Vectorization of Operation inside Matrix

DH is a 7*5 double.

The values in each row of DH are used for calculation in each loop.

To speed up, I've used pre-location. But can it be faster with vectorization?

DH = psm_m.DH;

n = size(DH,1);
T_i_All = zeros(4,4,n);

for i = 1:n
T_i_All (:,:,i)= [cos(DH(i,5)) -sin(DH(i,5)) 0 DH(i,3);
    (sin(DH(i,5)))*(cos(DH(i,2))) (cos(DH(i,5)))*(cos(DH(i,2))) -sin(DH(i,2)) -(sin(DH(i,2)))*DH(i,4);
    (sin(DH(i,5)))*(sin(DH(i,2))) (cos(DH(i,5)))*(sin(DH(i,2))) cos(DH(i,2)) (cos(DH(i,2)))*DH(i,4);
    0 0 0 1];
end

I followed the MATLAB example

t = 0:.01:10; %example
y = sin(t); %example

But it doesn't work.

i=1:n;
T_i_All (:,:,i)= [cos(DH(i,5)) -sin(DH(i,5)) 0 DH(i,3);
    (sin(DH(i,5)))*(cos(DH(i,2))) (cos(DH(i,5)))*(cos(DH(i,2))) -sin(DH(i,2)) -(sin(DH(i,2)))*DH(i,4);
    (sin(DH(i,5)))*(sin(DH(i,2))) (cos(DH(i,5)))*(sin(DH(i,2))) cos(DH(i,2)) (cos(DH(i,2)))*DH(i,4);
    0 0 0 1];

(Error using horzcat

Dimensions of matrices being concatenated are not consistent.)

Any help? Thanks!

Answer 1

[Guillaume]

First, permute DH so that the rows are in the 3rd dimension as in your output. Then you can vectorise your calculation:

DH = permute(psm_m.DH, [3 2 1]);
n = size(DH, 3);
T_i_All = [cos(DH(1, 5, :)), -sin(DH(1, 5, :)), repmat(0, 1, 1, n), DH(1, 3, :);
           sin(DH(1, 5, :)).*cos(DH(1, 2, :)), cos(DH(1, 5, :)).*cos(DH(1, 2, :)), -sin(DH(1, 2, :)), -sin(DH(1, 2, :)).*DH(1, 4, :);
           sin(DH(1, 5, :)).*sin(DH(1, 2, :)), cos(DH(1, 5, :)).*sin(DH(1, 2, :)), cos(DH(1, 2, :)), cos(DH(1, 2, :)).*DH(1, 4, :);
           repmat([0 0 0 1], 1, 1, n)]

[madhan ravi]

+1 amazing!

[Laurel Castillo]

agree, thanks so much!! First time to see permute and repmat function!

now T_i_All is 4*4*7, can we also obtain [T_i_All(:,:,1); T_i_All(:,:,:1)*T_i_All(:,:,:2); T_i_All(:,:,:1)*T_i_All(:,:,:2)*T_i_All(:,:,:3) ......]?

[Guillaume]

Is your multiply a matrix multiplication or an element-wise multiplication?

[Laurel Castillo]

matrix multiplication!

[Guillaume]

I don't see a way to vectorise that. You'll have to use a loop:

composition = T_i_all;
for page = 2:size(composition, 3)
    composition(:, :, page) = composition(:, :, page) * composition(:, :, page-1);
end