zgetrs.f

          SUBROUTINE ZGETRS( TRANS, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
    *
    *  -- LAPACK routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          TRANS
          INTEGER            INFO, LDA, LDB, N, NRHS
    *     ..
    *     .. Array Arguments ..
          INTEGER            IPIV( * )
          COMPLEX*16         A( LDA, * ), B( LDB, * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  ZGETRS solves a system of linear equations
    *     A * X = B,  A**T * X = B,  or  A**H * X = B
    *  with a general N-by-N matrix A using the LU factorization computed
    *  by ZGETRF.
    *
    *  Arguments
    *  =========
    *
    *  TRANS   (input) CHARACTER*1
    *          Specifies the form of the system of equations:
    *          = 'N':  A * X = B     (No transpose)
    *          = 'T':  A**T * X = B  (Transpose)
    *          = 'C':  A**H * X = B  (Conjugate transpose)
    *
    *  N       (input) INTEGER
    *          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) COMPLEX*16 array, dimension (LDA,N)
    *          The factors L and U from the factorization A = P*L*U
    *          as computed by ZGETRF.
    *
    *  LDA     (input) INTEGER
    *          The leading dimension of the array A.  LDA >= max(1,N).
    *
    *  IPIV    (input) INTEGER array, dimension (N)
    *          The pivot indices from ZGETRF; for 1<=i<=N, row i of the
    *          matrix was interchanged with row IPIV(i).
    *
    *  B       (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
    *          On entry, the right hand side matrix B.
    *          On exit, the 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
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          COMPLEX*16         ONE
          PARAMETER          ( ONE = ( 1.0D+0, 0.0D+0 ) )
    *     ..
    *     .. Local Scalars ..
          LOGICAL            NOTRAN
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          EXTERNAL           LSAME
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           XERBLA, ZLASWP, ZTRSM
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          MAX
    *     ..
    *     .. Executable Statements ..
    *
    *     Test the input parameters.
    *
          INFO = 0
          NOTRAN = LSAME( TRANS, 'N' )
          IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) .AND. .NOT.
         $    LSAME( TRANS, 'C' ) ) THEN
             INFO = -1
          ELSE IF( N.LT.0 ) THEN
             INFO = -2
          ELSE IF( NRHS.LT.0 ) THEN
             INFO = -3
          ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
             INFO = -5
          ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
             INFO = -8
          END IF
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'ZGETRS', -INFO )
             RETURN
          END IF
    *
    *     Quick return if possible
    *
          IF( N.EQ.0 .OR. NRHS.EQ.0 )
         $   RETURN
    *
          IF( NOTRAN ) THEN
    *
    *        Solve A * X = B.
    *
    *        Apply row interchanges to the right hand sides.
    *
             CALL ZLASWP( NRHS, B, LDB, 1, N, IPIV, 1 )
    *
    *        Solve L*X = B, overwriting B with X.
    *
             CALL ZTRSM( 'Left', 'Lower', 'No transpose', 'Unit', N, NRHS,
         $               ONE, A, LDA, B, LDB )
    *
    *        Solve U*X = B, overwriting B with X.
    *
             CALL ZTRSM( 'Left', 'Upper', 'No transpose', 'Non-unit', N,
         $               NRHS, ONE, A, LDA, B, LDB )
          ELSE
    *
    *        Solve A**T * X = B  or A**H * X = B.
    *
    *        Solve U'*X = B, overwriting B with X.
    *
             CALL ZTRSM( 'Left', 'Upper', TRANS, 'Non-unit', N, NRHS, ONE,
         $               A, LDA, B, LDB )
    *
    *        Solve L'*X = B, overwriting B with X.
    *
             CALL ZTRSM( 'Left', 'Lower', TRANS, 'Unit', N, NRHS, ONE, A,
         $               LDA, B, LDB )
    *
    *        Apply row interchanges to the solution vectors.
    *
             CALL ZLASWP( NRHS, B, LDB, 1, N, IPIV, -1 )
          END IF
    *
          RETURN
    *
    *     End of ZGETRS
    *
          END