integral() doesn't accept scalar function as input

Question

Julian Groß-Funk 2023-7-5

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1992048-integral-doesn-t-accept-scalar-function-as-input

评论： Star Strider 2023-7-5

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?

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Answer 1

Star Strider 2023-7-5

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1992048-integral-doesn-t-accept-scalar-function-as-input#answer_1267598

在 MATLAB Online 中打开

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

.

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Julian Groß-Funk 2023-7-5

Thank you very much!

Star Strider 2023-7-5

As always, my pleasure!

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Answer 2

Jayant 2023-7-5

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1992048-integral-doesn-t-accept-scalar-function-as-input#answer_1267563

在 MATLAB Online 中打开

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.

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Jayant 2023-7-5

在 MATLAB Online 中打开

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 2023-7-5

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.

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