integral() doesn't accept scalar function as input

Psi = @(x) [1 x]

Psi = function_handle with value:
    @(x)[1,x]

fun = @(x) abs(Psi(x)*Psi(x)')

fun = function_handle with value:
    @(x)abs(Psi(x)*Psi(x)')

integral(fun,0,1)

Error using integralCalc/finalInputChecks
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 integralCalc/iterateScalarValued (line 315)
finalInputChecks(x,fx);

Error in integralCalc/vadapt (line 132)
[q,errbnd] = iterateScalarValued(u,tinterval,pathlen);

Error in integralCalc (line 75)
[q,errbnd] = vadapt(@AtoBInvTransform,interval);

Error in integral (line 87)
Q = integralCalc(fun,a,b,opstruct);

It is necessary for me to numerically integrate over a function (fun), that gets a vector-function (Psi) as input. fun is NOT array-valued. Why doesn't this work?

Answer 1

[Star Strider]

It works correctly with the 'ArrayValued' name-value pair —

Psi = @(x) [1 x]

Psi = function_handle with value:
    @(x)[1,x]

fun = @(x) abs(Psi(x)*Psi(x)')

fun = function_handle with value:
    @(x)abs(Psi(x)*Psi(x)')

integral(fun,0,1, 'ArrayValued',1)

ans = 1.3333

.

[Julian Groß-Funk]

Thank you very much!

[Star Strider]

As always, my pleasure!

Answer 2

[Jayant]

The error you encountered occurs because the function fun you defined is not compatible with the integral function in MATLAB. The integral function expects the integrand function to have a scalar output for each input value, but in your case, the fun function returns a vector output.

To resolve this issue, you can modify the fun function to return a scalar value by taking the norm (magnitude) of the vector output of Psi(x):

Psi = @(x) [1 x];
fun = @(x) norm(Psi(x))^2;
integral(fun, 0, 1)

Error using integralCalc/finalInputChecks
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 integralCalc/iterateScalarValued (line 315)
finalInputChecks(x,fx);

Error in integralCalc/vadapt (line 132)
[q,errbnd] = iterateScalarValued(u,tinterval,pathlen);

Error in integralCalc (line 75)
[q,errbnd] = vadapt(@AtoBInvTransform,interval);

Error in integral (line 87)
Q = integralCalc(fun,a,b,opstruct);

Please note that I used norm(Psi(x))^2 instead of abs(Psi(x)*Psi(x)') to calculate the squared norm, as it is more efficient and mathematically equivalent.

[Julian Groß-Funk]

My fun-function does not return a vector output.

Your code produces the same error:

Psi = @(x) [1 x];
fun = @(x) norm(Psi(x))^2;
integral(fun, 0, 1)

Error using integralCalc/finalInputChecks
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 integralCalc/iterateScalarValued (line 315)
finalInputChecks(x,fx);

Error in integralCalc/vadapt (line 132)
[q,errbnd] = iterateScalarValued(u,tinterval,pathlen);

Error in integralCalc (line 75)
[q,errbnd] = vadapt(@AtoBInvTransform,interval);

Error in integral (line 87)
Q = integralCalc(fun,a,b,opstruct);

[Jayant]

I misunderstood your previous statement. To resolve the error, you can modify the fun function to handle array-valued inputs by setting the 'ArrayValued' option to true in the integral function. This will inform MATLAB that the integrand function is array-valued. Below is the modified code:

Psi = @(x) [1 x];
fun = @(x) abs(Psi(x)*Psi(x)');
integral(fun, 0, 1, 'ArrayValued', true)

By including the 'ArrayValued', true option in the integral function, the error related to array-valued inputs should be resolved, and the integration should proceed correctly.

Please try the updated code & let me know if you face any further issues. Apologies for the confusion.

[Julian Groß-Funk]

Great, thank you! I even randomly tried the ArrayValued-option before posting here, but got a wrong result due to another error that was still in my script back then.