CGESV(3)       LAPACK routine of NEC Numeric Library Collection       CGESV(3)



NAME
       CGESV

SYNOPSIS
       SUBROUTINE CGESV (N, NRHS, A, LDA, IPIV, B, LDB, INFO)



PURPOSE
            CGESV computes the solution to a complex system of linear equations
               A * X = B,
            where A is an N-by-N matrix and X and B are N-by-NRHS matrices.

            The 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 of equations A * X = B.




ARGUMENTS
           N         (input)
                     N is INTEGER
                     The number of linear equations, i.e., the order of the
                     matrix A.  N >= 0.

           NRHS      (input)
                     NRHS is INTEGER
                     The number of right hand sides, i.e., the number of columns
                     of the matrix B.  NRHS >= 0.

           A         (input/output)
                     A is COMPLEX array, dimension (LDA,N)
                     On entry, the N-by-N coefficient matrix A.
                     On exit, the factors L and U from the factorization
                     A = P*L*U; the unit diagonal elements of L are not stored.

           LDA       (input)
                     LDA is INTEGER
                     The leading dimension of the array A.  LDA >= max(1,N).

           IPIV      (output)
                     IPIV is INTEGER array, dimension (N)
                     The pivot indices that define the permutation matrix P;
                     row i of the matrix was interchanged with row IPIV(i).

           B         (input/output)
                     B is COMPLEX array, dimension (LDB,NRHS)
                     On entry, the N-by-NRHS matrix of right hand side matrix B.
                     On exit, if INFO = 0, the N-by-NRHS solution matrix X.

           LDB       (input)
                     LDB is INTEGER
                     The leading dimension of the array B.  LDB >= max(1,N).

           INFO      (output)
                     INFO is INTEGER
                     = 0:  successful exit
                     < 0:  if INFO = -i, the i-th argument had an illegal value
                     > 0:  if INFO = i, U(i,i) is exactly zero.  The factorization
                           has been completed, but the factor U is exactly
                           singular, so the solution could not be computed.



LAPACK routine                  31 October 2017                       CGESV(3)