Vectorization of Operation inside Matrix

2018 12 18
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回答已采纳
更新时间：2018 12 18
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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!

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Guillaume
Guillaume 2018-12-18

1 个投票

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)]

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Laurel Castillo
Laurel Castillo 2018-12-18
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
Guillaume 2018-12-18
Is your multiply a matrix multiplication or an element-wise multiplication?
Guillaume
Guillaume 2018-12-18
编辑：Guillaume 2018-12-18
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

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