--- rpl/lapack/lapack/dlaqr5.f 2010/04/21 13:45:18 1.2
+++ rpl/lapack/lapack/dlaqr5.f 2017/06/17 11:06:24 1.19
@@ -1,11 +1,268 @@
+*> \brief \b DLAQR5 performs a single small-bulge multi-shift QR sweep.
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DLAQR5 + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DLAQR5( WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS,
+* SR, SI, H, LDH, ILOZ, IHIZ, Z, LDZ, V, LDV, U,
+* LDU, NV, WV, LDWV, NH, WH, LDWH )
+*
+* .. Scalar Arguments ..
+* INTEGER IHIZ, ILOZ, KACC22, KBOT, KTOP, LDH, LDU, LDV,
+* $ LDWH, LDWV, LDZ, N, NH, NSHFTS, NV
+* LOGICAL WANTT, WANTZ
+* ..
+* .. Array Arguments ..
+* DOUBLE PRECISION H( LDH, * ), SI( * ), SR( * ), U( LDU, * ),
+* $ V( LDV, * ), WH( LDWH, * ), WV( LDWV, * ),
+* $ Z( LDZ, * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DLAQR5, called by DLAQR0, performs a
+*> single small-bulge multi-shift QR sweep.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] WANTT
+*> \verbatim
+*> WANTT is logical scalar
+*> WANTT = .true. if the quasi-triangular Schur factor
+*> is being computed. WANTT is set to .false. otherwise.
+*> \endverbatim
+*>
+*> \param[in] WANTZ
+*> \verbatim
+*> WANTZ is logical scalar
+*> WANTZ = .true. if the orthogonal Schur factor is being
+*> computed. WANTZ is set to .false. otherwise.
+*> \endverbatim
+*>
+*> \param[in] KACC22
+*> \verbatim
+*> KACC22 is integer with value 0, 1, or 2.
+*> Specifies the computation mode of far-from-diagonal
+*> orthogonal updates.
+*> = 0: DLAQR5 does not accumulate reflections and does not
+*> use matrix-matrix multiply to update far-from-diagonal
+*> matrix entries.
+*> = 1: DLAQR5 accumulates reflections and uses matrix-matrix
+*> multiply to update the far-from-diagonal matrix entries.
+*> = 2: DLAQR5 accumulates reflections, uses matrix-matrix
+*> multiply to update the far-from-diagonal matrix entries,
+*> and takes advantage of 2-by-2 block structure during
+*> matrix multiplies.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is integer scalar
+*> N is the order of the Hessenberg matrix H upon which this
+*> subroutine operates.
+*> \endverbatim
+*>
+*> \param[in] KTOP
+*> \verbatim
+*> KTOP is integer scalar
+*> \endverbatim
+*>
+*> \param[in] KBOT
+*> \verbatim
+*> KBOT is integer scalar
+*> These are the first and last rows and columns of an
+*> isolated diagonal block upon which the QR sweep is to be
+*> applied. It is assumed without a check that
+*> either KTOP = 1 or H(KTOP,KTOP-1) = 0
+*> and
+*> either KBOT = N or H(KBOT+1,KBOT) = 0.
+*> \endverbatim
+*>
+*> \param[in] NSHFTS
+*> \verbatim
+*> NSHFTS is integer scalar
+*> NSHFTS gives the number of simultaneous shifts. NSHFTS
+*> must be positive and even.
+*> \endverbatim
+*>
+*> \param[in,out] SR
+*> \verbatim
+*> SR is DOUBLE PRECISION array of size (NSHFTS)
+*> \endverbatim
+*>
+*> \param[in,out] SI
+*> \verbatim
+*> SI is DOUBLE PRECISION array of size (NSHFTS)
+*> SR contains the real parts and SI contains the imaginary
+*> parts of the NSHFTS shifts of origin that define the
+*> multi-shift QR sweep. On output SR and SI may be
+*> reordered.
+*> \endverbatim
+*>
+*> \param[in,out] H
+*> \verbatim
+*> H is DOUBLE PRECISION array of size (LDH,N)
+*> On input H contains a Hessenberg matrix. On output a
+*> multi-shift QR sweep with shifts SR(J)+i*SI(J) is applied
+*> to the isolated diagonal block in rows and columns KTOP
+*> through KBOT.
+*> \endverbatim
+*>
+*> \param[in] LDH
+*> \verbatim
+*> LDH is integer scalar
+*> LDH is the leading dimension of H just as declared in the
+*> calling procedure. LDH.GE.MAX(1,N).
+*> \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. IHIZ .LE. N
+*> \endverbatim
+*>
+*> \param[in,out] Z
+*> \verbatim
+*> Z is DOUBLE PRECISION array of size (LDZ,IHIZ)
+*> If WANTZ = .TRUE., then the QR Sweep orthogonal
+*> similarity transformation is accumulated into
+*> Z(ILOZ:IHIZ,ILOZ:IHIZ) from the right.
+*> If WANTZ = .FALSE., then Z is unreferenced.
+*> \endverbatim
+*>
+*> \param[in] LDZ
+*> \verbatim
+*> LDZ is integer scalar
+*> LDA is the leading dimension of Z just as declared in
+*> the calling procedure. LDZ.GE.N.
+*> \endverbatim
+*>
+*> \param[out] V
+*> \verbatim
+*> V is DOUBLE PRECISION array of size (LDV,NSHFTS/2)
+*> \endverbatim
+*>
+*> \param[in] LDV
+*> \verbatim
+*> LDV is integer scalar
+*> LDV is the leading dimension of V as declared in the
+*> calling procedure. LDV.GE.3.
+*> \endverbatim
+*>
+*> \param[out] U
+*> \verbatim
+*> U is DOUBLE PRECISION array of size
+*> (LDU,3*NSHFTS-3)
+*> \endverbatim
+*>
+*> \param[in] LDU
+*> \verbatim
+*> LDU is integer scalar
+*> LDU is the leading dimension of U just as declared in the
+*> in the calling subroutine. LDU.GE.3*NSHFTS-3.
+*> \endverbatim
+*>
+*> \param[in] NH
+*> \verbatim
+*> NH is integer scalar
+*> NH is the number of columns in array WH available for
+*> workspace. NH.GE.1.
+*> \endverbatim
+*>
+*> \param[out] WH
+*> \verbatim
+*> WH is DOUBLE PRECISION array of size (LDWH,NH)
+*> \endverbatim
+*>
+*> \param[in] LDWH
+*> \verbatim
+*> LDWH is integer scalar
+*> Leading dimension of WH just as declared in the
+*> calling procedure. LDWH.GE.3*NSHFTS-3.
+*> \endverbatim
+*>
+*> \param[in] NV
+*> \verbatim
+*> NV is integer scalar
+*> NV is the number of rows in WV agailable for workspace.
+*> NV.GE.1.
+*> \endverbatim
+*>
+*> \param[out] WV
+*> \verbatim
+*> WV is DOUBLE PRECISION array of size
+*> (LDWV,3*NSHFTS-3)
+*> \endverbatim
+*>
+*> \param[in] LDWV
+*> \verbatim
+*> LDWV is integer scalar
+*> LDWV is the leading dimension of WV as declared in the
+*> in the calling subroutine. LDWV.GE.NV.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date June 2016
+*
+*> \ingroup doubleOTHERauxiliary
+*
+*> \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.
+*>
+* =====================================================================
SUBROUTINE DLAQR5( WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS,
$ SR, SI, H, LDH, ILOZ, IHIZ, Z, LDZ, V, LDV, U,
$ LDU, NV, WV, LDWV, NH, WH, LDWH )
*
-* -- LAPACK auxiliary routine (version 3.2) --
+* -- LAPACK auxiliary routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* November 2006
+* June 2016
*
* .. Scalar Arguments ..
INTEGER IHIZ, ILOZ, KACC22, KBOT, KTOP, LDH, LDU, LDV,
@@ -18,127 +275,7 @@
$ Z( LDZ, * )
* ..
*
-* This auxiliary subroutine called by DLAQR0 performs a
-* single small-bulge multi-shift QR sweep.
-*
-* WANTT (input) logical scalar
-* WANTT = .true. if the quasi-triangular Schur factor
-* is being computed. WANTT is set to .false. otherwise.
-*
-* WANTZ (input) logical scalar
-* WANTZ = .true. if the orthogonal Schur factor is being
-* computed. WANTZ is set to .false. otherwise.
-*
-* KACC22 (input) integer with value 0, 1, or 2.
-* Specifies the computation mode of far-from-diagonal
-* orthogonal updates.
-* = 0: DLAQR5 does not accumulate reflections and does not
-* use matrix-matrix multiply to update far-from-diagonal
-* matrix entries.
-* = 1: DLAQR5 accumulates reflections and uses matrix-matrix
-* multiply to update the far-from-diagonal matrix entries.
-* = 2: DLAQR5 accumulates reflections, uses matrix-matrix
-* multiply to update the far-from-diagonal matrix entries,
-* and takes advantage of 2-by-2 block structure during
-* matrix multiplies.
-*
-* N (input) integer scalar
-* N is the order of the Hessenberg matrix H upon which this
-* subroutine operates.
-*
-* KTOP (input) integer scalar
-* KBOT (input) integer scalar
-* These are the first and last rows and columns of an
-* isolated diagonal block upon which the QR sweep is to be
-* applied. It is assumed without a check that
-* either KTOP = 1 or H(KTOP,KTOP-1) = 0
-* and
-* either KBOT = N or H(KBOT+1,KBOT) = 0.
-*
-* NSHFTS (input) integer scalar
-* NSHFTS gives the number of simultaneous shifts. NSHFTS
-* must be positive and even.
-*
-* SR (input/output) DOUBLE PRECISION array of size (NSHFTS)
-* SI (input/output) DOUBLE PRECISION array of size (NSHFTS)
-* SR contains the real parts and SI contains the imaginary
-* parts of the NSHFTS shifts of origin that define the
-* multi-shift QR sweep. On output SR and SI may be
-* reordered.
-*
-* H (input/output) DOUBLE PRECISION array of size (LDH,N)
-* On input H contains a Hessenberg matrix. On output a
-* multi-shift QR sweep with shifts SR(J)+i*SI(J) is applied
-* to the isolated diagonal block in rows and columns KTOP
-* through KBOT.
-*
-* LDH (input) integer scalar
-* LDH is the leading dimension of H just as declared in the
-* calling procedure. LDH.GE.MAX(1,N).
-*
-* ILOZ (input) INTEGER
-* IHIZ (input) INTEGER
-* Specify the rows of Z to which transformations must be
-* applied if WANTZ is .TRUE.. 1 .LE. ILOZ .LE. IHIZ .LE. N
-*
-* Z (input/output) DOUBLE PRECISION array of size (LDZ,IHI)
-* If WANTZ = .TRUE., then the QR Sweep orthogonal
-* similarity transformation is accumulated into
-* Z(ILOZ:IHIZ,ILO:IHI) from the right.
-* If WANTZ = .FALSE., then Z is unreferenced.
-*
-* LDZ (input) integer scalar
-* LDA is the leading dimension of Z just as declared in
-* the calling procedure. LDZ.GE.N.
-*
-* V (workspace) DOUBLE PRECISION array of size (LDV,NSHFTS/2)
-*
-* LDV (input) integer scalar
-* LDV is the leading dimension of V as declared in the
-* calling procedure. LDV.GE.3.
-*
-* U (workspace) DOUBLE PRECISION array of size
-* (LDU,3*NSHFTS-3)
-*
-* LDU (input) integer scalar
-* LDU is the leading dimension of U just as declared in the
-* in the calling subroutine. LDU.GE.3*NSHFTS-3.
-*
-* NH (input) integer scalar
-* NH is the number of columns in array WH available for
-* workspace. NH.GE.1.
-*
-* WH (workspace) DOUBLE PRECISION array of size (LDWH,NH)
-*
-* LDWH (input) integer scalar
-* Leading dimension of WH just as declared in the
-* calling procedure. LDWH.GE.3*NSHFTS-3.
-*
-* NV (input) integer scalar
-* NV is the number of rows in WV agailable for workspace.
-* NV.GE.1.
-*
-* WV (workspace) DOUBLE PRECISION array of size
-* (LDWV,3*NSHFTS-3)
-*
-* LDWV (input) integer scalar
-* LDWV is the leading dimension of WV as declared in the
-* in the calling subroutine. LDWV.GE.NV.
-*
-* ================================================================
-* Based on contributions by
-* Karen Braman and Ralph Byers, Department of Mathematics,
-* University of Kansas, USA
-*
-* ================================================================
-* Reference:
-*
-* 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.
-*
-* ================================================================
+* ================================================================
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0d0, ONE = 1.0d0 )
@@ -453,29 +590,32 @@
* ==== Special case: 2-by-2 reflection (if needed) ====
*
K = KRCOL + 3*( M22-1 )
- IF( BMP22 .AND. ( V( 1, M22 ).NE.ZERO ) ) THEN
- DO 100 J = JTOP, MIN( KBOT, K+3 )
- REFSUM = V( 1, M22 )*( H( J, K+1 )+V( 2, M22 )*
- $ H( J, K+2 ) )
- H( J, K+1 ) = H( J, K+1 ) - REFSUM
- H( J, K+2 ) = H( J, K+2 ) - REFSUM*V( 2, M22 )
- 100 CONTINUE
-*
- IF( ACCUM ) THEN
- KMS = K - INCOL
- DO 110 J = MAX( 1, KTOP-INCOL ), KDU
- REFSUM = V( 1, M22 )*( U( J, KMS+1 )+V( 2, M22 )*
- $ U( J, KMS+2 ) )
- U( J, KMS+1 ) = U( J, KMS+1 ) - REFSUM
- U( J, KMS+2 ) = U( J, KMS+2 ) - REFSUM*V( 2, M22 )
+ IF( BMP22 ) THEN
+ IF ( V( 1, M22 ).NE.ZERO ) THEN
+ DO 100 J = JTOP, MIN( KBOT, K+3 )
+ REFSUM = V( 1, M22 )*( H( J, K+1 )+V( 2, M22 )*
+ $ H( J, K+2 ) )
+ H( J, K+1 ) = H( J, K+1 ) - REFSUM
+ H( J, K+2 ) = H( J, K+2 ) - REFSUM*V( 2, M22 )
+ 100 CONTINUE
+*
+ IF( ACCUM ) THEN
+ KMS = K - INCOL
+ DO 110 J = MAX( 1, KTOP-INCOL ), KDU
+ REFSUM = V( 1, M22 )*( U( J, KMS+1 )+
+ $ V( 2, M22 )*U( J, KMS+2 ) )
+ U( J, KMS+1 ) = U( J, KMS+1 ) - REFSUM
+ U( J, KMS+2 ) = U( J, KMS+2 ) -
+ $ REFSUM*V( 2, M22 )
110 CONTINUE
- ELSE IF( WANTZ ) THEN
- DO 120 J = ILOZ, IHIZ
- REFSUM = V( 1, M22 )*( Z( J, K+1 )+V( 2, M22 )*
- $ Z( J, K+2 ) )
- Z( J, K+1 ) = Z( J, K+1 ) - REFSUM
- Z( J, K+2 ) = Z( J, K+2 ) - REFSUM*V( 2, M22 )
- 120 CONTINUE
+ ELSE IF( WANTZ ) THEN
+ DO 120 J = ILOZ, IHIZ
+ REFSUM = V( 1, M22 )*( Z( J, K+1 )+V( 2, M22 )*
+ $ Z( J, K+2 ) )
+ Z( J, K+1 ) = Z( J, K+1 ) - REFSUM
+ Z( J, K+2 ) = Z( J, K+2 ) - REFSUM*V( 2, M22 )
+ 120 CONTINUE
+ END IF
END IF
END IF
*
@@ -639,14 +779,14 @@
CALL DLACPY( 'ALL', KNZ, JLEN, H( INCOL+1+J2, JCOL ),
$ LDH, WH( KZS+1, 1 ), LDWH )
*
-* ==== Multiply by U21' ====
+* ==== Multiply by U21**T ====
*
CALL DLASET( 'ALL', KZS, JLEN, ZERO, ZERO, WH, LDWH )
CALL DTRMM( 'L', 'U', 'C', 'N', KNZ, JLEN, ONE,
$ U( J2+1, 1+KZS ), LDU, WH( KZS+1, 1 ),
$ LDWH )
*
-* ==== Multiply top of H by U11' ====
+* ==== Multiply top of H by U11**T ====
*
CALL DGEMM( 'C', 'N', I2, JLEN, J2, ONE, U, LDU,
$ H( INCOL+1, JCOL ), LDH, ONE, WH, LDWH )
@@ -656,7 +796,7 @@
CALL DLACPY( 'ALL', J2, JLEN, H( INCOL+1, JCOL ), LDH,
$ WH( I2+1, 1 ), LDWH )
*
-* ==== Multiply by U21' ====
+* ==== Multiply by U21**T ====
*
CALL DTRMM( 'L', 'L', 'C', 'N', J2, JLEN, ONE,
$ U( 1, I2+1 ), LDU, WH( I2+1, 1 ), LDWH )