Corrections to claqr4.f and slaqr4.f code, and update comments in other xLAQR routines

Author: eshpc

SRC/claqr0.f

@@ -555,7 +555,7 @@ SUBROUTINE CLAQR0( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,
 *
 *                 ==== Got NS/2 or fewer shifts? Use CLAQR4 or
 *                 .    CLAHQR on a trailing principal submatrix to
-*                 .    get more. (Since NS.LE.NSMAX.LE.(N+6)/9,
+*                 .    get more. (Since NS.LE.NSMAX.LE.(N-3)/6,
 *                 .    there is enough space below the subdiagonal
 *                 .    to fit an NS-by-NS scratch array.) ====
 *

SRC/claqr4.f

@@ -377,7 +377,7 @@ SUBROUTINE CLAQR4( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,
 *        .    and greater than or equal to two as required. ====
 *
          NSR = ILAENV( 15, 'CLAQR4', 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 ====
@@ -425,7 +425,7 @@ SUBROUTINE CLAQR4( 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. ====
@@ -565,7 +565,7 @@ SUBROUTINE CLAQR4( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,
 *
 *                 ==== Got NS/2 or fewer shifts? Use CLAHQR
 *                 .    on a trailing principal submatrix to
-*                 .    get more. (Since NS.LE.NSMAX.LE.(N+6)/9,
+*                 .    get more. (Since NS.LE.NSMAX.LE.(N-3)/6,
 *                 .    there is enough space below the subdiagonal
 *                 .    to fit an NS-by-NS scratch array.) ====
 *

SRC/dlaqr0.f

@@ -359,7 +359,7 @@ SUBROUTINE DLAQR0( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI,
          END IF
 *
 *        ==== NWR = recommended deflation window size.  At this
-*        .    point,  N .GT. NTINY = 14, 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.4.) ====
@@ -573,7 +573,7 @@ SUBROUTINE DLAQR0( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI,
 *
 *                 ==== Got NS/2 or fewer shifts? Use DLAQR4 or
 *                 .    DLAHQR on a trailing principal submatrix to
-*                 .    get more. (Since NS.LE.NSMAX.LE.(N+6)/9,
+*                 .    get more. (Since NS.LE.NSMAX.LE.(N-3)/6,
 *                 .    there is enough space below the subdiagonal
 *                 .    to fit an NS-by-NS scratch array.) ====
 *

SRC/dlaqr4.f

@@ -579,7 +579,7 @@ SUBROUTINE DLAQR4( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI,
 *
 *                 ==== Got NS/2 or fewer shifts? Use DLAHQR
 *                 .    on a trailing principal submatrix to
-*                 .    get more. (Since NS.LE.NSMAX.LE.(N+6)/9,
+*                 .    get more. (Since NS.LE.NSMAX.LE.(N-3)/6,
 *                 .    there is enough space below the subdiagonal
 *                 .    to fit an NS-by-NS scratch array.) ====
 *

SRC/slaqr0.f

@@ -572,7 +572,7 @@ SUBROUTINE SLAQR0( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI,
 *
 *                 ==== Got NS/2 or fewer shifts? Use SLAQR4 or
 *                 .    SLAHQR on a trailing principal submatrix to
-*                 .    get more. (Since NS.LE.NSMAX.LE.(N+6)/9,
+*                 .    get more. (Since NS.LE.NSMAX.LE.(N-3)/6,
 *                 .    there is enough space below the subdiagonal
 *                 .    to fit an NS-by-NS scratch array.) ====
 *

SRC/slaqr4.f

@@ -582,7 +582,7 @@ SUBROUTINE SLAQR4( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI,
 *
 *                 ==== Got NS/2 or fewer shifts? Use SLAHQR
 *                 .    on a trailing principal submatrix to
-*                 .    get more. (Since NS.LE.NSMAX.LE.(N+6)/9,
+*                 .    get more. (Since NS.LE.NSMAX.LE.(N-3)/6,
 *                 .    there is enough space below the subdiagonal
 *                 .    to fit an NS-by-NS scratch array.) ====
 *
@@ -697,7 +697,7 @@ SUBROUTINE SLAQR4( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI,
 *              .      (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/zlaqr0.f

@@ -557,7 +557,7 @@ SUBROUTINE ZLAQR0( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,
 *
 *                 ==== Got NS/2 or fewer shifts? Use ZLAQR4 or
 *                 .    ZLAHQR on a trailing principal submatrix to
-*                 .    get more. (Since NS.LE.NSMAX.LE.(N+6)/9,
+*                 .    get more. (Since NS.LE.NSMAX.LE.(N-3)/6,
 *                 .    there is enough space below the subdiagonal
 *                 .    to fit an NS-by-NS scratch array.) ====
 *

SRC/zlaqr4.f

@@ -563,7 +563,7 @@ SUBROUTINE ZLAQR4( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,
 *
 *                 ==== Got NS/2 or fewer shifts? Use ZLAHQR
 *                 .    on a trailing principal submatrix to
-*                 .    get more. (Since NS.LE.NSMAX.LE.(N+6)/9,
+*                 .    get more. (Since NS.LE.NSMAX.LE.(N-3)/6,
 *                 .    there is enough space below the subdiagonal
 *                 .    to fit an NS-by-NS scratch array.) ====
 *