--- rpl/lapack/lapack/dsygvx.f 2011/07/22 07:38:11 1.9
+++ rpl/lapack/lapack/dsygvx.f 2011/11/21 20:43:05 1.10
@@ -1,11 +1,299 @@
+*> \brief \b DSYGST
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DSYGVX + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DSYGVX( ITYPE, JOBZ, RANGE, UPLO, N, A, LDA, B, LDB,
+* VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK,
+* LWORK, IWORK, IFAIL, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER JOBZ, RANGE, UPLO
+* INTEGER IL, INFO, ITYPE, IU, LDA, LDB, LDZ, LWORK, M, N
+* DOUBLE PRECISION ABSTOL, VL, VU
+* ..
+* .. Array Arguments ..
+* INTEGER IFAIL( * ), IWORK( * )
+* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), W( * ), WORK( * ),
+* $ Z( LDZ, * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DSYGVX computes selected eigenvalues, and optionally, eigenvectors
+*> of a real generalized symmetric-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 symmetric and B is also positive definite.
+*> Eigenvalues and eigenvectors can be selected by specifying either a
+*> range of values or a range of indices for the desired eigenvalues.
+*> \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] 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] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> = 'U': Upper triangle of A and B are stored;
+*> = 'L': Lower triangle of A and B are stored.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrix pencil (A,B). 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, 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[in,out] B
+*> \verbatim
+*> B is DOUBLE PRECISION array, dimension (LDB, N)
+*> On entry, the symmetric 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**T*U or B = L*L**T.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*> LDB is INTEGER
+*> The leading dimension of the array B. LDB >= max(1,N).
+*> \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; IL = 1 and IU = 0 if N = 0.
+*> Not referenced if RANGE = 'A' or 'V'.
+*> \endverbatim
+*>
+*> \param[in] ABSTOL
+*> \verbatim
+*> ABSTOL is DOUBLE PRECISION
+*> The absolute error tolerance for the eigenvalues.
+*> An approximate eigenvalue is accepted as converged
+*> when it is determined to lie in an interval [a,b]
+*> of width less than or equal to
+*>
+*> ABSTOL + EPS * max( |a|,|b| ) ,
+*>
+*> where EPS is the machine precision. If ABSTOL is less than
+*> or equal to zero, then EPS*|T| will be used in its place,
+*> where |T| is the 1-norm of the tridiagonal matrix obtained
+*> by reducing C to tridiagonal form, where C is the symmetric
+*> matrix of the standard symmetric problem to which the
+*> generalized problem is transformed.
+*>
+*> Eigenvalues will be computed most accurately when ABSTOL is
+*> set to twice the underflow threshold 2*DLAMCH('S'), not zero.
+*> If this routine returns with INFO>0, indicating that some
+*> eigenvectors did not converge, try setting ABSTOL to
+*> 2*DLAMCH('S').
+*> \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)
+*> On normal exit, the first M elements contain the selected
+*> eigenvalues in ascending order.
+*> \endverbatim
+*>
+*> \param[out] Z
+*> \verbatim
+*> Z is DOUBLE PRECISION array, dimension (LDZ, max(1,M))
+*> If JOBZ = 'N', then Z is not referenced.
+*> If JOBZ = 'V', then if INFO = 0, the first M columns of Z
+*> contain the orthonormal eigenvectors of the matrix A
+*> corresponding to the selected eigenvalues, with the i-th
+*> column of Z holding the eigenvector associated with W(i).
+*> The eigenvectors are normalized as follows:
+*> if ITYPE = 1 or 2, Z**T*B*Z = I;
+*> if ITYPE = 3, Z**T*inv(B)*Z = I.
+*>
+*> If an eigenvector fails to converge, then that column of Z
+*> contains the latest approximation to the eigenvector, and the
+*> index of the eigenvector is returned in IFAIL.
+*> 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.
+*> \endverbatim
+*>
+*> \param[in] LDZ
+*> \verbatim
+*> LDZ is INTEGER
+*> The leading dimension of the array Z. LDZ >= 1, and if
+*> JOBZ = 'V', LDZ >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is DOUBLE PRECISION 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. LWORK >= max(1,8*N).
+*> For optimal efficiency, LWORK >= (NB+3)*N,
+*> where NB is the blocksize for DSYTRD returned by ILAENV.
+*>
+*> 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 (5*N)
+*> \endverbatim
+*>
+*> \param[out] IFAIL
+*> \verbatim
+*> IFAIL is INTEGER array, dimension (N)
+*> If JOBZ = 'V', then if INFO = 0, the first M elements of
+*> IFAIL are zero. If INFO > 0, then IFAIL contains the
+*> indices of the eigenvectors that failed to converge.
+*> If JOBZ = 'N', then IFAIL is not referenced.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> > 0: DPOTRF or DSYEVX returned an error code:
+*> <= N: if INFO = i, DSYEVX failed to converge;
+*> i eigenvectors failed to converge. Their indices
+*> are stored in array IFAIL.
+*> > 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.
+*
+*> \date November 2011
+*
+*> \ingroup doubleSYeigen
+*
+*> \par Contributors:
+* ==================
+*>
+*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
+*
+* =====================================================================
SUBROUTINE DSYGVX( ITYPE, JOBZ, RANGE, UPLO, N, A, LDA, B, LDB,
$ VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK,
$ LWORK, IWORK, IFAIL, INFO )
*
-* -- LAPACK driver routine (version 3.3.1) --
+* -- 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..--
-* -- April 2011 --
+* November 2011
*
* .. Scalar Arguments ..
CHARACTER JOBZ, RANGE, UPLO
@@ -18,170 +306,6 @@
$ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
-*
-* DSYGVX computes selected eigenvalues, and optionally, eigenvectors
-* of a real generalized symmetric-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 symmetric and B is also positive definite.
-* Eigenvalues and eigenvectors can be selected by specifying either a
-* range of values or a range of indices for the desired eigenvalues.
-*
-* 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.
-*
-* 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.
-*
-* UPLO (input) CHARACTER*1
-* = 'U': Upper triangle of A and B are stored;
-* = 'L': Lower triangle of A and B are stored.
-*
-* N (input) INTEGER
-* The order of the matrix pencil (A,B). 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, 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).
-*
-* B (input/output) DOUBLE PRECISION array, dimension (LDB, N)
-* On entry, the symmetric 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**T*U or B = L*L**T.
-*
-* LDB (input) INTEGER
-* The leading dimension of the array B. LDB >= max(1,N).
-*
-* 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; IL = 1 and IU = 0 if N = 0.
-* Not referenced if RANGE = 'A' or 'V'.
-*
-* ABSTOL (input) DOUBLE PRECISION
-* The absolute error tolerance for the eigenvalues.
-* An approximate eigenvalue is accepted as converged
-* when it is determined to lie in an interval [a,b]
-* of width less than or equal to
-*
-* ABSTOL + EPS * max( |a|,|b| ) ,
-*
-* where EPS is the machine precision. If ABSTOL is less than
-* or equal to zero, then EPS*|T| will be used in its place,
-* where |T| is the 1-norm of the tridiagonal matrix obtained
-* by reducing A to tridiagonal form.
-*
-* Eigenvalues will be computed most accurately when ABSTOL is
-* set to twice the underflow threshold 2*DLAMCH('S'), not zero.
-* If this routine returns with INFO>0, indicating that some
-* eigenvectors did not converge, try setting ABSTOL to
-* 2*DLAMCH('S').
-*
-* 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)
-* On normal exit, the first M elements contain the selected
-* eigenvalues in ascending order.
-*
-* Z (output) DOUBLE PRECISION array, dimension (LDZ, max(1,M))
-* If JOBZ = 'N', then Z is not referenced.
-* If JOBZ = 'V', then if INFO = 0, the first M columns of Z
-* contain the orthonormal eigenvectors of the matrix A
-* corresponding to the selected eigenvalues, with the i-th
-* column of Z holding the eigenvector associated with W(i).
-* The eigenvectors are normalized as follows:
-* if ITYPE = 1 or 2, Z**T*B*Z = I;
-* if ITYPE = 3, Z**T*inv(B)*Z = I.
-*
-* If an eigenvector fails to converge, then that column of Z
-* contains the latest approximation to the eigenvector, and the
-* index of the eigenvector is returned in IFAIL.
-* 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.
-*
-* LDZ (input) INTEGER
-* The leading dimension of the array Z. LDZ >= 1, and if
-* JOBZ = 'V', LDZ >= max(1,N).
-*
-* WORK (workspace/output) DOUBLE PRECISION 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. LWORK >= max(1,8*N).
-* For optimal efficiency, LWORK >= (NB+3)*N,
-* where NB is the blocksize for DSYTRD returned by ILAENV.
-*
-* 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) INTEGER array, dimension (5*N)
-*
-* IFAIL (output) INTEGER array, dimension (N)
-* If JOBZ = 'V', then if INFO = 0, the first M elements of
-* IFAIL are zero. If INFO > 0, then IFAIL contains the
-* indices of the eigenvectors that failed to converge.
-* If JOBZ = 'N', then IFAIL is not referenced.
-*
-* INFO (output) INTEGER
-* = 0: successful exit
-* < 0: if INFO = -i, the i-th argument had an illegal value
-* > 0: DPOTRF or DSYEVX returned an error code:
-* <= N: if INFO = i, DSYEVX failed to converge;
-* i eigenvectors failed to converge. Their indices
-* are stored in array IFAIL.
-* > 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
-*
* =====================================================================
*
* .. Parameters ..