{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def step_function(x):\n",
    "    # if x > 0:\n",
    "    #     return 1\n",
    "    # else:\n",
    "    #     return 0\n",
    "    y = x > 0\n",
    "    return y.astype(np.int)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = np.array([-1.0, 1.0, 2.0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False,  True,  True], dtype=bool)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = x > 0\n",
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 1])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.astype(np.int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.1, 1.1)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAD8CAYAAACMwORRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n1WIQXfsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa47421cba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(-5.0, 5.0, 0.1)\n",
    "y = step_function(x)\n",
    "plt.plot(x, y)\n",
    "plt.ylim(-0.1, 1.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def sigmoid(x):\n",
    "    return 1 / (1 + np.exp(-x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.26894142,  0.73105858,  0.88079708])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([-1.0, 1.0, 2.0])\n",
    "sigmoid(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2.,  3.,  4.])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = np.array([1.0, 2.0, 3.0])\n",
    "1.0 + t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.        ,  0.5       ,  0.33333333])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1.0 / t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.1, 1.1)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAD8CAYAAACMwORRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nVO4iImFI5S4iEob+DxH15vm8DFuTAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa4738db4e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(-5.0, 5.0, 0.1)\n",
    "y = sigmoid(x)\n",
    "plt.plot(x, y)\n",
    "plt.ylim(-0.1, 1.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.1, 1.1)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAD8CAYAAACMwORRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nIYW7iEgcUriLiMQhhbuISBz6f1srbbSBsiyzAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa473546080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(-5.0, 5.0, 0.1)\n",
    "y1 = step_function(x)\n",
    "y2 = sigmoid(x)\n",
    "plt.plot(x, y1, \"--\")\n",
    "1plt.plot(x, y2)\n",
    "plt.ylim(-0.1, 1.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def relu(x):\n",
    "    return np.maximum(0, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1, 6)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXYAAAD8CAYAAABjAo9vAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa4736bf3c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(-5.0, 5.0, 0.1)\n",
    "# y1 = step_function(x)\n",
    "# y2 = sigmoid(x)\n",
    "# plt.plot(x, y1, \"--\")\n",
    "# plt.plot(x, y2)\n",
    "y = relu(x)\n",
    "plt.plot(x, y)\n",
    "plt.ylim(-1, 6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 4])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.array([1, 2, 3, 4])\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.ndim(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4,)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.shape[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2],\n",
       "       [3, 4],\n",
       "       [5, 6]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B = np.array([[1, 2], [3, 4], [5, 6]])\n",
    "B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.ndim(B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 2)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\left(\\begin{array}{cc}1 & 2\\\\3 & 4\\\\5 & 6\\\\\\end{array}\\right)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[19, 22],\n",
       "       [43, 50]])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.array([[1, 2], [3, 4]])\n",
    "B = np.array([[5, 6], [7, 8]])\n",
    "# np.dot(A, B)\n",
    "A.dot(B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[22, 28],\n",
       "       [49, 64]])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.array([[1, 2, 3], [4, 5, 6]])\n",
    "B = np.array([[1, 2], [3, 4], [5, 6]])\n",
    "# np.dot(A, B)\n",
    "A.dot(B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "shapes (2,3) and (2,2) not aligned: 3 (dim 1) != 2 (dim 0)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-28-d891270025f5>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0mC\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m4\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mA\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mC\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m: shapes (2,3) and (2,2) not aligned: 3 (dim 1) != 2 (dim 0)"
     ]
    }
   ],
   "source": [
    "C = np.array([[1, 2], [3, 4]])\n",
    "A.dot(C)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([23, 53, 83])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.array([[1, 2], [3, 4], [5, 6]])\n",
    "B = np.array([7, 8])\n",
    "A.dot(B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2],\n",
       "       [3, 4],\n",
       "       [5, 6]])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 3, 5],\n",
       "       [2, 4, 6]])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "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": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}