`zgesv:`procedureThe routines compute the solution to a system of linear equations ''A

- X = B
*, where*A*is an N-by-N matrix and*X*and*B*are N-by-NRHS matrices. Optional arguments*LDA*and*LDB*are the leading dimensions of arrays*A*and*B*, respectively. LU decomposition with partial pivoting and row interchanges is used to factor*A*as*A = P * L * U*, where*P*is a permutation matrix,*L*is unit lower triangular, and*U*is upper triangular. The factored form of*A'' is then used to solve the system. The return values are: - a matrix containing the factors
*L*and*U*from the factorization*A = P*L*U*; - the N-by-NRHS solution matrix
*X* - a vector with pivot indices: for 1 <= i <= min(M,N), row
*i*of the matrix*A*was interchanged with row pivot(*i*)

- X = B