--- rpl/lapack/lapack/zstegr.f 2010/12/21 13:53:55 1.7 +++ rpl/lapack/lapack/zstegr.f 2011/11/21 20:43:21 1.8 @@ -1,14 +1,265 @@ +*> \brief \b ZSTEGR +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ZSTEGR + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE ZSTEGR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, +* ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK, +* LIWORK, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER JOBZ, RANGE +* INTEGER IL, INFO, IU, LDZ, LIWORK, LWORK, M, N +* DOUBLE PRECISION ABSTOL, VL, VU +* .. +* .. Array Arguments .. +* INTEGER ISUPPZ( * ), IWORK( * ) +* DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * ) +* COMPLEX*16 Z( LDZ, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ZSTEGR computes selected eigenvalues and, optionally, eigenvectors +*> of a real symmetric tridiagonal matrix T. Any such unreduced matrix has +*> a well defined set of pairwise different real eigenvalues, the corresponding +*> real eigenvectors are pairwise orthogonal. +*> +*> The spectrum may be computed either completely or partially by specifying +*> either an interval (VL,VU] or a range of indices IL:IU for the desired +*> eigenvalues. +*> +*> ZSTEGR is a compatability wrapper around the improved ZSTEMR routine. +*> See DSTEMR for further details. +*> +*> One important change is that the ABSTOL parameter no longer provides any +*> benefit and hence is no longer used. +*> +*> Note : ZSTEGR and ZSTEMR work only on machines which follow +*> IEEE-754 floating-point standard in their handling of infinities and +*> NaNs. Normal execution may create these exceptiona values and hence +*> may abort due to a floating point exception in environments which +*> do not conform to the IEEE-754 standard. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] JOBZ +*> \verbatim +*> JOBZ is CHARACTER*1 +*> = 'N': Compute eigenvalues only; +*> = 'V': Compute eigenvalues and eigenvectors. +*> \endverbatim +*> +*> \param[in] RANGE +*> \verbatim +*> RANGE is CHARACTER*1 +*> = 'A': all eigenvalues will be found. +*> = 'V': all eigenvalues in the half-open interval (VL,VU] +*> will be found. +*> = 'I': the IL-th through IU-th eigenvalues will be found. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix. N >= 0. +*> \endverbatim +*> +*> \param[in,out] D +*> \verbatim +*> D is DOUBLE PRECISION array, dimension (N) +*> On entry, the N diagonal elements of the tridiagonal matrix +*> T. On exit, D is overwritten. +*> \endverbatim +*> +*> \param[in,out] E +*> \verbatim +*> E is DOUBLE PRECISION array, dimension (N) +*> On entry, the (N-1) subdiagonal elements of the tridiagonal +*> matrix T in elements 1 to N-1 of E. E(N) need not be set on +*> input, but is used internally as workspace. +*> On exit, E is overwritten. +*> \endverbatim +*> +*> \param[in] VL +*> \verbatim +*> VL is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in] VU +*> \verbatim +*> VU is DOUBLE PRECISION +*> +*> If RANGE='V', the lower and upper bounds of the interval to +*> be searched for eigenvalues. VL < VU. +*> Not referenced if RANGE = 'A' or 'I'. +*> \endverbatim +*> +*> \param[in] IL +*> \verbatim +*> IL is INTEGER +*> \endverbatim +*> +*> \param[in] IU +*> \verbatim +*> IU is INTEGER +*> +*> If RANGE='I', the indices (in ascending order) of the +*> smallest and largest eigenvalues to be returned. +*> 1 <= IL <= IU <= N, if N > 0. +*> Not referenced if RANGE = 'A' or 'V'. +*> \endverbatim +*> +*> \param[in] ABSTOL +*> \verbatim +*> ABSTOL is DOUBLE PRECISION +*> Unused. Was the absolute error tolerance for the +*> eigenvalues/eigenvectors in previous versions. +*> \endverbatim +*> +*> \param[out] M +*> \verbatim +*> M is INTEGER +*> The total number of eigenvalues found. 0 <= M <= N. +*> If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. +*> \endverbatim +*> +*> \param[out] W +*> \verbatim +*> W is DOUBLE PRECISION array, dimension (N) +*> The first M elements contain the selected eigenvalues in +*> ascending order. +*> \endverbatim +*> +*> \param[out] Z +*> \verbatim +*> Z is COMPLEX*16 array, dimension (LDZ, max(1,M) ) +*> If JOBZ = 'V', and if INFO = 0, then the first M columns of Z +*> contain the orthonormal eigenvectors of the matrix T +*> corresponding to the selected eigenvalues, with the i-th +*> column of Z holding the eigenvector associated with W(i). +*> If JOBZ = 'N', then Z is not referenced. +*> Note: the user must ensure that at least max(1,M) columns are +*> supplied in the array Z; if RANGE = 'V', the exact value of M +*> is not known in advance and an upper bound must be used. +*> Supplying N columns is always safe. +*> \endverbatim +*> +*> \param[in] LDZ +*> \verbatim +*> LDZ is INTEGER +*> The leading dimension of the array Z. LDZ >= 1, and if +*> JOBZ = 'V', then LDZ >= max(1,N). +*> \endverbatim +*> +*> \param[out] ISUPPZ +*> \verbatim +*> ISUPPZ is INTEGER ARRAY, dimension ( 2*max(1,M) ) +*> The support of the eigenvectors in Z, i.e., the indices +*> indicating the nonzero elements in Z. The i-th computed eigenvector +*> is nonzero only in elements ISUPPZ( 2*i-1 ) through +*> ISUPPZ( 2*i ). This is relevant in the case when the matrix +*> is split. ISUPPZ is only accessed when JOBZ is 'V' and N > 0. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is DOUBLE PRECISION array, dimension (LWORK) +*> On exit, if INFO = 0, WORK(1) returns the optimal +*> (and minimal) LWORK. +*> \endverbatim +*> +*> \param[in] LWORK +*> \verbatim +*> LWORK is INTEGER +*> The dimension of the array WORK. LWORK >= max(1,18*N) +*> if JOBZ = 'V', and LWORK >= max(1,12*N) if JOBZ = 'N'. +*> If LWORK = -1, then a workspace query is assumed; the routine +*> only calculates the optimal size of the WORK array, returns +*> this value as the first entry of the WORK array, and no error +*> message related to LWORK is issued by XERBLA. +*> \endverbatim +*> +*> \param[out] IWORK +*> \verbatim +*> IWORK is INTEGER array, dimension (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. LIWORK >= max(1,10*N) +*> if the eigenvectors are desired, and LIWORK >= max(1,8*N) +*> if only the eigenvalues are to be computed. +*> If LIWORK = -1, then a workspace query is assumed; the +*> routine only calculates the optimal size of the IWORK array, +*> returns this value as the first entry of the IWORK array, and +*> no error message related to LIWORK is issued by XERBLA. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> On exit, INFO +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> > 0: if INFO = 1X, internal error in DLARRE, +*> if INFO = 2X, internal error in ZLARRV. +*> Here, the digit X = ABS( IINFO ) < 10, where IINFO is +*> the nonzero error code returned by DLARRE or +*> ZLARRV, respectively. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex16OTHERcomputational +* +*> \par Contributors: +* ================== +*> +*> Inderjit Dhillon, IBM Almaden, USA \n +*> Osni Marques, LBNL/NERSC, USA \n +*> Christof Voemel, LBNL/NERSC, USA \n +* +* ===================================================================== SUBROUTINE ZSTEGR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, $ ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK, $ LIWORK, INFO ) - - IMPLICIT NONE -* * -* -- LAPACK computational routine (version 3.2) -- +* -- LAPACK computational 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, RANGE @@ -21,145 +272,6 @@ COMPLEX*16 Z( LDZ, * ) * .. * -* Purpose -* ======= -* -* ZSTEGR computes selected eigenvalues and, optionally, eigenvectors -* of a real symmetric tridiagonal matrix T. Any such unreduced matrix has -* a well defined set of pairwise different real eigenvalues, the corresponding -* real eigenvectors are pairwise orthogonal. -* -* The spectrum may be computed either completely or partially by specifying -* either an interval (VL,VU] or a range of indices IL:IU for the desired -* eigenvalues. -* -* ZSTEGR is a compatability wrapper around the improved ZSTEMR routine. -* See DSTEMR for further details. -* -* One important change is that the ABSTOL parameter no longer provides any -* benefit and hence is no longer used. -* -* Note : ZSTEGR and ZSTEMR work only on machines which follow -* IEEE-754 floating-point standard in their handling of infinities and -* NaNs. Normal execution may create these exceptiona values and hence -* may abort due to a floating point exception in environments which -* do not conform to the IEEE-754 standard. -* -* Arguments -* ========= -* -* JOBZ (input) CHARACTER*1 -* = 'N': Compute eigenvalues only; -* = 'V': Compute eigenvalues and eigenvectors. -* -* RANGE (input) CHARACTER*1 -* = 'A': all eigenvalues will be found. -* = 'V': all eigenvalues in the half-open interval (VL,VU] -* will be found. -* = 'I': the IL-th through IU-th eigenvalues will be found. -* -* N (input) INTEGER -* The order of the matrix. N >= 0. -* -* D (input/output) DOUBLE PRECISION array, dimension (N) -* On entry, the N diagonal elements of the tridiagonal matrix -* T. On exit, D is overwritten. -* -* E (input/output) DOUBLE PRECISION array, dimension (N) -* On entry, the (N-1) subdiagonal elements of the tridiagonal -* matrix T in elements 1 to N-1 of E. E(N) need not be set on -* input, but is used internally as workspace. -* On exit, E is overwritten. -* -* VL (input) DOUBLE PRECISION -* VU (input) DOUBLE PRECISION -* If RANGE='V', the lower and upper bounds of the interval to -* be searched for eigenvalues. VL < VU. -* Not referenced if RANGE = 'A' or 'I'. -* -* IL (input) INTEGER -* IU (input) INTEGER -* If RANGE='I', the indices (in ascending order) of the -* smallest and largest eigenvalues to be returned. -* 1 <= IL <= IU <= N, if N > 0. -* Not referenced if RANGE = 'A' or 'V'. -* -* ABSTOL (input) DOUBLE PRECISION -* Unused. Was the absolute error tolerance for the -* eigenvalues/eigenvectors in previous versions. -* -* M (output) INTEGER -* The total number of eigenvalues found. 0 <= M <= N. -* If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. -* -* W (output) DOUBLE PRECISION array, dimension (N) -* The first M elements contain the selected eigenvalues in -* ascending order. -* -* Z (output) COMPLEX*16 array, dimension (LDZ, max(1,M) ) -* If JOBZ = 'V', and if INFO = 0, then the first M columns of Z -* contain the orthonormal eigenvectors of the matrix T -* corresponding to the selected eigenvalues, with the i-th -* column of Z holding the eigenvector associated with W(i). -* If JOBZ = 'N', then Z is not referenced. -* Note: the user must ensure that at least max(1,M) columns are -* supplied in the array Z; if RANGE = 'V', the exact value of M -* is not known in advance and an upper bound must be used. -* Supplying N columns is always safe. -* -* LDZ (input) INTEGER -* The leading dimension of the array Z. LDZ >= 1, and if -* JOBZ = 'V', then LDZ >= max(1,N). -* -* ISUPPZ (output) INTEGER ARRAY, dimension ( 2*max(1,M) ) -* The support of the eigenvectors in Z, i.e., the indices -* indicating the nonzero elements in Z. The i-th computed eigenvector -* is nonzero only in elements ISUPPZ( 2*i-1 ) through -* ISUPPZ( 2*i ). This is relevant in the case when the matrix -* is split. ISUPPZ is only accessed when JOBZ is 'V' and N > 0. -* -* WORK (workspace/output) DOUBLE PRECISION array, dimension (LWORK) -* On exit, if INFO = 0, WORK(1) returns the optimal -* (and minimal) LWORK. -* -* LWORK (input) INTEGER -* The dimension of the array WORK. LWORK >= max(1,18*N) -* if JOBZ = 'V', and LWORK >= max(1,12*N) if JOBZ = 'N'. -* If LWORK = -1, then a workspace query is assumed; the routine -* only calculates the optimal size of the WORK array, returns -* this value as the first entry of the WORK array, and no error -* message related to LWORK is issued by XERBLA. -* -* IWORK (workspace/output) INTEGER array, dimension (LIWORK) -* On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. -* -* LIWORK (input) INTEGER -* The dimension of the array IWORK. LIWORK >= max(1,10*N) -* if the eigenvectors are desired, and LIWORK >= max(1,8*N) -* if only the eigenvalues are to be computed. -* If LIWORK = -1, then a workspace query is assumed; the -* routine only calculates the optimal size of the IWORK array, -* returns this value as the first entry of the IWORK array, and -* no error message related to LIWORK is issued by XERBLA. -* -* INFO (output) INTEGER -* On exit, INFO -* = 0: successful exit -* < 0: if INFO = -i, the i-th argument had an illegal value -* > 0: if INFO = 1X, internal error in DLARRE, -* if INFO = 2X, internal error in ZLARRV. -* Here, the digit X = ABS( IINFO ) < 10, where IINFO is -* the nonzero error code returned by DLARRE or -* ZLARRV, respectively. -* -* Further Details -* =============== -* -* Based on contributions by -* Inderjit Dhillon, IBM Almaden, USA -* Osni Marques, LBNL/NERSC, USA -* Christof Voemel, LBNL/NERSC, USA -* * ===================================================================== * * .. Local Scalars ..