How to reduce the computation time of for loop?

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Dear Experts,
I have a query regarding my code below, it takes long time to process the loop, could you please guide how to reduce the processing time.
img = zeros(M,N);
for ii = 3264:64:86610 % sorted for one complete rotation
dR = sqrt((R0*cos(alpha*pi/180).*cos(Turntable_angle(ii)*pi/180) + x_mat).^2 + (R0*cos(alpha*pi/180).*sin(Turntable_angle(ii)*pi/180) + y_mat).^2 + (z_mat - R0*sin(alpha*pi/180)).^2) - R0;
for jj = 1:length(Freq_vec)
S1 = data_matrix; % data
Sc_win = S1.*repmat(hanning(size(S1,2)).',size(S1,1),1); % apply window
S = ifftshift(ifft(Sc_win,Nfft,2),2);
img = img + S(ii,jj).*exp(1j*4*pi*Freq_vec(jj)/c0*dR);
end
end
I look forward to receive your valueable suggestions, thank you so much!

Accepted Answer

Johan
Johan on 8 Jul 2022
Edited: Johan on 8 Jul 2022
You can likely vectorize your code:
i_loop = 3264:64:86610 ;
M = size(i_loop,1);
N = 25;
Freq_vec = rand(N,1);
Turntable_angle = rand(i_loop(end),1);
R0 = 1;
x_mat = 1;
y_mat = 1;
z_mat = 1;
alpha = 1;
c0 = 1;
S1 = rand(i_loop(end),N); % data
% You did not share these function but I assume S is the same size as S1
% Sc_win = S1.*repmat(hanning(size(S1,2)).',size(S1,1),1); % apply window
% S = ifftshift(ifft(Sc_win,Nfft,2),2);
tic
dR = sqrt((R0*cos(alpha*pi/180).*cos(Turntable_angle(i_loop)*pi/180) + x_mat).^2 +...
(R0*cos(alpha*pi/180).*sin(Turntable_angle(i_loop)*pi/180) + y_mat).^2 +...
(z_mat - R0*sin(alpha*pi/180)).^2) - R0;
imgvec = S1(i_loop,:).*exp(1j*4*pi*dR*Freq_vec'/c0);
toc
Elapsed time is 0.008215 seconds.
imgloop = zeros(size(i_loop,2),N);
tic
for i_row = 3264:64:i_loop(end) % sorted for one complete rotation
dR = sqrt((R0*cos(alpha*pi/180).*cos(Turntable_angle(i_row)*pi/180) + x_mat).^2 + (R0*cos(alpha*pi/180).*sin(Turntable_angle(i_row)*pi/180) + y_mat).^2 + (z_mat - R0*sin(alpha*pi/180)).^2) - R0;
for i_col = 1:length(Freq_vec)
%This make all value of imgloop the same, I don't think this is
%intended ?
imgloop = imgloop + S1(i_row,i_col)*exp(1j*4*pi*Freq_vec(i_col)/c0*dR);
end
end
toc
Elapsed time is 0.665726 seconds.
unique(imgloop)
ans = -7.4497e+02 + 3.1083e+03i
unique(imgvec)
ans =
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  1 Comment
Amjad Iqbal
Amjad Iqbal on 8 Jul 2022
Thank you for your quick code, I need little integration to your code, since x_mat, y_mat, z_mat are 2D matrices given below,
x_vect = -6:0.02:6;
y_vect = -6:0.02:6;
z_vect = 0;
%x,y,z grid
[x_mat,y_mat, z_mat] = meshgrid(x_vect,y_vect, z_vect);
freq_vec = rand(235,1);
R0 = 135;
alpha = 3;
S1 = rand(88821,235);
Ndeg = 86610-3263;
Turntable_angle = linspace(-180,180, Ndeg);
could you please check with 2D x_mat, y_mat, z_mat?

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More Answers (1)

Jon
Jon on 8 Jul 2022
With the code you show, it appears that the values of S1, Sc_win, and S do not change as a function of any of the loop variables. If this is really the case (and not just due to some simplification in how you presented your example), then these variables can just be computed once before entering the first loop.
So
img = zeros(M,N);
% the following three lines were moved out of the loop as they do not
% change
S1 = data_matrix; % data
Sc_win = S1.*repmat(hanning(size(S1,2)).',size(S1,1),1); % apply window
S = ifftshift(ifft(Sc_win,Nfft,2),2);
for ii = 3264:64:86610 % sorted for one complete rotation
dR = sqrt((R0*cos(alpha*pi/180).*cos(Turntable_angle(ii)*pi/180) + x_mat).^2 + (R0*cos(alpha*pi/180).*sin(Turntable_angle(ii)*pi/180) + y_mat).^2 + (z_mat - R0*sin(alpha*pi/180)).^2) - R0;
for jj = 1:length(Freq_vec)
img = img + S(ii,jj).*exp(1j*4*pi*Freq_vec(jj)/c0*dR);
end
end
  4 Comments
Amjad Iqbal
Amjad Iqbal on 8 Jul 2022
Edited: Amjad Iqbal on 8 Jul 2022
one more thing to integrate for this line:
since x_mat, y_mat, z_mat are 2D matrices
dR = sqrt((R0*cA.*cTA + x_mat).^2 + (R0*cA.*sTA + y_mat).^2 + (z_mat - R0*sA).^2) - R0;
x_vect = -6:0.05:6;
y_vect = -6:0.05:6;
z_vect = 0;
% x,y,z grid
[x_mat,y_mat, z_mat] = meshgrid(x_vect,y_vect, z_vect);
I believe this will be much faster, however, still facing an issue >> Arrays have incompatible sizes for this operation

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