zhesv.f

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*> \brief <b> ZHESV computes the solution to system of linear equations A * X = B for HE matrices</b>
*
*  =========== DOCUMENTATION ===========
*
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*
*  Definition:
*  ===========
*
*       SUBROUTINE ZHESV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
*                         LWORK, INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          UPLO
*       INTEGER            INFO, LDA, LDB, LWORK, N, NRHS
*       ..
*       .. Array Arguments ..
*       INTEGER            IPIV( * )
*       COMPLEX*16         A( LDA, * ), B( LDB, * ), WORK( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> 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.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] UPLO
*> \verbatim
*>          UPLO is CHARACTER*1
*>          = 'U':  Upper triangle of A is stored;
*>          = 'L':  Lower triangle of A is stored.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The number of linear equations, i.e., 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,out] A
*> \verbatim
*>          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.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.  LDA >= max(1,N).
*> \endverbatim
*>
*> \param[out] IPIV
*> \verbatim
*>          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.
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*>          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.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*>          LDB is INTEGER
*>          The leading dimension of the array B.  LDB >= max(1,N).
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
*>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*>          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.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*>          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.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup hesv
*
*  =====================================================================
      SUBROUTINE zhesv( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
     $                  LWORK, INFO )
*
*  -- 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
*
      SUBROUTINE zhesv( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, …
      END