sci2c arduino updated

1 files changed, 330 insertions, 0 deletions

diff --git a/src/fortran/lapack/dlazq4.f b/src/fortran/lapack/dlazq4.f
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+      SUBROUTINE DLAZQ4( I0, N0, Z, PP, N0IN, DMIN, DMIN1, DMIN2, DN,
+     $                   DN1, DN2, TAU, TTYPE, G )
+*
+*  -- LAPACK auxiliary routine (version 3.1) --
+*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
+*     November 2006
+*
+*     .. Scalar Arguments ..
+      INTEGER            I0, N0, N0IN, PP, TTYPE
+      DOUBLE PRECISION   DMIN, DMIN1, DMIN2, DN, DN1, DN2, G, TAU
+*     ..
+*     .. Array Arguments ..
+      DOUBLE PRECISION   Z( * )
+*     ..
+*
+*  Purpose
+*  =======
+*
+*  DLAZQ4 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.
+*
+*  Z     (input) DOUBLE PRECISION array, dimension ( 4*N )
+*        Z holds the qd array.
+*
+*  PP    (input) INTEGER
+*        PP=0 for ping, PP=1 for pong.
+*
+*  N0IN  (input) INTEGER
+*        The value of N0 at start of EIGTEST.
+*
+*  DMIN  (input) DOUBLE PRECISION
+*        Minimum value of d.
+*
+*  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 ).
+*
+*  DN    (input) DOUBLE PRECISION
+*        d(N)
+*
+*  DN1   (input) DOUBLE PRECISION
+*        d(N-1)
+*
+*  DN2   (input) DOUBLE PRECISION
+*        d(N-2)
+*
+*  TAU   (output) DOUBLE PRECISION
+*        This is the shift.
+*
+*  TTYPE (output) INTEGER
+*        Shift type.
+*
+*  G     (input/output) DOUBLE PRECISION
+*        G is passed as an argument in order to save its value between
+*        calls to DLAZQ4
+*
+*  Further Details
+*  ===============
+*  CNST1 = 9/16
+*
+*  This is a thread safe version of DLASQ4, which passes G through the
+*  argument list in place of declaring G in a SAVE statment.
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      DOUBLE PRECISION   CNST1, CNST2, CNST3
+      PARAMETER          ( CNST1 = 0.5630D0, CNST2 = 1.010D0,
+     $                   CNST3 = 1.050D0 )
+      DOUBLE PRECISION   QURTR, THIRD, HALF, ZERO, ONE, TWO, HUNDRD
+      PARAMETER          ( QURTR = 0.250D0, THIRD = 0.3330D0,
+     $                   HALF = 0.50D0, ZERO = 0.0D0, ONE = 1.0D0,
+     $                   TWO = 2.0D0, HUNDRD = 100.0D0 )
+*     ..
+*     .. Local Scalars ..
+      INTEGER            I4, NN, NP
+      DOUBLE PRECISION   A2, B1, B2, GAM, GAP1, GAP2, S
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          MAX, MIN, SQRT
+*     ..
+*     .. Executable Statements ..
+*
+*     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
+*       
+      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.
+*
+               TTYPE = -4
+               S = QURTR*DMIN
+               IF( DMIN.EQ.DN ) THEN
+                  GAM = DN
+                  A2 = ZERO
+                  IF( Z( NN-5 ) .GT. Z( NN-7 ) )
+     $               RETURN
+                  B2 = Z( NN-5 ) / Z( NN-7 )
+                  NP = NN - 9
+               ELSE
+                  NP = NN - 2*PP
+                  B2 = Z( NP-2 )
+                  GAM = DN1
+                  IF( Z( NP-4 ) .GT. Z( NP-2 ) )
+     $               RETURN
+                  A2 = Z( NP-4 ) / Z( NP-2 )
+                  IF( Z( NN-9 ) .GT. Z( NN-11 ) )
+     $               RETURN
+                  B2 = Z( NN-9 ) / Z( NN-11 )
+                  NP = NN - 13
+               END IF
+*
+*              Approximate contribution to norm squared from I < NN-1.
+*
+               A2 = A2 + B2
+               DO 10 I4 = NP, 4*I0 - 1 + PP, -4
+                  IF( B2.EQ.ZERO )
+     $               GO TO 20
+                  B1 = B2
+                  IF( Z( I4 ) .GT. Z( I4-2 ) )
+     $               RETURN
+                  B2 = B2*( Z( I4 ) / Z( I4-2 ) )
+                  A2 = A2 + B2
+                  IF( HUNDRD*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 )
+     $            S = GAM*( ONE-SQRT( A2 ) ) / ( ONE+A2 )
+            END IF
+         ELSE IF( DMIN.EQ.DN2 ) THEN
+*
+*           Case 5.
+*
+            TTYPE = -5
+            S = QURTR*DMIN
+*
+*           Compute contribution to norm squared from I > NN-2.
+*
+            NP = NN - 2*PP
+            B1 = Z( NP-2 )
+            B2 = Z( NP-6 )
+            GAM = DN2
+            IF( Z( NP-8 ).GT.B2 .OR. Z( NP-4 ).GT.B1 )
+     $         RETURN
+            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 )
+               A2 = A2 + B2
+               DO 30 I4 = NN - 17, 4*I0 - 1 + PP, -4
+                  IF( B2.EQ.ZERO )
+     $               GO TO 40
+                  B1 = B2
+                  IF( Z( I4 ) .GT. Z( I4-2 ) )
+     $               RETURN
+                  B2 = B2*( Z( I4 ) / Z( I4-2 ) )
+                  A2 = A2 + B2
+                  IF( HUNDRD*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 )
+     $         S = GAM*( ONE-SQRT( A2 ) ) / ( ONE+A2 )
+         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
+*
+      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.
+*
+            TTYPE = -7
+            S = THIRD*DMIN1
+            IF( Z( NN-5 ).GT.Z( NN-7 ) )
+     $         RETURN
+            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
+               IF( Z( I4 ).GT.Z( I4-2 ) )
+     $            RETURN
+               B1 = B1*( Z( I4 ) / Z( I4-2 ) )
+               B2 = B2 + B1
+               IF( HUNDRD*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( S, A2*( ONE-CNST2*A2*( B2 / GAP2 )*B2 ) )
+            ELSE 
+               S = MAX( S, A2*( ONE-CNST2*B2 ) )
+               TTYPE = -8
+            END IF
+         ELSE
+*
+*           Case 9.
+*
+            S = QURTR*DMIN1
+            IF( DMIN1.EQ.DN1 )
+     $         S = HALF*DMIN1
+            TTYPE = -9
+         END IF
+*
+      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 
+            TTYPE = -10
+            S = THIRD*DMIN2
+            IF( Z( NN-5 ).GT.Z( NN-7 ) )
+     $         RETURN
+            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
+               IF( Z( I4 ).GT.Z( I4-2 ) )
+     $            RETURN
+               B1 = B1*( Z( I4 ) / Z( I4-2 ) )
+               B2 = B2 + B1
+               IF( HUNDRD*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( S, A2*( ONE-CNST2*A2*( B2 / GAP2 )*B2 ) )
+            ELSE 
+               S = MAX( S, A2*( ONE-CNST2*B2 ) )
+            END IF
+         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 DLAZQ4
+*
+      END