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Merge pull request #3832 from martin-frbg/lapack681+698 

Improve ?LAQR5 and use normwise criterion in ?LAQZ0 (Reference-LAPACK PRs 681+698)
This commit is contained in:
Martin Kroeker 2022-11-20 22:40:52 +01:00 committed by GitHub
parent f63c93274c c6816bb576
commit 1d5a3aff0d
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GPG Key ID: 4AEE18F83AFDEB23
8 changed files with 249 additions and 214 deletions
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96
lapack-netlib/SRC/claqr5.f
View File

@ -279,7 +279,7 @@
PARAMETER ( RZERO = 0.0e0, RONE = 1.0e0 )
* ..
* .. Local Scalars ..
COMPLEX ALPHA, BETA, CDUM, REFSUM
COMPLEX ALPHA, BETA, CDUM, REFSUM, T1, T2, T3
REAL H11, H12, H21, H22, SAFMAX, SAFMIN, SCL,
$ SMLNUM, TST1, TST2, ULP
INTEGER I2, I4, INCOL, J, JBOT, JCOL, JLEN,
@ -424,12 +424,12 @@
* ==== Perform update from right within
* . computational window. ====
*
T1 = V( 1, M22 )
T2 = T1*CONJG( V( 2, M22 ) )
DO 30 J = JTOP, MIN( KBOT, K+3 )
REFSUM = V( 1, M22 )*( H( J, K+1 )+V( 2, M22 )*
$ H( J, K+2 ) )
H( J, K+1 ) = H( J, K+1 ) - REFSUM
H( J, K+2 ) = H( J, K+2 ) -
$ REFSUM*CONJG( V( 2, M22 ) )
REFSUM = H( J, K+1 ) + V( 2, M22 )*H( J, K+2 )
H( J, K+1 ) = H( J, K+1 ) - REFSUM*T1
H( J, K+2 ) = H( J, K+2 ) - REFSUM*T2
30 CONTINUE
*
* ==== Perform update from left within
@ -442,12 +442,13 @@
ELSE
JBOT = KBOT
END IF
T1 = CONJG( V( 1, M22 ) )
T2 = T1*V( 2, M22 )
DO 40 J = K+1, JBOT
REFSUM = CONJG( V( 1, M22 ) )*
$ ( H( K+1, J )+CONJG( V( 2, M22 ) )*
$ H( K+2, J ) )
H( K+1, J ) = H( K+1, J ) - REFSUM
H( K+2, J ) = H( K+2, J ) - REFSUM*V( 2, M22 )
REFSUM = H( K+1, J ) +
$ CONJG( V( 2, M22 ) )*H( K+2, J )
H( K+1, J ) = H( K+1, J ) - REFSUM*T1
H( K+2, J ) = H( K+2, J ) - REFSUM*T2
40 CONTINUE
*
* ==== The following convergence test requires that
@ -610,25 +611,28 @@
* . deflation check. We still delay most of the
* . updates from the left for efficiency. ====
*
T1 = V( 1, M )
T2 = T1*CONJG( V( 2, M ) )
T3 = T1*CONJG( V( 3, M ) )
DO 70 J = JTOP, MIN( KBOT, K+3 )
REFSUM = V( 1, M )*( H( J, K+1 )+V( 2, M )*
$ H( J, K+2 )+V( 3, M )*H( J, K+3 ) )
H( J, K+1 ) = H( J, K+1 ) - REFSUM
H( J, K+2 ) = H( J, K+2 ) -
$ REFSUM*CONJG( V( 2, M ) )
H( J, K+3 ) = H( J, K+3 ) -
$ REFSUM*CONJG( V( 3, M ) )
REFSUM = H( J, K+1 ) + V( 2, M )*H( J, K+2 )
$ + V( 3, M )*H( J, K+3 )
H( J, K+1 ) = H( J, K+1 ) - REFSUM*T1
H( J, K+2 ) = H( J, K+2 ) - REFSUM*T2
H( J, K+3 ) = H( J, K+3 ) - REFSUM*T3
70 CONTINUE
*
* ==== Perform update from left for subsequent
* . column. ====
*
REFSUM = CONJG( V( 1, M ) )*( H( K+1, K+1 )
$ +CONJG( V( 2, M ) )*H( K+2, K+1 )
$ +CONJG( V( 3, M ) )*H( K+3, K+1 ) )
H( K+1, K+1 ) = H( K+1, K+1 ) - REFSUM
H( K+2, K+1 ) = H( K+2, K+1 ) - REFSUM*V( 2, M )
H( K+3, K+1 ) = H( K+3, K+1 ) - REFSUM*V( 3, M )
T1 = CONJG( V( 1, M ) )
T2 = T1*V( 2, M )
T3 = T1*V( 3, M )
REFSUM = H( K+1, K+1 ) + CONJG( V( 2, M ) )*H( K+2, K+1 )
$ + CONJG( V( 3, M ) )*H( K+3, K+1 )
H( K+1, K+1 ) = H( K+1, K+1 ) - REFSUM*T1
H( K+2, K+1 ) = H( K+2, K+1 ) - REFSUM*T2
H( K+3, K+1 ) = H( K+3, K+1 ) - REFSUM*T3
*
* ==== The following convergence test requires that
* . the tradition small-compared-to-nearby-diagonals
@ -688,13 +692,15 @@
*
DO 100 M = MBOT, MTOP, -1
K = KRCOL + 2*( M-1 )
T1 = CONJG( V( 1, M ) )
T2 = T1*V( 2, M )
T3 = T1*V( 3, M )
DO 90 J = MAX( KTOP, KRCOL + 2*M ), JBOT
REFSUM = CONJG( V( 1, M ) )*
$ ( H( K+1, J )+CONJG( V( 2, M ) )*
$ H( K+2, J )+CONJG( V( 3, M ) )*H( K+3, J ) )
H( K+1, J ) = H( K+1, J ) - REFSUM
H( K+2, J ) = H( K+2, J ) - REFSUM*V( 2, M )
H( K+3, J ) = H( K+3, J ) - REFSUM*V( 3, M )
REFSUM = H( K+1, J ) + CONJG( V( 2, M ) )*
$ H( K+2, J ) + CONJG( V( 3, M ) )*H( K+3, J )
H( K+1, J ) = H( K+1, J ) - REFSUM*T1
H( K+2, J ) = H( K+2, J ) - REFSUM*T2
H( K+3, J ) = H( K+3, J ) - REFSUM*T3
90 CONTINUE
100 CONTINUE
*
@ -712,14 +718,15 @@
I2 = MAX( 1, KTOP-INCOL )
I2 = MAX( I2, KMS-(KRCOL-INCOL)+1 )
I4 = MIN( KDU, KRCOL + 2*( MBOT-1 ) - INCOL + 5 )
T1 = V( 1, M )
T2 = T1*CONJG( V( 2, M ) )
T3 = T1*CONJG( V( 3, M ) )
DO 110 J = I2, I4
REFSUM = V( 1, M )*( U( J, KMS+1 )+V( 2, M )*
$ U( J, KMS+2 )+V( 3, M )*U( J, KMS+3 ) )
U( J, KMS+1 ) = U( J, KMS+1 ) - REFSUM
U( J, KMS+2 ) = U( J, KMS+2 ) -
$ REFSUM*CONJG( V( 2, M ) )
U( J, KMS+3 ) = U( J, KMS+3 ) -
$ REFSUM*CONJG( V( 3, M ) )
REFSUM = U( J, KMS+1 ) + V( 2, M )*U( J, KMS+2 )
$ + V( 3, M )*U( J, KMS+3 )
U( J, KMS+1 ) = U( J, KMS+1 ) - REFSUM*T1
U( J, KMS+2 ) = U( J, KMS+2 ) - REFSUM*T2
U( J, KMS+3 ) = U( J, KMS+3 ) - REFSUM*T3
110 CONTINUE
120 CONTINUE
ELSE IF( WANTZ ) THEN
@ -730,14 +737,15 @@
*
DO 140 M = MBOT, MTOP, -1
K = KRCOL + 2*( M-1 )
T1 = V( 1, M )
T2 = T1*CONJG( V( 2, M ) )
T3 = T1*CONJG( V( 3, M ) )
DO 130 J = ILOZ, IHIZ
REFSUM = V( 1, M )*( Z( J, K+1 )+V( 2, M )*
$ Z( J, K+2 )+V( 3, M )*Z( J, K+3 ) )
Z( J, K+1 ) = Z( J, K+1 ) - REFSUM
Z( J, K+2 ) = Z( J, K+2 ) -
$ REFSUM*CONJG( V( 2, M ) )
Z( J, K+3 ) = Z( J, K+3 ) -
$ REFSUM*CONJG( V( 3, M ) )
REFSUM = Z( J, K+1 ) + V( 2, M )*Z( J, K+2 )
$ + V( 3, M )*Z( J, K+3 )
Z( J, K+1 ) = Z( J, K+1 ) - REFSUM*T1
Z( J, K+2 ) = Z( J, K+2 ) - REFSUM*T2
Z( J, K+3 ) = Z( J, K+3 ) - REFSUM*T3
130 CONTINUE
140 CONTINUE
END IF

16
lapack-netlib/SRC/claqz0.f
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@ -299,7 +299,7 @@
PARAMETER( ZERO = 0.0, ONE = 1.0, HALF = 0.5 )
* Local scalars
REAL :: SMLNUM, ULP, SAFMIN, SAFMAX, C1, TEMPR
REAL :: SMLNUM, ULP, SAFMIN, SAFMAX, C1, TEMPR, BNORM, BTOL
COMPLEX :: ESHIFT, S1, TEMP
INTEGER :: ISTART, ISTOP, IITER, MAXIT, ISTART2, K, LD, NSHIFTS,
$ NBLOCK, NW, NMIN, NIBBLE, N_UNDEFLATED, N_DEFLATED,
@ -312,7 +312,7 @@
* External Functions
EXTERNAL :: XERBLA, CHGEQZ, CLAQZ2, CLAQZ3, CLASET, SLABAD,
$ CLARTG, CROT
REAL, EXTERNAL :: SLAMCH
REAL, EXTERNAL :: SLAMCH, CLANHS
LOGICAL, EXTERNAL :: LSAME
INTEGER, EXTERNAL :: ILAENV
@ -466,6 +466,9 @@
ULP = SLAMCH( 'PRECISION' )
SMLNUM = SAFMIN*( REAL( N )/ULP )
BNORM = CLANHS( 'F', IHI-ILO+1, B( ILO, ILO ), LDB, RWORK )
BTOL = MAX( SAFMIN, ULP*BNORM )
ISTART = ILO
ISTOP = IHI
MAXIT = 30*( IHI-ILO+1 )
@ -528,15 +531,8 @@
* slow down the method when many infinite eigenvalues are present
K = ISTOP
DO WHILE ( K.GE.ISTART2 )
TEMPR = ZERO
IF( K .LT. ISTOP ) THEN
TEMPR = TEMPR+ABS( B( K, K+1 ) )
END IF
IF( K .GT. ISTART2 ) THEN
TEMPR = TEMPR+ABS( B( K-1, K ) )
END IF
IF( ABS( B( K, K ) ) .LT. MAX( SMLNUM, ULP*TEMPR ) ) THEN
IF( ABS( B( K, K ) ) .LT. BTOL ) THEN
* A diagonal element of B is negligable, move it
* to the top and deflate it

102
lapack-netlib/SRC/dlaqr5.f
View File

@ -286,8 +286,8 @@
* ..
* .. Local Scalars ..
DOUBLE PRECISION ALPHA, BETA, H11, H12, H21, H22, REFSUM,
$ SAFMAX, SAFMIN, SCL, SMLNUM, SWAP, TST1, TST2,
$ ULP
$ SAFMAX, SAFMIN, SCL, SMLNUM, SWAP, T1, T2,
$ T3, TST1, TST2, ULP
INTEGER I, I2, I4, INCOL, J, JBOT, JCOL, JLEN,
$ JROW, JTOP, K, K1, KDU, KMS, KRCOL,
$ M, M22, MBOT, MTOP, NBMPS, NDCOL,
@ -447,11 +447,12 @@
* ==== Perform update from right within
* . computational window. ====
*
T1 = V( 1, M22 )
T2 = T1*V( 2, M22 )
DO 30 J = JTOP, MIN( KBOT, K+3 )
REFSUM = V( 1, M22 )*( H( J, K+1 )+V( 2, M22 )*
$ H( J, K+2 ) )
H( J, K+1 ) = H( J, K+1 ) - REFSUM
H( J, K+2 ) = H( J, K+2 ) - REFSUM*V( 2, M22 )
REFSUM = H( J, K+1 ) + V( 2, M22 )*H( J, K+2 )
H( J, K+1 ) = H( J, K+1 ) - REFSUM*T1
H( J, K+2 ) = H( J, K+2 ) - REFSUM*T2
30 CONTINUE
*
* ==== Perform update from left within
@ -464,11 +465,12 @@
ELSE
JBOT = KBOT
END IF
T1 = V( 1, M22 )
T2 = T1*V( 2, M22 )
DO 40 J = K+1, JBOT
REFSUM = V( 1, M22 )*( H( K+1, J )+V( 2, M22 )*
$ H( K+2, J ) )
H( K+1, J ) = H( K+1, J ) - REFSUM
H( K+2, J ) = H( K+2, J ) - REFSUM*V( 2, M22 )
REFSUM = H( K+1, J ) + V( 2, M22 )*H( K+2, J )
H( K+1, J ) = H( K+1, J ) - REFSUM*T1
H( K+2, J ) = H( K+2, J ) - REFSUM*T2
40 CONTINUE
*
* ==== The following convergence test requires that
@ -522,18 +524,20 @@
*
IF( ACCUM ) THEN
KMS = K - INCOL
T1 = V( 1, M22 )
T2 = T1*V( 2, M22 )
DO 50 J = MAX( 1, KTOP-INCOL ), KDU
REFSUM = V( 1, M22 )*( U( J, KMS+1 )+
$ V( 2, M22 )*U( J, KMS+2 ) )
U( J, KMS+1 ) = U( J, KMS+1 ) - REFSUM
U( J, KMS+2 ) = U( J, KMS+2 ) - REFSUM*V( 2, M22 )
REFSUM = U( J, KMS+1 ) + V( 2, M22 )*U( J, KMS+2 )
U( J, KMS+1 ) = U( J, KMS+1 ) - REFSUM*T1
U( J, KMS+2 ) = U( J, KMS+2 ) - REFSUM*T2
50 CONTINUE
ELSE IF( WANTZ ) THEN
T1 = V( 1, M22 )
T2 = T1*V( 2, M22 )
DO 60 J = ILOZ, IHIZ
REFSUM = V( 1, M22 )*( Z( J, K+1 )+V( 2, M22 )*
$ Z( J, K+2 ) )
Z( J, K+1 ) = Z( J, K+1 ) - REFSUM
Z( J, K+2 ) = Z( J, K+2 ) - REFSUM*V( 2, M22 )
REFSUM = Z( J, K+1 )+V( 2, M22 )*Z( J, K+2 )
Z( J, K+1 ) = Z( J, K+1 ) - REFSUM*T1
Z( J, K+2 ) = Z( J, K+2 ) - REFSUM*T2
60 CONTINUE
END IF
END IF
@ -631,22 +635,25 @@
* . deflation check. We still delay most of the
* . updates from the left for efficiency. ====
*
T1 = V( 1, M )
T2 = T1*V( 2, M )
T3 = T1*V( 3, M )
DO 70 J = JTOP, MIN( KBOT, K+3 )
REFSUM = V( 1, M )*( H( J, K+1 )+V( 2, M )*
$ H( J, K+2 )+V( 3, M )*H( J, K+3 ) )
H( J, K+1 ) = H( J, K+1 ) - REFSUM
H( J, K+2 ) = H( J, K+2 ) - REFSUM*V( 2, M )
H( J, K+3 ) = H( J, K+3 ) - REFSUM*V( 3, M )
REFSUM = H( J, K+1 ) + V( 2, M )*H( J, K+2 )
$ + V( 3, M )*H( J, K+3 )
H( J, K+1 ) = H( J, K+1 ) - REFSUM*T1
H( J, K+2 ) = H( J, K+2 ) - REFSUM*T2
H( J, K+3 ) = H( J, K+3 ) - REFSUM*T3
70 CONTINUE
*
* ==== Perform update from left for subsequent
* . column. ====
*
REFSUM = V( 1, M )*( H( K+1, K+1 )+V( 2, M )*
$ H( K+2, K+1 )+V( 3, M )*H( K+3, K+1 ) )
H( K+1, K+1 ) = H( K+1, K+1 ) - REFSUM
H( K+2, K+1 ) = H( K+2, K+1 ) - REFSUM*V( 2, M )
H( K+3, K+1 ) = H( K+3, K+1 ) - REFSUM*V( 3, M )
REFSUM = H( K+1, K+1 ) + V( 2, M )*H( K+2, K+1 )
$ + V( 3, M )*H( K+3, K+1 )
H( K+1, K+1 ) = H( K+1, K+1 ) - REFSUM*T1
H( K+2, K+1 ) = H( K+2, K+1 ) - REFSUM*T2
H( K+3, K+1 ) = H( K+3, K+1 ) - REFSUM*T3
*
* ==== The following convergence test requires that
* . the tradition small-compared-to-nearby-diagonals
@ -706,12 +713,15 @@
*
DO 100 M = MBOT, MTOP, -1
K = KRCOL + 2*( M-1 )
T1 = V( 1, M )
T2 = T1*V( 2, M )
T3 = T1*V( 3, M )
DO 90 J = MAX( KTOP, KRCOL + 2*M ), JBOT
REFSUM = V( 1, M )*( H( K+1, J )+V( 2, M )*
$ H( K+2, J )+V( 3, M )*H( K+3, J ) )
H( K+1, J ) = H( K+1, J ) - REFSUM
H( K+2, J ) = H( K+2, J ) - REFSUM*V( 2, M )
H( K+3, J ) = H( K+3, J ) - REFSUM*V( 3, M )
REFSUM = H( K+1, J ) + V( 2, M )*H( K+2, J )
$ + V( 3, M )*H( K+3, J )
H( K+1, J ) = H( K+1, J ) - REFSUM*T1
H( K+2, J ) = H( K+2, J ) - REFSUM*T2
H( K+3, J ) = H( K+3, J ) - REFSUM*T3
90 CONTINUE
100 CONTINUE
*
@ -729,12 +739,15 @@
I2 = MAX( 1, KTOP-INCOL )
I2 = MAX( I2, KMS-(KRCOL-INCOL)+1 )
I4 = MIN( KDU, KRCOL + 2*( MBOT-1 ) - INCOL + 5 )
T1 = V( 1, M )
T2 = T1*V( 2, M )
T3 = T1*V( 3, M )
DO 110 J = I2, I4
REFSUM = V( 1, M )*( U( J, KMS+1 )+V( 2, M )*
$ U( J, KMS+2 )+V( 3, M )*U( J, KMS+3 ) )
U( J, KMS+1 ) = U( J, KMS+1 ) - REFSUM
U( J, KMS+2 ) = U( J, KMS+2 ) - REFSUM*V( 2, M )
U( J, KMS+3 ) = U( J, KMS+3 ) - REFSUM*V( 3, M )
REFSUM = U( J, KMS+1 ) + V( 2, M )*U( J, KMS+2 )
$ + V( 3, M )*U( J, KMS+3 )
U( J, KMS+1 ) = U( J, KMS+1 ) - REFSUM*T1
U( J, KMS+2 ) = U( J, KMS+2 ) - REFSUM*T2
U( J, KMS+3 ) = U( J, KMS+3 ) - REFSUM*T3
110 CONTINUE
120 CONTINUE
ELSE IF( WANTZ ) THEN
@ -745,12 +758,15 @@
*
DO 140 M = MBOT, MTOP, -1
K = KRCOL + 2*( M-1 )
T1 = V( 1, M )
T2 = T1*V( 2, M )
T3 = T1*V( 3, M )
DO 130 J = ILOZ, IHIZ
REFSUM = V( 1, M )*( Z( J, K+1 )+V( 2, M )*
$ Z( J, K+2 )+V( 3, M )*Z( J, K+3 ) )
Z( J, K+1 ) = Z( J, K+1 ) - REFSUM
Z( J, K+2 ) = Z( J, K+2 ) - REFSUM*V( 2, M )
Z( J, K+3 ) = Z( J, K+3 ) - REFSUM*V( 3, M )
REFSUM = Z( J, K+1 ) + V( 2, M )*Z( J, K+2 )
$ + V( 3, M )*Z( J, K+3 )
Z( J, K+1 ) = Z( J, K+1 ) - REFSUM*T1
Z( J, K+2 ) = Z( J, K+2 ) - REFSUM*T2
Z( J, K+3 ) = Z( J, K+3 ) - REFSUM*T3
130 CONTINUE
140 CONTINUE
END IF

16
lapack-netlib/SRC/dlaqz0.f
View File

@ -322,7 +322,7 @@
* Local scalars
DOUBLE PRECISION :: SMLNUM, ULP, ESHIFT, SAFMIN, SAFMAX, C1, S1,
$ TEMP, SWAP
$ TEMP, SWAP, BNORM, BTOL
INTEGER :: ISTART, ISTOP, IITER, MAXIT, ISTART2, K, LD, NSHIFTS,
$ NBLOCK, NW, NMIN, NIBBLE, N_UNDEFLATED, N_DEFLATED,
$ NS, SWEEP_INFO, SHIFTPOS, LWORKREQ, K2, ISTARTM,
@ -334,7 +334,7 @@
* External Functions
EXTERNAL :: XERBLA, DHGEQZ, DLASET, DLAQZ3, DLAQZ4, DLABAD,
$ DLARTG, DROT
DOUBLE PRECISION, EXTERNAL :: DLAMCH
DOUBLE PRECISION, EXTERNAL :: DLAMCH, DLANHS
LOGICAL, EXTERNAL :: LSAME
INTEGER, EXTERNAL :: ILAENV
@ -486,6 +486,9 @@
ULP = DLAMCH( 'PRECISION' )
SMLNUM = SAFMIN*( DBLE( N )/ULP )
BNORM = DLANHS( 'F', IHI-ILO+1, B( ILO, ILO ), LDB, WORK )
BTOL = MAX( SAFMIN, ULP*BNORM )
ISTART = ILO
ISTOP = IHI
MAXIT = 3*( IHI-ILO+1 )
@ -562,15 +565,8 @@
* slow down the method when many infinite eigenvalues are present
K = ISTOP
DO WHILE ( K.GE.ISTART2 )
TEMP = ZERO
IF( K .LT. ISTOP ) THEN
TEMP = TEMP+ABS( B( K, K+1 ) )
END IF
IF( K .GT. ISTART2 ) THEN
TEMP = TEMP+ABS( B( K-1, K ) )
END IF
IF( ABS( B( K, K ) ) .LT. MAX( SMLNUM, ULP*TEMP ) ) THEN
IF( ABS( B( K, K ) ) .LT. BTOL ) THEN
* A diagonal element of B is negligable, move it
* to the top and deflate it

102
lapack-netlib/SRC/slaqr5.f
View File

@ -286,8 +286,8 @@
* ..
* .. Local Scalars ..
REAL ALPHA, BETA, H11, H12, H21, H22, REFSUM,
$ SAFMAX, SAFMIN, SCL, SMLNUM, SWAP, TST1, TST2,
$ ULP
$ SAFMAX, SAFMIN, SCL, SMLNUM, SWAP, T1, T2,
$ T3, TST1, TST2, ULP
INTEGER I, I2, I4, INCOL, J, JBOT, JCOL, JLEN,
$ JROW, JTOP, K, K1, KDU, KMS, KRCOL,
$ M, M22, MBOT, MTOP, NBMPS, NDCOL,
@ -447,11 +447,12 @@
* ==== Perform update from right within
* . computational window. ====
*
T1 = V( 1, M22 )
T2 = T1*V( 2, M22 )
DO 30 J = JTOP, MIN( KBOT, K+3 )
REFSUM = V( 1, M22 )*( H( J, K+1 )+V( 2, M22 )*
$ H( J, K+2 ) )
H( J, K+1 ) = H( J, K+1 ) - REFSUM
H( J, K+2 ) = H( J, K+2 ) - REFSUM*V( 2, M22 )
REFSUM = H( J, K+1 ) + V( 2, M22 )*H( J, K+2 )
H( J, K+1 ) = H( J, K+1 ) - REFSUM*T1
H( J, K+2 ) = H( J, K+2 ) - REFSUM*T2
30 CONTINUE
*
* ==== Perform update from left within
@ -464,11 +465,12 @@
ELSE
JBOT = KBOT
END IF
T1 = V( 1, M22 )
T2 = T1*V( 2, M22 )
DO 40 J = K+1, JBOT
REFSUM = V( 1, M22 )*( H( K+1, J )+V( 2, M22 )*
$ H( K+2, J ) )
H( K+1, J ) = H( K+1, J ) - REFSUM
H( K+2, J ) = H( K+2, J ) - REFSUM*V( 2, M22 )
REFSUM = H( K+1, J ) + V( 2, M22 )*H( K+2, J )
H( K+1, J ) = H( K+1, J ) - REFSUM*T1
H( K+2, J ) = H( K+2, J ) - REFSUM*T2
40 CONTINUE
*
* ==== The following convergence test requires that
@ -522,18 +524,20 @@
*
IF( ACCUM ) THEN
KMS = K - INCOL
T1 = V( 1, M22 )
T2 = T1*V( 2, M22 )
DO 50 J = MAX( 1, KTOP-INCOL ), KDU
REFSUM = V( 1, M22 )*( U( J, KMS+1 )+
$ V( 2, M22 )*U( J, KMS+2 ) )
U( J, KMS+1 ) = U( J, KMS+1 ) - REFSUM
U( J, KMS+2 ) = U( J, KMS+2 ) - REFSUM*V( 2, M22 )
REFSUM = U( J, KMS+1 ) + V( 2, M22 )*U( J, KMS+2 )
U( J, KMS+1 ) = U( J, KMS+1 ) - REFSUM*T1
U( J, KMS+2 ) = U( J, KMS+2 ) - REFSUM*T2
50 CONTINUE
ELSE IF( WANTZ ) THEN
T1 = V( 1, M22 )
T2 = T1*V( 2, M22 )
DO 60 J = ILOZ, IHIZ
REFSUM = V( 1, M22 )*( Z( J, K+1 )+V( 2, M22 )*
$ Z( J, K+2 ) )
Z( J, K+1 ) = Z( J, K+1 ) - REFSUM
Z( J, K+2 ) = Z( J, K+2 ) - REFSUM*V( 2, M22 )
REFSUM = Z( J, K+1 )+V( 2, M22 )*Z( J, K+2 )
Z( J, K+1 ) = Z( J, K+1 ) - REFSUM*T1
Z( J, K+2 ) = Z( J, K+2 ) - REFSUM*T2
60 CONTINUE
END IF
END IF
@ -631,22 +635,25 @@
* . deflation check. We still delay most of the
* . updates from the left for efficiency. ====
*
T1 = V( 1, M )
T2 = T1*V( 2, M )
T3 = T1*V( 3, M )
DO 70 J = JTOP, MIN( KBOT, K+3 )
REFSUM = V( 1, M )*( H( J, K+1 )+V( 2, M )*
$ H( J, K+2 )+V( 3, M )*H( J, K+3 ) )
H( J, K+1 ) = H( J, K+1 ) - REFSUM
H( J, K+2 ) = H( J, K+2 ) - REFSUM*V( 2, M )
H( J, K+3 ) = H( J, K+3 ) - REFSUM*V( 3, M )
REFSUM = H( J, K+1 ) + V( 2, M )*H( J, K+2 )
$ + V( 3, M )*H( J, K+3 )
H( J, K+1 ) = H( J, K+1 ) - REFSUM*T1
H( J, K+2 ) = H( J, K+2 ) - REFSUM*T2
H( J, K+3 ) = H( J, K+3 ) - REFSUM*T3
70 CONTINUE
*
* ==== Perform update from left for subsequent
* . column. ====
*
REFSUM = V( 1, M )*( H( K+1, K+1 )+V( 2, M )*
$ H( K+2, K+1 )+V( 3, M )*H( K+3, K+1 ) )
H( K+1, K+1 ) = H( K+1, K+1 ) - REFSUM
H( K+2, K+1 ) = H( K+2, K+1 ) - REFSUM*V( 2, M )
H( K+3, K+1 ) = H( K+3, K+1 ) - REFSUM*V( 3, M )
REFSUM = H( K+1, K+1 ) + V( 2, M )*H( K+2, K+1 )
$ + V( 3, M )*H( K+3, K+1 )
H( K+1, K+1 ) = H( K+1, K+1 ) - REFSUM*T1
H( K+2, K+1 ) = H( K+2, K+1 ) - REFSUM*T2
H( K+3, K+1 ) = H( K+3, K+1 ) - REFSUM*T3
*
* ==== The following convergence test requires that
* . the tradition small-compared-to-nearby-diagonals
@ -706,12 +713,15 @@
*
DO 100 M = MBOT, MTOP, -1
K = KRCOL + 2*( M-1 )
T1 = V( 1, M )
T2 = T1*V( 2, M )
T3 = T1*V( 3, M )
DO 90 J = MAX( KTOP, KRCOL + 2*M ), JBOT
REFSUM = V( 1, M )*( H( K+1, J )+V( 2, M )*
$ H( K+2, J )+V( 3, M )*H( K+3, J ) )
H( K+1, J ) = H( K+1, J ) - REFSUM
H( K+2, J ) = H( K+2, J ) - REFSUM*V( 2, M )
H( K+3, J ) = H( K+3, J ) - REFSUM*V( 3, M )
REFSUM = H( K+1, J ) + V( 2, M )*H( K+2, J )
$ + V( 3, M )*H( K+3, J )
H( K+1, J ) = H( K+1, J ) - REFSUM*T1
H( K+2, J ) = H( K+2, J ) - REFSUM*T2
H( K+3, J ) = H( K+3, J ) - REFSUM*T3
90 CONTINUE
100 CONTINUE
*
@ -729,12 +739,15 @@
I2 = MAX( 1, KTOP-INCOL )
I2 = MAX( I2, KMS-(KRCOL-INCOL)+1 )
I4 = MIN( KDU, KRCOL + 2*( MBOT-1 ) - INCOL + 5 )
T1 = V( 1, M )
T2 = T1*V( 2, M )
T3 = T1*V( 3, M )
DO 110 J = I2, I4
REFSUM = V( 1, M )*( U( J, KMS+1 )+V( 2, M )*
$ U( J, KMS+2 )+V( 3, M )*U( J, KMS+3 ) )
U( J, KMS+1 ) = U( J, KMS+1 ) - REFSUM
U( J, KMS+2 ) = U( J, KMS+2 ) - REFSUM*V( 2, M )
U( J, KMS+3 ) = U( J, KMS+3 ) - REFSUM*V( 3, M )
REFSUM = U( J, KMS+1 ) + V( 2, M )*U( J, KMS+2 )
$ + V( 3, M )*U( J, KMS+3 )
U( J, KMS+1 ) = U( J, KMS+1 ) - REFSUM*T1
U( J, KMS+2 ) = U( J, KMS+2 ) - REFSUM*T2
U( J, KMS+3 ) = U( J, KMS+3 ) - REFSUM*T3
110 CONTINUE
120 CONTINUE
ELSE IF( WANTZ ) THEN
@ -745,12 +758,15 @@
*
DO 140 M = MBOT, MTOP, -1
K = KRCOL + 2*( M-1 )
T1 = V( 1, M )
T2 = T1*V( 2, M )
T3 = T1*V( 3, M )
DO 130 J = ILOZ, IHIZ
REFSUM = V( 1, M )*( Z( J, K+1 )+V( 2, M )*
$ Z( J, K+2 )+V( 3, M )*Z( J, K+3 ) )
Z( J, K+1 ) = Z( J, K+1 ) - REFSUM
Z( J, K+2 ) = Z( J, K+2 ) - REFSUM*V( 2, M )
Z( J, K+3 ) = Z( J, K+3 ) - REFSUM*V( 3, M )
REFSUM = Z( J, K+1 ) + V( 2, M )*Z( J, K+2 )
$ + V( 3, M )*Z( J, K+3 )
Z( J, K+1 ) = Z( J, K+1 ) - REFSUM*T1
Z( J, K+2 ) = Z( J, K+2 ) - REFSUM*T2
Z( J, K+3 ) = Z( J, K+3 ) - REFSUM*T3
130 CONTINUE
140 CONTINUE
END IF

17
lapack-netlib/SRC/slaqz0.f
View File

@ -318,7 +318,8 @@
PARAMETER( ZERO = 0.0, ONE = 1.0, HALF = 0.5 )
* Local scalars
REAL :: SMLNUM, ULP, ESHIFT, SAFMIN, SAFMAX, C1, S1, TEMP, SWAP
REAL :: SMLNUM, ULP, ESHIFT, SAFMIN, SAFMAX, C1, S1, TEMP, SWAP,
$ BNORM, BTOL
INTEGER :: ISTART, ISTOP, IITER, MAXIT, ISTART2, K, LD, NSHIFTS,
$ NBLOCK, NW, NMIN, NIBBLE, N_UNDEFLATED, N_DEFLATED,
$ NS, SWEEP_INFO, SHIFTPOS, LWORKREQ, K2, ISTARTM,
@ -330,7 +331,7 @@
* External Functions
EXTERNAL :: XERBLA, SHGEQZ, SLAQZ3, SLAQZ4, SLASET, SLABAD,
$ SLARTG, SROT
REAL, EXTERNAL :: SLAMCH
REAL, EXTERNAL :: SLAMCH, SLANHS
LOGICAL, EXTERNAL :: LSAME
INTEGER, EXTERNAL :: ILAENV
@ -482,6 +483,9 @@
ULP = SLAMCH( 'PRECISION' )
SMLNUM = SAFMIN*( REAL( N )/ULP )
BNORM = SLANHS( 'F', IHI-ILO+1, B( ILO, ILO ), LDB, WORK )
BTOL = MAX( SAFMIN, ULP*BNORM )
ISTART = ILO
ISTOP = IHI
MAXIT = 3*( IHI-ILO+1 )
@ -558,15 +562,8 @@
* slow down the method when many infinite eigenvalues are present
K = ISTOP
DO WHILE ( K.GE.ISTART2 )
TEMP = ZERO
IF( K .LT. ISTOP ) THEN
TEMP = TEMP+ABS( B( K, K+1 ) )
END IF
IF( K .GT. ISTART2 ) THEN
TEMP = TEMP+ABS( B( K-1, K ) )
END IF
IF( ABS( B( K, K ) ) .LT. MAX( SMLNUM, ULP*TEMP ) ) THEN
IF( ABS( B( K, K ) ) .LT. BTOL ) THEN
* A diagonal element of B is negligable, move it
* to the top and deflate it

97
lapack-netlib/SRC/zlaqr5.f
View File

@ -279,7 +279,7 @@
PARAMETER ( RZERO = 0.0d0, RONE = 1.0d0 )
* ..
* .. Local Scalars ..
COMPLEX*16 ALPHA, BETA, CDUM, REFSUM
COMPLEX*16 ALPHA, BETA, CDUM, REFSUM, T1, T2, T3
DOUBLE PRECISION H11, H12, H21, H22, SAFMAX, SAFMIN, SCL,
$ SMLNUM, TST1, TST2, ULP
INTEGER I2, I4, INCOL, J, JBOT, JCOL, JLEN,
@ -424,12 +424,12 @@
* ==== Perform update from right within
* . computational window. ====
*
T1 = V( 1, M22 )
T2 = T1*DCONJG( V( 2, M22 ) )
DO 30 J = JTOP, MIN( KBOT, K+3 )
REFSUM = V( 1, M22 )*( H( J, K+1 )+V( 2, M22 )*
$ H( J, K+2 ) )
H( J, K+1 ) = H( J, K+1 ) - REFSUM
H( J, K+2 ) = H( J, K+2 ) -
$ REFSUM*DCONJG( V( 2, M22 ) )
REFSUM = H( J, K+1 ) + V( 2, M22 )*H( J, K+2 )
H( J, K+1 ) = H( J, K+1 ) - REFSUM*T1
H( J, K+2 ) = H( J, K+2 ) - REFSUM*T2
30 CONTINUE
*
* ==== Perform update from left within
@ -442,12 +442,13 @@
ELSE
JBOT = KBOT
END IF
T1 = DCONJG( V( 1, M22 ) )
T2 = T1*V( 2, M22 )
DO 40 J = K+1, JBOT
REFSUM = DCONJG( V( 1, M22 ) )*
$ ( H( K+1, J )+DCONJG( V( 2, M22 ) )*
$ H( K+2, J ) )
H( K+1, J ) = H( K+1, J ) - REFSUM
H( K+2, J ) = H( K+2, J ) - REFSUM*V( 2, M22 )
REFSUM = H( K+1, J ) +
$ DCONJG( V( 2, M22 ) )*H( K+2, J )
H( K+1, J ) = H( K+1, J ) - REFSUM*T1
H( K+2, J ) = H( K+2, J ) - REFSUM*T2
40 CONTINUE
*
* ==== The following convergence test requires that
@ -610,25 +611,29 @@
* . deflation check. We still delay most of the
* . updates from the left for efficiency. ====
*
T1 = V( 1, M )
T2 = T1*DCONJG( V( 2, M ) )
T3 = T1*DCONJG( V( 3, M ) )
DO 70 J = JTOP, MIN( KBOT, K+3 )
REFSUM = V( 1, M )*( H( J, K+1 )+V( 2, M )*
$ H( J, K+2 )+V( 3, M )*H( J, K+3 ) )
H( J, K+1 ) = H( J, K+1 ) - REFSUM
H( J, K+2 ) = H( J, K+2 ) -
$ REFSUM*DCONJG( V( 2, M ) )
H( J, K+3 ) = H( J, K+3 ) -
$ REFSUM*DCONJG( V( 3, M ) )
REFSUM = H( J, K+1 ) + V( 2, M )*H( J, K+2 )
$ + V( 3, M )*H( J, K+3 )
H( J, K+1 ) = H( J, K+1 ) - REFSUM*T1
H( J, K+2 ) = H( J, K+2 ) - REFSUM*T2
H( J, K+3 ) = H( J, K+3 ) - REFSUM*T3
70 CONTINUE
*
* ==== Perform update from left for subsequent
* . column. ====
*
REFSUM = DCONJG( V( 1, M ) )*( H( K+1, K+1 )
$ +DCONJG( V( 2, M ) )*H( K+2, K+1 )
$ +DCONJG( V( 3, M ) )*H( K+3, K+1 ) )
H( K+1, K+1 ) = H( K+1, K+1 ) - REFSUM
H( K+2, K+1 ) = H( K+2, K+1 ) - REFSUM*V( 2, M )
H( K+3, K+1 ) = H( K+3, K+1 ) - REFSUM*V( 3, M )
T1 = DCONJG( V( 1, M ) )
T2 = T1*V( 2, M )
T3 = T1*V( 3, M )
REFSUM = H( K+1, K+1 )
$ + DCONJG( V( 2, M ) )*H( K+2, K+1 )
$ + DCONJG( V( 3, M ) )*H( K+3, K+1 )
H( K+1, K+1 ) = H( K+1, K+1 ) - REFSUM*T1
H( K+2, K+1 ) = H( K+2, K+1 ) - REFSUM*T2
H( K+3, K+1 ) = H( K+3, K+1 ) - REFSUM*T3
*
* ==== The following convergence test requires that
* . the tradition small-compared-to-nearby-diagonals
@ -688,13 +693,15 @@
*
DO 100 M = MBOT, MTOP, -1
K = KRCOL + 2*( M-1 )
T1 = DCONJG( V( 1, M ) )
T2 = T1*V( 2, M )
T3 = T1*V( 3, M )
DO 90 J = MAX( KTOP, KRCOL + 2*M ), JBOT
REFSUM = DCONJG( V( 1, M ) )*
$ ( H( K+1, J )+DCONJG( V( 2, M ) )*
$ H( K+2, J )+DCONJG( V( 3, M ) )*H( K+3, J ) )
H( K+1, J ) = H( K+1, J ) - REFSUM
H( K+2, J ) = H( K+2, J ) - REFSUM*V( 2, M )
H( K+3, J ) = H( K+3, J ) - REFSUM*V( 3, M )
REFSUM = H( K+1, J ) + DCONJG( V( 2, M ) )*H( K+2, J )
$ + DCONJG( V( 3, M ) )*H( K+3, J )
H( K+1, J ) = H( K+1, J ) - REFSUM*T1
H( K+2, J ) = H( K+2, J ) - REFSUM*T2
H( K+3, J ) = H( K+3, J ) - REFSUM*T3
90 CONTINUE
100 CONTINUE
*
@ -712,14 +719,15 @@
I2 = MAX( 1, KTOP-INCOL )
I2 = MAX( I2, KMS-(KRCOL-INCOL)+1 )
I4 = MIN( KDU, KRCOL + 2*( MBOT-1 ) - INCOL + 5 )
T1 = V( 1, M )
T2 = T1*DCONJG( V( 2, M ) )
T3 = T1*DCONJG( V( 3, M ) )
DO 110 J = I2, I4
REFSUM = V( 1, M )*( U( J, KMS+1 )+V( 2, M )*
$ U( J, KMS+2 )+V( 3, M )*U( J, KMS+3 ) )
U( J, KMS+1 ) = U( J, KMS+1 ) - REFSUM
U( J, KMS+2 ) = U( J, KMS+2 ) -
$ REFSUM*DCONJG( V( 2, M ) )
U( J, KMS+3 ) = U( J, KMS+3 ) -
$ REFSUM*DCONJG( V( 3, M ) )
REFSUM = U( J, KMS+1 ) + V( 2, M )*U( J, KMS+2 )
$ + V( 3, M )*U( J, KMS+3 )
U( J, KMS+1 ) = U( J, KMS+1 ) - REFSUM*T1
U( J, KMS+2 ) = U( J, KMS+2 ) - REFSUM*T2
U( J, KMS+3 ) = U( J, KMS+3 ) - REFSUM*T3
110 CONTINUE
120 CONTINUE
ELSE IF( WANTZ ) THEN
@ -730,14 +738,15 @@
*
DO 140 M = MBOT, MTOP, -1
K = KRCOL + 2*( M-1 )
T1 = V( 1, M )
T2 = T1*DCONJG( V( 2, M ) )
T3 = T1*DCONJG( V( 3, M ) )
DO 130 J = ILOZ, IHIZ
REFSUM = V( 1, M )*( Z( J, K+1 )+V( 2, M )*
$ Z( J, K+2 )+V( 3, M )*Z( J, K+3 ) )
Z( J, K+1 ) = Z( J, K+1 ) - REFSUM
Z( J, K+2 ) = Z( J, K+2 ) -
$ REFSUM*DCONJG( V( 2, M ) )
Z( J, K+3 ) = Z( J, K+3 ) -
$ REFSUM*DCONJG( V( 3, M ) )
REFSUM = Z( J, K+1 ) + V( 2, M )*Z( J, K+2 )
$ + V( 3, M )*Z( J, K+3 )
Z( J, K+1 ) = Z( J, K+1 ) - REFSUM*T1
Z( J, K+2 ) = Z( J, K+2 ) - REFSUM*T2
Z( J, K+3 ) = Z( J, K+3 ) - REFSUM*T3
130 CONTINUE
140 CONTINUE
END IF

17
lapack-netlib/SRC/zlaqz0.f
View File

@ -300,7 +300,8 @@
PARAMETER( ZERO = 0.0D0, ONE = 1.0D0, HALF = 0.5D0 )
* Local scalars
DOUBLE PRECISION :: SMLNUM, ULP, SAFMIN, SAFMAX, C1, TEMPR
DOUBLE PRECISION :: SMLNUM, ULP, SAFMIN, SAFMAX, C1, TEMPR,
$ BNORM, BTOL
COMPLEX*16 :: ESHIFT, S1, TEMP
INTEGER :: ISTART, ISTOP, IITER, MAXIT, ISTART2, K, LD, NSHIFTS,
$ NBLOCK, NW, NMIN, NIBBLE, N_UNDEFLATED, N_DEFLATED,
@ -313,7 +314,7 @@
* External Functions
EXTERNAL :: XERBLA, ZHGEQZ, ZLAQZ2, ZLAQZ3, ZLASET, DLABAD,
$ ZLARTG, ZROT
DOUBLE PRECISION, EXTERNAL :: DLAMCH
DOUBLE PRECISION, EXTERNAL :: DLAMCH, ZLANHS
LOGICAL, EXTERNAL :: LSAME
INTEGER, EXTERNAL :: ILAENV
@ -467,6 +468,9 @@
ULP = DLAMCH( 'PRECISION' )
SMLNUM = SAFMIN*( DBLE( N )/ULP )
BNORM = ZLANHS( 'F', IHI-ILO+1, B( ILO, ILO ), LDB, RWORK )
BTOL = MAX( SAFMIN, ULP*BNORM )
ISTART = ILO
ISTOP = IHI
MAXIT = 30*( IHI-ILO+1 )
@ -529,15 +533,8 @@
* slow down the method when many infinite eigenvalues are present
K = ISTOP
DO WHILE ( K.GE.ISTART2 )
TEMPR = ZERO
IF( K .LT. ISTOP ) THEN
TEMPR = TEMPR+ABS( B( K, K+1 ) )
END IF
IF( K .GT. ISTART2 ) THEN
TEMPR = TEMPR+ABS( B( K-1, K ) )
END IF
IF( ABS( B( K, K ) ) .LT. MAX( SMLNUM, ULP*TEMPR ) ) THEN
IF( ABS( B( K, K ) ) .LT. BTOL ) THEN
* A diagonal element of B is negligable, move it
* to the top and deflate it