--- rpl/lapack/lapack/zlaqr4.f 2010/12/21 13:53:51 1.7
+++ rpl/lapack/lapack/zlaqr4.f 2011/11/21 20:43:16 1.8
@@ -1,9 +1,256 @@
+*> \brief \b ZLAQR4
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZLAQR4 + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE ZLAQR4( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,
+* IHIZ, Z, LDZ, WORK, LWORK, INFO )
+*
+* .. Scalar Arguments ..
+* INTEGER IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, LWORK, N
+* LOGICAL WANTT, WANTZ
+* ..
+* .. Array Arguments ..
+* COMPLEX*16 H( LDH, * ), W( * ), WORK( * ), Z( LDZ, * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> ZLAQR4 implements one level of recursion for ZLAQR0.
+*> It is a complete implementation of the small bulge multi-shift
+*> QR algorithm. It may be called by ZLAQR0 and, for large enough
+*> deflation window size, it may be called by ZLAQR3. This
+*> subroutine is identical to ZLAQR0 except that it calls ZLAQR2
+*> instead of ZLAQR3.
+*>
+*> ZLAQR4 computes the eigenvalues of a Hessenberg matrix H
+*> and, optionally, the matrices T and Z from the Schur decomposition
+*> H = Z T Z**H, where T is an upper triangular matrix (the
+*> Schur form), and Z is the unitary matrix of Schur vectors.
+*>
+*> Optionally Z may be postmultiplied into an input unitary
+*> matrix Q so that this routine can give the Schur factorization
+*> of a matrix A which has been reduced to the Hessenberg form H
+*> by the unitary matrix Q: A = Q*H*Q**H = (QZ)*H*(QZ)**H.
+*> \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 .GE. 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 triangular in rows
+*> and columns 1:ILO-1 and IHI+1:N and, if ILO.GT.1,
+*> H(ILO,ILO-1) is zero. ILO and IHI are normally set by a
+*> previous call to ZGEBAL, and then passed to ZGEHRD when the
+*> matrix output by ZGEBAL is reduced to Hessenberg form.
+*> Otherwise, ILO and IHI should be set to 1 and N,
+*> respectively. If N.GT.0, then 1.LE.ILO.LE.IHI.LE.N.
+*> If N = 0, then ILO = 1 and IHI = 0.
+*> \endverbatim
+*>
+*> \param[in,out] H
+*> \verbatim
+*> H is COMPLEX*16 array, dimension (LDH,N)
+*> On entry, the upper Hessenberg matrix H.
+*> On exit, if INFO = 0 and WANTT is .TRUE., then H
+*> contains the upper triangular matrix T from the Schur
+*> decomposition (the Schur form). If INFO = 0 and WANT is
+*> .FALSE., then the contents of H are unspecified on exit.
+*> (The output value of H when INFO.GT.0 is given under the
+*> description of INFO below.)
+*>
+*> This subroutine may explicitly set H(i,j) = 0 for i.GT.j and
+*> j = 1, 2, ... ILO-1 or j = IHI+1, IHI+2, ... N.
+*> \endverbatim
+*>
+*> \param[in] LDH
+*> \verbatim
+*> LDH is INTEGER
+*> The leading dimension of the array H. LDH .GE. max(1,N).
+*> \endverbatim
+*>
+*> \param[out] W
+*> \verbatim
+*> W is COMPLEX*16 array, dimension (N)
+*> The computed eigenvalues of H(ILO:IHI,ILO:IHI) are stored
+*> in W(ILO:IHI). If WANTT is .TRUE., then the eigenvalues are
+*> stored in the same order as on the diagonal of the Schur
+*> form returned in H, with W(i) = H(i,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 .LE. ILOZ .LE. ILO; IHI .LE. IHIZ .LE. N.
+*> \endverbatim
+*>
+*> \param[in,out] Z
+*> \verbatim
+*> Z is COMPLEX*16 array, dimension (LDZ,IHI)
+*> If WANTZ is .FALSE., then Z is not referenced.
+*> If WANTZ is .TRUE., then Z(ILO:IHI,ILOZ:IHIZ) is
+*> replaced by Z(ILO:IHI,ILOZ:IHIZ)*U where U is the
+*> orthogonal Schur factor of H(ILO:IHI,ILO:IHI).
+*> (The output value of Z when INFO.GT.0 is given under
+*> the description of INFO below.)
+*> \endverbatim
+*>
+*> \param[in] LDZ
+*> \verbatim
+*> LDZ is INTEGER
+*> The leading dimension of the array Z. if WANTZ is .TRUE.
+*> then LDZ.GE.MAX(1,IHIZ). Otherwize, LDZ.GE.1.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is COMPLEX*16 array, dimension LWORK
+*> On exit, if LWORK = -1, WORK(1) returns an estimate of
+*> the optimal value for LWORK.
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*> LWORK is INTEGER
+*> The dimension of the array WORK. LWORK .GE. max(1,N)
+*> is sufficient, but LWORK typically as large as 6*N may
+*> be required for optimal performance. A workspace query
+*> to determine the optimal workspace size is recommended.
+*>
+*> If LWORK = -1, then ZLAQR4 does a workspace query.
+*> In this case, ZLAQR4 checks the input parameters and
+*> estimates the optimal workspace size for the given
+*> values of N, ILO and IHI. The estimate is returned
+*> in WORK(1). No error message related to LWORK is
+*> issued by XERBLA. Neither H nor Z are accessed.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> .GT. 0: if INFO = i, ZLAQR4 failed to compute all of
+*> the eigenvalues. Elements 1:ilo-1 and i+1:n of WR
+*> and WI contain those eigenvalues which have been
+*> successfully computed. (Failures are rare.)
+*>
+*> If INFO .GT. 0 and WANT is .FALSE., then on exit,
+*> the remaining unconverged eigenvalues are the eigen-
+*> values of the upper Hessenberg matrix rows and
+*> columns ILO through 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 a unitary 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(ILO:IHI,ILOZ:IHIZ)
+*> = (initial value of Z(ILO:IHI,ILOZ:IHIZ)*U
+*>
+*> where U is the unitary matrix in (*) (regard-
+*> less of the value of WANTT.)
+*>
+*> If INFO .GT. 0 and WANTZ is .FALSE., then Z is not
+*> accessed.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2011
+*
+*> \ingroup complex16OTHERauxiliary
+*
+*> \par Contributors:
+* ==================
+*>
+*> Karen Braman and Ralph Byers, Department of Mathematics,
+*> University of Kansas, USA
+*
+*> \par References:
+* ================
+*>
+*> K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
+*> Algorithm Part I: Maintaining Well Focused Shifts, and Level 3
+*> Performance, SIAM Journal of Matrix Analysis, volume 23, pages
+*> 929--947, 2002.
+*> \n
+*> K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
+*> Algorithm Part II: Aggressive Early Deflation, SIAM Journal
+*> of Matrix Analysis, volume 23, pages 948--973, 2002.
+*>
+* =====================================================================
SUBROUTINE ZLAQR4( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,
$ IHIZ, Z, LDZ, WORK, LWORK, 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, LWORK, N
@@ -13,151 +260,8 @@
COMPLEX*16 H( LDH, * ), W( * ), WORK( * ), Z( LDZ, * )
* ..
*
-* This subroutine implements one level of recursion for ZLAQR0.
-* It is a complete implementation of the small bulge multi-shift
-* QR algorithm. It may be called by ZLAQR0 and, for large enough
-* deflation window size, it may be called by ZLAQR3. This
-* subroutine is identical to ZLAQR0 except that it calls ZLAQR2
-* instead of ZLAQR3.
-*
-* Purpose
-* =======
-*
-* ZLAQR4 computes the eigenvalues of a Hessenberg matrix H
-* and, optionally, the matrices T and Z from the Schur decomposition
-* H = Z T Z**H, where T is an upper triangular matrix (the
-* Schur form), and Z is the unitary matrix of Schur vectors.
-*
-* Optionally Z may be postmultiplied into an input unitary
-* matrix Q so that this routine can give the Schur factorization
-* of a matrix A which has been reduced to the Hessenberg form H
-* by the unitary matrix Q: A = Q*H*Q**H = (QZ)*H*(QZ)**H.
-*
-* 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 .GE. 0.
-*
-* ILO (input) INTEGER
-* IHI (input) INTEGER
-* It is assumed that H is already upper triangular in rows
-* and columns 1:ILO-1 and IHI+1:N and, if ILO.GT.1,
-* H(ILO,ILO-1) is zero. ILO and IHI are normally set by a
-* previous call to ZGEBAL, and then passed to ZGEHRD when the
-* matrix output by ZGEBAL is reduced to Hessenberg form.
-* Otherwise, ILO and IHI should be set to 1 and N,
-* respectively. If N.GT.0, then 1.LE.ILO.LE.IHI.LE.N.
-* If N = 0, then ILO = 1 and IHI = 0.
-*
-* H (input/output) COMPLEX*16 array, dimension (LDH,N)
-* On entry, the upper Hessenberg matrix H.
-* On exit, if INFO = 0 and WANTT is .TRUE., then H
-* contains the upper triangular matrix T from the Schur
-* decomposition (the Schur form). If INFO = 0 and WANT is
-* .FALSE., then the contents of H are unspecified on exit.
-* (The output value of H when INFO.GT.0 is given under the
-* description of INFO below.)
-*
-* This subroutine may explicitly set H(i,j) = 0 for i.GT.j and
-* j = 1, 2, ... ILO-1 or j = IHI+1, IHI+2, ... N.
-*
-* LDH (input) INTEGER
-* The leading dimension of the array H. LDH .GE. max(1,N).
-*
-* W (output) COMPLEX*16 array, dimension (N)
-* The computed eigenvalues of H(ILO:IHI,ILO:IHI) are stored
-* in W(ILO:IHI). If WANTT is .TRUE., then the eigenvalues are
-* stored in the same order as on the diagonal of the Schur
-* form returned in H, with W(i) = H(i,i).
-*
-* Z (input/output) COMPLEX*16 array, dimension (LDZ,IHI)
-* If WANTZ is .FALSE., then Z is not referenced.
-* If WANTZ is .TRUE., then Z(ILO:IHI,ILOZ:IHIZ) is
-* replaced by Z(ILO:IHI,ILOZ:IHIZ)*U where U is the
-* orthogonal Schur factor of H(ILO:IHI,ILO:IHI).
-* (The output value of Z when INFO.GT.0 is given under
-* the description of INFO below.)
-*
-* LDZ (input) INTEGER
-* The leading dimension of the array Z. if WANTZ is .TRUE.
-* then LDZ.GE.MAX(1,IHIZ). Otherwize, LDZ.GE.1.
-*
-* WORK (workspace/output) COMPLEX*16 array, dimension LWORK
-* On exit, if LWORK = -1, WORK(1) returns an estimate of
-* the optimal value for LWORK.
-*
-* LWORK (input) INTEGER
-* The dimension of the array WORK. LWORK .GE. max(1,N)
-* is sufficient, but LWORK typically as large as 6*N may
-* be required for optimal performance. A workspace query
-* to determine the optimal workspace size is recommended.
-*
-* If LWORK = -1, then ZLAQR4 does a workspace query.
-* In this case, ZLAQR4 checks the input parameters and
-* estimates the optimal workspace size for the given
-* values of N, ILO and IHI. The estimate is returned
-* in WORK(1). No error message related to LWORK is
-* issued by XERBLA. Neither H nor Z are accessed.
-*
-*
-* INFO (output) INTEGER
-* = 0: successful exit
-* .GT. 0: if INFO = i, ZLAQR4 failed to compute all of
-* the eigenvalues. Elements 1:ilo-1 and i+1:n of WR
-* and WI contain those eigenvalues which have been
-* successfully computed. (Failures are rare.)
-*
-* If INFO .GT. 0 and WANT is .FALSE., then on exit,
-* the remaining unconverged eigenvalues are the eigen-
-* values of the upper Hessenberg matrix rows and
-* columns ILO through 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 a unitary 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(ILO:IHI,ILOZ:IHIZ)
-* = (initial value of Z(ILO:IHI,ILOZ:IHIZ)*U
-*
-* where U is the unitary matrix in (*) (regard-
-* less of the value of WANTT.)
-*
-* If INFO .GT. 0 and WANTZ is .FALSE., then Z is not
-* accessed.
-*
-* ================================================================
-* Based on contributions by
-* Karen Braman and Ralph Byers, Department of Mathematics,
-* University of Kansas, USA
-*
-* ================================================================
-* References:
-* K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
-* Algorithm Part I: Maintaining Well Focused Shifts, and Level 3
-* Performance, SIAM Journal of Matrix Analysis, volume 23, pages
-* 929--947, 2002.
-*
-* K. Braman, R. Byers and R. Mathias, The Multi-Shift QR
-* Algorithm Part II: Aggressive Early Deflation, SIAM Journal
-* of Matrix Analysis, volume 23, pages 948--973, 2002.
+* ================================================================
*
-* ================================================================
* .. Parameters ..
*
* ==== Matrices of order NTINY or smaller must be processed by