*> \brief \b DLARNV 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 DLARNV + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLARNV( IDIST, ISEED, N, X ) * * .. Scalar Arguments .. * INTEGER IDIST, N * .. * .. Array Arguments .. * INTEGER ISEED( 4 ) * DOUBLE PRECISION X( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLARNV returns a vector of n random real numbers from a uniform or *> normal distribution. *> \endverbatim * * Arguments: * ========== * *> \param[in] IDIST *> \verbatim *> IDIST is INTEGER *> Specifies the distribution of the random numbers: *> = 1: uniform (0,1) *> = 2: uniform (-1,1) *> = 3: normal (0,1) *> \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 DOUBLE PRECISION 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 OTHERauxiliary * *> \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 DLARNV( 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 ) DOUBLE PRECISION X( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, TWO PARAMETER ( 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, IL2, IV * .. * .. Local Arrays .. DOUBLE PRECISION U( LV ) * .. * .. Intrinsic Functions .. INTRINSIC COS, LOG, MIN, SQRT * .. * .. External Subroutines .. EXTERNAL DLARUV * .. * .. Executable Statements .. * DO 40 IV = 1, N, LV / 2 IL = MIN( LV / 2, N-IV+1 ) IF( IDIST.EQ.3 ) THEN IL2 = 2*IL ELSE IL2 = IL END IF * * Call DLARUV to generate IL2 numbers from a uniform (0,1) * distribution (IL2 <= LV) * CALL DLARUV( ISEED, IL2, U ) * IF( IDIST.EQ.1 ) THEN * * Copy generated numbers * DO 10 I = 1, IL X( IV+I-1 ) = U( 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 ) = TWO*U( 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 ) ) )* $ COS( TWOPI*U( 2*I ) ) 30 CONTINUE END IF 40 CONTINUE RETURN * * End of DLARNV * END