slazq3.f.html

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      SUBROUTINE <a name="SLAZQ3.1"></a><a href="slazq3.f.html#SLAZQ3.1">SLAZQ3</a>( I0, N0, Z, PP, DMIN, SIGMA, DESIG, QMAX, NFAIL,
     $                   ITER, NDIV, IEEE, TTYPE, DMIN1, DMIN2, DN, DN1,
     $                   DN2, TAU )
<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>      LOGICAL            IEEE
      INTEGER            I0, ITER, N0, NDIV, NFAIL, PP, TTYPE
      REAL               DESIG, DMIN, DMIN1, DMIN2, DN, DN1, DN2, QMAX,
     $                   SIGMA, TAU
<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="SLAZQ3.22"></a><a href="slazq3.f.html#SLAZQ3.1">SLAZQ3</a> checks for deflation, computes a shift (TAU) and calls dqds.
</span><span class="comment">*</span><span class="comment">  In case of failure it changes shifts, and tries again until output
</span><span class="comment">*</span><span class="comment">  is positive.
</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.
</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">  SIGMA  (output) REAL
</span><span class="comment">*</span><span class="comment">         Sum of shifts used in current segment.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  DESIG  (input/output) REAL
</span><span class="comment">*</span><span class="comment">         Lower order part of SIGMA
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  QMAX   (input) REAL
</span><span class="comment">*</span><span class="comment">         Maximum value of q.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  NFAIL  (output) INTEGER
</span><span class="comment">*</span><span class="comment">         Number of times shift was too big.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  ITER   (output) INTEGER
</span><span class="comment">*</span><span class="comment">         Number of iterations.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  NDIV   (output) INTEGER
</span><span class="comment">*</span><span class="comment">         Number of divisions.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  IEEE   (input) LOGICAL
</span><span class="comment">*</span><span class="comment">         Flag for IEEE or non IEEE arithmetic (passed to <a name="SLASQ5.63"></a><a href="slasq5.f.html#SLASQ5.1">SLASQ5</a>).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  TTYPE  (input/output) INTEGER
</span><span class="comment">*</span><span class="comment">         Shift type.  TTYPE is passed as an argument in order to save
</span><span class="comment">*</span><span class="comment">         its value between calls to <a name="SLAZQ3.67"></a><a href="slazq3.f.html#SLAZQ3.1">SLAZQ3</a>
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  DMIN1  (input/output) REAL
</span><span class="comment">*</span><span class="comment">  DMIN2  (input/output) REAL
</span><span class="comment">*</span><span class="comment">  DN     (input/output) REAL
</span><span class="comment">*</span><span class="comment">  DN1    (input/output) REAL
</span><span class="comment">*</span><span class="comment">  DN2    (input/output) REAL
</span><span class="comment">*</span><span class="comment">  TAU    (input/output) REAL
</span><span class="comment">*</span><span class="comment">         These are passed as arguments in order to save their values
</span><span class="comment">*</span><span class="comment">         between calls to <a name="SLAZQ3.76"></a><a href="slazq3.f.html#SLAZQ3.1">SLAZQ3</a>
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  This is a thread safe version of <a name="SLASQ3.78"></a><a href="slasq3.f.html#SLASQ3.1">SLASQ3</a>, which passes TTYPE, DMIN1,
</span><span class="comment">*</span><span class="comment">  DMIN2, DN, DN1. DN2 and TAU through the argument list in place of
</span><span class="comment">*</span><span class="comment">  declaring them in a SAVE statment.
</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">     .. Parameters ..
</span>      REAL               CBIAS
      PARAMETER          ( CBIAS = 1.50E0 )
      REAL               ZERO, QURTR, HALF, ONE, TWO, HUNDRD
      PARAMETER          ( ZERO = 0.0E0, QURTR = 0.250E0, HALF = 0.5E0,
     $                     ONE = 1.0E0, TWO = 2.0E0, HUNDRD = 100.0E0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      INTEGER            IPN4, J4, N0IN, NN
      REAL               EPS, G, S, SAFMIN, T, TEMP, TOL, TOL2
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           <a name="SLASQ5.96"></a><a href="slasq5.f.html#SLASQ5.1">SLASQ5</a>, <a name="SLASQ6.96"></a><a href="slasq6.f.html#SLASQ6.1">SLASQ6</a>, <a name="SLAZQ4.96"></a><a href="slazq4.f.html#SLAZQ4.1">SLAZQ4</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Function ..
</span>      REAL               <a name="SLAMCH.99"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>
      EXTERNAL           <a name="SLAMCH.100"></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          ABS, MIN, SQRT
<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>      N0IN   = N0
      EPS    = <a name="SLAMCH.108"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>( <span class="string">'Precision'</span> )
      SAFMIN = <a name="SLAMCH.109"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>( <span class="string">'Safe minimum'</span> )
      TOL    = EPS*HUNDRD
      TOL2   = TOL**2
      G      = ZERO
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Check for deflation.
</span><span class="comment">*</span><span class="comment">
</span>   10 CONTINUE
<span class="comment">*</span><span class="comment">
</span>      IF( N0.LT.I0 )
     $   RETURN
      IF( N0.EQ.I0 )
     $   GO TO 20
      NN = 4*N0 + PP
      IF( N0.EQ.( I0+1 ) )
     $   GO TO 40
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Check whether E(N0-1) is negligible, 1 eigenvalue.
</span><span class="comment">*</span><span class="comment">
</span>      IF( Z( NN-5 ).GT.TOL2*( SIGMA+Z( NN-3 ) ) .AND.
     $    Z( NN-2*PP-4 ).GT.TOL2*Z( NN-7 ) )
     $   GO TO 30
<span class="comment">*</span><span class="comment">
</span>   20 CONTINUE
<span class="comment">*</span><span class="comment">
</span>      Z( 4*N0-3 ) = Z( 4*N0+PP-3 ) + SIGMA
      N0 = N0 - 1
      GO TO 10
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Check  whether E(N0-2) is negligible, 2 eigenvalues.
</span><span class="comment">*</span><span class="comment">
</span>   30 CONTINUE
<span class="comment">*</span><span class="comment">
</span>      IF( Z( NN-9 ).GT.TOL2*SIGMA .AND.
     $    Z( NN-2*PP-8 ).GT.TOL2*Z( NN-11 ) )
     $   GO TO 50
<span class="comment">*</span><span class="comment">
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