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Vectorize Matrix Formation & Multiplication

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How can I vectorize the following code
clear;clc
t = 1:10;
v = rand(10,3);
a = rand(10,1);
m = 6:15;
n = 6:15;
M = 1:20;
N = 1:20;
P = ones(20,20);
V = zeros(size(v))';
D = zeros(size(m))';
for i = 1:length(t)
B = [1,0,0;0,cos(a(i)),sin(a(i));0,-sin(a(i)),cos(a(i))];
V(:,i) = B*v(i,:).';
D(i,1) = interp2(M,N,P,m(i),n(i));
end
V = V.'; % (size has to be same as v)
how can I rewrite this code without using loops?

Accepted Answer

Matt J
Matt J on 17 Nov 2022
Edited: Matt J on 17 Nov 2022
N=length(t);
a=reshape(a,1,1,N);
B=zeros(3,3,N) ;
B(1,1,:)=1;
B(2:3,2:3,:)=[cos(a), sin(a); -sin(a),cos(a)];
V = pagemtimes(B,reshape(v',2,1,N));
V=reshape(V,2,[]).';
D = interp2(M,N,P,m,n);
  1 Comment
Fawad Farooq Ashraf
Fawad Farooq Ashraf on 17 Nov 2022
thank you. this works indeed
although, a minor correction may be
V = pagemtimes(B,reshape(v',3,1,N));
V=reshape(V,3,[]).';
as v has 3 columns instead of 2

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