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Annotation of rpl/lapack/lapack/dlarnv.f, revision 1.11

1.11    ! bertrand    1: *> \brief \b DLARNV returns a vector of random numbers from a uniform or normal distribution.
1.8       bertrand    2: *
                      3: *  =========== DOCUMENTATION ===========
                      4: *
                      5: * Online html documentation available at 
                      6: *            http://www.netlib.org/lapack/explore-html/ 
                      7: *
                      8: *> \htmlonly
                      9: *> Download DLARNV + dependencies 
                     10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarnv.f"> 
                     11: *> [TGZ]</a> 
                     12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarnv.f"> 
                     13: *> [ZIP]</a> 
                     14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarnv.f"> 
                     15: *> [TXT]</a>
                     16: *> \endhtmlonly 
                     17: *
                     18: *  Definition:
                     19: *  ===========
                     20: *
                     21: *       SUBROUTINE DLARNV( IDIST, ISEED, N, X )
                     22: * 
                     23: *       .. Scalar Arguments ..
                     24: *       INTEGER            IDIST, N
                     25: *       ..
                     26: *       .. Array Arguments ..
                     27: *       INTEGER            ISEED( 4 )
                     28: *       DOUBLE PRECISION   X( * )
                     29: *       ..
                     30: *  
                     31: *
                     32: *> \par Purpose:
                     33: *  =============
                     34: *>
                     35: *> \verbatim
                     36: *>
                     37: *> DLARNV returns a vector of n random real 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:  uniform (0,1)
                     49: *>          = 2:  uniform (-1,1)
                     50: *>          = 3:  normal (0,1)
                     51: *> \endverbatim
                     52: *>
                     53: *> \param[in,out] ISEED
                     54: *> \verbatim
                     55: *>          ISEED is INTEGER array, dimension (4)
                     56: *>          On entry, the seed of the random number generator; the array
                     57: *>          elements must be between 0 and 4095, and ISEED(4) must be
                     58: *>          odd.
                     59: *>          On exit, the seed is updated.
                     60: *> \endverbatim
                     61: *>
                     62: *> \param[in] N
                     63: *> \verbatim
                     64: *>          N is INTEGER
                     65: *>          The number of random numbers to be generated.
                     66: *> \endverbatim
                     67: *>
                     68: *> \param[out] X
                     69: *> \verbatim
                     70: *>          X is DOUBLE PRECISION array, dimension (N)
                     71: *>          The generated random numbers.
                     72: *> \endverbatim
                     73: *
                     74: *  Authors:
                     75: *  ========
                     76: *
                     77: *> \author Univ. of Tennessee 
                     78: *> \author Univ. of California Berkeley 
                     79: *> \author Univ. of Colorado Denver 
                     80: *> \author NAG Ltd. 
                     81: *
1.11    ! bertrand   82: *> \date September 2012
1.8       bertrand   83: *
                     84: *> \ingroup auxOTHERauxiliary
                     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 DLARNV( IDIST, ISEED, N, X )
                     99: *
1.11    ! bertrand  100: *  -- LAPACK auxiliary routine (version 3.4.2) --
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..--
1.11    ! bertrand  103: *     September 2012
1.1       bertrand  104: *
                    105: *     .. Scalar Arguments ..
                    106:       INTEGER            IDIST, N
                    107: *     ..
                    108: *     .. Array Arguments ..
                    109:       INTEGER            ISEED( 4 )
                    110:       DOUBLE PRECISION   X( * )
                    111: *     ..
                    112: *
                    113: *  =====================================================================
                    114: *
                    115: *     .. Parameters ..
                    116:       DOUBLE PRECISION   ONE, TWO
                    117:       PARAMETER          ( ONE = 1.0D+0, TWO = 2.0D+0 )
                    118:       INTEGER            LV
                    119:       PARAMETER          ( LV = 128 )
                    120:       DOUBLE PRECISION   TWOPI
                    121:       PARAMETER          ( TWOPI = 6.2831853071795864769252867663D+0 )
                    122: *     ..
                    123: *     .. Local Scalars ..
                    124:       INTEGER            I, IL, IL2, IV
                    125: *     ..
                    126: *     .. Local Arrays ..
                    127:       DOUBLE PRECISION   U( LV )
                    128: *     ..
                    129: *     .. Intrinsic Functions ..
                    130:       INTRINSIC          COS, LOG, MIN, SQRT
                    131: *     ..
                    132: *     .. External Subroutines ..
                    133:       EXTERNAL           DLARUV
                    134: *     ..
                    135: *     .. Executable Statements ..
                    136: *
                    137:       DO 40 IV = 1, N, LV / 2
                    138:          IL = MIN( LV / 2, N-IV+1 )
                    139:          IF( IDIST.EQ.3 ) THEN
                    140:             IL2 = 2*IL
                    141:          ELSE
                    142:             IL2 = IL
                    143:          END IF
                    144: *
                    145: *        Call DLARUV to generate IL2 numbers from a uniform (0,1)
                    146: *        distribution (IL2 <= LV)
                    147: *
                    148:          CALL DLARUV( ISEED, IL2, U )
                    149: *
                    150:          IF( IDIST.EQ.1 ) THEN
                    151: *
                    152: *           Copy generated numbers
                    153: *
                    154:             DO 10 I = 1, IL
                    155:                X( IV+I-1 ) = U( I )
                    156:    10       CONTINUE
                    157:          ELSE IF( IDIST.EQ.2 ) THEN
                    158: *
                    159: *           Convert generated numbers to uniform (-1,1) distribution
                    160: *
                    161:             DO 20 I = 1, IL
                    162:                X( IV+I-1 ) = TWO*U( I ) - ONE
                    163:    20       CONTINUE
                    164:          ELSE IF( IDIST.EQ.3 ) THEN
                    165: *
                    166: *           Convert generated numbers to normal (0,1) distribution
                    167: *
                    168:             DO 30 I = 1, IL
                    169:                X( IV+I-1 ) = SQRT( -TWO*LOG( U( 2*I-1 ) ) )*
                    170:      $                       COS( TWOPI*U( 2*I ) )
                    171:    30       CONTINUE
                    172:          END IF
                    173:    40 CONTINUE
                    174:       RETURN
                    175: *
                    176: *     End of DLARNV
                    177: *
                    178:       END