--- a/libcruft/lapack/dlasq4.f	Tue Nov 02 06:57:16 1999 +0000
+++ b/libcruft/lapack/dlasq4.f	Wed Nov 03 19:54:52 1999 +0000
@@ -1,101 +1,310 @@
-      SUBROUTINE DLASQ4( N, Q, E, TAU, SUP )
+      SUBROUTINE DLASQ4( I0, N0, Z, PP, N0IN, DMIN, DMIN1, DMIN2, DN,
+     $                   DN1, DN2, TAU, TTYPE )
 *
-*  -- LAPACK routine (version 2.0) --
+*  -- LAPACK auxiliary routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     September 30, 1994
+*     June 30, 1999
 *
 *     .. Scalar Arguments ..
-      INTEGER            N
-      DOUBLE PRECISION   SUP, TAU
+      INTEGER            I0, N0, N0IN, PP, TTYPE
+      DOUBLE PRECISION   DMIN, DMIN1, DMIN2, DN, DN1, DN2, TAU
 *     ..
 *     .. Array Arguments ..
-      DOUBLE PRECISION   E( * ), Q( * )
+      DOUBLE PRECISION   Z( * )
 *     ..
 *
-*     Purpose
-*     =======
+*  Purpose
+*  =======
+*  DLASQ4 computes an approximation TAU to the smallest eigenvalue
+*  using values of d from the previous transform.
+*
+*  I0    (input) INTEGER
+*        First index.
+*
+*  N0    (input) INTEGER
+*        Last index.
 *
-*     DLASQ4 estimates TAU, the smallest eigenvalue of a matrix. This
-*     routine improves the input value of SUP which is an upper bound
-*     for the smallest eigenvalue for this matrix .
+*  Z     (input) DOUBLE PRECISION array, dimension ( 4*N )
+*        Z holds the qd array.
+*
+*  PP    (input) INTEGER
+*        PP=0 for ping, PP=1 for pong.
 *
-*     Arguments
-*     =========
+*  NOIN  (input) INTEGER
+*        The value of N0 at start of EIGTEST.
+*
+*  DMIN  (input) DOUBLE PRECISION
+*        Minimum value of d.
 *
-*  N       (input) INTEGER
-*          On entry, N specifies the number of rows and columns
-*          in the matrix. N must be at least 0.
+*  DMIN1 (input) DOUBLE PRECISION
+*        Minimum value of d, excluding D( N0 ).
+*
+*  DMIN2 (input) DOUBLE PRECISION
+*        Minimum value of d, excluding D( N0 ) and D( N0-1 ).
 *
-*  Q       (input) DOUBLE PRECISION array, dimension (N)
-*          Q array
+*  DN    (input) DOUBLE PRECISION
+*        d(N)
+*
+*  DN1   (input) DOUBLE PRECISION
+*        d(N-1)
 *
-*  E       (input) DOUBLE PRECISION array, dimension (N)
-*          E array
+*  DN2   (input) DOUBLE PRECISION
+*        d(N-2)
+*
+*  TAU   (output) DOUBLE PRECISION
+*        This is the shift.
 *
-*  TAU     (output) DOUBLE PRECISION
-*          Estimate of the shift
+*  TTYPE (output) INTEGER
+*        Shift type.
 *
-*  SUP     (input/output) DOUBLE PRECISION
-*          Upper bound for the smallest singular value
+*  Further Details
+*  ===============
+*  CNST1 = 9/16
 *
 *  =====================================================================
 *
 *     .. Parameters ..
-      DOUBLE PRECISION   ZERO
-      PARAMETER          ( ZERO = 0.0D+0 )
-      DOUBLE PRECISION   BIS, BIS1
-      PARAMETER          ( BIS = 0.9999D+0, BIS1 = 0.7D+0 )
-      INTEGER            IFLMAX
-      PARAMETER          ( IFLMAX = 5 )
+      DOUBLE PRECISION   CNST1, CNST2, CNST3
+      PARAMETER          ( CNST1 = 0.5630D0, CNST2 = 1.010D0,
+     $                   CNST3 = 1.050D0 )
+      DOUBLE PRECISION   QURTR, THIRD, HALF, ZERO, ONE, TWO, HNDRD
+      PARAMETER          ( QURTR = 0.250D0, THIRD = 0.3330D0,
+     $                   HALF = 0.50D0, ZERO = 0.0D0, ONE = 1.0D0,
+     $                   TWO = 2.0D0, HNDRD = 100.0D0 )
 *     ..
 *     .. Local Scalars ..
-      INTEGER            I, IFL
-      DOUBLE PRECISION   D, DM, XINF
+      INTEGER            I4, NN, NP
+      DOUBLE PRECISION   A2, B1, B2, G, GAM, GAP1, GAP2, S
 *     ..
 *     .. Intrinsic Functions ..
-      INTRINSIC          MAX, MIN
+      INTRINSIC          MAX, MIN, SQRT
+*     ..
+*     .. Save statement ..
+      SAVE               G
+*     ..
+*     .. Data statements ..
+      DATA               G / ZERO /
 *     ..
 *     .. Executable Statements ..
-      IFL = 1
-      SUP = MIN( SUP, Q( 1 ), Q( 2 ), Q( 3 ), Q( N ), Q( N-1 ),
-     $      Q( N-2 ) )
-      TAU = SUP*BIS
-      XINF = ZERO
-   10 CONTINUE
-      IF( IFL.EQ.IFLMAX ) THEN
-         TAU = XINF
+*
+*     A negative DMIN forces the shift to take that absolute value
+*     TTYPE records the type of shift.
+*
+      IF( DMIN.LE.ZERO ) THEN
+         TAU = -DMIN
+         TTYPE = -1
          RETURN
       END IF
-      D = Q( 1 ) - TAU
-      DM = D
-      DO 20 I = 1, N - 2
-         D = ( D / ( D+E( I ) ) )*Q( I+1 ) - TAU
-         IF( DM.GT.D )
-     $      DM = D
-         IF( D.LT.ZERO ) THEN
-            SUP = TAU
-            TAU = MAX( SUP*BIS1**IFL, D+TAU )
-            IFL = IFL + 1
-            GO TO 10
+*
+      NN = 4*N0 + PP
+      IF( N0IN.EQ.N0 ) THEN
+*
+*        No eigenvalues deflated.
+*
+         IF( DMIN.EQ.DN .OR. DMIN.EQ.DN1 ) THEN
+*
+            B1 = SQRT( Z( NN-3 ) )*SQRT( Z( NN-5 ) )
+            B2 = SQRT( Z( NN-7 ) )*SQRT( Z( NN-9 ) )
+            A2 = Z( NN-7 ) + Z( NN-5 )
+*
+*           Cases 2 and 3.
+*
+            IF( DMIN.EQ.DN .AND. DMIN1.EQ.DN1 ) THEN
+               GAP2 = DMIN2 - A2 - DMIN2*QURTR
+               IF( GAP2.GT.ZERO .AND. GAP2.GT.B2 ) THEN
+                  GAP1 = A2 - DN - ( B2 / GAP2 )*B2
+               ELSE
+                  GAP1 = A2 - DN - ( B1+B2 )
+               END IF
+               IF( GAP1.GT.ZERO .AND. GAP1.GT.B1 ) THEN
+                  S = MAX( DN-( B1 / GAP1 )*B1, HALF*DMIN )
+                  TTYPE = -2
+               ELSE
+                  S = ZERO
+                  IF( DN.GT.B1 )
+     $               S = DN - B1
+                  IF( A2.GT.( B1+B2 ) )
+     $               S = MIN( S, A2-( B1+B2 ) )
+                  S = MAX( S, THIRD*DMIN )
+                  TTYPE = -3
+               END IF
+            ELSE
+*
+*              Case 4.
+*
+               IF( DMIN.EQ.DN ) THEN
+                  GAM = DN
+                  A2 = ZERO
+                  B2 = Z( NN-5 ) / Z( NN-7 )
+                  NP = NN - 9
+               ELSE
+                  NP = NN - 2*PP
+                  B2 = Z( NP-2 )
+                  GAM = DN1
+                  A2 = Z( NP-4 ) / Z( NP-2 )
+                  B2 = Z( NN-9 ) / Z( NN-11 )
+                  NP = NN - 13
+               END IF
+*
+*              Approximate contribution to norm squared from I < NN-1.
+*
+               IF( B2.EQ.ZERO )
+     $            GO TO 20
+               A2 = A2 + B2
+               DO 10 I4 = NP, 4*I0 - 1 + PP, -4
+                  B1 = B2
+                  B2 = B2*( Z( I4 ) / Z( I4-2 ) )
+                  A2 = A2 + B2
+                  IF( HNDRD*MAX( B2, B1 ).LT.A2 .OR. CNST1.LT.A2 )
+     $               GO TO 20
+   10          CONTINUE
+   20          CONTINUE
+               A2 = CNST3*A2
+*
+*              Rayleigh quotient residual bound.
+*
+               IF( A2.LT.CNST1 ) THEN
+                  S = GAM*( ONE-SQRT( A2 ) ) / ( ONE+A2 )
+               ELSE
+                  S = QURTR*GAM
+               END IF
+               TTYPE = -4
+            END IF
+         ELSE IF( DMIN.EQ.DN2 ) THEN
+*
+*           Case 5.
+*
+*           Compute contribution to norm squared from I > NN-2.
+*
+            NP = NN - 2*PP
+            B1 = Z( NP-2 )
+            B2 = Z( NP-6 )
+            GAM = DN2
+            A2 = ( Z( NP-8 ) / B2 )*( ONE+Z( NP-4 ) / B1 )
+*
+*           Approximate contribution to norm squared from I < NN-2.
+*
+            IF( N0-I0.GT.2 ) THEN
+               B2 = Z( NN-13 ) / Z( NN-15 )
+               IF( B2.EQ.ZERO )
+     $            GO TO 40
+               A2 = A2 + B2
+               DO 30 I4 = NN - 17, 4*I0 - 1 + PP, -4
+                  B1 = B2
+                  B2 = B2*( Z( I4 ) / Z( I4-2 ) )
+                  A2 = A2 + B2
+                  IF( HNDRD*MAX( B2, B1 ).LT.A2 .OR. CNST1.LT.A2 )
+     $               GO TO 40
+   30          CONTINUE
+   40          CONTINUE
+               A2 = CNST3*A2
+            END IF
+*
+            IF( A2.LT.CNST1 ) THEN
+               S = GAM*( ONE-SQRT( A2 ) ) / ( ONE+A2 )
+            ELSE
+               S = QURTR*GAM / ( ONE+A2 )
+            END IF
+            TTYPE = -5
+         ELSE
+*
+*           Case 6, no information to guide us.
+*
+            IF( TTYPE.EQ.-6 ) THEN
+               G = G + THIRD*( ONE-G )
+            ELSE IF( TTYPE.EQ.-18 ) THEN
+               G = QURTR*THIRD
+            ELSE
+               G = QURTR
+            END IF
+            S = G*DMIN
+            TTYPE = -6
          END IF
-   20 CONTINUE
-      D = ( D / ( D+E( N-1 ) ) )*Q( N ) - TAU
-      IF( DM.GT.D )
-     $   DM = D
-      IF( D.LT.ZERO ) THEN
-         SUP = TAU
-         XINF = MAX( XINF, D+TAU )
-         IF( SUP*BIS1**IFL.LE.XINF ) THEN
-            TAU = XINF
+*
+      ELSE IF( N0IN.EQ.( N0+1 ) ) THEN
+*
+*        One eigenvalue just deflated. Use DMIN1, DN1 for DMIN and DN.
+*
+         IF( DMIN1.EQ.DN1 .AND. DMIN2.EQ.DN2 ) THEN
+*
+*           Cases 7 and 8.
+*
+            B1 = Z( NN-5 ) / Z( NN-7 )
+            B2 = B1
+            IF( B2.EQ.ZERO )
+     $         GO TO 60
+            DO 50 I4 = 4*N0 - 9 + PP, 4*I0 - 1 + PP, -4
+               A2 = B1
+               B1 = B1*( Z( I4 ) / Z( I4-2 ) )
+               B2 = B2 + B1
+               IF( HNDRD*MAX( B1, A2 ).LT.B2 )
+     $            GO TO 60
+   50       CONTINUE
+   60       CONTINUE
+            B2 = SQRT( CNST3*B2 )
+            A2 = DMIN1 / ( ONE+B2**2 )
+            GAP2 = HALF*DMIN2 - A2
+            IF( GAP2.GT.ZERO .AND. GAP2.GT.B2*A2 ) THEN
+               S = MAX( A2*( ONE-CNST2*A2*( B2 / GAP2 )*B2 ),
+     $             THIRD*DMIN1 )
+               TTYPE = -7
+            ELSE
+               S = MAX( A2*( ONE-CNST2*B2 ), THIRD*DMIN1 )
+               TTYPE = -8
+            END IF
          ELSE
-            TAU = SUP*BIS1**IFL
-            IFL = IFL + 1
-            GO TO 10
+*
+*           Case 9.
+*
+            S = QURTR*DMIN1
+            IF( DMIN1.EQ.DN1 )
+     $         S = HALF*DMIN1
+            TTYPE = -9
          END IF
-      ELSE
-         SUP = MIN( SUP, DM+TAU )
+*
+      ELSE IF( N0IN.EQ.( N0+2 ) ) THEN
+*
+*        Two eigenvalues deflated. Use DMIN2, DN2 for DMIN and DN.
+*
+*        Cases 10 and 11.
+*
+         IF( DMIN2.EQ.DN2 .AND. TWO*Z( NN-5 ).LT.Z( NN-7 ) ) THEN
+            B1 = Z( NN-5 ) / Z( NN-7 )
+            B2 = B1
+            IF( B2.EQ.ZERO )
+     $         GO TO 80
+            DO 70 I4 = 4*N0 - 9 + PP, 4*I0 - 1 + PP, -4
+               B1 = B1*( Z( I4 ) / Z( I4-2 ) )
+               B2 = B2 + B1
+               IF( HNDRD*B1.LT.B2 )
+     $            GO TO 80
+   70       CONTINUE
+   80       CONTINUE
+            B2 = SQRT( CNST3*B2 )
+            A2 = DMIN2 / ( ONE+B2**2 )
+            GAP2 = Z( NN-7 ) + Z( NN-9 ) -
+     $             SQRT( Z( NN-11 ) )*SQRT( Z( NN-9 ) ) - A2
+            IF( GAP2.GT.ZERO .AND. GAP2.GT.B2*A2 ) THEN
+               S = MAX( A2*( ONE-CNST2*A2*( B2 / GAP2 )*B2 ),
+     $             THIRD*DMIN2 )
+            ELSE
+               S = MAX( A2*( ONE-CNST2*B2 ), THIRD*DMIN2 )
+            END IF
+            TTYPE = -10
+         ELSE
+            S = QURTR*DMIN2
+            TTYPE = -11
+         END IF
+      ELSE IF( N0IN.GT.( N0+2 ) ) THEN
+*
+*        Case 12, more than two eigenvalues deflated. No information.
+*
+         S = ZERO
+         TTYPE = -12
       END IF
+*
+      TAU = S
       RETURN
 *
 *     End of DLASQ4