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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)
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Martin Kroeker 2022-11-20 22:40:52 +01:00 committed by GitHub
parent f63c93274c c6816bb576
commit 1d5a3aff0d
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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 ) PARAMETER ( RZERO = 0.0e0, RONE = 1.0e0 )
* .. * ..
* .. Local Scalars .. * .. Local Scalars ..
COMPLEX ALPHA, BETA, CDUM, REFSUM COMPLEX ALPHA, BETA, CDUM, REFSUM, T1, T2, T3
REAL H11, H12, H21, H22, SAFMAX, SAFMIN, SCL, REAL H11, H12, H21, H22, SAFMAX, SAFMIN, SCL,
$ SMLNUM, TST1, TST2, ULP $ SMLNUM, TST1, TST2, ULP
INTEGER I2, I4, INCOL, J, JBOT, JCOL, JLEN, INTEGER I2, I4, INCOL, J, JBOT, JCOL, JLEN,
@ -424,12 +424,12 @@
* ==== Perform update from right within * ==== Perform update from right within
* . computational window. ==== * . computational window. ====
* *
T1 = V( 1, M22 )
T2 = T1*CONJG( V( 2, M22 ) )
DO 30 J = JTOP, MIN( KBOT, K+3 ) DO 30 J = JTOP, MIN( KBOT, K+3 )
REFSUM = V( 1, M22 )*( H( J, K+1 )+V( 2, M22 )* REFSUM = H( J, K+1 ) + V( 2, M22 )*H( J, K+2 )
$ H( J, K+2 ) ) H( J, K+1 ) = H( J, K+1 ) - REFSUM*T1
H( J, K+1 ) = H( J, K+1 ) - REFSUM H( J, K+2 ) = H( J, K+2 ) - REFSUM*T2
H( J, K+2 ) = H( J, K+2 ) -
$ REFSUM*CONJG( V( 2, M22 ) )
30 CONTINUE 30 CONTINUE
* *
* ==== Perform update from left within * ==== Perform update from left within
@ -442,12 +442,13 @@
ELSE ELSE
JBOT = KBOT JBOT = KBOT
END IF END IF
T1 = CONJG( V( 1, M22 ) )
T2 = T1*V( 2, M22 )
DO 40 J = K+1, JBOT DO 40 J = K+1, JBOT
REFSUM = CONJG( V( 1, M22 ) )* REFSUM = H( K+1, J ) +
$ ( H( K+1, J )+CONJG( V( 2, M22 ) )* $ CONJG( V( 2, M22 ) )*H( K+2, J )
$ H( K+2, J ) ) H( K+1, J ) = H( K+1, J ) - REFSUM*T1
H( K+1, J ) = H( K+1, J ) - REFSUM H( K+2, J ) = H( K+2, J ) - REFSUM*T2
H( K+2, J ) = H( K+2, J ) - REFSUM*V( 2, M22 )
40 CONTINUE 40 CONTINUE
* *
* ==== The following convergence test requires that * ==== The following convergence test requires that
@ -610,25 +611,28 @@
* . deflation check. We still delay most of the * . deflation check. We still delay most of the
* . updates from the left for efficiency. ==== * . 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 ) DO 70 J = JTOP, MIN( KBOT, K+3 )
REFSUM = V( 1, M )*( H( J, K+1 )+V( 2, M )* REFSUM = H( J, K+1 ) + V( 2, M )*H( J, K+2 )
$ H( J, K+2 )+V( 3, M )*H( J, K+3 ) ) $ + V( 3, M )*H( J, K+3 )
H( J, K+1 ) = H( J, K+1 ) - REFSUM H( J, K+1 ) = H( J, K+1 ) - REFSUM*T1
H( J, K+2 ) = H( J, K+2 ) - H( J, K+2 ) = H( J, K+2 ) - REFSUM*T2
$ REFSUM*CONJG( V( 2, M ) ) H( J, K+3 ) = H( J, K+3 ) - REFSUM*T3
H( J, K+3 ) = H( J, K+3 ) -
$ REFSUM*CONJG( V( 3, M ) )
70 CONTINUE 70 CONTINUE
* *
* ==== Perform update from left for subsequent * ==== Perform update from left for subsequent
* . column. ==== * . column. ====
* *
REFSUM = CONJG( V( 1, M ) )*( H( K+1, K+1 ) T1 = CONJG( V( 1, M ) )
$ +CONJG( V( 2, M ) )*H( K+2, K+1 ) T2 = T1*V( 2, M )
$ +CONJG( V( 3, M ) )*H( K+3, K+1 ) ) T3 = T1*V( 3, M )
H( K+1, K+1 ) = H( K+1, K+1 ) - REFSUM REFSUM = H( K+1, K+1 ) + CONJG( V( 2, M ) )*H( K+2, K+1 )
H( K+2, K+1 ) = H( K+2, K+1 ) - REFSUM*V( 2, M ) $ + CONJG( V( 3, M ) )*H( K+3, K+1 )
H( K+3, K+1 ) = H( K+3, K+1 ) - REFSUM*V( 3, M ) 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 following convergence test requires that
* . the tradition small-compared-to-nearby-diagonals * . the tradition small-compared-to-nearby-diagonals
@ -688,13 +692,15 @@
* *
DO 100 M = MBOT, MTOP, -1 DO 100 M = MBOT, MTOP, -1
K = KRCOL + 2*( M-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 DO 90 J = MAX( KTOP, KRCOL + 2*M ), JBOT
REFSUM = CONJG( V( 1, M ) )* REFSUM = H( K+1, J ) + CONJG( V( 2, M ) )*
$ ( H( K+1, J )+CONJG( V( 2, M ) )* $ H( K+2, J ) + CONJG( V( 3, M ) )*H( K+3, J )
$ H( K+2, J )+CONJG( V( 3, M ) )*H( K+3, J ) ) H( K+1, J ) = H( K+1, J ) - REFSUM*T1
H( K+1, J ) = H( K+1, J ) - REFSUM H( K+2, J ) = H( K+2, J ) - REFSUM*T2
H( K+2, J ) = H( K+2, J ) - REFSUM*V( 2, M ) H( K+3, J ) = H( K+3, J ) - REFSUM*T3
H( K+3, J ) = H( K+3, J ) - REFSUM*V( 3, M )
90 CONTINUE 90 CONTINUE
100 CONTINUE 100 CONTINUE
* *
@ -712,14 +718,15 @@
I2 = MAX( 1, KTOP-INCOL ) I2 = MAX( 1, KTOP-INCOL )
I2 = MAX( I2, KMS-(KRCOL-INCOL)+1 ) I2 = MAX( I2, KMS-(KRCOL-INCOL)+1 )
I4 = MIN( KDU, KRCOL + 2*( MBOT-1 ) - INCOL + 5 ) 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 DO 110 J = I2, I4
REFSUM = V( 1, M )*( U( J, KMS+1 )+V( 2, M )* REFSUM = U( J, KMS+1 ) + V( 2, M )*U( J, KMS+2 )
$ U( J, KMS+2 )+V( 3, M )*U( J, KMS+3 ) ) $ + V( 3, M )*U( J, KMS+3 )
U( J, KMS+1 ) = U( J, KMS+1 ) - REFSUM U( J, KMS+1 ) = U( J, KMS+1 ) - REFSUM*T1
U( J, KMS+2 ) = U( J, KMS+2 ) - U( J, KMS+2 ) = U( J, KMS+2 ) - REFSUM*T2
$ REFSUM*CONJG( V( 2, M ) ) U( J, KMS+3 ) = U( J, KMS+3 ) - REFSUM*T3
U( J, KMS+3 ) = U( J, KMS+3 ) -
$ REFSUM*CONJG( V( 3, M ) )
110 CONTINUE 110 CONTINUE
120 CONTINUE 120 CONTINUE
ELSE IF( WANTZ ) THEN ELSE IF( WANTZ ) THEN
@ -730,14 +737,15 @@
* *
DO 140 M = MBOT, MTOP, -1 DO 140 M = MBOT, MTOP, -1
K = KRCOL + 2*( M-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 DO 130 J = ILOZ, IHIZ
REFSUM = V( 1, M )*( Z( J, K+1 )+V( 2, M )* REFSUM = Z( J, K+1 ) + V( 2, M )*Z( J, K+2 )
$ Z( J, K+2 )+V( 3, M )*Z( J, K+3 ) ) $ + V( 3, M )*Z( J, K+3 )
Z( J, K+1 ) = Z( J, K+1 ) - REFSUM Z( J, K+1 ) = Z( J, K+1 ) - REFSUM*T1
Z( J, K+2 ) = Z( J, K+2 ) - Z( J, K+2 ) = Z( J, K+2 ) - REFSUM*T2
$ REFSUM*CONJG( V( 2, M ) ) Z( J, K+3 ) = Z( J, K+3 ) - REFSUM*T3
Z( J, K+3 ) = Z( J, K+3 ) -
$ REFSUM*CONJG( V( 3, M ) )
130 CONTINUE 130 CONTINUE
140 CONTINUE 140 CONTINUE
END IF 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 ) PARAMETER( ZERO = 0.0, ONE = 1.0, HALF = 0.5 )
* Local scalars * Local scalars
REAL :: SMLNUM, ULP, SAFMIN, SAFMAX, C1, TEMPR REAL :: SMLNUM, ULP, SAFMIN, SAFMAX, C1, TEMPR, BNORM, BTOL
COMPLEX :: ESHIFT, S1, TEMP COMPLEX :: ESHIFT, S1, TEMP
INTEGER :: ISTART, ISTOP, IITER, MAXIT, ISTART2, K, LD, NSHIFTS, INTEGER :: ISTART, ISTOP, IITER, MAXIT, ISTART2, K, LD, NSHIFTS,
$ NBLOCK, NW, NMIN, NIBBLE, N_UNDEFLATED, N_DEFLATED, $ NBLOCK, NW, NMIN, NIBBLE, N_UNDEFLATED, N_DEFLATED,
@ -312,7 +312,7 @@
* External Functions * External Functions
EXTERNAL :: XERBLA, CHGEQZ, CLAQZ2, CLAQZ3, CLASET, SLABAD, EXTERNAL :: XERBLA, CHGEQZ, CLAQZ2, CLAQZ3, CLASET, SLABAD,
$ CLARTG, CROT $ CLARTG, CROT
REAL, EXTERNAL :: SLAMCH REAL, EXTERNAL :: SLAMCH, CLANHS
LOGICAL, EXTERNAL :: LSAME LOGICAL, EXTERNAL :: LSAME
INTEGER, EXTERNAL :: ILAENV INTEGER, EXTERNAL :: ILAENV
@ -466,6 +466,9 @@
ULP = SLAMCH( 'PRECISION' ) ULP = SLAMCH( 'PRECISION' )
SMLNUM = SAFMIN*( REAL( N )/ULP ) SMLNUM = SAFMIN*( REAL( N )/ULP )
BNORM = CLANHS( 'F', IHI-ILO+1, B( ILO, ILO ), LDB, RWORK )
BTOL = MAX( SAFMIN, ULP*BNORM )
ISTART = ILO ISTART = ILO
ISTOP = IHI ISTOP = IHI
MAXIT = 30*( IHI-ILO+1 ) MAXIT = 30*( IHI-ILO+1 )
@ -528,15 +531,8 @@
* slow down the method when many infinite eigenvalues are present * slow down the method when many infinite eigenvalues are present
K = ISTOP K = ISTOP
DO WHILE ( K.GE.ISTART2 ) 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 * A diagonal element of B is negligable, move it
* to the top and deflate it * to the top and deflate it

102
lapack-netlib/SRC/dlaqr5.f
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@ -286,8 +286,8 @@
* .. * ..
* .. Local Scalars .. * .. Local Scalars ..
DOUBLE PRECISION ALPHA, BETA, H11, H12, H21, H22, REFSUM, DOUBLE PRECISION ALPHA, BETA, H11, H12, H21, H22, REFSUM,
$ SAFMAX, SAFMIN, SCL, SMLNUM, SWAP, TST1, TST2, $ SAFMAX, SAFMIN, SCL, SMLNUM, SWAP, T1, T2,
$ ULP $ T3, TST1, TST2, ULP
INTEGER I, I2, I4, INCOL, J, JBOT, JCOL, JLEN, INTEGER I, I2, I4, INCOL, J, JBOT, JCOL, JLEN,
$ JROW, JTOP, K, K1, KDU, KMS, KRCOL, $ JROW, JTOP, K, K1, KDU, KMS, KRCOL,
$ M, M22, MBOT, MTOP, NBMPS, NDCOL, $ M, M22, MBOT, MTOP, NBMPS, NDCOL,
@ -447,11 +447,12 @@
* ==== Perform update from right within * ==== Perform update from right within
* . computational window. ==== * . computational window. ====
* *
T1 = V( 1, M22 )
T2 = T1*V( 2, M22 )
DO 30 J = JTOP, MIN( KBOT, K+3 ) DO 30 J = JTOP, MIN( KBOT, K+3 )
REFSUM = V( 1, M22 )*( H( J, K+1 )+V( 2, M22 )* REFSUM = H( J, K+1 ) + V( 2, M22 )*H( J, K+2 )
$ H( J, K+2 ) ) H( J, K+1 ) = H( J, K+1 ) - REFSUM*T1
H( J, K+1 ) = H( J, K+1 ) - REFSUM H( J, K+2 ) = H( J, K+2 ) - REFSUM*T2
H( J, K+2 ) = H( J, K+2 ) - REFSUM*V( 2, M22 )
30 CONTINUE 30 CONTINUE
* *
* ==== Perform update from left within * ==== Perform update from left within
@ -464,11 +465,12 @@
ELSE ELSE
JBOT = KBOT JBOT = KBOT
END IF END IF
T1 = V( 1, M22 )
T2 = T1*V( 2, M22 )
DO 40 J = K+1, JBOT DO 40 J = K+1, JBOT
REFSUM = V( 1, M22 )*( H( K+1, J )+V( 2, M22 )* REFSUM = H( K+1, J ) + V( 2, M22 )*H( K+2, J )
$ H( K+2, J ) ) H( K+1, J ) = H( K+1, J ) - REFSUM*T1
H( K+1, J ) = H( K+1, J ) - REFSUM H( K+2, J ) = H( K+2, J ) - REFSUM*T2
H( K+2, J ) = H( K+2, J ) - REFSUM*V( 2, M22 )
40 CONTINUE 40 CONTINUE
* *
* ==== The following convergence test requires that * ==== The following convergence test requires that
@ -522,18 +524,20 @@
* *
IF( ACCUM ) THEN IF( ACCUM ) THEN
KMS = K - INCOL KMS = K - INCOL
T1 = V( 1, M22 )
T2 = T1*V( 2, M22 )
DO 50 J = MAX( 1, KTOP-INCOL ), KDU DO 50 J = MAX( 1, KTOP-INCOL ), KDU
REFSUM = V( 1, M22 )*( U( J, KMS+1 )+ REFSUM = U( J, KMS+1 ) + V( 2, M22 )*U( J, KMS+2 )
$ V( 2, M22 )*U( J, KMS+2 ) ) U( J, KMS+1 ) = U( J, KMS+1 ) - REFSUM*T1
U( J, KMS+1 ) = U( J, KMS+1 ) - REFSUM U( J, KMS+2 ) = U( J, KMS+2 ) - REFSUM*T2
U( J, KMS+2 ) = U( J, KMS+2 ) - REFSUM*V( 2, M22 )
50 CONTINUE 50 CONTINUE
ELSE IF( WANTZ ) THEN ELSE IF( WANTZ ) THEN
T1 = V( 1, M22 )
T2 = T1*V( 2, M22 )
DO 60 J = ILOZ, IHIZ DO 60 J = ILOZ, IHIZ
REFSUM = V( 1, M22 )*( Z( J, K+1 )+V( 2, M22 )* REFSUM = Z( J, K+1 )+V( 2, M22 )*Z( J, K+2 )
$ Z( J, K+2 ) ) Z( J, K+1 ) = Z( J, K+1 ) - REFSUM*T1
Z( J, K+1 ) = Z( J, K+1 ) - REFSUM Z( J, K+2 ) = Z( J, K+2 ) - REFSUM*T2
Z( J, K+2 ) = Z( J, K+2 ) - REFSUM*V( 2, M22 )
60 CONTINUE 60 CONTINUE
END IF END IF
END IF END IF
@ -631,22 +635,25 @@
* . deflation check. We still delay most of the * . deflation check. We still delay most of the
* . updates from the left for efficiency. ==== * . 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 ) DO 70 J = JTOP, MIN( KBOT, K+3 )
REFSUM = V( 1, M )*( H( J, K+1 )+V( 2, M )* REFSUM = H( J, K+1 ) + V( 2, M )*H( J, K+2 )
$ H( J, K+2 )+V( 3, M )*H( J, K+3 ) ) $ + V( 3, M )*H( J, K+3 )
H( J, K+1 ) = H( J, K+1 ) - REFSUM H( J, K+1 ) = H( J, K+1 ) - REFSUM*T1
H( J, K+2 ) = H( J, K+2 ) - REFSUM*V( 2, M ) H( J, K+2 ) = H( J, K+2 ) - REFSUM*T2
H( J, K+3 ) = H( J, K+3 ) - REFSUM*V( 3, M ) H( J, K+3 ) = H( J, K+3 ) - REFSUM*T3
70 CONTINUE 70 CONTINUE
* *
* ==== Perform update from left for subsequent * ==== Perform update from left for subsequent
* . column. ==== * . column. ====
* *
REFSUM = V( 1, M )*( H( K+1, K+1 )+V( 2, M )* REFSUM = H( K+1, K+1 ) + V( 2, M )*H( K+2, K+1 )
$ H( K+2, K+1 )+V( 3, M )*H( K+3, K+1 ) ) $ + V( 3, M )*H( K+3, K+1 )
H( K+1, K+1 ) = H( K+1, K+1 ) - REFSUM H( K+1, K+1 ) = H( K+1, K+1 ) - REFSUM*T1
H( K+2, K+1 ) = H( K+2, K+1 ) - REFSUM*V( 2, M ) H( K+2, K+1 ) = H( K+2, K+1 ) - REFSUM*T2
H( K+3, K+1 ) = H( K+3, K+1 ) - REFSUM*V( 3, M ) H( K+3, K+1 ) = H( K+3, K+1 ) - REFSUM*T3
* *
* ==== The following convergence test requires that * ==== The following convergence test requires that
* . the tradition small-compared-to-nearby-diagonals * . the tradition small-compared-to-nearby-diagonals
@ -706,12 +713,15 @@
* *
DO 100 M = MBOT, MTOP, -1 DO 100 M = MBOT, MTOP, -1
K = KRCOL + 2*( M-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 DO 90 J = MAX( KTOP, KRCOL + 2*M ), JBOT
REFSUM = V( 1, M )*( H( K+1, J )+V( 2, M )* REFSUM = H( K+1, J ) + V( 2, M )*H( K+2, J )
$ H( K+2, J )+V( 3, M )*H( K+3, J ) ) $ + V( 3, M )*H( K+3, J )
H( K+1, J ) = H( K+1, J ) - REFSUM H( K+1, J ) = H( K+1, J ) - REFSUM*T1
H( K+2, J ) = H( K+2, J ) - REFSUM*V( 2, M ) H( K+2, J ) = H( K+2, J ) - REFSUM*T2
H( K+3, J ) = H( K+3, J ) - REFSUM*V( 3, M ) H( K+3, J ) = H( K+3, J ) - REFSUM*T3
90 CONTINUE 90 CONTINUE
100 CONTINUE 100 CONTINUE
* *
@ -729,12 +739,15 @@
I2 = MAX( 1, KTOP-INCOL ) I2 = MAX( 1, KTOP-INCOL )
I2 = MAX( I2, KMS-(KRCOL-INCOL)+1 ) I2 = MAX( I2, KMS-(KRCOL-INCOL)+1 )
I4 = MIN( KDU, KRCOL + 2*( MBOT-1 ) - INCOL + 5 ) 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 DO 110 J = I2, I4
REFSUM = V( 1, M )*( U( J, KMS+1 )+V( 2, M )* REFSUM = U( J, KMS+1 ) + V( 2, M )*U( J, KMS+2 )
$ U( J, KMS+2 )+V( 3, M )*U( J, KMS+3 ) ) $ + V( 3, M )*U( J, KMS+3 )
U( J, KMS+1 ) = U( J, KMS+1 ) - REFSUM U( J, KMS+1 ) = U( J, KMS+1 ) - REFSUM*T1
U( J, KMS+2 ) = U( J, KMS+2 ) - REFSUM*V( 2, M ) U( J, KMS+2 ) = U( J, KMS+2 ) - REFSUM*T2
U( J, KMS+3 ) = U( J, KMS+3 ) - REFSUM*V( 3, M ) U( J, KMS+3 ) = U( J, KMS+3 ) - REFSUM*T3
110 CONTINUE 110 CONTINUE
120 CONTINUE 120 CONTINUE
ELSE IF( WANTZ ) THEN ELSE IF( WANTZ ) THEN
@ -745,12 +758,15 @@
* *
DO 140 M = MBOT, MTOP, -1 DO 140 M = MBOT, MTOP, -1
K = KRCOL + 2*( M-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 DO 130 J = ILOZ, IHIZ
REFSUM = V( 1, M )*( Z( J, K+1 )+V( 2, M )* REFSUM = Z( J, K+1 ) + V( 2, M )*Z( J, K+2 )
$ Z( J, K+2 )+V( 3, M )*Z( J, K+3 ) ) $ + V( 3, M )*Z( J, K+3 )
Z( J, K+1 ) = Z( J, K+1 ) - REFSUM Z( J, K+1 ) = Z( J, K+1 ) - REFSUM*T1
Z( J, K+2 ) = Z( J, K+2 ) - REFSUM*V( 2, M ) Z( J, K+2 ) = Z( J, K+2 ) - REFSUM*T2
Z( J, K+3 ) = Z( J, K+3 ) - REFSUM*V( 3, M ) Z( J, K+3 ) = Z( J, K+3 ) - REFSUM*T3
130 CONTINUE 130 CONTINUE
140 CONTINUE 140 CONTINUE
END IF END IF

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

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

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

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

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

@ -318,7 +318,8 @@
PARAMETER( ZERO = 0.0, ONE = 1.0, HALF = 0.5 ) PARAMETER( ZERO = 0.0, ONE = 1.0, HALF = 0.5 )
* Local scalars * 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, INTEGER :: ISTART, ISTOP, IITER, MAXIT, ISTART2, K, LD, NSHIFTS,
$ NBLOCK, NW, NMIN, NIBBLE, N_UNDEFLATED, N_DEFLATED, $ NBLOCK, NW, NMIN, NIBBLE, N_UNDEFLATED, N_DEFLATED,
$ NS, SWEEP_INFO, SHIFTPOS, LWORKREQ, K2, ISTARTM, $ NS, SWEEP_INFO, SHIFTPOS, LWORKREQ, K2, ISTARTM,
@ -330,7 +331,7 @@
* External Functions * External Functions
EXTERNAL :: XERBLA, SHGEQZ, SLAQZ3, SLAQZ4, SLASET, SLABAD, EXTERNAL :: XERBLA, SHGEQZ, SLAQZ3, SLAQZ4, SLASET, SLABAD,
$ SLARTG, SROT $ SLARTG, SROT
REAL, EXTERNAL :: SLAMCH REAL, EXTERNAL :: SLAMCH, SLANHS
LOGICAL, EXTERNAL :: LSAME LOGICAL, EXTERNAL :: LSAME
INTEGER, EXTERNAL :: ILAENV INTEGER, EXTERNAL :: ILAENV
@ -482,6 +483,9 @@
ULP = SLAMCH( 'PRECISION' ) ULP = SLAMCH( 'PRECISION' )
SMLNUM = SAFMIN*( REAL( N )/ULP ) SMLNUM = SAFMIN*( REAL( N )/ULP )
BNORM = SLANHS( 'F', IHI-ILO+1, B( ILO, ILO ), LDB, WORK )
BTOL = MAX( SAFMIN, ULP*BNORM )
ISTART = ILO ISTART = ILO
ISTOP = IHI ISTOP = IHI
MAXIT = 3*( IHI-ILO+1 ) MAXIT = 3*( IHI-ILO+1 )
@ -558,15 +562,8 @@
* slow down the method when many infinite eigenvalues are present * slow down the method when many infinite eigenvalues are present
K = ISTOP K = ISTOP
DO WHILE ( K.GE.ISTART2 ) 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 * A diagonal element of B is negligable, move it
* to the top and deflate 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 ) PARAMETER ( RZERO = 0.0d0, RONE = 1.0d0 )
* .. * ..
* .. Local Scalars .. * .. 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, DOUBLE PRECISION H11, H12, H21, H22, SAFMAX, SAFMIN, SCL,
$ SMLNUM, TST1, TST2, ULP $ SMLNUM, TST1, TST2, ULP
INTEGER I2, I4, INCOL, J, JBOT, JCOL, JLEN, INTEGER I2, I4, INCOL, J, JBOT, JCOL, JLEN,
@ -424,12 +424,12 @@
* ==== Perform update from right within * ==== Perform update from right within
* . computational window. ==== * . computational window. ====
* *
T1 = V( 1, M22 )
T2 = T1*DCONJG( V( 2, M22 ) )
DO 30 J = JTOP, MIN( KBOT, K+3 ) DO 30 J = JTOP, MIN( KBOT, K+3 )
REFSUM = V( 1, M22 )*( H( J, K+1 )+V( 2, M22 )* REFSUM = H( J, K+1 ) + V( 2, M22 )*H( J, K+2 )
$ H( J, K+2 ) ) H( J, K+1 ) = H( J, K+1 ) - REFSUM*T1
H( J, K+1 ) = H( J, K+1 ) - REFSUM H( J, K+2 ) = H( J, K+2 ) - REFSUM*T2
H( J, K+2 ) = H( J, K+2 ) -
$ REFSUM*DCONJG( V( 2, M22 ) )
30 CONTINUE 30 CONTINUE
* *
* ==== Perform update from left within * ==== Perform update from left within
@ -442,12 +442,13 @@
ELSE ELSE
JBOT = KBOT JBOT = KBOT
END IF END IF
T1 = DCONJG( V( 1, M22 ) )
T2 = T1*V( 2, M22 )
DO 40 J = K+1, JBOT DO 40 J = K+1, JBOT
REFSUM = DCONJG( V( 1, M22 ) )* REFSUM = H( K+1, J ) +
$ ( H( K+1, J )+DCONJG( V( 2, M22 ) )* $ DCONJG( V( 2, M22 ) )*H( K+2, J )
$ H( K+2, J ) ) H( K+1, J ) = H( K+1, J ) - REFSUM*T1
H( K+1, J ) = H( K+1, J ) - REFSUM H( K+2, J ) = H( K+2, J ) - REFSUM*T2
H( K+2, J ) = H( K+2, J ) - REFSUM*V( 2, M22 )
40 CONTINUE 40 CONTINUE
* *
* ==== The following convergence test requires that * ==== The following convergence test requires that
@ -610,25 +611,29 @@
* . deflation check. We still delay most of the * . deflation check. We still delay most of the
* . updates from the left for efficiency. ==== * . 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 ) DO 70 J = JTOP, MIN( KBOT, K+3 )
REFSUM = V( 1, M )*( H( J, K+1 )+V( 2, M )* REFSUM = H( J, K+1 ) + V( 2, M )*H( J, K+2 )
$ H( J, K+2 )+V( 3, M )*H( J, K+3 ) ) $ + V( 3, M )*H( J, K+3 )
H( J, K+1 ) = H( J, K+1 ) - REFSUM H( J, K+1 ) = H( J, K+1 ) - REFSUM*T1
H( J, K+2 ) = H( J, K+2 ) - H( J, K+2 ) = H( J, K+2 ) - REFSUM*T2
$ REFSUM*DCONJG( V( 2, M ) ) H( J, K+3 ) = H( J, K+3 ) - REFSUM*T3
H( J, K+3 ) = H( J, K+3 ) -
$ REFSUM*DCONJG( V( 3, M ) )
70 CONTINUE 70 CONTINUE
* *
* ==== Perform update from left for subsequent * ==== Perform update from left for subsequent
* . column. ==== * . column. ====
* *
REFSUM = DCONJG( V( 1, M ) )*( H( K+1, K+1 ) T1 = DCONJG( V( 1, M ) )
$ +DCONJG( V( 2, M ) )*H( K+2, K+1 ) T2 = T1*V( 2, M )
$ +DCONJG( V( 3, M ) )*H( K+3, K+1 ) ) T3 = T1*V( 3, M )
H( K+1, K+1 ) = H( K+1, K+1 ) - REFSUM REFSUM = H( K+1, K+1 )
H( K+2, K+1 ) = H( K+2, K+1 ) - REFSUM*V( 2, M ) $ + DCONJG( V( 2, M ) )*H( K+2, K+1 )
H( K+3, K+1 ) = H( K+3, K+1 ) - REFSUM*V( 3, M ) $ + 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 following convergence test requires that
* . the tradition small-compared-to-nearby-diagonals * . the tradition small-compared-to-nearby-diagonals
@ -688,13 +693,15 @@
* *
DO 100 M = MBOT, MTOP, -1 DO 100 M = MBOT, MTOP, -1
K = KRCOL + 2*( M-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 DO 90 J = MAX( KTOP, KRCOL + 2*M ), JBOT
REFSUM = DCONJG( V( 1, M ) )* REFSUM = H( K+1, J ) + DCONJG( V( 2, M ) )*H( K+2, J )
$ ( H( K+1, J )+DCONJG( V( 2, M ) )* $ + DCONJG( V( 3, M ) )*H( K+3, J )
$ H( K+2, J )+DCONJG( V( 3, M ) )*H( K+3, J ) ) H( K+1, J ) = H( K+1, J ) - REFSUM*T1
H( K+1, J ) = H( K+1, J ) - REFSUM H( K+2, J ) = H( K+2, J ) - REFSUM*T2
H( K+2, J ) = H( K+2, J ) - REFSUM*V( 2, M ) H( K+3, J ) = H( K+3, J ) - REFSUM*T3
H( K+3, J ) = H( K+3, J ) - REFSUM*V( 3, M )
90 CONTINUE 90 CONTINUE
100 CONTINUE 100 CONTINUE
* *
@ -712,14 +719,15 @@
I2 = MAX( 1, KTOP-INCOL ) I2 = MAX( 1, KTOP-INCOL )
I2 = MAX( I2, KMS-(KRCOL-INCOL)+1 ) I2 = MAX( I2, KMS-(KRCOL-INCOL)+1 )
I4 = MIN( KDU, KRCOL + 2*( MBOT-1 ) - INCOL + 5 ) 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 DO 110 J = I2, I4
REFSUM = V( 1, M )*( U( J, KMS+1 )+V( 2, M )* REFSUM = U( J, KMS+1 ) + V( 2, M )*U( J, KMS+2 )
$ U( J, KMS+2 )+V( 3, M )*U( J, KMS+3 ) ) $ + V( 3, M )*U( J, KMS+3 )
U( J, KMS+1 ) = U( J, KMS+1 ) - REFSUM U( J, KMS+1 ) = U( J, KMS+1 ) - REFSUM*T1
U( J, KMS+2 ) = U( J, KMS+2 ) - U( J, KMS+2 ) = U( J, KMS+2 ) - REFSUM*T2
$ REFSUM*DCONJG( V( 2, M ) ) U( J, KMS+3 ) = U( J, KMS+3 ) - REFSUM*T3
U( J, KMS+3 ) = U( J, KMS+3 ) -
$ REFSUM*DCONJG( V( 3, M ) )
110 CONTINUE 110 CONTINUE
120 CONTINUE 120 CONTINUE
ELSE IF( WANTZ ) THEN ELSE IF( WANTZ ) THEN
@ -730,14 +738,15 @@
* *
DO 140 M = MBOT, MTOP, -1 DO 140 M = MBOT, MTOP, -1
K = KRCOL + 2*( M-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 DO 130 J = ILOZ, IHIZ
REFSUM = V( 1, M )*( Z( J, K+1 )+V( 2, M )* REFSUM = Z( J, K+1 ) + V( 2, M )*Z( J, K+2 )
$ Z( J, K+2 )+V( 3, M )*Z( J, K+3 ) ) $ + V( 3, M )*Z( J, K+3 )
Z( J, K+1 ) = Z( J, K+1 ) - REFSUM Z( J, K+1 ) = Z( J, K+1 ) - REFSUM*T1
Z( J, K+2 ) = Z( J, K+2 ) - Z( J, K+2 ) = Z( J, K+2 ) - REFSUM*T2
$ REFSUM*DCONJG( V( 2, M ) ) Z( J, K+3 ) = Z( J, K+3 ) - REFSUM*T3
Z( J, K+3 ) = Z( J, K+3 ) -
$ REFSUM*DCONJG( V( 3, M ) )
130 CONTINUE 130 CONTINUE
140 CONTINUE 140 CONTINUE
END IF END IF

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

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