zsytrs_aa_2stage()

subroutine zsytrs_aa_2stage	(	character	uplo,
		integer	n,
		integer	nrhs,
		complex*16, dimension( lda, * )	a,
		integer	lda,
		complex*16, dimension( * )	tb,
		integer	ltb,
		integer, dimension( * )	ipiv,
		integer, dimension( * )	ipiv2,
		complex*16, dimension( ldb, * )	b,
		integer	ldb,
		integer	info )

ZSYTRS_AA_2STAGE

Download ZSYTRS_AA_2STAGE + dependencies [TGZ] [ZIP] [TXT]

Purpose:

!>
!> 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.
!> 

Parameters

[in]	UPLO	!> 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. !>
[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) !> Details of factors computed by ZSYTRF_AA_2STAGE. !>
[in]	LDA	!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !>
[out]	TB	!> TB is COMPLEX*16 array, dimension (LTB) !> Details of factors computed by ZSYTRF_AA_2STAGE. !>
[in]	LTB	!> LTB is INTEGER !> The size of the array TB. LTB >= 4*N. !>
[in]	IPIV	!> IPIV is INTEGER array, dimension (N) !> Details of the interchanges as computed by !> ZSYTRF_AA_2STAGE. !>
[in]	IPIV2	!> IPIV2 is INTEGER array, dimension (N) !> Details of the interchanges as computed by !> ZSYTRF_AA_2STAGE. !>
[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 135 of file zsytrs_aa_2stage.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..--
*
      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' )
      IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) 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( ltb.LT.( 4*n ) ) THEN
         info = -7
      ELSE IF( ldb.LT.max( 1, n ) ) THEN
         info = -11
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'ZSYTRS_AA_2STAGE', -info )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( n.EQ.0 .OR. nrhs.EQ.0 )
     $   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.
*
         IF( n.GT.nb ) 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)
         IF( n.GT.nb ) 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
*

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