zhesv()

subroutine zhesv	(	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 )

ZHESV computes the solution to system of linear equations A * X = B for HE matrices

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Purpose:

!>
!> ZHESV computes the solution to a complex system of linear equations
!>    A * X = B,
!> where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS
!> matrices.
!>
!> The diagonal pivoting method is used to factor A as
!>    A = U * D * U**H,  if UPLO = 'U', or
!>    A = L * D * L**H,  if UPLO = 'L',
!> where U (or L) is a product of permutation and unit upper (lower)
!> triangular matrices, and D is Hermitian and block diagonal with
!> 1-by-1 and 2-by-2 diagonal blocks.  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 Hermitian 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 block diagonal matrix D and the !> multipliers used to obtain the factor U or L from the !> factorization A = U*D*U**H or A = L*D*L**H as computed by !> ZHETRF. !>
[in]	LDA	!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !>
[out]	IPIV	!> IPIV is INTEGER array, dimension (N) !> Details of the interchanges and the block structure of D, as !> determined by ZHETRF. If IPIV(k) > 0, then rows and columns !> k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1 !> diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, !> then rows and columns k-1 and -IPIV(k) were interchanged and !> D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and !> IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and !> -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 !> diagonal block. !>
[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 >= 1, and for best performance !> LWORK >= max(1,N*NB), where NB is the optimal blocksize for !> ZHETRF. !> for LWORK < N, TRS will be done with Level BLAS 2 !> for LWORK >= N, TRS will be done with Level BLAS 3 !> !> 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 167 of file zhesv.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, NB
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            ILAENV
      EXTERNAL           lsame, ilaenv
*     ..
*     .. External Subroutines ..
      EXTERNAL           xerbla, zhetrf, zhetrs, zhetrs2
*     ..
*     .. 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.1 .AND. .NOT.lquery ) THEN
         info = -10
      END IF
*
      IF( info.EQ.0 ) THEN
         IF( n.EQ.0 ) THEN
            lwkopt = 1
         ELSE
            nb = ilaenv( 1, 'ZHETRF', uplo, n, -1, -1, -1 )
            lwkopt = n*nb
         END IF
         work( 1 ) = lwkopt
      END IF
*
      IF( info.NE.0 ) THEN
         CALL xerbla( 'ZHESV ', -info )
         RETURN
      ELSE IF( lquery ) THEN
         RETURN
      END IF
*
*     Compute the factorization A = U*D*U**H or A = L*D*L**H.
*
      CALL zhetrf( uplo, n, a, lda, ipiv, work, lwork, info )
      IF( info.EQ.0 ) THEN
*
*        Solve the system A*X = B, overwriting B with X.
*
         IF ( lwork.LT.n ) THEN
*
*        Solve with TRS ( Use Level BLAS 2)
*
            CALL zhetrs( uplo, n, nrhs, a, lda, ipiv, b, ldb, info )
*
         ELSE
*
*        Solve with TRS2 ( Use Level BLAS 3)
*
            CALL zhetrs2( uplo,n,nrhs,a,lda,ipiv,b,ldb,work,info )
*
         END IF
*
      END IF
*
      work( 1 ) = lwkopt
*
      RETURN
*
*     End of ZHESV
*

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