*> \brief \b CHBGV * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download CHBGV + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE CHBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, * LDZ, WORK, RWORK, INFO ) * * .. Scalar Arguments .. * CHARACTER JOBZ, UPLO * INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, N * .. * .. Array Arguments .. * REAL RWORK( * ), W( * ) * COMPLEX AB( LDAB, * ), BB( LDBB, * ), WORK( * ), * \$ Z( LDZ, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> CHBGV 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. *> \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 (N) *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is REAL 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 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. * *> \date December 2016 * *> \ingroup complexOTHEReigen * * ===================================================================== SUBROUTINE CHBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, \$ LDZ, WORK, RWORK, 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 .. REAL RWORK( * ), W( * ) COMPLEX AB( LDAB, * ), BB( LDBB, * ), WORK( * ), \$ Z( LDZ, * ) * .. * * ===================================================================== * * .. Local Scalars .. LOGICAL UPPER, WANTZ CHARACTER VECT INTEGER IINFO, INDE, INDWRK * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL CHBGST, CHBTRD, CPBSTF, CSTEQR, SSTERF, 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( 'CHBGV ', -INFO ) 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 CALL CHBGST( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Z, LDZ, \$ WORK, RWORK( INDWRK ), IINFO ) * * Reduce 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 CSTEQR. * IF( .NOT.WANTZ ) THEN CALL SSTERF( N, W, RWORK( INDE ), INFO ) ELSE CALL CSTEQR( JOBZ, N, W, RWORK( INDE ), Z, LDZ, \$ RWORK( INDWRK ), INFO ) END IF RETURN * * End of CHBGV * END