cgesv.f

          SUBROUTINE CGESV( N, NRHS, A, LDA, IPIV, B, LDB, INFO )
    *
    *  -- LAPACK driver routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          INTEGER            INFO, LDA, LDB, N, NRHS
    *     ..
    *     .. Array Arguments ..
          INTEGER            IPIV( * )
          COMPLEX            A( LDA, * ), B( LDB, * )
    *     ..
    *
    *  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) 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 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 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.
    *
    *  =====================================================================
    *
    *     .. External Subroutines ..
          EXTERNAL           CGETRF, CGETRS, XERBLA
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          MAX
    *     ..
    *     .. Executable Statements ..
    *
    *     Test the input parameters.
    *
          INFO = 0
          IF( N.LT.0 ) THEN
             INFO = -1
          ELSE IF( NRHS.LT.0 ) THEN
             INFO = -2
          ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
             INFO = -4
          ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
             INFO = -7
          END IF
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'CGESV ', -INFO )
             RETURN
          END IF
    *
    *     Compute the LU factorization of A.
    *
          CALL CGETRF( N, N, A, LDA, IPIV, INFO )
          IF( INFO.EQ.0 ) THEN
    *
    *        Solve the system A*X = B, overwriting B with X.
    *
             CALL CGETRS( 'No transpose', N, NRHS, A, LDA, IPIV, B, LDB,
         $                INFO )
          END IF
          RETURN
    *
    *     End of CGESV
    *
          END