aweinstein · October 19, 2011 15:45
diff --git a/omp_issue.py b/omp_issue.py
 import numpy as np
 from numpy.linalg import norm, pinv
 from sklearn.linear_model import orthogonal_mp

 def omp_naive(D, y):
    """ Recover x using naive implementation of OMP.

    Parameter
    ---------
    D: Dictionary
    y: Measurement

    Return
    ------
    x_hat : Estimate of x
    """
    n = D.shape[1]
    r = y.copy()
    k = 1
    Delta = []
    while norm(r) > 1e-3:
        h = np.abs(np.dot(D.T, r))
        Delta.append(np.argmax(h))
        alpha = np.dot(pinv(D[:,Delta]), y)
        r = y - np.dot(D[:, Delta], alpha)
        k += 1

    x_hat = np.zeros(n)
    x_hat[Delta] = alpha

    return x_hat

 x = np.array([[0.0], [0.0], [0.0], [0.0], [0.0], [0.0], [0.0], [0.0], [0.0],
 [0.0], [0.82862194733849126], [0.0], [0.0], [0.0], [0.0], [0.0],
 [0.84873504784773945], [0.0], [0.0], [0.0], [1.3867504005079114], [0.0], [0.0],
 [0.0], [0.0], [0.0], [0.0], [0.0], [0.0], [0.0], [0.0], [0.0], [0.0], [0.0],
 [0.0], [-0.76469804474153291], [1.3557898017681884], [0.0], [0.0], [0.0],
 [0.0], [0.0], [0.0], [0.0], [1.0094776166954285], [0.0], [0.0], [0.0], [0.0],
 [0.0], [0.0], [0.0], [0.0], [0.0], [0.0], [0.0], [0.0], [0.0], [0.0], [0.0],
 [0.0], [0.0], [0.0], [0.0], [0.0], [0.0], [0.0], [0.0], [0.0],
 [-1.3914979417090434], [0.0], [0.0], [0.0], [0.0], [0.0], [0.0], [0.0], [0.0],
 [0.0], [0.0], [0.0], [0.0], [0.0], [0.0], [0.0], [1.1623559668118031], [0.0],
 [0.0], [0.0], [0.0], [0.0], [0.0], [0.0], [0.0], [-0.83617219110995966], [0.0],
 [0.0], [0.0], [0.90958791906740355], [0.0], [0.0], [0.0], [0.0], [0.0], [0.0],
 [0.0], [0.0], [0.0], [0.0], [0.0], [0.0], [0.0], [0.0], [0.0], [0.0], [0.0],
 [0.0], [0.0], [0.0], [0.0], [0.0], [0.0], [0.0], [0.0], [0.0], [0.0], [0.0],
 [0.0]])

 D = np.array([[0.047305713451924046, 0.35525537734054241,
 -0.053404481909537602, 0.04619995872469148, 0.069377391616028655,
 0.301125405399569, -0.071035430563171673, -0.23045982283110839,
 -0.16016796588543464, -0.046935529182257157, 0.019626876088473258,
 -0.052614003954835786, 0.11969153927171056, 0.049654092824237078,
 0.27973740915840434, 0.14935211168233425, -0.13598320205179953,
 0.14679319497073473, -0.040780050705206329, 0.14961481671961063,
 -0.088308983814051126, 0.29764358262968055, 0.19430003005640376,
 -0.18015626040086585, -0.062697065739570998, -0.10736094204962042,
 -0.28162342654073252, 0.065039574364592456, -0.035419031370895623,
 -0.062080523663098804, 0.17672838321687837, 0.15452162235852493,
 -0.32378728909328458, 0.12079571907791904, -0.031616783569321932,
 0.35731825079836022, -0.13097413180859982, -0.22251878964267166,
 0.14333399189487686, -0.27563807776493315, -0.27217367445139978,
 -0.090390973406598935, 0.0057285914433963438, 0.00010569894879300234,
 0.13996741676480171, 0.011929089330515331, 0.14396033795362079,
 0.21405049652938313, -0.27366818583595137, 0.16880274723426858,
 0.071327175935359796, 0.046416486348499937, 0.21870684787716699,
 -0.23675393685954968, 0.050120154191754085, 0.075450093441999252,
 0.11150699240720703, 0.055183557498846597, 0.13869280902178005,
 -0.089822414750906077, -0.16646069122841259, 0.086747164118399375,
 -0.016470351982383832, -0.19048138615730609, -0.20967072518369681,
 0.41030382049820818, 0.19469511293857544, -0.1536400652371098,
 -0.011324407658380354, -0.044113386935967162, 0.0033005453431591957,
 0.15250801062719721, -0.034431229122038151, -0.44942056188115959,
 0.014039256254384966, 0.090000773287112132, -0.17473991170956263,
 0.17541247915479713, 0.11125076433093631, -0.18224378203176661,
 -0.19201457858404777, 0.075769262782195812, 0.098073839092457649,
 0.05000835128683731, 0.17966332587411227, 0.12361859104923074,
 0.04601393652084998, 0.070228526190098242, -0.036286050408396803,
 -0.22741247539055348, -0.084227338696704485, -0.044984347586921186,
 -0.080178458583157752, 0.10401681952605819, 0.17373201775238201,
 0.18300911002836151, -0.15775628464943262, -0.19155517897862179,
 -0.14008448446740154, -0.069693335034489962, -0.021931176030778366,
 -0.13854517797624319, -0.12774752703055992, -0.12022786457829647,
 0.047025491921383722, 0.055305728485692748, 0.037091824881198381,
 -0.12670809595036547, 0.297791681137481, 0.014757300035318572,
 0.19035505088230467, 0.041795731207629888, -0.16540438825245923,
 -0.12748370139524876, 0.28108632658684995, -0.43083827847907563,
 0.2256868190260167, 0.11248988714569987, 0.078524743054897192,
 -0.13797473146198955, -0.016277285617781252, -0.040266449323811022,
 0.047086912900840473, 0.26793627732734832, -0.11074445800922336,
 0.10985670988618915, -0.12949971098157112, 0.061301655373261515],
 [0.14319565590359393, 0.17549261782537171, -0.034619107918981942,
 -0.096750497551366832, 0.15773372732606522, -0.22408529875631464,
 -0.33776215972622187, -0.2087294538552078, -0.094287982477693599,
 0.13501501951463429, -0.20033381565053504, 0.094828774484193218,
 0.069892731365222505, -0.069726095789911152, -0.10826411387652021,
 0.16600043296832273, -0.066595208283887403, 0.12223905421694466,
 0.1272681750581858, 0.14973871336106709, -0.14501510815824833,
 -0.072738246801835729, 0.056362086744082572, 0.21104310696057371,
 -0.0043022767662363928, -0.20811893881290094, 0.080051213392470108,
 0.026902001194540049, 0.30231926407300946, -0.10172953885243749,
 -0.061490544608632007, -0.23523509111593824, -0.021966027613207477,
 -0.277682992806769, 0.056841073643918653, -0.037710527707095404,
 0.1031189538588422, -0.12087555378019832, -0.19768622897238819,
 -0.2087467845212351, 0.1397513639260943, 0.09964200921616212,
 -0.030909766921690295, 0.082213251563523312, -0.245785638571413,
 0.21696803340729759, 0.062456513868023499, -0.00051804174033070842,
 -0.027021258001657417, 0.11987053369065599, -0.17806692105558436,
 -0.078654379617943485, 0.19306388109009326, -0.15787941033117342,
 -0.17412388825150044, 0.037887773003819798, 0.056879836438563605,
 -0.011870731430723291, 0.15214802481733436, -0.094786100442477442,
 -0.039163401965433234, -0.13611036716040709, 0.1870828495627074,
 0.27082079245807522, 0.084301130198070284, 0.13286978291690862,
 0.055807496648559662, -0.34406994772926108, -0.12410836060532743,
 -0.0030241906969496637, 0.30457978686199921, 0.083084737612517334,
 0.022003897883199158, 0.1736208495278187, 0.19044947781010751,
 0.061308066269496239, -0.13154682888976552, -0.25451478990796611,
 0.047119613565951991, 0.37224833708850635, -0.12120018908333083,
 0.035041121786465491, 0.060897777413640677, 0.25973387248493091,
 0.095625048107352853, -0.24499812591269771, 0.019535992339849161,
 0.008366664323738655, -0.017531458614322131, 0.2545463640544196,
 -0.099210002442502124, 0.071717000954938812, 0.025378175231836331,
 -0.12763685914099471, 0.035149266838971016, -0.18924728789234563,
 0.14846816856143927, 0.020632633774341318, 0.12094708701617263,
 -0.021011317947504778, 0.15774050893448976, 0.1131440909859365,
 0.079458241296153226, -0.17150331596017213, -0.15772153050770163,
 -0.084047540518156202, 0.40161606610674122, 0.22341428894670409,
 -0.17605704799472169, -0.046396882417322628, -0.071123032681806447,
 0.10080068581919795, 0.15360606730593868, 0.026694532035598854,
 0.12377040365606549, -0.051020250103519182, -0.025254233119595574,
 -0.14812619562167215, -0.012063622203025369, -0.19715037320370474,
 -0.19608556733116322, -0.10335378213840651, 0.40598611260953227,
 -0.12525670998819921, -0.068748947213872758, 0.35381621879068365,
 -0.10453119357644279, -0.12788263905491193], [0.067240651466125539,
 0.067179338441805986, -0.15645065261036431, -0.10291755408480383,
 -0.1724667930560681, -0.077363907808042365, -0.047665683132142395,
 -0.1046900425512208, -0.11029018881030858, 0.1053171777004103,
 0.11079416107905, -0.071212184632051936, 0.041525616041600377,
 0.10190562180049821, -0.21756550302840527, -0.1875932072210437,
 -0.35946912996984748, 0.054566025308077665, 0.070890170807467373,
 -0.026968403008488229, 0.15116985076927403, 0.03553626268308837,
 0.239095922545879, 0.049335698918339874, 0.016819387017330482,
 0.069036883542705874, 0.012971104218349462, 0.28897808496501604,
 0.012559874423094725, 0.00094146996947572573, 0.13774394933142275,
 -0.063102991900076316, 0.071480165414608818, 0.31598173380719896,
 -0.094251656483405166, -0.053681240110644492, 0.11012081263378989,
 -0.17392974348901263, -0.0081717706811090928, -0.057063776883348447,
 -0.4705973389022326, 0.033847271308543599, -0.016256622022993304,
 0.046619096184995816, -0.26790071923523912, 0.066058820643886282,
 0.1449035409875393, -0.011304712903376752, 0.28760040818646182,
 0.21121256411605493, 0.22789507186125774, -0.20395199462767091,
 -0.092997040483791399, 0.042992604442308097, -0.27304761856624893,
 0.12025763248261898, 0.018118191885281264, 0.13214563540412955,
 -0.26008050466689164, 0.12777115956481461, -0.10828063820422376,
 0.033522662497260158, 0.010183210021169401, 0.093132139690888488,
 0.019887597267594065, 0.043021521449315661, -0.20190280670375726,
 -0.055542560667936752, -0.018863191121497043, 0.21540830944741388,
 -0.029256635380337494, -0.025411639252543618, 0.21387621351788849,
 -0.049009590219683097, -0.055403181965423688, 0.27164792143565475,
 0.17993404009537492, -0.16275049011111101, 0.23760083833230103,
 -0.15540946164456682, -0.0088355708455733432, -0.022170011661791261,
 0.094221454842782437, -0.40096969735221155, 0.055858616233549006,
 -0.062260966157045503, -0.010164316885041963, -0.085597343342695212,
 0.00032206918276847095, -0.061300153715078291, 0.048723556773848091,
 0.15544851669571647, 0.057359244108993714, -0.10554925458626079,
 0.019882993226680735, 0.20800402527231754, 0.049942724370882617,
 0.045413072203104241, 0.17270856252627001, 0.17555596285446728,
 0.0098657860751482935, -0.04823083294099164, 0.20445303555830807,
 0.018491711494510732, 0.0070144202878065923, 0.04946776258332055,
 -0.28432272406420628, -0.21937982750534643, -0.032148604182989565,
 0.29535333464752744, -0.16245556388231039, 0.012023385888675566,
 0.073603924230678658, -0.050598167545813241, -0.15859098496597293,
 0.072316080203482028, -0.29527882037830083, 0.21564437268454889,
 -0.1347789855303603, 0.057157481141203205, -0.074216192636747627,
 0.10462504050830715, 0.11683344166135093, 0.08230865197998688,
 0.17017248046479638, 0.10323106316150943, -0.1149138422772287,
 0.19690386257333006], [0.00091005742899666288, 0.23920485100167765,
 -0.22092767528559756, 0.048507330640309258, -0.065668208157555114,
 -0.14213044274386905, -0.20670088669893533, 0.18963706584315929,
 0.28662570911608576, -0.096503336138106896, -0.12177020246537917,
 -0.1839689601060662, 0.12717859889003524, -0.22347435577622762,
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 0.10790805270730651, -0.1156405701331629, -0.033958334700897763,
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 0.091722918225484604, 0.07353241612137984, -0.1906567102049288,
 0.18989030899900849, -0.27603088197580239, -0.17934204954782265,
 0.18563788634547118, 0.034655607232616646, 0.069360003467074938,
 0.24899843453028697, -0.027245852169353827, -0.084438521489899873,
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 0.46254080363349953, -0.062560335094027184, -0.043600252451960322,
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 0.15282854006669594, 0.093321945270534945, 0.15785118204870369,
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 0.23864586192110818, 0.097386021851801896, 0.18959394967449761,
 0.062867469839291576, -0.015314339880016885, -0.32080807130125583,
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 0.06901892912993296, 0.11702954320119739, 0.10527802568292971,
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 s = (np.abs(x)>0).sum()
 n = x.size
 y = np.dot(D, x)
 x_naive = omp_naive(D, y)
 x_scikit = orthogonal_mp(D, y, s)
 error_naive = norm(x - x_naive.reshape(n,1))
 error_scikit = norm(x - x_scikit.reshape(n,1))

 print 'error naive: %d, error scikit: %s' % (error_naive, error_scikit)