r9y9/Coursera Digital Signal Processing Homework Week #2.json

## Coursera Digital Signal Processing Homework Week #2.json
{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Coursera Digital Signal Processing Homework Week #2\n",
      "graham schmidt algorithm"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "\n",
      "v1 = np.array([0.8660, 0.5, 0])\n",
      "v2 = np.array([0.0, 0.5, 0.8660])\n",
      "v3 = np.array([1.7320, 3.0, 3.4640])\n",
      "\n",
      "print v1\n",
      "print v2\n",
      "print v3"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 0.866  0.5    0.   ]\n",
        "[ 0.     0.5    0.866]\n",
        "[ 1.732  3.     3.464]\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "w1 = v1\n",
      "w2 = v2 - np.dot(np.dot(v2, w1), w1)\n",
      "w3 = v3 - np.dot(np.dot(v3, w2), w2) - np.dot(np.dot(v3, w1), w1)\n",
      "\n",
      "print w1\n",
      "print w2\n",
      "print w3"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 0.866  0.5    0.   ]\n",
        "[-0.2165  0.375   0.866 ]\n",
        "[-0.05408213  0.09385175  0.21663336]\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print np.dot(w1, w2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1.1e-05\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "E = np.zeros((3, 3))\n",
      "E[:,0] = w1\n",
      "E[:,1] = w2\n",
      "E[:,2] = w3\n",
      "print E\n",
      "print np.linalg.det(E)\n",
      "print np.dot(E.T, E)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[ 0.866      -0.2165     -0.05408213]\n",
        " [ 0.5         0.375       0.09385175]\n",
        " [ 0.          0.866       0.21663336]]\n",
        "4.16309209328e-17\n",
        "[[  9.99956000e-01   1.10000000e-05   9.07478220e-05]\n",
        " [  1.10000000e-05   9.37453250e-01   2.34507681e-01]\n",
        " [  9.07478220e-05   2.34507681e-01   5.86630425e-02]]\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = linspace(-1, 1)\n",
      "plot(x, sin(x))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "[<matplotlib.lines.Line2D at 0x7fb805b628d0>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7fb805ca0e10>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}
	{
	"metadata": {
	"name": ""
	},
	"nbformat": 3,
	"nbformat_minor": 0,
	"worksheets": [
	{
	"cells": [
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"## Coursera Digital Signal Processing Homework Week #2\n",
	"graham schmidt algorithm"
	]
	},
	{
	"cell_type": "code",
	"collapsed": false,
	"input": [
	"import numpy as np\n",
	"\n",
	"v1 = np.array([0.8660, 0.5, 0])\n",
	"v2 = np.array([0.0, 0.5, 0.8660])\n",
	"v3 = np.array([1.7320, 3.0, 3.4640])\n",
	"\n",
	"print v1\n",
	"print v2\n",
	"print v3"
	],
	"language": "python",
	"metadata": {},
	"outputs": [
	{
	"output_type": "stream",
	"stream": "stdout",
	"text": [
	"[ 0.866 0.5 0. ]\n",
	"[ 0. 0.5 0.866]\n",
	"[ 1.732 3. 3.464]\n"
	]
	}
	],
	"prompt_number": 9
	},
	{
	"cell_type": "code",
	"collapsed": false,
	"input": [
	"w1 = v1\n",
	"w2 = v2 - np.dot(np.dot(v2, w1), w1)\n",
	"w3 = v3 - np.dot(np.dot(v3, w2), w2) - np.dot(np.dot(v3, w1), w1)\n",
	"\n",
	"print w1\n",
	"print w2\n",
	"print w3"
	],
	"language": "python",
	"metadata": {},
	"outputs": [
	{
	"output_type": "stream",
	"stream": "stdout",
	"text": [
	"[ 0.866 0.5 0. ]\n",
	"[-0.2165 0.375 0.866 ]\n",
	"[-0.05408213 0.09385175 0.21663336]\n"
	]
	}
	],
	"prompt_number": 10
	},
	{
	"cell_type": "code",
	"collapsed": false,
	"input": [
	"print np.dot(w1, w2)"
	],
	"language": "python",
	"metadata": {},
	"outputs": [
	{
	"output_type": "stream",
	"stream": "stdout",
	"text": [
	"1.1e-05\n"
	]
	}
	],
	"prompt_number": 11
	},
	{
	"cell_type": "code",
	"collapsed": false,
	"input": [
	"E = np.zeros((3, 3))\n",
	"E[:,0] = w1\n",
	"E[:,1] = w2\n",
	"E[:,2] = w3\n",
	"print E\n",
	"print np.linalg.det(E)\n",
	"print np.dot(E.T, E)"
	],
	"language": "python",
	"metadata": {},
	"outputs": [
	{
	"output_type": "stream",
	"stream": "stdout",
	"text": [
	"[[ 0.866 -0.2165 -0.05408213]\n",
	" [ 0.5 0.375 0.09385175]\n",
	" [ 0. 0.866 0.21663336]]\n",
	"4.16309209328e-17\n",
	"[[ 9.99956000e-01 1.10000000e-05 9.07478220e-05]\n",
	" [ 1.10000000e-05 9.37453250e-01 2.34507681e-01]\n",
	" [ 9.07478220e-05 2.34507681e-01 5.86630425e-02]]\n"
	]
	}
	],
	"prompt_number": 12
	},
	{
	"cell_type": "code",
	"collapsed": false,
	"input": [
	"%pylab inline\n"
	],
	"language": "python",
	"metadata": {},
	"outputs": [
	{
	"output_type": "stream",
	"stream": "stdout",
	"text": [
	"Populating the interactive namespace from numpy and matplotlib\n"
	]
	}
	],
	"prompt_number": 4
	},
	{
	"cell_type": "code",
	"collapsed": false,
	"input": [
	"x = linspace(-1, 1)\n",
	"plot(x, sin(x))"
	],
	"language": "python",
	"metadata": {},
	"outputs": [
	{
	"metadata": {},
	"output_type": "pyout",
	"prompt_number": 7,
	"text": [
	"[<matplotlib.lines.Line2D at 0x7fb805b628d0>]"
	]
	},
	{
	"metadata": {},
	"output_type": "display_data",
	"png": 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	"text": [
	"<matplotlib.figure.Figure at 0x7fb805ca0e10>"
	]
	}
	],
	"prompt_number": 7
	},
	{
	"cell_type": "code",
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	"input": [],
	"language": "python",
	"metadata": {},
	"outputs": []
	}
	],
	"metadata": {}
	}
	]
	}