--- rpl/lapack/lapack/dlahqr.f 2012/12/14 12:30:22 1.11
+++ rpl/lapack/lapack/dlahqr.f 2023/08/07 08:38:54 1.20
@@ -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 DLAHQR + dependencies
-*>
-*> [TGZ]
-*>
-*> [ZIP]
-*>
+*> Download DLAHQR + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
*> [TXT]
-*> \endhtmlonly
+*> \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
@@ -28,7 +28,7 @@
* .. Array Arguments ..
* DOUBLE PRECISION H( LDH, * ), WI( * ), WR( * ), Z( LDZ, * )
* ..
-*
+*
*
*> \par Purpose:
* =============
@@ -150,26 +150,26 @@
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
-*> = 0: successful exit
-*> .GT. 0: If INFO = i, DLAHQR failed to compute all the
+*> = 0: successful exit
+*> > 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,
+*> If INFO > 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
+*> 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)
-*> where U is an orthognal matrix. The final
+*> where U is an orthogonal 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
+*> If INFO > 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.)
@@ -178,12 +178,10 @@
* 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
*
@@ -206,11 +204,11 @@
* =====================================================================
SUBROUTINE DLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI,
$ ILOZ, IHIZ, Z, LDZ, INFO )
+ IMPLICIT NONE
*
-* -- 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, N
@@ -223,19 +221,20 @@
* =========================================================
*
* .. Parameters ..
- INTEGER ITMAX
- PARAMETER ( ITMAX = 30 )
DOUBLE PRECISION ZERO, ONE, TWO
PARAMETER ( ZERO = 0.0d0, ONE = 1.0d0, TWO = 2.0d0 )
DOUBLE PRECISION DAT1, DAT2
PARAMETER ( DAT1 = 3.0d0 / 4.0d0, DAT2 = -0.4375d0 )
+ INTEGER KEXSH
+ PARAMETER ( KEXSH = 10 )
* ..
* .. Local Scalars ..
DOUBLE PRECISION AA, AB, BA, BB, CS, DET, H11, H12, H21, H21S,
$ H22, RT1I, RT1R, RT2I, RT2R, RTDISC, S, SAFMAX,
$ SAFMIN, SMLNUM, SN, SUM, T1, T2, T3, TR, TST,
$ ULP, V2, V3
- INTEGER I, I1, I2, ITS, J, K, L, M, NH, NR, NZ
+ INTEGER I, I1, I2, ITS, ITMAX, J, K, L, M, NH, NR, NZ,
+ $ KDEFL
* ..
* .. Local Arrays ..
DOUBLE PRECISION V( 3 )
@@ -292,6 +291,14 @@
I2 = N
END IF
*
+* ITMAX is the total number of QR iterations allowed.
+*
+ ITMAX = 30 * MAX( 10, NH )
+*
+* KDEFL counts the number of iterations since a deflation
+*
+ KDEFL = 0
+*
* The main loop begins here. I is the loop index and decreases from
* IHI to ILO in steps of 1 or 2. Each iteration of the loop works
* with the active submatrix in rows and columns L to I.
@@ -351,6 +358,7 @@
*
IF( L.GE.I-1 )
$ GO TO 150
+ KDEFL = KDEFL + 1
*
* Now the active submatrix is in rows and columns L to I. If
* eigenvalues only are being computed, only the active submatrix
@@ -361,21 +369,21 @@
I2 = I
END IF
*
- IF( ITS.EQ.10 ) THEN
+ IF( MOD(KDEFL,2*KEXSH).EQ.0 ) THEN
*
* Exceptional shift.
*
- S = ABS( H( L+1, L ) ) + ABS( H( L+2, L+1 ) )
- H11 = DAT1*S + H( L, L )
+ S = ABS( H( I, I-1 ) ) + ABS( H( I-1, I-2 ) )
+ H11 = DAT1*S + H( I, I )
H12 = DAT2*S
H21 = S
H22 = H11
- ELSE IF( ITS.EQ.20 ) THEN
+ ELSE IF( MOD(KDEFL,KEXSH).EQ.0 ) THEN
*
* Exceptional shift.
*
- S = ABS( H( I, I-1 ) ) + ABS( H( I-1, I-2 ) )
- H11 = DAT1*S + H( I, I )
+ S = ABS( H( L+1, L ) ) + ABS( H( L+2, L+1 ) )
+ H11 = DAT1*S + H( L, L )
H12 = DAT2*S
H21 = S
H22 = H11
@@ -597,6 +605,8 @@
CALL DROT( NZ, Z( ILOZ, I-1 ), 1, Z( ILOZ, I ), 1, CS, SN )
END IF
END IF
+* reset deflation counter
+ KDEFL = 0
*
* return to start of the main loop with new value of I.
*