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Annotation of rpl/lapack/lapack/zlarnv.f, revision 1.1

1.1     ! bertrand    1:       SUBROUTINE ZLARNV( IDIST, ISEED, N, X )
        !             2: *
        !             3: *  -- LAPACK auxiliary routine (version 3.2) --
        !             4: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
        !             5: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
        !             6: *     November 2006
        !             7: *
        !             8: *     .. Scalar Arguments ..
        !             9:       INTEGER            IDIST, N
        !            10: *     ..
        !            11: *     .. Array Arguments ..
        !            12:       INTEGER            ISEED( 4 )
        !            13:       COMPLEX*16         X( * )
        !            14: *     ..
        !            15: *
        !            16: *  Purpose
        !            17: *  =======
        !            18: *
        !            19: *  ZLARNV returns a vector of n random complex numbers from a uniform or
        !            20: *  normal distribution.
        !            21: *
        !            22: *  Arguments
        !            23: *  =========
        !            24: *
        !            25: *  IDIST   (input) INTEGER
        !            26: *          Specifies the distribution of the random numbers:
        !            27: *          = 1:  real and imaginary parts each uniform (0,1)
        !            28: *          = 2:  real and imaginary parts each uniform (-1,1)
        !            29: *          = 3:  real and imaginary parts each normal (0,1)
        !            30: *          = 4:  uniformly distributed on the disc abs(z) < 1
        !            31: *          = 5:  uniformly distributed on the circle abs(z) = 1
        !            32: *
        !            33: *  ISEED   (input/output) INTEGER array, dimension (4)
        !            34: *          On entry, the seed of the random number generator; the array
        !            35: *          elements must be between 0 and 4095, and ISEED(4) must be
        !            36: *          odd.
        !            37: *          On exit, the seed is updated.
        !            38: *
        !            39: *  N       (input) INTEGER
        !            40: *          The number of random numbers to be generated.
        !            41: *
        !            42: *  X       (output) COMPLEX*16 array, dimension (N)
        !            43: *          The generated random numbers.
        !            44: *
        !            45: *  Further Details
        !            46: *  ===============
        !            47: *
        !            48: *  This routine calls the auxiliary routine DLARUV to generate random
        !            49: *  real numbers from a uniform (0,1) distribution, in batches of up to
        !            50: *  128 using vectorisable code. The Box-Muller method is used to
        !            51: *  transform numbers from a uniform to a normal distribution.
        !            52: *
        !            53: *  =====================================================================
        !            54: *
        !            55: *     .. Parameters ..
        !            56:       DOUBLE PRECISION   ZERO, ONE, TWO
        !            57:       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0 )
        !            58:       INTEGER            LV
        !            59:       PARAMETER          ( LV = 128 )
        !            60:       DOUBLE PRECISION   TWOPI
        !            61:       PARAMETER          ( TWOPI = 6.2831853071795864769252867663D+0 )
        !            62: *     ..
        !            63: *     .. Local Scalars ..
        !            64:       INTEGER            I, IL, IV
        !            65: *     ..
        !            66: *     .. Local Arrays ..
        !            67:       DOUBLE PRECISION   U( LV )
        !            68: *     ..
        !            69: *     .. Intrinsic Functions ..
        !            70:       INTRINSIC          DCMPLX, EXP, LOG, MIN, SQRT
        !            71: *     ..
        !            72: *     .. External Subroutines ..
        !            73:       EXTERNAL           DLARUV
        !            74: *     ..
        !            75: *     .. Executable Statements ..
        !            76: *
        !            77:       DO 60 IV = 1, N, LV / 2
        !            78:          IL = MIN( LV / 2, N-IV+1 )
        !            79: *
        !            80: *        Call DLARUV to generate 2*IL real numbers from a uniform (0,1)
        !            81: *        distribution (2*IL <= LV)
        !            82: *
        !            83:          CALL DLARUV( ISEED, 2*IL, U )
        !            84: *
        !            85:          IF( IDIST.EQ.1 ) THEN
        !            86: *
        !            87: *           Copy generated numbers
        !            88: *
        !            89:             DO 10 I = 1, IL
        !            90:                X( IV+I-1 ) = DCMPLX( U( 2*I-1 ), U( 2*I ) )
        !            91:    10       CONTINUE
        !            92:          ELSE IF( IDIST.EQ.2 ) THEN
        !            93: *
        !            94: *           Convert generated numbers to uniform (-1,1) distribution
        !            95: *
        !            96:             DO 20 I = 1, IL
        !            97:                X( IV+I-1 ) = DCMPLX( TWO*U( 2*I-1 )-ONE,
        !            98:      $                       TWO*U( 2*I )-ONE )
        !            99:    20       CONTINUE
        !           100:          ELSE IF( IDIST.EQ.3 ) THEN
        !           101: *
        !           102: *           Convert generated numbers to normal (0,1) distribution
        !           103: *
        !           104:             DO 30 I = 1, IL
        !           105:                X( IV+I-1 ) = SQRT( -TWO*LOG( U( 2*I-1 ) ) )*
        !           106:      $                       EXP( DCMPLX( ZERO, TWOPI*U( 2*I ) ) )
        !           107:    30       CONTINUE
        !           108:          ELSE IF( IDIST.EQ.4 ) THEN
        !           109: *
        !           110: *           Convert generated numbers to complex numbers uniformly
        !           111: *           distributed on the unit disk
        !           112: *
        !           113:             DO 40 I = 1, IL
        !           114:                X( IV+I-1 ) = SQRT( U( 2*I-1 ) )*
        !           115:      $                       EXP( DCMPLX( ZERO, TWOPI*U( 2*I ) ) )
        !           116:    40       CONTINUE
        !           117:          ELSE IF( IDIST.EQ.5 ) THEN
        !           118: *
        !           119: *           Convert generated numbers to complex numbers uniformly
        !           120: *           distributed on the unit circle
        !           121: *
        !           122:             DO 50 I = 1, IL
        !           123:                X( IV+I-1 ) = EXP( DCMPLX( ZERO, TWOPI*U( 2*I ) ) )
        !           124:    50       CONTINUE
        !           125:          END IF
        !           126:    60 CONTINUE
        !           127:       RETURN
        !           128: *
        !           129: *     End of ZLARNV
        !           130: *
        !           131:       END