问题描述
我正在尝试使用非线性最小二乘法对函数进行优化，但是我似乎得到了一些非常大的值，从实际的角度来看这没有多大意义。
def Model(vCoef):
vK = np.arange(1,360+1)
vTerm1 = np.ones(len(vK))
vTerm2 = (1 - np.exp(-vCoef[3]*vK)) / (vCoef[3]*vK)
vTerm3 = vTerm2 - np.exp(-vCoef[3]*vK)
NS = vCoef[0]*vTerm1 + vCoef[1]*vTerm2 + vCoef[2]*vTerm3
return NS
def SSR(vCoef,y):
return (y - Model(vCoef))
y值的示例是
array([5.27529034,5.29560185,5.3268597,5.36827412,5.41710411,5.46992323,5.52362229,5.57591598,5.62538192,5.67124282,5.71312767,5.75090079,5.78453287,5.81401957,5.83939688,5.86084395,5.87877961,5.89383876,5.9066982,5.91785479,5.92750835,5.93561891,5.94208467,5.94692732,5.95039893,5.95298145,5.95528889,5.95791827,5.96132878,5.96580722,5.97149682,5.97841632,5.98643873,5.99527459,6.00451769,6.01375548,6.02268915,6.03119963,6.03933192,6.04722161,6.05501159,6.06278,6.0704587,6.07772661,6.08394116,6.08826676,6.09012987,6.08988299,6.08921934,6.09077189,6.09684071,6.10810782,6.12338393,6.14045757,6.15718216,6.17204988,6.18421973,6.19335232,6.19947848,6.20290471,6.2041021,6.20360154,6.20195385,6.1997257,6.19741254,6.19526544,6.19324036,6.19116462,6.18893652,6.18660888,6.18437798,6.18253541,6.18140214,6.1812485,6.18221833,6.18428917,6.18728914,6.19095869,6.1950229,6.19924476,6.20344945,6.20752586,6.21141626,6.21510252,6.2185933,6.22191361,6.22509669,6.22817763,6.23118837,6.23415395,6.23708996,6.24000154,6.24288371,6.24572295,6.24849965,6.25119113,6.25377519,6.25623398,6.25855818,6.26075141,6.26283408,6.26484611,6.26684722,6.26891392,6.27113289,6.27359143,6.27636684,6.27951726,6.28307594,6.2870501,6.29142384,6.29616387,6.30122616,6.30656214,6.31212361,6.31786599,6.3237502,6.32974325,6.33581823,6.34195367,6.34813286,6.35434299,6.36057437,6.36681978,6.37307386,6.37933268,6.38559335,6.39185374,6.39811227,6.40436774,6.41061925,6.41686608,6.42310764,6.42934347,6.43557315,6.44179632,6.44801264,6.45422183,6.4604236,6.46661768,6.47280379,6.47898165,6.48515096,6.49131138,6.49746252,6.50360389,6.50973491,6.51585483,6.52196268,6.52805724,6.5341369,6.54019962,6.54624277,6.55226298,6.55825601,6.5642165,6.57013779,6.57601164,6.581828,6.58757472,6.59323728,6.59879858,6.60423877,6.60953514,6.61466221,6.619592,6.62429448,6.62873833,6.63289204,6.63672524,6.64021034,6.64332435,6.64605072,6.64838107,6.65031662,6.6518691,6.65306094,6.65392478,6.65450217,6.65484164,6.65499631,6.65502124,6.65497089,6.65489674,6.6548454,6.6548572,6.65496539,6.65519572,6.65556655,6.65608925,6.65676877,6.65760439,6.65859043,6.65971699,6.6609706,6.6623348,6.66379061,6.66531693,6.66689092,6.66848826,6.67008353,6.67165053,6.6731627,6.67459357,6.67591737,6.67710968,6.67814807,6.67901283,6.67968759,6.68015979,6.68042103,6.68046709,6.68029772,6.6799162,6.67932867,6.67854335,6.6775697,6.67641769,6.67509714,6.6736173,6.67198661,6.67021269,6.66830256,6.66626288,6.66410041,6.66182238,6.6594368,6.65695262,6.6543797,6.6517285,6.64900961,6.64623312,6.6434079,6.64054098,6.63763709,6.63469842,6.63172467,6.62871328,6.62565997,6.62255928,6.61940526,6.61619206,6.61291448,6.6095684,6.60615105,6.60266114,6.59909882,6.59546548,6.59176352,6.58799587,6.58416564,6.58027564,6.57632791,6.57232346,6.56826191,6.56414137,6.55995843,6.55570832,6.55138514,6.54698237,6.54249341,6.5379123,6.53323444,6.52845743,6.52358175,6.51861147,6.5135547,6.50842389,6.50323585,6.49801146,6.49277503,6.48755347,6.48237508,6.47726827,6.47226021,6.46737548,6.46263498,6.45805515,6.45364743,6.44941821,6.44536905,6.44149714,6.43779603,6.4342564,6.43086686,6.42761475,6.42448684,6.42146993,6.41855134,6.4157193,6.41296324,6.41027401,6.40764395,6.40506698,6.40253859,6.40005574,6.39761676,6.39522117,6.39286935,6.3905623,6.38830118,6.38608695,6.38391993,6.3817994,6.37972337,6.37768836,6.37568941,6.37372018,6.37177319,6.36984009,6.36791193,6.36597947,6.36403327,6.36206377,6.36006124,6.35801556,6.35591601,6.35375085,6.35150693,6.34916931,6.34672075,6.34414142,6.34140857,6.33849647,6.33537652,6.33201775,6.32838766,6.32445349,6.32018397,6.31555126,6.31053306,6.30511458,6.29928998,6.29306315,6.28644753,6.27946515,6.27214482,6.26452002,6.25662656,6.24850047,6.24017628,6.23168568,6.22305686,6.2143141,6.20547796,6.19656569,6.18759202,6.17857019,6.16951326,6.16043571,6.15135513,6.14229412,6.13328208,6.12435686,6.11556588,6.10696669,6.09862667,6.09062162,6.08303343,6.07594653])
我尝试使用scipy.optimize中的minimumsq通过以下系数来解决此问题：
leastsq(SSR,vCoef,args=(y),full_output=1,maxfev=2500)
array([-1.01345719e+03,1.01905962e+03,1.07333189e+03,3.68129556e-04])
但是，该值并没有太大意义，因为期望所有这四个系数的系数大约在-10和10之间。
解决方法
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