--- rpl/lapack/lapack/zhegvd.f 2010/08/06 15:28:54 1.3
+++ rpl/lapack/lapack/zhegvd.f 2023/08/07 08:39:23 1.19
@@ -1,10 +1,255 @@
+*> \brief \b ZHEGVD
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZHEGVD + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE ZHEGVD( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
+* LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER JOBZ, UPLO
+* INTEGER INFO, ITYPE, LDA, LDB, LIWORK, LRWORK, LWORK, N
+* ..
+* .. Array Arguments ..
+* INTEGER IWORK( * )
+* DOUBLE PRECISION RWORK( * ), W( * )
+* COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> ZHEGVD computes all the eigenvalues, and optionally, the eigenvectors
+*> of a complex generalized Hermitian-definite eigenproblem, of the form
+*> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
+*> B are assumed to be Hermitian and B is also positive definite.
+*> 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] ITYPE
+*> \verbatim
+*> ITYPE is INTEGER
+*> Specifies the problem type to be solved:
+*> = 1: A*x = (lambda)*B*x
+*> = 2: A*B*x = (lambda)*x
+*> = 3: B*A*x = (lambda)*x
+*> \endverbatim
+*>
+*> \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 triangles of A and B are stored;
+*> = 'L': Lower triangles of A and B are stored.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrices A and B. 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
+*> matrix Z of eigenvectors. The eigenvectors are normalized
+*> as follows:
+*> if ITYPE = 1 or 2, Z**H*B*Z = I;
+*> if ITYPE = 3, Z**H*inv(B)*Z = I.
+*> If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')
+*> or the lower triangle (if UPLO='L') 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[in,out] B
+*> \verbatim
+*> B is COMPLEX*16 array, dimension (LDB, N)
+*> On entry, the Hermitian matrix B. If UPLO = 'U', the
+*> leading N-by-N upper triangular part of B contains the
+*> upper triangular part of the matrix B. If UPLO = 'L',
+*> the leading N-by-N lower triangular part of B contains
+*> the lower triangular part of the matrix B.
+*>
+*> On exit, if INFO <= N, the part of B containing the matrix is
+*> overwritten by the triangular factor U or L from the Cholesky
+*> factorization B = U**H*U or B = L*L**H.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*> LDB is INTEGER
+*> The leading dimension of the array B. LDB >= 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 >= 1.
+*> If JOBZ = 'N' and N > 1, LWORK >= N + 1.
+*> If JOBZ = 'V' and N > 1, LWORK >= 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 (MAX(1,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 >= 1.
+*> If JOBZ = 'N' and N > 1, LRWORK >= N.
+*> If JOBZ = 'V' and N > 1, LRWORK >= 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 >= 1.
+*> If JOBZ = 'N' and N > 1, LIWORK >= 1.
+*> If JOBZ = 'V' and N > 1, LIWORK >= 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: ZPOTRF or ZHEEVD returned an error code:
+*> <= N: 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);
+*> > N: if INFO = N + i, for 1 <= i <= N, then the leading
+*> minor of order i of B is not positive definite.
+*> The factorization of B could not be completed and
+*> no eigenvalues or eigenvectors were computed.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \ingroup complex16HEeigen
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
+*>
+*> Modified so that no backsubstitution is performed if ZHEEVD fails to
+*> converge (NEIG in old code could be greater than N causing out of
+*> bounds reference to A - reported by Ralf Meyer). Also corrected the
+*> description of INFO and the test on ITYPE. Sven, 16 Feb 05.
+*> \endverbatim
+*
+*> \par Contributors:
+* ==================
+*>
+*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
+*>
+* =====================================================================
SUBROUTINE ZHEGVD( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
$ 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, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* November 2006
*
* .. Scalar Arguments ..
CHARACTER JOBZ, UPLO
@@ -16,150 +261,6 @@
COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
-* Purpose
-* =======
-*
-* ZHEGVD computes all the eigenvalues, and optionally, the eigenvectors
-* of a complex generalized Hermitian-definite eigenproblem, of the form
-* A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
-* B are assumed to be Hermitian and B is also positive definite.
-* 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
-* =========
-*
-* ITYPE (input) INTEGER
-* Specifies the problem type to be solved:
-* = 1: A*x = (lambda)*B*x
-* = 2: A*B*x = (lambda)*x
-* = 3: B*A*x = (lambda)*x
-*
-* JOBZ (input) CHARACTER*1
-* = 'N': Compute eigenvalues only;
-* = 'V': Compute eigenvalues and eigenvectors.
-*
-* UPLO (input) CHARACTER*1
-* = 'U': Upper triangles of A and B are stored;
-* = 'L': Lower triangles of A and B are stored.
-*
-* N (input) INTEGER
-* The order of the matrices A and B. 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
-* matrix Z of eigenvectors. The eigenvectors are normalized
-* as follows:
-* if ITYPE = 1 or 2, Z**H*B*Z = I;
-* if ITYPE = 3, Z**H*inv(B)*Z = I.
-* If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')
-* or the lower triangle (if UPLO='L') of A, including the
-* diagonal, is destroyed.
-*
-* LDA (input) INTEGER
-* The leading dimension of the array A. LDA >= max(1,N).
-*
-* B (input/output) COMPLEX*16 array, dimension (LDB, N)
-* On entry, the Hermitian matrix B. If UPLO = 'U', the
-* leading N-by-N upper triangular part of B contains the
-* upper triangular part of the matrix B. If UPLO = 'L',
-* the leading N-by-N lower triangular part of B contains
-* the lower triangular part of the matrix B.
-*
-* On exit, if INFO <= N, the part of B containing the matrix is
-* overwritten by the triangular factor U or L from the Cholesky
-* factorization B = U**H*U or B = L*L**H.
-*
-* LDB (input) INTEGER
-* The leading dimension of the array B. LDB >= 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 >= 1.
-* If JOBZ = 'N' and N > 1, LWORK >= N + 1.
-* If JOBZ = 'V' and N > 1, LWORK >= 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 (MAX(1,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 >= 1.
-* If JOBZ = 'N' and N > 1, LRWORK >= N.
-* If JOBZ = 'V' and N > 1, LRWORK >= 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 >= 1.
-* If JOBZ = 'N' and N > 1, LIWORK >= 1.
-* If JOBZ = 'V' and N > 1, LIWORK >= 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: ZPOTRF or ZHEEVD returned an error code:
-* <= N: 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);
-* > N: if INFO = N + i, for 1 <= i <= N, then the leading
-* minor of order i of B is not positive definite.
-* The factorization of B could not be completed and
-* no eigenvalues or eigenvectors were computed.
-*
-* Further Details
-* ===============
-*
-* Based on contributions by
-* Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
-*
-* Modified so that no backsubstitution is performed if ZHEEVD fails to
-* converge (NEIG in old code could be greater than N causing out of
-* bounds reference to A - reported by Ralf Meyer). Also corrected the
-* description of INFO and the test on ITYPE. Sven, 16 Feb 05.
* =====================================================================
*
* .. Parameters ..
@@ -259,9 +360,9 @@
CALL ZHEGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
CALL ZHEEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, LRWORK,
$ IWORK, LIWORK, INFO )
- LOPT = MAX( DBLE( LOPT ), DBLE( WORK( 1 ) ) )
- LROPT = MAX( DBLE( LROPT ), DBLE( RWORK( 1 ) ) )
- LIOPT = MAX( DBLE( LIOPT ), DBLE( IWORK( 1 ) ) )
+ LOPT = INT( MAX( DBLE( LOPT ), DBLE( WORK( 1 ) ) ) )
+ LROPT = INT( MAX( DBLE( LROPT ), DBLE( RWORK( 1 ) ) ) )
+ LIOPT = INT( MAX( DBLE( LIOPT ), DBLE( IWORK( 1 ) ) ) )
*
IF( WANTZ .AND. INFO.EQ.0 ) THEN
*
@@ -270,7 +371,7 @@
IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
*
* For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
-* backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
+* backtransform eigenvectors: x = inv(L)**H *y or inv(U)*y
*
IF( UPPER ) THEN
TRANS = 'N'
@@ -284,7 +385,7 @@
ELSE IF( ITYPE.EQ.3 ) THEN
*
* For B*A*x=(lambda)*x;
-* backtransform eigenvectors: x = L*y or U'*y
+* backtransform eigenvectors: x = L*y or U**H *y
*
IF( UPPER ) THEN
TRANS = 'C'