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@olivierverdier
Created November 20, 2014 11:46
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{
"worksheets": [
{
"cells": [
{
"metadata": {},
"cell_type": "heading",
"source": "Exercise for the course [Python for MATLAB users](http://sese.nu/python-for-matlab-users/), by Olivier Verdier",
"level": 2
},
{
"metadata": {},
"cell_type": "code",
"input": "%pylab\n%matplotlib inline\nfrom __future__ import division",
"outputs": [],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Check out the formula for a [companion matrix on wikipedia](http://en.wikipedia.org/wiki/Companion_matrix).\nDefine a function `companion` which accepts a vector in argument, and returns the corresponding companion matrix.\nYou can use the command `diag` for that.\nThe resulting matrix should be of complex type."
},
{
"metadata": {},
"cell_type": "code",
"input": "diag?",
"prompt_number": 60,
"outputs": [],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "code",
"input": "ones?",
"outputs": [],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "code",
"input": "def companion(coefficients):\n n = len(coefficients)\n C = diag(ones(n-1, dtype=complex),-1)\n C[:,-1] = -coefficients\n return C\n\n",
"prompt_number": 32,
"outputs": [],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "code",
"input": "C = companion(ones(3))\nassert(C.dtype == complex)\nassert(len(C) == 3)",
"prompt_number": 62,
"outputs": [],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Fix a given size, say `size = 20`, and create a vector of length 20 with random, normally distributed, complex numbers. Use the `randn` function for that, and combine two random real vectors to get a random complex vector."
},
{
"metadata": {},
"cell_type": "code",
"input": "randn?",
"outputs": [],
"language": "python",
"trusted": true,
"collapsed": false
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Now, fix a standard deviation, say `sigma = 1./10`, and use the random complex coefficients obtained above, multiplied by sigma, in the `companion` function. Use `eigvals` to compute the eigenvalues, and plot them on the complex plane. You can use the command `axis('equal')` to make sure the plot has the same dimensions in x and y."
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Finally, repeat that, say 200 times. Plot all the eigenvalues on the same figure. What do you observe? What happens when you change the standard deviation `sigma`?"
},
{
"metadata": {},
"cell_type": "code",
"input": "size = 20\nfor i in range(200):\n coeffs = 1./20*(randn(size) + 1j*randn(size))\n eigenvalues = eigvals(companion(coeffs))\n plot(real(eigenvalues), imag(eigenvalues),'.')\n axis('equal')\nangles = linspace(0,2*pi,300)\n#plot(cos(angles), sin(angles), linewidth=10)",
"prompt_number": 65,
"outputs": [
{
"output_type": "display_data",
"metadata": {},
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23343Kjh2K4RVdWDxnmepnP4CSqcaCutdiff+jk2VsGPWLG7YtQuLqyu7uj9B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\nvPYOR/fCHZ+sQuX0F5GTlC2VD7JhISy9Y+pQTCGQEcNHiG1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OqZ9EIqNSAScWhhEcvPqK\nn1tLFahJARKou4HHQhfa6IRkARL+eoUc/TGQOPFY9ft8P/z6Sw9oRjNf7RX6V5KXzQ2Kaq2W+MGD\nLylhrmuCuTxMV/vZNHU6H//sKPuSDMgGuCAp9eP+NRUcHwI9zpfh0ieX0wQbryFoOotzViJJPgD9\nrVf11BqwrfgtxNfdv6ZbjrGqVeeiw6PEgwpJBc/aP8OhisMA/IgPY/oXUt3FQMZsqFTA/oNRJP60\n4Yq/x/ZovFVnZnKiOJeokje5L3QtXi7eVxxT07lvcfmEtMg0dIk6FGGKK0TFAItdaIoqxTwheUd7\nXzEhteXqu6l4LgtDd2EvAFGB97LhgfWXHtCM3VHt3ePEg9kNru7rIr80v94+gNq7icm74ERJzeWl\nq7jp4FO8depFnF57keLQICTHwf8j+OnAo/SyO4n2/Z74T95vtQJ4bYlNj78TcebiGQAyyOCI3REA\n7B0rcK8wJsACJP3p1d0Lj6MGuuyCfovtOVQAL28XdTbXNtZ4e0WIuwkxb21JCZsKqnmq4hWePpZb\n5zFtIQvdHC6PCZuoT0nSYhdaQ33SxiaaK4ndFoxw9wJgePcRxE789MoDmrE7qq0w2mh3eB2YihAu\nH/QzAz+h6IH7YOYCcrLknKoZ9ANOB3DnT3eyOHMKVQXZFM95ETRSqp8NJ3O3ClXxH0gHhTH4vmtj\n0L8asGxNVAfj6+4r5jBHrMJB7JA7i/xuN4jtIz4UCSQIlet14vj1EeKPwOHGxq6AADH6mxeF27Ny\nscS5h9gtDxfl4y6tpW6s9v2KSrwmlOZZY116a828O5pyXblIj06vV0nVEve4oVJf4wHtLLXaCBkZ\nU8SmjwYLzYKRQiNPEBOjRgjPFxEe0xXijf5viB5+PYTzA85i2gzEiqXOYuGC8UIu1wkXlyqRFfmU\ndXTzdSBYQJ2zLal5D9cG48ePZ8uWLex0kTCyxGgvt3GwjGReICZiCYEVDsi7z+D/fvmV9/4Txd3l\nc1nwbD4/XQCV6SS1tuGNRTKusGic1LhnY35FRYPx2TppZ7G3yLWRJB5JJKggiI+1HzP6y9EdEjdv\nr5BMXffYEuEfayFTnUneDQ9R1ScZgII9Kh4vOs9Fu3QA7A32VMmrAFg6yIFhXSsB+Ouv+5g06Rt6\n97bMdVuSloR6bAO/hZg8eTLde3zB7T3AwwCSzyXcOLEavcvfx0zM9qD4rmeZ6rEYBQbOaPz5qfhR\nzvjKcXFy4qvoaJReXk0aa3dN1vJqojezg08x+ptApBjaJ+bdztUz+aX53D/9fqZ+NhVFqaLOuHl7\n0JGy1haV0LaASqs6M5PUC2lIRQGvHlqHi04PYXspOB1A9bI++B3bjqzUi99lTxA7uR97w84hyspY\n6ryWoV1SOVo5gK9ypuM46Drihg27piZKsMX4OxXZ2dn4dAOGgm40/P6CcdAfeB7cSsC+/3R+v20e\n55yMM8GZEgXFcU+R4TuapJAQfhk0CPU5o7J1U4Q1pdkGXslLo2rLBaNzV3vFvNu5ekbprGTh8YUo\nShUdqsTYkd6+TX2tdmlNsIBKq7akhN0V3fizciDv9h8DJc6I/bfy7onXuHFXDiNyixhUkMW9OZso\n9+lKtddQhG8Yr3eZhwYVzzks4fee/UksLOywPElnxzbwWwiZTEZpqfHf2uN2BP73adYsW8LsZQkM\neF+DgyECfbch7JONZn71TP67v4r4iJ9xLLUHYITL34PC5WOtOjPzCvP0xpKMbUZcHHv69uVOJyci\nJ00ym7G3JY0mctuBliQua9NYo1NLXqtdxmgLlL2aJroAMpjj/D+6HFrImEcSOXXiZfZ1PwTAWUkv\ntEynotxg/KXM01ycOp95M4vppj/KdBbjXnaGhb3r0n+0cTm2UI+FyM/P54mnHuLWh1NZ+L4f/sNe\n4LSfF06l8PybJ3j/1TJ2jR5IYFUGC+1nsKd4ALs/2IxE+xQ7PLII8fbip27dcMrOpkIqY4o8jvdX\nK1Eq6w4VVORXoFVr8Y/xb/fBUqVSkVQT7omOjib+Gm6WMtEejlhX5G3aYvNmgbLX/IoK/p2ZTnnK\nw+RXeqBwciPu3jgGTIuk0u0vViaAtng2w05dx2n5cV58Qo9h+c9gMOo9Kr2vp2L5jRgOLSc6ILJF\nZjCdGVsDVydCqVTy9VcbAThQcD2JF5w4PASmLQKFXxXvfKFncY9tLPz2HZKe6cKiJ7/FcNIbp/u2\nU6bIYUsFZKxzJ6RcjxT458hB4JwBKOsMFUiV0g5zJarLjN3SWLqRqj1MWOLi2mGMbmN7M7VajVar\nRSaTERcXV6eGjlIqZf3Q4aj2erPt5N9uXhXFCgq6gV7qwI2nvKHSFXf9MDYkani1ZD+7AKldIGEz\n3dly8N1WmcFca9hCPVZAP7dcPAKNW1r/Q+Ca2RcywpgeW8nBJyT894sbMdz6L5wfmoCdssgogj0Q\ncj2cANglhbvzcnhs3WNA68MSrSUuLo7o6Gg2b95sMbEsU7jLb+1axtx+O7vW70KfpEeXqDPmODoY\nkyNW7Nkgxq+NuqIPoSVYqDWhWWi1WpKSkkhMTETdQDwqU51JRbIxLDmi6whcAl7A95eVYPDCP78S\nj0pjiMdZkYF0/mLef8FANLBXeDBv95UaQDYaxjbwWwFVWSdROuThVlhBtX3NNwMyOKpexgr3L3Ds\ndgL6JFE6cDMu7jUD+cUQ7s/fxdd4M6EC9MfBLsG42zOpRFqqukGpVBIfH98hg75arUalUhEZGXlJ\nPsHUGHXK15fto0ZxRmdsmLOUNZ+p0enAhWySspNIPJKIOqHjLS6bk2toC5qy+8vMVLPnrv/jH6pS\nvOzH4H20Dz8kPUX2E/9BnjeMYikE8SZLZ57hyW8rmclbVKyexwqGURnyFquiV5FryGXSt5NaPZle\nK9gGfgujVqv58V0nDhV0p8BVyozeH/K76w6elc5gavpF/pe2FMd+xtxHwOkAZmhWgGN37Oyc0N/3\nFP92G4YeGD5iOLGrYlv2h92JlSvrW1Gawl3uZ8/C4sVsDNmIe5R7hyaE66ItPGpbg0n2WKdLRKtt\nfOJp7aMRFxfH7bf3ZeHCk+zf34/U1PFXPJclJVp6uqYS5pnMx64OFHpMpvL0IYolP2MYdp5JNwTz\nnWI4G3v1IM1xKLsUwbz25I183udlbnnuBN+eSbHoZNoZscX4LYxWqyXpRBEcLIXRUJ2zj9cLv4N0\n4IwDeF6kRG/P2Je9uTPlDea+7g1HuiI8doIHeLzaG+c8L7oEdQHnS/XMtdqmafdbnXltM6hvRWkS\nB5u6Vkm2y0oCvQIZEjvEsiJpajU/Zhawr9CH/onrcbdAWKK5uYbWPhpKpZL583uh1ydRVQX5+Vuu\neC5N10RGAF1mTee1UgUzXf1JUaaDNJ1/n/kN+yeWMrRnBskMIjjjLKsXf4CsTM+oxfYUVJ1k0t0w\nsL8txt9UbCt+C2MauEKWLeNuFymDaraqkm5SnOUD4cg+ivJSSP08j09ueRKDcxFSe2cApMUhnD3q\ny3n5ebZkb+Hx79QtSyJai8RmC6gvn2AKd8kPC3zP+1K4pbDdYvt1lc/WiVaLw7bthKbm4D51Rrtc\nS2OYcg3BwZubpGXTFo+GeWAHFIrhlz6XajVBMwtw+CsMZiyiqkTBsapDpEnSIKsCDlfjV1qNl98x\nXnebgSrtAj/M+IDehh14V2YwJj2dyAw9q1dMQLn+Tyi1xfg7G5aUu7AYl/uN/nbj76I7d4rBZAl3\nbhWAUHhhtJqbi3BecbPw/vQOwZvugqfGCh4ZZ9SumRImJj6gE+XlOpGeHt1ki8aai7CoNkt7khqR\nKjRoxO6w3fXq5bSWJpusW5s7fBNoi0fj4L/SxLYRX4o/xnwminPzLv1hjWZUOXKxr8cqsbLrSiFH\nLuyc7QQgJL4ScUe3u0RwX4UYORKxdKVCaJ0HCAGiGIUQIPYzXLij60iXTasCm1ZP50atht+/NJA7\n/mkMI/+kUjjikGDHqAEH2R4gcMmRMPKEitSxF9CXpBl/6eBEqHZkSHYM235VtkmFh0kHXSKRERQU\n16lVDjuif6ExsxEz1qJh3UJaWhLboDT1Zc0I+cDataE4++WRd7KIN89C9dddKDlyAQD7UUF0PyNj\n0cmeVPE441jC/7GK3+jXtv0MnQibVk8nxyxz85gK+tQEVr1VdLcfRanmXXQ/CCiFriO7kRt5jmHe\nI+j52xaklUpWr267B749mo2uZlokZtcJacxboD4a9EqoYzKs/fwptiqY+oaEvyoLcJQF8dk3eXjK\nDDiUl2Nf6ohEO4isJc/x08iH+DRWcs0N+mAb+Ds1gYFqtNoHEOJWeOgGGPgXKAJw9JvKT/tXk7xy\nLE55vkjllYzfMY5XM+bXaV5R36qsKY00Ju6914+jR08hk7nxww/78Pa+BiUPbVxBo2Y39WDade0o\nL8T+ZAVVLnZM3DACL2+XOo9f++dN+JZv43RRL7bcc5JjFYJy7DhIKktjH6RPn4xLjneR3s2o8B9a\n/f46K7aBvxOjVKrQ61OBleCsJvBeP/JufJTYWY50fXUeRavmYJ8eAoDjhCN4Lt1VZzgmRZWCfsRs\n8DuF1MOVkZMSkEqVzZJRuOmmMWzbtr1Jx1oLlpQyVieo0V7QIpPKiLs37qptImpJ2Ky22Oedp/8k\naF85AD6+7xE4oABkMtRvv422qsr82T24/y9GFbzGYqYz6LZ72VNu/J3r6Y7dDSswGJQ4ORUze/Yk\nzpzpx9atv7FmzdV5z5uCTbKhEyOVygA98CCSUjdeWtuTsLUGurGWTMeB2MuMim6SQdkMXxNF5qk1\nLJo4ieyL/sjsdhI/eAlKTwkS6RvgdwpC0qjg75LO5sgoKBRuTT7WWjA1bMHffq8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eAAAg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\n05jVuD8h0/CRwzll7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"text": "<matplotlib.figure.Figure at 0x10b1b3410>"
}
],
"language": "python",
"trusted": true,
"collapsed": false
}
],
"metadata": {}
}
],
"metadata": {
"name": "",
"signature": "sha256:2e0136817bc25ec0e071487325539818f2b91cc81d31a5aa7a9279ca486d51fd"
},
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}
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