*
* =========== DOCUMENTATION ===========
*
-* Online html documentation available at
-* http://www.netlib.org/lapack/explore-html/
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
-*> Download DLASD4 + dependencies
-*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasd4.f">
-*> [TGZ]</a>
-*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasd4.f">
-*> [ZIP]</a>
-*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasd4.f">
+*> Download DLASD4 + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasd4.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasd4.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasd4.f">
*> [TXT]</a>
-*> \endhtmlonly
+*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DLASD4( N, I, D, Z, DELTA, RHO, SIGMA, WORK, INFO )
-*
+*
* .. Scalar Arguments ..
* INTEGER I, INFO, N
* DOUBLE PRECISION RHO, SIGMA
* .. Array Arguments ..
* DOUBLE PRECISION D( * ), DELTA( * ), WORK( * ), Z( * )
* ..
-*
+*
*
*> \par Purpose:
* =============
* Authors:
* ========
*
-*> \author Univ. of Tennessee
-*> \author Univ. of California Berkeley
-*> \author Univ. of Colorado Denver
-*> \author NAG Ltd.
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
*
*> \date August 2012
*
*
* .. Parameters ..
INTEGER MAXIT
-* set MAXIT to 40 from 64. RCL 8/26/2012
- PARAMETER ( MAXIT = 40 )
+ PARAMETER ( MAXIT = 400 )
DOUBLE PRECISION ZERO, ONE, TWO, THREE, FOUR, EIGHT, TEN
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0,
$ THREE = 3.0D+0, FOUR = 4.0D+0, EIGHT = 8.0D+0,
$ TEN = 10.0D+0 )
* ..
* .. Local Scalars ..
- LOGICAL ORGATI, SWTCH, SWTCH3
+ LOGICAL ORGATI, SWTCH, SWTCH3, GEOMAVG
INTEGER II, IIM1, IIP1, IP1, ITER, J, NITER
- DOUBLE PRECISION A, B, C, DELSQ, DELSQ2, DPHI, DPSI, DTIIM,
+ DOUBLE PRECISION A, B, C, DELSQ, DELSQ2, SQ2, DPHI, DPSI, DTIIM,
$ DTIIP, DTIPSQ, DTISQ, DTNSQ, DTNSQ1, DW, EPS,
- $ ERRETM, ETA, PHI, PREW, PSI, RHOINV, SG2LB,
- $ SG2UB, TAU, TEMP, TEMP1, TEMP2, W
+ $ ERRETM, ETA, PHI, PREW, PSI, RHOINV, SGLB,
+ $ SGUB, TAU, TAU2, TEMP, TEMP1, TEMP2, W
* ..
* .. Local Arrays ..
DOUBLE PRECISION DD( 3 ), ZZ( 3 )
$ ( D( N )-D( N-1 )+RHO / ( D( N )+TEMP1 ) ) ) +
$ Z( N )*Z( N ) / RHO
*
-* The following TAU is to approximate
+* The following TAU2 is to approximate
* SIGMA_n^2 - D( N )*D( N )
*
IF( C.LE.TEMP ) THEN
A = -C*DELSQ + Z( N-1 )*Z( N-1 ) + Z( N )*Z( N )
B = Z( N )*Z( N )*DELSQ
IF( A.LT.ZERO ) THEN
- TAU = TWO*B / ( SQRT( A*A+FOUR*B*C )-A )
+ TAU2 = TWO*B / ( SQRT( A*A+FOUR*B*C )-A )
ELSE
- TAU = ( A+SQRT( A*A+FOUR*B*C ) ) / ( TWO*C )
+ TAU2 = ( A+SQRT( A*A+FOUR*B*C ) ) / ( TWO*C )
END IF
END IF
*
* It can be proved that
-* D(N)^2+RHO/2 <= SIGMA_n^2 < D(N)^2+TAU <= D(N)^2+RHO
+* D(N)^2+RHO/2 <= SIGMA_n^2 < D(N)^2+TAU2 <= D(N)^2+RHO
*
ELSE
DELSQ = ( D( N )-D( N-1 ) )*( D( N )+D( N-1 ) )
A = -C*DELSQ + Z( N-1 )*Z( N-1 ) + Z( N )*Z( N )
B = Z( N )*Z( N )*DELSQ
*
-* The following TAU is to approximate
+* The following TAU2 is to approximate
* SIGMA_n^2 - D( N )*D( N )
*
IF( A.LT.ZERO ) THEN
- TAU = TWO*B / ( SQRT( A*A+FOUR*B*C )-A )
+ TAU2 = TWO*B / ( SQRT( A*A+FOUR*B*C )-A )
ELSE
- TAU = ( A+SQRT( A*A+FOUR*B*C ) ) / ( TWO*C )
+ TAU2 = ( A+SQRT( A*A+FOUR*B*C ) ) / ( TWO*C )
END IF
*
* It can be proved that
-* D(N)^2 < D(N)^2+TAU < SIGMA(N)^2 < D(N)^2+RHO/2
+* D(N)^2 < D(N)^2+TAU2 < SIGMA(N)^2 < D(N)^2+RHO/2
*
END IF
*
-* The following ETA is to approximate SIGMA_n - D( N )
+* The following TAU is to approximate SIGMA_n - D( N )
*
- ETA = TAU / ( D( N )+SQRT( D( N )*D( N )+TAU ) )
+ TAU = TAU2 / ( D( N )+SQRT( D( N )*D( N )+TAU2 ) )
*
- SIGMA = D( N ) + ETA
+ SIGMA = D( N ) + TAU
DO 30 J = 1, N
- DELTA( J ) = ( D( J )-D( I ) ) - ETA
- WORK( J ) = D( J ) + D( I ) + ETA
+ DELTA( J ) = ( D( J )-D( I ) ) - TAU
+ WORK( J ) = D( J ) + D( I ) + TAU
30 CONTINUE
*
* Evaluate PSI and the derivative DPSI
PHI = Z( N )*TEMP
DPHI = TEMP*TEMP
ERRETM = EIGHT*( -PHI-PSI ) + ERRETM - PHI + RHOINV +
- $ ABS( TAU )*( DPSI+DPHI )
+ $ ABS( TAU2 )*( DPSI+DPHI )
*
W = RHOINV + PHI + PSI
*
IF( TEMP.GT.RHO )
$ ETA = RHO + DTNSQ
*
- TAU = TAU + ETA
ETA = ETA / ( SIGMA+SQRT( ETA+SIGMA*SIGMA ) )
+ TAU = TAU + ETA
+ SIGMA = SIGMA + ETA
+*
DO 50 J = 1, N
DELTA( J ) = DELTA( J ) - ETA
WORK( J ) = WORK( J ) + ETA
50 CONTINUE
-*
- SIGMA = SIGMA + ETA
*
* Evaluate PSI and the derivative DPSI
*
*
* Evaluate PHI and the derivative DPHI
*
- TEMP = Z( N ) / ( WORK( N )*DELTA( N ) )
+ TAU2 = WORK( N )*DELTA( N )
+ TEMP = Z( N ) / TAU2
PHI = Z( N )*TEMP
DPHI = TEMP*TEMP
ERRETM = EIGHT*( -PHI-PSI ) + ERRETM - PHI + RHOINV +
- $ ABS( TAU )*( DPSI+DPHI )
+ $ ABS( TAU2 )*( DPSI+DPHI )
*
W = RHOINV + PHI + PSI
*
IF( TEMP.LE.ZERO )
$ ETA = ETA / TWO
*
- TAU = TAU + ETA
ETA = ETA / ( SIGMA+SQRT( ETA+SIGMA*SIGMA ) )
+ TAU = TAU + ETA
+ SIGMA = SIGMA + ETA
+*
DO 70 J = 1, N
DELTA( J ) = DELTA( J ) - ETA
WORK( J ) = WORK( J ) + ETA
70 CONTINUE
-*
- SIGMA = SIGMA + ETA
*
* Evaluate PSI and the derivative DPSI
*
*
* Evaluate PHI and the derivative DPHI
*
- TEMP = Z( N ) / ( WORK( N )*DELTA( N ) )
+ TAU2 = WORK( N )*DELTA( N )
+ TEMP = Z( N ) / TAU2
PHI = Z( N )*TEMP
DPHI = TEMP*TEMP
ERRETM = EIGHT*( -PHI-PSI ) + ERRETM - PHI + RHOINV +
- $ ABS( TAU )*( DPSI+DPHI )
+ $ ABS( TAU2 )*( DPSI+DPHI )
*
W = RHOINV + PHI + PSI
90 CONTINUE
*
DELSQ = ( D( IP1 )-D( I ) )*( D( IP1 )+D( I ) )
DELSQ2 = DELSQ / TWO
- TEMP = DELSQ2 / ( D( I )+SQRT( D( I )*D( I )+DELSQ2 ) )
+ SQ2=SQRT( ( D( I )*D( I )+D( IP1 )*D( IP1 ) ) / TWO )
+ TEMP = DELSQ2 / ( D( I )+SQ2 )
DO 100 J = 1, N
WORK( J ) = D( J ) + D( I ) + TEMP
DELTA( J ) = ( D( J )-D( I ) ) - TEMP
W = C + Z( I )*Z( I ) / ( WORK( I )*DELTA( I ) ) +
$ Z( IP1 )*Z( IP1 ) / ( WORK( IP1 )*DELTA( IP1 ) )
*
+ GEOMAVG = .FALSE.
IF( W.GT.ZERO ) THEN
*
* d(i)^2 < the ith sigma^2 < (d(i)^2+d(i+1)^2)/2
* We choose d(i) as origin.
*
ORGATI = .TRUE.
- SG2LB = ZERO
- SG2UB = DELSQ2
+ II = I
+ SGLB = ZERO
+ SGUB = DELSQ2 / ( D( I )+SQ2 )
A = C*DELSQ + Z( I )*Z( I ) + Z( IP1 )*Z( IP1 )
B = Z( I )*Z( I )*DELSQ
IF( A.GT.ZERO ) THEN
- TAU = TWO*B / ( A+SQRT( ABS( A*A-FOUR*B*C ) ) )
+ TAU2 = TWO*B / ( A+SQRT( ABS( A*A-FOUR*B*C ) ) )
ELSE
- TAU = ( A-SQRT( ABS( A*A-FOUR*B*C ) ) ) / ( TWO*C )
+ TAU2 = ( A-SQRT( ABS( A*A-FOUR*B*C ) ) ) / ( TWO*C )
END IF
*
-* TAU now is an estimation of SIGMA^2 - D( I )^2. The
+* TAU2 now is an estimation of SIGMA^2 - D( I )^2. The
* following, however, is the corresponding estimation of
* SIGMA - D( I ).
*
- ETA = TAU / ( D( I )+SQRT( D( I )*D( I )+TAU ) )
+ TAU = TAU2 / ( D( I )+SQRT( D( I )*D( I )+TAU2 ) )
+ TEMP = SQRT(EPS)
+ IF( (D(I).LE.TEMP*D(IP1)).AND.(ABS(Z(I)).LE.TEMP)
+ $ .AND.(D(I).GT.ZERO) ) THEN
+ TAU = MIN( TEN*D(I), SGUB )
+ GEOMAVG = .TRUE.
+ END IF
ELSE
*
* (d(i)^2+d(i+1)^2)/2 <= the ith sigma^2 < d(i+1)^2/2
* We choose d(i+1) as origin.
*
ORGATI = .FALSE.
- SG2LB = -DELSQ2
- SG2UB = ZERO
+ II = IP1
+ SGLB = -DELSQ2 / ( D( II )+SQ2 )
+ SGUB = ZERO
A = C*DELSQ - Z( I )*Z( I ) - Z( IP1 )*Z( IP1 )
B = Z( IP1 )*Z( IP1 )*DELSQ
IF( A.LT.ZERO ) THEN
- TAU = TWO*B / ( A-SQRT( ABS( A*A+FOUR*B*C ) ) )
+ TAU2 = TWO*B / ( A-SQRT( ABS( A*A+FOUR*B*C ) ) )
ELSE
- TAU = -( A+SQRT( ABS( A*A+FOUR*B*C ) ) ) / ( TWO*C )
+ TAU2 = -( A+SQRT( ABS( A*A+FOUR*B*C ) ) ) / ( TWO*C )
END IF
*
-* TAU now is an estimation of SIGMA^2 - D( IP1 )^2. The
+* TAU2 now is an estimation of SIGMA^2 - D( IP1 )^2. The
* following, however, is the corresponding estimation of
* SIGMA - D( IP1 ).
*
- ETA = TAU / ( D( IP1 )+SQRT( ABS( D( IP1 )*D( IP1 )+
- $ TAU ) ) )
+ TAU = TAU2 / ( D( IP1 )+SQRT( ABS( D( IP1 )*D( IP1 )+
+ $ TAU2 ) ) )
END IF
*
- IF( ORGATI ) THEN
- II = I
- SIGMA = D( I ) + ETA
- DO 130 J = 1, N
- WORK( J ) = D( J ) + D( I ) + ETA
- DELTA( J ) = ( D( J )-D( I ) ) - ETA
- 130 CONTINUE
- ELSE
- II = I + 1
- SIGMA = D( IP1 ) + ETA
- DO 140 J = 1, N
- WORK( J ) = D( J ) + D( IP1 ) + ETA
- DELTA( J ) = ( D( J )-D( IP1 ) ) - ETA
- 140 CONTINUE
- END IF
+ SIGMA = D( II ) + TAU
+ DO 130 J = 1, N
+ WORK( J ) = D( J ) + D( II ) + TAU
+ DELTA( J ) = ( D( J )-D( II ) ) - TAU
+ 130 CONTINUE
IIM1 = II - 1
IIP1 = II + 1
*
TEMP = Z( II )*TEMP
W = W + TEMP
ERRETM = EIGHT*( PHI-PSI ) + ERRETM + TWO*RHOINV +
- $ THREE*ABS( TEMP ) + ABS( TAU )*DW
+ $ THREE*ABS( TEMP ) + ABS( TAU2 )*DW
*
* Test for convergence
*
END IF
*
IF( W.LE.ZERO ) THEN
- SG2LB = MAX( SG2LB, TAU )
+ SGLB = MAX( SGLB, TAU )
ELSE
- SG2UB = MIN( SG2UB, TAU )
+ SGUB = MIN( SGUB, TAU )
END IF
*
* Calculate the new step
DD( 2 ) = DELTA( II )*WORK( II )
DD( 3 ) = DTIIP
CALL DLAED6( NITER, ORGATI, C, DD, ZZ, W, ETA, INFO )
- IF( INFO.NE.0 )
- $ GO TO 240
+*
+ IF( INFO.NE.0 ) THEN
+*
+* If INFO is not 0, i.e., DLAED6 failed, switch back to 2 pole interpolation.
+*
+ SWTCH3 = .FALSE.
+ INFO = 0
+ DTIPSQ = WORK( IP1 )*DELTA( IP1 )
+ DTISQ = WORK( I )*DELTA( I )
+ IF( ORGATI ) THEN
+ C = W - DTIPSQ*DW + DELSQ*( Z( I ) / DTISQ )**2
+ ELSE
+ C = W - DTISQ*DW - DELSQ*( Z( IP1 ) / DTIPSQ )**2
+ END IF
+ A = ( DTIPSQ+DTISQ )*W - DTIPSQ*DTISQ*DW
+ B = DTIPSQ*DTISQ*W
+ IF( C.EQ.ZERO ) THEN
+ IF( A.EQ.ZERO ) THEN
+ IF( ORGATI ) THEN
+ A = Z( I )*Z( I ) + DTIPSQ*DTIPSQ*( DPSI+DPHI )
+ ELSE
+ A = Z( IP1 )*Z( IP1 ) + DTISQ*DTISQ*( DPSI+DPHI)
+ END IF
+ END IF
+ ETA = B / A
+ ELSE IF( A.LE.ZERO ) THEN
+ ETA = ( A-SQRT( ABS( A*A-FOUR*B*C ) ) ) / ( TWO*C )
+ ELSE
+ ETA = TWO*B / ( A+SQRT( ABS( A*A-FOUR*B*C ) ) )
+ END IF
+ END IF
END IF
*
* Note, eta should be positive if w is negative, and
*
IF( W*ETA.GE.ZERO )
$ ETA = -W / DW
- IF( ORGATI ) THEN
- TEMP1 = WORK( I )*DELTA( I )
- TEMP = ETA - TEMP1
- ELSE
- TEMP1 = WORK( IP1 )*DELTA( IP1 )
- TEMP = ETA - TEMP1
- END IF
- IF( TEMP.GT.SG2UB .OR. TEMP.LT.SG2LB ) THEN
+*
+ ETA = ETA / ( SIGMA+SQRT( SIGMA*SIGMA+ETA ) )
+ TEMP = TAU + ETA
+ IF( TEMP.GT.SGUB .OR. TEMP.LT.SGLB ) THEN
IF( W.LT.ZERO ) THEN
- ETA = ( SG2UB-TAU ) / TWO
+ ETA = ( SGUB-TAU ) / TWO
ELSE
- ETA = ( SG2LB-TAU ) / TWO
+ ETA = ( SGLB-TAU ) / TWO
+ END IF
+ IF( GEOMAVG ) THEN
+ IF( W .LT. ZERO ) THEN
+ IF( TAU .GT. ZERO ) THEN
+ ETA = SQRT(SGUB*TAU)-TAU
+ END IF
+ ELSE
+ IF( SGLB .GT. ZERO ) THEN
+ ETA = SQRT(SGLB*TAU)-TAU
+ END IF
+ END IF
END IF
END IF
-*
- TAU = TAU + ETA
- ETA = ETA / ( SIGMA+SQRT( SIGMA*SIGMA+ETA ) )
*
PREW = W
*
+ TAU = TAU + ETA
SIGMA = SIGMA + ETA
+*
DO 170 J = 1, N
WORK( J ) = WORK( J ) + ETA
DELTA( J ) = DELTA( J ) - ETA
ERRETM = ERRETM + PHI
190 CONTINUE
*
- TEMP = Z( II ) / ( WORK( II )*DELTA( II ) )
+ TAU2 = WORK( II )*DELTA( II )
+ TEMP = Z( II ) / TAU2
DW = DPSI + DPHI + TEMP*TEMP
TEMP = Z( II )*TEMP
W = RHOINV + PHI + PSI + TEMP
ERRETM = EIGHT*( PHI-PSI ) + ERRETM + TWO*RHOINV +
- $ THREE*ABS( TEMP ) + ABS( TAU )*DW
-*
- IF( W.LE.ZERO ) THEN
- SG2LB = MAX( SG2LB, TAU )
- ELSE
- SG2UB = MIN( SG2UB, TAU )
- END IF
+ $ THREE*ABS( TEMP ) + ABS( TAU2 )*DW
*
SWTCH = .FALSE.
IF( ORGATI ) THEN
* Test for convergence
*
IF( ABS( W ).LE.EPS*ERRETM ) THEN
+* $ .OR. (SGUB-SGLB).LE.EIGHT*ABS(SGUB+SGLB) ) THEN
GO TO 240
END IF
+*
+ IF( W.LE.ZERO ) THEN
+ SGLB = MAX( SGLB, TAU )
+ ELSE
+ SGUB = MIN( SGUB, TAU )
+ END IF
*
* Calculate the new step
*
DD( 2 ) = DELTA( II )*WORK( II )
DD( 3 ) = DTIIP
CALL DLAED6( NITER, ORGATI, C, DD, ZZ, W, ETA, INFO )
- IF( INFO.NE.0 )
- $ GO TO 240
+*
+ IF( INFO.NE.0 ) THEN
+*
+* If INFO is not 0, i.e., DLAED6 failed, switch back to two pole interpolation
+*
+ SWTCH3 = .FALSE.
+ INFO = 0
+ DTIPSQ = WORK( IP1 )*DELTA( IP1 )
+ DTISQ = WORK( I )*DELTA( I )
+ IF( .NOT.SWTCH ) THEN
+ IF( ORGATI ) THEN
+ C = W - DTIPSQ*DW + DELSQ*( Z( I )/DTISQ )**2
+ ELSE
+ C = W - DTISQ*DW - DELSQ*( Z( IP1 )/DTIPSQ )**2
+ END IF
+ ELSE
+ TEMP = Z( II ) / ( WORK( II )*DELTA( II ) )
+ IF( ORGATI ) THEN
+ DPSI = DPSI + TEMP*TEMP
+ ELSE
+ DPHI = DPHI + TEMP*TEMP
+ END IF
+ C = W - DTISQ*DPSI - DTIPSQ*DPHI
+ END IF
+ A = ( DTIPSQ+DTISQ )*W - DTIPSQ*DTISQ*DW
+ B = DTIPSQ*DTISQ*W
+ IF( C.EQ.ZERO ) THEN
+ IF( A.EQ.ZERO ) THEN
+ IF( .NOT.SWTCH ) THEN
+ IF( ORGATI ) THEN
+ A = Z( I )*Z( I ) + DTIPSQ*DTIPSQ*
+ $ ( DPSI+DPHI )
+ ELSE
+ A = Z( IP1 )*Z( IP1 ) +
+ $ DTISQ*DTISQ*( DPSI+DPHI )
+ END IF
+ ELSE
+ A = DTISQ*DTISQ*DPSI + DTIPSQ*DTIPSQ*DPHI
+ END IF
+ END IF
+ ETA = B / A
+ ELSE IF( A.LE.ZERO ) THEN
+ ETA = ( A-SQRT( ABS( A*A-FOUR*B*C ) ) ) / ( TWO*C )
+ ELSE
+ ETA = TWO*B / ( A+SQRT( ABS( A*A-FOUR*B*C ) ) )
+ END IF
+ END IF
END IF
*
* Note, eta should be positive if w is negative, and
*
IF( W*ETA.GE.ZERO )
$ ETA = -W / DW
- IF( ORGATI ) THEN
- TEMP1 = WORK( I )*DELTA( I )
- TEMP = ETA - TEMP1
- ELSE
- TEMP1 = WORK( IP1 )*DELTA( IP1 )
- TEMP = ETA - TEMP1
- END IF
- IF( TEMP.GT.SG2UB .OR. TEMP.LT.SG2LB ) THEN
+*
+ ETA = ETA / ( SIGMA+SQRT( SIGMA*SIGMA+ETA ) )
+ TEMP=TAU+ETA
+ IF( TEMP.GT.SGUB .OR. TEMP.LT.SGLB ) THEN
IF( W.LT.ZERO ) THEN
- ETA = ( SG2UB-TAU ) / TWO
+ ETA = ( SGUB-TAU ) / TWO
ELSE
- ETA = ( SG2LB-TAU ) / TWO
+ ETA = ( SGLB-TAU ) / TWO
+ END IF
+ IF( GEOMAVG ) THEN
+ IF( W .LT. ZERO ) THEN
+ IF( TAU .GT. ZERO ) THEN
+ ETA = SQRT(SGUB*TAU)-TAU
+ END IF
+ ELSE
+ IF( SGLB .GT. ZERO ) THEN
+ ETA = SQRT(SGLB*TAU)-TAU
+ END IF
+ END IF
END IF
END IF
*
- TAU = TAU + ETA
- ETA = ETA / ( SIGMA+SQRT( SIGMA*SIGMA+ETA ) )
+ PREW = W
*
+ TAU = TAU + ETA
SIGMA = SIGMA + ETA
+*
DO 200 J = 1, N
WORK( J ) = WORK( J ) + ETA
DELTA( J ) = DELTA( J ) - ETA
200 CONTINUE
-*
- PREW = W
*
* Evaluate PSI and the derivative DPSI
*
ERRETM = ERRETM + PHI
220 CONTINUE
*
- TEMP = Z( II ) / ( WORK( II )*DELTA( II ) )
+ TAU2 = WORK( II )*DELTA( II )
+ TEMP = Z( II ) / TAU2
DW = DPSI + DPHI + TEMP*TEMP
TEMP = Z( II )*TEMP
W = RHOINV + PHI + PSI + TEMP
ERRETM = EIGHT*( PHI-PSI ) + ERRETM + TWO*RHOINV +
- $ THREE*ABS( TEMP ) + ABS( TAU )*DW
+ $ THREE*ABS( TEMP ) + ABS( TAU2 )*DW
+*
IF( W*PREW.GT.ZERO .AND. ABS( W ).GT.ABS( PREW ) / TEN )
$ SWTCH = .NOT.SWTCH
-* I don't understand the following 5 lines in the first place. RCL 8/26/2012
-* IF( W.LE.ZERO ) THEN
-* SG2LB = MAX( SG2LB, TAU )
-* ELSE
-* SG2UB = MIN( SG2UB, TAU )
-* END IF
*
230 CONTINUE
*
*
* =========== DOCUMENTATION ===========
*
-* Online html documentation available at
-* http://www.netlib.org/lapack/explore-html/
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
-*> Download SLASD4 + dependencies
-*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slasd4.f">
-*> [TGZ]</a>
-*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slasd4.f">
-*> [ZIP]</a>
-*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slasd4.f">
+*> Download SLASD4 + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasd4.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasd4.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasd4.f">
*> [TXT]</a>
-*> \endhtmlonly
+*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE SLASD4( N, I, D, Z, DELTA, RHO, SIGMA, WORK, INFO )
-*
+*
* .. Scalar Arguments ..
* INTEGER I, INFO, N
* REAL RHO, SIGMA
* .. Array Arguments ..
* REAL D( * ), DELTA( * ), WORK( * ), Z( * )
* ..
-*
+*
*
*> \par Purpose:
* =============
*>
*> \param[in] Z
*> \verbatim
-*> Z is REAL array, dimension (N)
+*> Z is REAL array, dimension ( N )
*> The components of the updating vector.
*> \endverbatim
*>
*> \param[out] DELTA
*> \verbatim
-*> DELTA is REAL array, dimension (N)
+*> DELTA is REAL array, dimension ( N )
*> If N .ne. 1, DELTA contains (D(j) - sigma_I) in its j-th
*> component. If N = 1, then DELTA(1) = 1. The vector DELTA
*> contains the information necessary to construct the
*>
*> \param[out] WORK
*> \verbatim
-*> WORK is REAL array, dimension (N)
+*> WORK is REAL array, dimension ( N )
*> If N .ne. 1, WORK contains (D(j) + sigma_I) in its j-th
*> component. If N = 1, then WORK( 1 ) = 1.
*> \endverbatim
* Authors:
* ========
*
-*> \author Univ. of Tennessee
-*> \author Univ. of California Berkeley
-*> \author Univ. of Colorado Denver
-*> \author NAG Ltd.
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
*
*> \date August 2012
*
*
* .. Parameters ..
INTEGER MAXIT
-* set MAXIT to 40 from 64. RCL 8/26/2012
- PARAMETER ( MAXIT = 40 )
+ PARAMETER ( MAXIT = 400 )
REAL ZERO, ONE, TWO, THREE, FOUR, EIGHT, TEN
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0, TWO = 2.0E+0,
$ THREE = 3.0E+0, FOUR = 4.0E+0, EIGHT = 8.0E+0,
$ TEN = 10.0E+0 )
* ..
* .. Local Scalars ..
- LOGICAL ORGATI, SWTCH, SWTCH3
+ LOGICAL ORGATI, SWTCH, SWTCH3, GEOMAVG
INTEGER II, IIM1, IIP1, IP1, ITER, J, NITER
- REAL A, B, C, DELSQ, DELSQ2, DPHI, DPSI, DTIIM,
+ REAL A, B, C, DELSQ, DELSQ2, SQ2, DPHI, DPSI, DTIIM,
$ DTIIP, DTIPSQ, DTISQ, DTNSQ, DTNSQ1, DW, EPS,
- $ ERRETM, ETA, PHI, PREW, PSI, RHOINV, SG2LB,
- $ SG2UB, TAU, TEMP, TEMP1, TEMP2, W
+ $ ERRETM, ETA, PHI, PREW, PSI, RHOINV, SGLB,
+ $ SGUB, TAU, TAU2, TEMP, TEMP1, TEMP2, W
* ..
* .. Local Arrays ..
REAL DD( 3 ), ZZ( 3 )
$ ( D( N )-D( N-1 )+RHO / ( D( N )+TEMP1 ) ) ) +
$ Z( N )*Z( N ) / RHO
*
-* The following TAU is to approximate
+* The following TAU2 is to approximate
* SIGMA_n^2 - D( N )*D( N )
*
IF( C.LE.TEMP ) THEN
A = -C*DELSQ + Z( N-1 )*Z( N-1 ) + Z( N )*Z( N )
B = Z( N )*Z( N )*DELSQ
IF( A.LT.ZERO ) THEN
- TAU = TWO*B / ( SQRT( A*A+FOUR*B*C )-A )
+ TAU2 = TWO*B / ( SQRT( A*A+FOUR*B*C )-A )
ELSE
- TAU = ( A+SQRT( A*A+FOUR*B*C ) ) / ( TWO*C )
+ TAU2 = ( A+SQRT( A*A+FOUR*B*C ) ) / ( TWO*C )
END IF
END IF
*
* It can be proved that
-* D(N)^2+RHO/2 <= SIGMA_n^2 < D(N)^2+TAU <= D(N)^2+RHO
+* D(N)^2+RHO/2 <= SIGMA_n^2 < D(N)^2+TAU2 <= D(N)^2+RHO
*
ELSE
DELSQ = ( D( N )-D( N-1 ) )*( D( N )+D( N-1 ) )
A = -C*DELSQ + Z( N-1 )*Z( N-1 ) + Z( N )*Z( N )
B = Z( N )*Z( N )*DELSQ
*
-* The following TAU is to approximate
+* The following TAU2 is to approximate
* SIGMA_n^2 - D( N )*D( N )
*
IF( A.LT.ZERO ) THEN
- TAU = TWO*B / ( SQRT( A*A+FOUR*B*C )-A )
+ TAU2 = TWO*B / ( SQRT( A*A+FOUR*B*C )-A )
ELSE
- TAU = ( A+SQRT( A*A+FOUR*B*C ) ) / ( TWO*C )
+ TAU2 = ( A+SQRT( A*A+FOUR*B*C ) ) / ( TWO*C )
END IF
*
* It can be proved that
-* D(N)^2 < D(N)^2+TAU < SIGMA(N)^2 < D(N)^2+RHO/2
+* D(N)^2 < D(N)^2+TAU2 < SIGMA(N)^2 < D(N)^2+RHO/2
*
END IF
*
-* The following ETA is to approximate SIGMA_n - D( N )
+* The following TAU is to approximate SIGMA_n - D( N )
*
- ETA = TAU / ( D( N )+SQRT( D( N )*D( N )+TAU ) )
+ TAU = TAU2 / ( D( N )+SQRT( D( N )*D( N )+TAU2 ) )
*
- SIGMA = D( N ) + ETA
+ SIGMA = D( N ) + TAU
DO 30 J = 1, N
- DELTA( J ) = ( D( J )-D( I ) ) - ETA
- WORK( J ) = D( J ) + D( I ) + ETA
+ DELTA( J ) = ( D( J )-D( I ) ) - TAU
+ WORK( J ) = D( J ) + D( I ) + TAU
30 CONTINUE
*
* Evaluate PSI and the derivative DPSI
PHI = Z( N )*TEMP
DPHI = TEMP*TEMP
ERRETM = EIGHT*( -PHI-PSI ) + ERRETM - PHI + RHOINV +
- $ ABS( TAU )*( DPSI+DPHI )
+ $ ABS( TAU2 )*( DPSI+DPHI )
*
W = RHOINV + PHI + PSI
*
IF( TEMP.GT.RHO )
$ ETA = RHO + DTNSQ
*
- TAU = TAU + ETA
ETA = ETA / ( SIGMA+SQRT( ETA+SIGMA*SIGMA ) )
+ TAU = TAU + ETA
+ SIGMA = SIGMA + ETA
+*
DO 50 J = 1, N
DELTA( J ) = DELTA( J ) - ETA
WORK( J ) = WORK( J ) + ETA
50 CONTINUE
-*
- SIGMA = SIGMA + ETA
*
* Evaluate PSI and the derivative DPSI
*
*
* Evaluate PHI and the derivative DPHI
*
- TEMP = Z( N ) / ( WORK( N )*DELTA( N ) )
+ TAU2 = WORK( N )*DELTA( N )
+ TEMP = Z( N ) / TAU2
PHI = Z( N )*TEMP
DPHI = TEMP*TEMP
ERRETM = EIGHT*( -PHI-PSI ) + ERRETM - PHI + RHOINV +
- $ ABS( TAU )*( DPSI+DPHI )
+ $ ABS( TAU2 )*( DPSI+DPHI )
*
W = RHOINV + PHI + PSI
*
IF( TEMP.LE.ZERO )
$ ETA = ETA / TWO
*
- TAU = TAU + ETA
ETA = ETA / ( SIGMA+SQRT( ETA+SIGMA*SIGMA ) )
+ TAU = TAU + ETA
+ SIGMA = SIGMA + ETA
+*
DO 70 J = 1, N
DELTA( J ) = DELTA( J ) - ETA
WORK( J ) = WORK( J ) + ETA
70 CONTINUE
-*
- SIGMA = SIGMA + ETA
*
* Evaluate PSI and the derivative DPSI
*
*
* Evaluate PHI and the derivative DPHI
*
- TEMP = Z( N ) / ( WORK( N )*DELTA( N ) )
+ TAU2 = WORK( N )*DELTA( N )
+ TEMP = Z( N ) / TAU2
PHI = Z( N )*TEMP
DPHI = TEMP*TEMP
ERRETM = EIGHT*( -PHI-PSI ) + ERRETM - PHI + RHOINV +
- $ ABS( TAU )*( DPSI+DPHI )
+ $ ABS( TAU2 )*( DPSI+DPHI )
*
W = RHOINV + PHI + PSI
90 CONTINUE
*
DELSQ = ( D( IP1 )-D( I ) )*( D( IP1 )+D( I ) )
DELSQ2 = DELSQ / TWO
- TEMP = DELSQ2 / ( D( I )+SQRT( D( I )*D( I )+DELSQ2 ) )
+ SQ2=SQRT( ( D( I )*D( I )+D( IP1 )*D( IP1 ) ) / TWO )
+ TEMP = DELSQ2 / ( D( I )+SQ2 )
DO 100 J = 1, N
WORK( J ) = D( J ) + D( I ) + TEMP
DELTA( J ) = ( D( J )-D( I ) ) - TEMP
W = C + Z( I )*Z( I ) / ( WORK( I )*DELTA( I ) ) +
$ Z( IP1 )*Z( IP1 ) / ( WORK( IP1 )*DELTA( IP1 ) )
*
+ GEOMAVG = .FALSE.
IF( W.GT.ZERO ) THEN
*
* d(i)^2 < the ith sigma^2 < (d(i)^2+d(i+1)^2)/2
* We choose d(i) as origin.
*
ORGATI = .TRUE.
- SG2LB = ZERO
- SG2UB = DELSQ2
+ II = I
+ SGLB = ZERO
+ SGUB = DELSQ2 / ( D( I )+SQ2 )
A = C*DELSQ + Z( I )*Z( I ) + Z( IP1 )*Z( IP1 )
B = Z( I )*Z( I )*DELSQ
IF( A.GT.ZERO ) THEN
- TAU = TWO*B / ( A+SQRT( ABS( A*A-FOUR*B*C ) ) )
+ TAU2 = TWO*B / ( A+SQRT( ABS( A*A-FOUR*B*C ) ) )
ELSE
- TAU = ( A-SQRT( ABS( A*A-FOUR*B*C ) ) ) / ( TWO*C )
+ TAU2 = ( A-SQRT( ABS( A*A-FOUR*B*C ) ) ) / ( TWO*C )
END IF
*
-* TAU now is an estimation of SIGMA^2 - D( I )^2. The
+* TAU2 now is an estimation of SIGMA^2 - D( I )^2. The
* following, however, is the corresponding estimation of
* SIGMA - D( I ).
*
- ETA = TAU / ( D( I )+SQRT( D( I )*D( I )+TAU ) )
+ TAU = TAU2 / ( D( I )+SQRT( D( I )*D( I )+TAU2 ) )
+ TEMP = SQRT(EPS)
+ IF( (D(I).LE.TEMP*D(IP1)).AND.(ABS(Z(I)).LE.TEMP)
+ $ .AND.(D(I).GT.ZERO) ) THEN
+ TAU = MIN( TEN*D(I), SGUB )
+ GEOMAVG = .TRUE.
+ END IF
ELSE
*
* (d(i)^2+d(i+1)^2)/2 <= the ith sigma^2 < d(i+1)^2/2
* We choose d(i+1) as origin.
*
ORGATI = .FALSE.
- SG2LB = -DELSQ2
- SG2UB = ZERO
+ II = IP1
+ SGLB = -DELSQ2 / ( D( II )+SQ2 )
+ SGUB = ZERO
A = C*DELSQ - Z( I )*Z( I ) - Z( IP1 )*Z( IP1 )
B = Z( IP1 )*Z( IP1 )*DELSQ
IF( A.LT.ZERO ) THEN
- TAU = TWO*B / ( A-SQRT( ABS( A*A+FOUR*B*C ) ) )
+ TAU2 = TWO*B / ( A-SQRT( ABS( A*A+FOUR*B*C ) ) )
ELSE
- TAU = -( A+SQRT( ABS( A*A+FOUR*B*C ) ) ) / ( TWO*C )
+ TAU2 = -( A+SQRT( ABS( A*A+FOUR*B*C ) ) ) / ( TWO*C )
END IF
*
-* TAU now is an estimation of SIGMA^2 - D( IP1 )^2. The
+* TAU2 now is an estimation of SIGMA^2 - D( IP1 )^2. The
* following, however, is the corresponding estimation of
* SIGMA - D( IP1 ).
*
- ETA = TAU / ( D( IP1 )+SQRT( ABS( D( IP1 )*D( IP1 )+
- $ TAU ) ) )
+ TAU = TAU2 / ( D( IP1 )+SQRT( ABS( D( IP1 )*D( IP1 )+
+ $ TAU2 ) ) )
END IF
*
- IF( ORGATI ) THEN
- II = I
- SIGMA = D( I ) + ETA
- DO 130 J = 1, N
- WORK( J ) = D( J ) + D( I ) + ETA
- DELTA( J ) = ( D( J )-D( I ) ) - ETA
- 130 CONTINUE
- ELSE
- II = I + 1
- SIGMA = D( IP1 ) + ETA
- DO 140 J = 1, N
- WORK( J ) = D( J ) + D( IP1 ) + ETA
- DELTA( J ) = ( D( J )-D( IP1 ) ) - ETA
- 140 CONTINUE
- END IF
+ SIGMA = D( II ) + TAU
+ DO 130 J = 1, N
+ WORK( J ) = D( J ) + D( II ) + TAU
+ DELTA( J ) = ( D( J )-D( II ) ) - TAU
+ 130 CONTINUE
IIM1 = II - 1
IIP1 = II + 1
*
TEMP = Z( II )*TEMP
W = W + TEMP
ERRETM = EIGHT*( PHI-PSI ) + ERRETM + TWO*RHOINV +
- $ THREE*ABS( TEMP ) + ABS( TAU )*DW
+ $ THREE*ABS( TEMP ) + ABS( TAU2 )*DW
*
* Test for convergence
*
END IF
*
IF( W.LE.ZERO ) THEN
- SG2LB = MAX( SG2LB, TAU )
+ SGLB = MAX( SGLB, TAU )
ELSE
- SG2UB = MIN( SG2UB, TAU )
+ SGUB = MIN( SGUB, TAU )
END IF
*
* Calculate the new step
DD( 2 ) = DELTA( II )*WORK( II )
DD( 3 ) = DTIIP
CALL SLAED6( NITER, ORGATI, C, DD, ZZ, W, ETA, INFO )
- IF( INFO.NE.0 )
- $ GO TO 240
+*
+ IF( INFO.NE.0 ) THEN
+*
+* If INFO is not 0, i.e., SLAED6 failed, switch back to 2 pole interpolation.
+*
+ SWTCH3 = .FALSE.
+ INFO = 0
+ DTIPSQ = WORK( IP1 )*DELTA( IP1 )
+ DTISQ = WORK( I )*DELTA( I )
+ IF( ORGATI ) THEN
+ C = W - DTIPSQ*DW + DELSQ*( Z( I ) / DTISQ )**2
+ ELSE
+ C = W - DTISQ*DW - DELSQ*( Z( IP1 ) / DTIPSQ )**2
+ END IF
+ A = ( DTIPSQ+DTISQ )*W - DTIPSQ*DTISQ*DW
+ B = DTIPSQ*DTISQ*W
+ IF( C.EQ.ZERO ) THEN
+ IF( A.EQ.ZERO ) THEN
+ IF( ORGATI ) THEN
+ A = Z( I )*Z( I ) + DTIPSQ*DTIPSQ*( DPSI+DPHI )
+ ELSE
+ A = Z( IP1 )*Z( IP1 ) + DTISQ*DTISQ*( DPSI+DPHI)
+ END IF
+ END IF
+ ETA = B / A
+ ELSE IF( A.LE.ZERO ) THEN
+ ETA = ( A-SQRT( ABS( A*A-FOUR*B*C ) ) ) / ( TWO*C )
+ ELSE
+ ETA = TWO*B / ( A+SQRT( ABS( A*A-FOUR*B*C ) ) )
+ END IF
+ END IF
END IF
*
* Note, eta should be positive if w is negative, and
*
IF( W*ETA.GE.ZERO )
$ ETA = -W / DW
- IF( ORGATI ) THEN
- TEMP1 = WORK( I )*DELTA( I )
- TEMP = ETA - TEMP1
- ELSE
- TEMP1 = WORK( IP1 )*DELTA( IP1 )
- TEMP = ETA - TEMP1
- END IF
- IF( TEMP.GT.SG2UB .OR. TEMP.LT.SG2LB ) THEN
+*
+ ETA = ETA / ( SIGMA+SQRT( SIGMA*SIGMA+ETA ) )
+ TEMP = TAU + ETA
+ IF( TEMP.GT.SGUB .OR. TEMP.LT.SGLB ) THEN
IF( W.LT.ZERO ) THEN
- ETA = ( SG2UB-TAU ) / TWO
+ ETA = ( SGUB-TAU ) / TWO
ELSE
- ETA = ( SG2LB-TAU ) / TWO
+ ETA = ( SGLB-TAU ) / TWO
+ END IF
+ IF( GEOMAVG ) THEN
+ IF( W .LT. ZERO ) THEN
+ IF( TAU .GT. ZERO ) THEN
+ ETA = SQRT(SGUB*TAU)-TAU
+ END IF
+ ELSE
+ IF( SGLB .GT. ZERO ) THEN
+ ETA = SQRT(SGLB*TAU)-TAU
+ END IF
+ END IF
END IF
END IF
-*
- TAU = TAU + ETA
- ETA = ETA / ( SIGMA+SQRT( SIGMA*SIGMA+ETA ) )
*
PREW = W
*
+ TAU = TAU + ETA
SIGMA = SIGMA + ETA
+*
DO 170 J = 1, N
WORK( J ) = WORK( J ) + ETA
DELTA( J ) = DELTA( J ) - ETA
ERRETM = ERRETM + PHI
190 CONTINUE
*
- TEMP = Z( II ) / ( WORK( II )*DELTA( II ) )
+ TAU2 = WORK( II )*DELTA( II )
+ TEMP = Z( II ) / TAU2
DW = DPSI + DPHI + TEMP*TEMP
TEMP = Z( II )*TEMP
W = RHOINV + PHI + PSI + TEMP
ERRETM = EIGHT*( PHI-PSI ) + ERRETM + TWO*RHOINV +
- $ THREE*ABS( TEMP ) + ABS( TAU )*DW
-*
- IF( W.LE.ZERO ) THEN
- SG2LB = MAX( SG2LB, TAU )
- ELSE
- SG2UB = MIN( SG2UB, TAU )
- END IF
+ $ THREE*ABS( TEMP ) + ABS( TAU2 )*DW
*
SWTCH = .FALSE.
IF( ORGATI ) THEN
* Test for convergence
*
IF( ABS( W ).LE.EPS*ERRETM ) THEN
+* $ .OR. (SGUB-SGLB).LE.EIGHT*ABS(SGUB+SGLB) ) THEN
GO TO 240
END IF
+*
+ IF( W.LE.ZERO ) THEN
+ SGLB = MAX( SGLB, TAU )
+ ELSE
+ SGUB = MIN( SGUB, TAU )
+ END IF
*
* Calculate the new step
*
DD( 2 ) = DELTA( II )*WORK( II )
DD( 3 ) = DTIIP
CALL SLAED6( NITER, ORGATI, C, DD, ZZ, W, ETA, INFO )
- IF( INFO.NE.0 )
- $ GO TO 240
+*
+ IF( INFO.NE.0 ) THEN
+*
+* If INFO is not 0, i.e., SLAED6 failed, switch back to two pole interpolation
+*
+ SWTCH3 = .FALSE.
+ INFO = 0
+ DTIPSQ = WORK( IP1 )*DELTA( IP1 )
+ DTISQ = WORK( I )*DELTA( I )
+ IF( .NOT.SWTCH ) THEN
+ IF( ORGATI ) THEN
+ C = W - DTIPSQ*DW + DELSQ*( Z( I )/DTISQ )**2
+ ELSE
+ C = W - DTISQ*DW - DELSQ*( Z( IP1 )/DTIPSQ )**2
+ END IF
+ ELSE
+ TEMP = Z( II ) / ( WORK( II )*DELTA( II ) )
+ IF( ORGATI ) THEN
+ DPSI = DPSI + TEMP*TEMP
+ ELSE
+ DPHI = DPHI + TEMP*TEMP
+ END IF
+ C = W - DTISQ*DPSI - DTIPSQ*DPHI
+ END IF
+ A = ( DTIPSQ+DTISQ )*W - DTIPSQ*DTISQ*DW
+ B = DTIPSQ*DTISQ*W
+ IF( C.EQ.ZERO ) THEN
+ IF( A.EQ.ZERO ) THEN
+ IF( .NOT.SWTCH ) THEN
+ IF( ORGATI ) THEN
+ A = Z( I )*Z( I ) + DTIPSQ*DTIPSQ*
+ $ ( DPSI+DPHI )
+ ELSE
+ A = Z( IP1 )*Z( IP1 ) +
+ $ DTISQ*DTISQ*( DPSI+DPHI )
+ END IF
+ ELSE
+ A = DTISQ*DTISQ*DPSI + DTIPSQ*DTIPSQ*DPHI
+ END IF
+ END IF
+ ETA = B / A
+ ELSE IF( A.LE.ZERO ) THEN
+ ETA = ( A-SQRT( ABS( A*A-FOUR*B*C ) ) ) / ( TWO*C )
+ ELSE
+ ETA = TWO*B / ( A+SQRT( ABS( A*A-FOUR*B*C ) ) )
+ END IF
+ END IF
END IF
*
* Note, eta should be positive if w is negative, and
*
IF( W*ETA.GE.ZERO )
$ ETA = -W / DW
- IF( ORGATI ) THEN
- TEMP1 = WORK( I )*DELTA( I )
- TEMP = ETA - TEMP1
- ELSE
- TEMP1 = WORK( IP1 )*DELTA( IP1 )
- TEMP = ETA - TEMP1
- END IF
- IF( TEMP.GT.SG2UB .OR. TEMP.LT.SG2LB ) THEN
+*
+ ETA = ETA / ( SIGMA+SQRT( SIGMA*SIGMA+ETA ) )
+ TEMP=TAU+ETA
+ IF( TEMP.GT.SGUB .OR. TEMP.LT.SGLB ) THEN
IF( W.LT.ZERO ) THEN
- ETA = ( SG2UB-TAU ) / TWO
+ ETA = ( SGUB-TAU ) / TWO
ELSE
- ETA = ( SG2LB-TAU ) / TWO
+ ETA = ( SGLB-TAU ) / TWO
+ END IF
+ IF( GEOMAVG ) THEN
+ IF( W .LT. ZERO ) THEN
+ IF( TAU .GT. ZERO ) THEN
+ ETA = SQRT(SGUB*TAU)-TAU
+ END IF
+ ELSE
+ IF( SGLB .GT. ZERO ) THEN
+ ETA = SQRT(SGLB*TAU)-TAU
+ END IF
+ END IF
END IF
END IF
*
- TAU = TAU + ETA
- ETA = ETA / ( SIGMA+SQRT( SIGMA*SIGMA+ETA ) )
+ PREW = W
*
+ TAU = TAU + ETA
SIGMA = SIGMA + ETA
+*
DO 200 J = 1, N
WORK( J ) = WORK( J ) + ETA
DELTA( J ) = DELTA( J ) - ETA
200 CONTINUE
-*
- PREW = W
*
* Evaluate PSI and the derivative DPSI
*
ERRETM = ERRETM + PHI
220 CONTINUE
*
- TEMP = Z( II ) / ( WORK( II )*DELTA( II ) )
+ TAU2 = WORK( II )*DELTA( II )
+ TEMP = Z( II ) / TAU2
DW = DPSI + DPHI + TEMP*TEMP
TEMP = Z( II )*TEMP
W = RHOINV + PHI + PSI + TEMP
ERRETM = EIGHT*( PHI-PSI ) + ERRETM + TWO*RHOINV +
- $ THREE*ABS( TEMP ) + ABS( TAU )*DW
+ $ THREE*ABS( TEMP ) + ABS( TAU2 )*DW
+*
IF( W*PREW.GT.ZERO .AND. ABS( W ).GT.ABS( PREW ) / TEN )
$ SWTCH = .NOT.SWTCH
-* I don't understand the following 5 lines in the first place. RCL 8/26/2012
-* IF( W.LE.ZERO ) THEN
-* SG2LB = MAX( SG2LB, TAU )
-* ELSE
-* SG2UB = MIN( SG2UB, TAU )
-* END IF
*
230 CONTINUE
*
projects / platform / upstream / lapack.git / commitdiff