--- rpl/lapack/lapack/zlahqr.f 2011/11/21 22:19:51 1.9
+++ rpl/lapack/lapack/zlahqr.f 2020/05/21 21:46:07 1.19
@@ -1,26 +1,26 @@
-*> \brief \b ZLAHQR
+*> \brief \b ZLAHQR computes the eigenvalues and Schur factorization of an upper Hessenberg matrix, using the double-shift/single-shift QR algorithm.
*
* =========== 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 +166,12 @@
* Authors:
* ========
*
-*> \author Univ. of Tennessee
-*> \author Univ. of California Berkeley
-*> \author Univ. of Colorado Denver
-*> \author NAG Ltd.
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
*
-*> \date November 2011
+*> \date December 2016
*
*> \ingroup complex16OTHERauxiliary
*
@@ -195,10 +195,10 @@
SUBROUTINE ZLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,
$ IHIZ, Z, LDZ, INFO )
*
-* -- LAPACK auxiliary routine (version 3.4.0) --
+* -- 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 2011
+* December 2016
*
* .. Scalar Arguments ..
INTEGER IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, N
@@ -211,8 +211,6 @@
* =========================================================
*
* .. Parameters ..
- INTEGER ITMAX
- PARAMETER ( ITMAX = 30 )
COMPLEX*16 ZERO, ONE
PARAMETER ( ZERO = ( 0.0d0, 0.0d0 ),
$ ONE = ( 1.0d0, 0.0d0 ) )
@@ -226,7 +224,8 @@
$ 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
* ..
* .. Local Arrays ..
COMPLEX*16 V( 2 )
@@ -312,6 +311,10 @@
I2 = N
END IF
*
+* ITMAX is the total number of QR iterations allowed.
+*
+ ITMAX = 30 * MAX( 10, NH )
+*
* 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.