dd/de2/zhegv_8f_source.html

*> \brief \b ZHEGV

*

*  =========== DOCUMENTATION ===========

*

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*            http://www.netlib.org/lapack/explore-html/

*

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*

*  Definition:

*  ===========

*

*       SUBROUTINE ZHEGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,

*                         LWORK, RWORK, INFO )

*

*       .. Scalar Arguments ..

*       CHARACTER          JOBZ, UPLO

*       INTEGER            INFO, ITYPE, LDA, LDB, LWORK, N

*       ..

*       .. Array Arguments ..

*       DOUBLE PRECISION   RWORK( * ), W( * )

*       COMPLEX*16         A( LDA, * ), B( LDB, * ), WORK( * )

*       ..

*

*

*> \par Purpose:

*  =============

*>

*> \verbatim

*>

*> ZHEGV computes all the eigenvalues, and optionally, the eigenvectors

*> of a complex generalized Hermitian-definite eigenproblem, of the form

*> A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x.

*> Here A and B are assumed to be Hermitian and B is also

*> positive definite.

*> \endverbatim

*

*  Arguments:

*  ==========

*

*> \param[in] ITYPE

*> \verbatim

*>          ITYPE is INTEGER

*>          Specifies the problem type to be solved:

*>          = 1:  A*x = (lambda)*B*x

*>          = 2:  A*B*x = (lambda)*x

*>          = 3:  B*A*x = (lambda)*x

*> \endverbatim

*>

*> \param[in] JOBZ

*> \verbatim

*>          JOBZ is CHARACTER*1

*>          = 'N':  Compute eigenvalues only;

*>          = 'V':  Compute eigenvalues and eigenvectors.

*> \endverbatim

*>

*> \param[in] UPLO

*> \verbatim

*>          UPLO is CHARACTER*1

*>          = 'U':  Upper triangles of A and B are stored;

*>          = 'L':  Lower triangles of A and B are stored.

*> \endverbatim

*>

*> \param[in] N

*> \verbatim

*>          N is INTEGER

*>          The order of the matrices A and B.  N >= 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.  If UPLO = 'L',

*>          the leading N-by-N lower triangular part of A contains

*>          the lower triangular part of the matrix A.

*>

*>          On exit, if JOBZ = 'V', then if INFO = 0, A contains the

*>          matrix Z of eigenvectors.  The eigenvectors are normalized

*>          as follows:

*>          if ITYPE = 1 or 2, Z**H*B*Z = I;

*>          if ITYPE = 3, Z**H*inv(B)*Z = I.

*>          If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')

*>          or the lower triangle (if UPLO='L') of A, including the

*>          diagonal, is destroyed.

*> \endverbatim

*>

*> \param[in] LDA

*> \verbatim

*>          LDA is INTEGER

*>          The leading dimension of the array A.  LDA >= max(1,N).

*> \endverbatim

*>

*> \param[in,out] B

*> \verbatim

*>          B is COMPLEX*16 array, dimension (LDB, N)

*>          On entry, the Hermitian positive definite matrix B.

*>          If UPLO = 'U', the leading N-by-N upper triangular part of B

*>          contains the upper triangular part of the matrix B.

*>          If UPLO = 'L', the leading N-by-N lower triangular part of B

*>          contains the lower triangular part of the matrix B.

*>

*>          On exit, if INFO <= N, the part of B containing the matrix is

*>          overwritten by the triangular factor U or L from the Cholesky

*>          factorization B = U**H*U or B = L*L**H.

*> \endverbatim

*>

*> \param[in] LDB

*> \verbatim

*>          LDB is INTEGER

*>          The leading dimension of the array B.  LDB >= max(1,N).

*> \endverbatim

*>

*> \param[out] W

*> \verbatim

*>          W is DOUBLE PRECISION array, dimension (N)

*>          If INFO = 0, the eigenvalues in ascending order.

*> \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 the array WORK.  LWORK >= max(1,2*N-1).

*>          For optimal efficiency, LWORK >= (NB+1)*N,

*>          where NB is the blocksize for ZHETRD returned by ILAENV.

*>

*>          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] RWORK

*> \verbatim

*>          RWORK is DOUBLE PRECISION array, dimension (max(1, 3*N-2))

*> \endverbatim

*>

*> \param[out] INFO

*> \verbatim

*>          INFO is INTEGER

*>          = 0:  successful exit

*>          < 0:  if INFO = -i, the i-th argument had an illegal value

*>          > 0:  ZPOTRF or ZHEEV returned an error code:

*>             <= N:  if INFO = i, ZHEEV failed to converge;

*>                    i off-diagonal elements of an intermediate

*>                    tridiagonal form did not converge to zero;

*>             > N:   if INFO = N + i, for 1 <= i <= N, then the leading

*>                    principal minor of order i of B is not positive.

*>                    The factorization of B could not be completed and

*>                    no eigenvalues or eigenvectors were computed.

*> \endverbatim

*

*  Authors:

*  ========

*

*> \author Univ. of Tennessee

*> \author Univ. of California Berkeley

*> \author Univ. of Colorado Denver

*> \author NAG Ltd.

*

*> \ingroup hegv

*

*  =====================================================================


      SUBROUTINE zhegv( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W,

     $                  WORK,

     $                  LWORK, RWORK, 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          JOBZ, UPLO

      INTEGER            INFO, ITYPE, LDA, LDB, LWORK, N

*     ..

*     .. Array Arguments ..

      DOUBLE PRECISION   RWORK( * ), W( * )

      COMPLEX*16         A( LDA, * ), B( LDB, * ), WORK( * )

*     ..

*

*  =====================================================================

*

*     .. Parameters ..

      COMPLEX*16         ONE

      PARAMETER          ( ONE = ( 1.0d+0, 0.0d+0 ) )

*     ..

*     .. Local Scalars ..

      LOGICAL            LQUERY, UPPER, WANTZ

      CHARACTER          TRANS

      INTEGER            LWKOPT, NB, NEIG

*     ..

*     .. External Functions ..

      LOGICAL            LSAME

      INTEGER            ILAENV

      EXTERNAL           lsame, ilaenv

*     ..

*     .. External Subroutines ..

      EXTERNAL           xerbla, zheev, zhegst, zpotrf, ztrmm,

     $                   ztrsm

*     ..

*     .. Intrinsic Functions ..

      INTRINSIC          max

*     ..

*     .. Executable Statements ..

*

*     Test the input parameters.

*

      wantz = lsame( jobz, 'V' )

      upper = lsame( uplo, 'U' )

      lquery = ( lwork.EQ.-1 )

*

      info = 0

      IF( itype.LT.1 .OR. itype.GT.3 ) THEN

         info = -1

      ELSE IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN

         info = -2

      ELSE IF( .NOT.( upper .OR. lsame( uplo, 'L' ) ) ) THEN

         info = -3

      ELSE IF( n.LT.0 ) THEN

         info = -4

      ELSE IF( lda.LT.max( 1, n ) ) THEN

         info = -6

      ELSE IF( ldb.LT.max( 1, n ) ) THEN

         info = -8

      END IF

*

      IF( info.EQ.0 ) THEN

         nb = ilaenv( 1, 'ZHETRD', uplo, n, -1, -1, -1 )

         lwkopt = max( 1, ( nb + 1 )*n )

         work( 1 ) = lwkopt

*

         IF( lwork.LT.max( 1, 2*n - 1 ) .AND. .NOT.lquery ) THEN

            info = -11

         END IF

      END IF

*

      IF( info.NE.0 ) THEN

         CALL xerbla( 'ZHEGV ', -info )

         RETURN

      ELSE IF( lquery ) THEN

         RETURN

      END IF

*

*     Quick return if possible

*

      IF( n.EQ.0 )

     $   RETURN

*

*     Form a Cholesky factorization of B.

*

      CALL zpotrf( uplo, n, b, ldb, info )

      IF( info.NE.0 ) THEN

         info = n + info

         RETURN

      END IF

*

*     Transform problem to standard eigenvalue problem and solve.

*

      CALL zhegst( itype, uplo, n, a, lda, b, ldb, info )

      CALL zheev( jobz, uplo, n, a, lda, w, work, lwork, rwork,

     $            info )

*

      IF( wantz ) THEN

*

*        Backtransform eigenvectors to the original problem.

*

         neig = n

         IF( info.GT.0 )

     $      neig = info - 1

         IF( itype.EQ.1 .OR. itype.EQ.2 ) THEN

*

*           For A*x=(lambda)*B*x and A*B*x=(lambda)*x;

*           backtransform eigenvectors: x = inv(L)**H *y or inv(U)*y

*

            IF( upper ) THEN

               trans = 'N'

            ELSE

               trans = 'C'

            END IF

*

            CALL ztrsm( 'Left', uplo, trans, 'Non-unit', n, neig,

     $                  one,

     $                  b, ldb, a, lda )

*

         ELSE IF( itype.EQ.3 ) THEN

*

*           For B*A*x=(lambda)*x;

*           backtransform eigenvectors: x = L*y or U**H *y

*

            IF( upper ) THEN

               trans = 'C'

            ELSE

               trans = 'N'

            END IF

*

            CALL ztrmm( 'Left', uplo, trans, 'Non-unit', n, neig,

     $                  one,

     $                  b, ldb, a, lda )

         END IF

      END IF

*

      work( 1 ) = lwkopt

*

      RETURN

*

*     End of ZHEGV

*


      END

xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285

zheev
subroutine zheev(jobz, uplo, n, a, lda, w, work, lwork, rwork, info)
ZHEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices
Definition zheev.f:138

zhegst
subroutine zhegst(itype, uplo, n, a, lda, b, ldb, info)
ZHEGST
Definition zhegst.f:126

zhegv
subroutine zhegv(itype, jobz, uplo, n, a, lda, b, ldb, w, work, lwork, rwork, info)
ZHEGV
Definition zhegv.f:180

zpotrf
subroutine zpotrf(uplo, n, a, lda, info)
ZPOTRF
Definition zpotrf.f:105

ztrmm
subroutine ztrmm(side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)
ZTRMM
Definition ztrmm.f:177

ztrsm
subroutine ztrsm(side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)
ZTRSM
Definition ztrsm.f:180