--- rpl/lapack/lapack/zhsein.f 2010/12/21 13:53:47 1.7
+++ rpl/lapack/lapack/zhsein.f 2011/11/21 20:43:13 1.8
@@ -1,11 +1,253 @@
+*> \brief \b ZHSEIN
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZHSEIN + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE ZHSEIN( SIDE, EIGSRC, INITV, SELECT, N, H, LDH, W, VL,
+* LDVL, VR, LDVR, MM, M, WORK, RWORK, IFAILL,
+* IFAILR, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER EIGSRC, INITV, SIDE
+* INTEGER INFO, LDH, LDVL, LDVR, M, MM, N
+* ..
+* .. Array Arguments ..
+* LOGICAL SELECT( * )
+* INTEGER IFAILL( * ), IFAILR( * )
+* DOUBLE PRECISION RWORK( * )
+* COMPLEX*16 H( LDH, * ), VL( LDVL, * ), VR( LDVR, * ),
+* $ W( * ), WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> ZHSEIN uses inverse iteration to find specified right and/or left
+*> eigenvectors of a complex upper Hessenberg matrix H.
+*>
+*> The right eigenvector x and the left eigenvector y of the matrix H
+*> corresponding to an eigenvalue w are defined by:
+*>
+*> H * x = w * x, y**h * H = w * y**h
+*>
+*> where y**h denotes the conjugate transpose of the vector y.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] SIDE
+*> \verbatim
+*> SIDE is CHARACTER*1
+*> = 'R': compute right eigenvectors only;
+*> = 'L': compute left eigenvectors only;
+*> = 'B': compute both right and left eigenvectors.
+*> \endverbatim
+*>
+*> \param[in] EIGSRC
+*> \verbatim
+*> EIGSRC is CHARACTER*1
+*> Specifies the source of eigenvalues supplied in W:
+*> = 'Q': the eigenvalues were found using ZHSEQR; thus, if
+*> H has zero subdiagonal elements, and so is
+*> block-triangular, then the j-th eigenvalue can be
+*> assumed to be an eigenvalue of the block containing
+*> the j-th row/column. This property allows ZHSEIN to
+*> perform inverse iteration on just one diagonal block.
+*> = 'N': no assumptions are made on the correspondence
+*> between eigenvalues and diagonal blocks. In this
+*> case, ZHSEIN must always perform inverse iteration
+*> using the whole matrix H.
+*> \endverbatim
+*>
+*> \param[in] INITV
+*> \verbatim
+*> INITV is CHARACTER*1
+*> = 'N': no initial vectors are supplied;
+*> = 'U': user-supplied initial vectors are stored in the arrays
+*> VL and/or VR.
+*> \endverbatim
+*>
+*> \param[in] SELECT
+*> \verbatim
+*> SELECT is LOGICAL array, dimension (N)
+*> Specifies the eigenvectors to be computed. To select the
+*> eigenvector corresponding to the eigenvalue W(j),
+*> SELECT(j) must be set to .TRUE..
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrix H. N >= 0.
+*> \endverbatim
+*>
+*> \param[in] H
+*> \verbatim
+*> H is COMPLEX*16 array, dimension (LDH,N)
+*> The upper Hessenberg matrix H.
+*> \endverbatim
+*>
+*> \param[in] LDH
+*> \verbatim
+*> LDH is INTEGER
+*> The leading dimension of the array H. LDH >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in,out] W
+*> \verbatim
+*> W is COMPLEX*16 array, dimension (N)
+*> On entry, the eigenvalues of H.
+*> On exit, the real parts of W may have been altered since
+*> close eigenvalues are perturbed slightly in searching for
+*> independent eigenvectors.
+*> \endverbatim
+*>
+*> \param[in,out] VL
+*> \verbatim
+*> VL is COMPLEX*16 array, dimension (LDVL,MM)
+*> On entry, if INITV = 'U' and SIDE = 'L' or 'B', VL must
+*> contain starting vectors for the inverse iteration for the
+*> left eigenvectors; the starting vector for each eigenvector
+*> must be in the same column in which the eigenvector will be
+*> stored.
+*> On exit, if SIDE = 'L' or 'B', the left eigenvectors
+*> specified by SELECT will be stored consecutively in the
+*> columns of VL, in the same order as their eigenvalues.
+*> If SIDE = 'R', VL is not referenced.
+*> \endverbatim
+*>
+*> \param[in] LDVL
+*> \verbatim
+*> LDVL is INTEGER
+*> The leading dimension of the array VL.
+*> LDVL >= max(1,N) if SIDE = 'L' or 'B'; LDVL >= 1 otherwise.
+*> \endverbatim
+*>
+*> \param[in,out] VR
+*> \verbatim
+*> VR is COMPLEX*16 array, dimension (LDVR,MM)
+*> On entry, if INITV = 'U' and SIDE = 'R' or 'B', VR must
+*> contain starting vectors for the inverse iteration for the
+*> right eigenvectors; the starting vector for each eigenvector
+*> must be in the same column in which the eigenvector will be
+*> stored.
+*> On exit, if SIDE = 'R' or 'B', the right eigenvectors
+*> specified by SELECT will be stored consecutively in the
+*> columns of VR, in the same order as their eigenvalues.
+*> If SIDE = 'L', VR is not referenced.
+*> \endverbatim
+*>
+*> \param[in] LDVR
+*> \verbatim
+*> LDVR is INTEGER
+*> The leading dimension of the array VR.
+*> LDVR >= max(1,N) if SIDE = 'R' or 'B'; LDVR >= 1 otherwise.
+*> \endverbatim
+*>
+*> \param[in] MM
+*> \verbatim
+*> MM is INTEGER
+*> The number of columns in the arrays VL and/or VR. MM >= M.
+*> \endverbatim
+*>
+*> \param[out] M
+*> \verbatim
+*> M is INTEGER
+*> The number of columns in the arrays VL and/or VR required to
+*> store the eigenvectors (= the number of .TRUE. elements in
+*> SELECT).
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is COMPLEX*16 array, dimension (N*N)
+*> \endverbatim
+*>
+*> \param[out] RWORK
+*> \verbatim
+*> RWORK is DOUBLE PRECISION array, dimension (N)
+*> \endverbatim
+*>
+*> \param[out] IFAILL
+*> \verbatim
+*> IFAILL is INTEGER array, dimension (MM)
+*> If SIDE = 'L' or 'B', IFAILL(i) = j > 0 if the left
+*> eigenvector in the i-th column of VL (corresponding to the
+*> eigenvalue w(j)) failed to converge; IFAILL(i) = 0 if the
+*> eigenvector converged satisfactorily.
+*> If SIDE = 'R', IFAILL is not referenced.
+*> \endverbatim
+*>
+*> \param[out] IFAILR
+*> \verbatim
+*> IFAILR is INTEGER array, dimension (MM)
+*> If SIDE = 'R' or 'B', IFAILR(i) = j > 0 if the right
+*> eigenvector in the i-th column of VR (corresponding to the
+*> eigenvalue w(j)) failed to converge; IFAILR(i) = 0 if the
+*> eigenvector converged satisfactorily.
+*> If SIDE = 'L', IFAILR 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: if INFO = i, i is the number of eigenvectors which
+*> failed to converge; see IFAILL and IFAILR for further
+*> details.
+*> \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 Further Details:
+* =====================
+*>
+*> \verbatim
+*>
+*> Each eigenvector is normalized so that the element of largest
+*> magnitude has magnitude 1; here the magnitude of a complex number
+*> (x,y) is taken to be |x|+|y|.
+*> \endverbatim
+*>
+* =====================================================================
SUBROUTINE ZHSEIN( SIDE, EIGSRC, INITV, SELECT, N, H, LDH, W, VL,
$ LDVL, VR, LDVR, MM, M, WORK, RWORK, IFAILL,
$ IFAILR, INFO )
*
-* -- LAPACK 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 EIGSRC, INITV, SIDE
@@ -19,135 +261,6 @@
$ W( * ), WORK( * )
* ..
*
-* Purpose
-* =======
-*
-* ZHSEIN uses inverse iteration to find specified right and/or left
-* eigenvectors of a complex upper Hessenberg matrix H.
-*
-* The right eigenvector x and the left eigenvector y of the matrix H
-* corresponding to an eigenvalue w are defined by:
-*
-* H * x = w * x, y**h * H = w * y**h
-*
-* where y**h denotes the conjugate transpose of the vector y.
-*
-* Arguments
-* =========
-*
-* SIDE (input) CHARACTER*1
-* = 'R': compute right eigenvectors only;
-* = 'L': compute left eigenvectors only;
-* = 'B': compute both right and left eigenvectors.
-*
-* EIGSRC (input) CHARACTER*1
-* Specifies the source of eigenvalues supplied in W:
-* = 'Q': the eigenvalues were found using ZHSEQR; thus, if
-* H has zero subdiagonal elements, and so is
-* block-triangular, then the j-th eigenvalue can be
-* assumed to be an eigenvalue of the block containing
-* the j-th row/column. This property allows ZHSEIN to
-* perform inverse iteration on just one diagonal block.
-* = 'N': no assumptions are made on the correspondence
-* between eigenvalues and diagonal blocks. In this
-* case, ZHSEIN must always perform inverse iteration
-* using the whole matrix H.
-*
-* INITV (input) CHARACTER*1
-* = 'N': no initial vectors are supplied;
-* = 'U': user-supplied initial vectors are stored in the arrays
-* VL and/or VR.
-*
-* SELECT (input) LOGICAL array, dimension (N)
-* Specifies the eigenvectors to be computed. To select the
-* eigenvector corresponding to the eigenvalue W(j),
-* SELECT(j) must be set to .TRUE..
-*
-* N (input) INTEGER
-* The order of the matrix H. N >= 0.
-*
-* H (input) COMPLEX*16 array, dimension (LDH,N)
-* The upper Hessenberg matrix H.
-*
-* LDH (input) INTEGER
-* The leading dimension of the array H. LDH >= max(1,N).
-*
-* W (input/output) COMPLEX*16 array, dimension (N)
-* On entry, the eigenvalues of H.
-* On exit, the real parts of W may have been altered since
-* close eigenvalues are perturbed slightly in searching for
-* independent eigenvectors.
-*
-* VL (input/output) COMPLEX*16 array, dimension (LDVL,MM)
-* On entry, if INITV = 'U' and SIDE = 'L' or 'B', VL must
-* contain starting vectors for the inverse iteration for the
-* left eigenvectors; the starting vector for each eigenvector
-* must be in the same column in which the eigenvector will be
-* stored.
-* On exit, if SIDE = 'L' or 'B', the left eigenvectors
-* specified by SELECT will be stored consecutively in the
-* columns of VL, in the same order as their eigenvalues.
-* If SIDE = 'R', VL is not referenced.
-*
-* LDVL (input) INTEGER
-* The leading dimension of the array VL.
-* LDVL >= max(1,N) if SIDE = 'L' or 'B'; LDVL >= 1 otherwise.
-*
-* VR (input/output) COMPLEX*16 array, dimension (LDVR,MM)
-* On entry, if INITV = 'U' and SIDE = 'R' or 'B', VR must
-* contain starting vectors for the inverse iteration for the
-* right eigenvectors; the starting vector for each eigenvector
-* must be in the same column in which the eigenvector will be
-* stored.
-* On exit, if SIDE = 'R' or 'B', the right eigenvectors
-* specified by SELECT will be stored consecutively in the
-* columns of VR, in the same order as their eigenvalues.
-* If SIDE = 'L', VR is not referenced.
-*
-* LDVR (input) INTEGER
-* The leading dimension of the array VR.
-* LDVR >= max(1,N) if SIDE = 'R' or 'B'; LDVR >= 1 otherwise.
-*
-* MM (input) INTEGER
-* The number of columns in the arrays VL and/or VR. MM >= M.
-*
-* M (output) INTEGER
-* The number of columns in the arrays VL and/or VR required to
-* store the eigenvectors (= the number of .TRUE. elements in
-* SELECT).
-*
-* WORK (workspace) COMPLEX*16 array, dimension (N*N)
-*
-* RWORK (workspace) DOUBLE PRECISION array, dimension (N)
-*
-* IFAILL (output) INTEGER array, dimension (MM)
-* If SIDE = 'L' or 'B', IFAILL(i) = j > 0 if the left
-* eigenvector in the i-th column of VL (corresponding to the
-* eigenvalue w(j)) failed to converge; IFAILL(i) = 0 if the
-* eigenvector converged satisfactorily.
-* If SIDE = 'R', IFAILL is not referenced.
-*
-* IFAILR (output) INTEGER array, dimension (MM)
-* If SIDE = 'R' or 'B', IFAILR(i) = j > 0 if the right
-* eigenvector in the i-th column of VR (corresponding to the
-* eigenvalue w(j)) failed to converge; IFAILR(i) = 0 if the
-* eigenvector converged satisfactorily.
-* If SIDE = 'L', IFAILR is not referenced.
-*
-* INFO (output) INTEGER
-* = 0: successful exit
-* < 0: if INFO = -i, the i-th argument had an illegal value
-* > 0: if INFO = i, i is the number of eigenvectors which
-* failed to converge; see IFAILL and IFAILR for further
-* details.
-*
-* Further Details
-* ===============
-*
-* Each eigenvector is normalized so that the element of largest
-* magnitude has magnitude 1; here the magnitude of a complex number
-* (x,y) is taken to be |x|+|y|.
-*
* =====================================================================
*
* .. Parameters ..