MATLAB: Construct Power of Matrix without for loop

MATLABpower of matrix

Hi, everyone:

Suppose I have a 2 by 2 matrix A, if I want construct a larger matrix B that is defined as:

B=[A, A^2, A^3, A^4, … A^N];

is it possible to do it without for loop?

Thanks

Best Answer

Example

A=magic(2);
N=3;
B=cell2mat(arrayfun(@(x) A^x,1:N,'un',0))

Related Solutions

MATLAB: Construct product of matrices without for loop

I assume a FOR loop is the best way to go. Perhaps the slow speed is caused by a forgotten pre-allocation or if you calculate the power operation by the expensive ^ operator instead of a cumulative multiplication.

C = zeros(2, 2, n+1, N-n);
for i2 = 1:N-n
  AA = A(:, :, i2);
  PA = AA ^ (N-n-1);
  for i1 = 1:n+1
    PA = PA * AA;
    C(:, :, i1, i2) = PA;
  end
end

But if N is large and n is small, the power operation will be the bottleneck again. Then try these functions written by James: FEX: MTimesX or FEX: MPower2.

Another approach could be to avoid calling the powerful BLAS function for the matrix multiplication for a tiny 2x2 matrix:

function MatrixMultTest
x = rand(2, 2);
y = rand(2, 2)
tic; for k = 1:1e6; v = mult1(x,y); end, toc
tic; for k = 1:1e6; v = mult1(x,y); end, toc
function v = mult1(x, y)
v = x * y
function v = mult2(x, y)
v(2,2) = x(2,1)*y(1,2) + x(2,2)*y(2,2);  % Implicit pre-allocation
v(1,1) = x(1,1)*y(1,1) + x(1,2)*y(2,1);
v(1,2) = x(1,1)*y(1,2) + x(1,2)*y(2,2);
v(2,1) = x(2,1)*y(1,1) + x(2,2)*y(2,1);

Well, it seems like the manual product is 10% slower under R2009a. But it was worth to try.

MATLAB: Repeat element of a vector n times without loop.

 n=3 ; x=(1:3)' % example
 r=repmat(x,1,n)';
 r=r(:)'

Best Answer

Related Solutions

MATLAB: Construct product of matrices without for loop

MATLAB: Repeat element of a vector n times without loop.

Related Question