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LAPACK 3.3.1
Linear Algebra PACKage
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LAPACK 3.3.1
Linear Algebra PACKage
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00001 SUBROUTINE SLARUV( ISEED, N, X ) 00002 * 00003 * -- LAPACK auxiliary routine (version 3.2) -- 00004 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00005 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00006 * November 2006 00007 * 00008 * .. Scalar Arguments .. 00009 INTEGER N 00010 * .. 00011 * .. Array Arguments .. 00012 INTEGER ISEED( 4 ) 00013 REAL X( N ) 00014 * .. 00015 * 00016 * Purpose 00017 * ======= 00018 * 00019 * SLARUV returns a vector of n random real numbers from a uniform (0,1) 00020 * distribution (n <= 128). 00021 * 00022 * This is an auxiliary routine called by SLARNV and CLARNV. 00023 * 00024 * Arguments 00025 * ========= 00026 * 00027 * ISEED (input/output) INTEGER array, dimension (4) 00028 * On entry, the seed of the random number generator; the array 00029 * elements must be between 0 and 4095, and ISEED(4) must be 00030 * odd. 00031 * On exit, the seed is updated. 00032 * 00033 * N (input) INTEGER 00034 * The number of random numbers to be generated. N <= 128. 00035 * 00036 * X (output) REAL array, dimension (N) 00037 * The generated random numbers. 00038 * 00039 * Further Details 00040 * =============== 00041 * 00042 * This routine uses a multiplicative congruential method with modulus 00043 * 2**48 and multiplier 33952834046453 (see G.S.Fishman, 00044 * 'Multiplicative congruential random number generators with modulus 00045 * 2**b: an exhaustive analysis for b = 32 and a partial analysis for 00046 * b = 48', Math. Comp. 189, pp 331-344, 1990). 00047 * 00048 * 48-bit integers are stored in 4 integer array elements with 12 bits 00049 * per element. Hence the routine is portable across machines with 00050 * integers of 32 bits or more. 00051 * 00052 * ===================================================================== 00053 * 00054 * .. Parameters .. 00055 REAL ONE 00056 PARAMETER ( ONE = 1.0E0 ) 00057 INTEGER LV, IPW2 00058 REAL R 00059 PARAMETER ( LV = 128, IPW2 = 4096, R = ONE / IPW2 ) 00060 * .. 00061 * .. Local Scalars .. 00062 INTEGER I, I1, I2, I3, I4, IT1, IT2, IT3, IT4, J 00063 * .. 00064 * .. Local Arrays .. 00065 INTEGER MM( LV, 4 ) 00066 * .. 00067 * .. Intrinsic Functions .. 00068 INTRINSIC MIN, MOD, REAL 00069 * .. 00070 * .. Data statements .. 00071 DATA ( MM( 1, J ), J = 1, 4 ) / 494, 322, 2508, 00072 $ 2549 / 00073 DATA ( MM( 2, J ), J = 1, 4 ) / 2637, 789, 3754, 00074 $ 1145 / 00075 DATA ( MM( 3, J ), J = 1, 4 ) / 255, 1440, 1766, 00076 $ 2253 / 00077 DATA ( MM( 4, J ), J = 1, 4 ) / 2008, 752, 3572, 00078 $ 305 / 00079 DATA ( MM( 5, J ), J = 1, 4 ) / 1253, 2859, 2893, 00080 $ 3301 / 00081 DATA ( MM( 6, J ), J = 1, 4 ) / 3344, 123, 307, 00082 $ 1065 / 00083 DATA ( MM( 7, J ), J = 1, 4 ) / 4084, 1848, 1297, 00084 $ 3133 / 00085 DATA ( MM( 8, J ), J = 1, 4 ) / 1739, 643, 3966, 00086 $ 2913 / 00087 DATA ( MM( 9, J ), J = 1, 4 ) / 3143, 2405, 758, 00088 $ 3285 / 00089 DATA ( MM( 10, J ), J = 1, 4 ) / 3468, 2638, 2598, 00090 $ 1241 / 00091 DATA ( MM( 11, J ), J = 1, 4 ) / 688, 2344, 3406, 00092 $ 1197 / 00093 DATA ( MM( 12, J ), J = 1, 4 ) / 1657, 46, 2922, 00094 $ 3729 / 00095 DATA ( MM( 13, J ), J = 1, 4 ) / 1238, 3814, 1038, 00096 $ 2501 / 00097 DATA ( MM( 14, J ), J = 1, 4 ) / 3166, 913, 2934, 00098 $ 1673 / 00099 DATA ( MM( 15, J ), J = 1, 4 ) / 1292, 3649, 2091, 00100 $ 541 / 00101 DATA ( MM( 16, J ), J = 1, 4 ) / 3422, 339, 2451, 00102 $ 2753 / 00103 DATA ( MM( 17, J ), J = 1, 4 ) / 1270, 3808, 1580, 00104 $ 949 / 00105 DATA ( MM( 18, J ), J = 1, 4 ) / 2016, 822, 1958, 00106 $ 2361 / 00107 DATA ( MM( 19, J ), J = 1, 4 ) / 154, 2832, 2055, 00108 $ 1165 / 00109 DATA ( MM( 20, J ), J = 1, 4 ) / 2862, 3078, 1507, 00110 $ 4081 / 00111 DATA ( MM( 21, J ), J = 1, 4 ) / 697, 3633, 1078, 00112 $ 2725 / 00113 DATA ( MM( 22, J ), J = 1, 4 ) / 1706, 2970, 3273, 00114 $ 3305 / 00115 DATA ( MM( 23, J ), J = 1, 4 ) / 491, 637, 17, 00116 $ 3069 / 00117 DATA ( MM( 24, J ), J = 1, 4 ) / 931, 2249, 854, 00118 $ 3617 / 00119 DATA ( MM( 25, J ), J = 1, 4 ) / 1444, 2081, 2916, 00120 $ 3733 / 00121 DATA ( MM( 26, J ), J = 1, 4 ) / 444, 4019, 3971, 00122 $ 409 / 00123 DATA ( MM( 27, J ), J = 1, 4 ) / 3577, 1478, 2889, 00124 $ 2157 / 00125 DATA ( MM( 28, J ), J = 1, 4 ) / 3944, 242, 3831, 00126 $ 1361 / 00127 DATA ( MM( 29, J ), J = 1, 4 ) / 2184, 481, 2621, 00128 $ 3973 / 00129 DATA ( MM( 30, J ), J = 1, 4 ) / 1661, 2075, 1541, 00130 $ 1865 / 00131 DATA ( MM( 31, J ), J = 1, 4 ) / 3482, 4058, 893, 00132 $ 2525 / 00133 DATA ( MM( 32, J ), J = 1, 4 ) / 657, 622, 736, 00134 $ 1409 / 00135 DATA ( MM( 33, J ), J = 1, 4 ) / 3023, 3376, 3992, 00136 $ 3445 / 00137 DATA ( MM( 34, J ), J = 1, 4 ) / 3618, 812, 787, 00138 $ 3577 / 00139 DATA ( MM( 35, J ), J = 1, 4 ) / 1267, 234, 2125, 00140 $ 77 / 00141 DATA ( MM( 36, J ), J = 1, 4 ) / 1828, 641, 2364, 00142 $ 3761 / 00143 DATA ( MM( 37, J ), J = 1, 4 ) / 164, 4005, 2460, 00144 $ 2149 / 00145 DATA ( MM( 38, J ), J = 1, 4 ) / 3798, 1122, 257, 00146 $ 1449 / 00147 DATA ( MM( 39, J ), J = 1, 4 ) / 3087, 3135, 1574, 00148 $ 3005 / 00149 DATA ( MM( 40, J ), J = 1, 4 ) / 2400, 2640, 3912, 00150 $ 225 / 00151 DATA ( MM( 41, J ), J = 1, 4 ) / 2870, 2302, 1216, 00152 $ 85 / 00153 DATA ( MM( 42, J ), J = 1, 4 ) / 3876, 40, 3248, 00154 $ 3673 / 00155 DATA ( MM( 43, J ), J = 1, 4 ) / 1905, 1832, 3401, 00156 $ 3117 / 00157 DATA ( MM( 44, J ), J = 1, 4 ) / 1593, 2247, 2124, 00158 $ 3089 / 00159 DATA ( MM( 45, J ), J = 1, 4 ) / 1797, 2034, 2762, 00160 $ 1349 / 00161 DATA ( MM( 46, J ), J = 1, 4 ) / 1234, 2637, 149, 00162 $ 2057 / 00163 DATA ( MM( 47, J ), J = 1, 4 ) / 3460, 1287, 2245, 00164 $ 413 / 00165 DATA ( MM( 48, J ), J = 1, 4 ) / 328, 1691, 166, 00166 $ 65 / 00167 DATA ( MM( 49, J ), J = 1, 4 ) / 2861, 496, 466, 00168 $ 1845 / 00169 DATA ( MM( 50, J ), J = 1, 4 ) / 1950, 1597, 4018, 00170 $ 697 / 00171 DATA ( MM( 51, J ), J = 1, 4 ) / 617, 2394, 1399, 00172 $ 3085 / 00173 DATA ( MM( 52, J ), J = 1, 4 ) / 2070, 2584, 190, 00174 $ 3441 / 00175 DATA ( MM( 53, J ), J = 1, 4 ) / 3331, 1843, 2879, 00176 $ 1573 / 00177 DATA ( MM( 54, J ), J = 1, 4 ) / 769, 336, 153, 00178 $ 3689 / 00179 DATA ( MM( 55, J ), J = 1, 4 ) / 1558, 1472, 2320, 00180 $ 2941 / 00181 DATA ( MM( 56, J ), J = 1, 4 ) / 2412, 2407, 18, 00182 $ 929 / 00183 DATA ( MM( 57, J ), J = 1, 4 ) / 2800, 433, 712, 00184 $ 533 / 00185 DATA ( MM( 58, J ), J = 1, 4 ) / 189, 2096, 2159, 00186 $ 2841 / 00187 DATA ( MM( 59, J ), J = 1, 4 ) / 287, 1761, 2318, 00188 $ 4077 / 00189 DATA ( MM( 60, J ), J = 1, 4 ) / 2045, 2810, 2091, 00190 $ 721 / 00191 DATA ( MM( 61, J ), J = 1, 4 ) / 1227, 566, 3443, 00192 $ 2821 / 00193 DATA ( MM( 62, J ), J = 1, 4 ) / 2838, 442, 1510, 00194 $ 2249 / 00195 DATA ( MM( 63, J ), J = 1, 4 ) / 209, 41, 449, 00196 $ 2397 / 00197 DATA ( MM( 64, J ), J = 1, 4 ) / 2770, 1238, 1956, 00198 $ 2817 / 00199 DATA ( MM( 65, J ), J = 1, 4 ) / 3654, 1086, 2201, 00200 $ 245 / 00201 DATA ( MM( 66, J ), J = 1, 4 ) / 3993, 603, 3137, 00202 $ 1913 / 00203 DATA ( MM( 67, J ), J = 1, 4 ) / 192, 840, 3399, 00204 $ 1997 / 00205 DATA ( MM( 68, J ), J = 1, 4 ) / 2253, 3168, 1321, 00206 $ 3121 / 00207 DATA ( MM( 69, J ), J = 1, 4 ) / 3491, 1499, 2271, 00208 $ 997 / 00209 DATA ( MM( 70, J ), J = 1, 4 ) / 2889, 1084, 3667, 00210 $ 1833 / 00211 DATA ( MM( 71, J ), J = 1, 4 ) / 2857, 3438, 2703, 00212 $ 2877 / 00213 DATA ( MM( 72, J ), J = 1, 4 ) / 2094, 2408, 629, 00214 $ 1633 / 00215 DATA ( MM( 73, J ), J = 1, 4 ) / 1818, 1589, 2365, 00216 $ 981 / 00217 DATA ( MM( 74, J ), J = 1, 4 ) / 688, 2391, 2431, 00218 $ 2009 / 00219 DATA ( MM( 75, J ), J = 1, 4 ) / 1407, 288, 1113, 00220 $ 941 / 00221 DATA ( MM( 76, J ), J = 1, 4 ) / 634, 26, 3922, 00222 $ 2449 / 00223 DATA ( MM( 77, J ), J = 1, 4 ) / 3231, 512, 2554, 00224 $ 197 / 00225 DATA ( MM( 78, J ), J = 1, 4 ) / 815, 1456, 184, 00226 $ 2441 / 00227 DATA ( MM( 79, J ), J = 1, 4 ) / 3524, 171, 2099, 00228 $ 285 / 00229 DATA ( MM( 80, J ), J = 1, 4 ) / 1914, 1677, 3228, 00230 $ 1473 / 00231 DATA ( MM( 81, J ), J = 1, 4 ) / 516, 2657, 4012, 00232 $ 2741 / 00233 DATA ( MM( 82, J ), J = 1, 4 ) / 164, 2270, 1921, 00234 $ 3129 / 00235 DATA ( MM( 83, J ), J = 1, 4 ) / 303, 2587, 3452, 00236 $ 909 / 00237 DATA ( MM( 84, J ), J = 1, 4 ) / 2144, 2961, 3901, 00238 $ 2801 / 00239 DATA ( MM( 85, J ), J = 1, 4 ) / 3480, 1970, 572, 00240 $ 421 / 00241 DATA ( MM( 86, J ), J = 1, 4 ) / 119, 1817, 3309, 00242 $ 4073 / 00243 DATA ( MM( 87, J ), J = 1, 4 ) / 3357, 676, 3171, 00244 $ 2813 / 00245 DATA ( MM( 88, J ), J = 1, 4 ) / 837, 1410, 817, 00246 $ 2337 / 00247 DATA ( MM( 89, J ), J = 1, 4 ) / 2826, 3723, 3039, 00248 $ 1429 / 00249 DATA ( MM( 90, J ), J = 1, 4 ) / 2332, 2803, 1696, 00250 $ 1177 / 00251 DATA ( MM( 91, J ), J = 1, 4 ) / 2089, 3185, 1256, 00252 $ 1901 / 00253 DATA ( MM( 92, J ), J = 1, 4 ) / 3780, 184, 3715, 00254 $ 81 / 00255 DATA ( MM( 93, J ), J = 1, 4 ) / 1700, 663, 2077, 00256 $ 1669 / 00257 DATA ( MM( 94, J ), J = 1, 4 ) / 3712, 499, 3019, 00258 $ 2633 / 00259 DATA ( MM( 95, J ), J = 1, 4 ) / 150, 3784, 1497, 00260 $ 2269 / 00261 DATA ( MM( 96, J ), J = 1, 4 ) / 2000, 1631, 1101, 00262 $ 129 / 00263 DATA ( MM( 97, J ), J = 1, 4 ) / 3375, 1925, 717, 00264 $ 1141 / 00265 DATA ( MM( 98, J ), J = 1, 4 ) / 1621, 3912, 51, 00266 $ 249 / 00267 DATA ( MM( 99, J ), J = 1, 4 ) / 3090, 1398, 981, 00268 $ 3917 / 00269 DATA ( MM( 100, J ), J = 1, 4 ) / 3765, 1349, 1978, 00270 $ 2481 / 00271 DATA ( MM( 101, J ), J = 1, 4 ) / 1149, 1441, 1813, 00272 $ 3941 / 00273 DATA ( MM( 102, J ), J = 1, 4 ) / 3146, 2224, 3881, 00274 $ 2217 / 00275 DATA ( MM( 103, J ), J = 1, 4 ) / 33, 2411, 76, 00276 $ 2749 / 00277 DATA ( MM( 104, J ), J = 1, 4 ) / 3082, 1907, 3846, 00278 $ 3041 / 00279 DATA ( MM( 105, J ), J = 1, 4 ) / 2741, 3192, 3694, 00280 $ 1877 / 00281 DATA ( MM( 106, J ), J = 1, 4 ) / 359, 2786, 1682, 00282 $ 345 / 00283 DATA ( MM( 107, J ), J = 1, 4 ) / 3316, 382, 124, 00284 $ 2861 / 00285 DATA ( MM( 108, J ), J = 1, 4 ) / 1749, 37, 1660, 00286 $ 1809 / 00287 DATA ( MM( 109, J ), J = 1, 4 ) / 185, 759, 3997, 00288 $ 3141 / 00289 DATA ( MM( 110, J ), J = 1, 4 ) / 2784, 2948, 479, 00290 $ 2825 / 00291 DATA ( MM( 111, J ), J = 1, 4 ) / 2202, 1862, 1141, 00292 $ 157 / 00293 DATA ( MM( 112, J ), J = 1, 4 ) / 2199, 3802, 886, 00294 $ 2881 / 00295 DATA ( MM( 113, J ), J = 1, 4 ) / 1364, 2423, 3514, 00296 $ 3637 / 00297 DATA ( MM( 114, J ), J = 1, 4 ) / 1244, 2051, 1301, 00298 $ 1465 / 00299 DATA ( MM( 115, J ), J = 1, 4 ) / 2020, 2295, 3604, 00300 $ 2829 / 00301 DATA ( MM( 116, J ), J = 1, 4 ) / 3160, 1332, 1888, 00302 $ 2161 / 00303 DATA ( MM( 117, J ), J = 1, 4 ) / 2785, 1832, 1836, 00304 $ 3365 / 00305 DATA ( MM( 118, J ), J = 1, 4 ) / 2772, 2405, 1990, 00306 $ 361 / 00307 DATA ( MM( 119, J ), J = 1, 4 ) / 1217, 3638, 2058, 00308 $ 2685 / 00309 DATA ( MM( 120, J ), J = 1, 4 ) / 1822, 3661, 692, 00310 $ 3745 / 00311 DATA ( MM( 121, J ), J = 1, 4 ) / 1245, 327, 1194, 00312 $ 2325 / 00313 DATA ( MM( 122, J ), J = 1, 4 ) / 2252, 3660, 20, 00314 $ 3609 / 00315 DATA ( MM( 123, J ), J = 1, 4 ) / 3904, 716, 3285, 00316 $ 3821 / 00317 DATA ( MM( 124, J ), J = 1, 4 ) / 2774, 1842, 2046, 00318 $ 3537 / 00319 DATA ( MM( 125, J ), J = 1, 4 ) / 997, 3987, 2107, 00320 $ 517 / 00321 DATA ( MM( 126, J ), J = 1, 4 ) / 2573, 1368, 3508, 00322 $ 3017 / 00323 DATA ( MM( 127, J ), J = 1, 4 ) / 1148, 1848, 3525, 00324 $ 2141 / 00325 DATA ( MM( 128, J ), J = 1, 4 ) / 545, 2366, 3801, 00326 $ 1537 / 00327 * .. 00328 * .. Executable Statements .. 00329 * 00330 I1 = ISEED( 1 ) 00331 I2 = ISEED( 2 ) 00332 I3 = ISEED( 3 ) 00333 I4 = ISEED( 4 ) 00334 * 00335 DO 10 I = 1, MIN( N, LV ) 00336 * 00337 20 CONTINUE 00338 * 00339 * Multiply the seed by i-th power of the multiplier modulo 2**48 00340 * 00341 IT4 = I4*MM( I, 4 ) 00342 IT3 = IT4 / IPW2 00343 IT4 = IT4 - IPW2*IT3 00344 IT3 = IT3 + I3*MM( I, 4 ) + I4*MM( I, 3 ) 00345 IT2 = IT3 / IPW2 00346 IT3 = IT3 - IPW2*IT2 00347 IT2 = IT2 + I2*MM( I, 4 ) + I3*MM( I, 3 ) + I4*MM( I, 2 ) 00348 IT1 = IT2 / IPW2 00349 IT2 = IT2 - IPW2*IT1 00350 IT1 = IT1 + I1*MM( I, 4 ) + I2*MM( I, 3 ) + I3*MM( I, 2 ) + 00351 $ I4*MM( I, 1 ) 00352 IT1 = MOD( IT1, IPW2 ) 00353 * 00354 * Convert 48-bit integer to a real number in the interval (0,1) 00355 * 00356 X( I ) = R*( REAL( IT1 )+R*( REAL( IT2 )+R*( REAL( IT3 )+R* 00357 $ REAL( IT4 ) ) ) ) 00358 * 00359 IF (X( I ).EQ.1.0) THEN 00360 * If a real number has n bits of precision, and the first 00361 * n bits of the 48-bit integer above happen to be all 1 (which 00362 * will occur about once every 2**n calls), then X( I ) will 00363 * be rounded to exactly 1.0. In IEEE single precision arithmetic, 00364 * this will happen relatively often since n = 24. 00365 * Since X( I ) is not supposed to return exactly 0.0 or 1.0, 00366 * the statistically correct thing to do in this situation is 00367 * simply to iterate again. 00368 * N.B. the case X( I ) = 0.0 should not be possible. 00369 I1 = I1 + 2 00370 I2 = I2 + 2 00371 I3 = I3 + 2 00372 I4 = I4 + 2 00373 GOTO 20 00374 END IF 00375 * 00376 10 CONTINUE 00377 * 00378 * Return final value of seed 00379 * 00380 ISEED( 1 ) = IT1 00381 ISEED( 2 ) = IT2 00382 ISEED( 3 ) = IT3 00383 ISEED( 4 ) = IT4 00384 RETURN 00385 * 00386 * End of SLARUV 00387 * 00388 END
1.7.3 
