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278 lines
8.2 KiB
278 lines
8.2 KiB
2 years ago
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*> \brief \b SSBGV
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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*> \htmlonly
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*> Download SSBGV + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ssbgv.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ssbgv.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ssbgv.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE SSBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
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* LDZ, WORK, INFO )
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*
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* .. Scalar Arguments ..
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* CHARACTER JOBZ, UPLO
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* INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, N
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* ..
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* .. Array Arguments ..
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* REAL AB( LDAB, * ), BB( LDBB, * ), W( * ),
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* $ WORK( * ), Z( LDZ, * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> SSBGV computes all the eigenvalues, and optionally, the eigenvectors
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*> of a real generalized symmetric-definite banded eigenproblem, of
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*> the form A*x=(lambda)*B*x. Here A and B are assumed to be symmetric
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*> and banded, and B is also positive definite.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] JOBZ
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*> \verbatim
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*> JOBZ is CHARACTER*1
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*> = 'N': Compute eigenvalues only;
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*> = 'V': Compute eigenvalues and eigenvectors.
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*> \endverbatim
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*>
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*> \param[in] UPLO
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*> \verbatim
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*> UPLO is CHARACTER*1
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*> = 'U': Upper triangles of A and B are stored;
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*> = 'L': Lower triangles of A and B are stored.
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The order of the matrices A and B. N >= 0.
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*> \endverbatim
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*>
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*> \param[in] KA
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*> \verbatim
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*> KA is INTEGER
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*> The number of superdiagonals of the matrix A if UPLO = 'U',
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*> or the number of subdiagonals if UPLO = 'L'. KA >= 0.
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*> \endverbatim
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*>
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*> \param[in] KB
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*> \verbatim
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*> KB is INTEGER
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*> The number of superdiagonals of the matrix B if UPLO = 'U',
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*> or the number of subdiagonals if UPLO = 'L'. KB >= 0.
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*> \endverbatim
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*>
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*> \param[in,out] AB
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*> \verbatim
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*> AB is REAL array, dimension (LDAB, N)
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*> On entry, the upper or lower triangle of the symmetric band
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*> matrix A, stored in the first ka+1 rows of the array. The
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*> j-th column of A is stored in the j-th column of the array AB
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*> as follows:
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*> if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
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*> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka).
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*>
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*> On exit, the contents of AB are destroyed.
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*> \endverbatim
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*>
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*> \param[in] LDAB
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*> \verbatim
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*> LDAB is INTEGER
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*> The leading dimension of the array AB. LDAB >= KA+1.
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*> \endverbatim
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*>
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*> \param[in,out] BB
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*> \verbatim
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*> BB is REAL array, dimension (LDBB, N)
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*> On entry, the upper or lower triangle of the symmetric band
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*> matrix B, stored in the first kb+1 rows of the array. The
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*> j-th column of B is stored in the j-th column of the array BB
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*> as follows:
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*> if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
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*> if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb).
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*>
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*> On exit, the factor S from the split Cholesky factorization
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*> B = S**T*S, as returned by SPBSTF.
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*> \endverbatim
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*>
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*> \param[in] LDBB
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*> \verbatim
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*> LDBB is INTEGER
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*> The leading dimension of the array BB. LDBB >= KB+1.
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*> \endverbatim
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*>
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*> \param[out] W
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*> \verbatim
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*> W is REAL array, dimension (N)
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*> If INFO = 0, the eigenvalues in ascending order.
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*> \endverbatim
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*>
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*> \param[out] Z
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*> \verbatim
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*> Z is REAL array, dimension (LDZ, N)
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*> If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
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*> eigenvectors, with the i-th column of Z holding the
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*> eigenvector associated with W(i). The eigenvectors are
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*> normalized so that Z**T*B*Z = I.
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*> If JOBZ = 'N', then Z is not referenced.
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*> \endverbatim
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*>
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*> \param[in] LDZ
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*> \verbatim
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*> LDZ is INTEGER
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*> The leading dimension of the array Z. LDZ >= 1, and if
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*> JOBZ = 'V', LDZ >= N.
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is REAL array, dimension (3*N)
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*> \endverbatim
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*>
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*> \param[out] INFO
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*> \verbatim
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*> INFO is INTEGER
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*> = 0: successful exit
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*> < 0: if INFO = -i, the i-th argument had an illegal value
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*> > 0: if INFO = i, and i is:
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*> <= N: the algorithm failed to converge:
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*> i off-diagonal elements of an intermediate
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*> tridiagonal form did not converge to zero;
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*> > N: if INFO = N + i, for 1 <= i <= N, then SPBSTF
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*> returned INFO = i: B is not positive definite.
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*> The factorization of B could not be completed and
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*> no eigenvalues or eigenvectors were computed.
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \ingroup realOTHEReigen
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*
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* =====================================================================
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SUBROUTINE SSBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
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$ LDZ, WORK, INFO )
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*
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* -- LAPACK driver routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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CHARACTER JOBZ, UPLO
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INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, N
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* ..
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* .. Array Arguments ..
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REAL AB( LDAB, * ), BB( LDBB, * ), W( * ),
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$ WORK( * ), Z( LDZ, * )
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* ..
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*
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* =====================================================================
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*
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* .. Local Scalars ..
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LOGICAL UPPER, WANTZ
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CHARACTER VECT
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INTEGER IINFO, INDE, INDWRK
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* ..
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* .. External Subroutines ..
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EXTERNAL SPBSTF, SSBGST, SSBTRD, SSTEQR, SSTERF, XERBLA
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* ..
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* .. Executable Statements ..
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*
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* Test the input parameters.
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*
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WANTZ = LSAME( JOBZ, 'V' )
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UPPER = LSAME( UPLO, 'U' )
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*
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INFO = 0
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IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
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INFO = -1
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ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
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INFO = -2
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ELSE IF( N.LT.0 ) THEN
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INFO = -3
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ELSE IF( KA.LT.0 ) THEN
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INFO = -4
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ELSE IF( KB.LT.0 .OR. KB.GT.KA ) THEN
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INFO = -5
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ELSE IF( LDAB.LT.KA+1 ) THEN
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INFO = -7
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ELSE IF( LDBB.LT.KB+1 ) THEN
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INFO = -9
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ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
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INFO = -12
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'SSBGV', -INFO )
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RETURN
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END IF
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*
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* Quick return if possible
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*
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IF( N.EQ.0 )
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$ RETURN
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*
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* Form a split Cholesky factorization of B.
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*
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CALL SPBSTF( UPLO, N, KB, BB, LDBB, INFO )
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IF( INFO.NE.0 ) THEN
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INFO = N + INFO
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RETURN
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END IF
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*
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* Transform problem to standard eigenvalue problem.
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*
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INDE = 1
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INDWRK = INDE + N
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CALL SSBGST( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Z, LDZ,
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$ WORK( INDWRK ), IINFO )
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*
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* Reduce to tridiagonal form.
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*
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IF( WANTZ ) THEN
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VECT = 'U'
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ELSE
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VECT = 'N'
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END IF
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CALL SSBTRD( VECT, UPLO, N, KA, AB, LDAB, W, WORK( INDE ), Z, LDZ,
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$ WORK( INDWRK ), IINFO )
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*
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* For eigenvalues only, call SSTERF. For eigenvectors, call SSTEQR.
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*
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IF( .NOT.WANTZ ) THEN
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CALL SSTERF( N, W, WORK( INDE ), INFO )
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ELSE
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CALL SSTEQR( JOBZ, N, W, WORK( INDE ), Z, LDZ, WORK( INDWRK ),
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$ INFO )
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END IF
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RETURN
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*
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* End of SSBGV
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*
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END
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