zsysv_aa()

subroutine zsysv_aa	(	character	uplo,
		integer	n,
		integer	nrhs,
		complex*16, dimension( lda, * )	a,
		integer	lda,
		integer, dimension( * )	ipiv,
		complex*16, dimension( ldb, * )	b,
		integer	ldb,
		complex*16, dimension( * )	work,
		integer	lwork,
		integer	info )

ZSYSV_AA computes the solution to system of linear equations A * X = B for SY matrices

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Purpose:

!>
!> ZSYSV computes the solution to a complex system of linear equations
!>    A * X = B,
!> where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
!> matrices.
!>
!> Aasen's algorithm is used to factor A as
!>    A = U**T * T * U,  if UPLO = 'U', or
!>    A = L * T * L**T,  if UPLO = 'L',
!> where U (or L) is a product of permutation and unit upper (lower)
!> triangular matrices, and T is symmetric tridiagonal. The factored
!> form of A is then used to solve the system of equations A * X = B.
!> 

Parameters

[in]	UPLO	!> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !>
[in]	N	!> N is INTEGER !> The number of linear equations, i.e., 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,out]	A	!> A is COMPLEX*16 array, dimension (LDA,N) !> On entry, the symmetric matrix A. If UPLO = 'U', the leading !> N-by-N upper triangular part of A contains the upper !> triangular part of the matrix A, and the strictly lower !> triangular part of A is not referenced. If UPLO = 'L', the !> leading N-by-N lower triangular part of A contains the lower !> triangular part of the matrix A, and the strictly upper !> triangular part of A is not referenced. !> !> On exit, if INFO = 0, the tridiagonal matrix T and the !> multipliers used to obtain the factor U or L from the !> factorization A = U**T*T*U or A = L*T*L**T as computed by !> ZSYTRF. !>
[in]	LDA	!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !>
[out]	IPIV	!> IPIV is INTEGER array, dimension (N) !> On exit, it contains the details of the interchanges, i.e., !> the row and column k of A were interchanged with the !> row and column IPIV(k). !>
[in,out]	B	!> B is COMPLEX*16 array, dimension (LDB,NRHS) !> On entry, the N-by-NRHS right hand side matrix B. !> On exit, if INFO = 0, the N-by-NRHS solution matrix X. !>
[in]	LDB	!> LDB is INTEGER !> The leading dimension of the array B. LDB >= max(1,N). !>
[out]	WORK	!> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. !>
[in]	LWORK	!> LWORK is INTEGER !> The length of WORK. LWORK >= MAX(1,2*N,3*N-2), and for !> the best performance, LWORK >= MAX(1,N*NB), where NB is !> the optimal blocksize for ZSYTRF_AA. !> !> If LWORK = -1, then a workspace query is assumed; the routine !> only calculates the optimal size of the WORK array, returns !> this value as the first entry of the WORK array, and no error !> message related to LWORK is issued by XERBLA. !>
[out]	INFO	!> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> > 0: if INFO = i, D(i,i) is exactly zero. The factorization !> has been completed, but the block diagonal matrix D is !> exactly singular, so the solution could not be computed. !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 158 of file zsysv_aa.f.

*
*  -- LAPACK driver 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          UPLO
      INTEGER            INFO, LDA, LDB, LWORK, N, NRHS
*     ..
*     .. Array Arguments ..
      INTEGER            IPIV( * )
      COMPLEX*16         A( LDA, * ), B( LDB, * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Local Scalars ..
      LOGICAL            LQUERY
      INTEGER            LWKOPT, LWKOPT_SYTRF, LWKOPT_SYTRS
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            ILAENV
      EXTERNAL           ilaenv, lsame
*     ..
*     .. External Subroutines ..
      EXTERNAL           xerbla, zsytrf_aa, zsytrs_aa
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      info = 0
      lquery = ( lwork.EQ.-1 )
      IF( .NOT.lsame( uplo, 'U' ) .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( ldb.LT.max( 1, n ) ) THEN
         info = -8
      ELSE IF( lwork.LT.max(2*n, 3*n-2) .AND. .NOT.lquery ) THEN
         info = -10
      END IF
*
      IF( info.EQ.0 ) THEN
         CALL zsytrf_aa( uplo, n, a, lda, ipiv, work, -1, info )
         lwkopt_sytrf = int( work(1) )
         CALL zsytrs_aa( uplo, n, nrhs, a, lda, ipiv, b, ldb, work,
     $                   -1, info )
         lwkopt_sytrs = int( work(1) )
         lwkopt = max( lwkopt_sytrf, lwkopt_sytrs )
         work( 1 ) = lwkopt
      END IF
*
      IF( info.NE.0 ) THEN
         CALL xerbla( 'ZSYSV_AA ', -info )
         RETURN
      ELSE IF( lquery ) THEN
         RETURN
      END IF
*
*     Compute the factorization A = U**T*T*U or A = L*T*L**T.
*
      CALL zsytrf_aa( uplo, n, a, lda, ipiv, work, lwork, info )
      IF( info.EQ.0 ) THEN
*
*        Solve the system A*X = B, overwriting B with X.
*
         CALL zsytrs_aa( uplo, n, nrhs, a, lda, ipiv, b, ldb, work,
     $                      lwork, info )
*
      END IF
*
      work( 1 ) = lwkopt
*
      RETURN
*
*     End of ZSYSV_AA
*

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