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[bug-gsl] bug with function gsl_ran_beta (2008-11-18)
Dear Sir/Madam, May you please help with the following problem when simulate Beta distribution using gsl library: When simulate in win32 I get: beta1 464345 7.5026 5.9392 8300450000 329 1 464345 13.441800000000001 8300450000 1193280084.4218726 21329415807424.934 5498164443.7639704 5498111471.3260374 5498144966.7457933 5498107103.712388 5498097874.8369331 5497804839.1091223 5497962879.3275862 5498348140.7388935 5498310651.8006067 5498270628.820529 5498054322.7919359 5498114609.4608183 5498119109.7864475 5498159584.3738947 5498164700.2170744 5498086011.0154991 5498095680.8744516 5498006848.90833 5498070811.9395857 5498087417.6389866 5498026807.1669159 5498122445.9367285 5497952392.579668 5498106066.6511822 5498203756.786993 5498108846.2309923 5498048637.4160185 5498151840.4392099 5498191930.6450663 5497996830.5539083 5498051552.32374 5498060640.6092615 5497908399.5466995 5498119935.7092371 5498054853.0958071 5498098226.5945492 5498101849.9197855 5498154699.9752598 5497992952.4353313 5498057197.8844662 5498015676.8957071 5498104254.3332033 5497960503.8702707 5498091301.6851301 5498029113.6702051 5498116631.3597965 5498066298.9317265 5498147791.8874512 5498056680.7958651 5498007637.0482969 5498085947.1416807 5497977825.1033039 5498126344.0534906 5497943681.895689 5498163203.1894474 5497990924.5686588 5498078829.9846001 5498125133.7805986 5498126501.7405233 5498147393.4957542 5498181263.1347551 5498038604.6117105 5497974387.1937456 5498106367.9541016 5498043565.5655966 5497896470.6596165 5498154591.5600348 5498308920.7537546 5498012728.1607122 5498194171.7008448 5498083501.718545 5498023710.8567181 5497988464.5554075 5498122782.873313 5497946974.8896408 5498144160.6934872 5498086515.258625 5497955644.7909317 5498068356.5687408 5498192170.2630072 5498198662.2533474 5497997234.045969 5498118160.7723637 5498049511.2312117 5498000236.4571705 5498073273.3911152 5497990030.3130503 5498140238.7627163 5498102065.8602667 5498127414.6714096 5498018887.4798365 5498029817.9354734 5498024947.6399403 5498060491.0687075 5498036543.1245022 5498174801.9893436 5497970185.2885733 5498110399.3685369 5498014715.5597124 5498047981.7149143 5498075351.4674835 5498137763.5835609 5498012657.4867449 5497947453.3960915 5497977423.6984177 5497960772.4670792 5498003081.9502954 5497973383.6471834 5498098063.3361225 5498041744.9137144 5498027495.7109413 5498090673.1023769 5498064066.1248541 5498207924.9280634 5498081106.2818975 5497943072.4467802 5498096609.7475853 5498220642.5656404 5498167845.3062859 5498125813.8247986 5497907118.7000313 5498127255.3560286 5498078497.8242331 5497869517.6220646 5498149018.3140697 5498012425.0153332 5497964966.6998148 5498177432.7819319 5498149358.7511101 5498181275.5855932 5498133912.8475208 5498213364.5493383 5498147281.668663 5498045673.2753859 5497973269.6462851 5498128384.7655172 5498260148.0239506 5497939743.4531565 5497999339.0928097 5498050825.0487995 5498119519.2014999 5498088477.3913441 5498095064.3265705 5498139659.8860121 5498244114.8872099 5498040502.1340752 5498095597.5587158 5498011086.1352654 5498059340.1906481 5498092555.9781256 5498123444.9248943 5498052449.2462616 5498089697.6707745 5497958759.6879606 5497992120.6431217 5498063860.1185141 5498127023.1734629 5498060596.2904644 5497981513.5078459 5498163083.0468979 5498042076.3541222 5498082485.7807312 5498043278.61479 5498123446.6665344 5498207329.559803 5497995912.4189501 5497996498.5050859 5498014757.3182001 5498075627.0751314 5498120358.1212864 5497970627.6951084 5498147984.3777084 5498166787.4462795 5498193599.8504629 5498182687.5663986 5497861013.0707989 5498158480.4439173 5498110438.8790092 5498201090.8593006 5498264622.5608797 5498173024.1196814 5498112140.6525526 5498040723.6754856 5498115745.3500347 5498033331.2528534 5498049004.4010153 5498114146.7494688 5498037849.2854586 5498064702.8039684 5498175832.0131741 5497978269.4638681 5497998362.6134758 5498187772.6146908 5498134265.9656506 5498267691.469902 5497944127.2410154 5498141714.6558084 5498141734.5905113 5498186845.8831282 5498152748.2444315 5498188498.3360434 5498077873.9247913 5498156160.0596457 5498059453.475214 5497951975.8820724 5498221487.443614 5498006040.883852 5498135849.5156908 5498110508.1014805 5498131625.0616179 5498146040.9545536 5498136711.9506149 5498164027.6623802 5497961489.3518772 5498180427.1510458 5498083445.224781 5498085991.1830301 5498142367.998311 5498123635.6560469 5497952801.0104322 5498238527.6224566 5498141012.518425 5498202935.7893934 5498051646.9158745 5498141885.1992722 5498105244.8359718 5498116622.3068619 5498163957.22577 5497881195.1165304 5498019718.7447433 5498158908.0958662 5498136780.6597586 5498123731.5479383 5498232592.5290852 5498170683.9177113 5498051835.9580393 5497888851.2281361 5498099096.011858 5498096703.4391031 5498099429.8669672 5498151863.1491537 5498006890.3472662 5498135302.9372225 5498262404.2520418 5497863518.4468622 5498129427.0945177 5497996664.0504627 5497994931.6007643 5497993405.808074 5497940902.34867 5497909396.3238029 5498045308.1801805 5498078272.1381035 5497989578.7105417 5497965773.4691162 5498313142.6747904 5498097597.958499 5498117616.759222 5498205358.9119568 5497939837.900136 5498113794.3725138 5498264686.4694738 5498112085.5278597 5498064476.7472687 5497988974.0035009 5498166824.0080853 5498072465.1644983 5497971976.083745 5498182626.3397961 5497968838.078002 5498062527.3973646 5498015224.0198345 5498118132.1908493 5498173673.243865 5498080603.7031746 5498112548.5317183 5497924624.4215937 5498013134.9718237 5498052228.1909838 5498108097.5465593 5498200935.1551161 5498097039.0748205 5498141636.5519476 5498138070.0584383 5498033902.5371656 5497909684.6499567 5497944203.7811089 5498055763.8821669 5498081675.5630207 5498077505.0113058 5497984575.5704041 5498065354.3164215 5497998015.6075115 5498183812.9243345 5498122377.7300406 5498085693.4464445 5498229079.9141474 5498107982.0801353 5498020094.8201342 5497992283.0903406 5498067280.6769161 5497984606.9435024 5498083686.9770784 5497962845.7865629 5497961744.3907318 5498093358.5380831 5498290730.2210369 5498078046.4653006 5498177811.6326399 5497976971.8353605 5498027229.393693 5497938058.3481283 5497908081.5252886 5498069473.4896698 5497935989.9066238 5497984623.4586678 5498116151.2639284 5498070449.9178791 5497987349.2325277 5498113221.978857 5498194808.5422373 5497890153.4793119 5497990584.7269793 5498176001.1739864 5498108435.381794 5497987037.386673 5498071774.6048336 5497979285.9371147 5498121885.1890821 where beta1 is from beta1.cc: #include <gsl/gsl_randist.h> #include <ctime> #include <iostream> #include <iomanip> #include <cmath>//for sqrt fabs using namespace std; void Simulation(double mean, double sd, double exposedValue, int size, bool fixRandomSeed); pair<double, double> calculate_betaAB(double& _meanLoss, double& _sd, double& _exposedValue); int main(int argc, char* argv[]) { if(argc < 5) { cout << "proper usage: " << argv[0] << " <mean>, <sdc>, <sdi>, <exposedValue>, <size>, <fixRandomSeed>" << endl; exit(-1); } double mean=atof(argv[1]); double sd=atof(argv[2])+atof(argv[3]); double exposedValue=atof(argv[4]); int size=(argc>5) ? atoi(argv[5]) : 1; int fixRandomSeed=(argc>6) ? atoi(argv[6]) : 0;//default not fixed cout << setprecision (17); Simulation(mean, sd, exposedValue, size, fixRandomSeed); } void Simulation(double mean, double sd, double exposedValue, int size, bool fixRandomSeed) { // initialize GSL simulator gsl_rng * r = NULL; gsl_rng_env_setup(); r = gsl_rng_alloc(gsl_rng_default); // if fixRandomSeed, same numbers simulated every time if(! fixRandomSeed) gsl_rng_set(r, time(NULL)); pair<double, double> betaAB = calculate_betaAB(mean, sd, exposedValue); cout << mean << "\n"; cout << sd << "\n"; cout << exposedValue << "\n"; cout << betaAB.first << "\n"; cout << betaAB.second << "\n"; for(int kE = 0; kE < size; kE++) { double loss = 0; if(sd > 1. && mean > 1.) { double x = gsl_ran_beta(r, betaAB.first, betaAB.second); loss = x * exposedValue; } else loss = mean; cout << loss << "\n"; } gsl_rng_free(r); } pair<double, double> calculate_betaAB(double& _meanLoss, double& _sd, double& _exposedValue) { double _betaA=0., _betaB=0.; if(_meanLoss < 1e-3 || _exposedValue < 1e-3) { _meanLoss = 0; _exposedValue = 0; _sd = 0; return pair<double, double>(_betaA, _betaB); } if(fabs(_meanLoss/_exposedValue-1.) < 1e-6) { _meanLoss = _exposedValue * (1. - 1e-6); } double meanN = _meanLoss/_exposedValue, sdN = _sd/_exposedValue, tao = meanN*(1-meanN)/(sdN*sdN) - 1; _betaA = meanN*tao; _betaB = (1-meanN)*tao; double betaMin = 0, reductionFactor = .99; while(_betaA < betaMin || _betaB < betaMin) { _sd *= reductionFactor; sdN = _sd/_exposedValue; tao = meanN*(1-meanN)/(sdN*sdN) - 1; _betaA = meanN*tao; _betaB = (1-meanN)*tao; } return pair<double, double>(_betaA, _betaB); } But if simulate using R, we get different result: > rbeta(329, 1193280084.4218726, 21329415807424.934) [1] 5.594445e-05 5.594277e-05 5.594354e-05 5.594050e-05 5.594074e-05 [6] 5.594426e-05 5.594026e-05 5.594201e-05 5.594110e-05 5.594346e-05 [11] 5.594403e-05 5.594535e-05 5.594419e-05 5.594407e-05 5.594161e-05 [16] 5.594294e-05 5.594217e-05 5.593945e-05 5.593883e-05 5.594225e-05 [21] 5.594243e-05 5.594571e-05 5.593928e-05 5.594388e-05 5.594312e-05 [26] 5.594367e-05 5.594108e-05 5.594201e-05 5.594463e-05 5.594263e-05 [31] 5.594289e-05 5.594433e-05 5.594028e-05 5.594110e-05 5.594119e-05 [36] 5.594300e-05 5.594299e-05 5.594561e-05 5.594345e-05 5.594257e-05 [41] 5.594158e-05 5.594366e-05 5.594335e-05 5.594219e-05 5.594365e-05 [46] 5.594101e-05 5.593933e-05 5.594015e-05 5.594319e-05 5.594238e-05 [51] 5.594186e-05 5.594386e-05 5.594119e-05 5.594130e-05 5.594050e-05 [56] 5.594102e-05 5.594232e-05 5.594113e-05 5.594193e-05 5.594267e-05 [61] 5.594136e-05 5.593963e-05 5.593794e-05 5.594142e-05 5.594095e-05 [66] 5.594115e-05 5.594217e-05 5.593979e-05 5.594480e-05 5.594138e-05 [71] 5.594285e-05 5.594130e-05 5.593942e-05 5.594182e-05 5.594318e-05 [76] 5.593919e-05 5.593988e-05 5.594188e-05 5.594290e-05 5.594239e-05 [81] 5.594066e-05 5.594294e-05 5.594135e-05 5.594201e-05 5.594177e-05 [86] 5.594377e-05 5.594021e-05 5.594274e-05 5.593951e-05 5.594261e-05 [91] 5.594487e-05 5.594258e-05 5.594133e-05 5.594065e-05 5.594237e-05 [96] 5.593873e-05 5.594128e-05 5.594353e-05 5.594223e-05 5.594369e-05 [101] 5.594228e-05 5.594388e-05 5.594116e-05 5.594293e-05 5.594146e-05 [106] 5.594222e-05 5.594292e-05 5.594440e-05 5.594108e-05 5.594313e-05 [111] 5.594474e-05 5.593997e-05 5.594203e-05 5.594301e-05 5.594165e-05 [116] 5.594212e-05 5.594359e-05 5.594142e-05 5.594114e-05 5.594120e-05 [121] 5.594227e-05 5.594267e-05 5.594197e-05 5.594538e-05 5.594057e-05 [126] 5.594154e-05 5.594435e-05 5.594001e-05 5.594156e-05 5.594275e-05 [131] 5.594251e-05 5.594130e-05 5.594472e-05 5.594372e-05 5.594260e-05 [136] 5.594267e-05 5.593690e-05 5.594505e-05 5.594006e-05 5.594287e-05 [141] 5.594439e-05 5.594246e-05 5.594435e-05 5.594239e-05 5.594062e-05 [146] 5.594252e-05 5.594419e-05 5.594113e-05 5.593961e-05 5.594040e-05 [151] 5.593999e-05 5.594146e-05 5.593852e-05 5.593921e-05 5.594168e-05 [156] 5.593964e-05 5.594289e-05 5.594339e-05 5.593856e-05 5.594197e-05 [161] 5.594156e-05 5.594319e-05 5.594095e-05 5.594196e-05 5.594132e-05 [166] 5.594177e-05 5.594375e-05 5.594045e-05 5.594368e-05 5.594328e-05 [171] 5.594123e-05 5.594327e-05 5.594481e-05 5.594258e-05 5.594224e-05 [176] 5.594217e-05 5.594470e-05 5.594100e-05 5.594050e-05 5.594392e-05 [181] 5.594286e-05 5.594098e-05 5.594224e-05 5.594150e-05 5.594235e-05 [186] 5.594088e-05 5.594233e-05 5.594305e-05 5.594176e-05 5.594239e-05 [191] 5.594128e-05 5.594219e-05 5.594513e-05 5.594214e-05 5.594238e-05 [196] 5.594378e-05 5.594185e-05 5.594144e-05 5.594140e-05 5.594242e-05 [201] 5.594088e-05 5.594103e-05 5.594178e-05 5.594487e-05 5.594353e-05 [206] 5.594087e-05 5.594305e-05 5.594160e-05 5.594033e-05 5.594344e-05 [211] 5.594156e-05 5.594271e-05 5.594007e-05 5.594266e-05 5.594269e-05 [216] 5.594166e-05 5.594239e-05 5.594109e-05 5.594187e-05 5.594226e-05 [221] 5.594193e-05 5.594232e-05 5.594003e-05 5.593911e-05 5.594184e-05 [226] 5.593988e-05 5.594104e-05 5.594009e-05 5.594232e-05 5.594231e-05 [231] 5.594228e-05 5.594038e-05 5.593935e-05 5.594128e-05 5.594143e-05 [236] 5.594116e-05 5.594042e-05 5.594234e-05 5.594281e-05 5.594365e-05 [241] 5.594301e-05 5.594025e-05 5.594347e-05 5.594235e-05 5.594177e-05 [246] 5.594063e-05 5.594187e-05 5.594398e-05 5.594265e-05 5.594255e-05 [251] 5.594352e-05 5.594207e-05 5.594279e-05 5.594230e-05 5.593914e-05 [256] 5.594071e-05 5.594485e-05 5.594489e-05 5.594354e-05 5.594184e-05 [261] 5.594363e-05 5.594086e-05 5.594353e-05 5.594287e-05 5.594258e-05 [266] 5.594421e-05 5.594278e-05 5.594275e-05 5.594548e-05 5.594268e-05 [271] 5.594029e-05 5.594222e-05 5.594243e-05 5.594377e-05 5.594353e-05 [276] 5.594323e-05 5.593824e-05 5.594059e-05 5.594146e-05 5.594592e-05 [281] 5.594266e-05 5.594038e-05 5.594052e-05 5.594303e-05 5.594231e-05 [286] 5.594155e-05 5.594306e-05 5.594096e-05 5.594184e-05 5.594487e-05 [291] 5.594224e-05 5.594317e-05 5.594265e-05 5.594409e-05 5.594360e-05 [296] 5.594264e-05 5.594013e-05 5.594477e-05 5.594184e-05 5.594099e-05 [301] 5.594113e-05 5.594177e-05 5.594521e-05 5.594329e-05 5.594008e-05 [306] 5.594067e-05 5.594113e-05 5.594378e-05 5.594422e-05 5.594210e-05 [311] 5.594377e-05 5.594098e-05 5.594304e-05 5.594554e-05 5.594239e-05 [316] 5.594028e-05 5.594354e-05 5.594524e-05 5.594026e-05 5.594232e-05 [321] 5.594202e-05 5.594115e-05 5.594259e-05 5.594282e-05 5.594354e-05 [326] 5.594104e-05 5.594483e-05 5.593957e-05 5.594359e-05 > rbeta(329, 1193280084.4218726, 21329415807424.934)*8300450000 [1] 464335.3 464325.8 464334.7 464343.6 464356.6 464349.4 464352.2 464366.4 [9] 464347.9 464335.8 464351.7 464357.4 464353.4 464359.0 464329.7 464360.9 [17] 464345.1 464358.6 464362.3 464337.5 464344.7 464334.8 464341.1 464351.5 [25] 464341.7 464336.1 464332.2 464328.4 464329.8 464334.5 464346.7 464357.9 [33] 464356.3 464324.9 464360.3 464350.0 464378.2 464354.1 464333.5 464352.7 [41] 464336.5 464354.8 464339.7 464346.1 464322.0 464345.9 464337.1 464324.2 [49] 464374.6 464334.4 464328.4 464352.0 464325.3 464344.7 464331.0 464335.8 [57] 464340.4 464332.1 464337.6 464345.9 464349.5 464373.0 464349.1 464377.2 [65] 464333.2 464354.3 464353.0 464353.9 464331.7 464336.2 464335.5 464325.5 [73] 464342.0 464348.8 464361.2 464334.0 464341.3 464340.6 464344.2 464356.5 [81] 464327.7 464346.6 464333.9 464371.8 464373.8 464352.4 464340.9 464349.6 [89] 464330.6 464361.3 464338.6 464349.9 464350.7 464344.8 464350.5 464344.5 [97] 464354.2 464344.8 464331.7 464335.6 464345.9 464348.4 464359.9 464345.7 [105] 464346.7 464328.6 464335.8 464333.8 464348.9 464359.7 464356.4 464342.5 [113] 464334.4 464364.1 464339.4 464360.3 464358.8 464323.2 464328.9 464353.9 [121] 464337.9 464332.3 464357.3 464354.3 464339.3 464337.4 464341.7 464328.3 [129] 464344.7 464340.1 464342.0 464328.1 464347.7 464336.8 464341.7 464320.6 [137] 464345.2 464357.3 464343.7 464344.4 464328.6 464346.4 464349.1 464353.1 [145] 464348.3 464328.3 464344.3 464342.1 464322.6 464340.8 464334.5 464353.9 [153] 464327.1 464337.5 464359.0 464352.7 464341.3 464347.6 464321.7 464337.0 [161] 464357.5 464343.1 464346.5 464346.0 464324.6 464324.2 464334.9 464340.2 [169] 464342.2 464333.0 464340.5 464355.9 464338.5 464360.2 464350.4 464348.8 [177] 464343.5 464339.9 464365.6 464369.5 464345.2 464333.2 464357.5 464364.4 [185] 464341.6 464341.9 464325.2 464344.8 464353.3 464337.4 464338.2 464360.2 [193] 464342.1 464349.2 464352.6 464354.2 464329.7 464350.8 464336.9 464348.7 [201] 464347.1 464324.3 464336.6 464334.8 464350.6 464358.3 464338.0 464338.6 [209] 464363.5 464343.2 464364.0 464364.7 464363.9 464360.6 464343.0 464342.7 [217] 464330.9 464325.1 464331.3 464329.9 464330.2 464357.4 464364.1 464359.3 [225] 464340.9 464365.6 464370.5 464354.5 464332.6 464334.5 464322.5 464354.4 [233] 464347.8 464349.8 464355.4 464330.1 464337.1 464328.7 464341.6 464347.7 [241] 464361.8 464365.6 464347.5 464342.6 464332.0 464340.8 464346.1 464336.2 [249] 464322.9 464334.9 464336.7 464366.6 464329.9 464360.3 464340.2 464349.6 [257] 464343.3 464363.2 464355.8 464337.8 464332.0 464318.7 464360.0 464354.3 [265] 464341.2 464344.3 464359.4 464362.8 464345.2 464353.1 464337.3 464356.3 [273] 464358.4 464338.9 464336.1 464342.5 464328.9 464326.8 464360.2 464339.9 [281] 464337.7 464353.6 464358.2 464349.9 464330.0 464357.4 464340.2 464348.8 [289] 464338.7 464349.3 464348.0 464328.9 464342.9 464341.8 464342.8 464347.4 [297] 464337.3 464339.2 464356.8 464365.3 464334.8 464335.5 464342.4 464337.4 [305] 464354.0 464342.4 464325.5 464340.6 464341.8 464351.3 464358.3 464347.3 [313] 464360.5 464360.7 464345.0 464364.6 464335.3 464359.2 464334.0 464323.4 [321] 464351.7 464343.8 464344.8 464348.9 464342.2 464352.9 464326.6 464331.2 [329] 464339.1 > And the simulation in matlab is compatible with R but not gsl: >> betarnd(1193280084.4218726, 21329415807424.934, 1, 329) ans = Columns 1 through 3 5.594116976517125e-005 5.594307509432876e-005 5.594070890122974e-005 Columns 4 through 6 5.594177332334754e-005 5.594144151553507e-005 5.594089053261321e-005 Columns 7 through 9 5.594030500205040e-005 5.594370275773622e-005 5.594213745341622e-005 Columns 10 through 12 5.594508351092454e-005 5.594269314195854e-005 5.594260866676804e-005 Columns 13 through 15 5.594451999240399e-005 5.594245963180348e-005 5.594305400875034e-005 Columns 16 through 18 5.594185433681699e-005 5.594072859438816e-005 5.594141031579324e-005 Columns 19 through 21 5.594228230021101e-005 5.594157297423446e-005 5.594146386826913e-005 Columns 22 through 24 5.594506058785692e-005 5.594329221525053e-005 5.594161379926234e-005 Columns 25 through 27 5.593958791539053e-005 5.594194047656521e-005 5.594408676813533e-005 Columns 28 through 30 5.594399083014427e-005 5.594122318673591e-005 5.594384986057607e-005 Columns 31 through 33 5.594234346127621e-005 5.594139477283736e-005 5.594293705011108e-005 Columns 34 through 36 5.594073086240927e-005 5.594230409215802e-005 5.594249441789473e-005 Columns 37 through 39 5.594553075221999e-005 5.594291187142863e-005 5.594105668859674e-005 Columns 40 through 42 5.594474433223231e-005 5.594074329107559e-005 5.594010078897129e-005 Columns 43 through 45 5.594440796414004e-005 5.594173916568297e-005 5.593968250297051e-005 Columns 46 through 48 5.594292458988601e-005 5.594175710458801e-005 5.594374032079844e-005 Columns 49 through 51 5.594354261165516e-005 5.594241347608163e-005 5.594378642817889e-005 Columns 52 through 54 5.594226333778176e-005 5.594154349143463e-005 5.594481529631574e-005 Columns 55 through 57 5.593979170178477e-005 5.594239162531335e-005 5.594259214731444e-005 Columns 58 through 60 5.594215536371488e-005 5.594321473593332e-005 5.594244544837260e-005 Columns 61 through 63 5.594155859466059e-005 5.593905054251839e-005 5.594245391668895e-005 Columns 64 through 66 5.594260396480363e-005 5.594319179026371e-005 5.594453284025467e-005 Columns 67 through 69 5.594068430005155e-005 5.594178843671324e-005 5.594245629130760e-005 Columns 70 through 72 5.594398474523334e-005 5.594106841321869e-005 5.594030015682613e-005 Columns 73 through 75 5.594333663766317e-005 5.594138443570487e-005 5.594397516473450e-005 Columns 76 through 78 5.594281600191298e-005 5.594075978985455e-005 5.594320400046854e-005 Columns 79 through 81 5.594138105917462e-005 5.594210639826208e-005 5.594058408505395e-005 Columns 82 through 84 5.594266783717796e-005 5.594206713640681e-005 5.594081825097903e-005 Columns 85 through 87 5.594213730886654e-005 5.594008901435652e-005 5.594189873018662e-005 Columns 88 through 90 5.594169509798270e-005 5.594136866381966e-005 5.594222549493435e-005 Columns 91 through 93 5.594064246729882e-005 5.593985770431319e-005 5.594122029901508e-005 Columns 94 through 96 5.594030451695832e-005 5.593945892646234e-005 5.594104332297637e-005 Columns 97 through 99 5.594241219867560e-005 5.593866245759906e-005 5.594097500386313e-005 Columns 100 through 102 5.594100509324315e-005 5.594400885590403e-005 5.593993830691756e-005 Columns 103 through 105 5.594176152143722e-005 5.594137037119920e-005 5.594196226574183e-005 Columns 106 through 108 5.593960013535379e-005 5.594621560343711e-005 5.594524577113060e-005 Columns 109 through 111 5.594258634026199e-005 5.594454537456687e-005 5.594362505350935e-005 Columns 112 through 114 5.594260321811156e-005 5.594271728515317e-005 5.594246637209145e-005 Columns 115 through 117 5.594098611836930e-005 5.594395758665778e-005 5.594355038726018e-005 Columns 118 through 120 5.594167220418465e-005 5.594275405866850e-005 5.594351847165871e-005 Columns 121 through 123 5.594495544372725e-005 5.594246115312925e-005 5.593923513945442e-005 Columns 124 through 126 5.594220682809798e-005 5.594391995351501e-005 5.594103179856737e-005 Columns 127 through 129 5.594240692054585e-005 5.594033265664693e-005 5.593920593543774e-005 Columns 130 through 132 5.594091578374392e-005 5.594182037546823e-005 5.593912629764593e-005 Columns 133 through 135 5.594149051810737e-005 5.594209611650324e-005 5.594545000733681e-005 Columns 136 through 138 5.594333543639773e-005 5.594149643630383e-005 5.593925544144164e-005 Columns 139 through 141 5.594321675311616e-005 5.594073960402282e-005 5.594057406079971e-005 Columns 142 through 144 5.594202908874395e-005 5.594091291722255e-005 5.594409765156205e-005 Columns 145 through 147 5.594211773076534e-005 5.594087586154840e-005 5.594363919983146e-005 Columns 148 through 150 5.594288490319442e-005 5.594473536677860e-005 5.594132183935755e-005 Columns 151 through 153 5.594263058202289e-005 5.594156873402826e-005 5.594489702331298e-005 Columns 154 through 156 5.594201320139460e-005 5.594240815296570e-005 5.594431162664804e-005 Columns 157 through 159 5.594295817210537e-005 5.594052615021553e-005 5.594047891681678e-005 Columns 160 through 162 5.594290645156473e-005 5.594163180689243e-005 5.594100397206000e-005 Columns 163 through 165 5.594083594230064e-005 5.594114818501491e-005 5.594208432218143e-005 Columns 166 through 168 5.594247814370323e-005 5.593967970475020e-005 5.594241362400399e-005 Columns 169 through 171 5.594082099691715e-005 5.593903507706743e-005 5.594149550480690e-005 Columns 172 through 174 5.594269428721707e-005 5.594346864349968e-005 5.594146089639748e-005 Columns 175 through 177 5.594368382047081e-005 5.594133611976175e-005 5.594147665613353e-005 Columns 178 through 180 5.594134977890160e-005 5.593953989915858e-005 5.594056565582853e-005 Columns 181 through 183 5.594188226933005e-005 5.594145969881027e-005 5.594339960737660e-005 Columns 184 through 186 5.594190904741590e-005 5.594286669580462e-005 5.594271515720490e-005 Columns 187 through 189 5.594146631883104e-005 5.594141108731878e-005 5.594057223278254e-005 Columns 190 through 192 5.594104770031066e-005 5.594221862833955e-005 5.594243597662458e-005 Columns 193 through 195 5.593941991444301e-005 5.594119877973989e-005 5.594112296741930e-005 Columns 196 through 198 5.594175570142940e-005 5.593824596957060e-005 5.594293119963867e-005 Columns 199 through 201 5.593969727673485e-005 5.593896272165682e-005 5.594330218284805e-005 Columns 202 through 204 5.594113686773274e-005 5.594264265140797e-005 5.594168352597651e-005 Columns 205 through 207 5.594346190079130e-005 5.594073495881464e-005 5.594006975886668e-005 Columns 208 through 210 5.594309873095819e-005 5.594220825072766e-005 5.594110137742228e-005 Columns 211 through 213 5.594248140008957e-005 5.594301367194254e-005 5.594254802363307e-005 Columns 214 through 216 5.594016293014028e-005 5.594001486993711e-005 5.594058293821071e-005 Columns 217 through 219 5.594256500910926e-005 5.594109425016141e-005 5.594289308331455e-005 Columns 220 through 222 5.594229249482568e-005 5.594163003832667e-005 5.594401442994122e-005 Columns 223 through 225 5.594384939608320e-005 5.594289037614979e-005 5.594203252874224e-005 Columns 226 through 228 5.594411711264699e-005 5.594121514640738e-005 5.593922191404365e-005 Columns 229 through 231 5.594277295951864e-005 5.594138843500717e-005 5.594299490048719e-005 Columns 232 through 234 5.594071626249620e-005 5.594125677616457e-005 5.594253401237773e-005 Columns 235 through 237 5.594252203194769e-005 5.594115318828081e-005 5.594213417931235e-005 Columns 238 through 240 5.594259326990705e-005 5.594481403040698e-005 5.593983125341854e-005 Columns 241 through 243 5.593917122026502e-005 5.594233464653753e-005 5.594271942127088e-005 Columns 244 through 246 5.594232442625555e-005 5.594113433884619e-005 5.594128324085816e-005 Columns 247 through 249 5.593929364343796e-005 5.594388967258510e-005 5.594324040873973e-005 Columns 250 through 252 5.594270581799822e-005 5.594190054410396e-005 5.594387425711262e-005 Columns 253 through 255 5.594083541261257e-005 5.594353015155433e-005 5.594430442956734e-005 Columns 256 through 258 5.594710087408985e-005 5.594119594638482e-005 5.594205477029677e-005 Columns 259 through 261 5.594314970488333e-005 5.594283431775281e-005 5.594498307742395e-005 Columns 262 through 264 5.593898261291080e-005 5.594334618912552e-005 5.594366627060224e-005 Columns 265 through 267 5.594518553487815e-005 5.594423467947670e-005 5.594061683737755e-005 Columns 268 through 270 5.594088856361101e-005 5.594068730231142e-005 5.594244387741737e-005 Columns 271 through 273 5.594148313145216e-005 5.594137933092187e-005 5.593862135746419e-005 Columns 274 through 276 5.594299286679637e-005 5.594403696531395e-005 5.594525254837375e-005 Columns 277 through 279 5.594328898839665e-005 5.594334593858451e-005 5.594147261137798e-005 Columns 280 through 282 5.594119186283944e-005 5.594348612167743e-005 5.594228776904790e-005 Columns 283 through 285 5.594172363285791e-005 5.594290446015821e-005 5.594062969341811e-005 Columns 286 through 288 5.594353108010688e-005 5.594150696853143e-005 5.594251017381045e-005 Columns 289 through 291 5.594531330427777e-005 5.594163540564062e-005 5.594386936929013e-005 Columns 292 through 294 5.594251703846868e-005 5.594548315499818e-005 5.594335030538874e-005 Columns 295 through 297 5.594155305696483e-005 5.594032361066344e-005 5.594296913704375e-005 Columns 298 through 300 5.593974613298600e-005 5.593941468098726e-005 5.594379423031764e-005 Columns 301 through 303 5.594014940080572e-005 5.594152329303092e-005 5.594364278695840e-005 Columns 304 through 306 5.593944901954120e-005 5.593895605105796e-005 5.594235791926526e-005 Columns 307 through 309 5.594285699970353e-005 5.593964731939407e-005 5.594174629831634e-005 Columns 310 through 312 5.594417928908562e-005 5.594108469010708e-005 5.594058634647589e-005 Columns 313 through 315 5.594336850020918e-005 5.594245905389128e-005 5.594187704864646e-005 Columns 316 through 318 5.594096636080247e-005 5.594468494523105e-005 5.594015345062150e-005 Columns 319 through 321 5.593892498592166e-005 5.594164487432806e-005 5.594202721686563e-005 Columns 322 through 324 5.594095907488165e-005 5.594507587798059e-005 5.594285778360690e-005 Columns 325 through 327 5.594064658371119e-005 5.593915342269825e-005 5.594187234125282e-005 Columns 328 through 329 5.594398967798522e-005 5.594186763116568e-005 >> betarnd(1193280084.4218726, 21329415807424.934, 1, 329)*8300450000 ans = Columns 1 through 5 4.643632275011640e+005 4.643398796883402e+005 4.643468629693436e+005 4.643219646395710e+005 4.643454759147766e+005 Columns 6 through 10 4.643123484260559e+005 4.643634182049825e+005 4.643585175792807e+005 4.643298196499965e+005 4.643705415353600e+005 Columns 11 through 15 4.643621234672779e+005 4.643311006028298e+005 4.643404501482427e+005 4.643436545108706e+005 4.643436021272134e+005 Columns 16 through 20 4.643293210731568e+005 4.643690225019546e+005 4.643484032541188e+005 4.643397160957493e+005 4.643610293196288e+005 Columns 21 through 25 4.643154353896919e+005 4.643446402328178e+005 4.643400062142421e+005 4.643295959149748e+005 4.643478468669749e+005 Columns 26 through 30 4.643435335050101e+005 4.643579103406923e+005 4.643524616517162e+005 4.643584472716897e+005 4.643418573022880e+005 Columns 31 through 35 4.643371631505659e+005 4.643384650179489e+005 4.643535931072372e+005 4.643552823833069e+005 4.643517201693080e+005 Columns 36 through 40 4.643494046401295e+005 4.643285093674614e+005 4.643580796692764e+005 4.643135727623609e+005 4.643179797630601e+005 Columns 41 through 45 4.643388882535854e+005 4.643261242738486e+005 4.643537726025506e+005 4.643677080464293e+005 4.643224087263740e+005 Columns 46 through 50 4.643720112785147e+005 4.643296982484204e+005 4.643362776499165e+005 4.643308059740513e+005 4.643371640036891e+005 Columns 51 through 55 4.643539375423049e+005 4.643589391592331e+005 4.643352608713623e+005 4.643426567244036e+005 4.643555144595868e+005 Columns 56 through 60 4.643624015577891e+005 4.643516167302441e+005 4.643184630555090e+005 4.643491298129691e+005 4.643305743963125e+005 Columns 61 through 65 4.643252628536691e+005 4.643335179898799e+005 4.643334529372681e+005 4.643609063271323e+005 4.643415604039882e+005 Columns 66 through 70 4.643515546051071e+005 4.643366269351653e+005 4.643330336514597e+005 4.643397790573603e+005 4.643620824212441e+005 Columns 71 through 75 4.643689676238144e+005 4.643392371603089e+005 4.643539357938063e+005 4.643485788819068e+005 4.643386388187275e+005 Columns 76 through 80 4.643592722300096e+005 4.643511989887276e+005 4.643557231388455e+005 4.643280432887639e+005 4.643428462004606e+005 Columns 81 through 85 4.643446976526951e+005 4.643703180037447e+005 4.643324495979446e+005 4.643270231148266e+005 4.643479137585869e+005 Columns 86 through 90 4.643285552443229e+005 4.643497320224798e+005 4.643682963700976e+005 4.643468523132139e+005 4.643681796457944e+005 Columns 91 through 95 4.643238592770349e+005 4.643527340808194e+005 4.643382581051545e+005 4.643308596926095e+005 4.643420183163197e+005 Columns 96 through 100 4.643463872295352e+005 4.643428775673898e+005 4.643486194788878e+005 4.643422110411792e+005 4.643409160503030e+005 Columns 101 through 105 4.643643522734116e+005 4.643458376472644e+005 4.643209376013739e+005 4.643477393960658e+005 4.643554928059244e+005 Columns 106 through 110 4.643433061765379e+005 4.643541382372177e+005 4.643406016184056e+005 4.643411767665339e+005 4.643291112816093e+005 Columns 111 through 115 4.643345942484544e+005 4.643334489767274e+005 4.643243199283715e+005 4.643546944775833e+005 4.643199128271390e+005 Columns 116 through 120 4.643535280642366e+005 4.643449431428578e+005 4.643355340600840e+005 4.643543382352680e+005 4.643625765383753e+005 Columns 121 through 125 4.643373158294369e+005 4.643442060014003e+005 4.643579584954574e+005 4.643382931928397e+005 4.643330377453567e+005 Columns 126 through 130 4.643544320927053e+005 4.643420748134670e+005 4.643490374981659e+005 4.643621399147669e+005 4.643673087480495e+005 Columns 131 through 135 4.643537992813899e+005 4.643533420670073e+005 4.643351222984800e+005 4.643466289321145e+005 4.643809062466746e+005 Columns 136 through 140 4.643190626934905e+005 4.643534464031382e+005 4.643476606548895e+005 4.643442722853824e+005 4.643380479466388e+005 Columns 141 through 145 4.643419676393427e+005 4.643455674219854e+005 4.643315251058494e+005 4.643422627785528e+005 4.643658369963028e+005 Columns 146 through 150 4.643486868065267e+005 4.643460593935046e+005 4.643442067059535e+005 4.643584844427633e+005 4.643401377461248e+005 Columns 151 through 155 4.643490111556829e+005 4.643481282964944e+005 4.643573791325794e+005 4.643313222659806e+005 4.643647923745302e+005 Columns 156 through 160 4.643539417191992e+005 4.643649112488547e+005 4.643678095202511e+005 4.643500058821677e+005 4.643375380537305e+005 Columns 161 through 165 4.643490069994099e+005 4.643429045957657e+005 4.643414880222358e+005 4.643615326310709e+005 4.643272055576847e+005 Columns 166 through 170 4.643456766366951e+005 4.643490670475120e+005 4.643365703479624e+005 4.643531013828349e+005 4.643546142686590e+005 Columns 171 through 175 4.643370892237912e+005 4.643277725704016e+005 4.643619434846910e+005 4.643460294895975e+005 4.643565796981872e+005 Columns 176 through 180 4.643740870838435e+005 4.643492459877483e+005 4.643637294138572e+005 4.643546075883882e+005 4.643335811834032e+005 Columns 181 through 185 4.643419569187990e+005 4.643400669702721e+005 4.643498522635567e+005 4.643454402406518e+005 4.643450666481066e+005 Columns 186 through 190 4.643416089798571e+005 4.643492875402543e+005 4.643333132784517e+005 4.643589265546824e+005 4.643487955969636e+005 Columns 191 through 195 4.643185494290022e+005 4.643493712638818e+005 4.643249015713516e+005 4.643575554129141e+005 4.643750533056700e+005 Columns 196 through 200 4.643295232034289e+005 4.643409412811477e+005 4.643598137831446e+005 4.643591033762975e+005 4.643520426510159e+005 Columns 201 through 205 4.643582152213663e+005 4.643513248886291e+005 4.643529985786041e+005 4.643588989306376e+005 4.643405572404293e+005 Columns 206 through 210 4.643607264756663e+005 4.643269038838187e+005 4.643589827249778e+005 4.643560590551210e+005 4.643269411530832e+005 Columns 211 through 215 4.643532804488290e+005 4.643608103600613e+005 4.643451858647363e+005 4.643484289391422e+005 4.643428390716066e+005 Columns 216 through 220 4.643373983298229e+005 4.643546118940772e+005 4.643267886875919e+005 4.643262664746865e+005 4.643295299666774e+005 Columns 221 through 225 4.643405380308517e+005 4.643253725780229e+005 4.643416531618026e+005 4.643614060550475e+005 4.643584701495933e+005 Columns 226 through 230 4.643186295302996e+005 4.643736476885003e+005 4.643201543037648e+005 4.643316645960849e+005 4.643515632181026e+005 Columns 231 through 235 4.643234393515186e+005 4.643526619888084e+005 4.643646675630445e+005 4.643522913564080e+005 4.643391036476305e+005 Columns 236 through 240 4.643204818076211e+005 4.643653946839592e+005 4.643416241458239e+005 4.643632703689794e+005 4.643511779329067e+005 Columns 241 through 245 4.643501373688814e+005 4.643535665383966e+005 4.643337887793146e+005 4.643246872703877e+005 4.643430460841355e+005 Columns 246 through 250 4.643472485948831e+005 4.643611417407431e+005 4.643488911763027e+005 4.643433345248755e+005 4.643284824845626e+005 Columns 251 through 255 4.643359203450010e+005 4.643515651992420e+005 4.643328435304719e+005 4.643415473230789e+005 4.643512589146242e+005 Columns 256 through 260 4.643441666357514e+005 4.643470442000009e+005 4.643431680038117e+005 4.643315277714049e+005 4.643636867361901e+005 Columns 261 through 265 4.643580780850057e+005 4.643498591853780e+005 4.643379006182123e+005 4.643677750677940e+005 4.643534609178956e+005 Columns 266 through 270 4.643355312905767e+005 4.643414713863077e+005 4.643432785670705e+005 4.643346300176565e+005 4.643409163850018e+005 Columns 271 through 275 4.643407158246979e+005 4.643416642311160e+005 4.643588544316301e+005 4.643269687623129e+005 4.643619018339601e+005 Columns 276 through 280 4.643397515337427e+005 4.643607933498398e+005 4.643280858735651e+005 4.643411077374230e+005 4.643495027330719e+005 Columns 281 through 285 4.643255324333838e+005 4.643411895076546e+005 4.643425946816248e+005 4.643551488206824e+005 4.643326650573082e+005 Columns 286 through 290 4.643765239685633e+005 4.643419318026134e+005 4.643598862957180e+005 4.643460507766492e+005 4.643460146183794e+005 Columns 291 through 295 4.643449351675858e+005 4.643411153174643e+005 4.643572044655832e+005 4.643602784236706e+005 4.643463008513494e+005 Columns 296 through 300 4.643385613931830e+005 4.643596008592218e+005 4.643520167635302e+005 4.643420537073856e+005 4.643541821260973e+005 Columns 301 through 305 4.643391453680849e+005 4.643713453262135e+005 4.643746668608572e+005 4.643206960167905e+005 4.643482957256964e+005 Columns 306 through 310 4.643356644732949e+005 4.643538264783296e+005 4.643487146737252e+005 4.643419335839302e+005 4.643593459637647e+005 Columns 311 through 315 4.643413723969312e+005 4.643307417397166e+005 4.643478223699888e+005 4.643242210645571e+005 4.643487571968277e+005 Columns 316 through 320 4.643514034924307e+005 4.643515331074679e+005 4.643532536224519e+005 4.643744618243399e+005 4.643601871972398e+005 Columns 321 through 325 4.643419462196911e+005 4.643320355220826e+005 4.643522681082228e+005 4.643426441267751e+005 4.643683841158581e+005 Columns 326 through 329 4.643499428782344e+005 4.643313150961776e+005 4.643463691049435e+005 4.643469157690397e+005 Thank you very much fro your help. Frank
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[bug-gsl] bug with function gsl_ran_beta (2008-11-18)
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