slasq6.f.html

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      SUBROUTINE <a name="SLASQ6.1"></a><a href="slasq6.f.html#SLASQ6.1">SLASQ6</a>( I0, N0, Z, PP, DMIN, DMIN1, DMIN2, DN,
     $                   DNM1, DNM2 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK auxiliary routine (version 3.1) --
</span><span class="comment">*</span><span class="comment">     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment">     November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      INTEGER            I0, N0, PP
      REAL               DMIN, DMIN1, DMIN2, DN, DNM1, DNM2
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      REAL               Z( * )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Purpose
</span><span class="comment">*</span><span class="comment">  =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  <a name="SLASQ6.19"></a><a href="slasq6.f.html#SLASQ6.1">SLASQ6</a> computes one dqd (shift equal to zero) transform in
</span><span class="comment">*</span><span class="comment">  ping-pong form, with protection against underflow and overflow.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Arguments
</span><span class="comment">*</span><span class="comment">  =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  I0    (input) INTEGER
</span><span class="comment">*</span><span class="comment">        First index.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  N0    (input) INTEGER
</span><span class="comment">*</span><span class="comment">        Last index.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Z     (input) REAL array, dimension ( 4*N )
</span><span class="comment">*</span><span class="comment">        Z holds the qd array. EMIN is stored in Z(4*N0) to avoid
</span><span class="comment">*</span><span class="comment">        an extra argument.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  PP    (input) INTEGER
</span><span class="comment">*</span><span class="comment">        PP=0 for ping, PP=1 for pong.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  DMIN  (output) REAL
</span><span class="comment">*</span><span class="comment">        Minimum value of d.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  DMIN1 (output) REAL
</span><span class="comment">*</span><span class="comment">        Minimum value of d, excluding D( N0 ).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  DMIN2 (output) REAL
</span><span class="comment">*</span><span class="comment">        Minimum value of d, excluding D( N0 ) and D( N0-1 ).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  DN    (output) REAL
</span><span class="comment">*</span><span class="comment">        d(N0), the last value of d.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  DNM1  (output) REAL
</span><span class="comment">*</span><span class="comment">        d(N0-1).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  DNM2  (output) REAL
</span><span class="comment">*</span><span class="comment">        d(N0-2).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Parameter ..
</span>      REAL               ZERO
      PARAMETER          ( ZERO = 0.0E0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      INTEGER            J4, J4P2
      REAL               D, EMIN, SAFMIN, TEMP
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Function ..
</span>      REAL               <a name="SLAMCH.67"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>
      EXTERNAL           <a name="SLAMCH.68"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          MIN
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span>      IF( ( N0-I0-1 ).LE.0 )
     $   RETURN
<span class="comment">*</span><span class="comment">
</span>      SAFMIN = <a name="SLAMCH.78"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>( <span class="string">'Safe minimum'</span> )
      J4 = 4*I0 + PP - 3
      EMIN = Z( J4+4 ) 
      D = Z( J4 )
      DMIN = D
<span class="comment">*</span><span class="comment">
</span>      IF( PP.EQ.0 ) THEN
         DO 10 J4 = 4*I0, 4*( N0-3 ), 4
            Z( J4-2 ) = D + Z( J4-1 ) 
            IF( Z( J4-2 ).EQ.ZERO ) THEN
               Z( J4 ) = ZERO
               D = Z( J4+1 )
               DMIN = D
               EMIN = ZERO
            ELSE IF( SAFMIN*Z( J4+1 ).LT.Z( J4-2 ) .AND.
     $               SAFMIN*Z( J4-2 ).LT.Z( J4+1 ) ) THEN
               TEMP = Z( J4+1 ) / Z( J4-2 )
               Z( J4 ) = Z( J4-1 )*TEMP
               D = D*TEMP
            ELSE 
               Z( J4 ) = Z( J4+1 )*( Z( J4-1 ) / Z( J4-2 ) )
               D = Z( J4+1 )*( D / Z( J4-2 ) )
            END IF
            DMIN = MIN( DMIN, D )
            EMIN = MIN( EMIN, Z( J4 ) )
   10    CONTINUE
      ELSE
         DO 20 J4 = 4*I0, 4*( N0-3 ), 4
            Z( J4-3 ) = D + Z( J4 ) 
            IF( Z( J4-3 ).EQ.ZERO ) THEN
               Z( J4-1 ) = ZERO
               D = Z( J4+2 )
               DMIN = D
               EMIN = ZERO
            ELSE IF( SAFMIN*Z( J4+2 ).LT.Z( J4-3 ) .AND.
     $               SAFMIN*Z( J4-3 ).LT.Z( J4+2 ) ) THEN
               TEMP = Z( J4+2 ) / Z( J4-3 )
               Z( J4-1 ) = Z( J4 )*TEMP
               D = D*TEMP
            ELSE 
               Z( J4-1 ) = Z( J4+2 )*( Z( J4 ) / Z( J4-3 ) )
               D = Z( J4+2 )*( D / Z( J4-3 ) )
            END IF
            DMIN = MIN( DMIN, D )
            EMIN = MIN( EMIN, Z( J4-1 ) )
   20    CONTINUE
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Unroll last two steps. 
</span><span class="comment">*</span><span class="comment">
</span>      DNM2 = D
      DMIN2 = DMIN
      J4 = 4*( N0-2 ) - PP
      J4P2 = J4 + 2*PP - 1
      Z( J4-2 ) = DNM2 + Z( J4P2 )
      IF( Z( J4-2 ).EQ.ZERO ) THEN
         Z( J4 ) = ZERO
         DNM1 = Z( J4P2+2 )
         DMIN = DNM1
         EMIN = ZERO
      ELSE IF( SAFMIN*Z( J4P2+2 ).LT.Z( J4-2 ) .AND.
     $         SAFMIN*Z( J4-2 ).LT.Z( J4P2+2 ) ) THEN
         TEMP = Z( J4P2+2 ) / Z( J4-2 )
         Z( J4 ) = Z( J4P2 )*TEMP
         DNM1 = DNM2*TEMP
      ELSE
         Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) )
         DNM1 = Z( J4P2+2 )*( DNM2 / Z( J4-2 ) )
      END IF
      DMIN = MIN( DMIN, DNM1 )
<span class="comment">*</span><span class="comment">
</span>      DMIN1 = DMIN
      J4 = J4 + 4
      J4P2 = J4 + 2*PP - 1
      Z( J4-2 ) = DNM1 + Z( J4P2 )
      IF( Z( J4-2 ).EQ.ZERO ) THEN
         Z( J4 ) = ZERO
         DN = Z( J4P2+2 )
         DMIN = DN
         EMIN = ZERO
      ELSE IF( SAFMIN*Z( J4P2+2 ).LT.Z( J4-2 ) .AND.
     $         SAFMIN*Z( J4-2 ).LT.Z( J4P2+2 ) ) THEN
         TEMP = Z( J4P2+2 ) / Z( J4-2 )
         Z( J4 ) = Z( J4P2 )*TEMP
         DN = DNM1*TEMP
      ELSE
         Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) )
         DN = Z( J4P2+2 )*( DNM1 / Z( J4-2 ) )
      END IF
      DMIN = MIN( DMIN, DN )
<span class="comment">*</span><span class="comment">
</span>      Z( J4+2 ) = DN
      Z( 4*N0-PP ) = EMIN
      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="SLASQ6.173"></a><a href="slasq6.f.html#SLASQ6.1">SLASQ6</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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