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Hello dear MATLAB community,

again I have a question to improve the efficiency of my code, by getting rid of the use of loops. Since my programming skills come from using LabVIEW, I often have a harder time using matrix operations instead of loops.

Let me first explain you what I want to do. I have a 3D data matrix "A(i,j,k)", that I want to multiply together with a sensitivity matrix "S" (values stay equal) to get forces and do a conversion from polar to cartesian. I want to do this calculation/conversion for every sub-matrix "A(:,:,k)" to calculate the single forces in the cartesian system. Afterwards I want to calculate the total resulting forces of all sub-matrices and convert them back in a polar system.

The matrices and it's dimension can differ:

- S_r & S_phi are not always square matrices
- Row nr. of A is always equal to col nr. of S_r/S_phi
- Col nr. of A is always equal to length of phipoints

% Input data matrix (3D): A(i,j,k)

A(:,:,1) = [-0.0468 -0.0652 0.2746 0.5272 0.2373 -0.2142 -0.5973 -0.1169

0.0633 0.6673 0.6416 0.3491 -0.0652 -0.0025 -0.8464 -0.7607

-0.0026 0.0000 -0.0373 -0.4378 -0.1612 0.2293 0.2458 0.1656

0.3124 0.2472 0.0048 -0.5034 -0.5051 -0.0434 0.1734 0.3376

-0.0815 -0.4423 0.0308 0.1411 0.1260 0.1881 0.0696 -0.0328];

A(:,:,2) = [-0.0468 -0.0652 0.2746 0.5272 0.2373 -0.2142 -0.5973 -0.1169

0.0633 0.6673 0.6416 0.3491 -0.0652 -0.0025 -0.8464 -0.7607

-0.0026 0.0000 -0.0373 -0.4378 -0.1612 0.2293 0.2458 0.1656

0.0696 0.1881 0.1260 0.1411 0.0308 -0.4423 -0.0815 -0.0328

0.1734 -0.0434 -0.5051 -0.5034 0.0048 0.2472 0.3124 0.3376];

A(:,:,3) = [-0.0468 -0.0652 0.2746 0.5272 0.2373 -0.2142 -0.5973 -0.1169

0.0633 0.6673 0.6416 0.3491 -0.0652 -0.0025 -0.8464 -0.7607

0.1734 -0.0434 -0.5051 -0.5034 0.0048 0.2472 0.3124 0.3376

0.2458 0.2293 -0.1612 -0.4378 -0.0373 0.0000 -0.0026 0.1656

-0.0815 -0.4423 0.0308 0.1411 0.1260 0.1881 0.0696 -0.0328];

% points of all to be calculated segments (index j)

phipoints = 0:2*pi/8:2*pi-2*pi/8;

% Sensitivity matrix: amplitude and phase

S_r = [ 0.0317 0.0378 0.0344 0.0394 0.0333;...

0.0331 0.0410 0.0380 0.0433 0.0375;...

0.0326 0.0415 0.0388 0.0443 0.0393;...

0.0296 0.0386 0.0360 0.0417 0.0383;...

0.0247 0.0334 0.0307 0.0366 0.0354];

S_phi = [ 0 0 0 0 0;...

0 0 0 0 0;...

0 0 0 0 0;...

0 0 0 0 0;...

0 0 0 0 0];

% To be calculate equation for every single sub-matrix A(:,:,k); only for

% documentation; code must be executed using loops

% pol2cart(S_phi+phipoints,S_r*A(:,:,k))

I can calculate this using loops, but my problem is that I have to do this calculation for many sub-matrices (dimension "k" can be up to millions). My current version (see below) takes way to much time, so I'm looking for an alternative way.

%% Current calculation using loop

% Calculation: single forces in cartesian system (X & Y)

for k = 1:size(A,3)

for i = 1:size(A,1)

[Fx(:,:,i,k),Fy(:,:,i,k)] = pol2cart(S_phi(:,i)+phipoints,S_r(:,i)*A(i,:,k));

end

end

% Calculation: resulting forces in X & Y

% - 1st: sum of single forces from all rows (2nd index) of Fx/Fy

% - 2nd: sum of forces of 3rd index of Fx/Fy

Fx_res = sum(sum(Fx,2),3);

Fy_res = sum(sum(Fy,2),3);

% Calculation: total resulting force

[F_res_phi,F_res] = cart2pol(Fx_res,Fy_res); % Conversion: cartesian to polar

Thanks in advance and best regards,

Pascal

J. Alex Lee
on 18 Jun 2021

It's not even clear what "S_phi + phipoints" is supposed to mean whenever S_phi [=] 5xL where L~=5.

Pascal Wielsch
on 18 Jun 2021

Matt J
on 18 Jun 2021

Note that in recent Matlab, the repmat's should really not be needed:

S_phi_ForCalc = reshape(S_phi,5,1,I);

S_r_ForCalc = reshape(S_r,5,1,I);

J. Alex Lee
on 17 Jun 2021

I found this: pagemtimes()

s = rand(5,5);

x = rand(5,8,100000);

tic

y = pagemtimes(s,x);

toc

tic

z = nan(size(x));

for k = 1:size(x,3)

z(:,:,k) = s*x(:,:,k);

end

toc

err = sum(abs(y-z),'all')

Matt J
on 17 Jun 2021

Edited: Matt J
on 17 Jun 2021

Assuming S_r will always be square,

B=reshape( S_r*A(:,:), size(A)); %B(:,:,k)=S_r*A(:,:,k)

J. Alex Lee
on 18 Jun 2021

You would just need to re-figure the size, but this should still work, it's neat!

clc;

clear;

L = 6;

N = 100000;

S_r = rand(5,L);

A = rand(L,8,N);

tic

x = pagemtimes(S_r,A);

toc

tic

y = reshape(S_r*A(:,:),[5,8,N]);

toc

tic

z = nan(5,8,N);

for k = 1:size(A,3)

z(:,:,k) = S_r*A(:,:,k);

end

toc

err = sum(abs(x-y),'all')

err = sum(abs(y-z),'all')

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