RuntimeWarning：使用curve_fit时exp遇到溢出

问题描述

我正在尝试将曲线拟合到时间序列数据，其中X轴是经过的天数，Y是相应的值。数据集中总共有2411天，但是当我尝试对整个数据集进行曲线拟合时，会出现错误RuntimeWarning: overflow encountered in exp，RuntimeWarning: overflow encountered in square和OptimizeWarning: Covariance of the parameters could not be estimated。

在阅读了此处的一些解决方案后，我得出的结论是，从np.exp()返回的值一定太大，因此我使用了sklearn.preprocessing.MinMaxScaler()，但没有变化。

通过反复试验，我发现如果仅传递前355个值，则该单元将运行而没有错误，但是在第356个值上，错误开始，而exp错误首先显示在第711个值上。以下是包含前711个元素的相关代码：

def func0(x,a,b,c):
    return a * np.exp(b*x) + c

yData = np.array([0.00765047,0.00791042,0.00870343,0.00819011,0.00806836,0.00780183,0.00768995,0.0076044,0.00808153,0.00914107,0.00996371,0.00852246,0.00690681,0.00541291,0.00522535,0.00517599,0.00474494,0.00772615,0.00334646,0.00285288,0.00366564,0.0041329,0.00419213,0.00492262,0.00508715,0.00726877,0.00800584,0.00830528,0.0093056,0.00969059,0.00923321,0.00844019,0.00881531,0.00840071,0.00640007,0.00516941,0.0055215,0.00535368,0.00405393,0.00278707,0.00363603,0.0038894,0.00352086,0.00266861,0.00194799,0.00265874,0.0017012,0.00233627,0.00189534,0.00135241,0.00122737,0.,0.00027969,0.00116814,0.00053636,0.00143138,0.0033333,0.00329381,0.00275746,0.00449156,0.00607102,0.00630464,0.00722928,0.00800255,0.00717005,0.00787751,0.0078117,0.00759124,0.00641981,0.0070154,0.00686074,0.00626516,0.00571564,0.00587358,0.0075353,0.00819998,0.00804533,0.00701869,0.01173401,0.01122069,0.01146418,0.01323449,0.01233288,0.01283304,0.01189195,0.01205319,0.01310616,0.01413938,0.01428416,0.01484026,0.01368529,0.01037831,0.01113513,0.01188537,0.01244805,0.01239869,0.0115991,0.01062839,0.01029605,0.01119765,0.01091138,0.01175375,0.01034212,0.01075343,0.00899958,0.00813417,0.00874621,0.00891074,0.00944709,0.00841058,0.00833161,0.00953923,0.0082296,0.00746291,0.00835793,0.00880215,0.01094428,0.01008875,0.01092125,0.01039147,0.01325423,0.01361619,0.01421835,0.01432036,0.01596562,0.01718311,0.01751217,0.01835125,0.01885799,0.01697252,0.01653817,0.01728512,0.01625848,0.01707782,0.01663689,0.0187856,0.01795968,0.0171897,0.01827886,0.01728183,0.01750888,0.02025317,0.02070727,0.01985831,0.01669283,0.01612028,0.01332991,0.01373136,0.01076988,0.01451779,0.01230327,0.01359973,0.01381362,0.01207951,0.01150367,0.00709108,0.00590978,0.0054524,0.01072053,0.01077976,0.01022037,0.01260271,0.01499163,0.01643617,0.01785438,0.01696923,0.01613344,0.01816698,0.01939106,0.01852236,0.01659082,0.01829202,0.01926931,0.02026963,0.02165494,0.02577467,0.02656111,0.0237839,0.02332981,0.0204868,0.02061184,0.02266513,0.02080927,0.02261906,0.02022685,0.01818343,0.01678496,0.01695607,0.01925943,0.01992083,0.02098367,0.02314883,0.02451769,0.02495533,0.02473816,0.02821295,0.0267717,0.02728173,0.02321793,0.02390236,0.02428735,0.02521857,0.02177669,0.01231643,0.01507389,0.0185421,0.01728841,0.01682445,0.01798271,0.01886128,0.0182657,0.0184368,0.01876257,0.01653488,0.01639339,0.01856513,0.01907187,0.01870992,0.01678825,0.01433023,0.01190182,0.01032237,0.00922005,0.00705159,0.01091796,0.00902262,0.01030592,0.01189853,0.01153658,0.01160568,0.0102072,0.01130295,0.00971034,0.01054942,0.00939444,0.00642968,0.00633097,0.00667647,0.0060414,0.00440272,0.00594269,0.00536684,0.0050345,0.00425136,0.00424148,0.00399141,0.00544253,0.00547543,0.00712069,0.00578803,0.00604469,0.00589991,0.00574196,0.00680809,0.00936812,0.01101667,0.00985841,0.0082658,0.00856523,0.00882847,0.01064484,0.0113194,0.01025985,0.01101338,0.00608418,0.00682784,0.00878899,0.00729509,0.0076406,0.00806507,0.00790055,0.00808482,0.01007558,0.00998016,0.00773273,0.00623883,0.0070845,0.00700552,0.00645272,0.00589662,0.00597559,0.00577816,0.00751227,0.00615986,0.00627503,0.00603153,0.00634742,0.00662053,0.00750239,0.00877583,0.00768337,0.00737735,0.00777222,0.00771957,0.00792358,0.00807824,0.01031908,0.01012165,0.01121081,0.01378729,0.01463296,0.01322461,0.01435985,0.01366884,0.01220126,0.01273104,0.01086531,0.01099693,0.01016772,0.00855865,0.00888441,0.00977944,0.00904565,0.00807165,0.00990448,0.00991435,0.00954581,0.00897326,0.00966098,0.0110068,0.01152341,0.02167797,0.02333968,0.02272765,0.02279675,0.02253351,0.02073688,0.02112187,0.02040454,0.02162532,0.02195108,0.02038808,0.0208685,0.02075991,0.01888432,0.01740029,0.01880205,0.01788729,0.01852894,0.01785767,0.0170844,0.01769644,0.01588007,0.01709098,0.01554772,0.01763721,0.0186474,0.0190291,0.0189238,0.01827228,0.01824595,0.01768985,0.01759772,0.01888102,0.02029924,0.02075004,0.0204177,0.01961152,0.02013471,0.01944699,0.02126994,0.02127324,0.01985502,0.02217155,0.02249073,0.02255983,0.02174707,0.02108568,0.01888761,0.01789716,0.01889419,0.01811104,0.01841377,0.01859146,0.02145421,0.02215181,0.02140157,0.02042428,0.01845326,0.01942725,0.02512315,0.02471841,0.02380036,0.0234022,0.02298102,0.02434987,0.0240274,0.02487307,0.02415573,0.02405044,0.02361938,0.02351737,0.02376416,0.02515605,0.02651504,0.02639,0.02612018,0.02582403,0.02702507,0.02639987,0.02789377,0.02729489,0.02801552,0.02834786,0.02805171,0.02872627,0.02859794,0.02974962,0.03230307,0.03162851,0.03116126,0.0311481,0.03266503,0.03300395,0.03192795,0.03217474,0.03313886,0.03285259,0.03175355,0.03087498,0.030105,0.02918694,0.03146399,0.03071704,0.02995693,0.02949296,0.03124352,0.03274071,0.03209577,0.03227675,0.02961142,0.02764698,0.02739361,0.02678157,0.02738045,0.02730147,0.02846961,0.02760091,0.02600501,0.0239583,0.0241327,0.02221762,0.02038479,0.02542588,0.02366545,0.02341866,0.02351079,0.02413928,0.02520212,0.02339233,0.0218425,0.02150028,0.02155293,0.02159571,0.02039467,0.01962139,0.0211449,0.02535678,0.02596552,0.02719618,0.02712379,0.02834457,0.02971343,0.02997009,0.02940412,0.03011487,0.03059858,0.03040444,0.03037153,0.02856175,0.02952258,0.02987466,0.02970685,0.029029,0.03056567,0.03271768,0.03192466,0.03307963,0.03157257,0.03213196,0.02884473,0.02873943,0.0277095,0.02958181,0.0317009,0.0320859,0.03230636,0.03536984,0.03468541,0.03467554,0.0343432,0.03519873,0.03677489,0.03650178,0.03552449,0.03603452,0.03657417,0.0359391,0.03525467,0.0370151,0.04048002,0.03786406,0.03270122,0.03678476,0.03439584,0.03423132,0.03257947,0.03485323,0.03331655,0.03266174,0.03322771,0.031668,0.03215829,0.03570218,0.0356265,0.03426093,0.03579432,0.03469528,0.03454063,0.03436952,0.03254328,0.03237546,0.03365548,0.03399111,0.03447482,0.03689993,0.03771598,0.03712369,0.0371533,0.03725531,0.0362846,0.03723557,0.03755475,0.03318493,0.03189175,0.03140476,0.03169103,0.03041102,0.03184569,0.03127643,0.03268806,0.03433003,0.03472161,0.03311583,0.03367851,0.03226687,0.03228333,0.03109874,0.03224055,0.03296118,0.03415564,0.03582722,0.03682096,0.03512634,0.03664656,0.03502104,0.03239521,0.03269135,0.03375419,0.03551462,0.03547514,0.03742313,0.03087827,0.02920998,0.03054922,0.02871311,0.03013462,0.0319444,0.03117771,0.03183911,0.03215171,0.0326387,0.03378052,0.03407008,0.03532706,0.03474464,0.03394175,0.03584367,0.03509672,0.03550146,0.03356005,0.03317835,0.03315861,0.03498485,0.03440571,0.03483348,0.03561334,0.03484994,0.03446165,0.03494536,0.03516254,0.03813717,0.03951919,0.03744945,0.0364261,0.03778179,0.0371895,0.03852874,0.03974623,0.03856165,0.03700852,0.03698219,0.0360773,0.0365643,0.03836751,0.03836092,0.03840699,0.03985811,0.04039447,0.04049318,0.04110193,0.04265177,0.04296108,0.04322432,0.04563627,0.0482325,0.04791002,0.04800874,0.04860761,0.04710056,0.04746909,0.04689325,0.04609695,0.04539935,0.04686693,0.04970007,0.04775537,0.04654117,0.04614959,0.04758097,0.04713346,0.04607391,0.04599494,0.04473138,0.04434639,0.04484655,0.04465899,0.04376396,0.04289856,0.04129607,0.04075314,0.04099992,0.04150008,0.04067087,0.04236878,0.04246092,0.04121052,0.03947312,0.03968701,0.04047673,0.03948957,0.04206276,0.04365538,0.04380674,0.04438587,0.04565272,0.04586661,0.04562969,0.04537303,0.04506372,0.04445168,0.0471203,0.04970665,0.04971652,0.05112487,0.04952896,0.05039766,0.04991066,0.05171058,0.05101628,0.04990737,0.0526418,0.05249701,0.05060496,0.05201331,0.04904855,0.04681099,0.04516573,0.04744935,0.04933153,0.04926901,0.04785409,0.04919991,0.04929204,0.05526763,0.05444829,0.05645551,0.05455359,0.05634693,0.06660678,0.06488584,0.06637973])
xData = np.array([*range(yData.shape[0])])

popt,pcov = curve_fit(func0,xData,yData)

这里的最后一个值既不是列表中的最高值也不是最低的，为什么在这里抛出错误？

解决方法

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