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    1: *> \brief \b DLARNV
    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: *
   82: *> \date November 2011
   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: *  =====================================================================
   98:       SUBROUTINE DLARNV( IDIST, ISEED, N, X )
   99: *
  100: *  -- LAPACK auxiliary routine (version 3.4.0) --
  101: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  102: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  103: *     November 2011
  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