zsytrs_aa_2stage.f

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*> \brief \b ZSYTRS_AA_2STAGE
*
*  =========== DOCUMENTATION ===========
*
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*
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*
*  Definition:
*  ===========
*
*      SUBROUTINE ZSYTRS_AA_2STAGE( UPLO, N, NRHS, A, LDA, TB, LTB, IPIV, 
*                                   IPIV2, B, LDB, INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          UPLO
*       INTEGER            N, NRHS, LDA, LTB, LDB, INFO
*       ..
*       .. Array Arguments ..
*       INTEGER            IPIV( * ), IPIV2( * )
*       COMPLEX*16         A( LDA, * ), TB( * ), B( LDB, * )
*       ..
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> ZSYTRS_AA_2STAGE solves a system of linear equations A*X = B with a complex
*> symmetric matrix A using the factorization A = U**T*T*U or
*> A = L*T*L**T computed by ZSYTRF_AA_2STAGE.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] UPLO
*> \verbatim
*>          UPLO is CHARACTER*1
*>          Specifies whether the details of the factorization are stored
*>          as an upper or lower triangular matrix.
*>          = 'U':  Upper triangular, form is A = U**T*T*U;
*>          = 'L':  Lower triangular, form is A = L*T*L**T.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the matrix A.  N >= 0.
*> \endverbatim
*>
*> \param[in] NRHS
*> \verbatim
*>          NRHS is INTEGER
*>          The number of right hand sides, i.e., the number of columns
*>          of the matrix B.  NRHS >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*>          A is COMPLEX*16 array, dimension (LDA,N)
*>          Details of factors computed by ZSYTRF_AA_2STAGE.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.  LDA >= max(1,N).
*> \endverbatim
*>
*> \param[out] TB
*> \verbatim
*>          TB is COMPLEX*16 array, dimension (LTB)
*>          Details of factors computed by ZSYTRF_AA_2STAGE.
*> \endverbatim
*>
*> \param[in] LTB
*> \verbatim
*>          LTB is INTEGER
*>          The size of the array TB. LTB >= 4*N.
*> \endverbatim
*>
*> \param[in] IPIV
*> \verbatim
*>          IPIV is INTEGER array, dimension (N)
*>          Details of the interchanges as computed by
*>          ZSYTRF_AA_2STAGE.
*> \endverbatim
*>
*> \param[in] IPIV2
*> \verbatim
*>          IPIV2 is INTEGER array, dimension (N)
*>          Details of the interchanges as computed by
*>          ZSYTRF_AA_2STAGE.
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*>          B is COMPLEX*16 array, dimension (LDB,NRHS)
*>          On entry, the right hand side matrix B.
*>          On exit, the solution matrix X.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*>          LDB is INTEGER
*>          The leading dimension of the array B.  LDB >= max(1,N).
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*>          INFO is INTEGER
*>          = 0:  successful exit
*>          < 0:  if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup complex16SYcomputational
*
*  =====================================================================
      SUBROUTINE zsytrs_aa_2stage( UPLO, N, NRHS, A, LDA, TB, LTB,
     $                             IPIV, IPIV2, B, LDB, INFO )
*
*  -- LAPACK computational routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
      IMPLICIT NONE
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            N, NRHS, LDA, LTB, LDB, INFO
*     ..
*     .. Array Arguments ..
      INTEGER            IPIV( * ), IPIV2( * )
      COMPLEX*16         A( LDA, * ), TB( * ), B( LDB, * )
*     ..
*
*  =====================================================================
*
      COMPLEX*16         ONE
      parameter( one  = ( 1.0e+0, 0.0e+0 ) )
*     ..
*     .. Local Scalars ..
      INTEGER            LDTB, NB
      LOGICAL            UPPER
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           lsame
*     ..
*     .. External Subroutines ..
      EXTERNAL           zgbtrs, zlaswp, ztrsm, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max
*     ..
*     .. Executable Statements ..
*
      info = 0
      upper = lsame( uplo, 'u' )
.NOT..AND..NOT.      IF( UPPER  LSAME( UPLO, 'l' ) ) THEN
         INFO = -1
.LT.      ELSE IF( N0 ) THEN
         INFO = -2
.LT.      ELSE IF( NRHS0 ) THEN
         INFO = -3
.LT.      ELSE IF( LDAMAX( 1, N ) ) THEN
         INFO = -5
.LT.      ELSE IF( LTB( 4*N ) ) THEN
         INFO = -7
.LT.      ELSE IF( LDBMAX( 1, N ) ) THEN
         INFO = -11
      END IF
.NE.      IF( INFO0 ) THEN
         CALL XERBLA( 'zsytrs_aa_2stage', -INFO )
         RETURN
      END IF
*
*     Quick return if possible
*
.EQ..OR..EQ.      IF( N0  NRHS0 )
     $   RETURN
*
*     Read NB and compute LDTB
*
      NB = INT( TB( 1 ) )
      LDTB = LTB/N
*
      IF( UPPER ) THEN
*
*        Solve A*X = B, where A = U**T*T*U.
*
.GT.         IF( NNB ) THEN
*
*           Pivot, P**T * B -> B
*
            CALL ZLASWP( NRHS, B, LDB, NB+1, N, IPIV, 1 )
*
*           Compute (U**T \ B) -> B    [ (U**T \P**T * B) ]
*
            CALL ZTRSM( 'l', 'u', 't', 'u', N-NB, NRHS, ONE, A(1, NB+1),
     $                 LDA, B(NB+1, 1), LDB)
*
         END IF
*
*        Compute T \ B -> B   [ T \ (U**T \P**T * B) ]
*
         CALL ZGBTRS( 'n', N, NB, NB, NRHS, TB, LDTB, IPIV2, B, LDB,
     $               INFO)
.GT.         IF( NNB ) THEN
*
*           Compute (U \ B) -> B   [ U \ (T \ (U**T \P**T * B) ) ]
*
            CALL ZTRSM( 'l', 'u', 'n', 'U', n-nb, nrhs, one, a(1, nb+1),
     $                  lda, b(nb+1, 1), ldb)
*
*           Pivot, P * B -> B  [ P * (U \ (T \ (U**T \P**T * B) )) ]
*
            CALL zlaswp( nrhs, b, ldb, nb+1, n, ipiv, -1 )
*
         END IF
*
      ELSE
*
*        Solve A*X = B, where A = L*T*L**T.
*
         IF( n.GT.nb ) THEN
*
*           Pivot, P**T * B -> B
*
            CALL zlaswp( nrhs, b, ldb, nb+1, n, ipiv, 1 )
*
*           Compute (L \ B) -> B    [ (L \P**T * B) ]
*
            CALL ztrsm( 'L', 'L', 'N', 'U', n-nb, nrhs, one, a(nb+1, 1),
     $                 lda, b(nb+1, 1), ldb)
*
         END IF
*
*        Compute T \ B -> B   [ T \ (L \P**T * B) ]
*
         CALL zgbtrs( 'N', n, nb, nb, nrhs, tb, ldtb, ipiv2, b, ldb,
     $               info)
         IF( n.GT.nb ) THEN
*
*           Compute (L**T \ B) -> B   [ L**T \ (T \ (L \P**T * B) ) ]
*
            CALL ztrsm( 'L', 'L', 'T', 'U', n-nb, nrhs, one, a(nb+1, 1),
     $                  lda, b(nb+1, 1), ldb)
*
*           Pivot, P * B -> B  [ P * (L**T \ (T \ (L \P**T * B) )) ]
*
            CALL zlaswp( nrhs, b, ldb, nb+1, n, ipiv, -1 )
*
         END IF
      END IF
*
      RETURN
*
*     End of ZSYTRS_AA_2STAGE
*
      END