How to reduce the computation time of for loop?

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Amjad Iqbal
Amjad Iqbal on 8 Jul 2022
Commented: Amjad Iqbal on 8 Jul 2022
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!

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Accepted Answer

Johan
Johan on 8 Jul 2022
Edited: Johan on 8 Jul 2022
Ran in:
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
@Johan
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
Show 2 older comments
Steven Lord
Steven Lord on 8 Jul 2022
A couple more small optimizations:
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);
Since Turntable_angle doesn't change inside the loop, compute the trig functions on the vector all at once. In addition, since those angles are in degrees use cosd instead of multiplying the angle by the "magic number" pi/180. Do the same for the alpha variable (which I would consider renaming since alpha has a meaning in MATLAB already.)
cTA = cosd(Turntable_angle);
sTA = sind(Turntable_angle);
cA = cosd(alpha);
sA = sind(alpha);
Now dR has no dependency on ii so pull it out of the loop as well.
dR = sqrt((R0*cA.*cTA + x_mat).^2 + (R0*cA.*sTA + y_mat).^2 + (z_mat - R0*sA).^2) - R0;
Looking at the inner loop, since the only dependency on jj in the exp call is to operate on individual elements of Freq_vec, compute that quantity outside the jj loop. In addition, since it doesn't depend on jj, we can pull that outside the outer loop as well.
I suspect you can probably eliminate the loops entirely with a sum call, perhaps combined with reshape and/or permute, but to be certain of that I'd want to see the sizes of each of the variables in your code.
E = exp(4j*pi*Freq_vec./c0.*dR);
for ii = 3264:64:86610 % sorted for one complete rotation
for jj = 1:length(Freq_vec)
img = img + S(ii,jj).*E;
end
end
Amjad Iqbal
Amjad Iqbal on 8 Jul 2022
Edited: Amjad Iqbal on 8 Jul 2022
@Steven Lord
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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