399 lines
12 KiB
Fortran
399 lines
12 KiB
Fortran
*> \brief \b CHBGVD
|
|
*
|
|
* =========== DOCUMENTATION ===========
|
|
*
|
|
* Online html documentation available at
|
|
* http://www.netlib.org/lapack/explore-html/
|
|
*
|
|
*> \htmlonly
|
|
*> Download CHBGVD + dependencies
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/chbgvd.f">
|
|
*> [TGZ]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/chbgvd.f">
|
|
*> [ZIP]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/chbgvd.f">
|
|
*> [TXT]</a>
|
|
*> \endhtmlonly
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* SUBROUTINE CHBGVD( 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( * )
|
|
* REAL RWORK( * ), W( * )
|
|
* COMPLEX AB( LDAB, * ), BB( LDBB, * ), WORK( * ),
|
|
* $ Z( LDZ, * )
|
|
* ..
|
|
*
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> CHBGVD 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.
|
|
*>
|
|
*> \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 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 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 CPBSTF.
|
|
*> \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 REAL array, dimension (N)
|
|
*> If INFO = 0, the eigenvalues in ascending order.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] Z
|
|
*> \verbatim
|
|
*> Z is COMPLEX 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 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 REAL 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 CPBSTF
|
|
*> 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.
|
|
*
|
|
*> \ingroup complexOTHEReigen
|
|
*
|
|
*> \par Contributors:
|
|
* ==================
|
|
*>
|
|
*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
|
|
*
|
|
* =====================================================================
|
|
SUBROUTINE CHBGVD( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W,
|
|
$ Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK,
|
|
$ LIWORK, 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, KA, KB, LDAB, LDBB, LDZ, LIWORK, LRWORK,
|
|
$ LWORK, N
|
|
* ..
|
|
* .. Array Arguments ..
|
|
INTEGER IWORK( * )
|
|
REAL RWORK( * ), W( * )
|
|
COMPLEX AB( LDAB, * ), BB( LDBB, * ), WORK( * ),
|
|
$ Z( LDZ, * )
|
|
* ..
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. Parameters ..
|
|
COMPLEX CONE, CZERO
|
|
PARAMETER ( CONE = ( 1.0E+0, 0.0E+0 ),
|
|
$ CZERO = ( 0.0E+0, 0.0E+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 SSTERF, XERBLA, CGEMM, CHBGST, CHBTRD, CLACPY,
|
|
$ CPBSTF, CSTEDC
|
|
* ..
|
|
* .. 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( 'CHBGVD', -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 CPBSTF( 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 CHBGST( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Z, LDZ,
|
|
$ WORK, RWORK, IINFO )
|
|
*
|
|
* Reduce Hermitian band matrix to tridiagonal form.
|
|
*
|
|
IF( WANTZ ) THEN
|
|
VECT = 'U'
|
|
ELSE
|
|
VECT = 'N'
|
|
END IF
|
|
CALL CHBTRD( VECT, UPLO, N, KA, AB, LDAB, W, RWORK( INDE ), Z,
|
|
$ LDZ, WORK, IINFO )
|
|
*
|
|
* For eigenvalues only, call SSTERF. For eigenvectors, call CSTEDC.
|
|
*
|
|
IF( .NOT.WANTZ ) THEN
|
|
CALL SSTERF( N, W, RWORK( INDE ), INFO )
|
|
ELSE
|
|
CALL CSTEDC( 'I', N, W, RWORK( INDE ), WORK, N, WORK( INDWK2 ),
|
|
$ LLWK2, RWORK( INDWRK ), LLRWK, IWORK, LIWORK,
|
|
$ INFO )
|
|
CALL CGEMM( 'N', 'N', N, N, N, CONE, Z, LDZ, WORK, N, CZERO,
|
|
$ WORK( INDWK2 ), N )
|
|
CALL CLACPY( 'A', N, N, WORK( INDWK2 ), N, Z, LDZ )
|
|
END IF
|
|
*
|
|
WORK( 1 ) = LWMIN
|
|
RWORK( 1 ) = LRWMIN
|
|
IWORK( 1 ) = LIWMIN
|
|
RETURN
|
|
*
|
|
* End of CHBGVD
|
|
*
|
|
END
|