Accelerating MATLAB Performance

278 Accelerating MATLAB

®

Performance

for i = 1 : N

for j = 1 : T

Trials(i,j) = Trials(i,j) - mean2(Trials);

end

end

As user gevang explained,

856

by observing the pattern created by the recursive subtrac-

tion of the mean, we can infer the following recursive relationship:

m(k) = m(k-1) - m(k-1)/n % n=numel(Trials)=N*T

= m(k-1) * ((n-1)/n)

= m(1) * ((n-1)/n)^(k-1)

where m(1) is the average of the original matrix. The subtraction is applied iteratively, for

each element of the input matrix: the rst element subtracts m(1), the second subtracts m(2),

and so on. This leads to the following optimized (vectorized) form:

n = numel(Trials);

Trials = Trials - mean2(Trials)*reshape(((n-1)/n).^(0:n-1), T, N)';

5.7.12 Vectorizing Structure ...