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

eshpc · eshpc · commit 4cd57794aaed · 2021-04-15T17:04:59.000+01:00
diff --git a/SRC/claqr0.f b/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.) ====
 *
diff --git a/SRC/claqr4.f b/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.) ====
 *
diff --git a/SRC/dlaqr0.f b/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.) ====
 *
diff --git a/SRC/dlaqr4.f b/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.) ====
 *
diff --git a/SRC/slaqr0.f b/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.) ====
 *
diff --git a/SRC/slaqr4.f b/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
diff --git a/SRC/zlaqr0.f b/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.) ====
 *
diff --git a/SRC/zlaqr4.f b/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.) ====
 *

Original file line number	Diff line number	Diff line change
`@@ -555,7 +555,7 @@ SUBROUTINE CLAQR0( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,`
`555`	`555`	`*`
`556`	`556`	`* ==== Got NS/2 or fewer shifts? Use CLAQR4 or`
`557`	`557`	`* . CLAHQR on a trailing principal submatrix to`
`558`		`-* . get more. (Since NS.LE.NSMAX.LE.(N+6)/9,`
	`558`	`+* . get more. (Since NS.LE.NSMAX.LE.(N-3)/6,`
`559`	`559`	`* . there is enough space below the subdiagonal`
`560`	`560`	`* . to fit an NS-by-NS scratch array.) ====`
`561`	`561`	`*`
Original file line number	Diff line number	Diff line change
`@@ -377,7 +377,7 @@ SUBROUTINE CLAQR4( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,`
`377`	`377`	`* . and greater than or equal to two as required. ====`
`378`	`378`	`*`
`379`	`379`	`NSR = ILAENV( 15, 'CLAQR4', JBCMPZ, N, ILO, IHI, LWORK )`
`380`		`- NSR = MIN( NSR, ( N+6 ) / 9, IHI-ILO )`
	`380`	`+ NSR = MIN( NSR, ( N-3 ) / 6, IHI-ILO )`
`381`	`381`	`NSR = MAX( 2, NSR-MOD( NSR, 2 ) )`
`382`	`382`	`*`
`383`	`383`	`* ==== Estimate optimal workspace ====`
`@@ -425,7 +425,7 @@ SUBROUTINE CLAQR4( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,`
`425`	`425`	`* ==== NSMAX = the Largest number of simultaneous shifts`
`426`	`426`	`* . for which there is sufficient workspace. ====`
`427`	`427`	`*`
`428`		`- NSMAX = MIN( ( N+6 ) / 9, 2*LWORK / 3 )`
	`428`	`+ NSMAX = MIN( ( N-3 ) / 6, 2*LWORK / 3 )`
`429`	`429`	`NSMAX = NSMAX - MOD( NSMAX, 2 )`
`430`	`430`	`*`
`431`	`431`	`* ==== NDFL: an iteration count restarted at deflation. ====`
`@@ -565,7 +565,7 @@ SUBROUTINE CLAQR4( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,`
`565`	`565`	`*`
`566`	`566`	`* ==== Got NS/2 or fewer shifts? Use CLAHQR`
`567`	`567`	`* . on a trailing principal submatrix to`
`568`		`-* . get more. (Since NS.LE.NSMAX.LE.(N+6)/9,`
	`568`	`+* . get more. (Since NS.LE.NSMAX.LE.(N-3)/6,`
`569`	`569`	`* . there is enough space below the subdiagonal`
`570`	`570`	`* . to fit an NS-by-NS scratch array.) ====`
`571`	`571`	`*`
Original file line number	Diff line number	Diff line change
`@@ -359,7 +359,7 @@ SUBROUTINE DLAQR0( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI,`
`359`	`359`	`END IF`
`360`	`360`	`*`
`361`	`361`	`* ==== NWR = recommended deflation window size. At this`
`362`		`-* . point, N .GT. NTINY = 14, so there is enough`
	`362`	`+* . point, N .GT. NTINY = 15, so there is enough`
`363`	`363`	`* . subdiagonal workspace for NWR.GE.2 as required.`
`364`	`364`	`* . (In fact, there is enough subdiagonal space for`
`365`	`365`	`* . NWR.GE.4.) ====`
`@@ -573,7 +573,7 @@ SUBROUTINE DLAQR0( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI,`
`573`	`573`	`*`
`574`	`574`	`* ==== Got NS/2 or fewer shifts? Use DLAQR4 or`
`575`	`575`	`* . DLAHQR on a trailing principal submatrix to`
`576`		`-* . get more. (Since NS.LE.NSMAX.LE.(N+6)/9,`
	`576`	`+* . get more. (Since NS.LE.NSMAX.LE.(N-3)/6,`
`577`	`577`	`* . there is enough space below the subdiagonal`
`578`	`578`	`* . to fit an NS-by-NS scratch array.) ====`
`579`	`579`	`*`
Original file line number	Diff line number	Diff line change
`@@ -579,7 +579,7 @@ SUBROUTINE DLAQR4( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI,`
`579`	`579`	`*`
`580`	`580`	`* ==== Got NS/2 or fewer shifts? Use DLAHQR`
`581`	`581`	`* . on a trailing principal submatrix to`
`582`		`-* . get more. (Since NS.LE.NSMAX.LE.(N+6)/9,`
	`582`	`+* . get more. (Since NS.LE.NSMAX.LE.(N-3)/6,`
`583`	`583`	`* . there is enough space below the subdiagonal`
`584`	`584`	`* . to fit an NS-by-NS scratch array.) ====`
`585`	`585`	`*`
Original file line number	Diff line number	Diff line change
`@@ -572,7 +572,7 @@ SUBROUTINE SLAQR0( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI,`
`572`	`572`	`*`
`573`	`573`	`* ==== Got NS/2 or fewer shifts? Use SLAQR4 or`
`574`	`574`	`* . SLAHQR on a trailing principal submatrix to`
`575`		`-* . get more. (Since NS.LE.NSMAX.LE.(N+6)/9,`
	`575`	`+* . get more. (Since NS.LE.NSMAX.LE.(N-3)/6,`
`576`	`576`	`* . there is enough space below the subdiagonal`
`577`	`577`	`* . to fit an NS-by-NS scratch array.) ====`
`578`	`578`	`*`
Original file line number	Diff line number	Diff line change
`@@ -582,7 +582,7 @@ SUBROUTINE SLAQR4( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI,`
`582`	`582`	`*`
`583`	`583`	`* ==== Got NS/2 or fewer shifts? Use SLAHQR`
`584`	`584`	`* . on a trailing principal submatrix to`
`585`		`-* . get more. (Since NS.LE.NSMAX.LE.(N+6)/9,`
	`585`	`+* . get more. (Since NS.LE.NSMAX.LE.(N-3)/6,`
`586`	`586`	`* . there is enough space below the subdiagonal`
`587`	`587`	`* . to fit an NS-by-NS scratch array.) ====`
`588`	`588`	`*`
`@@ -697,7 +697,7 @@ SUBROUTINE SLAQR4( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI,`
`697`	`697`	`* . (NVE-by-KDU) vertical work WV arrow along`
`698`	`698`	`* . the left-hand-edge. ====`
`699`	`699`	`*`
`700`		`- KDU = 3*NS - 3`
	`700`	`+ KDU = 2*NS`
`701`	`701`	`KU = N - KDU + 1`
`702`	`702`	`KWH = KDU + 1`
`703`	`703`	`NHO = ( N-KDU+1-4 ) - ( KDU+1 ) + 1`
Original file line number	Diff line number	Diff line change
`@@ -557,7 +557,7 @@ SUBROUTINE ZLAQR0( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,`
`557`	`557`	`*`
`558`	`558`	`* ==== Got NS/2 or fewer shifts? Use ZLAQR4 or`
`559`	`559`	`* . ZLAHQR on a trailing principal submatrix to`
`560`		`-* . get more. (Since NS.LE.NSMAX.LE.(N+6)/9,`
	`560`	`+* . get more. (Since NS.LE.NSMAX.LE.(N-3)/6,`
`561`	`561`	`* . there is enough space below the subdiagonal`
`562`	`562`	`* . to fit an NS-by-NS scratch array.) ====`
`563`	`563`	`*`
Original file line number	Diff line number	Diff line change
`@@ -563,7 +563,7 @@ SUBROUTINE ZLAQR4( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,`
`563`	`563`	`*`
`564`	`564`	`* ==== Got NS/2 or fewer shifts? Use ZLAHQR`
`565`	`565`	`* . on a trailing principal submatrix to`
`566`		`-* . get more. (Since NS.LE.NSMAX.LE.(N+6)/9,`
	`566`	`+* . get more. (Since NS.LE.NSMAX.LE.(N-3)/6,`
`567`	`567`	`* . there is enough space below the subdiagonal`
`568`	`568`	`* . to fit an NS-by-NS scratch array.) ====`
`569`	`569`	`*`