1_Array_creation_routines_Solution.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": {
    "collapsed": true
   },
   "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": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 0],\n",
       "       [0, 0]])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.empty([2,2], int)"
   ]
  },
  {
   "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": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = np.array([[1,2,3], [4,5,6]], np.int32)\n",
    "np.empty_like(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a 3-D array with ones on the diagonal and zeros elsewhere."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  0.,  0.],\n",
       "       [ 0.,  1.,  0.],\n",
       "       [ 0.,  0.,  1.]])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.eye(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  0.,  0.],\n",
       "       [ 0.,  1.,  0.],\n",
       "       [ 0.,  0.,  1.]])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.identity(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a new array of 3*2 float numbers, filled with ones."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  1.],\n",
       "       [ 1.,  1.],\n",
       "       [ 1.,  1.]])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.ones([3,2], 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": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 1, 1], dtype=int64)"
      ]
     },
     "execution_count": 59,
     "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": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  0.],\n",
       "       [ 0.,  0.],\n",
       "       [ 0.,  0.]])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.zeros((3,2), 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": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 0], dtype=int64)"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.arange(4, dtype=np.int64)\n",
    "np.zeros_like(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a new array of 2*5 uints, filled with 6."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[6, 6, 6, 6, 6],\n",
       "       [6, 6, 6, 6, 6]], dtype=uint32)"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.full((2, 5), 6, dtype=np.uint)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[6, 6, 6, 6, 6],\n",
       "       [6, 6, 6, 6, 6]], dtype=uint32)"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.ones([2, 5], dtype=np.uint) * 6"
   ]
  },
  {
   "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": 79,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([6, 6, 6, 6], dtype=int64)"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.arange(4, dtype=np.int64)\n",
    "np.full_like(x, 6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([6, 6, 6, 6], dtype=int64)"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.ones_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": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3])"
      ]
     },
     "execution_count": 53,
     "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": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2])"
      ]
     },
     "execution_count": 60,
     "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": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[1, 2],\n",
       "        [3, 4]])"
      ]
     },
     "execution_count": 62,
     "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": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.,  2.])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = [1, 2]\n",
    "np.asfarray(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.,  2.])"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.asarray(x, 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": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "30"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([30])\n",
    "np.asscalar(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "30"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[0]"
   ]
  },
  {
   "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": 76,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "70140352 [1 2 3]\n",
      "70140752 [1 2 3]\n"
     ]
    }
   ],
   "source": [
    "x = np.array([1, 2, 3])\n",
    "y = np.copy(x)\n",
    "print id(x), x\n",
    "print id(y), y"
   ]
  },
  {
   "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": 85,
   "metadata": {
    "collapsed": false
   },
   "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": 85,
     "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": 86,
   "metadata": {
    "collapsed": false
   },
   "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": 86,
     "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": 88,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  1.00000000e+03,   1.38038426e+03,   1.90546072e+03,\n",
       "         2.63026799e+03,   3.63078055e+03,   5.01187234e+03,\n",
       "         6.91830971e+03,   9.54992586e+03,   1.31825674e+04,\n",
       "         1.81970086e+04,   2.51188643e+04,   3.46736850e+04,\n",
       "         4.78630092e+04,   6.60693448e+04,   9.12010839e+04,\n",
       "         1.25892541e+05,   1.73780083e+05,   2.39883292e+05,\n",
       "         3.31131121e+05,   4.57088190e+05,   6.30957344e+05,\n",
       "         8.70963590e+05,   1.20226443e+06,   1.65958691e+06,\n",
       "         2.29086765e+06,   3.16227766e+06,   4.36515832e+06,\n",
       "         6.02559586e+06,   8.31763771e+06,   1.14815362e+07,\n",
       "         1.58489319e+07,   2.18776162e+07,   3.01995172e+07,\n",
       "         4.16869383e+07,   5.75439937e+07,   7.94328235e+07,\n",
       "         1.09647820e+08,   1.51356125e+08,   2.08929613e+08,\n",
       "         2.88403150e+08,   3.98107171e+08,   5.49540874e+08,\n",
       "         7.58577575e+08,   1.04712855e+09,   1.44543977e+09,\n",
       "         1.99526231e+09,   2.75422870e+09,   3.80189396e+09,\n",
       "         5.24807460e+09,   7.24435960e+09])"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.logspace(3., 10., 50, endpoint=False)"
   ]
  },
  {
   "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": 93,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  5, 10])"
      ]
     },
     "execution_count": 93,
     "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": "code",
   "execution_count": 94,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  5, 10])"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.diagonal()"
   ]
  },
  {
   "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": 95,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 0, 0, 0],\n",
       "       [0, 2, 0, 0],\n",
       "       [0, 0, 3, 0],\n",
       "       [0, 0, 0, 4]])"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.diagflat([1, 2, 3, 4])"
   ]
  },
  {
   "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": 97,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  0.,  0.,  0.,  0.],\n",
       "       [ 1.,  0.,  0.,  0.,  0.],\n",
       "       [ 1.,  1.,  0.,  0.,  0.]])"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.tri(3, 5, -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": 101,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  0,  0],\n",
       "       [ 4,  0,  0],\n",
       "       [ 7,  8,  0],\n",
       "       [10, 11, 12]])"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.tril(np.arange(1, 13).reshape(4, 3), -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": 102,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  2,  3],\n",
       "       [ 4,  5,  6],\n",
       "       [ 0,  8,  9],\n",
       "       [ 0,  0, 12]])"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.triu(np.arange(1, 13).reshape(4, 3), -1)"
   ]
  }
 ],
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   "display_name": "Python 2",
   "language": "python",
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   "codemirror_mode": {
    "name": "ipython",
    "version": 2
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   "file_extension": ".py",
   "mimetype": "text/x-python",
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   "nbconvert_exporter": "python",
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