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*> \brief \b DSBGV
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DSBGV + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsbgv.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsbgv.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsbgv.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DSBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
* LDZ, WORK, INFO )
*
* .. Scalar Arguments ..
* CHARACTER JOBZ, UPLO
* INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, N
* ..
* .. Array Arguments ..
* DOUBLE PRECISION AB( LDAB, * ), BB( LDBB, * ), W( * ),
* $ WORK( * ), Z( LDZ, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DSBGV computes all the eigenvalues, and optionally, the eigenvectors
*> of a real generalized symmetric-definite banded eigenproblem, of
*> the form A*x=(lambda)*B*x. Here A and B are assumed to be symmetric
*> and banded, and B is also positive definite.
*> \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 DOUBLE PRECISION array, dimension (LDAB, N)
*> On entry, the upper or lower triangle of the symmetric 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 DOUBLE PRECISION array, dimension (LDBB, N)
*> On entry, the upper or lower triangle of the symmetric 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**T*S, as returned by DPBSTF.
*> \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 DOUBLE PRECISION 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**T*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 DOUBLE PRECISION array, dimension (3*N)
*> \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 DPBSTF
*> 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 December 2016
*
*> \ingroup doubleOTHEReigen
*
* =====================================================================
SUBROUTINE DSBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
$ LDZ, WORK, INFO )
*
* -- LAPACK driver routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
*
* .. Scalar Arguments ..
CHARACTER JOBZ, UPLO
INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION AB( LDAB, * ), BB( LDBB, * ), W( * ),
$ WORK( * ), Z( LDZ, * )
* ..
*
* =====================================================================
*
* .. Local Scalars ..
LOGICAL UPPER, WANTZ
CHARACTER VECT
INTEGER IINFO, INDE, INDWRK
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL DPBSTF, DSBGST, DSBTRD, DSTEQR, DSTERF, XERBLA
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
WANTZ = LSAME( JOBZ, 'V' )
UPPER = LSAME( UPLO, 'U' )
*
INFO = 0
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.NE.0 ) THEN
CALL XERBLA( 'DSBGV ', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
* Form a split Cholesky factorization of B.
*
CALL DPBSTF( 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
CALL DSBGST( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Z, LDZ,
$ WORK( INDWRK ), IINFO )
*
* Reduce to tridiagonal form.
*
IF( WANTZ ) THEN
VECT = 'U'
ELSE
VECT = 'N'
END IF
CALL DSBTRD( VECT, UPLO, N, KA, AB, LDAB, W, WORK( INDE ), Z, LDZ,
$ WORK( INDWRK ), IINFO )
*
* For eigenvalues only, call DSTERF. For eigenvectors, call SSTEQR.
*
IF( .NOT.WANTZ ) THEN
CALL DSTERF( N, W, WORK( INDE ), INFO )
ELSE
CALL DSTEQR( JOBZ, N, W, WORK( INDE ), Z, LDZ, WORK( INDWRK ),
$ INFO )
END IF
RETURN
*
* End of DSBGV
*
END
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