Fitting multiple curves with multiple data sets, partial and global... (2024)

rng("default")

b1 = 1; b2 = 0.85; b3 = 2.5;

b4 = 1.1; b5 = 2.2; b6 = 4.5;

b7 = 1.3; b8 = 7.2; b9 = 9.5;

b10 = 0.5;

%x data

x1 = linspace(0, 10, 20).'; x2 = linspace(0, 10, 23).'; x3 = linspace(0, 10, 14).';

%constants

C1 = 3.7 ; C2 = 4.2; C3 = 20.2;

%measurement dataset 1

A1 = b1 + b2*x1 + C1 * b10 + rand(20,1);

B1 = b3 - b2*x1 + C1 * b10 + rand(20,1);

%measurement dataset 2

A2 = b4 + b5*x2 + C2 * b10 + rand(23,1);

B2 = b6 - b5*x2 + C2 * b10 + rand(23,1);

%measurement dataset 3

A3 = b7 + b8*x3 + C3 * b10 + rand(14,1);

B3 = b9 - b8*x3 + C3 * b10 + rand(14,1);

beta0 = [0.92, 0.8, 2, 0.7, 2, 4, 1, 7, 9, 1];

lb = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0];

ub = [15, 15, 15, 15, 15, 15, 15, 15, 15, 15];

fun = @(beta,x)[beta(1) + beta(2).*x1 + C1* beta(10) ;

beta(3) - beta(2).*x1 + C1* beta(10) ;

beta(4) + beta(5).*x2 + C2* beta(10) ;

beta(6) - beta(5).*x2 + C2* beta(10) ;

beta(7) + beta(8).*x3 + C3* beta(10) ;

beta(9) - beta(8).*x3 + C3* beta(10) ];

beta = lsqcurvefit(fun,beta0,[x1;x1;x2;x2;x3;x3],[A1;B1;A2;B2;A3;B3],lb,ub)

A1_fit = beta(1) + beta(2)*x1 + C1 * beta(10);

B1_fit = beta(3) - beta(2)*x1 + C1 * beta(10);

A2_fit = beta(4) + beta(5)*x2 + C2 * beta(10);

B2_fit = beta(6) - beta(5)*x2 + C2 * beta(10);

A3_fit = beta(7) + beta(8)*x3 + C3 * beta(10);

B3_fit = beta(9) - beta(8)*x3 + C3 * beta(10);

figure(1);

subplot(2,1,1);

hold on;

plot(x1, A1,'s');

plot(x1, A1_fit);

plot(x2, A2,'d');

plot(x2, A2_fit);

plot(x3, A3,'p');

plot(x3, A3_fit);

subplot(2,1,2);

hold on;

plot(x1, B1,'s');

plot(x1, B1_fit);

plot(x2, B2,'d');

plot(x2, B2_fit);

plot(x3, B3,'p');

plot(x3, B3_fit);

hold off

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  https://de.mathworks.com/matlabcentral/answers/2129121-fitting-multiple-curves-with-multiple-data-sets-partial-and-globally-shared-parameters-using-lsqcur#comment_3187741