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$$ y= a_1 e^{\lambda_1 x} + a_2 e^{\lambda_2 x} $$

䤤 $a_1$ $a_2$ uʰѼơA$\lambda_2$ $\lambda_2$ DuʰѼơA]ڭ̥iH復̤}BzApUG

knBOG̤pkbDuʰѼơ]$\lambda_2$ $\lambda_2$^TwpUA@̦nuʰѼơ]$a_1$ $a_2$^ȡA]jMŶץ 4]$a_1$B$a_2$B$\lambda_1$B$\lambda_2$^A 2]$\lambda_1$B$\lambda_2$^ĄΤƷ|󦳮IJvC

pGnϥΤWzV]Hybrid^kA禡 errorMeasure1 g errorMeasure2ApUG

Example 1: 10-uXPjkR/errorMeasure2.mfunction squaredError = errorMeasure2(lambda, data) if nargin<1; return; end x = data(:,1); y = data(:,2); A = [exp(lambda(1)*x) exp(lambda(2)*x)]; a = A\y; y2 = a(1)*exp(lambda(1)*x)+a(2)*exp(lambda(2)*x); squaredError = sum((y-y2).^2);

䤤 lambda ODuʰѼƦVqAu]t $\lambda_2$ $\lambda_2$Adata O[쪺IAa hOQγ̤pkX̨νuʰѼƦVq]Y $a_1$ $a_2$ HǤJ $\lambda_2$ $\lambda_2$ ܡ^AӶǦ^ squareError O`~tCƩM@errorMeasure1@̤jPbڭ̥uǤJuʰѼơ]$\lambda_2$ $\lambda_2$^ĄνuʰѼơ]$a_1$ $a_2$^ȫhb禡ѳ̤pkMwC

ΦVkDX~tM̤pȡAiJpUG

Example 2: 10-uXPjkR/nonlinearFit02.mload data.txt lambda0 = [0 0]; tic lambda = fminsearch(@(x)errorMeasure2(x, data), lambda0); fprintf('pɶ = %g\n', toc); x = data(:, 1); y = data(:, 2); A = [exp(lambda(1)*x) exp(lambda(2)*x)]; a = A\y; y2 = A*a; plot(x, y, 'ro', x, y2, 'b-'); legend('Sample data', 'Regression curve'); fprintf('~tM = %d\n', sum((y-y2).^2));[Warning: Rank deficient, rank = 1, tol = 2.136826e-14.] [> In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('errorMeasure2', 'D:\users\jang\books\matlabProgramming4guru\example\10-uXPjkR\errorMeasure2.m', 6)" style="font-weight:bold">errorMeasure2</a> (<a href="matlab: opentoline('D:\users\jang\books\matlabProgramming4guru\example\10-uXPjkR\errorMeasure2.m',6,0)">line 6</a>) In %4287963446>@(x)errorMeasure2(x,data) In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('fminsearch', 'C:\Program Files\MATLAB\R2015a\toolbox\matlab\optimfun\fminsearch.p', 190)" style="font-weight:bold">fminsearch</a> (<a href="matlab: opentoline('C:\Program Files\MATLAB\R2015a\toolbox\matlab\optimfun\fminsearch.p',190,0)">line 190</a>) In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('nonlinearFit02', 'D:\users\jang\books\matlabProgramming4guru\example\10-uXPjkR\nonlinearFit02.m', 4)" style="font-weight:bold">nonlinearFit02</a> (<a href="matlab: opentoline('D:\users\jang\books\matlabProgramming4guru\example\10-uXPjkR\nonlinearFit02.m',4,0)">line 4</a>) In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('goWriteOutputFile>dummyFunction', 'd:\users\jang\books\goWriteOutputFile.m', 85)" style="font-weight:bold">goWriteOutputFile>dummyFunction</a> (<a href="matlab: opentoline('d:\users\jang\books\goWriteOutputFile.m',85,0)">line 85</a>) In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('goWriteOutputFile', 'd:\users\jang\books\goWriteOutputFile.m', 55)" style="font-weight:bold">goWriteOutputFile</a> (<a href="matlab: opentoline('d:\users\jang\books\goWriteOutputFile.m',55,0)">line 55</a>)] [Warning: Rank deficient, rank = 1, tol = 2.137360e-14.] [> In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('errorMeasure2', 'D:\users\jang\books\matlabProgramming4guru\example\10-uXPjkR\errorMeasure2.m', 6)" style="font-weight:bold">errorMeasure2</a> (<a href="matlab: opentoline('D:\users\jang\books\matlabProgramming4guru\example\10-uXPjkR\errorMeasure2.m',6,0)">line 6</a>) In %4287963446>@(x)errorMeasure2(x,data) In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('fminsearch', 'C:\Program Files\MATLAB\R2015a\toolbox\matlab\optimfun\fminsearch.p', 309)" style="font-weight:bold">fminsearch</a> (<a href="matlab: opentoline('C:\Program Files\MATLAB\R2015a\toolbox\matlab\optimfun\fminsearch.p',309,0)">line 309</a>) In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('nonlinearFit02', 'D:\users\jang\books\matlabProgramming4guru\example\10-uXPjkR\nonlinearFit02.m', 4)" style="font-weight:bold">nonlinearFit02</a> (<a href="matlab: opentoline('D:\users\jang\books\matlabProgramming4guru\example\10-uXPjkR\nonlinearFit02.m',4,0)">line 4</a>) In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('goWriteOutputFile>dummyFunction', 'd:\users\jang\books\goWriteOutputFile.m', 85)" style="font-weight:bold">goWriteOutputFile>dummyFunction</a> (<a href="matlab: opentoline('d:\users\jang\books\goWriteOutputFile.m',85,0)">line 85</a>) In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('goWriteOutputFile', 'd:\users\jang\books\goWriteOutputFile.m', 55)" style="font-weight:bold">goWriteOutputFile</a> (<a href="matlab: opentoline('d:\users\jang\books\goWriteOutputFile.m',55,0)">line 55</a>)] [Warning: Rank deficient, rank = 1, tol = 2.136960e-14.] [> In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('errorMeasure2', 'D:\users\jang\books\matlabProgramming4guru\example\10-uXPjkR\errorMeasure2.m', 6)" style="font-weight:bold">errorMeasure2</a> (<a href="matlab: opentoline('D:\users\jang\books\matlabProgramming4guru\example\10-uXPjkR\errorMeasure2.m',6,0)">line 6</a>) In %4287963446>@(x)errorMeasure2(x,data) In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('fminsearch', 'C:\Program Files\MATLAB\R2015a\toolbox\matlab\optimfun\fminsearch.p', 350)" style="font-weight:bold">fminsearch</a> (<a href="matlab: opentoline('C:\Program Files\MATLAB\R2015a\toolbox\matlab\optimfun\fminsearch.p',350,0)">line 350</a>) In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('nonlinearFit02', 'D:\users\jang\books\matlabProgramming4guru\example\10-uXPjkR\nonlinearFit02.m', 4)" style="font-weight:bold">nonlinearFit02</a> (<a href="matlab: opentoline('D:\users\jang\books\matlabProgramming4guru\example\10-uXPjkR\nonlinearFit02.m',4,0)">line 4</a>) In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('goWriteOutputFile>dummyFunction', 'd:\users\jang\books\goWriteOutputFile.m', 85)" style="font-weight:bold">goWriteOutputFile>dummyFunction</a> (<a href="matlab: opentoline('d:\users\jang\books\goWriteOutputFile.m',85,0)">line 85</a>) In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('goWriteOutputFile', 'd:\users\jang\books\goWriteOutputFile.m', 55)" style="font-weight:bold">goWriteOutputFile</a> (<a href="matlab: opentoline('d:\users\jang\books\goWriteOutputFile.m',55,0)">line 55</a>)] [Warning: Rank deficient, rank = 1, tol = 2.137093e-14.] [> In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('errorMeasure2', 'D:\users\jang\books\matlabProgramming4guru\example\10-uXPjkR\errorMeasure2.m', 6)" style="font-weight:bold">errorMeasure2</a> (<a href="matlab: opentoline('D:\users\jang\books\matlabProgramming4guru\example\10-uXPjkR\errorMeasure2.m',6,0)">line 6</a>) In %4287963446>@(x)errorMeasure2(x,data) In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('fminsearch', 'C:\Program Files\MATLAB\R2015a\toolbox\matlab\optimfun\fminsearch.p', 365)" style="font-weight:bold">fminsearch</a> (<a href="matlab: opentoline('C:\Program Files\MATLAB\R2015a\toolbox\matlab\optimfun\fminsearch.p',365,0)">line 365</a>) In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('nonlinearFit02', 'D:\users\jang\books\matlabProgramming4guru\example\10-uXPjkR\nonlinearFit02.m', 4)" style="font-weight:bold">nonlinearFit02</a> (<a href="matlab: opentoline('D:\users\jang\books\matlabProgramming4guru\example\10-uXPjkR\nonlinearFit02.m',4,0)">line 4</a>) In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('goWriteOutputFile>dummyFunction', 'd:\users\jang\books\goWriteOutputFile.m', 85)" style="font-weight:bold">goWriteOutputFile>dummyFunction</a> (<a href="matlab: opentoline('d:\users\jang\books\goWriteOutputFile.m',85,0)">line 85</a>) In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('goWriteOutputFile', 'd:\users\jang\books\goWriteOutputFile.m', 55)" style="font-weight:bold">goWriteOutputFile</a> (<a href="matlab: opentoline('d:\users\jang\books\goWriteOutputFile.m',55,0)">line 55</a>)] pɶ = 0.153491 ~tM = 1.477226e-01

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Hint
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  • ˵WzjkL{ʵeܡAib MATLAB OUJ fitdemoC


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