Error using integral function with anonymous function

I am trying to use the following code to calculate the values of F(i,j) which is the integral of the anonymous function that I parameterized as a function of T and lambda. I believe I vectorized it correclty. However, the error I get says that the array has incompatible sizes, which I don't understand because the same size of array worked fine for another section of the code.

```C1 = 3.742e8;

C2 = 1.4388e4;

SB = 1.38*10.^-23; %Boltzmann's constant

C1 = 3.742*10^8; % First constant W-micron^4/m^2

C2 = 1.4388*10^4; %Second constant microns-K

T = [300,500,1000,2000,3000,5800]; %Temperature in Kelvins

lambda = 0.1:0.1:30;%wavelength in microns

lengthT = length(T);

length_L = length(lambda);

E = zeros(lengthT,length_L);

E_prime = zeros(lengthT,length_L);

F = zeros(lengthT,length_L);```

```for i = 1:lengthT

for j = 1:length_L

fun = @(T, lambda) C1./(SB.*T.^4*(lambda.^5.*(exp(C2/(lambda.*T))-1)));

F(i,j) = integral(fun(T,lambda),0,length_L);

end

end```

[Dyuman Joshi]

With respect to which variable are you performing the integration?

And as the integrand is not varying w.r.t any loop, you should define it outside the loops.

[Matthew Palermo]

the integral should be varying lambda with wrt T, then take the next step in T, and integrate again wrt the update T

Answer 1

[Karl]

In your function call, you're passing T as a 6-element row vector and lambda as a 300-element row vector. Your function needs T and lambda to have the same size, to be able to evaluate lambda.*T

[Matthew Palermo]

As you can see in the code, my intention is to perform the intergration for lambda with respect to T, update the T value, and then perform the process again for the stated values of T. This is why T is only a 1x6 array vs a 1x300 array like Lambda. Is there a way to vecotrize these taking this into account, or maybe an alternative method to using the anonymous function without having to vecotrize so I can preserve the array sizes?

[Karl]

Sorry that I might not have understood exactly what you're trying to do. If your aim is to evaluate for selected values of T, you could use something like:

C1 = 3.742e8;
C2 = 1.4388e4;
SB = 1.38*10.^-23; %Boltzmann's constant
C1 = 3.742*10^8; % First constant W-micron^4/m^2
C2 = 1.4388*10^4; %Second constant microns-K
T = [300,500,1000,2000,3000,5800]; %Temperature in Kelvins
lengthT = length(T);
lambdaMin = 0; % minimum wavelength in microns
lambdaMax = 30; % maximum wavelength in microns
F = 0;
fun = @(T, lambda) C1./(SB*T^4*(lambda.^5.*(exp(C2./(lambda.*T))-1)));
for i = 1:lengthT
    F(i) = integral(@(x) fun(T(i), x),lambdaMin,lambdaMax);
    fprintf('T=%d; F=%.4e\n', T(i), F(i))
end

T=300; F=3.6569e+15
T=500; F=3.9813e+15
T=1000; F=4.0896e+15
T=2000; F=4.1063e+15
T=3000; F=4.1081e+15
T=5800; F=4.1088e+15

Answer 2

[Star Strider]

Perhjaps using integral2 instead will work here —

C1 = 3.742e8;
C2 = 1.4388e4;
SB = 1.38*10.^-23; %Boltzmann's constant
C1 = 3.742*10^8; % First constant W-micron^4/m^2
C2 = 1.4388*10^4; %Second constant microns-K
T = [300,500,1000,2000,3000,5800]; %Temperature in Kelvins
lambda = 0.1:0.1:30;%wavelength in microns
lengthT = length(T);
length_L = length(lambda);
E = zeros(lengthT,length_L);
E_prime = zeros(lengthT,length_L);
F = zeros(lengthT,length_L);

for i = 1:lengthT
    for j = 1:length_L
        fun = @(T, lambda) C1./(SB.*T.^4.*(lambda.^5.*(exp(C2./(lambda.*T))-1)));
        F(i,j) = integral2(fun,0,T(i),0,lambda(j));
    end
end

figure
surfc(lambda, T, F, 'FaceColor','interp', 'EdgeColor','interp')
colormap(turbo)
xlabel('\lambda')
ylabel('T')
zlabel('F(T,\lambda)')
view(200,30)

EDIT — (10 Dec 2023 at 17:37)

I still don’t understand what the objective is here. The statement ‘my intention is to perform the intergration for lambda with respect to T’ is a bit mystifying, since λ does not appear to be a function of T.

So perhaps this instead —

C1 = 3.742e8;
C2 = 1.4388e4;
SB = 1.38*10.^-23; %Boltzmann's constant
C1 = 3.742*10^8; % First constant W-micron^4/m^2
C2 = 1.4388*10^4; %Second constant microns-K
T = [300,500,1000,2000,3000,5800]; %Temperature in Kelvins
lambda = 0.1:0.1:30;%wavelength in microns
lengthT = length(T);
length_L = length(lambda);
E = zeros(lengthT,length_L);
E_prime = zeros(lengthT,length_L);
F = zeros(lengthT,length_L);

for i = 1:lengthT
    % for j = 1:length_L
        fun = @(T, lambda) C1./(SB.*T.^4.*(lambda.^5.*(exp(C2./(lambda.*T))-1)));
        F(i,:) = integral(@(T)fun(T,lambda),0,T(i), 'ArrayValued',1);
    % end
end

figure
surfc(lambda, T, F, 'FaceColor','interp', 'EdgeColor','interp')
colormap(turbo)
xlabel('\lambda')
ylabel('T')
zlabel('F(T,\lambda)')
view(200,30)

.