Numpy Arrays and Objects

Week 03 Fall 2015.ipynb

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   "cells": [
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     "cell_type": "code",
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     "input": [
      "import numpy as np\n",
      "\n",
      "# Slide 8\n",
      "myonedim = np.array(range(0,9))\n",
      "print myonedim\n",
      "\n",
      "# This makes an array out of a nested sequence (can be nested tuples, nested lists, or combination of them)\n",
      "a = [ [[1,2],[3,4]],\n",
      "      [[5,6],[7,8]],\n",
      "      [[9,10],[11,12]]\n",
      "     ]\n",
      "print a\n",
      "print a[0]\n",
      "print a[0][0]\n",
      "print a[0][0][1]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Slide 9\n",
      "# Arange\n",
      "\n",
      "import numpy as np\n",
      "print np.arange(3)\n",
      "print np.arange(3.0)\n",
      "print np.arange(3, dtype=float)\n",
      "print np.arange(3,10) # start,stop\n",
      "print np.arange(3,10,2) # start,stop,step"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Slide 9\n",
      "# Linspace\n",
      "print np.linspace(2.0, 3.0, num=5)\n",
      "print np.linspace(2.0, 3.0, num=5, endpoint=False)\n",
      "print np.linspace(2.0, 3.0, num=5, retstep=True)\n",
      "\n",
      "# Logspace\n",
      "print np.logspace(0,4,5)\n",
      "np.set_printoptions(suppress=True)\n",
      "print np.logspace(0,4,5)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Slide 9\n",
      "# Mgrid\n",
      "\n",
      "import numpy as np\n",
      "## 2 rows and 4 columns\n",
      "mygrid = np.mgrid[0:2, 0:4]\n",
      "grid_x, grid_y = np.mgrid[0:2, 0:4]\n",
      "print mygrid\n",
      "print grid_x\n",
      "print grid_y\n",
      "# Change the numbers and see what happens"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Slide 9\n",
      "# Random\n",
      "from numpy import random\n",
      "# uniform random numbers in [0,1]\n",
      "print random.rand(2,5)\n",
      " \n",
      "# standard normal distributed random numbers\n",
      "print random.randn(5,2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Slide 9\n",
      "import numpy as np\n",
      "\n",
      "# a diagonal matrix\n",
      "print np.diag([1,2,3])\n",
      " \n",
      "# diagonal with offset from main diagonal\n",
      "print np.diag([1,2,3], k=2)\n",
      "\n",
      "# matrix with all zeros\n",
      "print np.zeros([3,3])\n",
      "\n",
      "# matrix with all ones\n",
      "print np.ones([3,3])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Slide 10\n",
      "\n",
      "# Create a csv file in spreadsheet -- mycsv.csv\n",
      "# Name, Age Height\n",
      "# Tom, 23, 167\n",
      "# Dick, 28, 172\n",
      "# Mary, 27, 168\n",
      "\n",
      "import numpy as np \n",
      "mydata = np.loadtxt('mycsv.csv', delimiter=',', dtype=str)\n",
      "print mydata\n",
      "print mydata.dtype\n",
      "\n",
      "\n",
      "# Another method\n",
      "mydata = np.genfromtxt('myfile.csv', dtype=float, delimiter=',', names=True) \n",
      "print mydata"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Slide 10\n",
      "# Another example\n",
      "# Create a a csv file with ALL numbers and no headers -- myfile.csv\n",
      "# 12,23,45\n",
      "# 1,34,54\n",
      "# 3,4,67\n",
      "\n",
      "import numpy as np\n",
      "# Simpler version\n",
      "mydata = np.genfromtxt('myfile.csv', delimiter=',') "
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Slide 10\n",
      "# NPY format\n",
      "from numpy import random as nrand\n",
      "a = nrand.randn(2,3)\n",
      "np.save('myarray', a)\n",
      "np.load('myarray.npy')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Slide 10\n",
      "# NPZ format\n",
      "import numpy as np\n",
      "a = np.array([[3, 2, 1], [7, 8, 9]])\n",
      "b = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9])\n",
      "np.savez('myarrays.npz', a=a, b=b)\n",
      "myarraydata = np.load('myarrays.npz')\n",
      "myarraydata['a'] \n",
      "myarraydata['b']\n",
      "myarraydata.close()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Slide 15\n",
      "print a[0:2,0:2]\n",
      "print a[1:3,1:3]\n",
      "print a[2:,2:]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Slide 16\n",
      "import numpy as np\n",
      "a = np.reshape(np.arange(9),(3,3))\n",
      "# for row sums\n",
      "for r in range(a.shape[0]):\n",
      "    print sum(a[r,:])\n",
      "# for column sums\n",
      "for r in range(a.shape[1]):\n",
      "    print sum(a[:,r])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Slide 19\n",
      "import numpy as np\n",
      "y = np.zeros((2, 3, 4))\n",
      "y.shape\n",
      "\n",
      "\n",
      "x = np.array([[1, 2],\n",
      "              [3, 4],\n",
      "              [5, 6]\n",
      "             ]) \n",
      "print x\n",
      "print x.T"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Slide 20\n",
      "import numpy as np\n",
      "x.diagonal()\n",
      "x.diagonal(offset=1)\n",
      "x.diagonal(offset=-1)\n",
      "\n",
      "import numpy as np\n",
      "a = np.array(range(9))\n",
      "b = a.reshape(3,3)\n",
      "print b"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Slide 22\n",
      "# Dot product is like matrix multiplication\n",
      "a = [[1, 0], [0, 1]]\n",
      "b = [[4, 1], [2, 2]]\n",
      "print np.dot(a, b)\n",
      "\n",
      "# Ref http://cs.brown.edu/courses/cs053/current/slides/The_Matrix-6.pdf\n",
      "\n",
      "# Inner product with vectors\n",
      "a = np.array([1,2,3])\n",
      "b = np.array([0,1,0])\n",
      "print np.inner(a, b)\n",
      "\n",
      "# Inner product with arrays\n",
      "a = np.arange(6).reshape((2,3))\n",
      "b = np.arange(3)\n",
      "print np.inner(a, b)\n",
      "\n",
      "# Outer product\n",
      "a = [1, 2]\n",
      "b = [1, 2, 3]\n",
      "print np.outer(a, b)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Slide 24\n",
      "import numpy as np\n",
      "from scipy import linalg\n",
      "A = np.array([[1,2],[3,4]])\n",
      "print linalg.inv(A)\n",
      "print A.dot(linalg.inv(A)) #double check"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Slide 31\n",
      "import numpy as np\n",
      "A = np.matrix([[1,2,3],[0,2,4],[0,0,3]])\n",
      "print A\n",
      "b = np.matrix([[2],[1],[4]])\n",
      "print b\n",
      "x = A.I*b\n",
      "print x"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Slide 35\n",
      "# Using arrays\n",
      "\n",
      "import numpy as np\n",
      "xi = [3,2,8,5,2,6,3,7,5,3]\n",
      "X = np.array(zip(np.ones(10),xi))\n",
      "y = [6,3,11,6,3,9,4,12,7,5]\n",
      "XTX = np.dot(X.T,X)\n",
      "XTXinv = np.linalg.inv(XTX)\n",
      "XTy = np.dot(X.T,y)\n",
      "b = np.dot(XTXinv, XTy)\n",
      "print b"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Slide 35\n",
      "# Using matrices\n",
      "\n",
      "import numpy as np\n",
      "xi = [3,2,8,5,2,6,3,7,5,3]\n",
      "X = np.array(zip(np.ones(10),xi))\n",
      "y = [6,3,11,6,3,9,4,12,7,5]\n",
      "X = np.matrix(zip(np.ones(10),xi))\n",
      "y = np.reshape(y,(10,1))\n",
      "b = (X.T*X).I*X.T*y\n",
      "print b"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
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