU3yJa0mWmvH\nZkYsiOSSfX8SG9yEwb1GM2X847k+Xz01RUREcqaQJvmStHsPby2ZSreNi9hX6Tz63zKIOc3aY4zJ\n/ckiIiKSK4U0yZtTp+Dtt1k0+UX8k5N4r82dvH/VHZwo69z0r83/IiIiBUMhTTxjLcydC08/Ddu3\nc6R9GA80u5M/Kp/Zd6bN/yIiIgVHbaFKuag1DtqOiab+kHm0HRNN1BpH9os2b4bOnaFrVwgIgPnz\nqbnoB554JIyQoEAMEBIUyOhuLbXPTEREpIBoJq0Uy3hCE8CRtT1TfDy89BKMH09i+Qq8f/MTvNf0\nf1RfXYaIag5t/hcRESlECmmlWNoJzYwSEpN58/tNhMd+D889BwcOsCO8B/fWuxVH2cqAizAnIiIi\nBU7LnaWYqzZMl+3ZxPvj+sCjj0KjRhATw71XPJwe0NKk9doUERGRwqGQVoplPIlZ49gB3p77BjOn\nD6ZGwhGYPh2WLYPWrd321FSvTRERkcKj5c5SJGsbpw5NqjF35d/c+/NMnvzlK8qkJPPBNT2o9dqL\n3Hp1w/TnqdemiIhI0VNIKyWyHRI4fIL4GV+zaOnHnPfPHr5vdDUfdX2C+3q0JxloOyY6U5ibGetQ\nr00REZEipJBWSmQ8JHDRgV2MWBBJu51r+atGPc5bsIAbO3bkRlyf+JwZ66D7ZSEs2rJfvTZFRESK\niEJaCZV1adMRn8A5J48zYPkMeq7+P/4rG8gLnR5jRqub2NaxY/rz3J34XLRlPyuGXF/UfwwREZFS\nSyGtBMo6G7b30HHuWfcTg5ZOI+jkcT6/JIw3293H4QpVCMmyr0yHBERERHyDQloJlHE27PLdGxix\ncBIt/tnOytoteLFjbzbVuBBwva9MhwRERER8g0JaCRQXn0DNo/sZuvhjumxeiqNyNfp2Gcz/NWlH\nyLkVMDnsK4sIa5xpFg50SEBERMQbFNJKmoQEnov9hnuXfI6ftbx7dQ8+uKo7JwPKExIUmOu+srTQ\nlnE/mw4JiIiIFD2FtGIu/YDA4RP0cMQybNFHPBq3mx+aXsOo63qxp0oNIG+zYerJKSIi4n1eCWnG\nmDuAkUBT4AprbYyb63YAx4BkIMlaG1pUYywO0g4I1I7bzmcLI2m7cx1/VKvHvx9+ycnL22Lnb81x\naVNERER8l7dm0jYA3YAPPbi2g7X2QCGPx+dkLaHhKmRNnL2KZ7/7iPvXfMexchUYfsPjzLj0Ri44\nVIkVmg0TEREp1rwS0qy1mwGMMd54e5/nqqDs0FnrgdQ9Y8nJEBnJjDeGUOXkcaZfeiNvtbuX+MBz\nAJXLEBERKQl8fU+aBX40xljgQ2ttpLcHVBTcFZQdO38r4ce2Q79+8Pvv7LjwEp677hG2VK+f6VqV\nyxARESn+Ci2kGWMWABe4eGiYtXaOhy9zjbXWYYypDvxkjNlirV3q5v16A70B6tSpk68x+wpXM2HB\nR/9l6JyPYegyqFMHvvqKXQ3asHP2BlC5DBERkRKn0EKatbZTAbyGI/X7v8aY2cAVgMuQljrLFgkQ\nGhpqz/a9vSljQdlyiad4fOVMHl85Ez8sjBwJERFQoQLhAMaoXIaIiEgJ5LPLncaYioCftfZY6s//\nA17y8rCKRERYY4bOXEf7DUsZtmgKtY7+y/dN2+E3dixhN1+Z6VqVyxARESmZvFWC4zZgPFANmGeM\nWWutDTPGBAOTrbU3ATWA2amHC8oAM6y1P3hjvEUtvMwh2s5/mWoxv7C5Wj36PvomnfrcBUDbMdGa\nNRMRESkFjLXFemXQpdDQUBsT47L0mm87eBBeeAEmToSgIBg1Ch59FMqUyXbiE5z7z0Z3a6mgJiIi\nUowZY2Jd1YL188ZgJLM5q3byRtf+HK5Vn6SJE/nrjp7w55/Qpw+UcU525nTiU0REREoehTQvWz7p\na5rc0p5nvh3H5ur1ufnBcdzc8C6idmY+4emu9plqoomIiJRMPntwoCRw1TUAnLNiZudOXlo+les3\nLGXPOdV5PHwoPzS6GoyBtJpoGZYxM574zEg10UREREomhbRC4qprQMTXv1M+6SQP//wNj6+cicXw\n5jX3EnlFN04FlMv0/KwzZBFhjV3uSVNNNBERkZJJIa2QZNtDZi3/27iM5xZNIeTYfuY2acfoDr2I\nO6e6y+dnnSFLm1VTTTQREZHSQSGtkGScCWv671+MXBDJlbs3sKl6fQbeOojfardw+1x3M2SqiSYi\nIlJ6KKQVkuCgQE7E7WPQss/o8ft8jpSvxHNhT/LFxf8jxc8/07VBgQFULFdGM2QiIiKSTiGtMCQl\n8f7hn6k76TUqnTrBtNY38/Y195JQoTL+BlKSz9SmCwzwZ2SX5gplIiIikolCWj64OrWZHrKio6F/\nfy7ZsIF/r2zHg20eZEW5GgQHBfJShtOdmjUTERGRnKjjQB65q/z/cG0IHfcq7Tcuw3FuTfY8/zJX\nDnzIWVJDRERExA13HQc0k5ZHWU9tBp4+SZ+lX/PYb7NI9vNjbLv7mXzFbfgdDmT02jjNkomIiEi+\nKKTlUfqpTWu5dfNShi7+mOBjB4hqdh1jruvFvnOqOh93UZBWRERExFMKaXkUHBTIKUccE6LGcOWe\njayv0YCnugwmtlazbNeqZZOIiIjkl0JaHkWENeb5bxJI9C/DkLC+fHXxDdgsJTXSqGWTiIiI5JdC\nWh6lLV8+W/mt9BOaHZpUY2asQy2bREREpMAopOWDq8r/oXXPU2kNERERKTAKaQVELZtERESkIPl5\newAiIiIikp1CmoiIiIgPUkgTERER8UEKaSIiIiI+SCFNRERExAcppImIiIj4IIU0ERERER+kkCYi\nIiLigxTSRERERHyQQpqIiIiID1JIExEREfFBxlrr7TEUOGPMfmCnt8dRyKoCB7w9iGJAn5Nn9Dl5\nRp9T7vQZeUafk2dKy+dU11pbLeudJTKklQbGmBhrbai3x+Hr9Dl5Rp+TZ/Q55U6fkWf0OXmmtH9O\nWu4UERER8UEKaSIiIiI+SCGt+Ir09gCKCX1OntHn5Bl9TrnTZ+QZfU6eKdWfk/akiYiIiPggzaSJ\niIiI+CCFtGLCGHOHMWajMSbFGOP2pIsxZocxZr0xZq0xJqYox+gL8vA5dTbGbDXGbDPGDCnKMfoC\nY8x5xpifjDF/pn4/1811yam/S2uNMd8W9Ti9IbffDWNMOWPMl6mPrzTG1Cv6UXqfB5/Tg8aY/Rl+\nfx7xxji9yRgzxRjzrzFmg5vHjTFmXOpnuM4Y07qox+gLPPic2htjjmT4XXqhqMfoLQppxccGoBuw\n1INrO1hrLy2lx5Zz/ZyMMf7ABOBGoBnQwxjTrGiG5zOGAAuttQ2Bham3XUlI/V261FrbpeiG5x0e\n/m48DBy21l4EvA28VrSj9L48/B36MsPvz+QiHaRvmAp0zuHxG4GGqV+9gQ+KYEy+aCo5f04AyzL8\nLr1UBGPyCQppxYS1drO1dqu3x+HrPPycrgC2WWv/staeBr4Auhb+6HxKV+CT1J8/AcK9OBZf4snv\nRsbP7hugozHGFOEYfYH+DnnAWrsUOJTDJV2BadbpVyDIGFOzaEbnOzz4nEothbSSxwI/GmNijTG9\nvT0YHxUC7M5we0/qfaVJDWvt3tSf9wE13FxX3hgTY4z51RhTGoKcJ78b6ddYa5OAI8D5RTI63+Hp\n36Huqct43xhjahfN0IoV/VvkuTbGmN+NMd8bY5p7ezBFpYy3ByBnGGMWABe4eGiYtXaOhy9zjbXW\nYYypDvxkjNmS+n8pUenTbgAAA7BJREFUJUYBfU4lXk6fU8Yb1lprjHF3zLtu6u/ThUC0MWa9tXZ7\nQY9VSqS5wOfW2lPGmMdwzj5e7+UxSfG0Gue/RceNMTcBUTiXiEs8hTQfYq3tVACv4Uj9/q8xZjbO\nZYkSFdIK4HNyABn/r75W6n0lSk6fkzHmH2NMTWvt3tTllX/dvEba79Nf/9/e3YPYUYVhHP8/usZC\nggRWkFRRtFAQDIooIqRSSLEgLLpaGEULBRHt7ASrJY2CIhGjBEQDNuKCITYSsBCixRrxo0ixwpZa\nxE+ETV6LmQs3fnAvJntn9s7/18xhGIb3HobhuWfOzElyCtgPzHNIm+baGB2zmWQBuBb4aTbl9cbE\nfqqq8T45ChyeQV07zSDuRZeqqn4ea59I8kaSxaqa+zU9fdw5R5Jck2T3qA3cTzORXhf7Arg5yQ1J\ndgErwCDeXByzBhxq24eAf4xAJtmT5Oq2vQjcC3w7swq7Mc21Md53y8CnNbwPTk7sp7/NrVoCvpth\nfTvFGvBY+5bn3cC5sWkIaiW5fjTvM8ldNNllEH+MHEnbIZI8CLwGXAd8nGS9qh5Ishc4WlUHaeYV\nfdheywvA+1V1srOiOzBNP1XVVpJngU+AK4F3quqbDsvuwirwQZIngR+AhwDaz5Y8XVVPAbcAbya5\nQHNTXK2quQ5p/3VtJHkZ+LKq1oC3gXeTnKWZ7LzSXcXdmLKfnkuyBGzR9NPjnRXckSTHgQPAYpJN\n4CXgKoCqOgKcAA4CZ4HfgSe6qbRbU/TTMvBMki3gD2BlKH+MXHFAkiSph3zcKUmS1EOGNEmSpB4y\npEmSJPWQIU2SJKmHDGmSJEk9ZEiTNFhJft2Gc+5L8ujlPq+k4TGkSdLltQ8wpEm6ZIY0SYOX5ECS\nU+1C4N8neW/sC+cbSQ4n+TrJ6SQ3tfuPJVkeO8doVG4VuC/JepIXZv9rJM0LQ5okNfYDzwO3AjfS\nLIM1cq6qbgNeB16dcJ4Xgc+q6vaqemVbKpU0CIY0SWqcrqrNqroArNM8thw5Pra9Z9aFSRomQ5ok\nNf4ca5/n4rWN61/aW7T30CRXALu2tTpJg2NIk6TJHh7bft62N4A72vYS7YLQwC/A7plVJmluLUw+\nRJIGb0+SMzSjbY+0+94CPkryFXAS+K3dfwY43+4/5rw0Sf9XqmryUZI0UEk2gDur6seua5E0LD7u\nlCRJ6iFH0iRJknrIkTRJkqQeMqRJkiT1kCFNkiSphwxpkiRJPWRIkyRJ6iFDmiRJUg/9BRDXXyKN\nadz1AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x, g)\n",
    "plt.plot(x, y, color=\"red\");\n",
    "plt.xlabel(\"Input\")\n",
    "plt.ylabel(\"Output\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regression for nonlinear problems\n",
    "\n",
    "As it's name suggests, linear regression is purely linear in it's inputs, meaning that it is not directly able to model nonlinear curves.  Consider the nonlinear example below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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q0E5WiwLtdDKE2ev3XtTxonrWWrUTyDpzb7wvyb6RkRGfnJwM3QwAyLTRsYnI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\nAEghgjQAAIAUIkgDAABIIYI0AACAFPr/GzdsbmVpCNQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# a quadratic curve\n",
    "g_curved = 10*x**2 + np.random.normal(size=(ns,1))\n",
    "g_curved -= g_curved.mean(axis=0)\n",
    "g_curved /= g_curved.std(axis=0)\n",
    "\n",
    "lm_curved = LinearRegression(x, g_curved)\n",
    "y_curved = lm_curved.predict(x)\n",
    "\n",
    "plt.scatter(x, g_curved);\n",
    "plt.plot(x, y_curved, color=\"red\");\n",
    "plt.xlabel(\"Input\")\n",
    "plt.ylabel(\"Output\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are, however, many tricks that can be used to model nonlinear problems using the linear least squares approach.  For example, we can transform our inputs so that the model is nonlinear over the original inputs.  Below, we combine both $X$ and $X**2$ so that our linear regression model can fit our quadratic curve.  The approach can be further extended using the kernel trick, known as kernel ridge regression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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GweHDLkQlIiJS+jz9zgs7lsHQRW9A48bQp0/5B+UnlKT5oUFxjYgIz72lWaVSOLseeRy2\nbIGXXnInMBERkVLm6XfeLT/Np97OrSTE9qTBo3NplbjAOaMWYpSk+aH4mGhGdWlKdGQEBoiOjGBU\nl6a0ursHtGvnzC47cMDtMEVEREos7++8M6saBi59m5Wnn8PbURfkLyYIISocCDTLlkGLFs4efYgM\nmBURkRCSmAhDhtD95kSWn9Ek15eiIyNYnNDOpcDKjrfCAb/ukyYeXHwxdO8OY8fC3XeT/HuG994y\nIiIigWT3bkhMZF7Di/MlaOC9yCBYabszgCSvTKVV4gKuqHk1R9MO8W2f+733lhEREQk0o0bB/v28\n2qmfxy97KjIIZkrSAkTOZn+ba0YxvXl7LvzsfU77Y0uu69KOOCtrIiIiAeW33+D55+G22+h2W/t8\nxQQR4WEMimvkUnDuUJIWIJLmriPtSEb2589d2pND4ZUZ9NXr+a4NteVgEREJAsOHO38+8YTXArpQ\nO86jM2kBIm/iteuESCZf3IUBi6ZzQerPfBd9TvbXoiIjCp6DJiIi4k9Wr4bXXoMBA6BuXcCp+gz1\n31taSQsQnvbhp1wUz84TIklY+ApkVulGhIfRtnEdnVUTEZHA8fDDUKOGM6NTsilJCxCemv3ZE6rx\nTa/7uHjbGq7esCx7OfiLtTtzbY2CzqqJiIifmjcPPv0UHn0UTjrJ7Wj8ivqkBRCPW5hNToYmTZyh\n6z/8ABUr0iBhDp7+VQ2wKbFTeYctIiLi2bFjcOGFsHcvrF0LlSu7HZEr1CctCHjdnx81Crp2hWnT\noF8/oiIjSPVQPBBqpcsiIuLn3nwTVq2Ct94K2QStINruDAY33ACtWjnD1w8c8Lg1GoqlyyIi4sfS\n0pwtzthYuOkmt6PxS0rSgoExMG4c7NgBSUkqXRYREf/37LOwdSskJUEFpSOe6ExaMOnRA2bPhl9+\ngWglZCIi4qd27oSGDaF1a/jwQ7ejcZ23M2lKXYPJqFGQkeEsH4uIiPirkSPh779h9Gi3I/FrStKC\nSYMGcP/9TkPAVavcjkZERCS/X36BSZPgzjvh3HPdjsavKUkLNkOHQs2aMHBgdoNbERERv/Hww1Cl\nCjzxhNuR+D0lacGmZk2nynP+fPjkE7ejEREROW7hQkhOhiFD4NRT3Y7G76lwIBilp8N550GlSvD9\n91BR7fBERMRlx4457Tb++gvWrYMI9e7MosKBUFKpknMYc80amDLF7WhERETg9ddh5UpITFSC5iOt\npAUra+GKK5xEbcMGZ3CtiIhIOck5yvDMqvDR832JOKs+LFni9PeUbFpJCzXGwDPPwK5d8OSTbkcj\nIiIhJHllKkNmriZ1bxoWuO6z6UT8tYOv7h5C8qrttEpcQIOEObRKXEDyylS3w/VbStKC2QUXQJ8+\nTlfnDRvcjkZEREJE0tx1pB3JAODU/X/R/9uZfNT4cu7fEpEreUvdm8aQmauVqHmhJC3Y/d//OWfU\nHn7Y7UhERCREbN+blv3xoK9fp4I9RuIVfdibdiQ7ecuSdiSDpLnryjvEgKAkLdiddprTO+2DD+CL\nL9yORkREQkBUpFMY0PT3X+j64wKmxXZmW41TvF6fM6mT45SkhYKHHoJ69Zw/M3K/g0lemaqzASIi\nUqoGxTUiomIFhs+fzM6qkUxseSMR4WHUrBru8fqspE5yU5IWCiIiYMwYp2faK69k3533YKfOBoiI\nSGmIj4nm9RM2Epv6M2Nb30qNU2oxqktThl93HhHhYbmujQgPY1BcI5ci9W9qwREqrIXLL3cKCNav\nhxNPpFXiAlI9LDFHR0awOKGdC0GKiEhQ+OcfaNwYTj4Zli2DsOOJWc7WHFGREQyKa0R8TLSLwbrP\nWwsOtaIPFcbA+PFw0UVOMcHo0V7PAOhsgIiIlMiYMbBtG8yYkStBA2eVLdSTMl9puzOUxMY6LTme\neQZ++cXrGQCdDRARkWLbssVJ0nr0gMsuczuagOZqkmaMmWaM+dMY86OXrxtjzHPGmA3GmB+MMReU\nd4xBZ9QoqFIFBgxwDnbqbICIiJSmhx92dm9Gj3Y7koDn9kraq0D7Ar7eATg789YPmFQOMQW3U0+F\nYcPgo4+I/+MHRnVpSnRkBAbnLNqoLk21DC0iIsXz1Vfw7rsweDDUret2NAHP9cIBY0x94CNrbRMP\nX3sJWGitnZH5+TrgCmvt7wU9pgoHCpGeDk2bOh+vXu00uxURESmJjAznWM2uXbB2LVSt6nZEASNQ\nZ3dGA1tzfL4t8758jDH9jDEpxpiUnTt3lktwAatSJaeIYP16eO45t6MREZFgMHUqrFoFSUlK0EqJ\nvydpPrPWTrbWxlprY+vUqeN2OP6vQwfo1AlGjIA//nA7GhERCWS7dzvTbS6/HG680e1ogoa/J2mp\nwBk5Pj898z4pDc88A4cOwZAhbkciIiKB7LHHYM8emDDBKRqQUuHvSdps4NbMKs9LgH2FnUeTIjj7\nbGdU1Kuvwrffuh2NiIj4GZ9GB65aBS++CPfeC+efX/5BBjFXCweMMTOAK4DawA5gOBAOYK190Rhj\ngAk4FaAHgduttYVWBKhwoAgOHIBGjSA6GpYuzdd0UEREQlPW6MC0I8dnPkeEh+XuApA1zWbdOuec\nc82aLkUb2Pxy4oC1tmchX7fAveUUTtDzOoojKQl69XIOffbr53aYIiLiB5LmrsuVoAGkHckgae66\n40na9OmweDFMmaIErQz4+3anlJICh6nffDO0bu2cTdu1y+1QRUTEDxQ6OnD/fhg0yBk3ePvt5RhZ\n6FCSFiIKekeEMTBxIuzbB4884lKEIiLiTwodHThyJOzYARMnkvz974WfXZMiU5IWIgp9R9SkCfzn\nPzB5Mug8n4hIyCtwdODPPzv9Nu+4g+SKUd53aqRElKSFCJ+GqT/+OJxyCrtvv4vLnpqnd0QiIiEs\nPiba8+jA5lFw331QrRo89VTBOzVSIq4WDkj5GRTXyGOVTq5h6jVqkHLvEGIfe4BWX8/mnWZx2e+I\nAM30FBEJMfEx0flf+2fMgAUL4IUX4OSTC9+pkWLTSlqI8PqOKM//fA+Ence3p5/H4C9fo0baAUDv\niEREJNO+fTBggDOjM7MbgE87NVIsStJCSHxMNIsT2rEpsROLE9p5XBnbvu8Qw6++mxMP/c3DX712\n/H69IxIRkeHDnWKBSZOy+2oWeHZNSkRJmuQSFRnB2pMb8NqF19Fz1Vyab1+Xfb+IiISwVavg+efh\n7rudlbRMvu7USNG5OnGgrGjiQPFl9VOr8PcB5k35N7ur1uCmO5/jyW7N9T+ciEioOnYMWrWCX391\npguocW2p8jZxQCtpkkvWO6LIU2ox8sq7OO/PjbyVnqIETUQklE2b5owOHDtWCVo50kqaeGctdOwI\nixbB2rXOfE8REQktf/3lzHg+7zz48kuSV233PGJQik0raVJ0xsCECXD0KDz0kNvRiIiIGxISnKrO\nF14gedV2Na4tR0rSpGBnneWMivrf/+DTT92ORkREytPXX8PUqU7bjSZN1Li2nClJk8INGuQsdd97\nL6SpFYeISEhIT4f+/aFePaf1Bj6MGJRSpSRNCle5stNZeuNGeOqp7LuTV6ZqoK6ISLBKSnJmdL7w\nApxwAqDGteVNSZr4pl076NULRo+GNWuyW3XoXIKISOAp9E32hg0wciR07+4UkGVS49rypSRNfDdu\nHFSvDv36MfaTn3UuQUQkABX6Jtta+Pe/nV2U8eNzfa8a15YvDVgXnySvTCVp7jpaXnIrYz8ez+XV\nZjGjeft81+lcgoiIfyvo8H98TDS89RbMmwcTJ0JUVL7v9zh0XcqEVtKkUDnfdb3X5Eq+qXs+Qxa+\nQp2/d+e7VucSRET8W4GH/3fvdio5W7RwigbEVUrSpFC53nUZw9C4e6l8NJ3H503OdZ3OJYiI+L8C\nD/8PHgy7dsFLL2UPUBf3KEmTQuV917X5pGieu7QHndYtovvvq3QuQUQkgHg7/D+61i6YMsVZSWvW\nzKXoJCeNhZJCtUpcQGqeRC084whz33iIMytlwJo1UK2aS9GJiEhRZZ0zzhrtNLhNXa6/tYNTNPDD\nD1C1qtshhhSNhZJi8/Suq2KVKmxNfBa2bYPHHnMpMhERKY74mGgWJ7RjU2InFie04/rZU2HDBv7T\n9t80GPGFel/6CVV3SqGytjDzDtRtExMNy/8Nzz0HPXo4B01FRCSwrFzJsaQkPmh2DR/Wagwcb8sB\n6BiLi7TdKSWzfz+cdx7UqAHffQeVKrkdkYiI+OroUWjRgl3rN9G27yT2V8l9dCU6MoLFCe1cCi50\naLtTysaJJ8KLL8JPP+UaGSUiIgHgmWfgu+947Mr++RI0UO9LtylJk5Lr1AluucVJ0lavdjsaERHx\nxYYNMGwYdO7M9y2u8niJel+6S0malI7x4yEyEvr2hYyMwq8XERH3WOs0q61UCSZOZFD7xprJ6YeU\npEnpqF0bnn8eli+HZ591OxoRESnI5MmwYAGMGQPR0ZrJ6adUOCClx1qIj4fPP3e2Pc86y+2IREQk\nr99+gyZN4KKLnBmdxrgdUcgrUeGAMaaVL/dJiDMGXngBwsPhrrvg2DG3IxIRkZysPf76PGWKEjQ/\n5+t25/M+3iehLjoaxo2DL75wZr+JiIj/eOUV+OwzSEyEBg3cjkYKUWCSZoxpaYz5L1DHGDMgx+1x\noMSTV40x7Y0x64wxG4wxCR6+3scYs9MYsyrzdmdJn1PKQd++cM01MGgQbNrkdjQiIgKQmurM5Wzd\nGu65x+1oxAeFraRVAqrhTCaonuO2H+hWkic2xoQBE4EOwLlAT2PMuR4ufcda2zzzNqUkzynlxBh4\n+WWoUMFJ2LTtKSLirqxqzvR0mDrVeX0Wv1fgWChr7ZfAl8aYV621W0r5uS8GNlhrNwIYY94GOgNr\nSvl5xA1168LTTztnH158Ue/aRETc9OabMGeO87rcsKHb0YiPfE2lXzXGLMh7K+FzRwNbc3y+LfO+\nvLoaY34wxrxnjDnD24MZY/oZY1KMMSk7d+4sYWhSKvr2hbg4ePhhbXuKiLjkk8++Y3//e1kR1ZjL\n05pocHoA8XXA+sAcH1cBugJHSz+cfD4EZlhrDxtj+gOvAR6HiFlrJwOTwWnBUQ6xiQfJK1NzDWIf\n9sBI4pZcBXfcAfPna4ldRKQM5X0NbtuoNlc9/G/Cj6QzqOODbN2frsHpAcSn35jW2hU5bouttQOA\nK0r43KlAzpWx0zPvy/m8u6y1hzM/nQJcWMLnlDKUvDKVITNXk7o3DQuk7k3jwW92sfLBx2DhQpg0\nye0QRUSClqfX4PSXp3LFhmWMbnMbG2udDkDakQyS5q5zN1jxia990k7KcattjIkDapTwuZcDZxtj\nGhhjKgE9gNl5nve0HJ9eD/xcwueUMpQ0dx1pR3KPhEo7ksF9VWKgfXtn23PDBpeiExEJbnlfg6P3\n/clj819mSd2mvHbhtbmu1eD0wODrducKwAIGZ5tzE9C3JE9srT1qjLkPmIvTzmOatfYnY8wIIMVa\nOxu43xhzfeZz7gb6lOQ5pWx5+59++75DTrVnkyZw223w1VcQVuIOLiIikkPO12BjjzHmk/EYYFDH\nB7Em95qMBqcHBp+SNGttmXS8s9Z+DHyc575hOT4eAgwpi+eW0hcVGUGqh0QtKjICTj8dJk6EXr1g\n7FiSr+mV69zEoLhGxMdE5ztPkXW/iIgULOdrcO/v5tBqyw8Mbv8fUmuckus6DU4PHL5ud1bJbGI7\n0xjzvjHmQWNMlbIOTgLLoLhGRITnXiGLCA+jbeM6tEpcQIMfarCgSWuOPvoor0yanevcxJCZq3k0\neXW+8xRDZq5WJZKIiA+yXoPr705lyMJX+eLMC5l9YQduuaSuBqcHKJ8GrBtj3gUOAG9m3nUzEGmt\n7V6GsRWbBqy7J19lUeM6vL8iNfucRM2D+/hs2r38VTWSzrc+Q3rF8OzvDTOGDA8/j9GRESxO8FjU\nKyIiOSSn/MaZ3TpS74/N3PrQVG6/8TIlZAHA24B1X8+kNbHW5pwG8IUxRk1nJZ/4mOhcLwitEhfk\nOsi6p2oNBre/n2nvj+DBxdMZ06ZP9tc8JWigA64iIr6K/+xN2PITvPkms265ye1wpIR8bVr1nTHm\nkqxPjDEtAC1VSaE8JVgLGl7MjPOvof+3M7lw2/FcP8wYj4+hA64iIj5YsQKGD4ebboKbb3Y7GikF\nviZpFwLfGGM2G2M2A0uAi4HO9kUAACAASURBVIwxq40xP5RZdBLwvCVY/9fuTrafWIen5zxN1fQ0\nIsLD6NniDI9n2nTAVUQkv+SVqc5534Q5tBvxMQe69YBTTnF6Unp50yuBxdftzvZlGoUErUFxjRgy\nc3WuLc+I8DDiL2nMqIMJTJg8gNFfTyNj8svEx0QTW+8kVXeKiBQiq3Ft1mvrrbMmUX3zBhZNepvL\natZ0OTopLb4maU9aa3vnvMMY80be+0TyykqwPCZe8U3hpB1cl5gIm5dBzA35zrSJiEh+ORvXttm4\ngj7ffcTU2M5M21uHxS7HJqXH1yTtvJyfGGMqohFN4qMCE68nnoDPP4c774QWLSAqqnyDExEJQFnn\nfWse3EfSx+NZV7suY9rcRroKrYJKgWfSjDFDjDEHgPONMfuNMQcyP98BzCqXCCW4VaoE06fDoUPO\nNIJjx9yOSETE70VFRoC1PDV3IpFpB3jwuoEcrlhJhVZBpsAkzVo7ylpbHUiy1p5ora2eeauVOQ1A\npOQaNYKnn4Z58+DZZ92ORkTE7w2Ka0Svn+bTYf03jGvdi59PPlOFVkHI12a2rT3db639qtQjKgVq\nZhuArIX4ePj0U1i2DJo1czsiERH/tW4dR5vHsCq6MTd2fYLTap6gQqsA5q2Zra9J2oc5Pq0CXAys\nsNb6ZRt4JWkBaudOOP98qFULli+HCC3bi4jkc/gwtGwJv/0G338P0UrMAp23JM2nPmnW2uty3K4G\nmgB7SjtICXF16sArr8BPP8HAgW5HIyLin4YOhZUrYepUJWhBztfqzry2AeeUZiAiALRvDwMGOGfU\nrroKbrjB52/NOzdUS/8iEnQ+/dR5fbznHujc2e1opIz5ut35PJB1YQUgBthkre1VhrEVm7Y7A1x6\nOlx6KWzcCKtWQd26hX5L3saO4DTNHdWlqRI1EQkOO3Y4R0JOPtk5u6sjIUGjRNudwBpgfeZtKfCw\nvyZoEgQqVYK334YjR+CWW+Do0UK/JWdjxyxpRzJImruurKIUESk/x47B7bfDvn0wY4YStBBRWJ+0\nisaYMcBI4I7M23igszEmvBzik1DVsKEzf27RIhg5stDLPQ1yL+h+EZGAMn48fPIJjBsHTZq4HY2U\nk8JW0pKAk4AG1toLrLUXAGcCkcDYsg5OQlyvXk6D2yefhC+/LPBSbw0c1dhRRALet9/C4MHOGd17\n7nE7GilHhSVp1wJ3WWsPZN1hrd0P/BvoWJaBiQAwYQIHzqjPn9d344L736JV4gKSV6bmu2xQXCMi\nwsNy3afGjiIS8Pbs4eAN3dhevTbN6t5Eq9FfeHwNlOBUWJJmrYfKAmttBscLCUTKTPIv+7jt6oeo\n8c9exs55hu17/mHIzNX5XqTiY6IZ1aUp0ZERGCA6MkJFAyIS2Kxle9ebCd/xO/dcO4h9VaqRujfN\n42ugBKfCkrQ1xphb895pjOkFrC2bkESOS5q7ju9qNeDJdnfSbmMK/b+d6bUgID4mmsUJ7diU2InF\nCe2UoIlIYJswgagvPmV0m9tYFXV8V0BFUaGjsD5p9wIzjTF3ACsy74sFIgDfG1iJFFPWwf83YjrR\n4rcfGfjV66Scfg4rOM/lyEREytCKFTBwIPPPuogpF+X/dauiqNBQ2ID1VGttC2AEsDnzNsJae7G1\nVmutUuayD/4bQ0KH+9kaeQoTZo3m3IqH3Q1MRKSs7N8PN90Ep5zC2J5DwJh8l6goKjT4OhZqgbX2\n+czb/LIOSiRLzoKAvytX5d7OQ6iZdoBp859z+gaJiAQTa+GOO2DzZpgxg/5dLlZRVAjztZmtiCvy\nFgTsa3QeaxJGcsrSL+Gpp9wOT0SkdI0fD++/D6NHQ6tWKooKcT6NhQo0GgsV5Kx1eqi9/TbMmwdt\n27odkYhItmLPEV68mGNXXMHXjS6hT6fBRNWsqhnEIaKkY6FE/Icx8NJL8K9/QY8ekKrjkSLiH7Lm\nCKfuTcOC7y0z/vyTtBu6srX6ydx39X+wxqjdhihJkwBVrRrMnAkHD8KNNzpD2UVEXFasOcIZGdCz\nJxX27OHu+AQOVD7B9++VoKYkTQLXOefAtGnwzTcwcKDb0YiIFG+O8LBhsGABj1xzDz+ffGbRvleC\nmpI0CWzdu8OAAfD88zB9er4vJ69MpVXiAhokzPE6UkpEpLQUeY7wRx85RVB9+7Lk8uuK9r0S9JSk\nSeBLTITWraFfP1i9OvvuYp8NEREppiLNEV6/Hm65BWJi4PnnNYNY8lGSJgEp1wrZuK/55NHxUKMG\ndOkC+/YBxTwbIiJSAj63zDhwAG64AcLD4YMPICJC7TYkH1dbcBhj2gPPAmHAFGttYp6vVwZeBy4E\ndgE3WWs3F/a4asER3LJWyHImYBHhYbx05iFa9+sOHTvCBx/QYOgnePrpNsCmxE7lFq+ISC7WOkc1\nPvgAPvsMrrzS7YjEZX7XgsMYEwZMBDoA5wI9jTHn5rmsL7DHWtsQeAYYXb5Rij/ytkI2ZMeJ8Mwz\nMHs2PPFE0c+GiIiUh9GjnYa1Y8YoQZMCubndeTGwwVq70VqbDrwNdM5zTWfgtcyP3wOuNMbDEDMJ\nKQVWT917rzNSZcQInq74q8fzHW0b11ExgYiUq6wjGrfdOIJjQ4eyLa6zU/QkUgA3k7RoYGuOz7dl\n3ufxGmvtUWAfUMvTgxlj+hljUowxKTt37iyDcMVfFLhCZgy88AK0aEGLxx9iwvnhuc53dL0wmvdX\npKqYQETKTdYRjQqbN/Hsh0msq12P65v1IXnVdrdDEz8XNIUD1trJ1tpYa21snTp13A5HylChFVCV\nKzuNbqtX58qEfizu15xNiZ1YnNCOL9buVDGBiJSrpLnrqPD3AV5+fyQA/W94hN0mnMdn/6RVfSmQ\nm0laKnBGjs9Pz7zP4zXGmIpADZwCAglhPlVARUU5idq2bdCzJxw9ChSz0aSISAn8vucfnpnzNA13\nbeXezgn8VvM0APamHdGqvhSooovPvRw42xjTACcZ6wHcnOea2cBtwBKgG7DABuNEeCmy+JjowsvS\nW7aEiRPhrrsgIQHGjiUqMoJUDwmZiglEpKwMX/Y21/yylOFX9Wdx/eZer8ta1VfLDcni2kpa5hmz\n+4C5wM/Au9ban4wxI4wx12deNhWoZYzZAAwAEtyJVgLWnXc6xQTjxsErr6hZpIiUrxkzuG3hW7wb\n057XLri20Mu1qi85ubmShrX2Y+DjPPcNy/HxIaB7ecclQeaZZ2DdOujfn/j586FLU5LmrmP73jSi\nIiMYFNdI71xFpPQtX+5Um7duTeWkF4hesCn7dedg+lH2HDyS71u0qi85udrMtqyoma3ks2cPXHIJ\n7NoFy5bBmfmHGIuIlJrt2+Gii6BSJec1J09Bm7em3JowEJr8rpmtSLmqWdMZZHzsGFx3Hezf73ZE\nIhKsDh6E+HhnRN2sWfkSNCjC+CgJaa5ud4qUq7PPhvfeg7g46NEDPvwQwsIK/z4REV8dOwa33gop\nKZCcDOef7/VSnwqgJKRpJU1CS7t2MGECfPIJDBzodjQiEmyGDnVGPj39NFx/feHXixRAK2kSevr3\nh59/hvHjoWFDp/pTRKSkpkxx5nL++9/wwANuRyNBQEmahKZx42DTJrj/fqhb1zmnJiJSXPPnO8lZ\n+/bw3HPOiDqREtJ2p4SmsDB46y244ALnfNqKFW5HJCKB6uefoWtXaNwY3nkHKmr9Q0qHkjQJXSec\n4BQP1KkD114LW7a4HZGI+Inklam+zdX84w/o2BGqVHEqyE88sXwDlaCmdF9C26mnwscfw6WXQqdO\nsGgRREYCzou0mt6KhJ68Pcyy5moCuV8DDhxwXjd27oSFC6FePReilWCmlTSRc891hrGvX+9sWaSn\nZ79Ia/ixSOhJmrsuV5NZOD5XM9uRI9C9O3z/PfzvfxCbrw+pSIkpSRMBpzXH1KmwYAH06cPYT34u\n/EVaRIKSt/mZ2fdbC3fdBXPnwuTJ0KFDOUYnoURJmkiW3r0hMRFmzOD2DyY4L8R5aPixSPDzNj8z\n+/5hw+C11+Dxx53ZnCJlREmaSE4PPwwPPEDflFn0WzYz35c1/Fgk+A2Ka0REeO5pJBHhYQyKa+Ss\nnD35JNx5p5OsiZQhFQ6I5GQMPP00237exNDPXmHnCTX5oEk7IMeLtIgEtazigHyFQ5u+dXqhdewI\nkyapF5qUOWM9bOkEutjYWJuSkuJ2GBLIDh/mz9ZXcVLKEvp2HcaGCy7LTtBU8SkSghYscM6eXXgh\nfP6508JHpJQYY1ZYa/NVnyhJE/Fm/35o08ap+pw/n+TKZ+QqywdndW1Ul6ZK1EQCWKHtdlJSoG1b\nqF8fvvwSTjrJ9+8V8YG3JE1n0kS8OfFEZxB7VBR06MDMVz9WxadIkCm03c7atc4KWu3aTjVnngRN\nrXqkLClJEynIqafCvHlwwgmMm/ow9fZsz3eJKj5F/I+vEwMK7In2229wzTVQoYKzxRkV5fv3ipQC\nJWkihalXDz7/nIpYpr/9KKfu/yvXl1XxKeJfirLC5e1N1uHU3yEuDvbtc1bQGjb0+Xv1xk1Ki5I0\nEV+ccw6rJr9NjcN/8+Y7j3LSwX2AKj5F/FFRVrg8vcmqkXaAGe8Pd+b5fvQRNG/u8XkK7acmUkJK\n0kR81Pbm9qya+AZn7P+T194dRqPKGSoaEPFDRVnhytsTrdrhg7zx3nDO/GsrzJoFl1/u9XkK7Kcm\nUgqUpIkUweV9u1B5djJNd//G3M9GEX9WdbdDEpE8irLCFR8TzaguTYmOjKBq+iHeTB5Jkz83Evb+\ne3D11QU+T87vNUB0ZITeuEmpUgsOkeJITnaGK19yiVMBWq2a2xGJSKasM2lFapdz6BBcd53TD23G\nDLjxxnKKVkQtOERKV3y880K+ZInzwn7woE/f5mvFmYgUX5FXuNLTnaRs3jyYNk0JmvgNraSJlMRb\nbzmD2du1gw8/hCpVvF5arHf3IlK2shK0WbOcUU933+31UjWulbKilTSRsnDzzTBtGnb+fJY0a02j\ngcleV8jUU0nEz+RM0CZMKDRBU+NaKW8asC5SQsnnX0VKxwd4cs54XvzgSe6+4RGGzFxNypbdfLF2\nZ/a77lT1VBLxH+npzrnS2bOdBO3eewu8vKA3WVpNk7KiJE2Ekm1jJM1dR2qTqziSkcGoTyfw8vsj\n6dflEaYv/Y2swwSpe9MwgKfDBeqpJFLOciZoEyfCPfcU+i1qXCtu0HanhLySbmNkvUi/0yyOQR0f\n5LLNq5j23giqpB/KdZ0FTJ7vVU8lkXJ2+DB061akBA3UuFbcoSRNQl5Jz4rlfJF+v+mVDLh2AC22\n/sir7z1O1fTc77ItqKeSiFsOHnQqsz/8sEgJGqhxrbhD250S8kq6jTEorlGuqs3k89qSYSrwzEfj\neO3d4dze/XH+rlwVcBKzxQntSidwVG0m4rMDB5x2OV99BVOmQN++Rfr2rP+v9P+blCclaRLyvB3q\n93Ubw9OLd407evPfSuGM/WA0099+hD7dH+dQjZNK9V133pYeWdu0OWMSEWDPHujQAVJSYPp06Nmz\nWA8THxOt/7ekXLmSpBljTgLeAeoDm4EbrbV7PFyXAazO/PQ3a+315RWjhI68K2FQ9G0MTy/eyfVO\nYugJVRn51ghmvjOUda+/R/tSfIFXtZmID3buhGuugTVr4L33nO1OkQDh1pm0BGC+tfZsYH7m556k\nWWubZ96UoEmZKKv5e/Ex0SS99ghVPp9Lg4O7aH93d/j119IJGlWbiRQqNRXatIG1a51Cgfh4Tf2Q\ngOLWdmdn4IrMj18DFgKDXYpFpGy3Ma64wpkH2L49XHYZfP45NGlS4oct6TatSFBbtw7i4mDXLvj0\nU2jTRkcEJOC4tZJ2irX298yP/wBO8XJdFWNMijFmqTFGa9QSuC66yDmwbAy0bg3fflvih1S1mYgX\nKSnOG6KDB2HhQmc1DU39kMBTZkmaMWaeMeZHD7fOOa+zzvBQbwNE62XOsroZGG+MOauA5+uXmdCl\n7Ny5s/T+Q0RKy3nnwaJFULOmM+tzzpwSPVxZbdOKBLR586BtW6hWDRYvhgsvzP6SjghIoCmz7U5r\n7VXevmaM2WGMOc1a+7sx5jTgTy+PkZr550ZjzEIgBvB4qMdaOxmYDM6A9RKGL1I2zjwTvvkGOnaE\nzp1h8mS4445iP5yqzSQQlVnrmHfegd69oXFjZ4szKirXl3VEQAKNW9uds4HbMj++DZiV9wJjTE1j\nTOXMj2sDrYA15RahSFk55RRnC+bKK51eTU8+CVbvKyQ0lNmg8ueec1prXHKJc7QgT4IGOiIggcet\nJC0RuNoY8wtwVebnGGNijTFTMq85B0gxxnwPfAEkWmuVpElwqF7d6Xreuzc89pjT+Twjo/DvEwlw\npX4uLCMDHnoIHnjAWZ2eOxciIz1eqiMCEmhcqe601u4CrvRwfwpwZ+bH3wBNyzk0kfJTqRK89prz\njn/0aKddwFtvOWdpRIJUqZ4LO3gQevWCDz5wkrRx4yAsrMBv0REBCSSa3SniJmNIvuk/jLv+P2R8\nNIf1/4rh00+Xux2VSJkptUHlf/7pFAgkJ8P48c6tkARNJNAoSRNxUdb5nOfPiaNv12FE7Uol5sYO\nfDFjrtuhiZSJUjkXtnatc/Zs9WqYOdNZRRMJQkrSRFyU83zOwrNi6XbLGI5SgUtui3c6pIsEmRKf\nC5s710nQ/v7bKcDRmCcJYsYGYVVZbGysTUlJcTsMkUI1SJiTr0lgnb/3MGXmCJr9sQGSkmDAAKcJ\nrkgZK7PWGKXBWqeCc8AAaNoUZs2CevXcjkqkVBhjVmT2hc1FK2kiLvJ0DmdntZo8dPd46NoVBg6E\nW2+FNDXblLJVZq0xSkN6Otx1Fzz4oFPBuWiREjQJCUrSRFzk7XzO/dc1g3ffhZEj4c034fLLYetW\nnx5TA6SlOPx2ZNLOnXDVVTB1Kjz6KLz3niqgJWS4NWBdRDg+1NnrFtOjj8L550OvXhxqfgEPdX+U\nTyMbet2K0gBpKa7SaI1R2tulC9+cQ+P77iDyn7081eMRLuhyN/EVtLYgoUNJmojLCu3bdP31zHtl\nNg379eK5l//LE1f1583mHTwmXwWthihJk4KUdGRSab9BWPnYGC4d9Qh/nnAS3W4Zw4+nNuR/esMh\nIUZvSUQCwPBfjnF973Esqt+cJz97gXFznoZ//sm3FaUB0lJcJW2NUWrbpYcOwZ13EvPkYJae0ZRr\n+4znx1MbZj/e47N/0na+hAytpIkEgO1707BVqtG36zDuW/IuDy56iyY7fuWe+CFAu+zrNEBaisvb\n1jtAq8QFhW5hlsobhC1bnIKZFSuY0PImnr7sZo5VyJ047k07wt60I4C28yX4aSVNJABkJVnHKoTx\nXKue3HrjCGr/s5cPXx8A77yTfZ0GSEtJxMdEszihHZsSO7E4wUn+fa34LPEkgVmzICYGfvkFZs1i\nxvX98iVonvhFcYNIGVGSJhIA8iZfixrE0PWuCaQ1Phd69ID//AcOHdIAaSlVRdnCLPYbhMOHndYa\n8fHQoAGsWAHXX+/x8bzRdr4EK213igQAT1tRD97Ujlpje8DgwfDMM/D11zBjBvEx5ygpk1JRlC3M\nQiuVPdmwAW66Cb77Du6/H8aMgcqVvT7ewfSj7Dl4JN/D1IgI92lLViTQaOKASDCYMwf69IF//nEG\nTd91l6YUSIm1Slzg8YxjdGYiVKJ2G2+/Df36QcWKMG2aT+Od8laQAoRXMGDgSMbx32UR4WFaQZaA\nookDIsGsUyf44Qdo1Qr694du3WD3brejkgDnbQuzbeM6xZ9OsHcv9OoFPXtCkyawapXP8zc9bedX\nq1IxV4IGOqcmwUNJmkiwOO00Z/j0mDHOcPZmzWDePLejkgDm7YzjF2t3Fq/dxhdfOM2Z334bnngC\nvvoK6tYtckw5ixv2etj+BJ1Tk+CgM2kiwaRCBRg0CNq2hd694eqr4Z57nMTthBPcjk4CkKdmyw+9\ns8rjtV4To0OHnOkZTz8NDRvCN9/AxReXSnxqOyPBTCtpIn6oxPM3Y2Odw9gPPQSTJjmraosWlU2w\nEnKK0m5j4fSP+bX+uTBuHDMvvo4PX51TagkaqO2MBDclaSJ+JutwdLHO++QUEeGsXHzxBf8cOsKx\n1q2Z3KIrbUd+oi7tUiI+JUZpaazvcw+X976OE/7ZR59uwxlwRT8e/uTXUv35U9sZCWaq7hTxMwVV\n1GU1GC2K5JWpjJzxLf/97GVu/v5TNkeexhOd/kPn/96qX2RSbAUOU1+0CPr2hfXrmXH+NYxqewf7\nq1TL/t7i/iyLBCtv1Z06kybiZ0p7/mbS3HXsqlCZoe3v48NzLuepuRN4ZfpQ5qz9EuZOh1q1ShKu\nhChPZ9XYvx8eeQQmToR69eh105Msqt8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      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_curved = np.hstack((x, x**2))\n",
    "lm_curved2 = LinearRegression(x_curved, g_curved)\n",
    "y_curved2 = lm_curved2.predict(x_curved)\n",
    "\n",
    "plt.scatter(x, g_curved);\n",
    "plt.plot(x, y_curved2, color=\"red\");\n",
    "plt.xlabel(\"Input\")\n",
    "plt.ylabel(\"Output\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Neural networks are generic function approximators\n",
    "\n",
    "One of the primary challenges with transforming the inputs to a linear model is that it requires some level of a priori knowledge about the type of transformation that is necessary.  In the above example, we knew that a quadratic transformation was appropriate through visualization.  In sophisticated, high-dimensional problems we often have no way to know what type of input transformation will work.\n",
    "\n",
    "In order to solve this problem in a generic way, we can add a new layer to our model that contains flexible nonlinearities that can automatically learn to fit inputs.  This approach is known as a Neural Network (NN) and is also sometimes called a Multilayer Perceptron (MLP).\n",
    "\n",
    "Universal approximator..."
   ]
  },
  {
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    "![ann.svg](attachment:ann.svg)"
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    "Again, assume that our input matrix $\\mathbf{X} \\in \\mathbb{R}^{N \\times F}$.  We now have two weight matrices: a hidden weight matrix for our nonlinearities and a visible weight matrix for our final linear regression. $\\mathbf{W}_h \\in \\mathbb{R}^{F+1 \\times M}$ and $\\mathbf{W}_v \\in \\mathbb{R}^{M+1 \\times K}$\n",
    "\n",
    "Equations for the forward pass (to evaluate the network):\n",
    "\\begin{align}\n",
    "  \\mathbf{Z} = & \\phi( \\mathbf{W}_h \\mathbf{\\tilde{X}} ) \\\\\n",
    "  \\mathbf{Y} = & \\mathbf{W}_v \\mathbf{\\tilde{Z}}\n",
    "\\end{align}\n",
    "\n",
    "Our error function is, again, squared error:\n",
    "\\begin{align}\n",
    "  E = & (\\mathbf{Y} - \\mathbf{G})^2\n",
    "\\end{align}\n",
    "\n",
    "We can find the gradient of the visible layer\n",
    "\\begin{align}\n",
    "  \\nabla_{W_v} E = & \\nabla_{Y} E \\cdot \\nabla_{W_v} Y \\\\\n",
    "   = & \\mathbf{Z}^T 2(\\mathbf{Y} - \\mathbf{G}) \\\\\n",
    "   = & \\phi(\\mathbf{W}_h \\mathbf{\\tilde{X}})^T 2(\\mathbf{Y} - \\mathbf{G})\n",
    "\\end{align}\n",
    "\n",
    "and the gradient of our hidden layer\n",
    "\\begin{align}\n",
    "  \\nabla_{W_h} E = & \\nabla_{Y} E \\cdot \\nabla_{H_v} Y \\\\\n",
    "  % = & \\mathbf{\\tilde{X}}^T 2(\\mathbf{Y} - \\mathbf{G})^T \\phi^\\prime(\\mathbf{W}_h \\mathbf{\\tilde{X}})\n",
    "\\end{align}"
   ]
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   "source": [
    "We cannot, however, set the gradient to zero like we did for linear regression.\n",
    "\n",
    "This is because optimizing a neural network is not a convex problem.  There may be many optimal solutions, called local minima.\n",
    "\n",
    "To see this, notice that there are symmetries for each hidden unit."
   ]
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   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def weight_init(size):\n",
    "    \"\"\"Initialize NN weight matrices, Lecun fast backprop\n",
    "    \"\"\"\n",
    "    return np.random.uniform(-np.sqrt(3.0 / size[0]),\n",
    "                np.sqrt(3.0 / size[0]), size=size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "class ForwardNet(object):\n",
    "    def __init__(self, x, g, nh,\n",
    "                 phi=np.tanh,\n",
    "                 phi_prime=lambda v: 1.0 - np.tanh(v)**2,\n",
    "                 **kwargs):\n",
    "        \"\"\"Feedforward neural network with two fully-connected layers.\n",
    "        \"\"\"\n",
    "        ni = x.shape[1] # num inputs\n",
    "        no = g.shape[1] # num outputs\n",
    "        self.phi = phi  # transfer func\n",
    "        self.phi_prime = phi_prime # grad of trans func\n",
    "\n",
    "        # initialize hidden weights\n",
    "        self.hw = weight_init((ni+1, nh))\n",
    "        \n",
    "        # initialize visible weights\n",
    "        self.vw = weight_init((nh+1, no))\n",
    "        \n",
    "        self.train(x, g, **kwargs)\n",
    "\n",
    "    def gradient(self, x, g):\n",
    "        \"\"\"Compute MSE and error gradients\n",
    "        \"\"\"\n",
    "        # forward pass\n",
    "        x1 = bias(x)\n",
    "        h = x1 @ self.hw\n",
    "        z1 = bias(self.phi(h))\n",
    "        z_prime = self.phi_prime(h)\n",
    "        y = z1 @ self.vw\n",
    "        \n",
    "        # error components\n",
    "        e = y - g\n",
    "        delta = 2.0 * (y - g) / e.size\n",
    "\n",
    "        # visible layer gradient\n",
    "        vg = z1.T @ delta\n",
    "\n",
    "        # error backprop through visible layer\n",
    "        delta = delta @ self.vw[:-1].T * z_prime\n",
    "\n",
    "        # hidden layer gradient\n",
    "        hg = x1.T @ delta\n",
    "\n",
    "        # error, hidden grad, visible grad\n",
    "        return np.mean(e**2), hg, vg\n",
    "    \n",
    "    def train(self, x, g,\n",
    "              learning_rate=0.1, maxiter=5000, tol=1.0e-5):\n",
    "        \"\"\"Steepest descent\n",
    "        \"\"\"\n",
    "        i = 0\n",
    "        prev_error = np.inf\n",
    "        while True:\n",
    "            error, hg, vg = self.gradient(x, g)\n",
    "            \n",
    "            if (i % 100) == 0:\n",
    "                print(i, error)\n",
    "\n",
    "            if np.abs(prev_error - error) < tol:\n",
    "                print(\"reached tol\")\n",
    "                break\n",
    "            \n",
    "            if i > maxiter:\n",
    "                print(\"reached iter\")\n",
    "                break\n",
    "\n",
    "            self.hw -= learning_rate * hg\n",
    "            self.vw -= learning_rate * vg\n",
    "            \n",
    "            prev_error = error\n",
    "            i += 1\n",
    "\n",
    "    def predict(self, x):\n",
    "        \"\"\"Compute predictions for inputs x\n",
    "        \"\"\"\n",
    "        h = x @ self.hw[:-1] + self.hw[-1]\n",
    "        z = self.phi(h)\n",
    "        y = z @ self.vw[:-1] + self.vw[-1]\n",
    "        return y\n",
    "    \n",
    "    def eval_hidden(self, x):\n",
    "        \"\"\"Generate outputs of hidden units.\n",
    "        \"\"\"\n",
    "        h = x @ self.hw[:-1] + self.hw[-1]\n",
    "        z = self.phi(h)\n",
    "        return z"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our quadric example again..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 1.2723877003432735\n",
      "100 0.1112930946913207\n",
      "200 0.04307358497418107\n",
      "300 0.028289726612308108\n",
      "400 0.022211492667359445\n",
      "500 0.01915311024513723\n",
      "600 0.017435331235376474\n",
      "reached tol\n"
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Gvfsu/9f5RrZ8vZPXl/1Q1JezsHE6oBpoYcDXBuszjTFlEh9rrceEyUfZQPGR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\nZpYgN2lmZmZmCfoTSGCvxeqVN/oAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nn_curved = ForwardNet(x, g_curved, nh=5, learning_rate=0.1)\n",
    "y_curved_nn = nn_curved.predict(x)\n",
    "\n",
    "plt.scatter(x, g_curved);\n",
    "plt.plot(x, y_curved_nn, color=\"red\");\n",
    "plt.xlabel(\"Input\")\n",
    "plt.ylabel(\"Output\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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PIrV/NJEJdknoOrkKRwV7K/eyp2oPeyr3sL96P3ur9lLrqj1SJtwcTlZkFpmRmWRFZvmX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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "z_curved_nn = nn_curved.eval_hidden(x)\n",
    "plt.plot(x, z_curved_nn);\n",
    "plt.xlabel(\"Input (x)\")\n",
    "plt.ylabel(\"Hidden unit response (z)\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Something a little more sophisticated"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 1.6171976294298265\n",
      "100 0.11186027633140838\n",
      "200 0.11024823513110617\n",
      "300 0.1089209635292726\n",
      "400 0.10759353403007871\n",
      "500 0.10608882308015342\n",
      "600 0.10427279235774833\n",
      "700 0.10201478818278634\n",
      "800 0.09916321157636462\n",
      "900 0.09553540684355748\n",
      "1000 0.09093770500961687\n",
      "1100 0.08523943368063996\n",
      "1200 0.07847174842907936\n",
      "1300 0.07084730964255596\n",
      "1400 0.06268887575174613\n",
      "1500 0.05437468447478249\n",
      "1600 0.04632270787501674\n",
      "1700 0.03895016204410438\n",
      "1800 0.03257916637565257\n",
      "1900 0.027351673446375374\n",
      "2000 0.023225231994035086\n",
      "2100 0.020036337854225216\n",
      "2200 0.017577306849734263\n",
      "2300 0.015652417040407568\n",
      "2400 0.014105440873672801\n",
      "2500 0.012824823826253638\n",
      "2600 0.011736725831783376\n",
      "reached tol\n"
     ]
    },
    {
     "data": {
      "image/png": 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4917Yay8gdP9F9WUUEVCSJiISfdu2wciRXj20oUN3HQ63GbeI1E3aOCAiEm0P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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "g_ripple = g + 0.5 * np.sin(4*x)\n",
    "g_ripple -= g.mean(axis=0)\n",
    "g_ripple /= g.std(axis=0)\n",
    "\n",
    "nn_ripple = ForwardNet(x, g_ripple, nh=10, learning_rate=0.1)\n",
    "y_ripple = nn_ripple.predict(x)\n",
    "\n",
    "plt.scatter(x, g_ripple);\n",
    "plt.plot(x, y_ripple, color=\"red\");\n",
    "plt.xlabel(\"Input\")\n",
    "plt.ylabel(\"Output\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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1sbTVT0MsgUmBE90ZLMzLYkFOJiW2/rk0FAuH2PTfpWxY+iJhv4+iUWOYtehi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lM/jc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\n+AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "z_ripple = nn_ripple.eval_hidden(x)\n",
    "plt.plot(x, z_ripple);\n",
    "plt.xlabel(\"Input (x)\")\n",
    "plt.ylabel(\"Hidden unit response (z)\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Alternative optimization techniques\n",
    "\n",
    "Steepest descent has a lot of problems...\n",
    "\n",
    "Batch / offline:  full gradient\n",
    "\n",
    "Stochastic / online:  one sample at a time\n",
    "\n",
    "Mini-batch stochastic:  small mini-batch of samples for each update\n",
    "\n",
    "## Stochastic Gradient Descent\n",
    "\n",
    "Update weights for each observation, or a small mini-batch of them\n",
    "\n",
    "Can avoid local minima\n",
    "\n",
    "works well if cannot fit data into memory or are continually updating model\n",
    "\n",
    "tends to require fewer passes over all the data\n",
    "\n",
    "but is noisy (stochastic)\n",
    "\n",
    "and performs lots of small and expensive gradient evaluations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "class ForwardNetSGD(ForwardNet):\n",
    "    \"\"\"Feedforward network using Stochastic Gradient Descent\n",
    "    \"\"\"\n",
    "    def train(self, x, g, batch_size=10,\n",
    "              learning_rate=0.1, maxiter=5000, tol=1.0e-5):\n",
    "        i = 0\n",
    "        prev_error = np.mean((self.predict(x) - g)**2)\n",
    "\n",
    "        while True:\n",
    "            if i > maxiter:\n",
    "                print(\"reached iter\")\n",
    "                break\n",
    "            \n",
    "            for start in range(0, x.shape[0]-1, batch_size):\n",
    "                end = min(start+batch_size, x.shape[0]-1)                \n",
    "                _, hg, vg = self.gradient(x[start:end], g[start:end])\n",
    "                \n",
    "                self.hw -= learning_rate * hg\n",
    "                self.vw -= learning_rate * vg\n",
    "\n",
    "            error = np.mean((self.predict(x) - g)**2)\n",
    "            \n",
    "            if (i % 100) == 0:\n",
    "                print(i, error)\n",
    "\n",
    "            if np.abs(prev_error - error) < tol:\n",
    "                print(\"reached tol\")\n",
    "                break\n",
    "            \n",
    "            prev_error = error\n",
    "            i += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 1.59381196409321\n",
      "100 0.13399162650915225\n",
      "200 0.12721549764481888\n",
      "300 0.12500571258241205\n",
      "400 0.12345153113444972\n",
      "500 0.12195269061012654\n",
      "600 0.12042761244416149\n",
      "700 0.1188034098097414\n",
      "800 0.11695818995401604\n",
      "900 0.11473273876224432\n",
      "1000 0.11212174327286119\n",
      "1100 0.10931380706517672\n",
      "1200 0.10633119396964195\n",
      "1300 0.10311223698659912\n",
      "1400 0.09965964683605268\n",
      "1500 0.09601783521233984\n",
      "1600 0.09223883807715462\n",
      "1700 0.08837034938406786\n",
      "1800 0.08445184117778629\n",
      "1900 0.08051310142340302\n",
      "2000 0.07657667624604574\n",
      "2100 0.07266380633954346\n",
      "2200 0.06879864267526976\n",
      "2300 0.06500370221353298\n",
      "2400 0.06128314114772787\n",
      "2500 0.0576004238685464\n",
      "2600 0.053889210235500216\n",
      "2700 0.050176934315300174\n",
      "2800 0.04665651993392122\n",
      "2900 0.043443541333521976\n",
      "3000 0.04050268785972002\n",
      "3100 0.03777499396521457\n",
      "3200 0.03522088643077816\n",
      "3300 0.03281362017949456\n",
      "3400 0.030532830620618352\n",
      "3500 0.028362322238931977\n",
      "3600 0.026287711389304334\n",
      "3700 0.024294650456415066\n",
      "3800 0.02237228425429318\n",
      "3900 0.020520069466889012\n",
      "4000 0.01874927885359521\n",
      "4100 0.017077298439337075\n",
      "4200 0.015520881364415977\n",
      "4300 0.014092478005196212\n",
      "4400 0.01279923912977919\n",
      "4500 0.011643205005571073\n",
      "reached tol\n"
     ]
    },
    {
     "data": {
      "image/png": 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ElBIlTOf456dPc/hvq7j9wiEktDkYA5ITA4zq14W+3ZJ9i1Oi/wgOERERiaDCNWgAl879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\nDfobOnNVo+aFSEQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_scale = 1.0 * x + 2.0\n",
    "\n",
    "g = 20.0*x_scale + np.random.normal(size=(ns,1))\n",
    "g -= g.mean(axis=0)\n",
    "g /= g.std(axis=0)\n",
    "g_ripple = g + 0.5 * np.sin(4*x_scale)\n",
    "g_ripple -= g.mean(axis=0)\n",
    "g_ripple /= g.std(axis=0)\n",
    "\n",
    "nn_ripple_sgd = ForwardNetSGD(x_scale, g_ripple, nh=10, learning_rate=0.01)\n",
    "y_ripple_sgd = nn_ripple_sgd.predict(x_scale)\n",
    "\n",
    "plt.scatter(x_scale, g_ripple);\n",
    "plt.plot(x_scale, y_ripple_sgd, color=\"red\");\n",
    "plt.xlabel(\"Input\")\n",
    "plt.ylabel(\"Output\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Conjugate gradients\n",
    "\n",
    "Uses full gradient, assumes error surface can be approximated by quadratic function in a local neighborhood"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.optimize as spopt\n",
    "\n",
    "class ForwardNetCG(ForwardNet):\n",
    "    def train(self, x, g,\n",
    "              maxiter=500, tol=1.0e-6):\n",
    "\n",
    "        def error_func(v):\n",
    "            self.hw.flat[...] = v[:self.hw.size]\n",
    "            self.vw.flat[...] = v[self.hw.size:]\n",
    "            return np.mean((self.predict(x) - g)**2)\n",
    "        \n",
    "        def grad_func(v):\n",
    "            self.hw.flat[...] = v[:self.hw.size]\n",
    "            self.vw.flat[...] = v[self.hw.size:]\n",
    "            _, hg, vg = self.gradient(x, g)\n",
    "            return np.concatenate((hg.flatten(), vg.flatten()))\n",
    "        \n",
    "        def callback(v):\n",
    "            if (callback.i % 100) == 0:\n",
    "                self.hw.flat[...] = v[:self.hw.size]\n",
    "                self.vw.flat[...] = v[self.hw.size:]\n",
    "                print(callback.i, np.mean((self.predict(x) - g)**2))\n",
    "            callback.i += 1\n",
    "        callback.i = 0\n",
    "\n",
    "        method = \"BFGS\"\n",
    "        options = {\"maxiter\": maxiter}\n",
    "        w = np.concatenate((self.hw.flat, self.vw.flat))\n",
    "        optres = spopt.minimize(fun=error_func, method=method,\n",
    "                x0=w, tol=tol, jac=grad_func, options=options)#, callback=callback)\n",
    "\n",
    "        print(optres)\n",
    "        print(\"error: \", np.mean((self.predict(x) - g)**2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      fun: 0.00246915745731666\n",
      " hess_inv: array([[ 5.0327e+01,  2.8182e-02,  5.4347e+01,  9.7661e+00, ...,\n",
      "         3.5631e+00, -3.0847e+01, -4.0374e+01, -9.7853e+00],\n",
      "       [ 2.8182e-02,  2.7082e+01,  1.0074e+02,  2.9949e+01, ...,\n",
      "         1.8472e+01, -2.9060e+01, -1.0531e+02,  4.3195e+01],\n",
      "       [ 5.4347e+01,  1.0074e+02,  4.8906e+02,  1.3734e+02, ...,\n",
      "         8.2194e+01, -1.6427e+02, -4.8530e+02,  1.6620e+02],\n",
      "       [ 9.7661e+00,  2.9949e+01,  1.3734e+02,  4.7224e+01, ...,\n",
      "         2.8770e+01, -5.3429e+01, -1.5838e+02,  5.3672e+01],\n",
      "       ...,\n",
      "       [ 3.5631e+00,  1.8472e+01,  8.2194e+01,  2.8770e+01, ...,\n",
      "         1.9211e+01, -3.2451e+01, -9.8318e+01,  3.4489e+01],\n",
      "       [-3.0847e+01, -2.9060e+01, -1.6427e+02, -5.3429e+01, ...,\n",
      "        -3.2451e+01,  7.2523e+01,  1.8494e+02, -5.1743e+01],\n",
      "       [-4.0374e+01, -1.0531e+02, -4.8530e+02, -1.5838e+02, ...,\n",
      "        -9.8318e+01,  1.8494e+02,  5.5171e+02, -1.8725e+02],\n",
      "       [-9.7853e+00,  4.3195e+01,  1.6620e+02,  5.3672e+01, ...,\n",
      "         3.4489e+01, -5.1743e+01, -1.8725e+02,  7.9582e+01]])\n",
      "      jac: array([-9.7644e-04,  2.4594e-04, -5.2496e-06, -4.4166e-04,  5.0041e-05,\n",
      "       -1.5085e-04, -6.5780e-04,  2.2680e-04, -1.3022e-04, -5.2381e-04,\n",
      "       -9.3809e-04,  1.4269e-04,  6.4173e-06, -3.6616e-04,  1.9276e-04,\n",
      "        2.1294e-04,  1.3697e-03,  1.3742e-04,  3.4747e-05,  3.0874e-04,\n",
      "       -1.2928e-05, -1.7463e-04,  2.3611e-04,  1.0086e-04, -3.2683e-04,\n",
      "       -1.9041e-04,  2.3476e-04,  5.3742e-05,  3.8784e-04, -2.9698e-04,\n",
      "        2.3511e-04])\n",
      "  message: 'Maximum number of iterations has been exceeded.'\n",
      "     nfev: 155\n",
      "      nit: 150\n",
      "     njev: 155\n",
      "   status: 1\n",
      "  success: False\n",
      "        x: array([-2.0947, -0.0208,  2.9069,  1.1244, -1.2106, -1.035 ,  1.5862,\n",
      "       -0.0281,  1.7245, -1.6365,  2.2363, -0.9213,  6.8374, -0.9267,\n",
      "       -1.1209, -0.1256,  0.7542,  0.2795,  2.2306, -3.0978, -2.6676,\n",
      "        1.3533, -2.8993, -1.8429,  1.963 ,  2.1612,  4.7253,  0.6161,\n",
      "       -1.3654, -3.2126,  2.4249])\n",
      "error:  0.00246915745731666\n"
     ]
    },
    {
     "data": {
      "image/png": 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t27Kvi0t0ltlnk9XItUDHjjFu9hhuXhnP2x1vILbLndmnQh0hhIc6MLgrWlrR\nKcVNlS0R8W9Hjri7rc+cCY8/DrGxxK3eWWa2rkn2UMnyJFf15bzz4KOP4Omn4eWX3XPWxo2DwYOJ\n73kHw3/eU6afTYHP7PBh6N+fbqt+4JUrB/N+u77ZpxwhQTzXu2WpexZSuqmyJSL+a+9euOoq7KxZ\njO77CI2CuxL1+k+M/OaPM694+Jn8tgQqVPWlcWP3ljN//QV33AHjxtG1VxQjZr1NnQO7si8ra88m\nv+NxiU6uefZrljWLJP37uSx/5jUiXn1OVSzxOVW2RMQnCpz4vG0bREeT/td6Hu0/ghnndQQ8z2nK\nUtgqkT+JiY7w2PfrtKovDRvCBx/A8OF81fd+blwZzw0r5/BFm6t4/5KBOKvWLlPPxtP8qrhEJ+9+\nOIf/fPE8jfdu44E+w/gxoyWxoInv4nNKtkSkxBU48XntWoiOhv37GXpHLDOrF27ycmE3jvYnXm1W\n2rAh794Yw7sdr+eBX7/g+t+/54bf5zC9ZVemXn1rkeL0RVuN03k2v475kKlfvooF7rzuOX5ueCFo\no27xE2r9ICIl7pT7/HWv4e6gHhwMs2fTaIrT4wbMeWnrGreciWydA7sY8ts0bloZT4WMNMyNN8KI\nEdCy5Rl/Zha/ed6pqTBsGIwZw8pzm/JgnyfZFnpu9mn1z5KSpNYPIuI38hvSqvj3nxzr+jQpGeW4\nfsCLpM3eS2ilEI97GYY6QjirQnCpb2DqbbmqQdRi/HWPcG7sSM6bNI7wKROo9NlnLGp+Cfbxx+l8\n9wCPG3R76vuV3xw5Xz3zuEQnEz//kac/HclFyUlM7tCHZzvdwfHgkFzXlcZqp5Q9SrZEpMSFhTpO\nqmzVS9nB5M+f5kBGBjfe/DKbq9WBFBch5QwhQYbU9BP1La0oOyG/4b2czyYu0Unv+n2ocN9l3L5s\nJrcmzqLmPQPZ98YFVHtmOAwY4K4kUri+X1l8NQ8sbtlWlj43hg/nfkhwRhoP9BnG9y06u8tYeX5P\n1D9L/IGSLREpdnkTgq7NazF1mTP7H/RzD+xm8pSnKJ92nBtuimVj9ROJQmqGVRUrH4Vt+pnVr8rl\nqMJbnW5mbIcB9P9jAfcvi6PajTdCgwburvR33XVafb98UjX65RciBt5JX2cSy8Ka8/i1j7Kpejjo\n90T8mOZsiUixym++z4B24SxYt4vjzmSmThlOHVcKAwa8wO91mp70GZp349kp577lWIHXaNgsj/Pe\nytkMPquzm/Jvv8VFG1aSVi6I2U078tmF1/BLgzZYk393oBKfs7V9u3tu1sSJ7Khcndgud/J1iy65\nhkH1eyK+pjlbIuIT+XUBX/vqZWYAACAASURBVLBuF4vvbQuXPwJH9kJ8PHsWHQcPyYPm3XhW2Kaf\nnoZtAapUqsCde+rgGvgSTfZs5aYVsxmwej49kxaxsVod4lp0ZWbzzvxds16hq0ZeX7X411/urYn+\n+184fhyGD+eWClGs9/Cj6/dE/JWSLREpVvklBDv3HHRvKL1uHcyaBZ06EXOW5yqY5t14ll8SlTfp\nyK9flTFkH/u7Rj1e7HYPoy+/nR5Ji7lhZTxDF0/m0cWf8WethqQPGMD5QwdD8+b5xlPUvQyzpae7\nfyfefde9B2ZwsPt35YUX4LzzeCifaql+T8RfqYO8iBQrj9UGa3n9h3Ewf767A/pVVwHuf5Bj+7dW\nx+9CiomOwBESlOuYp6Qjv+ea4mGV57Hg8kxv2ZXHH3iLjg9MYEyvh6le9xzO/2AMnH++u2v9XXe5\n92jcsiXXe4u0l+H+/fDNN/Doo9CkCfTpA6tXw8iR7vtMnuzepugUP49+T8Rfac6WiBQrT3O27l8W\nx5Nzx7t7Pr30kg+jK/2KMmxX2DlfACQnw7Rp7gT5hx/cWykBzup1WFmrMbvqNGBVpdpsqBbOpuph\n7HVUyZ5PlWsu1dGj4HTy04JE5s1NpPbmP7l822paJP+JyciAChXg8sthyBDo3RtCcrdyEPFn+c3Z\nUrIlIsUuZ0JwffJyRk16FjNgAHz+OZRTgd1XzrhZaUYG87+cxy8fTaPdppU03b2F+ik7CMk48TkZ\nGI4Hh3A8KIS0kBCqh1Z2J1q7d+f6qNRyQayoE8HSRhfQ5rZ+dLq1F1Ss6PWfVaQkKNkSEd9LTIRO\nndwdzBcuhEqVfB1RwDvTyljeqlhwehrhB3bSeK+TRnuTCXUdoHx6KpVIp3P9KjQ6O9hdtQoP56WV\nB1gTVJUdlWvgrFqLoyHu5MpjRU2kFNFqRBHxre3boVcvqFEDvv5aiZafyNsAtbDyLnxICwpmc7Uw\nNlcL4892jlzJW6M8nz8+n1YUpXGzbJHCULIlIsUvNRWuvx5SUmDxYqhTx9cRSRHltxLSU3Uqb/Us\nvy2Y1LpByipNlhCR4jdiBCxaBOPGwQUX+Doa8YLCroTMmhfmTHFhcbeDOHQ0jZAgc9J7uzavRdSo\n+TQaNouoUfOJS3QW948hUiJU2RKR4jV9Orz2GjzwANx8s6+jES/JteH1KeZ7eWoH4WkLprxbOJ1x\njy4RP6QJ8iJSfP7+Gy66CCIi4Kef3BOkJaDkt1VQ3q11TqsNhYifym+CvIYRRaR4uFwwYAAEBcGX\nXyrRClD5zcPKe7ywWw+JlEZKtkTEq+ISnUSNms/nl/SFlSv5ZeSb0KCBr8MSHyns3K7CJmUipZGS\nLRHxmqzJ0B0WzeSG3+fwdscbuGtnbU10DmCF3VqnsEmZSGmkCfIi4jWj45OotXMbz38/liX1WvFG\np5vJyNwbT5OcA1dhenkVdsK9SGmkZEtEvOafvYf4fObrZJhyPNrzMTLKuSsVmncjhXGmDVZF/J1X\nhhGNMdcYY5KMMeuNMcM8nK9gjPk88/wSY0xDb9xXRPzLsMRptEtex9NXP0ByldrZxzXvRkQCWZGT\nLWNMEPAu0B1oAdxkjGmR57K7gX3W2vOAN4BXinpfEfEzv/7KXQsmMaNVV2a0uDz7sObdiEig80Zl\nqz2w3lq7wVp7HJgC9MlzTR/gk8w/fwV0M8YYRKRsOHgQbrmFcnXrUu7ddwucDC0iEki8MWcrHNia\n4/U2oEN+11hr04wx+4EawO68H2aMGQIMAahfv74XwhORYvfII7BxIyxcSM/O59PzsvN9HZGIiN/w\nu9YP1tpx1tpIa21krVq1fB2OiBRk+nT46CMYNgw6d/Z1NCIifscbyZYTqJfjdd3MYx6vMcYEA1WB\nPV64t4j40u7dcO+90K4dPPecr6MREfFL3ki2lgJNjTGNjDHlgRuBGXmumQHcnvnn64D51p83ZRSR\nwnn4YUhJgQkTICTE19GIiPilIidb1to04CEgHlgLfGGt/cMY87wxpnfmZR8CNYwx64HHgJPaQ4hI\nKTN9OkyZwn8vH0SjSZuJGjVfneJFRDww/lxgioyMtAkJCb4OQ0Ty2rOHoxHnsyH4bHrfOoa0IPda\nG0dIkFYfikjAMsYss9ZG5j3udxPkRaQUGDqU4H17ebzHI9mJFoArc2seERE5Qdv1iEihxCU6GR2f\nRIulC/nvtP/xTtRNrK3d+KTrtDWPiEhuSrZEpEBxiU6GT1tFyMH9vDjnXdbWash7Ha/3eK225hER\nyU3DiCJSoNHxSbhS0/n3vPHUOJzCv3o8wvGgEPJuA6GteURETqZkS0QKlJziouPmlQxcPZdxHfrz\nx7nnAWBBW/OIiBRAw4giUqCGZwXxUvy7bAqtw1uX3pR9PDzUweJhV/gwMhER/6fKlogUaOyW2TTe\nl8xT0Q9yLKQCoCFDEZHCUrIlIqf2xx9EfPIeW64dwKYLO2rIUETkNGkYUUROktXmYfu+w8R9PpyI\nsypT/+P3WazN4UVETpsqWyKSS1abB2eKixtXxtNm8x881/lO4rYd93VoIiKlkpItEcklq81DrUN7\nGbZwAj/Xb8Pk87uqM7yIyBlSsiUiuWR1gH9m3n+pkHacEdEPgjHqDC8icoaUbIlILmGhDjpvXE6v\ndT/xbsfr2VQ9PPu4iIicPk2QF5FcnuzakDajb2NDtTA+6DAAUJsHEZGiULIlIrn0/v4z2Ovk0Ttf\n4XhwecJDHcRER6jNg4jIGTLWWl/HkK/IyEibkJDg6zBEAsfGjdCiBfTqBV984etoRERKFWPMMmtt\nZN7jmrMlIm7WwsMPQ3AwvPGGr6MRESkzNIwoIm4zZsCsWfD66xCuIUMREW9RZUtE4PBh+L//g1at\n3NUtERHxGiVbIgEuLtHJp9feA1u2cH/UYOJW7/R1SCIiZYqGEUUCWFyikw/++x1f//QlX7Xqxneh\n57Fw2ioArT4UEfESVbZEAtjo2esY/t17HA2pwKgudwDgSk3X1jwiIl6kZEskgLVaOp/LNiUyptMg\ndp9VLfu4tuYREfEeJVsigerIEUYuGM/aWg359KJrc53S1jwiIt6jOVsiASQu0cno+CSSU1w8s3QK\nd6bsJObWV0kvF5R9jbbmERHxLlW2RAJEXKKT4dNW4UxxUW/fdm7+4XNmtOpKg/7XEB7qwADhoQ5i\n+7fW5HgRES9SZUskQIyOT8KVmg7AM/PGkRoUzIuX3UHIul0sHnaFj6MTESm7VNkSCRBZk96vWP8b\nV/69lLcuvYmdZ9fQZHgRkWKmZEskQISFOqiQdpxn543jrxr1+Diyd/ZxEREpPkq2RAJETHQEDyTE\n0SBlB89deS9pQcGaDC8iUgI0Z0ukjMq58jAs1MEzbSrz4JIvWNCqMz83vJDwUAcx0RGaDC8iUsyK\nlGwZY6oDnwMNgU3A9dbafR6uSwdWZb7cYq3tXZT7isipZa08zJoQ70xxkfGv5wDoOvNTNjZo4MPo\nREQCS1GHEYcB86y1TYF5ma89cVlrL8z8UqIlUsxyrjwEuHTTCrqv/YmPO90ISrREREpUUZOtPsAn\nmX/+BOhbxM8TES/IucIwOD2N5+aOY3Poubx2gf6/johISStqsnWOtXZ75p93AOfkc11FY0yCMeZX\nY4wSMpFilnOF4e3LZ9JszxZeuOIeatas6sOoREQCU4HJljFmrjFmtYevPjmvs9ZawObzMQ2stZHA\nzcCbxpgmp7jfkMzELGHXrl2n87OISKaY6AgcIUHUOrSPoYs+Y0Hjdiw+v6NWHoqI+ECBE+SttVfm\nd84Y848xpo61drsxpg6wM5/PcGZ+32CMWQi0Bf7O59pxwDiAyMjI/JI3ETmFrBWG5QffRcW043zQ\n92FiB7TRykMRER8oauuHGcDtwKjM71/nvcAYUw04Yq09ZoypCUQBrxbxviJSgL5Ht8DyOfDkk0wZ\ndbuvwxERCVhFnbM1CrjKGPMXcGXma4wxkcaY8ZnXnA8kGGNWAguAUdbaNUW8r4icSno6PPQQhIfD\n00/7OhoRkYBWpMqWtXYP0M3D8QRgcOaffwZaF+U+InKaxo2D5cthyhSoXNnX0YiIBDRt1yNS1uze\nDU89BV27wvXX+zoaEZGAp2RLpKwZMQIOHoS33wZjfB2NiEjAU7IlUpYsXQrjx8P//R+0bOnraERE\nBCVbImVHRoZ7Uvw558Czz/o6GhERyVTU1g8i4i8+/hh++w0+/RSqVPF1NCIikkmVLZEyYNbC1ewb\n+jhL67Ygamsd4hKdvg5JREQyKdkSKeXiEp0cfPxJqhw5yDNX3Ydz/1GGT1ulhEtExE8o2RIp5WaO\n/5rrl3/HhHa9WFu7MQCu1HRGxyf5ODIREQElWyKlW3o6Q6eOYVflarzRaVCuU8kpLh8FJSIiOSnZ\nEinNxo6l9T9/88IVgzlUoVKuU2GhDh8FJSIiOSnZEimtduyAp55iZ4fOzGvdJdcpR0gQMdERvolL\nRERyUbIlUlrFxIDLRe2J44kd0IbwUAcGCA91ENu/NX3bhvs6QhERQX22REqnhQth0iR4+mlo1oy+\noORKRMRPqbIlUtocPw4PPgiNGrn3QRQREb+mypZIafP667BmDXzzDTg0CV5ExN+psiVSmvz1F4wc\nCdddBz17+joaEREpBCVbIqWFtewadCcHTTDtz+lN1Kj56hIvIlIKKNkSKSWWvfAWtZYuJvbyO9hZ\nuTrOFJe25RERKQWUbImUBrt2cd6oZ1ga3oLJF0RnH9a2PCIi/k/Jlkhp8NhjOI65GH7NQ1iT+3+2\n2pZHRMS/KdkS8Xdz5sCkSUzqchPra9Y/6bS25RER8W9KtkT82ZEjcN99EBFBzZeexRESlOu0tuUR\nEfF/6rMl4s+eeQY2boSFC+l9SRMyKlRkdHwSySkuwkIdxERHqHO8iIifU7Il4q9+/hnGjHFXti6/\nHHBvyaPkSkSkdFGyJeIH4hKduSpWT15en9533gn168Orr/o6PBERKQIlWyI+FpfoZPi0VbhS0wFw\nprjY8+iT8OefMG8enH22jyMUEZGi0AR5ER8bHZ+UnWgBtNu2htuXTOeLyJ5E/QaNhs1St3gRkVJM\nlS0RH8vZJ6ti6lFGf/smzqq1ea7z7RzJPJfVLR7QnC0RkVJGlS0fiEt0EjVqvioWAuTuk/X4T5No\nvC+ZJ7oP5Uj53P2z1C1eRKR0UrJVwrLm5zhTXFjQ/nZCTHQEjpAg2m1bw91Lv2Zi22v5pUEbj9eq\nW7yISOmjYcQSlnd+DpyoWGh4KDD1bRtO8KGDtO1zF9uq1mZin/upZkLYdyT1pGvVLV5EpPRRslXC\n8qtMqGIROPK2eYiJjqDvuJfgwE746Sfmdux40gpFULd4EZHSqkjDiMaYgcaYP4wxGcaYyFNcd40x\nJskYs94YM6wo9yzt8qtMqGIRGDwNI/888i2YNMndLb5jR8Bd7Yrt35rwUAcGCA91ENu/taqfIiKl\nUFErW6uB/sAH+V1gjAkC3gWuArYBS40xM6y1a4p471IpJjpCFYsAlncYuV7KDv793TusbNiKC0aM\nyHWtusWLiJQNRapsWWvXWmsLWh7VHlhvrd1grT0OTAH6FOW+pZkqFoEt53BxUEY6b30zGmvK8eA1\nj0GwRvVFRMqikviveziwNcfrbUCHEriv3yqOioWneUCANi32M2GhDpyZCdf/LZ7MRclJPNwrBtug\ngY8jExGR4lJgsmWMmQuc6+HUU9bar70dkDFmCDAEoH79+t7+eK/xOMn5TBOZ9HT45x/Yts39PSQE\nKlY88VWpknuPvIoVPd67a/NaTF3mzLXdS8yXK8FAarrNPqammL6XNYzcasNKHvrlC75q1Y25F1xB\nrIaRRUTKrAKTLWvtlUW8hxOol+N13cxj+d1vHDAOIDIy0hbx3sXC0152+SUyeROjYZ3r0uvA3+49\n75YsgS1bIDkZ0tJOfdNy5eC880gOb8SO46G0q16PjLotcVKL//26hbwPKjXj5EenFhO+17dtOBV2\n7yTyP6PZWvUcPrjuEWJ7axhZRKQsK4lhxKVAU2NMI9xJ1o3AzSVw32JT2F5ZWUlZveS/eWTdIqI2\nr+SCp/6EjHQoXx4uvhguvxzq1YO6dd1f557rrnQdPQpHj7JkjZP4X9cT6txE6wNOGqxaw+A9ToJt\nBgDrajZgYeN2/NA4koS655MaFHLK2NViwsdSU+n+4iOQeoRav8zj+wsu8HVEIiJSzIqUbBlj+gFv\nA7WAWcaYFdbaaGNMGDDeWtvDWptmjHkIiAeCgI+stX8UOXIfKlSvrGPHWDnqXSYu/pqLnWtIN+X4\n/dymfNBhAH+2uJj/vP0gOE60e8iugC3eeWLOVVUYvhhcjc+Fxp2yrw1JT+W8PVuJ2rSCLhuWcVfC\nDO77bRoHyzv4vuklfN7mapbUawXGnBSjWkz42JNPwo8/wqefghItEZGAYKz1y5E6wD2MmJCQ4Osw\nThI1an72JOecwkMdLB7UFN5+Gz7+GHbvZmO1Ovzvwu5MbdWNfZWqAmCAjaOuzX5ffg0sK4aU89hF\nPK+zjh0hasvvdF3/G9euW0SV40fYWC2Mry68mi9adGNX5WrZn6mVjz40ZQrcdBM89JD7d0RERMoU\nY8wya+1JfUeVbJ0BT8lRrfSj/G/3fJpN/tA9/6pPH4ZWu4QZNZpjTe4OG+GhDhYPuyL7dX7JW2E5\nQoIY0C6cBet2sXfXPm7eupT7/15IzeVLSCtXjviml/Ll1bfQ986eHhMtr072D2CnfI6rV0OHDnDh\nhbBggXsYWUREypT8ki019jkDWf+Ajo5PYueeg9yfNI8Hf/ofFVL2wi23wIsvQoMGdE10MqcQDUxP\ndx5VqCOEsyoEnyI5GuD+lpRE8PjxXDtuHNe+fR/8dQ2MGAGdO2dfeTqT/SV/p3yOjStD//5QpQp8\n+aUSLRGRAKPKVlF89x0MHQp//QVdu7Lg7hie3lrhtHtd5VfZCnWEcCwt46Rk7bSHAvfvh/fegzfe\ngF27WNmgFWPaD2R92yiOpKZ7HKrMW32TU8vv77D+2eX58df/wOzZ7opWp04e3i0iImWBKltFkHd4\naHincHp+8hqMHw/Nm8PMmcTVuYDh01fjSnX/g5tV2Yjt37rApCW/LXye690S8EJj0qpVYfhwvrl8\nICueH8NdP3/FJ18+y89L2jCqyx3sq9PspLdo1eLp8fi8rOWeqW9C4rfuZFeJlohIQFKyVYC8w0N1\nVidwwSuDsPv/wTz5JIwcCRUqMHrU/EK1g/Ak57Ckp6TKW8N5o37cgvPCa5nY+mpuXjGb/1s8mRkT\nH2NmRCdeu+xWNlU/cR+tWjw9OTvDZ7lvyVRuTfwWnngC7r/fR5GJiIivKdkqQFZPrfJpqTy2aBJD\nlkxjW9XaPDDkDd4fNTT7ukK1gziFkth0OCuW1KAQPmnXi6mtunHPb9MZvHQ60X/9wmcXXsMbnQZx\nrEo1bYx9mvJWJ3uvWciwHyawsnN3Hqx6Fc5hs7T4QEQkQCnZKkByiouwAzv5YNpLtP7nbya3uZoX\nrxjMkQqVcl3nqbKRddxf5I3xUIVKvNF5EDM69ubBRZMZ9NtM+q39kY0PP8EFrU/eOECrFvOXszpZ\nf+USXv/2TTa0uphbo+7jwIFjgBYfiIgEqnIFXxLYuu/7ixmfPEqDfdu5p//TDO/+fxyuUOmkJCom\nOgJHSFCuY55WHvpSfjE+PKgz/X/9muDfV1Ll0vZc8Oq/oW1bmD8/+7qs4VRnigvLicQhLjHfnZcC\nTt+24SzuWZvJ344ipHkE9/d/mgM29/POGloWEZHAoWTrVMaO5Z2PYjhYsTL9bnud75teAnhOovq2\nDSe2f2vCQx0Y3Kv5/K2BaIExtmoF338P06bBoUPQrRsMGACbN59yiyLJ9NdfEB0NlSvDt9/y57Eg\nj5dp8YGISGDRMGIecYlO3pi1miFT32TQitns7HQFa156m6M/78AUMHxWEvOuiqrAGI2Bfv2ge3d4\n7TV4+WX47jv6XjyQ/17cj+PBufdeVOKQKSkJunZ1N7SdNw/q1ycsdL3fDy2LiEjxU2Urh7hEJ7H/\n+5lXx/2LQStm894l19HtssdIPbsqi4ddwcZR17J42BV+n1B5RcWK8PTTsHYtdO9OzI8Tmf3Rg1y2\nYVmuy5Q44H5Gl1/u3kB8wQJo3RooHUPLIiJS/JRs5fDxl4uZMPEJ2jrX8X+9/sWrl9/B4XQCcqgs\nLtFJ1Kj5NHp/NVEXP8gn/36PIGDil8/y/vSXCTuwU4kDwB9/QJcu7orgwoXQsmX2qdIwtCwiIsVP\nHeSz/PUXWy/uTDXXAe7t9xSLG16YfSrvxtFlXX4bY1/fphZh49/jtvn/wxjYcM9Q1t92L68s2BRw\nKxTjEp1M/eQ73hz3ODY4hBWfTOPKfpf5OiwREfEhdZA/leXLoXt3Kqcd46YbX2ZVnaa5TgfaUFl+\nk+Hn/r2fxfEfwuZn4PHHafHeq5w1eRJNu92Ds8nFZba1Qd6WF12b12LL1O/4z1cvcjS4PDfd+DL/\nLD9CbENnmfq5RUTEOwJ6GDEu0cnD97zOwY6d2HEcJrzyKevrN891TSAOlRXYoLVBA/jqKx698xXS\nTDkmfDWS/059gQb7kk+5QjF7aHLYLKJGzS8VbSM8tbzIGDuODz8bwZ5KVbnh5lFsqh6ulZkiIpKv\ngE224hKdvDlhPq99PJzkKrXoc/OrjNsRwoB24QE/xya/Sl7e43G1W3LNXW8T2+UOLt28ku/HP8Dw\nBR9x8J/dJ723tPbpylnlC8pI59m5H/By/DssbnAh/W57nS3V6mRfq5WZIiLiScAOI46OT8LpqE5M\nj6H80Kgd+x1nQ2o6C9btKnDj6LIuv42x81b43B3p4YMO1zGt5RX868dPuee36Vz/x3yI2AuDB0Ow\n+1fsVH26/DmZzUqgqhw9xDtfv8JlmxL578V9ie1yJxnlcq80DLThZhERKZyArWxl/SM6o0UXd6KV\n53ggK+wqupytDXZVrs6TPYYy8O7/kB4R4d54uW1b+OYbsLbIe0f6SliogwuSk5j+6eNcsmUVMd3/\nj5euGIwtp5YOIiJSOAFb2SoNexn6UmEatObcDzBr8vitN/Sj5oUPwvTp8MQT0Ls3XHIJvVoOYEbN\n80/6DL9+3keP8nHSVJpMGss/lasz6MYXWVqvFY6QIAa0C2fBul0BtwpTREROX8C2fsivvUEgztEq\nNqmpMGECPP88bNvGrw0u4NVOt7C8rjvpyu95+3LD66x7116zgjHxb9Fo5xY29buJIW1u5K+jQUqs\nREQkX/m1fgjYZAt8+496QDl6FMaN4+jIF6i4dzc/12/D9C7XE/V/t9G3Xb1cl/oyCY5LdPLi5F8Z\n/ONk7vltOjsq1+DZnkPpGXOHfi9ERKRASrbE9w4fhvffh7fegm3boFkzVlx3J49VaMPGI5awUAdH\njqex70jqSW8ND3UUauFCYRPovNcNjwrD+eJorv/xS6odPcjkNlfz8hV3c7DCWYW+t4iIBDYlW1Ki\nTpn0pKbCV1+x74VRVFv7O3sdVZjWsitft+jCqnPPc29940F4qOOUSVR+VbG886u6Nq/F1GVOXKnp\nVD52hNuWz2TI0umEug4yt8nF/CfqJn6v0yz7MwJtBwERETkzSrakxBR2KDAqdh5hqxO4K2EG3db/\nRvmMNP6uHs6M8y/n6xaXs6n6iWsNkPM31ePnjZrvcdFD3vcGZaRz8bY/uHbdInqt/ZHQo4eY2+Ri\n3uk0iBXnnnfS+1XZEhGRwtB2PVJiCttTK3n/UZz1WrG0XiuqHD1Ej3WL6LP2B4Yunsyjiz/jzxr1\n+a1eS5bUa8WSeq3YeXaNU39ePm0kLFA+LZW2yeu4dt0iuv+5mFqHUzgSUoF5Tdozrn3/7C2aHCFB\nBfYXExEROR1KtsTrCttTK2f7jQMVKzPlwmuYcuE1NDueQq+kn2i9NoF+a3/glhXfAbAptA6rz2lC\ncpVa2V8sqwrVqsHx43R2JbMv5TDl01Op7jpAxK5NNN+1mYhdm2i010mwzcAVXIH5TSKZ1bwzCxpH\n4ipfMTue8MzhSS2aEBERb1KyJV5X2B5m+XWqf+CGLvRtO8h9IC2Nux4dT6M1y+iwdTXn79rIlX//\nRsW04+7z01/Kfu9ED7FsqXoOSbUaMrvZpaw+pwk/NWrLkfIOj8OSWYmVkisREfEmJVvidYXd7sdT\nU9STKknBwfS+qxfDpzXkw9S+7mPWEpZ6iJciQ+la6Sjs3w8VKkD58vyy9SBfrPyHTWnBHGrSjA4X\nNMieDJ8zFjUlFRGRkqJkS7yuUElUjmtPu1N9tUrERLelq4f3dcz8yimyQXUNDYqIiM9oNaKUWmpK\nKyIi/kSrEaVMydtewpniYvi0VQBKuERExK+U83UAImfiVO0lRERE/EmRki1jzEBjzB/GmAxjzEll\nsxzXbTLGrDLGrDDGaFxQiqyw7SVERER8raiVrdVAf+DHQlzb1Vp7oaexTJHTlbeNREHHRUREfKVI\nyZa1dq21VuM2UuJioiNwhATlOqZu7yIi4o9Kas6WBeYYY5YZY4ac6kJjzBBjTIIxJmHXrl0lFJ6U\nNn3bhhPbvzXhoe4GpeGhjpP2ShQREfEHBa5GNMbMBc71cOopa+3XhbxPJ2ut0xhTG/jeGLPOWutx\n6NFaOw4YB+7WD4X8fAlA6vYuIiKlQYHJlrX2yqLexFrrzPy+0xgzHWhP4eZ5iYiIiJRqxT6MaIw5\nyxhzdtafgatxT6wXERERKfOK2vqhnzFmG+4dUmYZY+Izj4cZY77NvOwcYJExZiXwGzDLWju7KPcV\nERERKS2K1EHeWjsdmO7heDLQI/PPG4ALinIfERERkdJKHeRFREREipGSLREREZFipGRLREREpBgp\n2RIREREpRkq2RERERIqRki0RERGRYqRkS0RERKQYGWv9d/tBY8wuYLOv4yhmNYHdvg6iFNBzKhw9\np8LRcyqYnlHh6DkV0zFbDgAABLtJREFUTqA8pwbW2lp5D/p1shUIjDEJ1tpIX8fh7/ScCkfPqXD0\nnAqmZ1Q4ek6FE+jPScOIIiIiIsVIyZaIiIhIMVKy5XvjfB1AKaHnVDh6ToWj51QwPaPC0XMqnIB+\nTpqzJSIiIlKMVNkSERERKUZKtkqYMWagMeYPY0yGMSbflRnGmE3GmFXGmBXGmISSjNEfnMZzusYY\nk2SMWW+MGVaSMfoDY0x1Y8z3xpi/Mr9Xy+e6/2/vXkKsKuA4jn9/aBlEVGSpPehBs8g21kKKWtiD\nylnM9JCwTRqKFUTrIChwZW2CoheYaEFmCNZE9lTCNkYWVpYFJkSKZVQYkRRTvxb3TJzKmTnR3HPO\n3Pv7wDDnzjlcfvz538P/vO78XvTSbkkjdedswmS9IWmWpE3F+vcknVd/yuZVqNNySd+V+mdlEzmb\nJGmdpMOS9oyzXpIeLWr4saRL687YBhXqtEjSkVIvPVB3xqZk2KrfHuBmYEeFba+yvaBPH5edtE6S\nZgCPA4uB+cBtkubXE6817gO22R4AthWvj+Vo0UsLbA/VF68ZFXtjBfCj7QuBR4CH6k3ZvP/wGdpU\n6p+1tYZsh/XADROsXwwMFD+rgCdryNRG65m4TgDvlnppdQ2ZWiHDVs1s77X9RdM52q5inRYC+2zv\nt/0b8AIw3P10rTIMbCiWNwA3NpilTar0Rrl2m4FrJKnGjG2Qz1AFtncAP0ywyTDwrDt2AqdImldP\nuvaoUKe+lWGrvQy8KekDSauaDtNSZwFfl14fKP7WT+bYPlQsfwPMGWe7EyTtkrRTUj8MZFV6469t\nbI8CR4DTaknXHlU/Q7cUl8c2SzqnnmjTSvZF1V0u6SNJr0m6uOkwdZnZdIBeJOltYO4xVt1v++WK\nb3Ol7YOSzgDekvR5cdTQM6aoTj1vojqVX9i2pPEeLz636KcLgO2SPrH95VRnjZ70CrDR9q+S7qRz\nNvDqhjPF9PQhnX3Rz5IGgZfoXHrteRm2usD2tVPwHgeL34clbaFzur+nhq0pqNNBoHyUfXbxt54y\nUZ0kfStpnu1DxWWLw+O8x1g/7Zf0DnAJ0MvDVpXeGNvmgKSZwMnA9/XEa41J62S7XJO1wMM15Jpu\n+mJf9H/Z/qm0vFXSE5Jm2+75/5mYy4gtJOlESSeNLQPX0blhPP7ufWBA0vmSjgeWAn3xpF3JCLCs\nWF4G/OuMoKRTJc0qlmcDVwCf1ZawGVV6o1y7JcB2998XD05ap3/cezQE7K0x33QxAtxePJV4GXCk\ndHk/CpLmjt0XKWkhnRmkLw5wcmarZpJuAh4DTgdelbTb9vWSzgTW2h6kc9/NlqInZwLP2369sdAN\nqFIn26OS7gHeAGYA62x/2mDsJqwBXpS0AvgKuBWg+LqMu2yvBC4Cnpb0B52d2xrbPT1sjdcbklYD\nu2yPAM8Az0naR+em3qXNJW5GxTrdK2kIGKVTp+WNBW6IpI3AImC2pAPAg8BxALafArYCg8A+4Bfg\njmaSNqtCnZYAd0saBY4CS/vlACffIB8RERHRRbmMGBEREdFFGbYiIiIiuijDVkREREQXZdiKiIiI\n6KIMWxERERFdlGErIiIioosybEVERER0UYatiIiIiC76E08+yMnEXtHzAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nn_ripple_cg = ForwardNetCG(x, g_ripple, nh=10, maxiter=150)\n",
    "y_ripple_cg = nn_ripple_cg.predict(x)\n",
    "\n",
    "plt.scatter(x, g_ripple);\n",
    "plt.plot(x, y_ripple_cg, color=\"red\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}