version 1.5, 2010/08/07 13:22:33
|
version 1.13, 2014/01/27 09:28:34
|
Line 1
|
Line 1
|
|
*> \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, |
SUBROUTINE ZHBGVD( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, |
$ Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, |
$ Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, |
$ LIWORK, INFO ) |
$ LIWORK, INFO ) |
* |
* |
* -- LAPACK driver routine (version 3.2) -- |
* -- LAPACK driver routine (version 3.4.0) -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* November 2006 |
* November 2011 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER JOBZ, UPLO |
CHARACTER JOBZ, UPLO |
Line 19
|
Line 269
|
$ Z( LDZ, * ) |
$ Z( LDZ, * ) |
* .. |
* .. |
* |
* |
* Purpose |
|
* ======= |
|
* |
|
* 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. |
|
* |
|
* Arguments |
|
* ========= |
|
* |
|
* JOBZ (input) CHARACTER*1 |
|
* = 'N': Compute eigenvalues only; |
|
* = 'V': Compute eigenvalues and eigenvectors. |
|
* |
|
* UPLO (input) CHARACTER*1 |
|
* = 'U': Upper triangles of A and B are stored; |
|
* = 'L': Lower triangles of A and B are stored. |
|
* |
|
* N (input) INTEGER |
|
* The order of the matrices A and B. N >= 0. |
|
* |
|
* KA (input) INTEGER |
|
* The number of superdiagonals of the matrix A if UPLO = 'U', |
|
* or the number of subdiagonals if UPLO = 'L'. KA >= 0. |
|
* |
|
* KB (input) INTEGER |
|
* The number of superdiagonals of the matrix B if UPLO = 'U', |
|
* or the number of subdiagonals if UPLO = 'L'. KB >= 0. |
|
* |
|
* AB (input/output) 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. |
|
* |
|
* LDAB (input) INTEGER |
|
* The leading dimension of the array AB. LDAB >= KA+1. |
|
* |
|
* BB (input/output) 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. |
|
* |
|
* LDBB (input) INTEGER |
|
* The leading dimension of the array BB. LDBB >= KB+1. |
|
* |
|
* W (output) DOUBLE PRECISION array, dimension (N) |
|
* If INFO = 0, the eigenvalues in ascending order. |
|
* |
|
* Z (output) 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. |
|
* |
|
* LDZ (input) INTEGER |
|
* The leading dimension of the array Z. LDZ >= 1, and if |
|
* JOBZ = 'V', LDZ >= N. |
|
* |
|
* WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) |
|
* On exit, if INFO=0, WORK(1) returns the optimal LWORK. |
|
* |
|
* LWORK (input) 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. |
|
* |
|
* RWORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LRWORK)) |
|
* On exit, if INFO=0, RWORK(1) returns the optimal LRWORK. |
|
* |
|
* LRWORK (input) 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. |
|
* |
|
* IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) |
|
* On exit, if INFO=0, IWORK(1) returns the optimal LIWORK. |
|
* |
|
* LIWORK (input) 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. |
|
* |
|
* INFO (output) 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. |
|
* |
|
* Further Details |
|
* =============== |
|
* |
|
* Based on contributions by |
|
* Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA |
|
* |
|
* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
Line 191
|
Line 300
|
* |
* |
INFO = 0 |
INFO = 0 |
IF( N.LE.1 ) THEN |
IF( N.LE.1 ) THEN |
LWMIN = 1 |
LWMIN = 1+N |
LRWMIN = 1 |
LRWMIN = 1+N |
LIWMIN = 1 |
LIWMIN = 1 |
ELSE IF( WANTZ ) THEN |
ELSE IF( WANTZ ) THEN |
LWMIN = 2*N**2 |
LWMIN = 2*N**2 |