How to reduce the computation time for adding 3D-array?

Hi, I am trying to add multiple 3D-arrays to a bigger 3D-array at a specific index (x,y,z)

Below is the code, and it does work and compute the answer but it seems very ineffecient.

In this example, i only have 4 sets of coordiantes (x,y,z) but in real code, i have more than 1e6 sets of points.

It takes very long to compute the result with that many points.

Is there any way to reduce the computation time?

Thank you in advance

Regards

J

Big=zeros(500,500,500); %%%% Bigger Array
Small=rand(250,250,250);
x=[245; 220; 256; 270];
y=[245; 220; 256; 270];
z=[245; 220; 256; 270];
     for n = 1 : length(x)
        x_cord=x(n)-length(Small)/2; 
        y_cord=y(n)-length(Small)/2;
        z_cord=z(n)-length(Small)/2;

        x_end= x_cord + length(Small) -1 ;
        y_end= y_cord + length(Small) -1;
        z_end=z_cord + length(Small) -1;

            if x_end <= length(Big)    
                Big(x_cord:x_end, y_cord:y_end,z_cord:z_end)=Big(x_cord:x_end, y_cord:y_end,z_cord:z_end)+Small();
            end 
         
     end

[Walter Roberson]

could also be done with accumarray, but I am not sure that would be faster considering the time to generate the coordinate matrices... though I did just think of a shortcut for that.

[jae lee]

Hi Walter. Thank you for your comment.

What would be the coordinate matrices??

Does it mean x,y,z?

Thank you

Answer 1

[Bruno Luong]

You can reformulate the loop as convolution of

A = accumarray([x(:) y(:) z(:)]-length(Small)/2,1,[500 500 500])

and

B = flip(flip(flip(Small,1),2),3)

(I left out the detail of overflowed for simplicity)

You might look at convn function. The problem I see is that A is sparse (1/125 in density) and might not be efficient as for loop.

You also might try this FEX to see if you can exploit the sparsity

https://www.mathworks.com/matlabcentral/fileexchange/41310-sparse-matrix-convolution

Or this one using different method of compute convolution

https://www.mathworks.com/matlabcentral/fileexchange/24504-fft-based-convolution

[jae lee]

Thank you for your help.

Why do i need to perform the flip function for matrix B?

[jae lee]

I also don't understand how accumarray function can add "Small" matrix values to a "Big" matrix at a specific points.

[Walter Roberson]

Convolution integral is defined in terms of integral of f(t)*g(x-t). The discrete analog to the x-t involves flipping an array. Where time needs to sort of go backwards for one of the functions in integration, you need to progress backwards in a matrix for the discrete version.

[jae lee]

I tried the above method but it went into the infinite loop.

A = accumarray([x(:) y(:) z(:)]-length(Small)/2,1,[500 500 500])

B = flip(flip(flip(Small,1),2),3)

C=convn(A,B);

[Bruno Luong]

You might try the alternative convolution implementations in the links I post above.

As I said above, the alternative ways I have proposed might not be fater than your for-loop.

Answer 2

[Amrtanshu Raj]

Hi,

You can use the parfor loop to use parallel processing and get higher computation speeds. However you will have to modify your for loop to be used for parfor loop.

Hope this helps !!