clargv.f.html

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      SUBROUTINE <a name="CLARGV.1"></a><a href="clargv.f.html#CLARGV.1">CLARGV</a>( N, X, INCX, Y, INCY, C, INCC )
<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            INCC, INCX, INCY, N
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      REAL               C( * )
      COMPLEX            X( * ), Y( * )
<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="CLARGV.18"></a><a href="clargv.f.html#CLARGV.1">CLARGV</a> generates a vector of complex plane rotations with real
</span><span class="comment">*</span><span class="comment">  cosines, determined by elements of the complex vectors x and y.
</span><span class="comment">*</span><span class="comment">  For i = 1,2,...,n
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     (        c(i)   s(i) ) ( x(i) ) = ( r(i) )
</span><span class="comment">*</span><span class="comment">     ( -conjg(s(i))  c(i) ) ( y(i) ) = (   0  )
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     where c(i)**2 + ABS(s(i))**2 = 1
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  The following conventions are used (these are the same as in <a name="CLARTG.27"></a><a href="clartg.f.html#CLARTG.1">CLARTG</a>,
</span><span class="comment">*</span><span class="comment">  but differ from the BLAS1 routine CROTG):
</span><span class="comment">*</span><span class="comment">     If y(i)=0, then c(i)=1 and s(i)=0.
</span><span class="comment">*</span><span class="comment">     If x(i)=0, then c(i)=0 and s(i) is chosen so that r(i) is real.
</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">  N       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of plane rotations to be generated.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  X       (input/output) COMPLEX array, dimension (1+(N-1)*INCX)
</span><span class="comment">*</span><span class="comment">          On entry, the vector x.
</span><span class="comment">*</span><span class="comment">          On exit, x(i) is overwritten by r(i), for i = 1,...,n.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  INCX    (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The increment between elements of X. INCX &gt; 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Y       (input/output) COMPLEX array, dimension (1+(N-1)*INCY)
</span><span class="comment">*</span><span class="comment">          On entry, the vector y.
</span><span class="comment">*</span><span class="comment">          On exit, the sines of the plane rotations.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  INCY    (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The increment between elements of Y. INCY &gt; 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  C       (output) REAL array, dimension (1+(N-1)*INCC)
</span><span class="comment">*</span><span class="comment">          The cosines of the plane rotations.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  INCC    (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The increment between elements of C. INCC &gt; 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Further Details
</span><span class="comment">*</span><span class="comment">  ======= =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  6-6-96 - Modified with a new algorithm by W. Kahan and J. Demmel
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  This version has a few statements commented out for thread safety
</span><span class="comment">*</span><span class="comment">  (machine parameters are computed on each entry). 10 feb 03, SJH.
</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               TWO, ONE, ZERO
      PARAMETER          ( TWO = 2.0E+0, ONE = 1.0E+0, ZERO = 0.0E+0 )
      COMPLEX            CZERO
      PARAMETER          ( CZERO = ( 0.0E+0, 0.0E+0 ) )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span><span class="comment">*</span><span class="comment">     LOGICAL            FIRST
</span>      INTEGER            COUNT, I, IC, IX, IY, J
      REAL               CS, D, DI, DR, EPS, F2, F2S, G2, G2S, SAFMIN,
     $                   SAFMN2, SAFMX2, SCALE
      COMPLEX            F, FF, FS, G, GS, R, SN
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      REAL               <a name="SLAMCH.82"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>, <a name="SLAPY2.82"></a><a href="slapy2.f.html#SLAPY2.1">SLAPY2</a>
      EXTERNAL           <a name="SLAMCH.83"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>, <a name="SLAPY2.83"></a><a href="slapy2.f.html#SLAPY2.1">SLAPY2</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          ABS, AIMAG, CMPLX, CONJG, INT, LOG, MAX, REAL,
     $                   SQRT
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Statement Functions ..
</span>      REAL               ABS1, ABSSQ
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Save statement ..
</span><span class="comment">*</span><span class="comment">     SAVE               FIRST, SAFMX2, SAFMIN, SAFMN2
</span><span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Data statements ..
</span><span class="comment">*</span><span class="comment">     DATA               FIRST / .TRUE. /
</span><span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Statement Function definitions ..
</span>      ABS1( FF ) = MAX( ABS( REAL( FF ) ), ABS( AIMAG( FF ) ) )
      ABSSQ( FF ) = REAL( FF )**2 + AIMAG( FF )**2
<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><span class="comment">*</span><span class="comment">     IF( FIRST ) THEN
</span><span class="comment">*</span><span class="comment">        FIRST = .FALSE.
</span>         SAFMIN = <a name="SLAMCH.106"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>( <span class="string">'S'</span> )
         EPS = <a name="SLAMCH.107"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>( <span class="string">'E'</span> )
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