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Annotation of rpl/lapack/lapack/zlarnv.f, revision 1.3

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