integral() doesn't accept scalar function as input
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Psi = @(x) [1 x]
fun = @(x) abs(Psi(x)*Psi(x)')
integral(fun,0,1)
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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Star Strider
2023-7-5
It works correctly with the 'ArrayValued' name-value pair —
Psi = @(x) [1 x]
fun = @(x) abs(Psi(x)*Psi(x)')
integral(fun,0,1, 'ArrayValued',1)
.
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Jayant
2023-7-5
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)
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
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.
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