Annotation of rpl/lapack/lapack/zlarnv.f, revision 1.18

1.11      bertrand    1: *> \brief \b ZLARNV returns a vector of random numbers from a uniform or normal distribution.
1.8       bertrand    2: *
                      3: *  =========== DOCUMENTATION ===========
                      4: *
1.15      bertrand    5: * Online html documentation available at
                      6: *            http://www.netlib.org/lapack/explore-html/
1.8       bertrand    7: *
                      8: *> \htmlonly
1.15      bertrand    9: *> Download ZLARNV + dependencies
                     10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlarnv.f">
                     11: *> [TGZ]</a>
                     12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlarnv.f">
                     13: *> [ZIP]</a>
                     14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlarnv.f">
1.8       bertrand   15: *> [TXT]</a>
1.15      bertrand   16: *> \endhtmlonly
1.8       bertrand   17: *
                     18: *  Definition:
                     19: *  ===========
                     20: *
                     21: *       SUBROUTINE ZLARNV( IDIST, ISEED, N, X )
1.15      bertrand   22: *
1.8       bertrand   23: *       .. Scalar Arguments ..
                     24: *       INTEGER            IDIST, N
                     25: *       ..
                     26: *       .. Array Arguments ..
                     27: *       INTEGER            ISEED( 4 )
                     28: *       COMPLEX*16         X( * )
                     29: *       ..
1.15      bertrand   30: *
1.8       bertrand   31: *
                     32: *> \par Purpose:
                     33: *  =============
                     34: *>
                     35: *> \verbatim
                     36: *>
                     37: *> ZLARNV returns a vector of n random complex numbers from a uniform or
                     38: *> normal distribution.
                     39: *> \endverbatim
                     40: *
                     41: *  Arguments:
                     42: *  ==========
                     43: *
                     44: *> \param[in] IDIST
                     45: *> \verbatim
                     46: *>          IDIST is INTEGER
                     47: *>          Specifies the distribution of the random numbers:
                     48: *>          = 1:  real and imaginary parts each uniform (0,1)
                     49: *>          = 2:  real and imaginary parts each uniform (-1,1)
                     50: *>          = 3:  real and imaginary parts each normal (0,1)
                     51: *>          = 4:  uniformly distributed on the disc abs(z) < 1
                     52: *>          = 5:  uniformly distributed on the circle abs(z) = 1
                     53: *> \endverbatim
                     54: *>
                     55: *> \param[in,out] ISEED
                     56: *> \verbatim
                     57: *>          ISEED is INTEGER array, dimension (4)
                     58: *>          On entry, the seed of the random number generator; the array
                     59: *>          elements must be between 0 and 4095, and ISEED(4) must be
                     60: *>          odd.
                     61: *>          On exit, the seed is updated.
                     62: *> \endverbatim
                     63: *>
                     64: *> \param[in] N
                     65: *> \verbatim
                     66: *>          N is INTEGER
                     67: *>          The number of random numbers to be generated.
                     68: *> \endverbatim
                     69: *>
                     70: *> \param[out] X
                     71: *> \verbatim
                     72: *>          X is COMPLEX*16 array, dimension (N)
                     73: *>          The generated random numbers.
                     74: *> \endverbatim
                     75: *
                     76: *  Authors:
                     77: *  ========
                     78: *
1.15      bertrand   79: *> \author Univ. of Tennessee
                     80: *> \author Univ. of California Berkeley
                     81: *> \author Univ. of Colorado Denver
                     82: *> \author NAG Ltd.
1.8       bertrand   83: *
                     84: *> \ingroup complex16OTHERauxiliary
                     85: *
                     86: *> \par Further Details:
                     87: *  =====================
                     88: *>
                     89: *> \verbatim
                     90: *>
                     91: *>  This routine calls the auxiliary routine DLARUV to generate random
                     92: *>  real numbers from a uniform (0,1) distribution, in batches of up to
                     93: *>  128 using vectorisable code. The Box-Muller method is used to
                     94: *>  transform numbers from a uniform to a normal distribution.
                     95: *> \endverbatim
                     96: *>
                     97: *  =====================================================================
1.1       bertrand   98:       SUBROUTINE ZLARNV( IDIST, ISEED, N, X )
                     99: *
1.18    ! bertrand  100: *  -- LAPACK auxiliary routine --
1.1       bertrand  101: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
                    102: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
                    103: *
                    104: *     .. Scalar Arguments ..
                    105:       INTEGER            IDIST, N
                    106: *     ..
                    107: *     .. Array Arguments ..
                    108:       INTEGER            ISEED( 4 )
                    109:       COMPLEX*16         X( * )
                    110: *     ..
                    111: *
                    112: *  =====================================================================
                    113: *
                    114: *     .. Parameters ..
                    115:       DOUBLE PRECISION   ZERO, ONE, TWO
                    116:       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0 )
                    117:       INTEGER            LV
                    118:       PARAMETER          ( LV = 128 )
                    119:       DOUBLE PRECISION   TWOPI
1.18    ! bertrand  120:       PARAMETER  ( TWOPI = 6.28318530717958647692528676655900576839D+0 )
1.1       bertrand  121: *     ..
                    122: *     .. Local Scalars ..
                    123:       INTEGER            I, IL, IV
                    124: *     ..
                    125: *     .. Local Arrays ..
                    126:       DOUBLE PRECISION   U( LV )
                    127: *     ..
                    128: *     .. Intrinsic Functions ..
                    129:       INTRINSIC          DCMPLX, EXP, LOG, MIN, SQRT
                    130: *     ..
                    131: *     .. External Subroutines ..
                    132:       EXTERNAL           DLARUV
                    133: *     ..
                    134: *     .. Executable Statements ..
                    135: *
                    136:       DO 60 IV = 1, N, LV / 2
                    137:          IL = MIN( LV / 2, N-IV+1 )
                    138: *
                    139: *        Call DLARUV to generate 2*IL real numbers from a uniform (0,1)
                    140: *        distribution (2*IL <= LV)
                    141: *
                    142:          CALL DLARUV( ISEED, 2*IL, U )
                    143: *
                    144:          IF( IDIST.EQ.1 ) THEN
                    145: *
                    146: *           Copy generated numbers
                    147: *
                    148:             DO 10 I = 1, IL
                    149:                X( IV+I-1 ) = DCMPLX( U( 2*I-1 ), U( 2*I ) )
                    150:    10       CONTINUE
                    151:          ELSE IF( IDIST.EQ.2 ) THEN
                    152: *
                    153: *           Convert generated numbers to uniform (-1,1) distribution
                    154: *
                    155:             DO 20 I = 1, IL
                    156:                X( IV+I-1 ) = DCMPLX( TWO*U( 2*I-1 )-ONE,
                    157:      $                       TWO*U( 2*I )-ONE )
                    158:    20       CONTINUE
                    159:          ELSE IF( IDIST.EQ.3 ) THEN
                    160: *
                    161: *           Convert generated numbers to normal (0,1) distribution
                    162: *
                    163:             DO 30 I = 1, IL
                    164:                X( IV+I-1 ) = SQRT( -TWO*LOG( U( 2*I-1 ) ) )*
                    165:      $                       EXP( DCMPLX( ZERO, TWOPI*U( 2*I ) ) )
                    166:    30       CONTINUE
                    167:          ELSE IF( IDIST.EQ.4 ) THEN
                    168: *
                    169: *           Convert generated numbers to complex numbers uniformly
                    170: *           distributed on the unit disk
                    171: *
                    172:             DO 40 I = 1, IL
                    173:                X( IV+I-1 ) = SQRT( U( 2*I-1 ) )*
                    174:      $                       EXP( DCMPLX( ZERO, TWOPI*U( 2*I ) ) )
                    175:    40       CONTINUE
                    176:          ELSE IF( IDIST.EQ.5 ) THEN
                    177: *
                    178: *           Convert generated numbers to complex numbers uniformly
                    179: *           distributed on the unit circle
                    180: *
                    181:             DO 50 I = 1, IL
                    182:                X( IV+I-1 ) = EXP( DCMPLX( ZERO, TWOPI*U( 2*I ) ) )
                    183:    50       CONTINUE
                    184:          END IF
                    185:    60 CONTINUE
                    186:       RETURN
                    187: *
                    188: *     End of ZLARNV
                    189: *
                    190:       END

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