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xLAEIN: apply the growth test to the growth, not to |x| alone #1400

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Merged
langou merged 2 commits into from
Sep 12, 2026
+62 −46
Merged

xLAEIN: apply the growth test to the growth, not to |x| alone #1400

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f4b5da4
xLAEIN: apply the growth test to the growth, not to |x| alone
ACSimon33 Sep 10, 2026
dc0888a
xLAEIN: call the two norms V0NORM and V1NORM
ACSimon33 Sep 10, 2026
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20 changes: 12 additions & 8 deletions SRC/claein.f
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Original file line number Diff line number Diff line change
Expand Up @@ -173,7 +173,8 @@ SUBROUTINE CLAEIN( RIGHTV, NOINIT, N, H, LDH, W, V, B, LDB,
* .. Local Scalars ..
CHARACTER NORMIN, TRANS
INTEGER I, IERR, ITS, J
REAL GROWTO, NRMSML, ROOTN, RTEMP, SCALE, VNORM
REAL GROWTO, NRMSML, ROOTN, RTEMP, SCALE, V0NORM,
$ V1NORM
COMPLEX CDUM, EI, EJ, TEMP, X
* ..
* .. External Functions ..
Expand All @@ -198,11 +199,13 @@ SUBROUTINE CLAEIN( RIGHTV, NOINIT, N, H, LDH, W, V, B, LDB,
*
INFO = 0
*
* GROWTO is the threshold used in the acceptance test for an
* eigenvector.
* Each starting vector gets one solve, from v0 to v1. The residual
* of v1 is SCALE times the norm of v0, over the norm of v1, so
* GROWTO is the growth V1NORM/(SCALE*V0NORM) that the acceptance
* test below requires.
*
ROOTN = SQRT( REAL( N ) )
GROWTO = TENTH / ROOTN
GROWTO = TENTH / ( REAL( N )*EPS3 )
NRMSML = MAX( ONE, EPS3*ROOTN )*SMLNUM
*
* Form B = H - W*I (except that the subdiagonal elements are not
Expand All @@ -226,8 +229,8 @@ SUBROUTINE CLAEIN( RIGHTV, NOINIT, N, H, LDH, W, V, B, LDB,
*
* Scale supplied initial vector.
*
VNORM = SCNRM2( N, V, 1 )
CALL CSSCAL( N, ( EPS3*ROOTN ) / MAX( VNORM, NRMSML ), V,
V0NORM = SCNRM2( N, V, 1 )
CALL CSSCAL( N, ( EPS3*ROOTN ) / MAX( V0NORM, NRMSML ), V,
$ 1 )
END IF
*
Expand Down Expand Up @@ -309,6 +312,7 @@ SUBROUTINE CLAEIN( RIGHTV, NOINIT, N, H, LDH, W, V, B, LDB,
*
NORMIN = 'N'
DO 110 ITS = 1, N
V0NORM = SCASUM( N, V, 1 )
*
* Solve U*x = scale*v for a right eigenvector
* or U**H *x = scale*v for a left eigenvector,
Expand All @@ -321,8 +325,8 @@ SUBROUTINE CLAEIN( RIGHTV, NOINIT, N, H, LDH, W, V, B, LDB,
*
* Test for sufficient growth in the norm of v.
*
VNORM = SCASUM( N, V, 1 )
IF( VNORM.GE.GROWTO*SCALE )
V1NORM = SCASUM( N, V, 1 )
IF( V1NORM.GE.GROWTO*SCALE*V0NORM )
$ GO TO 120
*
* Choose new orthogonal starting vector and try again.
Expand Down
34 changes: 19 additions & 15 deletions SRC/dlaein.f
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Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -194,8 +194,8 @@ SUBROUTINE DLAEIN( RIGHTV, NOINIT, N, H, LDH, WR, WI, VR, VI,
CHARACTER NORMIN, TRANS
INTEGER I, I1, I2, I3, IERR, ITS, J
DOUBLE PRECISION ABSBII, ABSBJJ, EI, EJ, GROWTO, NORM, NRMSML,
$ REC, ROOTN, SCALE, TEMP, VCRIT, VMAX, VNORM, W,
$ W1, X, XI, XR, Y
$ REC, ROOTN, SCALE, TEMP, V0NORM, V1NORM,
$ VCRIT, VMAX, W, W1, X, XI, XR, Y
* ..
* .. External Functions ..
INTEGER IDAMAX
Expand All @@ -212,11 +212,13 @@ SUBROUTINE DLAEIN( RIGHTV, NOINIT, N, H, LDH, WR, WI, VR, VI,
*
INFO = 0
*
* GROWTO is the threshold used in the acceptance test for an
* eigenvector.
* Each starting vector gets one solve, from v0 to v1. The residual
* of v1 is SCALE times the norm of v0, over the norm of v1, so
* GROWTO is the growth V1NORM/(SCALE*V0NORM) that the acceptance
* test below requires.
*
ROOTN = SQRT( DBLE( N ) )
GROWTO = TENTH / ROOTN
GROWTO = TENTH / ( DBLE( N )*EPS3 )
NRMSML = MAX( ONE, EPS3*ROOTN )*SMLNUM
*
* Form B = H - (WR,WI)*I (except that the subdiagonal elements and
Expand Down Expand Up @@ -244,8 +246,8 @@ SUBROUTINE DLAEIN( RIGHTV, NOINIT, N, H, LDH, WR, WI, VR, VI,
*
* Scale supplied initial vector.
*
VNORM = DNRM2( N, VR, 1 )
CALL DSCAL( N, ( EPS3*ROOTN ) / MAX( VNORM, NRMSML ), VR,
V0NORM = DNRM2( N, VR, 1 )
CALL DSCAL( N, ( EPS3*ROOTN ) / MAX( V0NORM, NRMSML ), VR,
$ 1 )
END IF
*
Expand Down Expand Up @@ -327,6 +329,7 @@ SUBROUTINE DLAEIN( RIGHTV, NOINIT, N, H, LDH, WR, WI, VR, VI,
*
NORMIN = 'N'
DO 110 ITS = 1, N
V0NORM = DASUM( N, VR, 1 )
*
* Solve U*x = scale*v for a right eigenvector
* or U**T*x = scale*v for a left eigenvector,
Expand All @@ -339,8 +342,8 @@ SUBROUTINE DLAEIN( RIGHTV, NOINIT, N, H, LDH, WR, WI, VR, VI,
*
* Test for sufficient growth in the norm of v.
*
VNORM = DASUM( N, VR, 1 )
IF( VNORM.GE.GROWTO*SCALE )
V1NORM = DASUM( N, VR, 1 )
IF( V1NORM.GE.GROWTO*SCALE*V0NORM )
$ GO TO 120
*
* Choose new orthogonal starting vector and try again.
Expand Down Expand Up @@ -521,6 +524,7 @@ SUBROUTINE DLAEIN( RIGHTV, NOINIT, N, H, LDH, WR, WI, VR, VI,
END IF
*
DO 270 ITS = 1, N
V0NORM = DASUM( N, VR, 1 ) + DASUM( N, VI, 1 )
SCALE = ONE
VMAX = ONE
VCRIT = BIGNUM
Expand Down Expand Up @@ -591,8 +595,8 @@ SUBROUTINE DLAEIN( RIGHTV, NOINIT, N, H, LDH, WR, WI, VR, VI,
*
* Test for sufficient growth in the norm of (VR,VI).
*
VNORM = DASUM( N, VR, 1 ) + DASUM( N, VI, 1 )
IF( VNORM.GE.GROWTO*SCALE )
V1NORM = DASUM( N, VR, 1 ) + DASUM( N, VI, 1 )
IF( V1NORM.GE.GROWTO*SCALE*V0NORM )
$ GO TO 280
*
* Choose a new orthogonal starting vector and try again.
Expand All @@ -616,12 +620,12 @@ SUBROUTINE DLAEIN( RIGHTV, NOINIT, N, H, LDH, WR, WI, VR, VI,
*
* Normalize eigenvector.
*
VNORM = ZERO
V1NORM = ZERO
DO 290 I = 1, N
VNORM = MAX( VNORM, ABS( VR( I ) )+ABS( VI( I ) ) )
V1NORM = MAX( V1NORM, ABS( VR( I ) )+ABS( VI( I ) ) )
290 CONTINUE
CALL DSCAL( N, ONE / VNORM, VR, 1 )
CALL DSCAL( N, ONE / VNORM, VI, 1 )
CALL DSCAL( N, ONE / V1NORM, VR, 1 )
CALL DSCAL( N, ONE / V1NORM, VI, 1 )
*
END IF
*
Expand Down
34 changes: 19 additions & 15 deletions SRC/slaein.f
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Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -194,8 +194,8 @@ SUBROUTINE SLAEIN( RIGHTV, NOINIT, N, H, LDH, WR, WI, VR, VI,
CHARACTER NORMIN, TRANS
INTEGER I, I1, I2, I3, IERR, ITS, J
REAL ABSBII, ABSBJJ, EI, EJ, GROWTO, NORM, NRMSML,
$ REC, ROOTN, SCALE, TEMP, VCRIT, VMAX, VNORM, W,
$ W1, X, XI, XR, Y
$ REC, ROOTN, SCALE, TEMP, V0NORM, V1NORM,
$ VCRIT, VMAX, W, W1, X, XI, XR, Y
* ..
* .. External Functions ..
INTEGER ISAMAX
Expand All @@ -212,11 +212,13 @@ SUBROUTINE SLAEIN( RIGHTV, NOINIT, N, H, LDH, WR, WI, VR, VI,
*
INFO = 0
*
* GROWTO is the threshold used in the acceptance test for an
* eigenvector.
* Each starting vector gets one solve, from v0 to v1. The residual
* of v1 is SCALE times the norm of v0, over the norm of v1, so
* GROWTO is the growth V1NORM/(SCALE*V0NORM) that the acceptance
* test below requires.
*
ROOTN = SQRT( REAL( N ) )
GROWTO = TENTH / ROOTN
GROWTO = TENTH / ( REAL( N )*EPS3 )
NRMSML = MAX( ONE, EPS3*ROOTN )*SMLNUM
*
* Form B = H - (WR,WI)*I (except that the subdiagonal elements and
Expand Down Expand Up @@ -244,8 +246,8 @@ SUBROUTINE SLAEIN( RIGHTV, NOINIT, N, H, LDH, WR, WI, VR, VI,
*
* Scale supplied initial vector.
*
VNORM = SNRM2( N, VR, 1 )
CALL SSCAL( N, ( EPS3*ROOTN ) / MAX( VNORM, NRMSML ), VR,
V0NORM = SNRM2( N, VR, 1 )
CALL SSCAL( N, ( EPS3*ROOTN ) / MAX( V0NORM, NRMSML ), VR,
$ 1 )
END IF
*
Expand Down Expand Up @@ -327,6 +329,7 @@ SUBROUTINE SLAEIN( RIGHTV, NOINIT, N, H, LDH, WR, WI, VR, VI,
*
NORMIN = 'N'
DO 110 ITS = 1, N
V0NORM = SASUM( N, VR, 1 )
*
* Solve U*x = scale*v for a right eigenvector
* or U**T*x = scale*v for a left eigenvector,
Expand All @@ -339,8 +342,8 @@ SUBROUTINE SLAEIN( RIGHTV, NOINIT, N, H, LDH, WR, WI, VR, VI,
*
* Test for sufficient growth in the norm of v.
*
VNORM = SASUM( N, VR, 1 )
IF( VNORM.GE.GROWTO*SCALE )
V1NORM = SASUM( N, VR, 1 )
IF( V1NORM.GE.GROWTO*SCALE*V0NORM )
$ GO TO 120
*
* Choose new orthogonal starting vector and try again.
Expand Down Expand Up @@ -521,6 +524,7 @@ SUBROUTINE SLAEIN( RIGHTV, NOINIT, N, H, LDH, WR, WI, VR, VI,
END IF
*
DO 270 ITS = 1, N
V0NORM = SASUM( N, VR, 1 ) + SASUM( N, VI, 1 )
SCALE = ONE
VMAX = ONE
VCRIT = BIGNUM
Expand Down Expand Up @@ -591,8 +595,8 @@ SUBROUTINE SLAEIN( RIGHTV, NOINIT, N, H, LDH, WR, WI, VR, VI,
*
* Test for sufficient growth in the norm of (VR,VI).
*
VNORM = SASUM( N, VR, 1 ) + SASUM( N, VI, 1 )
IF( VNORM.GE.GROWTO*SCALE )
V1NORM = SASUM( N, VR, 1 ) + SASUM( N, VI, 1 )
IF( V1NORM.GE.GROWTO*SCALE*V0NORM )
$ GO TO 280
*
* Choose a new orthogonal starting vector and try again.
Expand All @@ -616,12 +620,12 @@ SUBROUTINE SLAEIN( RIGHTV, NOINIT, N, H, LDH, WR, WI, VR, VI,
*
* Normalize eigenvector.
*
VNORM = ZERO
V1NORM = ZERO
DO 290 I = 1, N
VNORM = MAX( VNORM, ABS( VR( I ) )+ABS( VI( I ) ) )
V1NORM = MAX( V1NORM, ABS( VR( I ) )+ABS( VI( I ) ) )
290 CONTINUE
CALL SSCAL( N, ONE / VNORM, VR, 1 )
CALL SSCAL( N, ONE / VNORM, VI, 1 )
CALL SSCAL( N, ONE / V1NORM, VR, 1 )
CALL SSCAL( N, ONE / V1NORM, VI, 1 )
*
END IF
*
Expand Down
20 changes: 12 additions & 8 deletions SRC/zlaein.f
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Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -173,7 +173,8 @@ SUBROUTINE ZLAEIN( RIGHTV, NOINIT, N, H, LDH, W, V, B, LDB,
* .. Local Scalars ..
CHARACTER NORMIN, TRANS
INTEGER I, IERR, ITS, J
DOUBLE PRECISION GROWTO, NRMSML, ROOTN, RTEMP, SCALE, VNORM
DOUBLE PRECISION GROWTO, NRMSML, ROOTN, RTEMP, SCALE, V0NORM,
$ V1NORM
COMPLEX*16 CDUM, EI, EJ, TEMP, X
* ..
* .. External Functions ..
Expand All @@ -198,11 +199,13 @@ SUBROUTINE ZLAEIN( RIGHTV, NOINIT, N, H, LDH, W, V, B, LDB,
*
INFO = 0
*
* GROWTO is the threshold used in the acceptance test for an
* eigenvector.
* Each starting vector gets one solve, from v0 to v1. The residual
* of v1 is SCALE times the norm of v0, over the norm of v1, so
* GROWTO is the growth V1NORM/(SCALE*V0NORM) that the acceptance
* test below requires.
*
ROOTN = SQRT( DBLE( N ) )
GROWTO = TENTH / ROOTN
GROWTO = TENTH / ( DBLE( N )*EPS3 )
NRMSML = MAX( ONE, EPS3*ROOTN )*SMLNUM
*
* Form B = H - W*I (except that the subdiagonal elements are not
Expand All @@ -226,8 +229,8 @@ SUBROUTINE ZLAEIN( RIGHTV, NOINIT, N, H, LDH, W, V, B, LDB,
*
* Scale supplied initial vector.
*
VNORM = DZNRM2( N, V, 1 )
CALL ZDSCAL( N, ( EPS3*ROOTN ) / MAX( VNORM, NRMSML ), V,
V0NORM = DZNRM2( N, V, 1 )
CALL ZDSCAL( N, ( EPS3*ROOTN ) / MAX( V0NORM, NRMSML ), V,
$ 1 )
END IF
*
Expand Down Expand Up @@ -309,6 +312,7 @@ SUBROUTINE ZLAEIN( RIGHTV, NOINIT, N, H, LDH, W, V, B, LDB,
*
NORMIN = 'N'
DO 110 ITS = 1, N
V0NORM = DZASUM( N, V, 1 )
*
* Solve U*x = scale*v for a right eigenvector
* or U**H *x = scale*v for a left eigenvector,
Expand All @@ -321,8 +325,8 @@ SUBROUTINE ZLAEIN( RIGHTV, NOINIT, N, H, LDH, W, V, B, LDB,
*
* Test for sufficient growth in the norm of v.
*
VNORM = DZASUM( N, V, 1 )
IF( VNORM.GE.GROWTO*SCALE )
V1NORM = DZASUM( N, V, 1 )
IF( V1NORM.GE.GROWTO*SCALE*V0NORM )
$ GO TO 120
*
* Choose new orthogonal starting vector and try again.
Expand Down
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