--- rpl/lapack/lapack/zlahqr.f 2012/12/14 14:22:50 1.12
+++ rpl/lapack/lapack/zlahqr.f 2023/08/07 08:39:29 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 ZLAHQR + dependencies
-*>
-*> [TGZ]
-*>
-*> [ZIP]
-*>
+*> Download ZLAHQR + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
*> [TXT]
-*> \endhtmlonly
+*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE ZLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, 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 ..
* COMPLEX*16 H( LDH, * ), W( * ), Z( LDZ, * )
* ..
-*
+*
*
*> \par Purpose:
* =============
@@ -138,26 +138,26 @@
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
-*> = 0: successful exit
-*> .GT. 0: if INFO = i, ZLAHQR failed to compute all the
+*> = 0: successful exit
+*> > 0: if INFO = i, ZLAHQR failed to compute all the
*> eigenvalues ILO to IHI in a total of 30 iterations
*> per eigenvalue; elements i+1:ihi of W 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,
+*> 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)
-*> 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.)
@@ -166,12 +166,10 @@
* 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 complex16OTHERauxiliary
*
@@ -194,11 +192,11 @@
* =====================================================================
SUBROUTINE ZLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, 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
@@ -211,8 +209,6 @@
* =========================================================
*
* .. Parameters ..
- INTEGER ITMAX
- PARAMETER ( ITMAX = 30 )
COMPLEX*16 ZERO, ONE
PARAMETER ( ZERO = ( 0.0d0, 0.0d0 ),
$ ONE = ( 1.0d0, 0.0d0 ) )
@@ -220,13 +216,16 @@
PARAMETER ( RZERO = 0.0d0, RONE = 1.0d0, HALF = 0.5d0 )
DOUBLE PRECISION DAT1
PARAMETER ( DAT1 = 3.0d0 / 4.0d0 )
+ INTEGER KEXSH
+ PARAMETER ( KEXSH = 10 )
* ..
* .. Local Scalars ..
COMPLEX*16 CDUM, H11, H11S, H22, SC, SUM, T, T1, TEMP, U,
$ V2, X, Y
DOUBLE PRECISION AA, AB, BA, BB, H10, H21, RTEMP, S, SAFMAX,
$ SAFMIN, SMLNUM, SX, T2, TST, ULP
- INTEGER I, I1, I2, ITS, J, JHI, JLO, K, L, M, NH, NZ
+ INTEGER I, I1, I2, ITS, ITMAX, J, JHI, JLO, K, L, M,
+ $ NH, NZ, KDEFL
* ..
* .. Local Arrays ..
COMPLEX*16 V( 2 )
@@ -312,6 +311,14 @@
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. Each iteration of the loop works
* with the active submatrix in rows and columns L to I.
@@ -371,6 +378,7 @@
*
IF( L.GE.I )
$ GO TO 140
+ 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
@@ -381,18 +389,18 @@
I2 = I
END IF
*
- IF( ITS.EQ.10 ) THEN
+ IF( MOD(KDEFL,2*KEXSH).EQ.0 ) THEN
*
* Exceptional shift.
*
- S = DAT1*ABS( DBLE( H( L+1, L ) ) )
- T = S + H( L, L )
- ELSE IF( ITS.EQ.20 ) THEN
+ S = DAT1*ABS( DBLE( H( I, I-1 ) ) )
+ T = S + H( I, I )
+ ELSE IF( MOD(KDEFL,KEXSH).EQ.0 ) THEN
*
* Exceptional shift.
*
- S = DAT1*ABS( DBLE( H( I, I-1 ) ) )
- T = S + H( I, I )
+ S = DAT1*ABS( DBLE( H( L+1, L ) ) )
+ T = S + H( L, L )
ELSE
*
* Wilkinson's shift.
@@ -554,6 +562,8 @@
* H(I,I-1) is negligible: one eigenvalue has converged.
*
W( I ) = H( I, I )
+* reset deflation counter
+ KDEFL = 0
*
* return to start of the main loop with new value of I.
*