Notebooks/13_Numpy.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction to Python  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [Numpy](https://numpy.org/)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
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     },
     "execution_count": 92,
     "metadata": {},
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    }
   ],
   "source": [
    "dir(np)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Numpy Basic Data Types\n",
    "\n",
    "#### Type Array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 4])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "my_numbers = [1,2,3,4]\n",
    "simple_array = np.array(my_numbers)\n",
    "simple_array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(simple_array)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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       " '__rlshift__',\n",
       " '__rmatmul__',\n",
       " '__rmod__',\n",
       " '__rmul__',\n",
       " '__ror__',\n",
       " '__rpow__',\n",
       " '__rrshift__',\n",
       " '__rshift__',\n",
       " '__rsub__',\n",
       " '__rtruediv__',\n",
       " '__rxor__',\n",
       " '__setattr__',\n",
       " '__setitem__',\n",
       " '__setstate__',\n",
       " '__sizeof__',\n",
       " '__str__',\n",
       " '__sub__',\n",
       " '__subclasshook__',\n",
       " '__truediv__',\n",
       " '__xor__',\n",
       " 'all',\n",
       " 'any',\n",
       " 'argmax',\n",
       " 'argmin',\n",
       " 'argpartition',\n",
       " 'argsort',\n",
       " 'astype',\n",
       " 'base',\n",
       " 'byteswap',\n",
       " 'choose',\n",
       " 'clip',\n",
       " 'compress',\n",
       " 'conj',\n",
       " 'conjugate',\n",
       " 'copy',\n",
       " 'ctypes',\n",
       " 'cumprod',\n",
       " 'cumsum',\n",
       " 'data',\n",
       " 'diagonal',\n",
       " 'dot',\n",
       " 'dtype',\n",
       " 'dump',\n",
       " 'dumps',\n",
       " 'fill',\n",
       " 'flags',\n",
       " 'flat',\n",
       " 'flatten',\n",
       " 'getfield',\n",
       " 'imag',\n",
       " 'item',\n",
       " 'itemset',\n",
       " 'itemsize',\n",
       " 'max',\n",
       " 'mean',\n",
       " 'min',\n",
       " 'nbytes',\n",
       " 'ndim',\n",
       " 'newbyteorder',\n",
       " 'nonzero',\n",
       " 'partition',\n",
       " 'prod',\n",
       " 'ptp',\n",
       " 'put',\n",
       " 'ravel',\n",
       " 'real',\n",
       " 'repeat',\n",
       " 'reshape',\n",
       " 'resize',\n",
       " 'round',\n",
       " 'searchsorted',\n",
       " 'setfield',\n",
       " 'setflags',\n",
       " 'shape',\n",
       " 'size',\n",
       " 'sort',\n",
       " 'squeeze',\n",
       " 'std',\n",
       " 'strides',\n",
       " 'sum',\n",
       " 'swapaxes',\n",
       " 'take',\n",
       " 'tobytes',\n",
       " 'tofile',\n",
       " 'tolist',\n",
       " 'tostring',\n",
       " 'trace',\n",
       " 'transpose',\n",
       " 'var',\n",
       " 'view']"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dir(simple_array)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(4,)\n",
      "4\n",
      "1\n"
     ]
    }
   ],
   "source": [
    "print(simple_array.shape)\n",
    "print(simple_array.size)\n",
    "print(simple_array.ndim)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3, 4],\n",
       "       [4, 5, 6, 7],\n",
       "       [8, 9, 0, 1]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "my_other_numbers = [[1,2,3,4],[4,5,6,7],[8,9,0,1]]\n",
    "other_simple_array = np.array(my_other_numbers)\n",
    "other_simple_array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3, 4)\n",
      "12\n",
      "2\n"
     ]
    }
   ],
   "source": [
    "print(other_simple_array.shape)\n",
    "print(other_simple_array.size)\n",
    "print(other_simple_array.ndim)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Operations between arrays (scalar and vectorial)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = np.array([[1,2,3],[4,5,6],[8,9,0]])\n",
    "B = np.array([[2,1,5],[9,2,1],[8,7,6]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6],\n",
       "       [8, 9, 0]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 1, 5],\n",
       "       [9, 2, 1],\n",
       "       [8, 7, 6]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 3,  4,  5],\n",
       "       [ 6,  7,  8],\n",
       "       [10, 11,  2]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A + 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 3,  6,  9],\n",
       "       [12, 15, 18],\n",
       "       [24, 27,  0]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A * 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.25, 0.5 , 0.75],\n",
       "       [1.  , 1.25, 1.5 ],\n",
       "       [2.  , 2.25, 0.  ]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A / 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 3,  3,  8],\n",
       "       [13,  7,  7],\n",
       "       [16, 16,  6]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A + B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2,  2, 15],\n",
       "       [36, 10,  6],\n",
       "       [64, 63,  0]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A * B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 44,  26,  25],\n",
       "       [101,  56,  61],\n",
       "       [ 97,  26,  49]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.dot(B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 4, 8],\n",
       "       [2, 5, 9],\n",
       "       [3, 6, 0]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.T\n",
    "#A.transpose()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[1., 2.],\n",
       "        [4., 3.]])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Creating arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,\n",
       "       17, 18, 19])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.arange(20)  # ==> np.arange(0,20,1)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1. , 1.2, 1.4, 1.6, 1.8, 2. , 2.2, 2.4, 2.6, 2.8, 3. , 3.2, 3.4,\n",
       "       3.6, 3.8, 4. , 4.2, 4.4, 4.6, 4.8])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.arange(1,5,0.2)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.        ,  1.31034483,  1.62068966,  1.93103448,  2.24137931,\n",
       "        2.55172414,  2.86206897,  3.17241379,  3.48275862,  3.79310345,\n",
       "        4.10344828,  4.4137931 ,  4.72413793,  5.03448276,  5.34482759,\n",
       "        5.65517241,  5.96551724,  6.27586207,  6.5862069 ,  6.89655172,\n",
       "        7.20689655,  7.51724138,  7.82758621,  8.13793103,  8.44827586,\n",
       "        8.75862069,  9.06896552,  9.37931034,  9.68965517, 10.        ])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = np.linspace(1,10,30)\n",
    "#b = np.linspace(1,2*np.pi,50)\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.00000000e+001, 2.59294380e+004, 6.72335754e+007, 1.74332882e+011,\n",
       "       4.52035366e+014, 1.17210230e+018, 3.03919538e+021, 7.88046282e+024,\n",
       "       2.04335972e+028, 5.29831691e+031, 1.37382380e+035, 3.56224789e+038,\n",
       "       9.23670857e+041, 2.39502662e+045, 6.21016942e+048, 1.61026203e+052,\n",
       "       4.17531894e+055, 1.08263673e+059, 2.80721620e+062, 7.27895384e+065,\n",
       "       1.88739182e+069, 4.89390092e+072, 1.26896100e+076, 3.29034456e+079,\n",
       "       8.53167852e+082, 2.21221629e+086, 5.73615251e+089, 1.48735211e+093,\n",
       "       3.85662042e+096, 1.00000000e+100])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b2 = np.logspace(1,100,30)\n",
    "b2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]]\n"
     ]
    }
   ],
   "source": [
    "a1 = np.zeros((3,4))\n",
    "print(a1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1. 1.]\n",
      " [1. 1.]]\n"
     ]
    }
   ],
   "source": [
    "a2 = np.ones((2,2))\n",
    "print(a2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[4.65775909e-310 0.00000000e+000 0.00000000e+000]\n",
      " [0.00000000e+000 0.00000000e+000 0.00000000e+000]]\n"
     ]
    }
   ],
   "source": [
    "a3 = np.empty((2,3))\n",
    "print(a3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1. 0. 0.]\n",
      " [0. 1. 0.]\n",
      " [0. 0. 1.]]\n"
     ]
    }
   ],
   "source": [
    "a4 = np.identity(3)\n",
    "print(a4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 0.],\n",
       "       [0., 1., 0.],\n",
       "       [0., 0., 1.]])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.eye(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Modifying Dimensions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = np.arange(10)\n",
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 2, 3, 4],\n",
       "       [5, 6, 7, 8, 9]])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d = c.reshape(2,5)\n",
    "#d = np.arange(10).reshape(2,5)\n",
    "d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(10,)\n",
      "(2, 5)\n",
      "2\n",
      "int64\n"
     ]
    }
   ],
   "source": [
    "print(c.shape)\n",
    "print(d.shape)\n",
    "print(np.ndim(d))\n",
    "print(d.dtype.name)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 0,  1,  2,  3,  4],\n",
       "        [ 5,  6,  7,  8,  9],\n",
       "        [10, 11, 12, 13, 14],\n",
       "        [15, 16, 17, 18, 19],\n",
       "        [20, 21, 22, 23, 24],\n",
       "        [25, 26, 27, 28, 29],\n",
       "        [30, 31, 32, 33, 34],\n",
       "        [35, 36, 37, 38, 39],\n",
       "        [40, 41, 42, 43, 44],\n",
       "        [45, 46, 47, 48, 49]],\n",
       "\n",
       "       [[50, 51, 52, 53, 54],\n",
       "        [55, 56, 57, 58, 59],\n",
       "        [60, 61, 62, 63, 64],\n",
       "        [65, 66, 67, 68, 69],\n",
       "        [70, 71, 72, 73, 74],\n",
       "        [75, 76, 77, 78, 79],\n",
       "        [80, 81, 82, 83, 84],\n",
       "        [85, 86, 87, 88, 89],\n",
       "        [90, 91, 92, 93, 94],\n",
       "        [95, 96, 97, 98, 99]]])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d2 = np.arange(100).reshape(2,10,5)\n",
    "d2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d2.ndim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 10, 5)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d2.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Slicing multidimensional arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 0,  1,  2,  3,  4],\n",
       "        [ 5,  6,  7,  8,  9],\n",
       "        [10, 11, 12, 13, 14],\n",
       "        [15, 16, 17, 18, 19],\n",
       "        [20, 21, 22, 23, 24],\n",
       "        [25, 26, 27, 28, 29],\n",
       "        [30, 31, 32, 33, 34],\n",
       "        [35, 36, 37, 38, 39],\n",
       "        [40, 41, 42, 43, 44],\n",
       "        [45, 46, 47, 48, 49]],\n",
       "\n",
       "       [[50, 51, 52, 53, 54],\n",
       "        [55, 56, 57, 58, 59],\n",
       "        [60, 61, 62, 63, 64],\n",
       "        [65, 66, 67, 68, 69],\n",
       "        [70, 71, 72, 73, 74],\n",
       "        [75, 76, 77, 78, 79],\n",
       "        [80, 81, 82, 83, 84],\n",
       "        [85, 86, 87, 88, 89],\n",
       "        [90, 91, 92, 93, 94],\n",
       "        [95, 96, 97, 98, 99]]])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[21, 22],\n",
       "        [26, 27]]])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d2[0:1,4:6,1:3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    }
   ],
   "source": [
    "d2[d2%2==0]\n",
    "print(np.ndim(d2[d2%2==0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "#np.mask_indices?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1,  3,  5,  7,  9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33,\n",
       "       35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67,\n",
       "       69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d2[~d2%2==0]  #negation of condition"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Stacking Arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11],\n",
       "       [12, 13, 14, 15]])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.arange(16).reshape(4,4)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11],\n",
       "       [12, 13, 14, 15],\n",
       "       [ 0,  1,  2,  3]])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.vstack([a,np.arange(4).reshape(1,4)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3,  0],\n",
       "       [ 4,  5,  6,  7,  1],\n",
       "       [ 8,  9, 10, 11,  2],\n",
       "       [12, 13, 14, 15,  3]])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.hstack([a,np.arange(4).reshape(4,1)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "#np.stack?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Type Matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.array([[1,2.],[4,3]])\n",
    "b = np.array([[1,9],[7,5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 2.],\n",
       "       [4., 3.]])"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 9],\n",
       "       [7, 5]])"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['T',\n",
       " '__abs__',\n",
       " '__add__',\n",
       " '__and__',\n",
       " '__array__',\n",
       " '__array_finalize__',\n",
       " '__array_function__',\n",
       " '__array_interface__',\n",
       " '__array_prepare__',\n",
       " '__array_priority__',\n",
       " '__array_struct__',\n",
       " '__array_ufunc__',\n",
       " '__array_wrap__',\n",
       " '__bool__',\n",
       " '__class__',\n",
       " '__complex__',\n",
       " '__contains__',\n",
       " '__copy__',\n",
       " '__deepcopy__',\n",
       " '__delattr__',\n",
       " '__delitem__',\n",
       " '__dir__',\n",
       " '__divmod__',\n",
       " '__doc__',\n",
       " '__eq__',\n",
       " '__float__',\n",
       " '__floordiv__',\n",
       " '__format__',\n",
       " '__ge__',\n",
       " '__getattribute__',\n",
       " '__getitem__',\n",
       " '__gt__',\n",
       " '__hash__',\n",
       " '__iadd__',\n",
       " '__iand__',\n",
       " '__ifloordiv__',\n",
       " '__ilshift__',\n",
       " '__imatmul__',\n",
       " '__imod__',\n",
       " '__imul__',\n",
       " '__index__',\n",
       " '__init__',\n",
       " '__init_subclass__',\n",
       " '__int__',\n",
       " '__invert__',\n",
       " '__ior__',\n",
       " '__ipow__',\n",
       " '__irshift__',\n",
       " '__isub__',\n",
       " '__iter__',\n",
       " '__itruediv__',\n",
       " '__ixor__',\n",
       " '__le__',\n",
       " '__len__',\n",
       " '__lshift__',\n",
       " '__lt__',\n",
       " '__matmul__',\n",
       " '__mod__',\n",
       " '__mul__',\n",
       " '__ne__',\n",
       " '__neg__',\n",
       " '__new__',\n",
       " '__or__',\n",
       " '__pos__',\n",
       " '__pow__',\n",
       " '__radd__',\n",
       " '__rand__',\n",
       " '__rdivmod__',\n",
       " '__reduce__',\n",
       " '__reduce_ex__',\n",
       " '__repr__',\n",
       " '__rfloordiv__',\n",
       " '__rlshift__',\n",
       " '__rmatmul__',\n",
       " '__rmod__',\n",
       " '__rmul__',\n",
       " '__ror__',\n",
       " '__rpow__',\n",
       " '__rrshift__',\n",
       " '__rshift__',\n",
       " '__rsub__',\n",
       " '__rtruediv__',\n",
       " '__rxor__',\n",
       " '__setattr__',\n",
       " '__setitem__',\n",
       " '__setstate__',\n",
       " '__sizeof__',\n",
       " '__str__',\n",
       " '__sub__',\n",
       " '__subclasshook__',\n",
       " '__truediv__',\n",
       " '__xor__',\n",
       " 'all',\n",
       " 'any',\n",
       " 'argmax',\n",
       " 'argmin',\n",
       " 'argpartition',\n",
       " 'argsort',\n",
       " 'astype',\n",
       " 'base',\n",
       " 'byteswap',\n",
       " 'choose',\n",
       " 'clip',\n",
       " 'compress',\n",
       " 'conj',\n",
       " 'conjugate',\n",
       " 'copy',\n",
       " 'ctypes',\n",
       " 'cumprod',\n",
       " 'cumsum',\n",
       " 'data',\n",
       " 'diagonal',\n",
       " 'dot',\n",
       " 'dtype',\n",
       " 'dump',\n",
       " 'dumps',\n",
       " 'fill',\n",
       " 'flags',\n",
       " 'flat',\n",
       " 'flatten',\n",
       " 'getfield',\n",
       " 'imag',\n",
       " 'item',\n",
       " 'itemset',\n",
       " 'itemsize',\n",
       " 'max',\n",
       " 'mean',\n",
       " 'min',\n",
       " 'nbytes',\n",
       " 'ndim',\n",
       " 'newbyteorder',\n",
       " 'nonzero',\n",
       " 'partition',\n",
       " 'prod',\n",
       " 'ptp',\n",
       " 'put',\n",
       " 'ravel',\n",
       " 'real',\n",
       " 'repeat',\n",
       " 'reshape',\n",
       " 'resize',\n",
       " 'round',\n",
       " 'searchsorted',\n",
       " 'setfield',\n",
       " 'setflags',\n",
       " 'shape',\n",
       " 'size',\n",
       " 'sort',\n",
       " 'squeeze',\n",
       " 'std',\n",
       " 'strides',\n",
       " 'sum',\n",
       " 'swapaxes',\n",
       " 'take',\n",
       " 'tobytes',\n",
       " 'tofile',\n",
       " 'tolist',\n",
       " 'tostring',\n",
       " 'trace',\n",
       " 'transpose',\n",
       " 'var',\n",
       " 'view']"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dir(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1., 18.],\n",
       "       [28., 15.]])"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a * b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = np.matrix(a)\n",
    "B = np.matrix(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[1, 9],\n",
       "        [7, 5]])"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['A',\n",
       " 'A1',\n",
       " 'H',\n",
       " 'I',\n",
       " 'T',\n",
       " '__abs__',\n",
       " '__add__',\n",
       " '__and__',\n",
       " '__array__',\n",
       " '__array_finalize__',\n",
       " '__array_function__',\n",
       " '__array_interface__',\n",
       " '__array_prepare__',\n",
       " '__array_priority__',\n",
       " '__array_struct__',\n",
       " '__array_ufunc__',\n",
       " '__array_wrap__',\n",
       " '__bool__',\n",
       " '__class__',\n",
       " '__complex__',\n",
       " '__contains__',\n",
       " '__copy__',\n",
       " '__deepcopy__',\n",
       " '__delattr__',\n",
       " '__delitem__',\n",
       " '__dict__',\n",
       " '__dir__',\n",
       " '__divmod__',\n",
       " '__doc__',\n",
       " '__eq__',\n",
       " '__float__',\n",
       " '__floordiv__',\n",
       " '__format__',\n",
       " '__ge__',\n",
       " '__getattribute__',\n",
       " '__getitem__',\n",
       " '__gt__',\n",
       " '__hash__',\n",
       " '__iadd__',\n",
       " '__iand__',\n",
       " '__ifloordiv__',\n",
       " '__ilshift__',\n",
       " '__imatmul__',\n",
       " '__imod__',\n",
       " '__imul__',\n",
       " '__index__',\n",
       " '__init__',\n",
       " '__init_subclass__',\n",
       " '__int__',\n",
       " '__invert__',\n",
       " '__ior__',\n",
       " '__ipow__',\n",
       " '__irshift__',\n",
       " '__isub__',\n",
       " '__iter__',\n",
       " '__itruediv__',\n",
       " '__ixor__',\n",
       " '__le__',\n",
       " '__len__',\n",
       " '__lshift__',\n",
       " '__lt__',\n",
       " '__matmul__',\n",
       " '__mod__',\n",
       " '__module__',\n",
       " '__mul__',\n",
       " '__ne__',\n",
       " '__neg__',\n",
       " '__new__',\n",
       " '__or__',\n",
       " '__pos__',\n",
       " '__pow__',\n",
       " '__radd__',\n",
       " '__rand__',\n",
       " '__rdivmod__',\n",
       " '__reduce__',\n",
       " '__reduce_ex__',\n",
       " '__repr__',\n",
       " '__rfloordiv__',\n",
       " '__rlshift__',\n",
       " '__rmatmul__',\n",
       " '__rmod__',\n",
       " '__rmul__',\n",
       " '__ror__',\n",
       " '__rpow__',\n",
       " '__rrshift__',\n",
       " '__rshift__',\n",
       " '__rsub__',\n",
       " '__rtruediv__',\n",
       " '__rxor__',\n",
       " '__setattr__',\n",
       " '__setitem__',\n",
       " '__setstate__',\n",
       " '__sizeof__',\n",
       " '__str__',\n",
       " '__sub__',\n",
       " '__subclasshook__',\n",
       " '__truediv__',\n",
       " '__xor__',\n",
       " '_align',\n",
       " '_collapse',\n",
       " '_getitem',\n",
       " 'all',\n",
       " 'any',\n",
       " 'argmax',\n",
       " 'argmin',\n",
       " 'argpartition',\n",
       " 'argsort',\n",
       " 'astype',\n",
       " 'base',\n",
       " 'byteswap',\n",
       " 'choose',\n",
       " 'clip',\n",
       " 'compress',\n",
       " 'conj',\n",
       " 'conjugate',\n",
       " 'copy',\n",
       " 'ctypes',\n",
       " 'cumprod',\n",
       " 'cumsum',\n",
       " 'data',\n",
       " 'diagonal',\n",
       " 'dot',\n",
       " 'dtype',\n",
       " 'dump',\n",
       " 'dumps',\n",
       " 'fill',\n",
       " 'flags',\n",
       " 'flat',\n",
       " 'flatten',\n",
       " 'getA',\n",
       " 'getA1',\n",
       " 'getH',\n",
       " 'getI',\n",
       " 'getT',\n",
       " 'getfield',\n",
       " 'imag',\n",
       " 'item',\n",
       " 'itemset',\n",
       " 'itemsize',\n",
       " 'max',\n",
       " 'mean',\n",
       " 'min',\n",
       " 'nbytes',\n",
       " 'ndim',\n",
       " 'newbyteorder',\n",
       " 'nonzero',\n",
       " 'partition',\n",
       " 'prod',\n",
       " 'ptp',\n",
       " 'put',\n",
       " 'ravel',\n",
       " 'real',\n",
       " 'repeat',\n",
       " 'reshape',\n",
       " 'resize',\n",
       " 'round',\n",
       " 'searchsorted',\n",
       " 'setfield',\n",
       " 'setflags',\n",
       " 'shape',\n",
       " 'size',\n",
       " 'sort',\n",
       " 'squeeze',\n",
       " 'std',\n",
       " 'strides',\n",
       " 'sum',\n",
       " 'swapaxes',\n",
       " 'take',\n",
       " 'tobytes',\n",
       " 'tofile',\n",
       " 'tolist',\n",
       " 'tostring',\n",
       " 'trace',\n",
       " 'transpose',\n",
       " 'var',\n",
       " 'view']"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dir(B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[-0.0862069 ,  0.15517241],\n",
       "        [ 0.12068966, -0.01724138]])"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B.I"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[15., 19.],\n",
       "        [25., 51.]])"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A * B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'numpy.ndarray'>\n",
      "<class 'numpy.matrix'>\n",
      "<class 'numpy.ndarray'>\n",
      "<class 'numpy.matrix'>\n",
      "<class 'numpy.matrix'>\n"
     ]
    }
   ],
   "source": [
    "print(type(a))\n",
    "print(type(A))\n",
    "print(type(a * b))\n",
    "print(type(A * B))\n",
    "print(type(a * B))"
   ]
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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  "language_info": {
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    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
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