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*> \brief \b ZLARNV returns a vector of random numbers from a uniform or normal distribution.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download ZLARNV + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlarnv.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlarnv.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlarnv.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE ZLARNV( IDIST, ISEED, N, X )
*
* .. Scalar Arguments ..
* INTEGER IDIST, N
* ..
* .. Array Arguments ..
* INTEGER ISEED( 4 )
* COMPLEX*16 X( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZLARNV returns a vector of n random complex numbers from a uniform or
*> normal distribution.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] IDIST
*> \verbatim
*> IDIST is INTEGER
*> Specifies the distribution of the random numbers:
*> = 1: real and imaginary parts each uniform (0,1)
*> = 2: real and imaginary parts each uniform (-1,1)
*> = 3: real and imaginary parts each normal (0,1)
*> = 4: uniformly distributed on the disc abs(z) < 1
*> = 5: uniformly distributed on the circle abs(z) = 1
*> \endverbatim
*>
*> \param[in,out] ISEED
*> \verbatim
*> ISEED is INTEGER array, dimension (4)
*> On entry, the seed of the random number generator; the array
*> elements must be between 0 and 4095, and ISEED(4) must be
*> odd.
*> On exit, the seed is updated.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of random numbers to be generated.
*> \endverbatim
*>
*> \param[out] X
*> \verbatim
*> X is COMPLEX*16 array, dimension (N)
*> The generated random numbers.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup complex16OTHERauxiliary
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> This routine calls the auxiliary routine DLARUV to generate random
*> real numbers from a uniform (0,1) distribution, in batches of up to
*> 128 using vectorisable code. The Box-Muller method is used to
*> transform numbers from a uniform to a normal distribution.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZLARNV( IDIST, ISEED, N, X )
*
* -- LAPACK auxiliary routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
*
* .. Scalar Arguments ..
INTEGER IDIST, N
* ..
* .. Array Arguments ..
INTEGER ISEED( 4 )
COMPLEX*16 X( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE, TWO
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0 )
INTEGER LV
PARAMETER ( LV = 128 )
DOUBLE PRECISION TWOPI
PARAMETER ( TWOPI = 6.2831853071795864769252867663D+0 )
* ..
* .. Local Scalars ..
INTEGER I, IL, IV
* ..
* .. Local Arrays ..
DOUBLE PRECISION U( LV )
* ..
* .. Intrinsic Functions ..
INTRINSIC DCMPLX, EXP, LOG, MIN, SQRT
* ..
* .. External Subroutines ..
EXTERNAL DLARUV
* ..
* .. Executable Statements ..
*
DO 60 IV = 1, N, LV / 2
IL = MIN( LV / 2, N-IV+1 )
*
* Call DLARUV to generate 2*IL real numbers from a uniform (0,1)
* distribution (2*IL <= LV)
*
CALL DLARUV( ISEED, 2*IL, U )
*
IF( IDIST.EQ.1 ) THEN
*
* Copy generated numbers
*
DO 10 I = 1, IL
X( IV+I-1 ) = DCMPLX( U( 2*I-1 ), U( 2*I ) )
10 CONTINUE
ELSE IF( IDIST.EQ.2 ) THEN
*
* Convert generated numbers to uniform (-1,1) distribution
*
DO 20 I = 1, IL
X( IV+I-1 ) = DCMPLX( TWO*U( 2*I-1 )-ONE,
$ TWO*U( 2*I )-ONE )
20 CONTINUE
ELSE IF( IDIST.EQ.3 ) THEN
*
* Convert generated numbers to normal (0,1) distribution
*
DO 30 I = 1, IL
X( IV+I-1 ) = SQRT( -TWO*LOG( U( 2*I-1 ) ) )*
$ EXP( DCMPLX( ZERO, TWOPI*U( 2*I ) ) )
30 CONTINUE
ELSE IF( IDIST.EQ.4 ) THEN
*
* Convert generated numbers to complex numbers uniformly
* distributed on the unit disk
*
DO 40 I = 1, IL
X( IV+I-1 ) = SQRT( U( 2*I-1 ) )*
$ EXP( DCMPLX( ZERO, TWOPI*U( 2*I ) ) )
40 CONTINUE
ELSE IF( IDIST.EQ.5 ) THEN
*
* Convert generated numbers to complex numbers uniformly
* distributed on the unit circle
*
DO 50 I = 1, IL
X( IV+I-1 ) = EXP( DCMPLX( ZERO, TWOPI*U( 2*I ) ) )
50 CONTINUE
END IF
60 CONTINUE
RETURN
*
* End of ZLARNV
*
END
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