Filling a matrix with predefined expression for each element

I have a matrix which I wish to generate, adm the matrix is a function of the parameter alpha. It is a matrix with dimensions dim. I have an analytic expression for each element of the matrix. I wish to know what is the fastest way to populate this matrix in matlab. My code is

```

function [matout]=dipso(dim,alpha)

for kk=0:dim-1

for jj=0:dim-1

matout(kk+1,jj+1)=exp(-(abs(alpha))^2/2)*dispen(kk,jj,alpha);

end

end

function dispenout=dispen(m,n,x)

if m < n

dispenout=sqrt(factorial(m)/factorial(n))*((-conj(x))^(n-m)*laguerreL(m,n-m,abs(x)^2));

elseif m > n

dispenout=sqrt(factorial(n)/factorial(m))*((x)^(m-n)*laguerreL(n,m-n,abs(x)^2));

elseif m == n

dispenout=laguerreL(m,abs(x)^2);

end

```

However this is very slow. Is there a faster way I can populate the elements of my matrix?

Answer 1

[Shivam]

Hi,

I understand you want to populate the matrix with faster execution than your existing code.

You can follow the below suggestions to make execution faster:

1. Preallocate the matrix:

matout = zeros(dim, dim);

2. Calculate exp(-abs(alpha)^2/2) outside the loop:

alpha_squared = abs(alpha)^2;
exp_alpha_squared = exp(-alpha_squared/2);

3. Precalculate factorials outside the loop and reuse them:

factorial_array = factorial(0:dim);

I hope it helps.