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449 lines
18 KiB
449 lines
18 KiB
2 years ago
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*> \brief \b DLARUV returns a vector of n random real numbers from a uniform distribution.
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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*> \htmlonly
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*> Download DLARUV + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaruv.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaruv.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaruv.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE DLARUV( ISEED, N, X )
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*
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* .. Scalar Arguments ..
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* INTEGER N
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* ..
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* .. Array Arguments ..
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* INTEGER ISEED( 4 )
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* DOUBLE PRECISION X( N )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> DLARUV returns a vector of n random real numbers from a uniform (0,1)
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*> distribution (n <= 128).
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*>
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*> This is an auxiliary routine called by DLARNV and ZLARNV.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in,out] ISEED
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*> \verbatim
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*> ISEED is INTEGER array, dimension (4)
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*> On entry, the seed of the random number generator; the array
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*> elements must be between 0 and 4095, and ISEED(4) must be
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*> odd.
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*> On exit, the seed is updated.
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The number of random numbers to be generated. N <= 128.
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*> \endverbatim
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*>
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*> \param[out] X
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*> \verbatim
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*> X is DOUBLE PRECISION array, dimension (N)
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*> The generated random numbers.
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \ingroup OTHERauxiliary
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*
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*> \par Further Details:
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* =====================
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*>
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*> \verbatim
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*>
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*> This routine uses a multiplicative congruential method with modulus
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*> 2**48 and multiplier 33952834046453 (see G.S.Fishman,
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*> 'Multiplicative congruential random number generators with modulus
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*> 2**b: an exhaustive analysis for b = 32 and a partial analysis for
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*> b = 48', Math. Comp. 189, pp 331-344, 1990).
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*>
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*> 48-bit integers are stored in 4 integer array elements with 12 bits
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*> per element. Hence the routine is portable across machines with
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*> integers of 32 bits or more.
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*> \endverbatim
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*>
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* =====================================================================
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SUBROUTINE DLARUV( ISEED, N, X )
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*
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* -- LAPACK auxiliary routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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INTEGER N
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* ..
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* .. Array Arguments ..
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INTEGER ISEED( 4 )
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DOUBLE PRECISION X( N )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ONE
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PARAMETER ( ONE = 1.0D0 )
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INTEGER LV, IPW2
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DOUBLE PRECISION R
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PARAMETER ( LV = 128, IPW2 = 4096, R = ONE / IPW2 )
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* ..
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* .. Local Scalars ..
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INTEGER I, I1, I2, I3, I4, IT1, IT2, IT3, IT4, J
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* ..
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* .. Local Arrays ..
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INTEGER MM( LV, 4 )
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC DBLE, MIN, MOD
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* ..
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* .. Data statements ..
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DATA ( MM( 1, J ), J = 1, 4 ) / 494, 322, 2508,
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$ 2549 /
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DATA ( MM( 2, J ), J = 1, 4 ) / 2637, 789, 3754,
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$ 1145 /
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DATA ( MM( 3, J ), J = 1, 4 ) / 255, 1440, 1766,
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$ 2253 /
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DATA ( MM( 4, J ), J = 1, 4 ) / 2008, 752, 3572,
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$ 305 /
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DATA ( MM( 5, J ), J = 1, 4 ) / 1253, 2859, 2893,
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$ 3301 /
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DATA ( MM( 6, J ), J = 1, 4 ) / 3344, 123, 307,
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$ 1065 /
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DATA ( MM( 7, J ), J = 1, 4 ) / 4084, 1848, 1297,
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$ 3133 /
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DATA ( MM( 8, J ), J = 1, 4 ) / 1739, 643, 3966,
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$ 2913 /
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DATA ( MM( 9, J ), J = 1, 4 ) / 3143, 2405, 758,
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$ 3285 /
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DATA ( MM( 10, J ), J = 1, 4 ) / 3468, 2638, 2598,
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$ 1241 /
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DATA ( MM( 11, J ), J = 1, 4 ) / 688, 2344, 3406,
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$ 1197 /
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DATA ( MM( 12, J ), J = 1, 4 ) / 1657, 46, 2922,
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$ 3729 /
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DATA ( MM( 13, J ), J = 1, 4 ) / 1238, 3814, 1038,
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$ 2501 /
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DATA ( MM( 14, J ), J = 1, 4 ) / 3166, 913, 2934,
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$ 1673 /
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DATA ( MM( 15, J ), J = 1, 4 ) / 1292, 3649, 2091,
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$ 541 /
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DATA ( MM( 16, J ), J = 1, 4 ) / 3422, 339, 2451,
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$ 2753 /
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DATA ( MM( 17, J ), J = 1, 4 ) / 1270, 3808, 1580,
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$ 949 /
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DATA ( MM( 18, J ), J = 1, 4 ) / 2016, 822, 1958,
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$ 2361 /
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DATA ( MM( 19, J ), J = 1, 4 ) / 154, 2832, 2055,
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$ 1165 /
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DATA ( MM( 20, J ), J = 1, 4 ) / 2862, 3078, 1507,
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$ 4081 /
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DATA ( MM( 21, J ), J = 1, 4 ) / 697, 3633, 1078,
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$ 2725 /
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DATA ( MM( 22, J ), J = 1, 4 ) / 1706, 2970, 3273,
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$ 3305 /
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DATA ( MM( 23, J ), J = 1, 4 ) / 491, 637, 17,
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$ 3069 /
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DATA ( MM( 24, J ), J = 1, 4 ) / 931, 2249, 854,
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$ 3617 /
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DATA ( MM( 25, J ), J = 1, 4 ) / 1444, 2081, 2916,
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$ 3733 /
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DATA ( MM( 26, J ), J = 1, 4 ) / 444, 4019, 3971,
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$ 409 /
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DATA ( MM( 27, J ), J = 1, 4 ) / 3577, 1478, 2889,
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$ 2157 /
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DATA ( MM( 28, J ), J = 1, 4 ) / 3944, 242, 3831,
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$ 1361 /
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DATA ( MM( 29, J ), J = 1, 4 ) / 2184, 481, 2621,
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$ 3973 /
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DATA ( MM( 30, J ), J = 1, 4 ) / 1661, 2075, 1541,
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$ 1865 /
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DATA ( MM( 31, J ), J = 1, 4 ) / 3482, 4058, 893,
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$ 2525 /
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DATA ( MM( 32, J ), J = 1, 4 ) / 657, 622, 736,
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$ 1409 /
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DATA ( MM( 33, J ), J = 1, 4 ) / 3023, 3376, 3992,
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$ 3445 /
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DATA ( MM( 34, J ), J = 1, 4 ) / 3618, 812, 787,
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$ 3577 /
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DATA ( MM( 35, J ), J = 1, 4 ) / 1267, 234, 2125,
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$ 77 /
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DATA ( MM( 36, J ), J = 1, 4 ) / 1828, 641, 2364,
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$ 3761 /
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DATA ( MM( 37, J ), J = 1, 4 ) / 164, 4005, 2460,
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$ 2149 /
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DATA ( MM( 38, J ), J = 1, 4 ) / 3798, 1122, 257,
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$ 1449 /
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DATA ( MM( 39, J ), J = 1, 4 ) / 3087, 3135, 1574,
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$ 3005 /
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DATA ( MM( 40, J ), J = 1, 4 ) / 2400, 2640, 3912,
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$ 225 /
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DATA ( MM( 41, J ), J = 1, 4 ) / 2870, 2302, 1216,
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$ 85 /
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DATA ( MM( 42, J ), J = 1, 4 ) / 3876, 40, 3248,
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$ 3673 /
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DATA ( MM( 43, J ), J = 1, 4 ) / 1905, 1832, 3401,
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$ 3117 /
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DATA ( MM( 44, J ), J = 1, 4 ) / 1593, 2247, 2124,
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$ 3089 /
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DATA ( MM( 45, J ), J = 1, 4 ) / 1797, 2034, 2762,
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$ 1349 /
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DATA ( MM( 46, J ), J = 1, 4 ) / 1234, 2637, 149,
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$ 2057 /
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DATA ( MM( 47, J ), J = 1, 4 ) / 3460, 1287, 2245,
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$ 413 /
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DATA ( MM( 48, J ), J = 1, 4 ) / 328, 1691, 166,
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$ 65 /
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DATA ( MM( 49, J ), J = 1, 4 ) / 2861, 496, 466,
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$ 1845 /
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DATA ( MM( 50, J ), J = 1, 4 ) / 1950, 1597, 4018,
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$ 697 /
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DATA ( MM( 51, J ), J = 1, 4 ) / 617, 2394, 1399,
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$ 3085 /
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DATA ( MM( 52, J ), J = 1, 4 ) / 2070, 2584, 190,
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$ 3441 /
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DATA ( MM( 53, J ), J = 1, 4 ) / 3331, 1843, 2879,
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$ 1573 /
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DATA ( MM( 54, J ), J = 1, 4 ) / 769, 336, 153,
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$ 3689 /
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DATA ( MM( 55, J ), J = 1, 4 ) / 1558, 1472, 2320,
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$ 2941 /
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DATA ( MM( 56, J ), J = 1, 4 ) / 2412, 2407, 18,
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$ 929 /
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DATA ( MM( 57, J ), J = 1, 4 ) / 2800, 433, 712,
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$ 533 /
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DATA ( MM( 58, J ), J = 1, 4 ) / 189, 2096, 2159,
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$ 2841 /
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DATA ( MM( 59, J ), J = 1, 4 ) / 287, 1761, 2318,
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$ 4077 /
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DATA ( MM( 60, J ), J = 1, 4 ) / 2045, 2810, 2091,
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$ 721 /
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DATA ( MM( 61, J ), J = 1, 4 ) / 1227, 566, 3443,
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$ 2821 /
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DATA ( MM( 62, J ), J = 1, 4 ) / 2838, 442, 1510,
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$ 2249 /
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DATA ( MM( 63, J ), J = 1, 4 ) / 209, 41, 449,
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$ 2397 /
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DATA ( MM( 64, J ), J = 1, 4 ) / 2770, 1238, 1956,
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$ 2817 /
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DATA ( MM( 65, J ), J = 1, 4 ) / 3654, 1086, 2201,
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$ 245 /
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DATA ( MM( 66, J ), J = 1, 4 ) / 3993, 603, 3137,
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$ 1913 /
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DATA ( MM( 67, J ), J = 1, 4 ) / 192, 840, 3399,
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$ 1997 /
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DATA ( MM( 68, J ), J = 1, 4 ) / 2253, 3168, 1321,
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$ 3121 /
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DATA ( MM( 69, J ), J = 1, 4 ) / 3491, 1499, 2271,
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$ 997 /
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DATA ( MM( 70, J ), J = 1, 4 ) / 2889, 1084, 3667,
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$ 1833 /
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DATA ( MM( 71, J ), J = 1, 4 ) / 2857, 3438, 2703,
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$ 2877 /
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DATA ( MM( 72, J ), J = 1, 4 ) / 2094, 2408, 629,
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$ 1633 /
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DATA ( MM( 73, J ), J = 1, 4 ) / 1818, 1589, 2365,
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$ 981 /
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DATA ( MM( 74, J ), J = 1, 4 ) / 688, 2391, 2431,
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$ 2009 /
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DATA ( MM( 75, J ), J = 1, 4 ) / 1407, 288, 1113,
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$ 941 /
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DATA ( MM( 76, J ), J = 1, 4 ) / 634, 26, 3922,
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$ 2449 /
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DATA ( MM( 77, J ), J = 1, 4 ) / 3231, 512, 2554,
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$ 197 /
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DATA ( MM( 78, J ), J = 1, 4 ) / 815, 1456, 184,
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$ 2441 /
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DATA ( MM( 79, J ), J = 1, 4 ) / 3524, 171, 2099,
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$ 285 /
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DATA ( MM( 80, J ), J = 1, 4 ) / 1914, 1677, 3228,
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$ 1473 /
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DATA ( MM( 81, J ), J = 1, 4 ) / 516, 2657, 4012,
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$ 2741 /
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DATA ( MM( 82, J ), J = 1, 4 ) / 164, 2270, 1921,
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$ 3129 /
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DATA ( MM( 83, J ), J = 1, 4 ) / 303, 2587, 3452,
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$ 909 /
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DATA ( MM( 84, J ), J = 1, 4 ) / 2144, 2961, 3901,
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$ 2801 /
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DATA ( MM( 85, J ), J = 1, 4 ) / 3480, 1970, 572,
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$ 421 /
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DATA ( MM( 86, J ), J = 1, 4 ) / 119, 1817, 3309,
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$ 4073 /
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DATA ( MM( 87, J ), J = 1, 4 ) / 3357, 676, 3171,
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$ 2813 /
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DATA ( MM( 88, J ), J = 1, 4 ) / 837, 1410, 817,
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$ 2337 /
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DATA ( MM( 89, J ), J = 1, 4 ) / 2826, 3723, 3039,
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$ 1429 /
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DATA ( MM( 90, J ), J = 1, 4 ) / 2332, 2803, 1696,
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$ 1177 /
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DATA ( MM( 91, J ), J = 1, 4 ) / 2089, 3185, 1256,
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$ 1901 /
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DATA ( MM( 92, J ), J = 1, 4 ) / 3780, 184, 3715,
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$ 81 /
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DATA ( MM( 93, J ), J = 1, 4 ) / 1700, 663, 2077,
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$ 1669 /
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DATA ( MM( 94, J ), J = 1, 4 ) / 3712, 499, 3019,
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$ 2633 /
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DATA ( MM( 95, J ), J = 1, 4 ) / 150, 3784, 1497,
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$ 2269 /
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DATA ( MM( 96, J ), J = 1, 4 ) / 2000, 1631, 1101,
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$ 129 /
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DATA ( MM( 97, J ), J = 1, 4 ) / 3375, 1925, 717,
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$ 1141 /
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DATA ( MM( 98, J ), J = 1, 4 ) / 1621, 3912, 51,
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$ 249 /
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|
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DATA ( MM( 99, J ), J = 1, 4 ) / 3090, 1398, 981,
|
||
|
|
$ 3917 /
|
||
|
|
DATA ( MM( 100, J ), J = 1, 4 ) / 3765, 1349, 1978,
|
||
|
|
$ 2481 /
|
||
|
|
DATA ( MM( 101, J ), J = 1, 4 ) / 1149, 1441, 1813,
|
||
|
|
$ 3941 /
|
||
|
|
DATA ( MM( 102, J ), J = 1, 4 ) / 3146, 2224, 3881,
|
||
|
|
$ 2217 /
|
||
|
|
DATA ( MM( 103, J ), J = 1, 4 ) / 33, 2411, 76,
|
||
|
|
$ 2749 /
|
||
|
|
DATA ( MM( 104, J ), J = 1, 4 ) / 3082, 1907, 3846,
|
||
|
|
$ 3041 /
|
||
|
|
DATA ( MM( 105, J ), J = 1, 4 ) / 2741, 3192, 3694,
|
||
|
|
$ 1877 /
|
||
|
|
DATA ( MM( 106, J ), J = 1, 4 ) / 359, 2786, 1682,
|
||
|
|
$ 345 /
|
||
|
|
DATA ( MM( 107, J ), J = 1, 4 ) / 3316, 382, 124,
|
||
|
|
$ 2861 /
|
||
|
|
DATA ( MM( 108, J ), J = 1, 4 ) / 1749, 37, 1660,
|
||
|
|
$ 1809 /
|
||
|
|
DATA ( MM( 109, J ), J = 1, 4 ) / 185, 759, 3997,
|
||
|
|
$ 3141 /
|
||
|
|
DATA ( MM( 110, J ), J = 1, 4 ) / 2784, 2948, 479,
|
||
|
|
$ 2825 /
|
||
|
|
DATA ( MM( 111, J ), J = 1, 4 ) / 2202, 1862, 1141,
|
||
|
|
$ 157 /
|
||
|
|
DATA ( MM( 112, J ), J = 1, 4 ) / 2199, 3802, 886,
|
||
|
|
$ 2881 /
|
||
|
|
DATA ( MM( 113, J ), J = 1, 4 ) / 1364, 2423, 3514,
|
||
|
|
$ 3637 /
|
||
|
|
DATA ( MM( 114, J ), J = 1, 4 ) / 1244, 2051, 1301,
|
||
|
|
$ 1465 /
|
||
|
|
DATA ( MM( 115, J ), J = 1, 4 ) / 2020, 2295, 3604,
|
||
|
|
$ 2829 /
|
||
|
|
DATA ( MM( 116, J ), J = 1, 4 ) / 3160, 1332, 1888,
|
||
|
|
$ 2161 /
|
||
|
|
DATA ( MM( 117, J ), J = 1, 4 ) / 2785, 1832, 1836,
|
||
|
|
$ 3365 /
|
||
|
|
DATA ( MM( 118, J ), J = 1, 4 ) / 2772, 2405, 1990,
|
||
|
|
$ 361 /
|
||
|
|
DATA ( MM( 119, J ), J = 1, 4 ) / 1217, 3638, 2058,
|
||
|
|
$ 2685 /
|
||
|
|
DATA ( MM( 120, J ), J = 1, 4 ) / 1822, 3661, 692,
|
||
|
|
$ 3745 /
|
||
|
|
DATA ( MM( 121, J ), J = 1, 4 ) / 1245, 327, 1194,
|
||
|
|
$ 2325 /
|
||
|
|
DATA ( MM( 122, J ), J = 1, 4 ) / 2252, 3660, 20,
|
||
|
|
$ 3609 /
|
||
|
|
DATA ( MM( 123, J ), J = 1, 4 ) / 3904, 716, 3285,
|
||
|
|
$ 3821 /
|
||
|
|
DATA ( MM( 124, J ), J = 1, 4 ) / 2774, 1842, 2046,
|
||
|
|
$ 3537 /
|
||
|
|
DATA ( MM( 125, J ), J = 1, 4 ) / 997, 3987, 2107,
|
||
|
|
$ 517 /
|
||
|
|
DATA ( MM( 126, J ), J = 1, 4 ) / 2573, 1368, 3508,
|
||
|
|
$ 3017 /
|
||
|
|
DATA ( MM( 127, J ), J = 1, 4 ) / 1148, 1848, 3525,
|
||
|
|
$ 2141 /
|
||
|
|
DATA ( MM( 128, J ), J = 1, 4 ) / 545, 2366, 3801,
|
||
|
|
$ 1537 /
|
||
|
|
* ..
|
||
|
|
* .. Executable Statements ..
|
||
|
|
*
|
||
|
|
* Quick return for N < 1
|
||
|
|
IF ( N < 1 ) THEN
|
||
|
|
RETURN
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
I1 = ISEED( 1 )
|
||
|
|
I2 = ISEED( 2 )
|
||
|
|
I3 = ISEED( 3 )
|
||
|
|
I4 = ISEED( 4 )
|
||
|
|
*
|
||
|
|
DO 10 I = 1, MIN( N, LV )
|
||
|
|
*
|
||
|
|
20 CONTINUE
|
||
|
|
*
|
||
|
|
* Multiply the seed by i-th power of the multiplier modulo 2**48
|
||
|
|
*
|
||
|
|
IT4 = I4*MM( I, 4 )
|
||
|
|
IT3 = IT4 / IPW2
|
||
|
|
IT4 = IT4 - IPW2*IT3
|
||
|
|
IT3 = IT3 + I3*MM( I, 4 ) + I4*MM( I, 3 )
|
||
|
|
IT2 = IT3 / IPW2
|
||
|
|
IT3 = IT3 - IPW2*IT2
|
||
|
|
IT2 = IT2 + I2*MM( I, 4 ) + I3*MM( I, 3 ) + I4*MM( I, 2 )
|
||
|
|
IT1 = IT2 / IPW2
|
||
|
|
IT2 = IT2 - IPW2*IT1
|
||
|
|
IT1 = IT1 + I1*MM( I, 4 ) + I2*MM( I, 3 ) + I3*MM( I, 2 ) +
|
||
|
|
$ I4*MM( I, 1 )
|
||
|
|
IT1 = MOD( IT1, IPW2 )
|
||
|
|
*
|
||
|
|
* Convert 48-bit integer to a real number in the interval (0,1)
|
||
|
|
*
|
||
|
|
X( I ) = R*( DBLE( IT1 )+R*( DBLE( IT2 )+R*( DBLE( IT3 )+R*
|
||
|
|
$ DBLE( IT4 ) ) ) )
|
||
|
|
*
|
||
|
|
IF (X( I ).EQ.1.0D0) THEN
|
||
|
|
* If a real number has n bits of precision, and the first
|
||
|
|
* n bits of the 48-bit integer above happen to be all 1 (which
|
||
|
|
* will occur about once every 2**n calls), then X( I ) will
|
||
|
|
* be rounded to exactly 1.0.
|
||
|
|
* Since X( I ) is not supposed to return exactly 0.0 or 1.0,
|
||
|
|
* the statistically correct thing to do in this situation is
|
||
|
|
* simply to iterate again.
|
||
|
|
* N.B. the case X( I ) = 0.0 should not be possible.
|
||
|
|
I1 = I1 + 2
|
||
|
|
I2 = I2 + 2
|
||
|
|
I3 = I3 + 2
|
||
|
|
I4 = I4 + 2
|
||
|
|
GOTO 20
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
10 CONTINUE
|
||
|
|
*
|
||
|
|
* Return final value of seed
|
||
|
|
*
|
||
|
|
ISEED( 1 ) = IT1
|
||
|
|
ISEED( 2 ) = IT2
|
||
|
|
ISEED( 3 ) = IT3
|
||
|
|
ISEED( 4 ) = IT4
|
||
|
|
RETURN
|
||
|
|
*
|
||
|
|
* End of DLARUV
|
||
|
|
*
|
||
|
|
END
|