--- 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 
-*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlahqr.f"> 
-*> [TGZ]</a> 
-*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlahqr.f"> 
-*> [ZIP]</a> 
-*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlahqr.f"> 
+*> Download ZLAHQR + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlahqr.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlahqr.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlahqr.f">
 *> [TXT]</a>
-*> \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.