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Merge pull request #3206 from martin-frbg/lapack480535
Import packing improvements to LAPACK xLAQR from Reference-LAPACK (PR 480+535)
2 parents c9a82f5 + 87d2e31 commit dc6b04c

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Lines changed: 1267 additions & 1670 deletions

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‎lapack-netlib/SRC/chseqr.f‎

Lines changed: 2 additions & 2 deletions
Original file line numberDiff line numberDiff line change
@@ -320,10 +320,10 @@ SUBROUTINE CHSEQR( JOB, COMPZ, N, ILO, IHI, H, LDH, W, Z, LDZ,
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* . CLAHQR because of insufficient subdiagonal scratch space.
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* . (This is a hard limit.) ====
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INTEGER NTINY
323-
PARAMETER ( NTINY = 11 )
323+
PARAMETER ( NTINY = 15 )
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*
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* ==== NL allocates some local workspace to help small matrices
326-
* . through a rare CLAHQR failure. NL > NTINY = 11 is
326+
* . through a rare CLAHQR failure. NL > NTINY = 15 is
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* . required and NL <= NMIN = ILAENV(ISPEC=12,...) is recom-
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* . mended. (The default value of NMIN is 75.) Using NL = 49
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* . allows up to six simultaneous shifts and a 16-by-16

‎lapack-netlib/SRC/claqr0.f‎

Lines changed: 8 additions & 8 deletions
Original file line numberDiff line numberDiff line change
@@ -260,7 +260,7 @@ SUBROUTINE CLAQR0( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,
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* . CLAHQR because of insufficient subdiagonal scratch space.
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* . (This is a hard limit.) ====
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INTEGER NTINY
263-
PARAMETER ( NTINY = 11 )
263+
PARAMETER ( NTINY = 15 )
264264
*
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* ==== Exceptional deflation windows: try to cure rare
266266
* . slow convergence by varying the size of the
@@ -355,22 +355,22 @@ SUBROUTINE CLAQR0( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,
355355
END IF
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*
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* ==== NWR = recommended deflation window size. At this
358-
* . point, N .GT. NTINY = 11, so there is enough
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* . point, N .GT. NTINY = 15, so there is enough
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* . subdiagonal workspace for NWR.GE.2 as required.
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* . (In fact, there is enough subdiagonal space for
361-
* . NWR.GE.3.) ====
361+
* . NWR.GE.4.) ====
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*
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NWR = ILAENV( 13, 'CLAQR0', JBCMPZ, N, ILO, IHI, LWORK )
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NWR = MAX( 2, NWR )
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NWR = MIN( IHI-ILO+1, ( N-1 ) / 3, NWR )
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*
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* ==== NSR = recommended number of simultaneous shifts.
368-
* . At this point N .GT. NTINY = 11, so there is at
368+
* . At this point N .GT. NTINY = 15, so there is at
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* . enough subdiagonal workspace for NSR to be even
370370
* . and greater than or equal to two as required. ====
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*
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NSR = ILAENV( 15, 'CLAQR0', JBCMPZ, N, ILO, IHI, LWORK )
373-
NSR = MIN( NSR, ( N+6 ) / 9, IHI-ILO )
373+
NSR = MIN( NSR, ( N-3 ) / 6, IHI-ILO )
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NSR = MAX( 2, NSR-MOD( NSR, 2 ) )
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*
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* ==== Estimate optimal workspace ====
@@ -418,7 +418,7 @@ SUBROUTINE CLAQR0( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,
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* ==== NSMAX = the Largest number of simultaneous shifts
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* . for which there is sufficient workspace. ====
420420
*
421-
NSMAX = MIN( ( N+6 ) / 9, 2*LWORK / 3 )
421+
NSMAX = MIN( ( N-3 ) / 6, 2*LWORK / 3 )
422422
NSMAX = NSMAX - MOD( NSMAX, 2 )
423423
*
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* ==== NDFL: an iteration count restarted at deflation. ====
@@ -558,7 +558,7 @@ SUBROUTINE CLAQR0( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,
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*
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* ==== Got NS/2 or fewer shifts? Use CLAQR4 or
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* . CLAHQR on a trailing principal submatrix to
561-
* . get more. (Since NS.LE.NSMAX.LE.(N+6)/9,
561+
* . get more. (Since NS.LE.NSMAX.LE.(N-3)/6,
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* . there is enough space below the subdiagonal
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* . to fit an NS-by-NS scratch array.) ====
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*
@@ -659,7 +659,7 @@ SUBROUTINE CLAQR0( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,
659659
* . (NVE-by-KDU) vertical work WV arrow along
660660
* . the left-hand-edge. ====
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*
662-
KDU = 3*NS - 3
662+
KDU = 2*NS
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KU = N - KDU + 1
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KWH = KDU + 1
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NHO = ( N-KDU+1-4 ) - ( KDU+1 ) + 1

‎lapack-netlib/SRC/claqr4.f‎

Lines changed: 8 additions & 8 deletions
Original file line numberDiff line numberDiff line change
@@ -270,7 +270,7 @@ SUBROUTINE CLAQR4( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,
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* . CLAHQR because of insufficient subdiagonal scratch space.
271271
* . (This is a hard limit.) ====
272272
INTEGER NTINY
273-
PARAMETER ( NTINY = 11 )
273+
PARAMETER ( NTINY = 15 )
274274
*
275275
* ==== Exceptional deflation windows: try to cure rare
276276
* . slow convergence by varying the size of the
@@ -365,22 +365,22 @@ SUBROUTINE CLAQR4( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,
365365
END IF
366366
*
367367
* ==== NWR = recommended deflation window size. At this
368-
* . point, N .GT. NTINY = 11, so there is enough
368+
* . point, N .GT. NTINY = 15, so there is enough
369369
* . subdiagonal workspace for NWR.GE.2 as required.
370370
* . (In fact, there is enough subdiagonal space for
371-
* . NWR.GE.3.) ====
371+
* . NWR.GE.4.) ====
372372
*
373373
NWR = ILAENV( 13, 'CLAQR4', JBCMPZ, N, ILO, IHI, LWORK )
374374
NWR = MAX( 2, NWR )
375375
NWR = MIN( IHI-ILO+1, ( N-1 ) / 3, NWR )
376376
*
377377
* ==== NSR = recommended number of simultaneous shifts.
378-
* . At this point N .GT. NTINY = 11, so there is at
378+
* . At this point N .GT. NTINY = 15, so there is at
379379
* . enough subdiagonal workspace for NSR to be even
380380
* . and greater than or equal to two as required. ====
381381
*
382382
NSR = ILAENV( 15, 'CLAQR4', JBCMPZ, N, ILO, IHI, LWORK )
383-
NSR = MIN( NSR, ( N+6 ) / 9, IHI-ILO )
383+
NSR = MIN( NSR, ( N-3 ) / 6, IHI-ILO )
384384
NSR = MAX( 2, NSR-MOD( NSR, 2 ) )
385385
*
386386
* ==== Estimate optimal workspace ====
@@ -428,7 +428,7 @@ SUBROUTINE CLAQR4( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,
428428
* ==== NSMAX = the Largest number of simultaneous shifts
429429
* . for which there is sufficient workspace. ====
430430
*
431-
NSMAX = MIN( ( N+6 ) / 9, 2*LWORK / 3 )
431+
NSMAX = MIN( ( N-3 ) / 6, 2*LWORK / 3 )
432432
NSMAX = NSMAX - MOD( NSMAX, 2 )
433433
*
434434
* ==== NDFL: an iteration count restarted at deflation. ====
@@ -568,7 +568,7 @@ SUBROUTINE CLAQR4( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,
568568
*
569569
* ==== Got NS/2 or fewer shifts? Use CLAHQR
570570
* . on a trailing principal submatrix to
571-
* . get more. (Since NS.LE.NSMAX.LE.(N+6)/9,
571+
* . get more. (Since NS.LE.NSMAX.LE.(N-3)/6,
572572
* . there is enough space below the subdiagonal
573573
* . to fit an NS-by-NS scratch array.) ====
574574
*
@@ -663,7 +663,7 @@ SUBROUTINE CLAQR4( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ,
663663
* . (NVE-by-KDU) vertical work WV arrow along
664664
* . the left-hand-edge. ====
665665
*
666-
KDU = 3*NS - 3
666+
KDU = 2*NS
667667
KU = N - KDU + 1
668668
KWH = KDU + 1
669669
NHO = ( N-KDU+1-4 ) - ( KDU+1 ) + 1

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