How to compile large matrix

Hello!

I am trying compile a matrix with one row and a large number of columns (matrix A). I have a problem with compiling matrix A, which contains only three different values, as an example

A = [a,b,c,a,b,c,a,b,c,...] 

and so on. I tried with repmat command, but because there is a lot of data (size of matrix A is 1x600.000 or with even more columns), Matlab needs to a lot of time to calculate.

I need this matrix in for loop to multiply it with another matrix (matrix B), which has a large number or rows and only 4 columns. I have compile matrix B in for loop.

Below there is a matlab code I have use.

Thank you in advance for all the answers. Tamara

%data = matrix with 3 columns and a lot of rows (the number of rows varies according to the number of scanned points, number of columns is always the same, xyz coordinate)
%plane_par = matrix with 1 column and 4 rows (size is always the same, they are plane parameters)
size_data = size(data); 
size_repmat = size_data(1,1);
Adel = [plane_par(1,1), plane_par(2,1), plane_par(3,1)];
A = repmat(Adel,1,size_repmat);
for i = 1:size(data,1)
   B = [data(i,1), data(i,2), data(i,3), 1];
   f = [-plane_par(1,1)*data(i,1)-plane_par(2,1)*data(i,2)-plane_par(3,1)*data(i,3)+plane_par(4,1)];
   delta = pinv(B'*pinv(A*A')*B)*(B'*pinv(A*A')*f);
end

[per isakson]

"lot of time" how much is that?

>> tic, M = repmat( [1,2,3], 1, 6e5 ); toc
Elapsed time is 0.003957 seconds.
>> tic, M = repmat( {'a','b','c'}, 1, 6e5 ); toc
Elapsed time is 0.034483 seconds.

btw: do a, b, c stand for numbers?

[Tamara Znidarsic]

It means even half an hour. I think that the problem is when Matlab must multiply matrix A and B, where matrix A has around 600.000 columns. Yes, parameters a,b,c are numbers.

[per isakson]

See Profile to Improve Performance , don't guess.

Note that delta is overwritten inside the loop.

Break out pinv(A*A') from the expression, pinv(B'*pinv(A*A')*B)*(B'*pinv(A*A')*f) and calculate it outside the loop. A doesn't change in the loop.

Answer 1

[Andrei Bobrov]

for your case:

s = size(data,1);
B = [data,ones(s,1)]';
BB = permute(B,[3,1,2]).*permute(B,[1,3,2]);
f = B.*(B'*(plane_par.*[-1;-1;-1;1]))';
delta = zeros(4,s);
for ii = 1:s
    delta(:,ii) = pinv(BB(:,:,ii))*f(:,ii);
end