--- rpl/lapack/lapack/zstegr.f 2010/01/26 15:22:45 1.1
+++ rpl/lapack/lapack/zstegr.f 2023/08/07 08:39:37 1.19
@@ -1,14 +1,271 @@
+*> \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 compatibility wrapper around the improved ZSTEMR routine.
+*> See ZSTEMR 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
+*>
+*> If RANGE='V', the lower bound of the interval to
+*> be searched for eigenvalues. VL < VU.
+*> Not referenced if RANGE = 'A' or 'I'.
+*> \endverbatim
+*>
+*> \param[in] VU
+*> \verbatim
+*> VU is DOUBLE PRECISION
+*>
+*> If RANGE='V', the upper bound 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
+*>
+*> If RANGE='I', the index of the
+*> smallest eigenvalue to be returned.
+*> 1 <= IL <= IU <= N, if N > 0.
+*> Not referenced if RANGE = 'A' or 'V'.
+*> \endverbatim
+*>
+*> \param[in] IU
+*> \verbatim
+*> IU is INTEGER
+*>
+*> If RANGE='I', the index of the
+*> largest eigenvalue 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.
+*
+*> \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 --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* November 2006
*
* .. Scalar Arguments ..
CHARACTER JOBZ, RANGE
@@ -21,145 +278,6 @@
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 ..