speed up 'for' loops

Hi,

How can I speed up following 'for' loops? Help me please.

 P=200;
N=40000000;
y(1:P)=3;
% a: P X 1 matrix (vector)
% Z: P X 1 matrix (vector)
% x: N X 1 matrix (vector)
%%%%%Loops
y(P+1:N)=0;
for i=P+1:N 
    for j=1:P
        y(i)=y(i)-a(j)*x(i-j);
    end
end
for i=1:N 
    for j=1:P 
        f(i,j)=Z(j)^(i-1); 
    end 
end

Thanks in advance.

Answer 1

[Jan]

P = 200;
N = 40000000;
a = rand(P, 1);
Z = rand(P, 1);
x = rand(N, 1);

y(P+1:N) = 0;  % This one at first! -> pre-allocation
y(1:P)   = 3;
at       = transpose(a);
for i=P+1:N 
  y(i) = y(i) - at * x(i-1:-1:i-P);  % Dot-product of vectors => SUM
end

f = ones(P, N);
for i = 2:N 
  f(:, i) = f(:, i - 1) .* Z; 
end
f = transpose(f);

[Azzi Abdelmalek]

Simon change Zt to Z (error typing)

[Jan]

Thanks, Azzi, this is fixed now.

[Coo Boo]

Thanks, but x(i-1:i-P) is an empty matrix, because i-1>i-P.

[Jan]

Thanks, Coo Boo, fixed now. Unfortunately I cannot test it, because I do not have a Matlab version installed on my current computer. But you are cordially invited to debug it.

[Coo Boo]

Thank you very much

Answer 2

[Azzi Abdelmalek]

for the second loop

c=repmat(Z',N,1)
f=bsxfun(@power,c,[0:N-1]')

[Jan]

The power operation is surprisingly expensive. See "type vander".

[Azzi Abdelmalek]

you are right, your code is faster for N=400000

Elapsed time is 0.489050 seconds.
Elapsed time is 0.757052 seconds. my code

[Coo Boo]

Thank you very much

[Matt Fig]

No need for REPMAT or [].

f = bsxfun(@power,Z.',(0:N-1).');