Error using integral2C​alc>integr​al2t/tenso​r (line 231) Input function must return 'double' or 'single' values. Found 'sym'.

I'd like to know where the mistake in this code, and the solution

h = 0.00172;  rho = 1620;  
L = 100*h;    c=L*L/4;
M=10; N=10;
syms xi eta
shape_w=sym(zeros(M,N));  x_m=sym(zeros(M,1));  y_n=sym(zeros(N,1));

for m=1:M
    for n=1:N
        x_m(m)=(xi^m)*(1+xi);
        y_n(n)=(eta^n)*(1-eta)*(1+eta)^2;
        shape_w(m,n)=x_m(m)*y_n(n);
    end
end
fun=(shape_w*shape_w');
M_w =c*(rho*h)*integral2(@(xi,eta)fun,-1,1,-1,1);

[khaled Elmorabie]

I have used

fun=matlabFunction(shape_w*shape_w');

but obtain another error

Error using integral2Calc>integral2t/tensor (line 231)

Input function must return 'double' or 'single' values. Found 'function_handle'.

Answer 1

[Harshavardhan]

Hi @khaled Elmorabie

The error in your original code arises because “integral2” cannot directly integrate symbolic expressions or matrices. It requires a numeric function handle that returns double or single values. To integrate the full matrix resulting from “shape_w * shape_w'”, you need to:

• Convert each element of the resulting matrix into a numeric function using matlabFunction.
• Integrate each element individually using integral2.

Here is the updated code after calculating “fun”:

% Initialize result matrix
integrated_matrix = zeros(M, M);
 
% Integrate each element of the matrix
for i = 1:M
    for j = 1:M
        integrand = matlabFunction(fun(i, j), 'Vars', [xi, eta]);
        integrated_matrix(i, j) = c * rho * h * integral2(integrand, -1, 1, -1, 1);
    end
end

For more information on “matlabFunction” and “integral2” refer to their respective links below: https://www.mathworks.com/help/symbolic/sym.matlabfunction.html

https://www.mathworks.com/help/matlab/ref/integral2.html

[khaled Elmorabie]

Thank you pro

your suggest is helpful.

Answer 2

[Walter Roberson]

h = 0.00172;  rho = 1620;  
L = 100*h;    c=L*L/4;
M=10; N=10;
syms xi eta
shape_w=sym(zeros(M,N));  x_m=sym(zeros(M,1));  y_n=sym(zeros(N,1));
for m=1:M
    for n=1:N
        x_m(m)=(xi^m)*(1+xi);
        y_n(n)=(eta^n)*(1-eta)*(1+eta)^2;
        shape_w(m,n)=x_m(m)*y_n(n);
    end
end
fun=(shape_w*shape_w');
M_w = c * (rho*h) * int(int(fun, eta, -1, 1), xi, -1, 1)

M_w = 

●

d_M_w = double(M_w)

ans = 10×10

0.0081 0.0061 0.0052 0.0043 0.0039 0.0034 0.0031 0.0028 0.0025 0.0023 0.0061 0.0052 0.0043 0.0039 0.0034 0.0031 0.0028 0.0025 0.0023 0.0022 0.0052 0.0043 0.0039 0.0034 0.0031 0.0028 0.0025 0.0023 0.0022 0.0020 0.0043 0.0039 0.0034 0.0031 0.0028 0.0025 0.0023 0.0022 0.0020 0.0019 0.0039 0.0034 0.0031 0.0028 0.0025 0.0023 0.0022 0.0020 0.0019 0.0018 0.0034 0.0031 0.0028 0.0025 0.0023 0.0022 0.0020 0.0019 0.0018 0.0017 0.0031 0.0028 0.0025 0.0023 0.0022 0.0020 0.0019 0.0018 0.0017 0.0016 0.0028 0.0025 0.0023 0.0022 0.0020 0.0019 0.0018 0.0017 0.0016 0.0015 0.0025 0.0023 0.0022 0.0020 0.0019 0.0018 0.0017 0.0016 0.0015 0.0014 0.0023 0.0022 0.0020 0.0019 0.0018 0.0017 0.0016 0.0015 0.0014 0.0014

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[Walter Roberson]

You can use matlabFunction() on fun, but the result would be a function handle that returns a 10 x 10 array, which is something that is incompatible with integral2(). integral2() passes arrays of coefficients to the given function, and the given function must return an array the same size as the arrays that were passed in.