Untitled.ipynb

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   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y = np.array([1,2,3,4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
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   "source": [
    "w = y[1:]"
   ]
  },
  {
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   "metadata": {},
   "outputs": [
    {
     "data": {
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       "array([2, 3, 4])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
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   "source": [
    "w"
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   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 4])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.insert(w,0,1)"
   ]
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   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 3, 4])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
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    "w"
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  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def sigmoid(x):\n",
    "    return 1 / (1 + np.exp(-x))"
   ]
  },
  {
   "cell_type": "code",
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   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.88079708,  0.95257413,  0.98201379])"
      ]
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     "metadata": {},
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   "source": [
    "sigmoid(w)"
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   "metadata": {
    "collapsed": true
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   "source": [
    "y = np.array([[1,2],[3,4]])"
   ]
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  {
   "cell_type": "code",
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   "metadata": {
    "collapsed": true
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   "source": [
    "x = np.array([2,5])"
   ]
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    {
     "data": {
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       "array([[2, 4],\n",
       "       [6, 8]])"
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    "y*2"
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      "text/plain": [
       "array([[ 2, 10],\n",
       "       [ 6, 20]])"
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   "source": [
    "y*x"
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    {
     "data": {
      "text/plain": [
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       "       [ 6, 20]])"
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     "execution_count": 22,
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   "source": [
    "x*y"
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2, 10],\n",
       "       [ 6, 20]])"
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   "source": [
    "x.T*y"
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   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
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    {
     "data": {
      "text/plain": [
       "array([[ 2,  4],\n",
       "       [15, 20]])"
      ]
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     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(x*y.T).T"
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   "cell_type": "code",
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 6, 35])"
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     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "((x*y.T).T).sum(axis=1)"
   ]
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   "cell_type": "code",
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   "metadata": {},
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    {
     "data": {
      "text/plain": [
       "2.2360679774997898"
      ]
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     "execution_count": 29,
     "metadata": {},
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   "source": [
    "np.linalg.norm([1,2])"
   ]
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   "cell_type": "code",
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   "metadata": {},
   "outputs": [
    {
     "data": {
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       "array([2, 5])"
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     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
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    "x"
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     "data": {
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       "array([3, 6])"
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    "x+1"
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   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True,  True], dtype=bool)"
      ]
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     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "x>0"
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  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": true
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   "outputs": [],
   "source": [
    "x = (x>0).astype(int)"
   ]
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  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1])"
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     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
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    "x"
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  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "UsageError: %%python3 is a cell magic, but the cell body is empty.\n"
     ]
    }
   ],
   "source": [
    "%%python3 logistic.py --type binary --output logistic_binary.out "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2],\n",
       "       [3, 4]])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
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  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
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     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "y.max()"
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  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-3, -2],\n",
       "       [-1,  0]])"
      ]
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     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "y-y.max()"
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   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 4])"
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     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "y.max(axis=1)"
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   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1, -2],\n",
       "       [ 1,  0]])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
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   "source": [
    "y-y.max(axis=1)"
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  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1,  0],\n",
       "       [-1,  0]])"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(y.T-y.max(axis=1)).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2],\n",
       "       [3, 4]])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
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  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = np.array([[1,2,3],[5,6,7]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [5, 6, 7]])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
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   "source": [
    "x"
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  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [5, 6, 7]])"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "w = np.array([2,2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "operands could not be broadcast together with shapes (2,) (2,3) ",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-65-903331d7476c>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mw\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m: operands could not be broadcast together with shapes (2,) (2,3) "
     ]
    }
   ],
   "source": [
    "w*x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 5],\n",
       "       [2, 6],\n",
       "       [3, 7]])"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.transpose()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Performing binary classification on synthetic data\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/lizeyu/anaconda3/lib/python3.6/site-packages/sklearn/model_selection/_split.py:2026: FutureWarning: From version 0.21, test_size will always complement train_size unless both are specified.\n",
      "  FutureWarning)\n"
     ]
    }
   ],
   "source": [
    "    from data_loader import toy_data_binary, \\\n",
    "                            data_loader_mnist \n",
    "\n",
    "    print('Performing binary classification on synthetic data')\n",
    "    X_train, X_test, y_train, y_test = toy_data_binary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0,\n",
       "       1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0,\n",
       "       0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1,\n",
       "       0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1,\n",
       "       0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0,\n",
       "       1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1,\n",
       "       1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0,\n",
       "       1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1,\n",
       "       0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0,\n",
       "       1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0,\n",
       "       1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1,\n",
       "       1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0,\n",
       "       0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0,\n",
       "       1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1,\n",
       "       1, 0, 1, 0, 0])"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from logistic import binary_train\n",
    "w, b = binary_train(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 6.94095063,  1.04783362]), -0.19352029080720606)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w,b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = X_train\n",
    "y = y_train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "N, D = X.shape\n",
    "w = np.zeros(D)\n",
    "b = 0\n",
    "wp = np.insert(w,0,b)\n",
    "X = np.column_stack((np.ones(N),X))\n",
    "iter = 0\n",
    "converge=False\n",
    "threshold=1e-2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "        z = wp*X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 181.77221486,  287.60545087,   -9.07627584],\n",
       "       [ 181.77221486, -248.390034  ,  -18.34519634],\n",
       "       [ 181.77221486,  280.76857682,   -4.01943031],\n",
       "       ..., \n",
       "       [ 181.77221486,  219.38929628,  -23.51415255],\n",
       "       [ 181.77221486, -299.17021289,   -3.88025338],\n",
       "       [ 181.77221486, -254.99933143,    0.78084663]])"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "temp = z.sum(axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 460.30138989,  -84.96301549,  458.52136137,  343.05161238,\n",
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       "        -13.74479672, -157.0322851 ,  500.36421187, -102.846367  ,\n",
       "        426.4656328 , -168.00193978,   87.28443953,  -16.27269486,\n",
       "        415.95727608,  -46.7810563 , -179.4342195 ,  445.03582307,\n",
       "        457.97821267,  -75.95620011,  441.08957396,  496.01719551,\n",
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       "       -147.33654943, -210.46035577, -128.21493074,  482.54158002,\n",
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       "       -114.77423924,  -90.39270401, -224.77872548,  -32.93278367,\n",
       "       -115.23952934,  438.50061849, -139.89422788,  391.51701003,\n",
       "        406.02899058,  406.49333134,  -50.94593213,  441.90476747,\n",
       "        452.0103275 ,   12.0568044 ,  499.41507456,  450.79188321,\n",
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       "        511.62404168,  440.27694414,   -6.02966612,  475.11977986,\n",
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       "        -52.69443776,    6.17650159,  441.04564822,  -32.47042933,\n",
       "        448.60113973,  430.618859  ,  -88.38591625,  384.17485677,\n",
       "        382.41863087,  431.29403917,  489.48335836,  447.01629392,\n",
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       "       -180.63835026,  407.54456618,  455.71098184,  -33.81728765,\n",
       "        471.43995499, -209.37542958,  510.22897839, -100.89563956,\n",
       "        435.76619976,  -71.04450314,  399.3625431 ,   34.85608719,\n",
       "        462.67685049, -102.07366893,  -11.80788312,   34.4188877 ,\n",
       "        405.3923595 ,  493.97634736, -106.72736987, -162.54774949,\n",
       "        -22.51176842,  -42.15718981,  408.38202383,  371.86695481,\n",
       "        -17.41978997,   41.03003055,  -72.51535827, -104.46368248,\n",
       "        442.39757179,   10.31340242,  494.08102926,  422.21537061,\n",
       "        465.60868213, -206.28205033,  -33.07396373,  475.77037389,\n",
       "        -80.39490942,  499.32190335,  506.72988797,  463.91697998,\n",
       "        434.08181354,  -92.75872672, -117.67555476,  450.56197578,\n",
       "        429.83823096,  455.42106626, -157.24973691,  377.64735859,\n",
       "       -121.27825141,  -72.44626994])"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "temp"
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  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {
    "collapsed": true
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   "outputs": [],
   "source": [
    "temp = temp - temp.max()"
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  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "       -694.19694322, -645.36496176])"
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     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "temp"
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  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/lizeyu/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:2: RuntimeWarning: overflow encountered in exp\n",
      "  \n"
     ]
    }
   ],
   "source": [
    "gradient = ((sigmoid(temp)-y)*X.T).sum(axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-179.49255297, -177.37771832,   -8.1303198 ])"
      ]
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     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "gradient"
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  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "collapsed": true
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   "outputs": [],
   "source": [
    "wp-=0.5*gradient"
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  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 181.77221486,  263.53007307,   16.23889974])"
      ]
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     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "wp"
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  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "251.72877883110237"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.norm(gradient)"
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  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/lizeyu/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:2: RuntimeWarning: overflow encountered in exp\n",
      "  \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sigmoid(-1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "w = np.zeros((3,3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "w[0] = np.ones(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  1.,  1.],\n",
       "       [ 0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'x' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-9-401b30e3b8b5>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mx\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m: name 'x' is not defined"
     ]
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = np.array([[1,2],[2,3],[5,6]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "w = np.array([[8,9,10],[5,4,3]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "operands could not be broadcast together with shapes (3,2) (3,) ",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-12-d3bed34732c6>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mx\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mw\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m: operands could not be broadcast together with shapes (3,2) (3,) "
     ]
    }
   ],
   "source": [
    "x*w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "operands could not be broadcast together with shapes (3,2) (3,) ",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-13-5c656df55b10>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mw\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m: operands could not be broadcast together with shapes (3,2) (3,) "
     ]
    }
   ],
   "source": [
    "np.dot(x*w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "shapes (3,2) and (3,) not aligned: 2 (dim 1) != 3 (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-14-b25c04e3d50f>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mw\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m: shapes (3,2) and (3,) not aligned: 2 (dim 1) != 3 (dim 0)"
     ]
    }
   ],
   "source": [
    "x.dot(w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "shapes (3,2) and (3,) not aligned: 2 (dim 1) != 3 (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-15-074aa4d965f4>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mw\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m: shapes (3,2) and (3,) not aligned: 2 (dim 1) != 3 (dim 0)"
     ]
    }
   ],
   "source": [
    "np.dot(x,w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 76,  28],\n",
       "       [103,  40]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(x.T,w.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2],\n",
       "       [2, 3],\n",
       "       [5, 6]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 6,  8],\n",
       "       [ 7,  9],\n",
       "       [10, 12]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x + [5,6]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2],\n",
       "       [2, 3],\n",
       "       [5, 6]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 5])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[:,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.5 ,  2.  ,  1.25])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[:,0]/[2,1,4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "delta = np.array([[1,2],[3,4],[5,6]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'detla' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-27-854828ed76cb>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mdetla\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m: name 'detla' is not defined"
     ]
    }
   ],
   "source": [
    "detla"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2],\n",
       "       [3, 4],\n",
       "       [5, 6]])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "delta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "delta[:,delta.shape[1]-1].sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 1])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "delta.argmax(axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "path = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "path.append(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1]"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "path"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "path[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 8,  9, 10],\n",
       "       [ 5,  4,  3]])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w[0].argmax()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from __future__ import print_function\n",
    "import json\n",
    "import numpy as np\n",
    "import sys\n",
    "\n",
    "def viterbi(pi, A, B, O):\n",
    "  \"\"\"\n",
    "  Viterbi algorithm\n",
    "\n",
    "  Inputs:\n",
    "  - pi: A numpy array of initial probailities. pi[i] = P(Z_1 = s_i)\n",
    "  - A: A numpy array of transition probailities. A[i, j] = P(Z_t = s_j|Z_t-1 = s_i)\n",
    "  - B: A numpy array of observation probabilities. B[i, k] = P(X_t = o_k| Z_t = s_i)\n",
    "  - O: A list of observation sequence (in terms of index, not the actual symbol)\n",
    "\n",
    "  Returns:\n",
    "  - path: A list of the most likely hidden state path k* (in terms of the state index)\n",
    "    argmax_k P(s_k1:s_kT | x_1:x_T)\n",
    "  \"\"\"\n",
    "  path = []\n",
    "  ###################################################\n",
    "  # Q3.3 Edit here\n",
    "  ###################################################\n",
    "  S = len(pi)\n",
    "  N = len(O)\n",
    "  delta = np.zeros([S, N])\n",
    "  dp = pi\n",
    "  for i in range(0,N):\n",
    "    temp = A.T*dp*B[:,O[i]]\n",
    "    dp = temp.max(axis=1)\n",
    "    delta[:,i] = temp.argmax(axis=1)\n",
    "  path.append(dp.argmax())\n",
    "  for i in range(0,N-1):\n",
    "        path.insert(0,delta[path[0],N-1-i])\n",
    "  return path\n",
    "\n",
    "def main():\n",
    "  model_file = sys.argv[1]\n",
    "  Osymbols = sys.argv[2]\n",
    "\n",
    "  #### load data ####\n",
    "  with open(model_file, 'r') as f:\n",
    "    data = json.load(f)\n",
    "  A = np.array(data['A'])\n",
    "  B = np.array(data['B'])\n",
    "  pi = np.array(data['pi'])\n",
    "  #### observation symbols #####\n",
    "  obs_symbols = data['observations']\n",
    "  #### state symbols #####\n",
    "  states_symbols = data['states']\n",
    "\n",
    "  N = len(Osymbols)\n",
    "  O = [obs_symbols[j] for j in Osymbols]\n",
    "\n",
    "\n",
    "  viterbi_path = viterbi(pi, A, B, O)\n",
    "\n",
    "  print('Viterbi best path is ')\n",
    "  for j in viterbi_path:\n",
    "    print(states_symbols[j], end=' ')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "ename": "FileNotFoundError",
     "evalue": "[Errno 2] No such file or directory: '-f'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mFileNotFoundError\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-38-58ca95c5b364>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mmain\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m<ipython-input-37-c83648fa15d4>\u001b[0m in \u001b[0;36mmain\u001b[0;34m()\u001b[0m\n\u001b[1;32m     40\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     41\u001b[0m   \u001b[0;31m#### load data ####\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 42\u001b[0;31m   \u001b[0;32mwith\u001b[0m \u001b[0mopen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmodel_file\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'r'\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     43\u001b[0m     \u001b[0mdata\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mjson\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mload\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     44\u001b[0m   \u001b[0mA\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[0mdata\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'A'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mFileNotFoundError\u001b[0m: [Errno 2] No such file or directory: '-f'"
     ]
    }
   ],
   "source": [
    "main()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 8,  9, 10],\n",
       "       [ 5,  4,  3]])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10\n",
      "9\n",
      "8\n"
     ]
    }
   ],
   "source": [
    "for i in range(0,3):\n",
    "    print(w[0,2-i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "ename": "SyntaxError",
     "evalue": "invalid syntax (<ipython-input-45-321e5b2cb4d2>, line 1)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;36m  File \u001b[0;32m\"<ipython-input-45-321e5b2cb4d2>\"\u001b[0;36m, line \u001b[0;32m1\u001b[0m\n\u001b[0;31m    (int)3.0\u001b[0m\n\u001b[0m           ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
     ]
    }
   ],
   "source": [
    "(int)3.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "int"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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