0-libraries/numpy-exercises/00-array-creation-routines.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Array creation routines"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ones and zeros"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a new array of 2*2 integers, without initializing entries."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.zeros([2, 2], int)\n",
    "??float"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let X = np.array([1,2,3], [4,5,6], np.int32). \n",
    "Create a new array with the same shape and type as X."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 0, 0],\n",
       "       [0, 0, 0]], dtype=int32)"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = np.array([[1,2,3], [4,5,6]], np.int32); X\n",
    "zeros = np.zeros_like(X); zeros"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a 3-D array with ones on the diagonal and zeros elsewhere."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 1.,  0.,  0.],\n",
       "        [ 0.,  0.,  0.],\n",
       "        [ 0.,  0.,  0.]],\n",
       "\n",
       "       [[ 0.,  0.,  0.],\n",
       "        [ 0.,  1.,  0.],\n",
       "        [ 0.,  0.,  0.]],\n",
       "\n",
       "       [[ 0.,  0.,  0.],\n",
       "        [ 0.,  0.,  0.],\n",
       "        [ 0.,  0.,  1.]]])"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.zeros((3, 3, 3))\n",
    "np.fill_diagonal(x, 1); x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a new array of 3*2 float numbers, filled with ones."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  1.],\n",
       "       [ 1.,  1.],\n",
       "       [ 1.,  1.]])"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.ones((3, 2), dtype=np.float)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let x = np.arange(4, dtype=np.int64). Create an array of ones with the same shape and type as X."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 1, 1])"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.arange(4, dtype=np.int64)\n",
    "np.ones_like(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a new array of 3*2 float numbers, filled with zeros."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  0.],\n",
       "       [ 0.,  0.],\n",
       "       [ 0.,  0.]])"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.zeros((3, 2), dtype=np.float)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let x = np.arange(4, dtype=np.int64). Create an array of zeros with the same shape and type as X."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3])"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.arange(4, dtype=np.int64); x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a new array of 2*5 uints, filled with 6."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[6, 6, 6, 6, 6],\n",
       "       [6, 6, 6, 6, 6]], dtype=uint32)"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.full((2, 5), 6, dtype=np.uint32)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let x = np.arange(4, dtype=np.int64). Create an array of 6's with the same shape and type as X."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([6, 6, 6, 6])"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.arange(4, dtype=np.int64)\n",
    "np.full_like(x, 6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## From existing data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create an array of [1, 2, 3]."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3])"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array([1, 2, 3])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let x = [1, 2]. Convert it into an array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2])"
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = [1,2]\n",
    "np.asarray(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let X = np.array([[1, 2], [3, 4]]). Convert it into a matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[1, 2],\n",
       "        [3, 4]])"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = np.array([[1, 2], [3, 4]])\n",
    "np.asmatrix(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let x = [1, 2]. Conver it into an array of `float`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.,  2.])"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = [1, 2]\n",
    "np.asarray(x, dtype=np.float)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let x = np.array([30]). Convert it into scalar of its single element, i.e. 30."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "30"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([30])\n",
    "np.asscalar(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let x = np.array([1, 2, 3]). Create a array copy of x, which has a different id from x."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3])"
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([1, 2, 3])\n",
    "np.copy(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Numerical ranges"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create an array of 2, 4, 6, 8, ..., 100."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  2,   4,   6,   8,  10,  12,  14,  16,  18,  20,  22,  24,  26,\n",
       "        28,  30,  32,  34,  36,  38,  40,  42,  44,  46,  48,  50,  52,\n",
       "        54,  56,  58,  60,  62,  64,  66,  68,  70,  72,  74,  76,  78,\n",
       "        80,  82,  84,  86,  88,  90,  92,  94,  96,  98, 100])"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.arange(2, 101, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a 1-D array of 50 evenly spaced elements between 3. and 10., inclusive."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  3.        ,   3.14285714,   3.28571429,   3.42857143,\n",
       "         3.57142857,   3.71428571,   3.85714286,   4.        ,\n",
       "         4.14285714,   4.28571429,   4.42857143,   4.57142857,\n",
       "         4.71428571,   4.85714286,   5.        ,   5.14285714,\n",
       "         5.28571429,   5.42857143,   5.57142857,   5.71428571,\n",
       "         5.85714286,   6.        ,   6.14285714,   6.28571429,\n",
       "         6.42857143,   6.57142857,   6.71428571,   6.85714286,\n",
       "         7.        ,   7.14285714,   7.28571429,   7.42857143,\n",
       "         7.57142857,   7.71428571,   7.85714286,   8.        ,\n",
       "         8.14285714,   8.28571429,   8.42857143,   8.57142857,\n",
       "         8.71428571,   8.85714286,   9.        ,   9.14285714,\n",
       "         9.28571429,   9.42857143,   9.57142857,   9.71428571,\n",
       "         9.85714286,  10.        ])"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linspace(3, 10, 50)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a 1-D array of 50 element spaced evenly on a log scale between 3. and 10., exclusive."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  1.00000000e+03,   1.38949549e+03,   1.93069773e+03,\n",
       "         2.68269580e+03,   3.72759372e+03,   5.17947468e+03,\n",
       "         7.19685673e+03,   1.00000000e+04,   1.38949549e+04,\n",
       "         1.93069773e+04,   2.68269580e+04,   3.72759372e+04,\n",
       "         5.17947468e+04,   7.19685673e+04,   1.00000000e+05,\n",
       "         1.38949549e+05,   1.93069773e+05,   2.68269580e+05,\n",
       "         3.72759372e+05,   5.17947468e+05,   7.19685673e+05,\n",
       "         1.00000000e+06,   1.38949549e+06,   1.93069773e+06,\n",
       "         2.68269580e+06,   3.72759372e+06,   5.17947468e+06,\n",
       "         7.19685673e+06,   1.00000000e+07,   1.38949549e+07,\n",
       "         1.93069773e+07,   2.68269580e+07,   3.72759372e+07,\n",
       "         5.17947468e+07,   7.19685673e+07,   1.00000000e+08,\n",
       "         1.38949549e+08,   1.93069773e+08,   2.68269580e+08,\n",
       "         3.72759372e+08,   5.17947468e+08,   7.19685673e+08,\n",
       "         1.00000000e+09,   1.38949549e+09,   1.93069773e+09,\n",
       "         2.68269580e+09,   3.72759372e+09,   5.17947468e+09,\n",
       "         7.19685673e+09,   1.00000000e+10])"
      ]
     },
     "execution_count": 141,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.logspace(3, 10, 50)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Building matrices"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let X = np.array([[ 0,  1,  2,  3],\n",
    "                  [ 4,  5,  6,  7],\n",
    "                 [ 8,  9, 10, 11]]).\n",
    "                 Get the diagonal of X, that is, [0, 5, 10]."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  5, 10])"
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = np.array([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]])\n",
    "np.diag(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a 2-D array whose diagonal equals [1, 2, 3, 4] and 0's elsewhere."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 0, 0, 0],\n",
       "       [0, 2, 0, 0],\n",
       "       [0, 0, 3, 0],\n",
       "       [0, 0, 0, 4]], dtype=uint8)"
      ]
     },
     "execution_count": 161,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.zeros((4, 4), dtype=np.uint8)\n",
    "np.fill_diagonal(x, np.arange(1, 5))\n",
    "x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create an array which looks like below.\n",
    "array([[ 0.,  0.,  0.,  0.,  0.],\n",
    "       [ 1.,  0.,  0.,  0.,  0.],\n",
    "       [ 1.,  1.,  0.,  0.,  0.]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  0.,  0.,  0.,  0.],\n",
       "       [ 1.,  0.,  0.,  0.,  0.],\n",
       "       [ 1.,  1.,  0.,  0.,  0.]])"
      ]
     },
     "execution_count": 173,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.ones((3, 5))\n",
    "np.tril(x, -1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create an array which looks like below.\n",
    "array([[ 0,  0,  0],\n",
    "       [ 4,  0,  0],\n",
    "       [ 7,  8,  0],\n",
    "       [10, 11, 12]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  0,  0],\n",
       "       [ 4,  0,  0],\n",
       "       [ 7,  8,  0],\n",
       "       [10, 11, 12]])"
      ]
     },
     "execution_count": 181,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.arange(1, 13).reshape(4, 3)\n",
    "np.tril(x, -1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create an array which looks like below. array([[ 1,  2,  3],\n",
    "       [ 4,  5,  6],\n",
    "       [ 0,  8,  9],\n",
    "       [ 0,  0, 12]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  2,  3],\n",
       "       [ 4,  5,  6],\n",
       "       [ 0,  8,  9],\n",
       "       [ 0,  0, 12]])"
      ]
     },
     "execution_count": 184,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.arange(1, 13).reshape(4, 3)\n",
    "np.triu(x, -1)"
   ]
  }
 ],
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