How do I find the minimum between a matrix and a varying matrix function? I get "Error in fmincon (line 563) initVals.f = feval(funf​cn{3},X,va​rargin{:})​;"

I am trying to analyse how close, percentually, my samples are to pure water (0%) and to "no water"/dried (100%). In theory my results should give me a value between 0% and 100% (or 0 and 1, labelled below as fitvar)

I have a 2D data array for water, a 2D data array for "dried" and a 2D data for each data set that I am trying to analyse. All data arrays are composed of complex numbers, hence why I can't solve this analytically.

% the size of the data arrays are 75 x 75 matrices.
num_x = 75;
num_y = 75;

perc_water = zeros(num_latex_measurements, num_x, num_y);

% loading a 75 x 75 matrix of the current sample to analyse, of pure water
% and of dried sample.
eps_current_sample = load('eps_1.mat');
eps_water = load('eps_water.mat');
eps_dried = load('eps_32.mat');

%relabelling the data (as it had been saved with the variable name of
%I3.epsilon)
eps_water = eps_water.I3_epsilon;
eps_dried = eps_dried.I3.epsilon;


    for x=1:num_x
        for y=1:num_y
             % calculating the theoretical values for eps over a range of
             % fit_var, from 0 to 1
             eps_theory = @(fit_var) FORMULA( eps_water(x, y), eps_dried(x,y),  fit_var );
             
             % calculate the absolute value between the difference of the
             % current sample data and of the theoretical values.
             loss_fx = @(fit_var) abs(eps_current_sample(x, y) - eps_theory(fit_var) );
             
             %finding the smallest difference for each 2D matrix, for each
             %fit_var value
             perc_water(x, y) =  fmincon(loss_fx, 0.5, [], [] , [], [], 0, 1);
        end
    end

The FORMULA function is shown below (this is simple multiplication and divisions resulting in a 75 x 75 matrix with complex numbers.

function eps_eff = FORMULA(eps_water, eps_dried, perc_water)

    eps_eff = eps_dried./2.0-eps_water./4.0-eps_dried.*perc_water.*(3.0./4.0)+eps_water.*perc_water.*(3.0./4.0)+sqrt(eps_dried.*eps_water.*4.0-eps_dried.^2.*perc_water.*1.2e+1-eps_water.^2.*perc_water.*6.0+eps_dried.^2.*4.0+eps_water.^2+eps_dried.^2.*perc_water.^2.*9.0+eps_water.^2.*perc_water.^2.*9.0+eps_dried.*eps_water.*perc_water.*1.8e+1-eps_dried.*eps_water.*perc_water.^2.*1.8e+1)./4.0;

end

Whenever I try to run it I get the following error message.

Operator '-' is not supported for operands of type 'struct'.

Error in @(fit_var)abs(eps_current_latex(x,y)-perc_water_fx(fit_var))

Error in fmincon (line 563)

initVals.f = feval(funfcn{3},X,varargin{:});

I have never used fmincon before, is there anything incorrect with my approach? I know the operator is not really the problem, but I don't see what is.

Thanks for your help.

Answer 1

[Star Strider]

There is one typo (. where _ should be) in:

eps_dried = eps_dried.I3.epsilon;

so change that to:

eps_dried = eps_dried.I3_epsilon;

and the displayed error is corrected by changing the current ‘loss_fx’ line to:

loss_fx = @(fit_var) abs(eps_current_sample.I3_epsilon(x, y) - eps_theory(fit_var) );

Consider suppressing the fmincon outputs as well, in an options structure:

opts = optimoptions('fmincon', 'Display','off');

perc_water(x, y) = fmincon(loss_fx, 0.5, [], [] , [], [], 0, 1, [], opts);

Then run it —

% the size of the data arrays are 75 x 75 matrices.
num_x = 75;
num_y = 75;
% perc_water = zeros(num_latex_measurements, num_x, num_y);             % Missing Variable

% loading a 75 x 75 matrix of the current sample to analyse, of pure water
% and of dried sample.
eps_current_sample = load('eps_1.mat');
eps_water = load('water.mat');
eps_dried = load('eps_32.mat');

%relabelling the data (as it had been saved with the variable name of
%I3.epsilon)
eps_water = eps_water.I3_epsilon;
eps_dried = eps_dried.I3_epsilon;
opts = optimoptions('fmincon', 'Display','off');

    for x=1:num_x
        for y=1:num_y
             % calculating the theoretical values for eps over a range of
             % fit_var, from 0 to 1
             eps_theory = @(fit_var) FORMULA( eps_water(x, y), eps_dried(x,y),  fit_var );
             
             % calculate the absolute value between the difference of the
             % current sample data and of the theoretical values.
             loss_fx = @(fit_var) abs(eps_current_sample.I3_epsilon(x, y) - eps_theory(fit_var) );
             
             %finding the smallest difference for each 2D matrix, for each
             %fit_var value
             perc_water(x, y) =  fmincon(loss_fx, 0.5, [], [] , [], [], 0, 1, [], opts);
        end
    end

Output = perc_water

Output = 75×75

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9754 0.7861 0.6034 0.4423 0.3177 0.2418 0.2217 0.2507 0.3124 0.3900 0.4749 0.5611 0.6415 0.7118 0.7701 0.8194 0.8621 0.8970 0.9241 0.9438 0.9580 0.9682 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.8517 0.6600 0.4878 0.3511 0.2622 0.2275 0.2450 0.3012 0.3784 0.4620 0.5465 0.6284 0.7022 0.7653 0.8168 0.8598 0.8966 0.9264 0.9494 0.9660 0.9778 0.9861 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.8280 0.6297 0.4578 0.3306 0.2576 0.2394 0.2692 0.3339 0.4165 0.5029 0.5847 0.6609 0.7308 0.7916 0.8423 0.8828 0.9161 0.9440 0.9663 0.9833 0.9953 0.9998 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 0.9964 0.7581 0.5477 0.3909 0.2933 0.2569 0.2723 0.3252 0.4019 0.4887 0.5744 0.6525 0.7205 0.7807 0.8340 0.8791 0.9159 0.9448 0.9681 0.9873 0.9997 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9384 0.6950 0.4767 0.3374 0.2778 0.2806 0.3270 0.3981 0.4804 0.5653 0.6458 0.7173 0.7784 0.8295 0.8735 0.9117 0.9435 0.9691 0.9888 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.8725 0.6552 0.4434 0.3141 0.2816 0.3130 0.3797 0.4610 0.5447 0.6247 0.6985 0.7636 0.8187 0.8645 0.9020 0.9338 0.9612 0.9837 0.9996 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9186 0.8737 0.7798 0.6208 0.4324 0.3073 0.2862 0.3362 0.4156 0.5034 0.5880 0.6648 0.7328 0.7925 0.8433 0.8855 0.9198 0.9477 0.9711 0.9910 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.7031 0.6551 0.5608 0.4233 0.3056 0.2817 0.3406 0.4315 0.5250 0.6118 0.6879 0.7532 0.8089 0.8565 0.8964 0.9290 0.9553 0.9764 0.9940 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.5150 0.4708 0.3919 0.3018 0.2686 0.3238 0.4247 0.5278 0.6191 0.6973 0.7627 0.8171 0.8626 0.9009 0.9326 0.9582 0.9787 0.9949 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.3659 0.3325 0.2822 0.2509 0.2913 0.3945 0.5108 0.6119 0.6951 0.7633 0.8188 0.8641 0.9015 0.9326 0.9581 0.9785 0.9947 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

figure
surfc(Output)
xlabel('X')
ylabel('Y')
zlabel('perc\_water')
title('Output')
colormap(turbo)

function eps_eff = FORMULA(eps_water, eps_dried, perc_water)

    eps_eff = eps_dried./2.0-eps_water./4.0-eps_dried.*perc_water.*(3.0./4.0)+eps_water.*perc_water.*(3.0./4.0)+sqrt(eps_dried.*eps_water.*4.0-eps_dried.^2.*perc_water.*1.2e+1-eps_water.^2.*perc_water.*6.0+eps_dried.^2.*4.0+eps_water.^2+eps_dried.^2.*perc_water.^2.*9.0+eps_water.^2.*perc_water.^2.*9.0+eps_dried.*eps_water.*perc_water.*1.8e+1-eps_dried.*eps_water.*perc_water.^2.*1.8e+1)./4.0;

end

EDIT — (1 Dec 2023 at 13:28)

Added surfc call, expanded explanation.

.

[Goncalo Costa]

I only have one question (and thank you so much for your help, I can't believe I didn't see such a silly mistake as labelling the variable correctly): why do you get a single 75 x 75 output (which is what I expected) and I get a 75 x 75 x75 3D matrix?

I pretty much copied the code, but still get this. Did you also get a 75 x 75 x 75 matrix?

Thanks for your help once again!

[Dyuman Joshi]

That is because you have preallocated the array as 75x75x75.

perc_water = zeros(num_latex_measurements, num_x, num_y);

which from the look of it, should be -

perc_water = zeros(num_x, num_y);

[Goncalo Costa]

Of course, thanks, that is because I wanted to do a for loop over several data sets to be analysed.

Thank you so much, and I apologise for the silly mistakes.

[Star Strider]

@Goncalo Costa — I removed the preallocation:

% perc_water = zeros(num_latex_measurements, num_x, num_y); % Missing Variable

because ‘num_latex_measurements’ was missing. The preallocation defines a 3D matrix, however since I didn’t know what the missing variable was, I just removed (commented-out) the entire preallocation. If you want to do a loop over a number of data sets, a 3D matrix is one option. A cell array with each 2D matrix being in a different cell is another option. It all depends on how you choose to index them.