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Created December 5, 2013 15:01
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{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
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"input": [
"try:\n",
" from scipy.stats import multivariate_normal\n",
"except ImportError: # scipy 0.13\n",
" import sys\n",
" sys.path.insert(0, '/home/phil/Dropbox/Masterarbeit/code/razorweb/Razorweb/razorweb')\n",
" from _multivariate import multivariate_normal\n",
"\n",
"import numpy as np\n",
"from scipy import optimize, linalg"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "code",
"collapsed": false,
"input": [
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10.135644894107475], [143.94655988896662, 13.67813823553103], [164.64205783566797, 12.423501615535264], [140.57812320144848, 14.623228555232279], [167.75766171103379, 10.470431274359195], [172.46814429394337, 11.042058815039681], [143.97153011172082, 14.604785130395058], [174.65347588696818, 11.275244951148988], [165.37264027910931, 11.480187471396128], [175.18278663596683, 9.1220298491442353], [140.46311136574178, 18.09812611114382], [157.60672445069213, 15.28320822034301], [173.92581608184105, 9.9392582551368296], [155.19062811586042, 13.848806037853963], [148.47250459542477, 12.823895775000443], [157.75078829492566, 12.765118395904958], [163.96161868733893, 11.942479469344867], [160.93134775845016, 11.528166849469176], [177.71027105070988, 10.602598160516973], [174.02656204337802, 8.5001626209535477], [167.27184776217231, 12.131089325853914], [157.6316612879684, 15.30397407452684], [161.87804148862085, 11.510174579899287], [145.85486201784113, 12.870772150482622], [151.29253881863968, 13.684441792326899], [164.6900147548466, 12.535632388717094], [161.18858397835101, 10.277738094841148], [151.34275375202557, 13.633468433755013], [160.59927833939918, 9.9786857085706799], [165.25466283204196, 12.520819049158309], [167.75753439972596, 10.230941012482338], [155.49988144697468, 13.689703272688611], [161.87688944299475, 9.3458802269273988], [177.841242458316, 8.8122778580872456], [138.70293446219722, 14.321461538162211], [158.94881422555341, 13.88315323317644], [149.27757238837691, 11.703639630899268], [158.64896086874427, 10.955945780434286], [171.64593736238561, 11.133313217849013], [161.16645583891204, 9.8327306691194636], [153.87109787130944, 13.66142297807419], [163.09531676652094, 10.054227725483912], [173.20991240654567, 8.567923207335653], [172.02711383370135, 9.4544059007406283], [148.50007616185405, 13.032038428914653], [152.07605807320311, 13.799821380366572], [164.46634116839047, 11.719975590897429], [156.47331735232171, 12.318313680863088], [154.86987021683404, 11.708878979618019], [160.2786990854319, 13.918431583617332], [150.40510196655822, 13.975923712182617], [171.83572590075985, 8.3996924383858751], [163.12196231396919, 11.443870038021885], [174.16514787425857, 8.5149089199291623], [165.81140340405449, 11.694683081610329], [158.5769242246775, 12.22751274738874], [149.80196908471356, 15.695242295898085], [170.67803140958037, 8.6357476771300021], [166.45518511745979, 8.4697669346674562], [152.70853155270873, 15.610843640628696], [160.86184976476005, 8.5542980073548094], [160.59516719708677, 9.6558124723271881], [153.32338216696192, 14.105816322399395], [164.141405519388, 12.774413139350242], [164.25607907450967, 13.169715085683482], [167.06056964713889, 13.791682111643073], [162.79180452056107, 10.038306504842801], [164.59793470635276, 9.4816820109544295], [171.86352599404708, 9.6134616083057356], [168.1467569950284, 10.242089128862602], [155.73143220607503, 13.90026689314719], [172.61637112130521, 9.6424749210675333], [167.29881609306312, 8.8062021832587618], [158.54923722835338, 12.512650768103093], [177.06723073864023, 10.347637528349226], [162.87954534255502, 13.088396595680358], [163.93226536361416, 8.7775183238233012], [155.63071341053583, 18.175690983144268], [158.98092765576939, 10.89041727193357], [163.63546559964661, 9.7421858361473923], [172.16047055396953, 8.246806657340608], [171.15697649211265, 10.526251588218402], [165.50208220543553, 9.792395499463538], [160.36737535445732, 13.171118943387883], [157.24684669818512, 14.633775565874602], [172.72338647850921, 10.33202578215205], [177.05530152617442, 9.9291250546657555], [156.79948622939665, 12.334847164024], [160.74754219712557, 15.358515026626083], [160.71136444039283, 12.040023532391677], [164.06108609120702, 8.9763554293169605], [163.55851309068146, 13.571676507194001], [154.81597012664943, 10.306810899567617], [170.79294842757051, 9.2405355568032199], [164.91466639707718, 12.838328609855559], [163.86482739630392, 10.779001347211009], [153.34281514118405, 16.076512817974908], [158.22750396579207, 12.801225838060992], [162.13321488796291, 10.657175016901789], [169.49896785498655, 10.365140906552062], [170.24301168930558, 8.3010123567420138], [159.84189680926195, 10.918867817803854], [164.51376872179654, 12.479548208530447], [158.76534738561278, 11.022225067392879], [174.7624514981045, 10.465655683120202], [164.79761453542949, 15.778324906267969], [152.48906109854266, 11.749004371971701], [158.40239050839401, 11.318913979128279], [145.16091168050275, 15.087859428403686], [169.13458767651866, 9.9446385086831892], [166.42557961058029, 10.605443117009063], [166.09425918945223, 10.14201130429721], [178.0974807096799, 10.232578027751938], [164.85480311787916, 11.805760268212977], [158.32338405837245, 10.572372709134163], [170.33221834872302, 7.7406468804993711], [179.80096081886396, 9.2078274094472938], [152.72877842179906, 15.610556587480763], [152.51817365013443, 11.979703211270818], [149.48752283709666, 15.951717091588284], [155.21250856070645, 14.336633736372203], [159.49704270111303, 10.93664656446569], [161.98568281811174, 10.466438606179338], [165.30828424503321, 11.827314452804861], [159.57986692832668, 14.223638013159494], [170.90784746278683, 7.9489019649545511], [160.56295626304464, 14.689573559294129], [163.55834475285056, 14.131485917425062], [160.80658443216967, 13.954661319536783], [156.6409078930393, 13.34831336622263], [149.49171888818518, 13.826341855879512], [150.27589076934342, 13.632269903812325], [171.76527100940925, 9.5927639590160432], [156.18671114758274, 14.154539317601081], [153.34005126275591, 12.969195485130355], [174.48790180955962, 8.8233742044863313], [165.80630252918698, 10.014464359950686], [131.50284028023771, 18.909125383117821], [159.09064689004919, 12.82408865202191], [161.02236006453998, 12.984190920597811], [156.91789991337359, 13.837641100747391], [161.51866206240794, 11.585539883190433], [170.44530826775767, 6.7662014358471252], [159.68655383089913, 12.194117079553497], [160.31060765636369, 10.819446864834749], [136.04408414508174, 15.978959856131862], [159.67939541396851, 13.75652136497011], [144.13745837004251, 14.705099760385526], [169.01804100125361, 8.8944342910156475]])"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def pcor2cov(lambda_, pcor):\n",
"\tscaled = np.dot(np.dot(lambda_, pcor), lambda_)\n",
"\tif np.linalg.det(scaled) != 0:\n",
"\t\treturn -np.linalg.inv(scaled)\n",
"\telse: # singular matrix, not inversible\n",
"\t\treturn np.zeros_like(pcor) + np.inf\n",
"\n",
"def pcor_from_angle(angle):\n",
"\tQ = np.array([[1, np.cos(angle)],\n",
"\t [0, np.sin(angle)]])\n",
"\t\n",
"\treturn -np.dot(Q.T, Q)\n",
"\n",
"def mix_from_params(params):\n",
"\tpcor = pcor_from_angle(params[0])\n",
"\t\n",
"\tcov1 = pcor2cov(np.diag(params[1:3]), pcor)\n",
"\tcov2 = pcor2cov(np.diag(params[3:5]), pcor)\n",
"\t\n",
"\treturn pcor, cov1, cov2\n",
"\n",
"def neg_loglik_from_params(params, data1, data2):\n",
"\tpcor, cov1, cov2 = mix_from_params(params)\n",
"\tif np.isinf(cov1).any() or np.isinf(cov2).any() or positive_semidefinite(cov1) or positive_semidefinite(cov2):\n",
"\t\treturn np.inf\n",
"\tloglik = multivariate_normal.logpdf(data1, np.mean(data1, 0), cov1).sum()\n",
"\tloglik += multivariate_normal.logpdf(data2, np.mean(data2, 0), cov2).sum()\n",
"\treturn -loglik\n",
"\n",
"def positive_semidefinite(cov):\n",
" return (linalg.eig(cov)[0] < 0).any()"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 9
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"matlab_params = np.array([0.6319, 0.1655, 0.6201, 0.3598, 0.4714])\n",
"matlab_mix = mix_from_params(matlab_params)\n",
"matlab_loglik = neg_loglik_from_params(matlab_params, data1, data2)\n",
"\n",
"matlab_loglik, matlab_mix, matlab_params"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 10,
"text": [
"(14947.158200058166,\n",
" (array([[-1. , -0.80690668],\n",
" [-0.80690668, -1. ]]),\n",
" array([[ 104.64079281, -22.53515744],\n",
" [ -22.53515744, 7.45372825]]),\n",
" array([[ 22.1398513 , -13.63545357],\n",
" [-13.63545357, 12.89786602]])),\n",
" array([ 0.6319, 0.1655, 0.6201, 0.3598, 0.4714]))"
]
}
],
"prompt_number": 10
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"lb = np.array([0, 1e-6, 1e-6, 1e-6, 1e-6])\n",
"ub = np.array([2*np.pi, 1e10, 1e10, 1e10, 1e10])\n",
"\n",
"x0 = np.random.rand(5) * (ub-lb) + lb\n",
"\n",
"bounds = list(zip(lb, ub))\n",
"params, loglik, info = optimize.fmin_l_bfgs_b(neg_loglik_from_params, x0, approx_grad=True, args=(data1, data2), bounds=bounds, pgtol=1e-50, factr=10, disp=3)\n",
"\n",
"#constraints = [\n",
"# lambda x: np.all(x > lb),\n",
"# lambda x: np.all(ub < x),\n",
"# lambda x: all(positive_semidefinite(cov) for cov in mix_from_params(x)[1:]),\n",
"# lambda x: not any(np.isinf(cov).any() for cov in mix_from_params(x)[1:]),\n",
"#]\n",
"#params = optimize.fmin_cobyla(neg_loglik_from_params, x0, constraints, (data1, data2), (), 1e10, 1e-10)\n",
"#loglik = neg_loglik_from_params(params, data1, data2)\n",
"#info = {}\n",
"\n",
"mix = mix_from_params(params)\n",
"\n",
"loglik, mix, params, info"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 104,
"text": [
"(2.8996691578994872e+23,\n",
" (array([[-1. , -0.29751162],\n",
" [-0.29751162, -1. ]]),\n",
" array([[ 9.76765875e-20, -2.66908618e-20],\n",
" [ -2.66908618e-20, 8.23999333e-20]]),\n",
" array([[ 1.02589429e-18, -5.77579360e-20],\n",
" [ -5.77579360e-20, 3.67377760e-20]])),\n",
" array([ 5.01447417e+00, 3.35142542e+09, 3.64889502e+09,\n",
" 1.03412608e+09, 5.46472570e+09]),\n",
" {'funcalls': 3,\n",
" 'grad': array([ -2.80810649e+23, 0.00000000e+00, 0.00000000e+00,\n",
" 0.00000000e+00, 0.00000000e+00]),\n",
" 'nit': 1,\n",
" 'task': b'CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH',\n",
" 'warnflag': 0})"
]
}
],
"prompt_number": 104
}
],
"metadata": {}
}
]
}
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