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zy_0824新蟲 (初入文壇)
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[求助]
非線性最小二乘擬合（初值問題）lsqcurvefit 函數(shù)的設定
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大家好，我現(xiàn)在在做非線性最小二乘擬合，遇到了點問題； 說明一下，其中y是x的函數(shù)，二者的函數(shù)關系式是這樣的：y=4*pi*x.*(l+n*d)+add; 其中,x和y，還有n都是已知的，是一個1*601的向量，想通過數(shù)據的擬合得出未知參量:l,d,add。ps:其中l(wèi)和d理論上差應該很大,d應該在0和1之間,n值的變化很小。 下面是我的程序和數(shù)據： x=1.80899213812017 1.80834769462794 1.80770371013109 1.80706018413943 1.80641711616346 1.80577450571437 1.80513235230407 1.80449065544514 1.80384941465086 1.80321188100244 1.80257154857119 1.80193167075105 1.80129224705804 1.80065327700890 1.80001476012103 1.79937669591254 1.79874231937030 1.79810515678578 1.79746844544144 1.79683218485810 1.79619960088445 1.79556423810618 1.79492932465784 1.79429486006294 1.79366406107067 1.79303049048349 1.79239736732675 1.79176790155310 1.79113566957129 1.79050388360292 1.78987574682566 1.78924484921139 1.78861759534673 1.78798758421422 1.78736121140193 1.78673208488407 1.78610340109810 1.78547834750408 1.78485054553957 1.78422636836781 1.78360262760339 1.78297614377920 1.78235327667826 1.78172767005254 1.78110567478079 1.78048094351246 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[beta2,resnorm2,residual,exitflag]=lsqcurvefit(@myfunc5, [-50 0 0],x,y,[-100 0 ],[100 1 ],options); yy=myfunc5(beta2,wavenumber); residual2=sum((unwrap_phase-yyy).^2)/sum((unwrap_phase.^2)); figure plot(x,y,'o',x,yy,'k'); %%%%%%%% function f=myfunc5(const,data) f=2*pi*data.*(2*const(1)+2*const(2)*n)+const(3);%n是已知的 end 在解算的時候，我去了l的范圍在-100到100之間，理論上也是這樣的。初值我是隨便選的，初值選-50、-30、-100時計算所得的結果都不同，lsqcurvefit函數(shù)中的Trust-Region-Reflective這是什么算法，而用L-M計算出來的結果是 l=-16.127957245741122;d=-13.324079733903535;add=671.1358160146965 用Trust-Region-Reflective算法，當初值設定為：[-50 0 0]時，計算的結果是：l=-36.363261975199510;d=0.371577025874681;add=676.6967071599734; l=-36.185407678096254;d=0.251201776023842;add=676.6967071599734; d隨著初值的變化而變化，相對l來說變化小，但對于d本身來說，變化很大，這個就不知道怎么辦了？我看過有篇文章中說到擬合的時候，如果數(shù)據差別很大的話，就需要做調整，類似歸一化。我都不太清楚，請求指教 |
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8樓2012-05-31 22:57:51
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10樓2012-06-01 13:14:00
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zy_0824
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dingd
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【答案】應助回帖
★ ★
感謝參與，應助指數(shù) +1
小雨萌萌: 金幣+2, 3Q 2012-09-06 15:31:33
感謝參與，應助指數(shù) +1
小雨萌萌: 金幣+2, 3Q 2012-09-06 15:31:33
|
1stOpt計算結果： 均方差(RMSE): 0.133957518319827 殘差平方和(SSE): 10.7847146453585 相關系數(shù)(R): 0.999994551830855 相關系數(shù)之平方(R^2): 0.999989103691393 決定系數(shù)(DC): 0.999989103691393 卡方系數(shù)(Chi-Square): -0.0634492020788441 F統(tǒng)計(F-Statistic): 27440485.6536139 參數(shù) 最佳估算 ---------- ------------- l -16.1279493333851 d -13.3240850891466 add 671.135813840382 |
5樓2012-05-31 15:47:40
dingd
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★ ★
小雨萌萌: 金幣+2, 謝謝關注~ 2012-09-06 15:31:43
小雨萌萌: 金幣+2, 謝謝關注~ 2012-09-06 15:31:43
|
如果要求d在0和1之間： 均方差(RMSE): 0.135288449065215 殘差平方和(SSE): 11.0000816347333 相關系數(shù)(R): 0.999994443032517 相關系數(shù)之平方(R^2): 0.999988886095913 決定系數(shù)(DC): 0.999988886095911 卡方系數(shù)(Chi-Square): -0.0791031472135278 F統(tǒng)計(F-Statistic): 26903237.3877882 參數(shù) 最佳估算 ---------- ------------- d 2.21801347089544E-9 l -35.8142575648338 add 676.545832058174 |
6樓2012-05-31 15:49:57
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7樓2012-05-31 16:42:33
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9樓2012-06-01 10:21:53
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