--- rpl/lapack/lapack/dsyevd.f 2010/04/21 13:45:25 1.2
+++ rpl/lapack/lapack/dsyevd.f 2023/08/07 08:39:08 1.18
@@ -1,10 +1,191 @@
+*> \brief DSYEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DSYEVD + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DSYEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, IWORK,
+* LIWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER JOBZ, UPLO
+* INTEGER INFO, LDA, LIWORK, LWORK, N
+* ..
+* .. Array Arguments ..
+* INTEGER IWORK( * )
+* DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DSYEVD computes all eigenvalues and, optionally, eigenvectors of a
+*> real symmetric 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.
+*>
+*> Because of large use of BLAS of level 3, DSYEVD needs N**2 more
+*> workspace than DSYEVX.
+*> \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 DOUBLE PRECISION array, dimension (LDA, N)
+*> On entry, the symmetric 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 DOUBLE PRECISION array,
+*> dimension (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 2*N+1.
+*> If JOBZ = 'V' and N > 1, LWORK must be at least
+*> 1 + 6*N + 2*N**2.
+*>
+*> If LWORK = -1, then a workspace query is assumed; the routine
+*> only calculates the optimal sizes of the WORK and IWORK
+*> arrays, returns these values as the first entries of the WORK
+*> and IWORK arrays, and no error message related to LWORK 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 and
+*> IWORK arrays, returns these values as the first entries of
+*> the WORK and IWORK arrays, and no error message related to
+*> LWORK 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.
+*
+*> \ingroup doubleSYeigen
+*
+*> \par Contributors:
+* ==================
+*>
+*> Jeff Rutter, Computer Science Division, University of California
+*> at Berkeley, USA \n
+*> Modified by Francoise Tisseur, University of Tennessee \n
+*> Modified description of INFO. Sven, 16 Feb 05. \n
+
+
+*>
+* =====================================================================
SUBROUTINE DSYEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, IWORK,
$ LIWORK, INFO )
*
-* -- LAPACK driver routine (version 3.2) --
+* -- LAPACK driver 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, UPLO
@@ -15,107 +196,6 @@
DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * )
* ..
*
-* Purpose
-* =======
-*
-* DSYEVD computes all eigenvalues and, optionally, eigenvectors of a
-* real symmetric 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.
-*
-* Because of large use of BLAS of level 3, DSYEVD needs N**2 more
-* workspace than DSYEVX.
-*
-* 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) DOUBLE PRECISION array, dimension (LDA, N)
-* On entry, the symmetric 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) DOUBLE PRECISION array,
-* dimension (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 2*N+1.
-* If JOBZ = 'V' and N > 1, LWORK must be at least
-* 1 + 6*N + 2*N**2.
-*
-* If LWORK = -1, then a workspace query is assumed; the routine
-* only calculates the optimal sizes of the WORK and IWORK
-* arrays, returns these values as the first entries of the WORK
-* and IWORK arrays, and no error message related to LWORK 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 and
-* IWORK arrays, returns these values as the first entries of
-* the WORK and IWORK arrays, and no error message related to
-* LWORK 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 by Francoise Tisseur, University of Tennessee.
-*
-* Modified description of INFO. Sven, 16 Feb 05.
* =====================================================================
*
* .. Parameters ..
@@ -177,7 +257,7 @@
LWMIN = 2*N + 1
END IF
LOPT = MAX( LWMIN, 2*N +
- $ ILAENV( 1, 'DSYTRD', UPLO, N, -1, -1, -1 ) )
+ $ N*ILAENV( 1, 'DSYTRD', UPLO, N, -1, -1, -1 ) )
LIOPT = LIWMIN
END IF
WORK( 1 ) = LOPT
@@ -243,7 +323,6 @@
*
CALL DSYTRD( UPLO, N, A, LDA, W, WORK( INDE ), WORK( INDTAU ),
$ WORK( INDWRK ), LLWORK, IINFO )
- LOPT = 2*N + WORK( INDWRK )
*
* For eigenvalues only, call DSTERF. For eigenvectors, first call
* DSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
@@ -258,7 +337,6 @@
CALL DORMTR( 'L', UPLO, 'N', N, N, A, LDA, WORK( INDTAU ),
$ WORK( INDWRK ), N, WORK( INDWK2 ), LLWRK2, IINFO )
CALL DLACPY( 'A', N, N, WORK( INDWRK ), N, A, LDA )
- LOPT = MAX( LOPT, 1+6*N+2*N**2 )
END IF
*
* If matrix was scaled, then rescale eigenvalues appropriately.