slaed4.f
来自「famous linear algebra library (LAPACK) p」· F 代码 · 共 845 行 · 第 1/2 页
F
845 行
C = RHOINV + PSI + PHI
W = C + Z( I )*Z( I ) / DELTA( I ) +
$ Z( IP1 )*Z( IP1 ) / DELTA( IP1 )
*
IF( W.GT.ZERO ) THEN
*
* d(i)< the ith eigenvalue < (d(i)+d(i+1))/2
*
* We choose d(i) as origin.
*
ORGATI = .TRUE.
A = C*DEL + Z( I )*Z( I ) + Z( IP1 )*Z( IP1 )
B = Z( I )*Z( I )*DEL
IF( A.GT.ZERO ) THEN
TAU = TWO*B / ( A+SQRT( ABS( A*A-FOUR*B*C ) ) )
ELSE
TAU = ( A-SQRT( ABS( A*A-FOUR*B*C ) ) ) / ( TWO*C )
END IF
DLTLB = ZERO
DLTUB = MIDPT
ELSE
*
* (d(i)+d(i+1))/2 <= the ith eigenvalue < d(i+1)
*
* We choose d(i+1) as origin.
*
ORGATI = .FALSE.
A = C*DEL - Z( I )*Z( I ) - Z( IP1 )*Z( IP1 )
B = Z( IP1 )*Z( IP1 )*DEL
IF( A.LT.ZERO ) THEN
TAU = TWO*B / ( A-SQRT( ABS( A*A+FOUR*B*C ) ) )
ELSE
TAU = -( A+SQRT( ABS( A*A+FOUR*B*C ) ) ) / ( TWO*C )
END IF
DLTLB = -MIDPT
DLTUB = ZERO
END IF
*
IF( ORGATI ) THEN
DO 130 J = 1, N
DELTA( J ) = ( D( J )-D( I ) ) - TAU
130 CONTINUE
ELSE
DO 140 J = 1, N
DELTA( J ) = ( D( J )-D( IP1 ) ) - TAU
140 CONTINUE
END IF
IF( ORGATI ) THEN
II = I
ELSE
II = I + 1
END IF
IIM1 = II - 1
IIP1 = II + 1
*
* Evaluate PSI and the derivative DPSI
*
DPSI = ZERO
PSI = ZERO
ERRETM = ZERO
DO 150 J = 1, IIM1
TEMP = Z( J ) / DELTA( J )
PSI = PSI + Z( J )*TEMP
DPSI = DPSI + TEMP*TEMP
ERRETM = ERRETM + PSI
150 CONTINUE
ERRETM = ABS( ERRETM )
*
* Evaluate PHI and the derivative DPHI
*
DPHI = ZERO
PHI = ZERO
DO 160 J = N, IIP1, -1
TEMP = Z( J ) / DELTA( J )
PHI = PHI + Z( J )*TEMP
DPHI = DPHI + TEMP*TEMP
ERRETM = ERRETM + PHI
160 CONTINUE
*
W = RHOINV + PHI + PSI
*
* W is the value of the secular function with
* its ii-th element removed.
*
SWTCH3 = .FALSE.
IF( ORGATI ) THEN
IF( W.LT.ZERO )
$ SWTCH3 = .TRUE.
ELSE
IF( W.GT.ZERO )
$ SWTCH3 = .TRUE.
END IF
IF( II.EQ.1 .OR. II.EQ.N )
$ SWTCH3 = .FALSE.
*
TEMP = Z( II ) / DELTA( II )
DW = DPSI + DPHI + TEMP*TEMP
TEMP = Z( II )*TEMP
W = W + TEMP
ERRETM = EIGHT*( PHI-PSI ) + ERRETM + TWO*RHOINV +
$ THREE*ABS( TEMP ) + ABS( TAU )*DW
*
* Test for convergence
*
IF( ABS( W ).LE.EPS*ERRETM ) THEN
IF( ORGATI ) THEN
DLAM = D( I ) + TAU
ELSE
DLAM = D( IP1 ) + TAU
END IF
GO TO 250
END IF
*
IF( W.LE.ZERO ) THEN
DLTLB = MAX( DLTLB, TAU )
ELSE
DLTUB = MIN( DLTUB, TAU )
END IF
*
* Calculate the new step
*
NITER = NITER + 1
IF( .NOT.SWTCH3 ) THEN
IF( ORGATI ) THEN
C = W - DELTA( IP1 )*DW - ( D( I )-D( IP1 ) )*
$ ( Z( I ) / DELTA( I ) )**2
ELSE
C = W - DELTA( I )*DW - ( D( IP1 )-D( I ) )*
$ ( Z( IP1 ) / DELTA( IP1 ) )**2
END IF
A = ( DELTA( I )+DELTA( IP1 ) )*W -
$ DELTA( I )*DELTA( IP1 )*DW
B = DELTA( I )*DELTA( IP1 )*W
IF( C.EQ.ZERO ) THEN
IF( A.EQ.ZERO ) THEN
IF( ORGATI ) THEN
A = Z( I )*Z( I ) + DELTA( IP1 )*DELTA( IP1 )*
$ ( DPSI+DPHI )
ELSE
A = Z( IP1 )*Z( IP1 ) + DELTA( I )*DELTA( I )*
$ ( 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
ELSE
*
* Interpolation using THREE most relevant poles
*
TEMP = RHOINV + PSI + PHI
IF( ORGATI ) THEN
TEMP1 = Z( IIM1 ) / DELTA( IIM1 )
TEMP1 = TEMP1*TEMP1
C = TEMP - DELTA( IIP1 )*( DPSI+DPHI ) -
$ ( D( IIM1 )-D( IIP1 ) )*TEMP1
ZZ( 1 ) = Z( IIM1 )*Z( IIM1 )
ZZ( 3 ) = DELTA( IIP1 )*DELTA( IIP1 )*
$ ( ( DPSI-TEMP1 )+DPHI )
ELSE
TEMP1 = Z( IIP1 ) / DELTA( IIP1 )
TEMP1 = TEMP1*TEMP1
C = TEMP - DELTA( IIM1 )*( DPSI+DPHI ) -
$ ( D( IIP1 )-D( IIM1 ) )*TEMP1
ZZ( 1 ) = DELTA( IIM1 )*DELTA( IIM1 )*
$ ( DPSI+( DPHI-TEMP1 ) )
ZZ( 3 ) = Z( IIP1 )*Z( IIP1 )
END IF
ZZ( 2 ) = Z( II )*Z( II )
CALL SLAED6( NITER, ORGATI, C, DELTA( IIM1 ), ZZ, W, ETA,
$ INFO )
IF( INFO.NE.0 )
$ GO TO 250
END IF
*
* Note, eta should be positive if w is negative, and
* eta should be negative otherwise. However,
* if for some reason caused by roundoff, eta*w > 0,
* we simply use one Newton step instead. This way
* will guarantee eta*w < 0.
*
IF( W*ETA.GE.ZERO )
$ ETA = -W / DW
TEMP = TAU + ETA
IF( TEMP.GT.DLTUB .OR. TEMP.LT.DLTLB ) THEN
IF( W.LT.ZERO ) THEN
ETA = ( DLTUB-TAU ) / TWO
ELSE
ETA = ( DLTLB-TAU ) / TWO
END IF
END IF
*
PREW = W
*
DO 180 J = 1, N
DELTA( J ) = DELTA( J ) - ETA
180 CONTINUE
*
* Evaluate PSI and the derivative DPSI
*
DPSI = ZERO
PSI = ZERO
ERRETM = ZERO
DO 190 J = 1, IIM1
TEMP = Z( J ) / DELTA( J )
PSI = PSI + Z( J )*TEMP
DPSI = DPSI + TEMP*TEMP
ERRETM = ERRETM + PSI
190 CONTINUE
ERRETM = ABS( ERRETM )
*
* Evaluate PHI and the derivative DPHI
*
DPHI = ZERO
PHI = ZERO
DO 200 J = N, IIP1, -1
TEMP = Z( J ) / DELTA( J )
PHI = PHI + Z( J )*TEMP
DPHI = DPHI + TEMP*TEMP
ERRETM = ERRETM + PHI
200 CONTINUE
*
TEMP = Z( II ) / DELTA( II )
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+ETA )*DW
*
SWTCH = .FALSE.
IF( ORGATI ) THEN
IF( -W.GT.ABS( PREW ) / TEN )
$ SWTCH = .TRUE.
ELSE
IF( W.GT.ABS( PREW ) / TEN )
$ SWTCH = .TRUE.
END IF
*
TAU = TAU + ETA
*
* Main loop to update the values of the array DELTA
*
ITER = NITER + 1
*
DO 240 NITER = ITER, MAXIT
*
* Test for convergence
*
IF( ABS( W ).LE.EPS*ERRETM ) THEN
IF( ORGATI ) THEN
DLAM = D( I ) + TAU
ELSE
DLAM = D( IP1 ) + TAU
END IF
GO TO 250
END IF
*
IF( W.LE.ZERO ) THEN
DLTLB = MAX( DLTLB, TAU )
ELSE
DLTUB = MIN( DLTUB, TAU )
END IF
*
* Calculate the new step
*
IF( .NOT.SWTCH3 ) THEN
IF( .NOT.SWTCH ) THEN
IF( ORGATI ) THEN
C = W - DELTA( IP1 )*DW -
$ ( D( I )-D( IP1 ) )*( Z( I ) / DELTA( I ) )**2
ELSE
C = W - DELTA( I )*DW - ( D( IP1 )-D( I ) )*
$ ( Z( IP1 ) / DELTA( IP1 ) )**2
END IF
ELSE
TEMP = Z( II ) / DELTA( II )
IF( ORGATI ) THEN
DPSI = DPSI + TEMP*TEMP
ELSE
DPHI = DPHI + TEMP*TEMP
END IF
C = W - DELTA( I )*DPSI - DELTA( IP1 )*DPHI
END IF
A = ( DELTA( I )+DELTA( IP1 ) )*W -
$ DELTA( I )*DELTA( IP1 )*DW
B = DELTA( I )*DELTA( IP1 )*W
IF( C.EQ.ZERO ) THEN
IF( A.EQ.ZERO ) THEN
IF( .NOT.SWTCH ) THEN
IF( ORGATI ) THEN
A = Z( I )*Z( I ) + DELTA( IP1 )*
$ DELTA( IP1 )*( DPSI+DPHI )
ELSE
A = Z( IP1 )*Z( IP1 ) +
$ DELTA( I )*DELTA( I )*( DPSI+DPHI )
END IF
ELSE
A = DELTA( I )*DELTA( I )*DPSI +
$ DELTA( IP1 )*DELTA( IP1 )*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
ELSE
*
* Interpolation using THREE most relevant poles
*
TEMP = RHOINV + PSI + PHI
IF( SWTCH ) THEN
C = TEMP - DELTA( IIM1 )*DPSI - DELTA( IIP1 )*DPHI
ZZ( 1 ) = DELTA( IIM1 )*DELTA( IIM1 )*DPSI
ZZ( 3 ) = DELTA( IIP1 )*DELTA( IIP1 )*DPHI
ELSE
IF( ORGATI ) THEN
TEMP1 = Z( IIM1 ) / DELTA( IIM1 )
TEMP1 = TEMP1*TEMP1
C = TEMP - DELTA( IIP1 )*( DPSI+DPHI ) -
$ ( D( IIM1 )-D( IIP1 ) )*TEMP1
ZZ( 1 ) = Z( IIM1 )*Z( IIM1 )
ZZ( 3 ) = DELTA( IIP1 )*DELTA( IIP1 )*
$ ( ( DPSI-TEMP1 )+DPHI )
ELSE
TEMP1 = Z( IIP1 ) / DELTA( IIP1 )
TEMP1 = TEMP1*TEMP1
C = TEMP - DELTA( IIM1 )*( DPSI+DPHI ) -
$ ( D( IIP1 )-D( IIM1 ) )*TEMP1
ZZ( 1 ) = DELTA( IIM1 )*DELTA( IIM1 )*
$ ( DPSI+( DPHI-TEMP1 ) )
ZZ( 3 ) = Z( IIP1 )*Z( IIP1 )
END IF
END IF
CALL SLAED6( NITER, ORGATI, C, DELTA( IIM1 ), ZZ, W, ETA,
$ INFO )
IF( INFO.NE.0 )
$ GO TO 250
END IF
*
* Note, eta should be positive if w is negative, and
* eta should be negative otherwise. However,
* if for some reason caused by roundoff, eta*w > 0,
* we simply use one Newton step instead. This way
* will guarantee eta*w < 0.
*
IF( W*ETA.GE.ZERO )
$ ETA = -W / DW
TEMP = TAU + ETA
IF( TEMP.GT.DLTUB .OR. TEMP.LT.DLTLB ) THEN
IF( W.LT.ZERO ) THEN
ETA = ( DLTUB-TAU ) / TWO
ELSE
ETA = ( DLTLB-TAU ) / TWO
END IF
END IF
*
DO 210 J = 1, N
DELTA( J ) = DELTA( J ) - ETA
210 CONTINUE
*
TAU = TAU + ETA
PREW = W
*
* Evaluate PSI and the derivative DPSI
*
DPSI = ZERO
PSI = ZERO
ERRETM = ZERO
DO 220 J = 1, IIM1
TEMP = Z( J ) / DELTA( J )
PSI = PSI + Z( J )*TEMP
DPSI = DPSI + TEMP*TEMP
ERRETM = ERRETM + PSI
220 CONTINUE
ERRETM = ABS( ERRETM )
*
* Evaluate PHI and the derivative DPHI
*
DPHI = ZERO
PHI = ZERO
DO 230 J = N, IIP1, -1
TEMP = Z( J ) / DELTA( J )
PHI = PHI + Z( J )*TEMP
DPHI = DPHI + TEMP*TEMP
ERRETM = ERRETM + PHI
230 CONTINUE
*
TEMP = Z( II ) / DELTA( II )
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*PREW.GT.ZERO .AND. ABS( W ).GT.ABS( PREW ) / TEN )
$ SWTCH = .NOT.SWTCH
*
240 CONTINUE
*
* Return with INFO = 1, NITER = MAXIT and not converged
*
INFO = 1
IF( ORGATI ) THEN
DLAM = D( I ) + TAU
ELSE
DLAM = D( IP1 ) + TAU
END IF
*
END IF
*
250 CONTINUE
*
RETURN
*
* End of SLAED4
*
END
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