MultiSolve 3x3

Vectorized solve of multiple 3x3 linear systems

xx = multisolve3x3(AA,b)

Highly optimized solution of multiple 3x3 linear systems.

The m 3-by-3-coefficient matrices can be given in 2 forms:
(1) The argument matrix AA is 3m x 3 (i.e., the k-th linear system occupies rows 3k-2:3k).
(2) The argument AA is an 3x3xm array. (the k-th linear system is AA(:,:,k) ).

Similarly, the result vectors b can be given in 2 forms (independent of AA):
(1) a 3m x 1 vector, where the k-th result is in rows 3k-2:3k,
(2) a 3xm matrix, whose k-th column contains the k-th result.

Either way, the solution xx is given in size identical to that of b.

Example:

m = 10 ; % system num
AA = rand(3,3,m);
bb = rand(3,m);

xx = multisolve3x3(AA,bb);

%test results:
for jj=1:m
max(abs( AA(:,:,jj) * xx(:,jj) - bb(:,jj) ))
end