--- rpl/lapack/lapack/zheevd.f 2010/12/21 13:53:46 1.7 +++ rpl/lapack/lapack/zheevd.f 2011/11/21 20:43:11 1.8 @@ -1,10 +1,214 @@ +*> \brief ZHEEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ZHEEVD + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE ZHEEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, +* LRWORK, IWORK, LIWORK, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER JOBZ, UPLO +* INTEGER INFO, LDA, LIWORK, LRWORK, LWORK, N +* .. +* .. Array Arguments .. +* INTEGER IWORK( * ) +* DOUBLE PRECISION RWORK( * ), W( * ) +* COMPLEX*16 A( LDA, * ), WORK( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ZHEEVD computes all eigenvalues and, optionally, eigenvectors of a +*> complex Hermitian 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,out] A +*> \verbatim +*> A is COMPLEX*16 array, dimension (LDA, N) +*> On entry, the Hermitian matrix A. If UPLO = 'U', the +*> leading N-by-N upper triangular part of A contains the +*> upper triangular part of the matrix A. If UPLO = 'L', +*> the leading N-by-N lower triangular part of A contains +*> the lower triangular part of the matrix A. +*> On exit, if JOBZ = 'V', then if INFO = 0, A contains the +*> orthonormal eigenvectors of the matrix A. +*> If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') +*> or the upper triangle (if UPLO='U') of A, including the +*> diagonal, is destroyed. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,N). +*> \endverbatim +*> +*> \param[out] W +*> \verbatim +*> W is DOUBLE PRECISION array, dimension (N) +*> If INFO = 0, the eigenvalues in ascending order. +*> \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 length 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 + 1. +*> If JOBZ = 'V' and N > 1, LWORK must be at least 2*N + 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 the 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 the array IWORK. +*> If N <= 1, LIWORK must be at least 1. +*> If JOBZ = 'N' and 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 and JOBZ = 'N', then the algorithm failed +*> to converge; i off-diagonal elements of an intermediate +*> tridiagonal form did not converge to zero; +*> if INFO = i and JOBZ = 'V', then the algorithm failed +*> to compute an eigenvalue while working on the submatrix +*> lying in rows and columns INFO/(N+1) through +*> mod(INFO,N+1). +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex16HEeigen +* +*> \par Further Details: +* ===================== +*> +*> Modified description of INFO. Sven, 16 Feb 05. +* +*> \par Contributors: +* ================== +*> +*> Jeff Rutter, Computer Science Division, University of California +*> at Berkeley, USA +*> +* ===================================================================== SUBROUTINE ZHEEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, $ LRWORK, IWORK, 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, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* November 2006 +* November 2011 * * .. Scalar Arguments .. CHARACTER JOBZ, UPLO @@ -16,118 +220,6 @@ COMPLEX*16 A( LDA, * ), WORK( * ) * .. * -* Purpose -* ======= -* -* ZHEEVD computes all eigenvalues and, optionally, eigenvectors of a -* complex Hermitian 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. -* -* A (input/output) COMPLEX*16 array, dimension (LDA, N) -* On entry, the Hermitian matrix A. If UPLO = 'U', the -* leading N-by-N upper triangular part of A contains the -* upper triangular part of the matrix A. If UPLO = 'L', -* the leading N-by-N lower triangular part of A contains -* the lower triangular part of the matrix A. -* On exit, if JOBZ = 'V', then if INFO = 0, A contains the -* orthonormal eigenvectors of the matrix A. -* If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') -* or the upper triangle (if UPLO='U') of A, including the -* diagonal, is destroyed. -* -* LDA (input) INTEGER -* The leading dimension of the array A. LDA >= max(1,N). -* -* W (output) DOUBLE PRECISION array, dimension (N) -* If INFO = 0, the eigenvalues in ascending order. -* -* 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 length 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 + 1. -* If JOBZ = 'V' and N > 1, LWORK must be at least 2*N + 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 the 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 the array IWORK. -* If N <= 1, LIWORK must be at least 1. -* If JOBZ = 'N' and 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 and JOBZ = 'N', then the algorithm failed -* to converge; i off-diagonal elements of an intermediate -* tridiagonal form did not converge to zero; -* if INFO = i and JOBZ = 'V', then the algorithm failed -* to compute an eigenvalue while working on the submatrix -* lying in rows and columns INFO/(N+1) through -* mod(INFO,N+1). -* -* Further Details -* =============== -* -* Based on contributions by -* Jeff Rutter, Computer Science Division, University of California -* at Berkeley, USA -* -* Modified description of INFO. Sven, 16 Feb 05. * ===================================================================== * * .. Parameters ..