Merge pull request #480 from thijssteel/optimal-packing-xlaqr5

Optimal packing xlaqr5

Author: langou

SRC/chseqr.f

@@ -320,10 +320,10 @@ SUBROUTINE CHSEQR( JOB, COMPZ, N, ILO, IHI, H, LDH, W, Z, LDZ,
 *     .    CLAHQR because of insufficient subdiagonal scratch space.
 *     .    (This is a hard limit.) ====
       INTEGER            NTINY
-      PARAMETER          ( NTINY = 11 )
+      PARAMETER          ( NTINY = 15 )
 *
 *     ==== NL allocates some local workspace to help small matrices
-*     .    through a rare CLAHQR failure.  NL > NTINY = 11 is
+*     .    through a rare CLAHQR failure.  NL > NTINY = 15 is
 *     .    required and NL <= NMIN = ILAENV(ISPEC=12,...) is recom-
 *     .    mended.  (The default value of NMIN is 75.)  Using NL = 49
 *     .    allows up to six simultaneous shifts and a 16-by-16

SRC/claqr0.f

@@ -260,7 +260,7 @@ SUBROUTINE CLAQR0( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,
 *     .    CLAHQR 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
@@ -355,22 +355,22 @@ SUBROUTINE CLAQR0( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,
          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, 'CLAQR0', 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, 'CLAQR0', 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 ====
@@ -418,7 +418,7 @@ SUBROUTINE CLAQR0( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,
 *        ==== 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. ====
@@ -659,7 +659,7 @@ SUBROUTINE CLAQR0( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,
 *              .      (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

SRC/claqr4.f

@@ -270,7 +270,7 @@ SUBROUTINE CLAQR4( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,
 *     .    CLAHQR 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
@@ -365,17 +365,17 @@ SUBROUTINE CLAQR4( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,
          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, 'CLAQR4', 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. ====
 *
@@ -663,7 +663,7 @@ SUBROUTINE CLAQR4( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,
 *              .      (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