--- rpl/lapack/lapack/dlahqr.f 2010/12/21 13:53:29 1.7
+++ rpl/lapack/lapack/dlahqr.f 2011/11/21 20:42:55 1.8
@@ -1,9 +1,216 @@
+*> \brief \b DLAHQR
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DLAHQR + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI,
+* ILOZ, IHIZ, Z, LDZ, INFO )
+*
+* .. Scalar Arguments ..
+* INTEGER IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, N
+* LOGICAL WANTT, WANTZ
+* ..
+* .. Array Arguments ..
+* DOUBLE PRECISION H( LDH, * ), WI( * ), WR( * ), Z( LDZ, * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DLAHQR is an auxiliary routine called by DHSEQR to update the
+*> eigenvalues and Schur decomposition already computed by DHSEQR, by
+*> dealing with the Hessenberg submatrix in rows and columns ILO to
+*> IHI.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] WANTT
+*> \verbatim
+*> WANTT is LOGICAL
+*> = .TRUE. : the full Schur form T is required;
+*> = .FALSE.: only eigenvalues are required.
+*> \endverbatim
+*>
+*> \param[in] WANTZ
+*> \verbatim
+*> WANTZ is LOGICAL
+*> = .TRUE. : the matrix of Schur vectors Z is required;
+*> = .FALSE.: Schur vectors are not required.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrix H. N >= 0.
+*> \endverbatim
+*>
+*> \param[in] ILO
+*> \verbatim
+*> ILO is INTEGER
+*> \endverbatim
+*>
+*> \param[in] IHI
+*> \verbatim
+*> IHI is INTEGER
+*> It is assumed that H is already upper quasi-triangular in
+*> rows and columns IHI+1:N, and that H(ILO,ILO-1) = 0 (unless
+*> ILO = 1). DLAHQR works primarily with the Hessenberg
+*> submatrix in rows and columns ILO to IHI, but applies
+*> transformations to all of H if WANTT is .TRUE..
+*> 1 <= ILO <= max(1,IHI); IHI <= N.
+*> \endverbatim
+*>
+*> \param[in,out] H
+*> \verbatim
+*> H is DOUBLE PRECISION array, dimension (LDH,N)
+*> On entry, the upper Hessenberg matrix H.
+*> On exit, if INFO is zero and if WANTT is .TRUE., H is upper
+*> quasi-triangular in rows and columns ILO:IHI, with any
+*> 2-by-2 diagonal blocks in standard form. If INFO is zero
+*> and WANTT is .FALSE., the contents of H are unspecified on
+*> exit. The output state of H if INFO is nonzero is given
+*> below under the description of INFO.
+*> \endverbatim
+*>
+*> \param[in] LDH
+*> \verbatim
+*> LDH is INTEGER
+*> The leading dimension of the array H. LDH >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] WR
+*> \verbatim
+*> WR is DOUBLE PRECISION array, dimension (N)
+*> \endverbatim
+*>
+*> \param[out] WI
+*> \verbatim
+*> WI is DOUBLE PRECISION array, dimension (N)
+*> The real and imaginary parts, respectively, of the computed
+*> eigenvalues ILO to IHI are stored in the corresponding
+*> elements of WR and WI. If two eigenvalues are computed as a
+*> complex conjugate pair, they are stored in consecutive
+*> elements of WR and WI, say the i-th and (i+1)th, with
+*> WI(i) > 0 and WI(i+1) < 0. If WANTT is .TRUE., the
+*> eigenvalues are stored in the same order as on the diagonal
+*> of the Schur form returned in H, with WR(i) = H(i,i), and, if
+*> H(i:i+1,i:i+1) is a 2-by-2 diagonal block,
+*> WI(i) = sqrt(H(i+1,i)*H(i,i+1)) and WI(i+1) = -WI(i).
+*> \endverbatim
+*>
+*> \param[in] ILOZ
+*> \verbatim
+*> ILOZ is INTEGER
+*> \endverbatim
+*>
+*> \param[in] IHIZ
+*> \verbatim
+*> IHIZ is INTEGER
+*> Specify the rows of Z to which transformations must be
+*> applied if WANTZ is .TRUE..
+*> 1 <= ILOZ <= ILO; IHI <= IHIZ <= N.
+*> \endverbatim
+*>
+*> \param[in,out] Z
+*> \verbatim
+*> Z is DOUBLE PRECISION array, dimension (LDZ,N)
+*> If WANTZ is .TRUE., on entry Z must contain the current
+*> matrix Z of transformations accumulated by DHSEQR, and on
+*> exit Z has been updated; transformations are applied only to
+*> the submatrix Z(ILOZ:IHIZ,ILO:IHI).
+*> If WANTZ is .FALSE., Z is not referenced.
+*> \endverbatim
+*>
+*> \param[in] LDZ
+*> \verbatim
+*> LDZ is INTEGER
+*> The leading dimension of the array Z. LDZ >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> .GT. 0: If INFO = i, DLAHQR failed to compute all the
+*> eigenvalues ILO to IHI in a total of 30 iterations
+*> per eigenvalue; elements i+1:ihi of WR and WI
+*> contain those eigenvalues which have been
+*> successfully computed.
+*>
+*> If INFO .GT. 0 and WANTT is .FALSE., then on exit,
+*> the remaining unconverged eigenvalues are the
+*> eigenvalues of the upper Hessenberg matrix rows
+*> and columns ILO thorugh INFO of the final, output
+*> value of H.
+*>
+*> If INFO .GT. 0 and WANTT is .TRUE., then on exit
+*> (*) (initial value of H)*U = U*(final value of H)
+*> where U is an orthognal matrix. The final
+*> value of H is upper Hessenberg and triangular in
+*> rows and columns INFO+1 through IHI.
+*>
+*> If INFO .GT. 0 and WANTZ is .TRUE., then on exit
+*> (final value of Z) = (initial value of Z)*U
+*> where U is the orthogonal matrix in (*)
+*> (regardless of the value of WANTT.)
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2011
+*
+*> \ingroup doubleOTHERauxiliary
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
+*>
+*> 02-96 Based on modifications by
+*> David Day, Sandia National Laboratory, USA
+*>
+*> 12-04 Further modifications by
+*> Ralph Byers, University of Kansas, USA
+*> This is a modified version of DLAHQR from LAPACK version 3.0.
+*> It is (1) more robust against overflow and underflow and
+*> (2) adopts the more conservative Ahues & Tisseur stopping
+*> criterion (LAWN 122, 1997).
+*> \endverbatim
+*>
+* =====================================================================
SUBROUTINE DLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI,
$ ILOZ, IHIZ, Z, LDZ, INFO )
*
-* -- LAPACK auxiliary routine (version 3.2) --
-* Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..
-* November 2006
+* -- LAPACK auxiliary 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 2011
*
* .. Scalar Arguments ..
INTEGER IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, N
@@ -13,117 +220,7 @@
DOUBLE PRECISION H( LDH, * ), WI( * ), WR( * ), Z( LDZ, * )
* ..
*
-* Purpose
-* =======
-*
-* DLAHQR is an auxiliary routine called by DHSEQR to update the
-* eigenvalues and Schur decomposition already computed by DHSEQR, by
-* dealing with the Hessenberg submatrix in rows and columns ILO to
-* IHI.
-*
-* Arguments
-* =========
-*
-* WANTT (input) LOGICAL
-* = .TRUE. : the full Schur form T is required;
-* = .FALSE.: only eigenvalues are required.
-*
-* WANTZ (input) LOGICAL
-* = .TRUE. : the matrix of Schur vectors Z is required;
-* = .FALSE.: Schur vectors are not required.
-*
-* N (input) INTEGER
-* The order of the matrix H. N >= 0.
-*
-* ILO (input) INTEGER
-* IHI (input) INTEGER
-* It is assumed that H is already upper quasi-triangular in
-* rows and columns IHI+1:N, and that H(ILO,ILO-1) = 0 (unless
-* ILO = 1). DLAHQR works primarily with the Hessenberg
-* submatrix in rows and columns ILO to IHI, but applies
-* transformations to all of H if WANTT is .TRUE..
-* 1 <= ILO <= max(1,IHI); IHI <= N.
-*
-* H (input/output) DOUBLE PRECISION array, dimension (LDH,N)
-* On entry, the upper Hessenberg matrix H.
-* On exit, if INFO is zero and if WANTT is .TRUE., H is upper
-* quasi-triangular in rows and columns ILO:IHI, with any
-* 2-by-2 diagonal blocks in standard form. If INFO is zero
-* and WANTT is .FALSE., the contents of H are unspecified on
-* exit. The output state of H if INFO is nonzero is given
-* below under the description of INFO.
-*
-* LDH (input) INTEGER
-* The leading dimension of the array H. LDH >= max(1,N).
-*
-* WR (output) DOUBLE PRECISION array, dimension (N)
-* WI (output) DOUBLE PRECISION array, dimension (N)
-* The real and imaginary parts, respectively, of the computed
-* eigenvalues ILO to IHI are stored in the corresponding
-* elements of WR and WI. If two eigenvalues are computed as a
-* complex conjugate pair, they are stored in consecutive
-* elements of WR and WI, say the i-th and (i+1)th, with
-* WI(i) > 0 and WI(i+1) < 0. If WANTT is .TRUE., the
-* eigenvalues are stored in the same order as on the diagonal
-* of the Schur form returned in H, with WR(i) = H(i,i), and, if
-* H(i:i+1,i:i+1) is a 2-by-2 diagonal block,
-* WI(i) = sqrt(H(i+1,i)*H(i,i+1)) and WI(i+1) = -WI(i).
-*
-* ILOZ (input) INTEGER
-* IHIZ (input) INTEGER
-* Specify the rows of Z to which transformations must be
-* applied if WANTZ is .TRUE..
-* 1 <= ILOZ <= ILO; IHI <= IHIZ <= N.
-*
-* Z (input/output) DOUBLE PRECISION array, dimension (LDZ,N)
-* If WANTZ is .TRUE., on entry Z must contain the current
-* matrix Z of transformations accumulated by DHSEQR, and on
-* exit Z has been updated; transformations are applied only to
-* the submatrix Z(ILOZ:IHIZ,ILO:IHI).
-* If WANTZ is .FALSE., Z is not referenced.
-*
-* LDZ (input) INTEGER
-* The leading dimension of the array Z. LDZ >= max(1,N).
-*
-* INFO (output) INTEGER
-* = 0: successful exit
-* .GT. 0: If INFO = i, DLAHQR failed to compute all the
-* eigenvalues ILO to IHI in a total of 30 iterations
-* per eigenvalue; elements i+1:ihi of WR and WI
-* contain those eigenvalues which have been
-* successfully computed.
-*
-* If INFO .GT. 0 and WANTT is .FALSE., then on exit,
-* the remaining unconverged eigenvalues are the
-* eigenvalues of the upper Hessenberg matrix rows
-* and columns ILO thorugh INFO of the final, output
-* value of H.
-*
-* If INFO .GT. 0 and WANTT is .TRUE., then on exit
-* (*) (initial value of H)*U = U*(final value of H)
-* where U is an orthognal matrix. The final
-* value of H is upper Hessenberg and triangular in
-* rows and columns INFO+1 through IHI.
-*
-* If INFO .GT. 0 and WANTZ is .TRUE., then on exit
-* (final value of Z) = (initial value of Z)*U
-* where U is the orthogonal matrix in (*)
-* (regardless of the value of WANTT.)
-*
-* Further Details
-* ===============
-*
-* 02-96 Based on modifications by
-* David Day, Sandia National Laboratory, USA
-*
-* 12-04 Further modifications by
-* Ralph Byers, University of Kansas, USA
-* This is a modified version of DLAHQR from LAPACK version 3.0.
-* It is (1) more robust against overflow and underflow and
-* (2) adopts the more conservative Ahues & Tisseur stopping
-* criterion (LAWN 122, 1997).
-*
-* =========================================================
+* =========================================================
*
* .. Parameters ..
INTEGER ITMAX