ch11-numpy.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 11: NumPy\n",
    "___\n",
    "\n",
    "* ndarray, dtype, and shape\n",
    "* Common Array Operations\n",
    "* Reshape and Update In-Place\n",
    "* Combine Arrays\n",
    "* Create Sample Data\n",
    "* `numpy.linalg` module"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. NumPy Arrays: `ndarray`, `dtype`, and `shape`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.1 Vectors: 1-d array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 3]\n",
      "(3,)\n",
      "int64\n"
     ]
    }
   ],
   "source": [
    "a = np.array([1, 2, 3])\n",
    "print(a)\n",
    "print(a.shape)\n",
    "print(a.dtype)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.2 Multi-dimensional array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 2 4]\n",
      " [1 3 5]]\n",
      "(2, 3)\n",
      "int64\n"
     ]
    }
   ],
   "source": [
    "b = np.array([[0, 2, 4], [1, 3, 5]])\n",
    "print(b)\n",
    "print(b.shape)\n",
    "print(b.dtype)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.3 Creating special arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.,  0.,  0.,  0.,  0.])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.zeros(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 1, 1, 1],\n",
       "       [1, 1, 1, 1],\n",
       "       [1, 1, 1, 1]], dtype=int32)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.ones(shape=(3, 4), dtype=np.int32)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Common Array Operations (`ufunc`)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.1 Array-scalar Multiplication"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.   1.   2. ]\n",
      " [ 0.5  1.5  2.5]]\n",
      "(2, 3)\n",
      "float64\n"
     ]
    }
   ],
   "source": [
    "c = b * 0.5\n",
    "print(c)\n",
    "print(c.shape)\n",
    "print(c.dtype)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2 Array addition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.   3.   5. ]\n",
      " [ 1.5  3.5  5.5]]\n"
     ]
    }
   ],
   "source": [
    "d = a + c\n",
    "print(d)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.3 Array indexing and slicing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.,  3.,  5.])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d[0, 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1. ,  1.5])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d[:, 0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.4 Array statisitcal operations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "19.5"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.25"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  2.5,   6.5,  10.5])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d.sum(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 3. ,  3.5])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d.mean(axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Reshape and Update In-Place"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.1 `arange`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0  1  2  3  4  5  6  7  8  9 10 11]\n"
     ]
    }
   ],
   "source": [
    "e = np.arange(12)\n",
    "print(e)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.2 `reshape()`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0  1  2  3]\n",
      " [ 4  5  6  7]\n",
      " [ 8  9 10 11]]\n"
     ]
    }
   ],
   "source": [
    "# f is a view of contents of e\n",
    "f = e.reshape(3, 4)\n",
    "print(f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2 3 4 0 0 0 0 0 0 0]\n"
     ]
    }
   ],
   "source": [
    "# Set values of e from index 5 onwards to 0\n",
    "e[5:] = 0\n",
    "print(e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 2, 3],\n",
       "       [4, 0, 0, 0],\n",
       "       [0, 0, 0, 0]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# f is also updated\n",
    "f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "  C_CONTIGUOUS : True\n",
       "  F_CONTIGUOUS : False\n",
       "  OWNDATA : False\n",
       "  WRITEABLE : True\n",
       "  ALIGNED : True\n",
       "  UPDATEIFCOPY : False"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# OWNDATA shows f does not own its data\n",
    "f.flags"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Combine Arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 2, 4],\n",
       "       [1, 3, 5]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1. ,  3. ,  5. ],\n",
       "       [ 1.5,  3.5,  5.5]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.1 `numpy.concatenate()`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 1, 2, 3, 1, 2, 3])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.concatenate([a, a, a])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.2 `numpy.vstack()`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1. ,  2. ,  3. ],\n",
       "       [ 0. ,  2. ,  4. ],\n",
       "       [ 1. ,  3. ,  5. ],\n",
       "       [ 1. ,  3. ,  5. ],\n",
       "       [ 1.5,  3.5,  5.5]])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Use broadcasting when needed to do this automatically\n",
    "np.vstack([a, b, d])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.3 `numpy.hstack()`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0. ,  2. ,  4. ,  1. ,  3. ,  5. ],\n",
       "       [ 1. ,  3. ,  5. ,  1.5,  3.5,  5.5]])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# In machine learning, useful to enrich or \n",
    "# add new/concatenate features with hstack\n",
    "np.hstack([b, d])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5. Create Sample Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import seaborn\n",
    "\n",
    "seaborn.set()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.1 `numpy.linspace()`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Vs/ryz5ana/pkqi+BYCKQAfSJ6ksgdAhkAL2i+hIILQIZwF0Mw1DRWa92FpRSfQmEEIEM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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f337368e110>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create evenly spaced numbers over the specified interval\n",
    "x = np.linspace(0, 2, 10)\n",
    "plt.plot(x, 'o-')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.2 `np.random` module"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f339c03b2d0>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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cnKN0dOQSCGj3Ky1tgL4+q+keGjd2TqfC6tUvR20Uo+UN6N8fQMTDM1Cz7yXj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\ni4iIhJj/DwWFTzSAUadEAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f33733ce1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create sample data, add some noise\n",
    "x = np.random.uniform(1, 100, 1000)\n",
    "y = np.log(x) + np.random.normal(0, .3, 1000)\n",
    "\n",
    "plt.scatter(x, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6. `numpy.linalg`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy.linalg as npl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['LinAlgError',\n",
       " '__builtins__',\n",
       " '__doc__',\n",
       " '__file__',\n",
       " '__name__',\n",
       " '__package__',\n",
       " '__path__',\n",
       " '_numpy_tester',\n",
       " '_umath_linalg',\n",
       " 'absolute_import',\n",
       " 'bench',\n",
       " 'cholesky',\n",
       " 'cond',\n",
       " 'det',\n",
       " 'division',\n",
       " 'eig',\n",
       " 'eigh',\n",
       " 'eigvals',\n",
       " 'eigvalsh',\n",
       " 'info',\n",
       " 'inv',\n",
       " 'lapack_lite',\n",
       " 'linalg',\n",
       " 'lstsq',\n",
       " 'matrix_power',\n",
       " 'matrix_rank',\n",
       " 'multi_dot',\n",
       " 'norm',\n",
       " 'pinv',\n",
       " 'print_function',\n",
       " 'qr',\n",
       " 'slogdet',\n",
       " 'solve',\n",
       " 'svd',\n",
       " 'tensorinv',\n",
       " 'tensorsolve',\n",
       " 'test']"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dir(npl)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.1 Singular value decomposition (SVD)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<function numpy.linalg.linalg.svd>"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "npl.svd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.2 Eigenvalue decomposition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<function numpy.linalg.linalg.eig>"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "npl.eig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<function numpy.linalg.linalg.eigvals>"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "npl.eigvals"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.3 QR-decomposition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<function numpy.linalg.linalg.qr>"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "npl.qr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.4 determinant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<function numpy.linalg.linalg.det>"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "npl.det"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.5 Inverse and Pseudo-inverse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<function numpy.linalg.linalg.solve>"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "npl.solve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<function numpy.linalg.linalg.pinv>"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "npl.pinv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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