How to determine coefficients by fit for multiple series of data?

Hey there,

I've searched for a while but did not find the right thing for my problem. I have several series of experiments with different amount of data, which might be described by an equation with 2 coefficents. The equation is:

D is a fixed value for each series of experiments, a and b are the coefficients I want to fit.

As an example x, y and D have the following values for three series of experiments (each row is one experiment):

x = [2,4,6,NaN,NaN; 2,4,6,8,10; 2,4,6,8,NaN];
y = [3,5,7,NaN,NaN; 4,8,11,25,32; 7,10,15,17,NaN];
D = [3;5;7];

Now I want to calculate the coefficients a and b by the fitting tool box, but the tool box throws just all values of y in and does not seperate the three cases with different value of D.

Is there a way to tell this the toolbox? or alternatively to calculate the coefficents by code?

Many thanks in advance for any help and best regards,

Benedikt

Answer 1

[Torsten]

x = [2,4,6,NaN,NaN; 2,4,6,8,10; 2,4,6,8,NaN];
y = [3,5,7,NaN,NaN; 4,8,11,25,32; 7,10,15,17,NaN];
D = [3;5;7];
N = size(x, 1);
A = [];
b = [];
for K = 1:N
    mask = ~(isnan(x(K,:)) | isnan(y(K,:)));
    tx = x(K,mask).';
    ty = y(K,mask).';
    A = [A;D(K)*tx.^2,tx];
    b = [b;ty];
end
ab = A\b   
a = ab(1)
b = ab(2) 

[Benedikt]

Hi Torsten,

thanks for the solution! this works fine for me!

Best regards,

Benedikt

Answer 2

[Walter Roberson]

x = [2,4,6,NaN,NaN; 2,4,6,8,10; 2,4,6,8,NaN];
y = [3,5,7,NaN,NaN; 4,8,11,25,32; 7,10,15,17,NaN];
D = [3;5;7];
N = size(x, 1);
ab = zeros(N, 2);
for K = 1 : N
    mask = ~(isnan(x(K,:)) | isnan(y(K,:)));
    tx = x(K,mask);
    ty = y(K,mask);
    ty2 = ty ./ tx;   %now it is A*D*x + b
    p = polyfit(tx(:), ty2(:), 1);
    ab(K,1) = p(1)./D(K);
    ab(K,2) = p(2);
end

ab

ab = 3×2

-0.0278 1.6389 0.0352 1.3742 -0.0295 3.6875

[Benedikt]

Hi Walter,

thank you for your solution!

But it is not exactly what I search for. I just want one value for each coefficient a and b over all series of experiments because I know that phyiscally all series of experiments are the same but with different input parameters, described by D, and different scope.

So I want to use the data of all the three series to get a more accurate value for a and b, as I calucalte them just by one series of experiments.

Best regards,

Benedikt