CODEWITHSUNDEEP
matlabmatrix
Jonatas Eduardo
Jonatas Eduardo

Reputation: 685

how to multiply each vector in a list by its transpose at once?

I have a list of vectors given by a matrix where each line is a vector x_i. Now i want to make the following matrix

M = sum_i c_i*(x_i*x_i' - E(x_i*x_i'))

where c_i is a number and E(x_i*x_i') = sum_i x_i*x_i'/n , n is the number of lines.

One poor code for this is 

x = rand(50,10000);
c = rand(10000,1);
M = zeros(50,50);
Y = zeros(50,50);
for i=1:size(x,2)
    M = M + x(:,i)*x(:,i)';
end;
M = M/size(x,2);
for i=1:size(x,2)
    Y = Y + c(i)*(x(:,i)*x(:,i)' - M);
end;

Upvotes: 1

Views: 1069

Answers (2)

Memming
Memming

Reputation: 1739

Your question is incomplete, but here's something that matches your code:

M = x*x' / size(x, 2); % first for loop
Y = x*diag(c)*x' - sum(c) * M;

Note that your c is probably wrong. Use c = rand(10000,1); to get a vector.

Upvotes: 1

Andrey Rubshtein
Andrey Rubshtein

Reputation: 20915

Since the multiplication by transpose is nothing but a sum of multiplications, the answer is:

s = sum(x.*x,2)

Upvotes: 0

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