Thu Sep 13 12:59:10 2018 PDFLIB_TEST Python version: 3.6.5 Test the PDFLIB library. INITIALIZE: The RNGLIB package has been initialized. I4_UNI_TEST Python version: 3.6.5 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 I4_UNI_TEST: Normal end of execution. I4_UNIFORM_AB_TEST Python version: 3.6.5 I4_UNIFORM_AB computes pseudorandom values in an interval [A,B]. The lower endpoint A = -100 The upper endpoint B = 200 The initial seed is 123456789 1 -35 2 187 3 149 4 69 5 25 6 -81 7 -23 8 -67 9 -87 10 90 11 -82 12 35 13 20 14 127 15 139 16 -100 17 170 18 5 19 -72 20 -96 I4_UNIFORM_AB_TEST: Normal end of execution. R8_CHOOSE_TEST Python version: 3.6.5 R8_CHOOSE evaluates C(N,K). N K CNK 0 0 1 1 0 1 1 1 1 2 0 1 2 1 2 2 2 1 3 0 1 3 1 3 3 2 3 3 3 1 4 0 1 4 1 4 4 2 6 4 3 4 4 4 1 5 0 1 5 1 5 5 2 10 5 3 10 5 4 5 5 5 1 R8_CHOOSE_TEST Normal end of execution. R8_GAMMA_LOG_TEST: Python version: 3.6.5 R8_GAMMA_LOG evaluates the logarithm of the Gamma function. X GAMMA_LOG(X) R8_GAMMA_LOG(X) 0.2 1.524063822430784 1.524063822430784 0.4 0.7966778177017837 0.7966778177017837 0.6 0.3982338580692348 0.3982338580692349 0.8 0.1520596783998375 0.1520596783998376 1 0 0 1.1 -0.04987244125983972 -0.04987244125983976 1.2 -0.08537409000331583 -0.08537409000331585 1.3 -0.1081748095078604 -0.1081748095078605 1.4 -0.1196129141723712 -0.1196129141723713 1.5 -0.1207822376352452 -0.1207822376352453 1.6 -0.1125917656967557 -0.1125917656967558 1.7 -0.09580769740706586 -0.09580769740706586 1.8 -0.07108387291437215 -0.07108387291437215 1.9 -0.03898427592308333 -0.03898427592308337 2 0 0 3 0.6931471805599453 0.6931471805599454 4 1.791759469228055 1.791759469228055 10 12.80182748008147 12.80182748008147 20 39.33988418719949 39.33988418719949 30 71.25703896716801 71.257038967168 R8_GAMMA_LOG_TEST Normal end of execution. R8_UNI_01_TEST Python version: 3.6.5 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 R8_UNI_01_TEST Normal end of execution. R8_UNIFORM_AB_TEST Python version: 3.6.5 R8_UNIFORM_AB returns random values in a given range: [ A, B ] For this problem: A = 10.000000 B = 20.000000 12.184183 19.563176 18.295092 15.616954 14.153071 10.661187 12.575778 11.099568 10.438290 16.339657 R8_UNIFORM_AB_TEST Normal end of execution R8GE_PRINT_TEST Python version: 3.6.5 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_TEST: Normal end of execution. R8GE_PRINT_SOME_TEST Python version: 3.6.5 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 R8GE_PRINT_SOME_TEST: Normal end of execution. R8MAT_NORM_FRO_AFFINE_TEST Python version: 3.6.5 R8MAT_NORM_FRO_AFFINE computes the Frobenius norm of the difference of two R8MAT's; Expected norm = 2.1594 Computed norm = 2.1594 R8MAT_NORM_FRO_AFFINE_TEST Normal end of execution. R8MAT_UNIFORM_01_TEST Python version: 3.6.5 R8MAT_UNIFORM_01 computes a random R8MAT. 0 <= X <= 1 Initial seed is 123456789 Random R8MAT: Col: 0 1 2 3 Row 0 : 0.218418 0.0661187 0.0617272 0.00183837 1 : 0.956318 0.257578 0.449539 0.897504 2 : 0.829509 0.109957 0.401306 0.350752 3 : 0.561695 0.043829 0.754673 0.0945448 4 : 0.415307 0.633966 0.797287 0.0136169 R8MAT_UNIFORM_01_TEST: Normal end of execution. R8PO_MV_TEST Python version: 3.6.5 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 R8PO_MV_TEST Normal end of execution. R8UT_SL_TEST Python version: 3.6.5 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 R8UT_SL_TEST Normal end of execution. R8VEC_INDICATOR1_TEST Python version: 3.6.5 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 R8VEC_INDICATOR1_TEST Normal end of execution. R8VEC_NORM_TEST Python version: 3.6.5 R8VEC_NORM computes the L2 norm of an R8VEC. Input vector: 0: 0.218418 1: 0.956318 2: 0.829509 3: 0.561695 4: 0.415307 5: 0.0661187 6: 0.257578 7: 0.109957 8: 0.043829 9: 0.633966 L2 norm = 1.62017 R8VEC_NORM_TEST: Normal end of execution. R8VEC_PRINT_TEST Python version: 3.6.5 R8VEC_PRINT prints an R8VEC. Here is an R8VEC: 0: 123.456 1: 5e-06 2: -1e+06 3: 3.14159 R8VEC_PRINT_TEST: Normal end of execution. R8VEC_UNIFORM_AB_TEST Python version: 3.6.5 R8VEC_UNIFORM_AB computes a random R8VEC. -1 <= X <= 5 Initial seed is 123456789 Random R8VEC: 0: 0.31051 1: 4.73791 2: 3.97706 3: 2.37017 4: 1.49184 5: -0.603288 6: 0.545467 7: -0.340259 8: -0.737026 9: 2.80379 R8VEC_UNIFORM_AB_TEST: Normal end of execution. I4_BINOMIAL_PDF_TEST: Python version: 3.6.5 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_PDF_TEST: Normal end of execution. I4_BINOMIAL_SAMPLE_TEST Python version: 3.6.5 I4_BINOMIAL_SAMPLE samples the binomial distribution. N P K PDF(N,P,K) 5 0.956318 5 0.799854 17 0.561695 15 0.00456672 9 0.0661187 2 0.0974974 6 0.109957 1 0.368493 1 0.633966 1 0.633966 2 0.449539 1 0.494907 9 0.754673 6 0.229122 16 0.00183837 0 0.970988 18 0.350752 4 0.109514 2 0.0136169 0 0.972952 I4_BINOMIAL_SAMPLE_TEST: Normal end of execution. INITIALIZE: The RNGLIB package has been initialized. I4_UNIFORM_SAMPLE_TEST Python version: 3.6.5 I4_UNIFORM_SAMPLE csamples the uniform distribution on integers. Generate C between A and B. A B C -4 4 0 -4 4 -3 1 17 6 -3 18 4 -5 8 5 -10 -9 -10 -9 13 -1 -6 -4 -6 4 10 9 3 11 10 I4_UNIFORM_SAMPLE_TEST: Normal end of execution. I4VEC_MULTINOMIAL_PDF_TEST: Python version: 3.6.5 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_PDF_TEST: Normal end of execution. I4VEC_MULTINOMIAL_SAMPLE_TEST Python version: 3.6.5 I4VEC_MULTINOMIAL_SAMPLE samples the multinomial distribution. N M I P X PDF() 0 0.4592 2 1 0.3109 3 2 0.2299 0 5 3 0.0633784 0 0.7150 0 1 0.2850 2 2 2 0.0812252 0 0.1231 0 1 0.1099 0 2 0.2066 0 3 0.2183 1 4 0.0005 0 5 0.2457 0 6 0.0960 0 1 7 0.218261 0 0.5054 1 1 0.4946 0 1 2 0.505368 0 0.2023 0 1 0.7093 1 2 0.0884 0 1 3 0.709303 0 0.0942 2 1 0.2440 0 2 0.1981 1 3 0.3037 1 4 0.1600 1 5 5 0.0051241 0 0.0431 0 1 0.1738 1 2 0.0906 0 3 0.0423 1 4 0.1311 0 5 0.0838 0 6 0.1409 0 7 0.0825 0 8 0.0486 0 9 0.1631 1 3 10 0.00719789 0 0.4820 1 1 0.4818 1 2 0.0361 0 2 3 0.464509 0 0.1389 0 1 0.1330 0 2 0.0551 0 3 0.1605 0 4 0.1363 0 5 0.1360 0 6 0.0726 0 7 0.1676 1 1 8 0.167564 0 0.2399 1 1 0.0201 0 2 0.1766 0 3 0.1301 0 4 0.4111 0 5 0.0139 0 6 0.0084 0 1 7 0.239919 I4VEC_MULTINOMIAL_SAMPLE_TEST: Normal end of execution. R8_BETA_PDF_TEST: Python version: 3.6.5 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_PDF_TEST: Normal end of execution. R8_BETA_SAMPLE_TEST Python version: 3.6.5 R8_BETA_SAMPLE samples the beta distribution. ALPHA BETA X PDF() 1.09209 4.78159 0.127774 2.88348 4.14755 2.80848 0.465716 1.57485 2.07654 0.330594 0.867633 1.48301 1.28789 0.549784 0.639495 0.901614 0.219145 3.16983 0.000326275 158.474 0.308636 2.24769 0.000172186 168.562 2.00653 3.77337 0.527275 1.19361 3.98643 0.00919186 1 0 4.48752 1.75376 0.587441 1.38921 0.472724 0.0680845 1 1.55426e+09 R8_BETA_SAMPLE_TEST: Normal end of execution. R8_CHI_PDF_TEST: Python version: 3.6.5 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_PDF_TEST Normal end of execution. R8_CHI_SAMPLE_TEST Python version: 3.6.5 R8_CHI_SAMPLE samples the CHI distribution: DF R PDF 4.36837 0.232938 0.0319311 19.1264 16.1829 0.0666008 16.5902 22.043 0.0356783 11.2339 11.5003 0.08088 8.30614 4.85604 0.0991158 1.32237 0.396564 0.520155 5.15156 4.39656 0.136752 2.19914 2.34364 0.165383 0.87658 0.437487 0.466813 12.6793 3.94506 0.0120874 R8_CHI_SAMPLE_TEST Normal end of execution R8_EXPONENTIAL_01_PDF_TEST: Python version: 3.6.5 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_PDF_TEST: Normal end of execution. R8_EXPONENTIAL_01_SAMPLE_TEST Python version: 3.6.5 R8_EXPONENTIAL_01_SAMPLE samples the standard exponential PDF: R PDF(R) 0.427732 0.651986 2.47944 0.0837897 0.344944 0.70826 0.932236 0.393673 0.364548 0.69451 0.660637 0.516522 0.1823 0.833351 0.447452 0.639255 0.519984 0.59453 0.0345493 0.966041 R8_EXPONENTIAL_01_SAMPLE_TEST Normal end of execution R8_EXPONENTIAL_PDF_TEST: Python version: 3.6.5 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_PDF_TEST: Normal end of execution. R8_EXPONENTIAL_SAMPLE_TEST Python version: 3.6.5 R8_EXPONENTIAL_SAMPLE samples the general exponential PDF: BETA R PDF 2.18418 3.52772 0.0910485 9.56318 21.7548 0.0107508 8.29509 3.76408 0.0765787 5.61695 1.46025 0.137276 4.15307 4.75233 0.076678 0.661187 0.520811 0.687995 2.57578 3.4771 0.100653 1.09957 0.657528 0.500121 0.43829 0.537187 0.669806 6.33966 43.3907 0.000168066 R8_EXPONENTIAL_SAMPLE_TEST Normal end of execution R8_GAMMA_01_PDF_TEST: Python version: 3.6.5 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_PDF_TEST Normal end of execution. R8_GAMMA_01_SAMPLE_TEST Python version: 3.6.5 R8_GAMMA_01_SAMPLE samples the standard gamma distribution. A X PDF() 1.09209 0.713933 0.497336 4.78159 5.74057 0.137176 4.14755 6.56963 0.0724651 2.80848 1.91401 0.282581 2.07654 4.14675 0.0706663 0.330594 0.0805134 1.84394 1.28789 1.17419 0.359903 0.549784 0.0911708 1.6598 0.219145 0.0667497 1.85805 3.16983 3.12645 0.221241 R8_GAMMA_01_SAMPLE_TEST: Normal end of execution. R8_GAMMA_PDF_TEST: Python version: 3.6.5 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_PDF_TEST Normal end of execution. R8_GAMMA_SAMPLE_TEST Python version: 3.6.5 R8_GAMMA_SAMPLE samples a gamma distribution. R A X PDF() 1.09209 4.78159 4.90547 0.169246 4.14755 2.80848 0.752455 0.848797 2.07654 0.330594 0.282916 0.609716 1.28789 0.549784 0.00594629 7.08787 0.219145 3.16983 10.9525 0.0564806 0.308636 2.24769 4.9148 0.100644 2.00653 3.77337 1.71629 0.434985 3.98643 0.00919186 3.15702e-30 1.58765e+27 4.48752 1.75376 0.0562763 1.34301 0.472724 0.0680845 1.28227e-05 2428.32 R8_GAMMA_SAMPLE_TEST: Normal end of execution. R8_INVCHI_PDF_TEST: Python version: 3.6.5 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_PDF_TEST: Normal end of execution. R8_INVCHI_SAMPLE_TEST Python version: 3.6.5 R8_INVCHI_SAMPLE samples an inverse chi square distribution. DF X PDF() 1.09209 2.9136 0.0678572 4.78159 0.14527 3.42629 4.14755 0.418059 1.01449 2.80848 0.325812 1.36082 2.07654 0.208974 1.10472 0.330594 192.66 0.000344591 1.28789 1.14777 0.236348 0.549784 2.99626 0.0526416 0.219145 6.95617e+06 2.7416e-09 3.16983 0.23315 1.88721 R8_INVCHI_SAMPLE_TEST: Normal end of execution. R8_INVGAM_PDF_TEST: Python version: 3.6.5 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 0.0009390345112621714 R8_INVGAM_PDF_TEST: Normal end of execution. R8_INVGAM_SAMPLE_TEST Python version: 3.6.5 R8_INVGAM_SAMPLE samples an inverse gamma distribution. R A X PDF() 1.09209 4.78159 0.203359 4.07681 4.14755 2.80848 0.467251 0.0814804 2.07654 0.330594 11.56 0.0151645 1.28789 0.549784 7.94462 0.0243472 0.219145 3.16983 0.043143 10.5904 0.308636 2.24769 0.132934 4.33136 2.00653 3.77337 0.542574 1.3961 3.98643 0.00919186 2.73443e+38 1.51714e-41 4.48752 1.75376 1.91652 0.242571 0.472724 0.0680845 3.37571e+07 6.10138e-10 R8_INVGAM_SAMPLE_TEST: Normal end of execution. R8_NORMAL_01_PDF_TEST: Python version: 3.6.5 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_PDF_TEST: Normal end of execution. R8_NORMAL_01_SAMPLE_TEST Python version: 3.6.5 R8_NORMAL_01_SAMPLE samples the normal distribution. X PDF(X) 1.19525 0.195295 0.913518 0.262844 -1.11036 0.215373 -0.253829 0.386295 -1.1448 0.207169 0.618234 0.329544 -0.534789 0.345785 -0.153352 0.394279 0.751109 0.300887 -0.529822 0.3467 R8_NORMAL_01_SAMPLE_TEST: Normal end of execution. R8_NORMAL_PDF_TEST: Python version: 3.6.5 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_PDF_TEST: Normal end of execution. R8_NORMAL_SAMPLE_TEST Python version: 3.6.5 R8_NORMAL_SAMPLE samples the normal distribution. MU SIGMA X PDF(MU,SIGMA) -56.3163 0.956318 -55.4487 0.276425 65.9018 0.561695 66.1538 0.642277 -16.9386 0.0661187 -16.9285 5.96328 -48.4844 0.109957 -48.4558 3.50692 -91.2342 0.633966 -91.04 0.600447 -87.6546 0.449539 -87.4367 0.789135 -19.7387 0.754673 -20.7064 0.232335 59.4574 0.00183837 59.4559 156.059 79.5008 0.350752 79.4157 1.10438 -81.091 0.0136169 -81.1201 3.01423 R8_NORMAL_SAMPLE_TEST: Normal end of execution. R8_SCINVCHI_PDF_TEST: Python version: 3.6.5 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_PDF_TEST: Normal end of execution. R8_SCINVCHI_SAMPLE_TEST Python version: 3.6.5 R8_SCINVCHI_SAMPLE samples a scaled inverse chi square distribution. DF XI X PDF 1.09209 4.78159 11.023 0.0200359 4.14755 2.80848 3.83273 0.131554 2.07654 0.330594 0.430307 0.84517 1.28789 0.549784 0.0810789 0.289697 0.219145 3.16983 9.63188e+09 8.61232e-13 0.308636 2.24769 0.371818 0.173398 2.00653 3.77337 11.3222 0.0211025 3.98643 0.00919186 0.00355924 42.9242 4.48752 1.75376 5.19019 0.0429621 0.472724 0.0680845 2.41477 0.032712 R8_SCINVCHI_SAMPLE_TEST: Normal end of execution. R8_UNIFORM_01_PDF_TEST: Python version: 3.6.5 R8_UNIFORM_01_PDF evaluates the standard uniform pdf. X PDF() -0.06316340603524839 0 1.412635153017859 0 1.159018467865401 0 0.6233908855337884 1 0.3306141629519225 1 -0.3677625301679374 0 0.01515558476408985 1 -0.2800864129350588 0 -0.4123420044417858 0 0.767931424604825 1 R8_UNIFORM_01_PDF_TEST: Normal end of execution. R8_UNIFORM_01_SAMPLE_TEST Python version: 3.6.5 R8_UNIFORM_01_SAMPLE returns random values in [0,1]: 0.779558 0.669352 0.787255 0.162451 0.752374 0.70437 0.248052 0.71484 0.935853 0.356169 R8_UNIFORM_01_SAMPLE_TEST Normal end of execution R8_UNIFORM_PDF_TEST: Python version: 3.6.5 R8_UNIFORM_PDF evaluates the uniform pdf over [A,B]. A B X PDF() -56.3163 91.2635 65.9018 0.00677599 -16.9386 12.3391 -86.7763 0 -78.0086 -48.4844 -91.2342 0 -87.6546 26.7931 -10.0922 0.00873762 -19.7387 50.9347 59.4574 0 -99.6323 79.5008 -29.8495 0.00558244 -97.2766 -81.091 71.8194 0 -75.3792 68.1695 -98.4975 0 -47.9394 82.4967 -77.2672 0 -29.6743 64.5775 -46.5735 0 R8_UNIFORM_PDF_TEST: Normal end of execution. R8_UNIFORM_SAMPLE_TEST Python version: 3.6.5 R8_UNIFORM_SAMPLE returns random values in [A,B]: A B R -56.3163 91.2635 22.6151 12.3391 65.9018 31.2743 -86.7763 -16.9386 -22.1543 -78.0086 -48.4844 -58.7672 -91.2342 26.7931 -49.9468 -87.6546 -10.0922 -27.8633 -19.7387 50.9347 40.8552 -99.6323 59.4574 41.8882 -29.8495 79.5008 -2.6928 -97.2766 -81.091 -86.5009 R8_UNIFORM_SAMPLE_TEST Normal end of execution INITIALIZE: The RNGLIB package has been initialized. R8VEC_MULTINORMAL_PDF_TEST Python version: 3.6.5 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 : 0.323711 0.324392 0.28873 0.566211 0.895177 1 : 0.493388 0.353007 0.82072 0.336599 2 : 0.153961 0.325495 0.285023 3 : 0.34008 0.503381 4 : 0.773531 C: Col: 0 1 2 3 4 Row 0 : 0.104789 0.105009 0.0934649 0.183289 0.289778 1 : 0.105009 0.348662 0.267831 0.588607 0.456462 2 : 0.0934649 0.267831 0.231683 0.503315 0.421168 3 : 0.183289 0.588607 0.503315 1.21578 1.04708 4 : 0.289778 0.456462 0.421168 1.04708 1.84762 R2: Col: 0 1 2 3 4 Row 0 : 0.323711 0.324392 0.28873 0.566211 0.895177 1 : 0.493388 0.353007 0.82072 0.336599 2 : 0.153961 0.325495 0.285023 3 : 0.34008 0.503381 4 : 0.773531 Determinant of C = 4.18435e-05 inverse(C): Col: 0 1 2 3 4 Row 0 : 23.6444 -2.36974 -17.3041 7.88943 -3.64946 1 : -2.36974 27.1525 -25.5779 -3.44532 1.44659 2 : -17.3041 -25.5779 83.563 -21.4414 2.13595 3 : 7.88943 -3.44532 -21.4414 12.3081 -2.47378 4 : -3.64946 1.44659 2.13595 -2.47378 1.67126 MU: 0: 2.70222 1: 1.34776 2: -0.484155 3: 1.55387 4: -0.508102 X: 0: 2.70555 1: 1.33534 2: -0.481492 3: 1.60178 4: -0.505191 PDF1 = 1.53494 PDF2 = 1.53494 R8VEC_MULTINORMAL_PDF_TEST Normal end of execution. INITIALIZE: The RNGLIB package has been initialized. R8VEC_MULTINORMAL_SAMPLE_TEST Python version: 3.6.5 R8VEC_MULTINORMAL_SAMPLE samples the multinormal distribution. N I MU X PDF() 0 -2.8158 -3.7729 1 4.5632 4.6909 2 3.2951 4.4746 3 0.6170 0.4204 4 -0.8469 -2.1371 5 0.00146813 0 -4.3388 -4.6833 1 -2.4242 -4.1920 2 -3.9004 -1.7868 3 -4.5617 -5.9012 4 1.3397 1.8824 5 0.000719047 0 -4.3827 -3.8566 1 -0.5046 0.8801 2 -0.9869 -2.8451 3 2.5467 2.6180 4 2.9729 4.2231 5 0.000839582 0 -4.9816 -3.3107 1 3.9750 3.1473 2 -1.4925 -2.9765 3 -4.0546 -2.2111 4 -4.8638 -3.6232 5 0.00018104 0 3.5910 3.4036 1 3.4085 3.3767 2 -3.7690 -3.9114 3 -4.9249 -3.5085 4 -2.3970 -4.4362 5 0.00136333 0 4.1248 5.5384 1 -3.8634 -6.1265 2 -1.4837 0.3853 3 3.2289 1.7711 4 -2.3287 -1.1040 5 0.00057309 0 1.9207 0.1677 1 0.6166 1.0925 2 3.6122 3.4844 3 -0.4621 -1.4755 4 4.1198 4.6720 5 0.000777761 0 0.9792 2.0533 1 -3.1105 -3.5202 2 2.6149 -1.1227 3 -1.0301 1.9356 4 -3.1469 -3.1812 5 2.00467e-05 0 0.7437 0.6399 1 -1.3297 -1.8371 2 1.1720 0.0825 3 -1.3847 -1.1131 4 -2.8707 -1.1644 5 0.000802443 0 2.1447 4.7432 1 -3.8229 -3.8734 2 -2.0067 -1.5067 3 3.2500 3.0905 4 3.2466 2.2111 5 0.000166335 R8VEC_MULTINORMAL_SAMPLE_TEST: Normal end of execution. PDFLIB_TEST: Normal end of execution. Thu Sep 13 12:59:10 2018