ZGESV (3lapack)

compute the solution to a complex system of linear equations A * X = B,

SYNOPSIS

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

      INTEGER       INFO, LDA, LDB, N, NRHS

      INTEGER       IPIV( * )

      COMPLEX*16    A( LDA, * ), B( LDB, * )

PURPOSE

  ZGESV 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) INTEGER
          The number of linear equations, i.e., the order of the matrix A.  N
          >= 0.

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

  A       (input/output) COMPLEX*16 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) INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).

  IPIV    (output) 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) COMPLEX*16 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) INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

  INFO    (output) 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.