Trying to create fittype using the convolution of two functions, "Expression is not a valid MATLAB expression, has non-scalar coefficients, or cannot be evaluated"

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Ethan Favorite
Ethan Favorite 2024-5-8
编辑： Paras Gupta 2024-5-15
Ran in:
I am attempting to fit the convolution of a Fermi-Dirac distribution and a Gaussian distribution to some data and am running into issues with defining the fittype inorder to use fit() function. I am able to fit the data using this function when only fitting the Fermi-Dirac distribution but when I attempt to use the convolution in the fittype() function I get an error.
Error using fittype/testCustomModelEvaluation
Expression integral(@(tau)(exp(1.0./x5.^2.*(tau-x7).^2.*(-1.0./2.0)).*(x1+x2./(exp((tau-x3)./(x4.*x6))+1.0)).*3.989422804014327e-1)./x5,-Inf,Inf) is not a valid MATLAB expression, has non-scalar coefficients, or cannot be evaluated:
Bellow is the code I am trying to use along with sample data.
xData = [35.9249999999992 35.9499999999992 35.9749999999992 35.9999999999992 36.0249999999992 36.0499999999992 36.0749999999992 36.0999999999992 36.1249999999992 36.1499999999992 36.1749999999992 36.1999999999992 36.2249999999992 36.2499999999992 36.2749999999992 36.2999999999992 36.3249999999992 36.3499999999992 36.3749999999992 36.3999999999992 36.4249999999992 36.4499999999992 36.4749999999992 36.4999999999992 36.5249999999992 36.5499999999992 36.5749999999992 36.5999999999992 36.6249999999992 36.6499999999992 36.6749999999992 36.6999999999992 36.7249999999992 36.7499999999992 36.7749999999992 36.7999999999992 36.8249999999992 36.8499999999992 36.8749999999992 36.8999999999992 36.9249999999992 36.9499999999992 36.9749999999992 36.9999999999992];
yData = [8547 9125 9066 8723 8455 7687 7797 9793 9825 8438 8030 8007 7433 3543 2352 1573 658 747 945 214 295 185 196 116 109 222 91 373 79 197 137 149 89 142 281 77 159 84 147 287 84 77 95 77];
plot(xData,yData,'.b','HandleVisibility','off')
x = sym('x',[1 7]);
% Function declarations
% Fermi-Dirac
F = x(1)+(x(2)/(exp((x(7)-x(3))/(x(6)*x(4)))+1));
% Gausian
G = (1/(x(5)*sqrt(2*pi())))*exp(-(1/2)*((x(7))/(x(5)))^2);
% Convolution
syms tau real;
atau = subs(F, x(7), tau); % transform all to the tau axis
btau = subs(G, x(7), x(7) - tau); % give one the t-tau
H = int(atau * btau, tau, -inf, inf);
% Convert to function handle
s = symvar(H);
j = matlabFunction(H);
Coef = cellstr(string([s(1:5)]));
prob = cellstr(string(s(6)));
ind = cellstr(string(s(end)));
ft = fittype(j,...
'coefficients',Coef,...
'dependent',{'y'},'independent',ind,...
'problem',prob);
Error using fittype/testCustomModelEvaluation (line 12)
Expression integral(@(tau)(exp(1.0./x5.^2.*(tau-x7).^2.*(-1.0./2.0)).*(x1+x2./(exp((tau-x3)./(x4.*x6))+1.0)).*3.989422804014327e-1)./x5,-Inf,Inf) is not a valid MATLAB expression, has non-scalar coefficients, or cannot be evaluated:
Error while trying to evaluate FITTYPE function :

Output of the function must be the same size as the input. If FUN is an array-valued integrand, set the 'ArrayValued' option to true.

Error in fittype>iCreateFittype (line 373)
testCustomModelEvaluation( obj );

Error in fittype (line 330)
obj = iCreateFittype( obj, varargin{:} );

Caused by:
Error using fittype/evaluate>I_ERROR_FCN_ (line 179)
Error while trying to evaluate FITTYPE function :

Output of the function must be the same size as the input. If FUN is an array-valued integrand, set the 'ArrayValued' option to true.

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回答（1 个）

Paras Gupta
Paras Gupta 2024-5-15
编辑：Paras Gupta 2024-5-15
Ran in:
Hi Ethan,
I understand that you get the error provided in the question when you use the 'fittype' function to fit the convolution of a Fermi-Dirac distribution and a Gaussian distribution.
The error occurs because the function handle 'j' contains the 'integral' function with an array-valued integrand but does not have the 'ArrayValued' property set to 'true'. You can refer to the following link for more information on the 'integral' function and 'ArrayValued' property:
https://www.mathworks.com/help/matlab/ref/integral.html
There does not seem to be an option to control the behavior of the 'matlabfunction' function such that the output function handle 'j' has the 'ArrayValued' property set. However, you can try adding the property programatically by modifying the function handle. The code below shows one way to achieve the same:
xData = [35.9249999999992 35.9499999999992 35.9749999999992 35.9999999999992 36.0249999999992 36.0499999999992 36.0749999999992 36.0999999999992 36.1249999999992 36.1499999999992 36.1749999999992 36.1999999999992 36.2249999999992 36.2499999999992 36.2749999999992 36.2999999999992 36.3249999999992 36.3499999999992 36.3749999999992 36.3999999999992 36.4249999999992 36.4499999999992 36.4749999999992 36.4999999999992 36.5249999999992 36.5499999999992 36.5749999999992 36.5999999999992 36.6249999999992 36.6499999999992 36.6749999999992 36.6999999999992 36.7249999999992 36.7499999999992 36.7749999999992 36.7999999999992 36.8249999999992 36.8499999999992 36.8749999999992 36.8999999999992 36.9249999999992 36.9499999999992 36.9749999999992 36.9999999999992];
yData = [8547 9125 9066 8723 8455 7687 7797 9793 9825 8438 8030 8007 7433 3543 2352 1573 658 747 945 214 295 185 196 116 109 222 91 373 79 197 137 149 89 142 281 77 159 84 147 287 84 77 95 77];
% plot(xData,yData,'.b','HandleVisibility','off')
x = sym('x',[1 7]);
% Function declarations
% Fermi-Dirac
F = x(1)+(x(2)/(exp((x(7)-x(3))/(x(6)*x(4)))+1));
% Gausian
G = (1/(x(5)*sqrt(2*pi())))*exp(-(1/2)*((x(7))/(x(5)))^2);
% Convolution
syms tau real;
atau = subs(F, x(7), tau); % transform all to the tau axis
btau = subs(G, x(7), x(7) - tau); % give one the t-tau
H = int(atau * btau, tau, -inf, inf);
% Convert to function handle
s = symvar(H);
Coef = cellstr(string([s(1:5)]));
prob = cellstr(string(s(6)));
ind = cellstr(string(s(end)));
j = matlabFunction(H)
j = function_handle with value:
@(x1,x2,x3,x4,x5,x6,x7)integral(@(tau)(exp(1.0./x5.^2.*(tau-x7).^2.*(-1.0./2.0)).*(x1+x2./(exp((tau-x3)./(x4.*x6))+1.0)).*3.989422804014327e-1)./x5,-Inf,Inf)
% Modifying the function handle by converting to string
jStr = functions(j).function; % string equivalent of the function expresion
lastParenPos = find(jStr == ')', 1, 'last'); % Finding the last parenthesis
modifiedStr = insertBefore(jStr, lastParenPos, "', 'ArrayValued', true"); % Inserting property before parenthesis
modifiedJ = str2func(modifiedStr) % converting string back to function handle
modifiedJ = function_handle with value:
@(x1,x2,x3,x4,x5,x6,x7)integral(@(tau)(exp(1.0./x5.^2.*(tau-x7).^2.*(-1.0./2.0)).*(x1+x2./(exp((tau-x3)./(x4.*x6))+1.0)).*3.989422804014327e-1)./x5,-Inf,Inf','ArrayValued',true)
ft = fittype(modifiedJ,...
'coefficients',Coef,...
'dependent',{'y'},'independent',ind,...
'problem',prob);
Please refer to the following documentations for more information on the functions used above:
Hope this helps.

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