Shortening run time to compute function

Hello, I am pretty new to MATLAB. I have created the following function which I am using to generate any n x n matrix. I need to generate a 256 x 256 matrix that I will then multiply by another 256 x 256 matrix.

When I set n to be equal to 256 to generate said matrix, the code runs on and on.

Is there a rounding or some sort of simplification I can make to the function?

function matrix=function1(n)
matrix=zeros(n);
for i=1:n
    for j=1:n
     
        matrix(i,j)=sqrt(2/n)*sin((pi*(i-(1/2))*(j-(1/2)))/n)
       
    end
end
end

I ultimately will apply the above function in this string of code.

Y_int=imread('Cat Photo 2.jpg');%Display photo 2
Y_double=double(Y_int); %Covert to double
Y_gray=0.3*Y_double(:,:,1)+0.3*Y_double(:,:,2)+0.3*Y_double(:,:,3);
colormap('gray');
DST=function1(256);
DSTMatrix=DST*Y_gray;
p=0.2
%when p=0, no data is saved
%when p=1 all data is saved
for i=1:n
    for j=1:n
        if i+j>p*2*n
            DSTMatrix(i,j)=0;
        end
    end
end
DSTMatrix2=DSTMatrix*DST
imagesc(uint8(DSTMatrix2));

If someone could please help that would be great!

Thanks

Answer 1

[KSSV]

This function:

function matrix=function1(n)
matrix=zeros(n);
for i=1:n
    for j=1:n     
        matrix(i,j)=sqrt(2/n)*sin((pi*(i-(1/2))*(j-(1/2)))/n)       
    end
end
end

You are printing the output for everytime on the screen. This will eat away your time. That function can be completely replaced with:

function matrix=function1(n)
[i,j] = meshgrid(1:n,1:n) ; 
matrix = sqrt(2/n)*sin((pi*(i-(1/2)).*(j-(1/2)))/n) ; 
end

The below lines of code:

for i=1:n
    for j=1:n
        if i+j>p*2*n
            DSTMatrix(i,j)=0;
        end
    end
end

can be repalced with:

[i,j] = meshgrid(1:n,1:n) ; 
idx = (i+j) > p*2*n ; 
DSTMatrix(idx) = 0 ; 

[Kyle Barber]

Thanks for the response. I played with the code a little more and was able to get it to work. Mods please close. Thanks!