zgetrs()

subroutine zgetrs	(	character	trans,
		integer	n,
		integer	nrhs,
		complex*16, dimension( lda, * )	a,
		integer	lda,
		integer, dimension( * )	ipiv,
		complex*16, dimension( ldb, * )	b,
		integer	ldb,
		integer	info )

ZGETRS

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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.
!> 

Parameters

[in]	TRANS	!> TRANS is 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) !>
[in]	N	!> N is INTEGER !> The order of the matrix A. N >= 0. !>
[in]	NRHS	!> NRHS is INTEGER !> The number of right hand sides, i.e., the number of columns !> of the matrix B. NRHS >= 0. !>
[in]	A	!> A is COMPLEX*16 array, dimension (LDA,N) !> The factors L and U from the factorization A = P*L*U !> as computed by ZGETRF. !>
[in]	LDA	!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !>
[in]	IPIV	!> IPIV is INTEGER array, dimension (N) !> The pivot indices from ZGETRF; for 1<=i<=N, row i of the !> matrix was interchanged with row IPIV(i). !>
[in,out]	B	!> B is COMPLEX*16 array, dimension (LDB,NRHS) !> On entry, the right hand side matrix B. !> On exit, the solution matrix X. !>
[in]	LDB	!> LDB is INTEGER !> The leading dimension of the array B. LDB >= max(1,N). !>
[out]	INFO	!> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 118 of file zgetrs.f.

*
*  -- LAPACK computational routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      CHARACTER          TRANS
      INTEGER            INFO, LDA, LDB, N, NRHS
*     ..
*     .. Array Arguments ..
      INTEGER            IPIV( * )
      COMPLEX*16         A( LDA, * ), B( LDB, * )
*     ..
*
*  =====================================================================
*
*     .. 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**T *X = B or U**H *X = B, overwriting B with X.
*
         CALL ztrsm( 'Left', 'Upper', trans, 'Non-unit', n, nrhs,
     $               one,
     $               a, lda, b, ldb )
*
*        Solve L**T *X = B, or L**H *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
*

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