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OpenBLAS/lapack-netlib/SRC/zhbgvd.f

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*> \brief \b ZHBGST
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download ZHBGVD + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhbgvd.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhbgvd.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhbgvd.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE ZHBGVD( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W,
* Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK,
* LIWORK, INFO )
*
* .. Scalar Arguments ..
* CHARACTER JOBZ, UPLO
* INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, LIWORK, LRWORK,
* $ LWORK, N
* ..
* .. Array Arguments ..
* INTEGER IWORK( * )
* DOUBLE PRECISION RWORK( * ), W( * )
* COMPLEX*16 AB( LDAB, * ), BB( LDBB, * ), WORK( * ),
* $ Z( LDZ, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZHBGVD computes all the eigenvalues, and optionally, the eigenvectors
*> of a complex generalized Hermitian-definite banded eigenproblem, of
*> the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian
*> and banded, and B is also positive definite. If eigenvectors are
*> desired, it uses a divide and conquer algorithm.
*>
*> The divide and conquer algorithm makes very mild assumptions about
*> floating point arithmetic. It will work on machines with a guard
*> digit in add/subtract, or on those binary machines without guard
*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
*> without guard digits, but we know of none.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \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] KA
*> \verbatim
*> KA is INTEGER
*> The number of superdiagonals of the matrix A if UPLO = 'U',
*> or the number of subdiagonals if UPLO = 'L'. KA >= 0.
*> \endverbatim
*>
*> \param[in] KB
*> \verbatim
*> KB is INTEGER
*> The number of superdiagonals of the matrix B if UPLO = 'U',
*> or the number of subdiagonals if UPLO = 'L'. KB >= 0.
*> \endverbatim
*>
*> \param[in,out] AB
*> \verbatim
*> AB is COMPLEX*16 array, dimension (LDAB, N)
*> On entry, the upper or lower triangle of the Hermitian band
*> matrix A, stored in the first ka+1 rows of the array. The
*> j-th column of A is stored in the j-th column of the array AB
*> as follows:
*> if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
*> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka).
*>
*> On exit, the contents of AB are destroyed.
*> \endverbatim
*>
*> \param[in] LDAB
*> \verbatim
*> LDAB is INTEGER
*> The leading dimension of the array AB. LDAB >= KA+1.
*> \endverbatim
*>
*> \param[in,out] BB
*> \verbatim
*> BB is COMPLEX*16 array, dimension (LDBB, N)
*> On entry, the upper or lower triangle of the Hermitian band
*> matrix B, stored in the first kb+1 rows of the array. The
*> j-th column of B is stored in the j-th column of the array BB
*> as follows:
*> if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
*> if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb).
*>
*> On exit, the factor S from the split Cholesky factorization
*> B = S**H*S, as returned by ZPBSTF.
*> \endverbatim
*>
*> \param[in] LDBB
*> \verbatim
*> LDBB is INTEGER
*> The leading dimension of the array BB. LDBB >= KB+1.
*> \endverbatim
*>
*> \param[out] W
*> \verbatim
*> W is DOUBLE PRECISION array, dimension (N)
*> If INFO = 0, the eigenvalues in ascending order.
*> \endverbatim
*>
*> \param[out] Z
*> \verbatim
*> Z is COMPLEX*16 array, dimension (LDZ, N)
*> If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
*> eigenvectors, with the i-th column of Z holding the
*> eigenvector associated with W(i). The eigenvectors are
*> normalized so that Z**H*B*Z = I.
*> If JOBZ = 'N', then Z is not referenced.
*> \endverbatim
*>
*> \param[in] LDZ
*> \verbatim
*> LDZ is INTEGER
*> The leading dimension of the array Z. LDZ >= 1, and if
*> JOBZ = 'V', LDZ >= 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 dimension of the array WORK.
*> If N <= 1, LWORK >= 1.
*> If JOBZ = 'N' and N > 1, LWORK >= N.
*> If JOBZ = 'V' and N > 1, LWORK >= 2*N**2.
*>
*> If LWORK = -1, then a workspace query is assumed; the routine
*> only calculates the optimal sizes of the WORK, RWORK and
*> IWORK arrays, returns these values as the first entries of
*> the WORK, RWORK and IWORK arrays, and no error message
*> related to LWORK or LRWORK or LIWORK is issued by XERBLA.
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*> RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
*> On exit, if INFO=0, RWORK(1) returns the optimal LRWORK.
*> \endverbatim
*>
*> \param[in] LRWORK
*> \verbatim
*> LRWORK is INTEGER
*> The dimension of array RWORK.
*> If N <= 1, LRWORK >= 1.
*> If JOBZ = 'N' and N > 1, LRWORK >= N.
*> If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
*>
*> If LRWORK = -1, then a workspace query is assumed; the
*> routine only calculates the optimal sizes of the WORK, RWORK
*> and IWORK arrays, returns these values as the first entries
*> of the WORK, RWORK and IWORK arrays, and no error message
*> related to LWORK or LRWORK or LIWORK is issued by XERBLA.
*> \endverbatim
*>
*> \param[out] IWORK
*> \verbatim
*> IWORK is INTEGER array, dimension (MAX(1,LIWORK))
*> On exit, if INFO=0, IWORK(1) returns the optimal LIWORK.
*> \endverbatim
*>
*> \param[in] LIWORK
*> \verbatim
*> LIWORK is INTEGER
*> The dimension of array IWORK.
*> If JOBZ = 'N' or N <= 1, LIWORK >= 1.
*> If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
*>
*> If LIWORK = -1, then a workspace query is assumed; the
*> routine only calculates the optimal sizes of the WORK, RWORK
*> and IWORK arrays, returns these values as the first entries
*> of the WORK, RWORK and IWORK arrays, and no error message
*> related to LWORK or LRWORK or LIWORK 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, and i is:
*> <= N: the algorithm 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 ZPBSTF
*> returned INFO = i: B is not positive definite.
*> 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.
*
*> \date November 2011
*
*> \ingroup complex16OTHEReigen
*
*> \par Contributors:
* ==================
*>
*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
*
* =====================================================================
SUBROUTINE ZHBGVD( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W,
$ Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK,
$ LIWORK, INFO )
*
* -- LAPACK driver routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
CHARACTER JOBZ, UPLO
INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, LIWORK, LRWORK,
$ LWORK, N
* ..
* .. Array Arguments ..
INTEGER IWORK( * )
DOUBLE PRECISION RWORK( * ), W( * )
COMPLEX*16 AB( LDAB, * ), BB( LDBB, * ), WORK( * ),
$ Z( LDZ, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
COMPLEX*16 CONE, CZERO
PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ),
$ CZERO = ( 0.0D+0, 0.0D+0 ) )
* ..
* .. Local Scalars ..
LOGICAL LQUERY, UPPER, WANTZ
CHARACTER VECT
INTEGER IINFO, INDE, INDWK2, INDWRK, LIWMIN, LLRWK,
$ LLWK2, LRWMIN, LWMIN
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL DSTERF, XERBLA, ZGEMM, ZHBGST, ZHBTRD, ZLACPY,
$ ZPBSTF, ZSTEDC
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
WANTZ = LSAME( JOBZ, 'V' )
UPPER = LSAME( UPLO, 'U' )
LQUERY = ( LWORK.EQ.-1 .OR. LRWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
*
INFO = 0
IF( N.LE.1 ) THEN
LWMIN = 1+N
LRWMIN = 1+N
LIWMIN = 1
ELSE IF( WANTZ ) THEN
LWMIN = 2*N**2
LRWMIN = 1 + 5*N + 2*N**2
LIWMIN = 3 + 5*N
ELSE
LWMIN = N
LRWMIN = N
LIWMIN = 1
END IF
IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
INFO = -1
ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
INFO = -2
ELSE IF( N.LT.0 ) THEN
INFO = -3
ELSE IF( KA.LT.0 ) THEN
INFO = -4
ELSE IF( KB.LT.0 .OR. KB.GT.KA ) THEN
INFO = -5
ELSE IF( LDAB.LT.KA+1 ) THEN
INFO = -7
ELSE IF( LDBB.LT.KB+1 ) THEN
INFO = -9
ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
INFO = -12
END IF
*
IF( INFO.EQ.0 ) THEN
WORK( 1 ) = LWMIN
RWORK( 1 ) = LRWMIN
IWORK( 1 ) = LIWMIN
*
IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
INFO = -14
ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN
INFO = -16
ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
INFO = -18
END IF
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'ZHBGVD', -INFO )
RETURN
ELSE IF( LQUERY ) THEN
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
* Form a split Cholesky factorization of B.
*
CALL ZPBSTF( UPLO, N, KB, BB, LDBB, INFO )
IF( INFO.NE.0 ) THEN
INFO = N + INFO
RETURN
END IF
*
* Transform problem to standard eigenvalue problem.
*
INDE = 1
INDWRK = INDE + N
INDWK2 = 1 + N*N
LLWK2 = LWORK - INDWK2 + 2
LLRWK = LRWORK - INDWRK + 2
CALL ZHBGST( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Z, LDZ,
$ WORK, RWORK( INDWRK ), IINFO )
*
* Reduce Hermitian band matrix to tridiagonal form.
*
IF( WANTZ ) THEN
VECT = 'U'
ELSE
VECT = 'N'
END IF
CALL ZHBTRD( VECT, UPLO, N, KA, AB, LDAB, W, RWORK( INDE ), Z,
$ LDZ, WORK, IINFO )
*
* For eigenvalues only, call DSTERF. For eigenvectors, call ZSTEDC.
*
IF( .NOT.WANTZ ) THEN
CALL DSTERF( N, W, RWORK( INDE ), INFO )
ELSE
CALL ZSTEDC( 'I', N, W, RWORK( INDE ), WORK, N, WORK( INDWK2 ),
$ LLWK2, RWORK( INDWRK ), LLRWK, IWORK, LIWORK,
$ INFO )
CALL ZGEMM( 'N', 'N', N, N, N, CONE, Z, LDZ, WORK, N, CZERO,
$ WORK( INDWK2 ), N )
CALL ZLACPY( 'A', N, N, WORK( INDWK2 ), N, Z, LDZ )
END IF
*
WORK( 1 ) = LWMIN
RWORK( 1 ) = LRWMIN
IWORK( 1 ) = LIWMIN
RETURN
*
* End of ZHBGVD
*
END
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