Computes the solution of a linear equation with Gauss and row pivoting.
x = linalg_gausspivotal ( A , b , verbose )
a n-by-n matrix of doubles
a n-by-1 matrix of doubles
a 1-by-1 matrix of boolean, set to true to display intermediate messages
a n-by-1 matrix of doubles
Returns the solution of Ax = b with a Gauss elimination and row exchanges. This algorithm might be sensitive to inaccuracies if A near singular. There is no solution is A is singular. If A is not ill-conditionned, the algorithm is accurate. Uses an effective algorithm with vectorization. TODO : add b at the end of A and performs the forward-backward loop in the same loop as factorization.