--- rpl/lapack/lapack/dlaqr0.f 2016/08/27 15:34:29 1.14
+++ rpl/lapack/lapack/dlaqr0.f 2023/08/07 08:38:55 1.19
@@ -2,25 +2,25 @@
*
* =========== DOCUMENTATION ===========
*
-* Online html documentation available at
-* http://www.netlib.org/lapack/explore-html/
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
-*> Download DLAQR0 + dependencies
-*>
-*> [TGZ]
-*>
-*> [ZIP]
-*>
+*> Download DLAQR0 + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
*> [TXT]
-*> \endhtmlonly
+*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DLAQR0( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI,
* ILOZ, IHIZ, Z, LDZ, WORK, LWORK, INFO )
-*
+*
* .. Scalar Arguments ..
* INTEGER IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, LWORK, N
* LOGICAL WANTT, WANTZ
@@ -29,7 +29,7 @@
* DOUBLE PRECISION H( LDH, * ), WI( * ), WORK( * ), WR( * ),
* $ Z( LDZ, * )
* ..
-*
+*
*
*> \par Purpose:
* =============
@@ -67,7 +67,7 @@
*> \param[in] N
*> \verbatim
*> N is INTEGER
-*> The order of the matrix H. N .GE. 0.
+*> The order of the matrix H. N >= 0.
*> \endverbatim
*>
*> \param[in] ILO
@@ -79,12 +79,12 @@
*> \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,
+*> and columns 1:ILO-1 and IHI+1:N and, if ILO > 1,
*> H(ILO,ILO-1) is zero. ILO and IHI are normally set by a
*> previous call to DGEBAL, and then passed to DGEHRD when the
*> matrix output by DGEBAL 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.
+*> respectively. If N > 0, then 1 <= ILO <= IHI <= N.
*> If N = 0, then ILO = 1 and IHI = 0.
*> \endverbatim
*>
@@ -97,19 +97,19 @@
*> decomposition (the Schur form); 2-by-2 diagonal blocks
*> (corresponding to complex conjugate pairs of eigenvalues)
*> are returned in standard form, with H(i,i) = H(i+1,i+1)
-*> and H(i+1,i)*H(i,i+1).LT.0. If INFO = 0 and WANTT is
+*> and H(i+1,i)*H(i,i+1) < 0. If INFO = 0 and WANTT is
*> .FALSE., then the contents of H are unspecified on exit.
-*> (The output value of H when INFO.GT.0 is given under the
+*> (The output value of H when INFO > 0 is given under the
*> description of INFO below.)
*>
-*> This subroutine may explicitly set H(i,j) = 0 for i.GT.j and
+*> This subroutine may explicitly set H(i,j) = 0 for i > 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).
+*> The leading dimension of the array H. LDH >= max(1,N).
*> \endverbatim
*>
*> \param[out] WR
@@ -125,7 +125,7 @@
*> and WI(ILO:IHI). 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) .GT. 0 and WI(i+1) .LT. 0. If WANTT is .TRUE., then
+*> WI(i) > 0 and WI(i+1) < 0. 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
*> WR(i) = H(i,i) and, if H(i:i+1,i:i+1) is a 2-by-2 diagonal
@@ -143,7 +143,7 @@
*> 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.
+*> 1 <= ILOZ <= ILO; IHI <= IHIZ <= N.
*> \endverbatim
*>
*> \param[in,out] Z
@@ -153,7 +153,7 @@
*> 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 output value of Z when INFO > 0 is given under
*> the description of INFO below.)
*> \endverbatim
*>
@@ -161,7 +161,7 @@
*> \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.
+*> then LDZ >= MAX(1,IHIZ). Otherwise, LDZ >= 1.
*> \endverbatim
*>
*> \param[out] WORK
@@ -174,7 +174,7 @@
*> \param[in] LWORK
*> \verbatim
*> LWORK is INTEGER
-*> The dimension of the array WORK. LWORK .GE. max(1,N)
+*> The dimension of the array WORK. LWORK >= 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.
@@ -190,19 +190,19 @@
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
-*> = 0: successful exit
-*> .GT. 0: if INFO = i, DLAQR0 failed to compute all of
+*> = 0: successful exit
+*> > 0: if INFO = i, DLAQR0 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,
+*> If INFO > 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
+*> If INFO > 0 and WANTT is .TRUE., then on exit
*>
*> (*) (initial value of H)*U = U*(final value of H)
*>
@@ -210,7 +210,7 @@
*> value of H is upper Hessenberg and quasi-triangular
*> in rows and columns INFO+1 through IHI.
*>
-*> If INFO .GT. 0 and WANTZ is .TRUE., then on exit
+*> If INFO > 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
@@ -218,7 +218,7 @@
*> where U is the orthogonal matrix in (*) (regard-
*> less of the value of WANTT.)
*>
-*> If INFO .GT. 0 and WANTZ is .FALSE., then Z is not
+*> If INFO > 0 and WANTZ is .FALSE., then Z is not
*> accessed.
*> \endverbatim
*
@@ -243,12 +243,10 @@
* Authors:
* ========
*
-*> \author Univ. of Tennessee
-*> \author Univ. of California Berkeley
-*> \author Univ. of Colorado Denver
-*> \author NAG Ltd.
-*
-*> \date September 2012
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
*
*> \ingroup doubleOTHERauxiliary
*
@@ -256,10 +254,9 @@
SUBROUTINE DLAQR0( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI,
$ ILOZ, IHIZ, Z, LDZ, WORK, LWORK, INFO )
*
-* -- LAPACK auxiliary routine (version 3.4.2) --
+* -- LAPACK auxiliary routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* September 2012
*
* .. Scalar Arguments ..
INTEGER IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, LWORK, N
@@ -278,7 +275,7 @@
* . DLAHQR because of insufficient subdiagonal scratch space.
* . (This is a hard limit.) ====
INTEGER NTINY
- PARAMETER ( NTINY = 11 )
+ PARAMETER ( NTINY = 15 )
*
* ==== Exceptional deflation windows: try to cure rare
* . slow convergence by varying the size of the
@@ -362,22 +359,22 @@
END IF
*
* ==== NWR = recommended deflation window size. At this
-* . point, N .GT. NTINY = 11, so there is enough
+* . point, N .GT. NTINY = 15, so there is enough
* . subdiagonal workspace for NWR.GE.2 as required.
* . (In fact, there is enough subdiagonal space for
-* . NWR.GE.3.) ====
+* . NWR.GE.4.) ====
*
NWR = ILAENV( 13, 'DLAQR0', JBCMPZ, N, ILO, IHI, LWORK )
NWR = MAX( 2, NWR )
NWR = MIN( IHI-ILO+1, ( N-1 ) / 3, NWR )
*
* ==== NSR = recommended number of simultaneous shifts.
-* . At this point N .GT. NTINY = 11, so there is at
+* . At this point N .GT. NTINY = 15, so there is at
* . enough subdiagonal workspace for NSR to be even
* . and greater than or equal to two as required. ====
*
NSR = ILAENV( 15, 'DLAQR0', JBCMPZ, N, ILO, IHI, LWORK )
- NSR = MIN( NSR, ( N+6 ) / 9, IHI-ILO )
+ NSR = MIN( NSR, ( N-3 ) / 6, IHI-ILO )
NSR = MAX( 2, NSR-MOD( NSR, 2 ) )
*
* ==== Estimate optimal workspace ====
@@ -425,7 +422,7 @@
* ==== NSMAX = the Largest number of simultaneous shifts
* . for which there is sufficient workspace. ====
*
- NSMAX = MIN( ( N+6 ) / 9, 2*LWORK / 3 )
+ NSMAX = MIN( ( N-3 ) / 6, 2*LWORK / 3 )
NSMAX = NSMAX - MOD( NSMAX, 2 )
*
* ==== NDFL: an iteration count restarted at deflation. ====
@@ -576,7 +573,7 @@
*
* ==== Got NS/2 or fewer shifts? Use DLAQR4 or
* . DLAHQR on a trailing principal submatrix to
-* . get more. (Since NS.LE.NSMAX.LE.(N+6)/9,
+* . get more. (Since NS.LE.NSMAX.LE.(N-3)/6,
* . there is enough space below the subdiagonal
* . to fit an NS-by-NS scratch array.) ====
*
@@ -678,7 +675,7 @@
END IF
END IF
*
-* ==== Use up to NS of the the smallest magnatiude
+* ==== Use up to NS of the the smallest magnitude
* . shifts. If there aren't NS shifts available,
* . then use them all, possibly dropping one to
* . make the number of shifts even. ====
@@ -698,7 +695,7 @@
* . (NVE-by-KDU) vertical work WV arrow along
* . the left-hand-edge. ====
*
- KDU = 3*NS - 3
+ KDU = 2*NS
KU = N - KDU + 1
KWH = KDU + 1
NHO = ( N-KDU+1-4 ) - ( KDU+1 ) + 1