Wed Oct 8 08:44:49 2025 pdflib_test(): python version: 3.10.12 numpy version: 1.26.4 Test pdflib(). initialize(): rnglib() has been initialized. i4_uni_test(): i4_uni() returns a random positive integer. 695163044 696626468 1059541850 620042603 758075822 330628445 1215929140 1762482382 698994348 730315574 1922376880 722841757 612082173 1081002351 1661144525 45434058 79485022 624052430 184849954 1605430415 r8_uni_01_test(): r8_uni_01 produces a sequence of random values. r8_uni_01() 0.359446 0.208128 0.0797663 0.147932 0.708155 0.395446 0.76442 0.645941 0.473061 0.859549 r8ge_print_test(): r8ge_print() prints an R8GE matrix. Here is an R8MAT: Col: 0 1 2 3 4 Row 0 : 11 12 13 14 15 1 : 21 22 23 24 25 2 : 31 32 33 34 35 3 : 41 42 43 44 45 Col: 5 Row 0 : 16 1 : 26 2 : 36 3 : 46 r8ge_print_some_test(): r8ge_print_some() prints some of an R8GE matrix. Here is an R8GE matrix: Col: 3 4 5 Row 0 : 14 15 16 1 : 24 25 26 2 : 34 35 36 r8mat_norm_fro_affine_test(): r8mat_norm_fro_affine() computes the Frobenius norm of the difference of two R8MAT's; Expected norm = 1.49863 Computed norm = 1.49863 r8po_mv_test(): r8po_mv computes the product of an R8PO matrix and a vector. Matrix order N = 5 Matrix A: Col: 0 1 2 3 4 Row 0 : 2 -1 0 0 0 1 : -1 2 -1 0 0 2 : 0 -1 2 -1 0 3 : 0 0 -1 2 -1 4 : 0 0 0 -1 2 Vector V: 0: 1 1: 2 2: 3 3: 4 4: 5 Product w = A * v: 0: 0 1: 0 2: 0 3: 0 4: 6 r8ut_sl_test(): r8ut_sl solves a linear system A*x=b with R8UT matrix Matrix order N = 5 The upper triangular matrix: Col: 0 1 2 3 4 Row 0 : 1 2 3 4 5 1 : 2 3 4 5 2 : 3 4 5 3 : 4 5 4 : 5 Right hand side b: 0: 55 1: 54 2: 50 3: 41 4: 25 Solution: 0: 1 1: 2 2: 3 3: 4 4: 5 r8vec_indicator1_test(): r8vec_indicator1 returns the 1-based indicator matrix. The 1-based indicator vector: 0: 1 1: 2 2: 3 3: 4 4: 5 5: 6 6: 7 7: 8 8: 9 9: 10 i4_binomial_pdf_test(): i4_binomial_pdf() evaluates the binomial pdf pdf(n,p,k) = probability, in n trials, of k successes, if a single success has probability p. N P K PDF(N,P,K) PDF(N,P,K) tabulated computed 5 0.829509 5 0.392741 0.392741 12 0.0661187 5 0.000619997 0.000619997 6 0.043829 0 0.764211 0.764211 13 0.449539 0 0.000426035 0.000426035 9 0.797287 7 0.302948 0.302948 1 0.350752 1 0.350752 0.350752 2 0.859097 0 0.0198537 0.0198537 17 0.00751236 2 0.00685439 0.00685439 6 0.113664 6 2.15645e-06 2.15645e-06 8 0.267132 7 0.000569115 0.000569115 i4_binomial_sample_test(): i4_binomial_sample() samples the binomial distribution. N P K PDF(N,P,K) 11 0.125821 0 0.227828 8 0.362741 1 0.123851 15 0.142831 3 0.208582 7 0.920136 6 0.339281 5 0.67999 2 0.151529 2 0.79452 2 0.631262 17 0.861563 16 0.216917 13 0.142962 1 0.291854 13 0.0498494 0 0.514401 12 0.772115 12 0.0448934 initialize(): rnglib() has been initialized. i4_uniform_sample_test(): i4_uniform_sample() samples the uniform distribution on integers. Generate C between A and B. A B C 2 8 4 3 14 7 8 16 8 2 7 7 7 18 12 4 5 4 -1 8 0 2 11 11 4 10 8 -4 14 6 i4vec_multinomial_pdf_test(): i4vec_multinomial_pdf() evaluates the multinomial PDF. Given M possible outcomes on a single trial, with each outcome having probability P, PDF is the probability that after N trials, outcome I occurred X(I) times. N M I P X PDF() PDF() tabulated computed 0 0.7000 2 1 0.3000 1 3 2 0.441 0.441 0 0.7000 2 1 0.3000 2 4 2 0.2646 0.2646 0 0.5000 2 1 0.5000 1 3 2 0.375 0.375 0 0.6000 1 1 0.0000 1 2 0.4000 1 3 3 0 0 0 0.6000 3 1 0.1000 0 2 0.1000 0 3 0.1000 0 4 0.1000 0 3 5 0.216 0.216 0 0.6000 2 1 0.1000 1 2 0.1000 0 3 0.1000 0 4 0.1000 0 3 5 0.108 0.108 0 0.6000 1 1 0.1000 0 2 0.1000 2 3 0.1000 0 4 0.1000 0 3 5 0.018 0.018 0 0.6000 1 1 0.1000 0 2 0.1000 0 3 0.1000 1 4 0.1000 1 3 5 0.036 0.036 0 0.6000 0 1 0.1000 0 2 0.1000 0 3 0.1000 3 4 0.1000 0 3 5 0.001 0.001 0 0.6000 0 1 0.1000 1 2 0.1000 1 3 0.1000 1 4 0.1000 0 3 5 0.006 0.006 i4vec_multinomial_sample_test(): i4vec_multinomial_sample() samples the multinomial distribution. N M I P X PDF() 0 0.1954 1 1 0.0904 0 2 0.0723 0 3 0.2496 1 4 0.0389 0 5 0.1026 0 6 0.2206 0 7 0.0302 0 2 8 0.0975592 0 0.2253 0 1 0.0681 1 2 0.2841 4 3 0.2254 0 4 0.1971 0 5 5 0.00221597 0 0.2056 0 1 0.0974 0 2 0.0616 0 3 0.0316 0 4 0.1112 0 5 0.1195 0 6 0.1600 2 7 0.0062 0 8 0.1728 0 9 0.0343 0 2 10 0.0255927 0 0.2391 1 1 0.1277 0 2 0.0526 0 3 0.1680 1 4 0.2030 0 5 0.0589 0 6 0.0344 0 7 0.1163 0 2 8 0.0803601 0 0.0938 0 1 0.1635 0 2 0.0156 0 3 0.0776 1 4 0.1258 0 5 0.1245 1 6 0.0290 0 7 0.0870 0 8 0.1653 1 9 0.1180 1 4 10 0.00452303 0 0.7413 2 1 0.2587 0 2 2 0.549545 0 0.2427 2 1 0.2901 0 2 0.1331 1 3 0.1440 0 4 0.1900 0 3 5 0.0235299 0 0.3648 2 1 0.5658 3 2 0.0695 0 5 3 0.240973 0 0.1345 0 1 0.1247 0 2 0.1008 1 3 0.1634 0 4 0.2108 1 5 0.1100 0 6 0.0018 0 7 0.1540 2 4 8 0.00604579 0 0.1428 1 1 0.0095 0 2 0.1908 3 3 0.1078 1 4 0.0064 0 5 0.0286 0 6 0.0363 0 7 0.1859 0 8 0.1783 0 9 0.1136 0 5 10 0.00213923 r8_beta_pdf_test(): r8_beta_pdf() evaluates the BETA PDF. ALPHA BETA X PDF() PDF() tabulated computed 1.09209 4.78159 0.866722 0.00282614 0.00282614 2.80848 2.07654 0.0460776 0.0420895 0.0420895 1.28789 0.549784 0.0221162 0.218406 0.218406 3.16983 0.308636 0.458254 0.133514 0.133514 2.00653 3.77337 0.832083 0.107057 0.107057 0.00919186 4.48752 0.352059 0.00579639 0.00579639 0.472724 0.0680845 0.898529 0.55188 0.55188 4.20424 0.61552 -0.0169242 0 0 1.30151 4.56242 0.0971888 2.87907 2.87907 1.75814 4.11444 0.262167 2.12699 2.12699 r8_beta_sample_test(): r8_beta_sample() samples the beta distribution. ALPHA BETA X PDF() 4.39925 1.47324 0.74646 2.08421 4.95559 2.0372 0.885117 2.0363 0.0602916 3.11501 0.00451364 10.4625 0.482532 0.230367 0.775762 0.634735 0.576315 2.66462 0.0718465 2.93136 4.80292 1.93625 0.720204 2.21534 3.16375 4.51281 0.456889 2.05451 3.46181 2.04015 0.567763 1.67939 3.11786 4.84989 0.306672 2.19863 0.856398 4.37532 0.00854962 6.07408 r8_chi_pdf_test(): r8_chi_pdf() evaluates the standard chi PDF. DF X PDF() PDF() tabulated computed 1 0.01 3.96953 3.96953 2 0.01 0.497506 0.497506 1 0.02 2.79288 2.79288 2 0.02 0.495025 0.495025 1 0.4 0.516442 0.516442 2 0.4 0.409365 0.409365 3 0.4 0.206577 0.206577 4 0.4 0.0818731 0.0818731 1 1 0.241971 0.241971 2 1 0.303265 0.303265 3 1 0.241971 0.241971 4 1 0.151633 0.151633 5 1 0.0806569 0.0806569 3 2 0.207554 0.207554 3 3 0.15418 0.15418 3 4 0.107982 0.107982 3 5 0.0732249 0.0732249 3 6 0.0486522 0.0486522 10 1 0.000789753 0.000789753 10 2 0.00766416 0.00766416 10 3 0.0235333 0.0235333 r8_chi_sample_test(): r8_chi_sample() samples the CHI distribution: DF R PDF 7.56025 10.4679 0.0579535 9.70415 10.4426 0.0816217 8.18641 11.5084 0.0526278 2.8548 2.36577 0.185754 14.5734 15.5653 0.0673039 8.56829 7.31861 0.105203 11.9749 19.8698 0.0193959 5.61459 6.78053 0.0907436 4.17215 3.42415 0.155677 0.575646 0.838469 0.195411 r8_exponential_01_pdf_test(): r8_exponential_01_pdf() evaluates the standard exponential pdf. X PDF() PDF() tabulated computed 0.701301 0.49594 0.49594 4.75975 0.00856778 0.00856778 4.0623 0.0172094 0.0172094 2.58932 0.0750707 0.0750707 1.78419 0.167933 0.167933 -0.136347 0 0 0.916678 0.399845 0.399845 0.104762 0.900538 0.900538 -0.258941 0 0 2.98681 0.050448 0.050448 r8_exponential_01_sample_test(): r8_exponential_01_sample() samples the standard exponential PDF: R PDF(R) 1.39169 0.248656 1.01353 0.362935 0.0702456 0.932165 0.329386 0.719365 0.615192 0.540537 2.60084 0.0742113 1.08103 0.339245 3.17825 0.0416585 0.289046 0.748978 0.91336 0.401174 r8_exponential_pdf_test(): r8_exponential_pdf() evaluates the exponential PDF. BETA X PDF() PDF() tabulated computed 1.09209 9.55881 0.0001447 0.0001447 4.14755 5.57312 0.0628985 0.0628985 2.07654 0.567799 0.366361 0.366361 1.28789 1.01056 0.354279 0.354279 0.219145 6.30305 1.47258e-12 1.47258e-12 0.308636 4.44034 1.82964e-06 1.82964e-06 2.00653 7.5222 0.011734 0.011734 3.98643 -0.0814325 0 0 4.48752 3.4426 0.103472 0.103472 0.472724 0.0375306 1.95395 1.95395 r8_exponential_sample_test(): r8_exponential_sample() samples the general exponential PDF: BETA R PDF 1.5199 1.24012 0.290961 0.368701 0.355585 1.0339 7.09117 1.95541 0.107035 6.31727 3.10737 0.0967939 3.80426 2.05367 0.153208 0.89609 0.391184 0.721206 7.67069 8.43294 0.0434225 8.60808 7.49058 0.0486608 6.85305 1.50912 0.117079 8.31826 14.7421 0.0204309 r8_gamma_01_pdf_test(): r8_gamma_01_pdf() evaluates the standard gamma PDF. ALPHA X PDF(0,1) PDF(0,1) tabulated computed 1.09209 9.54133 9.26081e-05 9.26081e-05 4.14755 5.3978 0.126034 0.126034 2.07654 0.194247 0.136354 0.136354 1.28789 0.654546 0.511445 0.511445 0.219145 6.15664 0.000123014 0.000123014 0.308636 4.22016 0.00187034 0.00187034 2.00653 7.42407 0.004476 0.004476 3.98643 -0.480697 0 0 4.48752 3.1829 0.205667 0.205667 0.472724 -0.357023 0 0 r8_gamma_01_sample_test(): r8_gamma_01_sample() samples the standard gamma distribution. A X PDF() 3.81845 1.75549 0.175892 3.14413 3.036 0.226495 2.416 0.234256 0.080724 1.35826 3.48035 0.0540735 4.9949 5.22012 0.167154 2.34137 4.50606 0.0695161 4.12164 2.27139 0.1907 2.1666 1.48522 0.331925 1.31145 0.453957 0.554391 0.792299 0.910766 0.349619 r8_gamma_pdf_test(): r8_gamma_pdf() evaluates a gamma PDF. BETA ALPHA X PDF PDF tabulated computed 1.09209 4.78159 4.94296 0.167202 0.167202 2.80848 2.07654 0.209936 0.852212 0.852212 1.28789 0.549784 0.0717398 2.12227 2.12227 3.16983 0.308636 2.58714 6.99377e-05 6.99377e-05 2.00653 3.77337 4.74318 0.0167938 0.0167938 0.00919186 4.48752 1.97466 6.68746e-10 6.68746e-10 0.472724 0.0680845 5.1264 0.00129544 0.00129544 4.20424 0.61552 -0.153423 0 0 1.30151 4.56242 0.504717 0.0118989 0.0118989 1.75814 4.11444 1.45622 0.365884 0.365884 r8_gamma_sample_test(): r8_gamma_sample() samples a gamma distribution. R A X PDF() 2.50931 2.40484 0.105535 0.238963 3.03703 0.636005 0.171363 1.62112 3.73218 0.642489 0.16322 1.73168 3.69494 3.67966 1.51813 0.337591 2.12487 0.64944 0.889302 0.185379 1.23745 3.00675 1.01457 0.276581 2.26957 3.67344 0.916741 0.496845 4.45765 2.15224 1.3931 0.0683738 1.72678 0.617905 0.378888 0.728249 3.62145 4.89664 1.15694 0.708952 r8_invchi_pdf_test: r8_invchi_pdf returns values of the inverse Chi Square Probability Density Function. DF X PDF PDF 1 0.1 0.08500366602520341 0.08500366602520341 2 0.1 0.3368973499542734 0.3368973499542732 1 0.2 0.3661245640481622 0.3661245640481621 2 0.2 1.026062482798735 1.026062482798735 1 0.4 0.4518059816704532 0.4518059816704532 2 0.4 0.8953274901880941 0.8953274901880941 3 0.4 1.129514954176133 1.129514954176133 4 0.4 1.119159362735118 1.119159362735117 1 1 0.2419707245191433 0.2419707245191434 2 1 0.3032653298563167 0.3032653298563167 3 1 0.2419707245191433 0.2419707245191434 4 1 0.1516326649281584 0.1516326649281584 5 1 0.08065690817304778 0.08065690817304777 3 2 0.0549239111834653 0.05492391118346532 3 3 0.02166329508030457 0.02166329508030457 3 4 0.01100204146138436 0.01100204146138436 3 5 0.006457369034861447 0.006457369034861448 3 6 0.004162370481945731 0.004162370481945732 10 1 0.0007897534631674914 0.0007897534631674914 10 2 1.584474249412852e-05 1.584474249412853e-05 10 3 1.511920090468204e-06 1.511920090468204e-06 r8_invchi_sample_test(): r8_invchi_sample() samples an inverse chi square distribution. DF X PDF() 2.31536 0.206233 1.286 2.85114 0.435653 1.00045 0.921313 1.93984 0.110968 2.32042 0.230306 1.3094 1.48312 1.50911 0.169559 0.082024 1.39005e+10 1.12523e-12 1.24819 1.17465 0.227223 4.03551 0.185601 2.67035 4.61419 0.404977 0.997114 4.96068 0.129729 3.53793 r8_invgam_pdf_test: r8_invgam_pdf evaluates the inverse gamma Probability Density Function. ALPHA BETA X PDF PDF 1 0.5 1 0.3032653298563167 0.3032653298563167 1 0.5 2 0.09735009788392561 0.09735009788392562 1 0.5 3 0.047026762493923 0.047026762493923 1 0.5 4 0.02757802820576861 0.02757802820576861 1 2 2 0.1839397205857212 0.1839397205857211 1 3 2 0.1673476201113224 0.1673476201113224 1 4 2 0.1353352832366127 0.1353352832366127 1 5 2 0.1026062482798735 0.1026062482798735 2 2 3 0.07606179541223586 0.07606179541223584 3 2 3 0.02535393180407862 0.02535393180407861 4 2 3 0.005634207067573026 0.005634207067573021 5 2 3 0.0009390345112621711 0.0009390345112621706 r8_invgam_sample_test(): r8_invgam_sample() samples an inverse gamma distribution. R A X PDF() 1.88898 2.37981 1.54492 0.250834 0.794545 2.50656 0.123359 1.03182 1.89565 2.25543 0.642006 0.822398 4.56657 4.30246 1.13239 0.710461 4.52327 3.17816 1.92941 0.314298 3.24232 4.73178 0.70184 1.21328 0.259326 3.59627 0.157821 1.97472 0.970439 3.739 0.253085 2.97745 0.0421862 0.61913 0.199897 1.06856 2.19865 4.53261 0.634595 1.13115 r8_normal_01_pdf_test: r8_normal_01_pdf evaluates the standard normal pdf with mean = 0 and standard deviation = 1. X PDF(0,1) PDF(0,1) tabulated computed -2.252653624140994 0.03155059887555709 0.03155059887555706 3.650540612071437 0.0005094586261557538 0.0005094586261557547 2.636073871461605 0.01235886992552887 0.01235886992552886 0.4935635421351536 0.353192862601275 0.353192862601275 -0.6775433481923101 0.3171212685764107 0.3171212685764107 -3.471050120671749 0.0009653372813755943 0.000965337281375596 -1.939377660943641 0.06083856556197816 0.0608385655619781 -3.120345651740235 0.003066504313116445 0.003066504313116445 -3.649368017767143 0.0005116437388114821 0.0005116437388114826 1.0717256984193 0.2246444116615346 0.2246444116615346 r8_normal_01_sample_test(): r8_normal_01_sample() samples the normal distribution. X PDF(X) -0.375628 0.371767 -0.0841264 0.397533 -0.0348571 0.3987 1.90223 0.0653378 -2.5749 0.0144945 0.236399 0.387949 0.984075 0.245824 0.28042 0.383561 -1.17247 0.200632 -0.789218 0.292184 r8_normal_pdf_test: r8_normal_pdf evaluates the normal pdf pdf(mu,sigma) is the normal pdf with mu = mean, sigma = standard deviation. MU SIGMA X PDF(MU,SIGMA) PDF(MU,SIGMA) tabulated computed -56.31634060352484 4.785956124893755 -46.85424018542929 0.01180775937213258 0.01180775937213258 12.33908855337884 2.13500469923221 6.781057314200307 0.006307849174478944 0.006307849174478969 -48.48444152359102 0.6387882883091059 -50.23282168570062 0.0147514774470322 0.0147514774470322 26.7931424604825 0.4024634224214489 26.67129012408019 0.9468437743011001 0.9468437743011002 -19.73874370047668 3.79790008346491 -12.9643468135976 0.02140312299941794 0.0214031229994179 -99.63232576831896 4.497769898408682 -103.6600156181528 0.05939959967353488 0.05939959967353472 -81.09104995766396 0.1667227687589636 -80.73183222587458 0.2348929157422787 0.2348929157422788 68.16949013113364 0.7032091872463158 66.09155915000321 0.007207515678571277 0.007207515678571277 -47.93940044652702 4.57117016420902 -58.53544475210675 0.005944396897656727 0.005944396897656727 -29.67426801922078 4.132147851761006 -35.44773135435396 0.03637663165771322 0.03637663165771318 r8_normal_sample_test(): r8_normal_sample() samples the normal distribution. MU SIGMA X PDF(MU,SIGMA) 71.1679 0.174392 71.2426 2.08722 -17.847 0.677047 -17.2243 0.386058 -86.5757 0.756897 -86.6405 0.52515 18.7612 0.475067 19.2731 0.469937 61.2043 0.0879721 61.102 2.30418 93.5112 0.880368 94.3807 0.278239 -18.0354 0.44448 -18.3741 0.671407 22.6806 0.878423 22.3019 0.413858 92.1088 0.199064 92.5452 0.181335 -6.54902 0.259736 -7.30724 0.0216722 r8_scinvchi_pdf_test: r8_scinvchi_pdf evaluates the scaled inverse Chi Square Probability Density Function. DF XI X PDF PDF 1 0.5 0.1 0.7322491280963244 0.7322491280963243 2 0.5 0.1 0.3368973499542734 0.3368973499542732 1 0.5 0.2 0.9036119633409063 0.9036119633409061 2 0.5 0.2 1.026062482798735 1.026062482798735 1 0.5 0.4 0.5968580144169457 0.5968580144169456 2 0.5 0.4 0.8953274901880941 0.8953274901880939 1 1 0.1 0.08500366602520341 0.08500366602520341 2 1 0.1 0.004539992976248485 0.004539992976248483 1 1 0.2 0.3661245640481622 0.3661245640481621 2 1 0.2 0.1684486749771367 0.1684486749771366 1 1 0.4 0.4518059816704532 0.4518059816704532 2 1 0.4 0.5130312413993675 0.5130312413993674 1 2 0.1 0.0008099910956089117 0.0008099910956089113 2 2 0.1 4.122307244877116e-07 4.122307244877103e-07 1 2 0.2 0.04250183301260171 0.0425018330126017 2 2 0.2 0.002269996488124243 0.002269996488124244 1 2 0.4 0.1830622820240811 0.1830622820240811 2 2 0.4 0.08422433748856833 0.08422433748856835 r8_scinvchi_sample_test(): r8_scinvchi_sample() samples a scaled inverse chi square distribution. DF XI X PDF 4.476 1.98112 3.19987 0.144155 3.0218 4.6172 9.08595 0.0386416 3.844 0.779224 1.79121 0.176925 3.80193 3.37588 2.30709 0.195106 1.99941 0.880251 2.83034 0.08051 0.249416 1.08261 4.70498e+07 2.42145e-10 0.391667 2.43999 2.78666e+08 1.46796e-11 3.98359 3.991 3.56992 0.14937 3.65016 3.90161 7.5708 0.0491441 2.17531 4.29532 1.902 0.125277 r8_uniform_01_pdf_test(): r8_uniform_01_pdf() evaluates the standard uniform PDF. X PDF() 0.9773039429468038 1 0.1467221075254863 1 1.498333307720428 0 1.162271798930835 0 0.5041595543972577 1 0.8541720086457725 1 1.137247358257005 0 0.3180689437450945 1 0.4657337665129162 1 -0.2930962012492579 0 r8_uniform_01_sample_test(): r8_uniform_01_sample returns random values in [0,1]: 0.323711 0.324392 0.493388 0.28873 0.353007 0.153961 0.566211 0.82072 0.325495 0.34008 r8_uniform_pdf_test(): r8_uniform_pdf() evaluates the uniform pdf over [A,B]. A B X PDF() -39.6272 47.2208 -69.5574 0 -4.07123 19.5057 -34.7055 0 -73.9842 -14.4156 2.09281 0 -67.6955 82.3743 -38.7534 0.00666356 -29.7113 60.6602 -6.97431 0.0110654 -52.2396 -7.53626 73.5526 0 -65.0887 88.972 -71.0261 0 -65.2342 78.4095 -97.5453 0 50.5828 88.6274 42.3116 0 -63.9013 28.3127 97.2075 0 r8_uniform_sample_test(): r8_uniform_sample() returns random values in [A,B]: A B R -47.8645 98.1255 74.1064 -21.6634 35.5824 -12.2286 69.2362 97.0888 93.5769 -55.6725 62.3873 32.8841 88.5217 97.8553 89.0676 -9.39972 63.8812 36.5711 5.55973 45.1635 34.028 -6.80299 80.4392 40.4986 -3.55605 3.46915 0.704173 -47.7109 33.1233 -36.8648 initialize(): rnglib() has been initialized. r8vec_multinormal_pdf_test(): r8vec_multinormal_pdf() evaluates the PDF for the multinormal distribution. The covariance matrix is C. The definition uses the inverse of C; r8vec_multinormal_pdf uses the Cholesky factor R Verify that the algorithms are equivalent. R1: Col: 0 1 2 3 4 Row 0 : 0.877055 0.582292 0.949617 0.142118 0.179652 1 : 0.475059 0.594447 0.187446 0.425916 2 : 0.715722 0.899509 0.835107 3 : 0.245017 0.214606 4 : 0.909154 C: Col: 0 1 2 3 4 Row 0 : 0.769225 0.510702 0.832866 0.124645 0.157565 1 : 0.510702 0.564745 0.835352 0.171802 0.306945 2 : 0.832866 0.835352 1.7674 0.890182 1.02149 3 : 0.124645 0.171802 0.890182 0.924482 0.909136 4 : 0.157565 0.306945 1.02149 0.909136 1.7837 R2: Col: 0 1 2 3 4 Row 0 : 0.877055 0.582292 0.949617 0.142118 0.179652 1 : 0.475059 0.594447 0.187446 0.425916 2 : 0.715722 0.899509 0.835107 3 : 0.245017 0.214606 4 : 0.909154 Determinant of C = 0.00441268 inverse(C): Col: 0 1 2 3 4 Row 0 : 6.39149 5.66759 -9.2387 6.6008 0.386556 1 : 5.66759 30.8706 -27.0678 20.1198 -0.566633 2 : -9.2387 -27.0678 28.2681 -20.8649 -0.0798581 3 : 6.6008 20.1198 -20.8649 17.5856 -1.05967 4 : 0.386556 -0.566633 -0.0798581 -1.05967 1.20983 MU: 0: 0.288888 1: 0.263202 2: -0.744072 3: 0.133409 4: -0.18945 X: 0: 0.288244 1: 0.26203 2: -0.745811 3: 0.132814 4: -0.18663 PDF1 = 0.1521229484126864 PDF2 = 0.1521229484126864 initialize(): rnglib() has been initialized. r8vec_multinormal_sample_test(): r8vec_multinormal_sample() samples the multinormal distribution. N I MU X PDF() 0 3.3108 2.5469 1 0.8114 2.0388 2 0.4582 0.3047 3 -3.5530 -3.7500 4 1.0253 0.9766 5 0.00262325 0 1.0831 1.8717 1 -2.3408 -2.0503 2 -1.1985 -3.2746 3 -3.1521 -1.2927 4 -1.7362 -1.0255 5 0.000511045 0 -0.4107 -1.6522 1 -3.7565 -2.9937 2 -2.2891 -2.5390 3 -3.1790 -2.6010 4 4.2668 4.0247 5 0.00251971 0 -1.9339 -2.3585 1 -4.1713 -4.3567 2 4.6291 4.3218 3 2.5519 2.4541 4 -4.9543 -4.4752 5 0.00295615 0 0.5602 -2.8076 1 -0.6695 1.4067 2 -4.1644 -2.7715 3 -0.7093 -0.5846 4 1.5241 1.3412 5 2.76905e-05 0 1.8418 -1.5502 1 1.1847 2.0255 2 -0.1653 0.1632 3 3.1913 1.9028 4 -2.3833 -2.5420 5 3.57522e-05 0 -3.7545 -2.9766 1 -3.6604 -5.3344 2 0.5817 2.6685 3 -4.4889 -6.0115 4 2.0481 3.2823 5 0.000792089 0 1.1149 1.0721 1 -3.2849 -1.9494 2 2.2529 -0.5883 3 -0.1874 0.1561 4 2.9587 3.5384 5 0.000312809 0 -1.4448 -1.4517 1 -2.3967 -2.2126 2 -0.5657 -1.5950 3 -1.9591 -0.0673 4 -0.0755 -1.0783 5 0.00166568 0 -3.5551 -3.9264 1 4.9973 5.5292 2 1.5804 1.3390 3 2.4707 1.2773 4 3.3179 3.2537 5 0.00138743 pdflib_test(): Normal end of execution. Wed Oct 8 08:44:50 2025