Fit sum parameters of an overdetermined system

I have a function that uses 9 inputs (cts(1) to cts (9)) and provides 1 value as result. The function needs 4 parameters (c(1) to c(4)). The code of the function is:

fun = @(c,cts) ((c(1) .* (4-c(4))) ./ (c(2)+c(3) .* 4)) *cts(1) +...
                ((c(1) .* (5-c(4))) ./ (c(2)+c(3) .* 5)) *cts(2)+ ...
                ((c(1) .* (6-c(4))) ./ (c(2)+c(3) .* 6)) *cts(3) + ...
                ((c(1) .* (7-c(4))) ./ (c(2)+c(3) .* 7)) *cts(4) + ...
                ((c(1) .* (8-c(4))) ./ (c(2)+c(3) .* 8)) *cts(5) + ... 
                ((c(1) .* (9-c(4))) ./ (c(2)+c(3) .* 9)) *cts(6) + ...
                ((c(1) .* (10-c(4))) ./ (c(2)+c(3) .* 10)) *cts(7) + ...
                ((c(1) .* (11-c(4))) ./ (c(2)+c(3) .* 11)) *cts(8) + ...
                ((c(1) .* (12-c(4))) ./ (c(2)+c(3) .* 12)) *cts(9)

I have 11 measured values with each 9 inputs. From this data set I want to fit the parameters c. Is there an algorithm which I can use for this problem? I already tried lsqcurvefit, but that atempt ended with the error:

Error using lsqcurvefit (line 263)

Function value and YDATA sizes are not equal.

Answer 1

[Matt J]

Your xdata should be a 9x11 matrix, your ydata should be a 1x11 vector, and the code for your function should look like this,

fun = @(c,cts) ((c(1) .* (4-c(4))) ./ (c(2)+c(3) .* 4)) *cts(1,:) +...
                ((c(1) .* (5-c(4))) ./ (c(2)+c(3) .* 5)) *cts(2,:)+ ...
                ((c(1) .* (6-c(4))) ./ (c(2)+c(3) .* 6)) *cts(3,:) + ...
                ((c(1) .* (7-c(4))) ./ (c(2)+c(3) .* 7)) *cts(4,:) + ...
                ((c(1) .* (8-c(4))) ./ (c(2)+c(3) .* 8)) *cts(5,:) + ... 
                ((c(1) .* (9-c(4))) ./ (c(2)+c(3) .* 9)) *cts(6,:) + ...
                ((c(1) .* (10-c(4))) ./ (c(2)+c(3) .* 10)) *cts(7,:) + ...
                ((c(1) .* (11-c(4))) ./ (c(2)+c(3) .* 11)) *cts(8,:) + ...
                ((c(1) .* (12-c(4))) ./ (c(2)+c(3) .* 12)) *cts(9,:)

[Marco Knobloch]

That one worked for me, thanks Matt