version 1.3, 2010/08/06 15:28:54
|
version 1.17, 2023/08/07 08:39:22
|
Line 1
|
Line 1
|
|
*> \brief <b> ZHBEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices</b> |
|
* |
|
* =========== DOCUMENTATION =========== |
|
* |
|
* Online html documentation available at |
|
* http://www.netlib.org/lapack/explore-html/ |
|
* |
|
*> \htmlonly |
|
*> Download ZHBEVD + dependencies |
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhbevd.f"> |
|
*> [TGZ]</a> |
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhbevd.f"> |
|
*> [ZIP]</a> |
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhbevd.f"> |
|
*> [TXT]</a> |
|
*> \endhtmlonly |
|
* |
|
* Definition: |
|
* =========== |
|
* |
|
* SUBROUTINE ZHBEVD( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, |
|
* LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO ) |
|
* |
|
* .. Scalar Arguments .. |
|
* CHARACTER JOBZ, UPLO |
|
* INTEGER INFO, KD, LDAB, LDZ, LIWORK, LRWORK, LWORK, N |
|
* .. |
|
* .. Array Arguments .. |
|
* INTEGER IWORK( * ) |
|
* DOUBLE PRECISION RWORK( * ), W( * ) |
|
* COMPLEX*16 AB( LDAB, * ), WORK( * ), Z( LDZ, * ) |
|
* .. |
|
* |
|
* |
|
*> \par Purpose: |
|
* ============= |
|
*> |
|
*> \verbatim |
|
*> |
|
*> ZHBEVD computes all the eigenvalues and, optionally, eigenvectors of |
|
*> a complex Hermitian band matrix A. 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 triangle of A is stored; |
|
*> = 'L': Lower triangle of A is stored. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] N |
|
*> \verbatim |
|
*> N is INTEGER |
|
*> The order of the matrix A. N >= 0. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] KD |
|
*> \verbatim |
|
*> KD is INTEGER |
|
*> The number of superdiagonals of the matrix A if UPLO = 'U', |
|
*> or the number of subdiagonals if UPLO = 'L'. KD >= 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 KD+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(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; |
|
*> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). |
|
*> |
|
*> On exit, AB is overwritten by values generated during the |
|
*> reduction to tridiagonal form. If UPLO = 'U', the first |
|
*> superdiagonal and the diagonal of the tridiagonal matrix T |
|
*> are returned in rows KD and KD+1 of AB, and if UPLO = 'L', |
|
*> the diagonal and first subdiagonal of T are returned in the |
|
*> first two rows of AB. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] LDAB |
|
*> \verbatim |
|
*> LDAB is INTEGER |
|
*> The leading dimension of the array AB. LDAB >= KD + 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 orthonormal |
|
*> eigenvectors of the matrix A, with the i-th column of Z |
|
*> holding the eigenvector associated with W(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 >= max(1,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 must be at least 1. |
|
*> If JOBZ = 'N' and N > 1, LWORK must be at least N. |
|
*> If JOBZ = 'V' and N > 1, LWORK must be at least 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 (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 must be at least 1. |
|
*> If JOBZ = 'N' and N > 1, LRWORK must be at least N. |
|
*> If JOBZ = 'V' and N > 1, LRWORK must be at least |
|
*> 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 must be at least 1. |
|
*> If JOBZ = 'V' and N > 1, LIWORK must be at least 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, the algorithm failed to converge; i |
|
*> off-diagonal elements of an intermediate tridiagonal |
|
*> form did not converge to zero. |
|
*> \endverbatim |
|
* |
|
* Authors: |
|
* ======== |
|
* |
|
*> \author Univ. of Tennessee |
|
*> \author Univ. of California Berkeley |
|
*> \author Univ. of Colorado Denver |
|
*> \author NAG Ltd. |
|
* |
|
*> \ingroup complex16OTHEReigen |
|
* |
|
* ===================================================================== |
SUBROUTINE ZHBEVD( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, |
SUBROUTINE ZHBEVD( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, |
$ LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO ) |
$ LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO ) |
* |
* |
* -- LAPACK driver routine (version 3.2) -- |
* -- LAPACK driver routine -- |
* -- 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 |
|
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER JOBZ, UPLO |
CHARACTER JOBZ, UPLO |
Line 16
|
Line 227
|
COMPLEX*16 AB( LDAB, * ), WORK( * ), Z( LDZ, * ) |
COMPLEX*16 AB( LDAB, * ), WORK( * ), Z( LDZ, * ) |
* .. |
* .. |
* |
* |
* Purpose |
|
* ======= |
|
* |
|
* ZHBEVD computes all the eigenvalues and, optionally, eigenvectors of |
|
* a complex Hermitian band matrix A. 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 triangle of A is stored; |
|
* = 'L': Lower triangle of A is stored. |
|
* |
|
* N (input) INTEGER |
|
* The order of the matrix A. N >= 0. |
|
* |
|
* KD (input) INTEGER |
|
* The number of superdiagonals of the matrix A if UPLO = 'U', |
|
* or the number of subdiagonals if UPLO = 'L'. KD >= 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 KD+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(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; |
|
* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). |
|
* |
|
* On exit, AB is overwritten by values generated during the |
|
* reduction to tridiagonal form. If UPLO = 'U', the first |
|
* superdiagonal and the diagonal of the tridiagonal matrix T |
|
* are returned in rows KD and KD+1 of AB, and if UPLO = 'L', |
|
* the diagonal and first subdiagonal of T are returned in the |
|
* first two rows of AB. |
|
* |
|
* LDAB (input) INTEGER |
|
* The leading dimension of the array AB. LDAB >= KD + 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 orthonormal |
|
* eigenvectors of the matrix A, with the i-th column of Z |
|
* holding the eigenvector associated with W(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 >= max(1,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 must be at least 1. |
|
* If JOBZ = 'N' and N > 1, LWORK must be at least N. |
|
* If JOBZ = 'V' and N > 1, LWORK must be at least 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 (LRWORK) |
|
* On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. |
|
* |
|
* LRWORK (input) INTEGER |
|
* The dimension of array RWORK. |
|
* If N <= 1, LRWORK must be at least 1. |
|
* If JOBZ = 'N' and N > 1, LRWORK must be at least N. |
|
* If JOBZ = 'V' and N > 1, LRWORK must be at least |
|
* 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 must be at least 1. |
|
* If JOBZ = 'V' and N > 1, LIWORK must be at least 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, the algorithm failed to converge; i |
|
* off-diagonal elements of an intermediate tridiagonal |
|
* form did not converge to zero. |
|
* |
|
* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
Line 225
|
Line 320
|
$ RETURN |
$ RETURN |
* |
* |
IF( N.EQ.1 ) THEN |
IF( N.EQ.1 ) THEN |
W( 1 ) = AB( 1, 1 ) |
W( 1 ) = DBLE( AB( 1, 1 ) ) |
IF( WANTZ ) |
IF( WANTZ ) |
$ Z( 1, 1 ) = CONE |
$ Z( 1, 1 ) = CONE |
RETURN |
RETURN |