SUBROUTINE ZLARNV( IDIST, ISEED, N, X ) * * -- LAPACK auxiliary routine (version 3.2) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2006 * * .. Scalar Arguments .. INTEGER IDIST, N * .. * .. Array Arguments .. INTEGER ISEED( 4 ) COMPLEX*16 X( * ) * .. * * Purpose * ======= * * ZLARNV returns a vector of n random complex numbers from a uniform or * normal distribution. * * Arguments * ========= * * IDIST (input) 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 * * ISEED (input/output) 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. * * N (input) INTEGER * The number of random numbers to be generated. * * X (output) COMPLEX*16 array, dimension (N) * The generated random numbers. * * Further Details * =============== * * 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. * * ===================================================================== * * .. 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