clarnv.f.html

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<pre>
      SUBROUTINE <a name="CLARNV.1"></a><a href="clarnv.f.html#CLARNV.1">CLARNV</a>( IDIST, ISEED, N, X )
<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            IDIST, N
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      INTEGER            ISEED( 4 )
      COMPLEX            X( * )
<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="CLARNV.18"></a><a href="clarnv.f.html#CLARNV.1">CLARNV</a> returns a vector of n random complex numbers from a uniform or
</span><span class="comment">*</span><span class="comment">  normal distribution.
</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">  IDIST   (input) INTEGER
</span><span class="comment">*</span><span class="comment">          Specifies the distribution of the random numbers:
</span><span class="comment">*</span><span class="comment">          = 1:  real and imaginary parts each uniform (0,1)
</span><span class="comment">*</span><span class="comment">          = 2:  real and imaginary parts each uniform (-1,1)
</span><span class="comment">*</span><span class="comment">          = 3:  real and imaginary parts each normal (0,1)
</span><span class="comment">*</span><span class="comment">          = 4:  uniformly distributed on the disc abs(z) &lt; 1
</span><span class="comment">*</span><span class="comment">          = 5:  uniformly distributed on the circle abs(z) = 1
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  ISEED   (input/output) INTEGER array, dimension (4)
</span><span class="comment">*</span><span class="comment">          On entry, the seed of the random number generator; the array
</span><span class="comment">*</span><span class="comment">          elements must be between 0 and 4095, and ISEED(4) must be
</span><span class="comment">*</span><span class="comment">          odd.
</span><span class="comment">*</span><span class="comment">          On exit, the seed is updated.
</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 random numbers to be generated.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  X       (output) COMPLEX array, dimension (N)
</span><span class="comment">*</span><span class="comment">          The generated random numbers.
</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">  This routine calls the auxiliary routine <a name="SLARUV.47"></a><a href="slaruv.f.html#SLARUV.1">SLARUV</a> to generate random
</span><span class="comment">*</span><span class="comment">  real numbers from a uniform (0,1) distribution, in batches of up to
</span><span class="comment">*</span><span class="comment">  128 using vectorisable code. The Box-Muller method is used to
</span><span class="comment">*</span><span class="comment">  transform numbers from a uniform to a normal distribution.
</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               ZERO, ONE, TWO
      PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0, TWO = 2.0E+0 )
      INTEGER            LV
      PARAMETER          ( LV = 128 )
      REAL               TWOPI
      PARAMETER          ( TWOPI = 6.2831853071795864769252867663E+0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      INTEGER            I, IL, IV
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Arrays ..
</span>      REAL               U( LV )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          CMPLX, EXP, LOG, MIN, SQRT
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           <a name="SLARUV.72"></a><a href="slaruv.f.html#SLARUV.1">SLARUV</a>
<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>      DO 60 IV = 1, N, LV / 2
         IL = MIN( LV / 2, N-IV+1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Call <a name="SLARUV.79"></a><a href="slaruv.f.html#SLARUV.1">SLARUV</a> to generate 2*IL real numbers from a uniform (0,1)
</span><span class="comment">*</span><span class="comment">        distribution (2*IL &lt;= LV)
</span><span class="comment">*</span><span class="comment">
</span>         CALL <a name="SLARUV.82"></a><a href="slaruv.f.html#SLARUV.1">SLARUV</a>( ISEED, 2*IL, U )
<span class="comment">*</span><span class="comment">
</span>         IF( IDIST.EQ.1 ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Copy generated numbers
</span><span class="comment">*</span><span class="comment">
</span>            DO 10 I = 1, IL
               X( IV+I-1 ) = CMPLX( U( 2*I-1 ), U( 2*I ) )
   10       CONTINUE
         ELSE IF( IDIST.EQ.2 ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Convert generated numbers to uniform (-1,1) distribution
</span><span class="comment">*</span><span class="comment">
</span>            DO 20 I = 1, IL
               X( IV+I-1 ) = CMPLX( TWO*U( 2*I-1 )-ONE,
     $                       TWO*U( 2*I )-ONE )
   20       CONTINUE
         ELSE IF( IDIST.EQ.3 ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Convert generated numbers to normal (0,1) distribution
</span><span class="comment">*</span><span class="comment">
</span>            DO 30 I = 1, IL
               X( IV+I-1 ) = SQRT( -TWO*LOG( U( 2*I-1 ) ) )*
     $                       EXP( CMPLX( ZERO, TWOPI*U( 2*I ) ) )
   30       CONTINUE
         ELSE IF( IDIST.EQ.4 ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Convert generated numbers to complex numbers uniformly
</span><span class="comment">*</span><span class="comment">           distributed on the unit disk
</span><span class="comment">*</span><span class="comment">
</span>            DO 40 I = 1, IL
               X( IV+I-1 ) = SQRT( U( 2*I-1 ) )*
     $                       EXP( CMPLX( ZERO, TWOPI*U( 2*I ) ) )
   40       CONTINUE
         ELSE IF( IDIST.EQ.5 ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Convert generated numbers to complex numbers uniformly
</span><span class="comment">*</span><span class="comment">           distributed on the unit circle
</span><span class="comment">*</span><span class="comment">
</span>            DO 50 I = 1, IL
               X( IV+I-1 ) = EXP( CMPLX( ZERO, TWOPI*U( 2*I ) ) )
   50       CONTINUE
         END IF
   60 CONTINUE
      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="CLARNV.128"></a><a href="clarnv.f.html#CLARNV.1">CLARNV</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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