integral() doesn't accept scalar function as input

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Julian Groß-Funk
评论： Star Strider 2023-7-5
Ran in:
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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采纳的回答

Star Strider
Star Strider 2023-7-5
Ran in:
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
.

更多回答（1 个）

Jayant
Jayant 2023-7-5
Ran in:
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
Jayant 2023-7-5
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
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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