22 March 2023 7:08:32.867 PM truncated_normal_rule(): FORTRAN90 version For the (truncated) Gaussian probability density function pdf(x) = exp(-0.5*((x-MU)/SIGMA)^2) / SIGMA / sqrt ( 2 * pi ) compute an N-point quadrature rule for approximating Integral ( A <= x <= B ) f(x) pdf(x) dx The value of OPTION determines the truncation interval [A,B]: 0: (-oo,+oo) 1: [A,+oo) 2: (-oo,B] 3: [A,B] The user specifies OPTION, N, MU, SIGMA, A, B and FILENAME. FILENAME is used to generate 3 files: filename_w.txt - the weight file filename_x.txt - the abscissa file. filename_r.txt - the region file, listing A and B. Enter OPTION, 0/1/2/3: Enter N, the number of quadrature points: Enter MU, the mean value of the normal distribution: Enter SIGMA, the standard deviation of the normal distribution: Enter FILENAME, the "root name" of the quadrature files). OPTION = 0 N = 5 MU = 1.00000 SIGMA = 2.00000 A = -oo B = +oo FILENAME = "option0". Moments: 1: 1.000000000000000 2: 1.000000000000000 3: 5.000000000000000 4: 13.00000000000000 5: 73.00000000000000 6: 281.0000000000000 7: 1741.000000000000 8: 8485.000000000000 9: 57233.00000000000 10: 328753.0000000000 11: 2389141.000000000 Hankel matrix H: Col 1 2 3 4 5 Row 1: 1. 1. 5. 13. 73. 2: 1. 5. 13. 73. 281. 3: 5. 13. 73. 281. 1741. 4: 13. 73. 281. 1741. 8485. 5: 73. 281. 1741. 8485. 57233. 6: 281. 1741. 8485. 57233. 328753. Col 6 Row 1: 281. 2: 1741. 3: 8485. 4: 57233. 5: 328753. 6:2389141. Froebenius norm H-R'*R = 0.00000 Cholesky factor R: Col 1 2 3 4 5 Row 1: 1. 1. 5. 13. 73. 2: 0. 2. 4. 30. 104. 3: 0. 0. 5.65685 16.9706 169.706 4: 0. 0. 0. 19.5959 78.3837 5: 0. 0. 0. 0. 78.3837 6: 0. 0. 0. 0. 0. Col 6 Row 1: 281. 2: 730. 3: 735.391 4: 979.796 5: 391.918 6: 350.542 Jacobi matrix J: Col 1 2 3 4 5 Row 1: 1. 2. 0. 0. 0. 2: 2. 1. 2.82843 0. 0. 3: 0. 2.82843 1.00000 3.46410 0. 4: 0. 0. 3.46410 1.00000 4.00000 5: 0. 0. 0. 4.00000 1.00000 Eigenvector matrix V: Col 1 2 3 4 5 Row 1: 0.106101 0.471249 0.730297 -0.471249 0.106101 2: -0.303127 -0.638838 -0.323910E-15 -0.638838 0.303127 3: 0.537348 0.279149 -0.516398 -0.279149 0.537348 4: -0.638838 0.303127 0.561469E-15 0.303127 0.638838 5: 0.447214 -0.447214 0.447214 0.447214 0.447214 Creating quadrature files. "Root" file name is "option0". Weight file will be "option0_w.txt". Abscissa file will be "option0_x.txt". Region file will be "option0_r.txt". truncated_normal_rule(): Normal end of execution. 22 March 2023 7:08:32.869 PM 22 March 2023 7:08:32.871 PM truncated_normal_rule(): FORTRAN90 version For the (truncated) Gaussian probability density function pdf(x) = exp(-0.5*((x-MU)/SIGMA)^2) / SIGMA / sqrt ( 2 * pi ) compute an N-point quadrature rule for approximating Integral ( A <= x <= B ) f(x) pdf(x) dx The value of OPTION determines the truncation interval [A,B]: 0: (-oo,+oo) 1: [A,+oo) 2: (-oo,B] 3: [A,B] The user specifies OPTION, N, MU, SIGMA, A, B and FILENAME. FILENAME is used to generate 3 files: filename_w.txt - the weight file filename_x.txt - the abscissa file. filename_r.txt - the region file, listing A and B. Enter OPTION, 0/1/2/3: Enter N, the number of quadrature points: Enter MU, the mean value of the normal distribution: Enter SIGMA, the standard deviation of the normal distribution: Enter A, the left endpoint: Enter FILENAME, the "root name" of the quadrature files). OPTION = 1 N = 9 MU = 2.00000 SIGMA = 0.500000 A = 0.00000 B = +oo FILENAME = "option1". ORDER = 0, b = -0.00000 , MU = -2.00000 , S = 0.500000 ORDER = 0, H = 4.00000 , H_PDF = 0.133830E-03, H_CDF = 0.999968 MOMENT = 1.00000 ORDER = 1, b = -0.00000 , MU = -2.00000 , S = 0.500000 ORDER = 1, H = 4.00000 , H_PDF = 0.133830E-03, H_CDF = 0.999968 MOMENT = -2.00007 ORDER = 2, b = -0.00000 , MU = -2.00000 , S = 0.500000 ORDER = 2, H = 4.00000 , H_PDF = 0.133830E-03, H_CDF = 0.999968 MOMENT = 4.25013 ORDER = 3, b = -0.00000 , MU = -2.00000 , S = 0.500000 ORDER = 3, H = 4.00000 , H_PDF = 0.133830E-03, H_CDF = 0.999968 MOMENT = -9.50030 ORDER = 4, b = -0.00000 , MU = -2.00000 , S = 0.500000 ORDER = 4, H = 4.00000 , H_PDF = 0.133830E-03, H_CDF = 0.999968 MOMENT = 22.1882 ORDER = 5, b = -0.00000 , MU = -2.00000 , S = 0.500000 ORDER = 5, H = 4.00000 , H_PDF = 0.133830E-03, H_CDF = 0.999968 MOMENT = -53.8767 ORDER = 6, b = -0.00000 , MU = -2.00000 , S = 0.500000 ORDER = 6, H = 4.00000 , H_PDF = 0.133830E-03, H_CDF = 0.999968 MOMENT = 135.489 ORDER = 7, b = -0.00000 , MU = -2.00000 , S = 0.500000 ORDER = 7, H = 4.00000 , H_PDF = 0.133830E-03, H_CDF = 0.999968 MOMENT = -351.792 ORDER = 8, b = -0.00000 , MU = -2.00000 , S = 0.500000 ORDER = 8, H = 4.00000 , H_PDF = 0.133830E-03, H_CDF = 0.999968 MOMENT = 940.690 ORDER = 9, b = -0.00000 , MU = -2.00000 , S = 0.500000 ORDER = 9, H = 4.00000 , H_PDF = 0.133830E-03, H_CDF = 0.999968 MOMENT = -2584.96 ORDER = 10, b = -0.00000 , MU = -2.00000 , S = 0.500000 ORDER = 10, H = 4.00000 , H_PDF = 0.133830E-03, H_CDF = 0.999968 MOMENT = 7286.48 ORDER = 11, b = -0.00000 , MU = -2.00000 , S = 0.500000 ORDER = 11, H = 4.00000 , H_PDF = 0.133830E-03, H_CDF = 0.999968 MOMENT = -21035.4 ORDER = 12, b = -0.00000 , MU = -2.00000 , S = 0.500000 ORDER = 12, H = 4.00000 , H_PDF = 0.133830E-03, H_CDF = 0.999968 MOMENT = 62108.6 ORDER = 13, b = -0.00000 , MU = -2.00000 , S = 0.500000 ORDER = 13, H = 4.00000 , H_PDF = 0.133830E-03, H_CDF = 0.999968 MOMENT = -187323. ORDER = 14, b = -0.00000 , MU = -2.00000 , S = 0.500000 ORDER = 14, H = 4.00000 , H_PDF = 0.133830E-03, H_CDF = 0.999968 MOMENT = 576499. ORDER = 15, b = -0.00000 , MU = -2.00000 , S = 0.500000 ORDER = 15, H = 4.00000 , H_PDF = 0.133830E-03, H_CDF = 0.999968 MOMENT = -0.180863E+07 ORDER = 16, b = -0.00000 , MU = -2.00000 , S = 0.500000 ORDER = 16, H = 4.00000 , H_PDF = 0.133830E-03, H_CDF = 0.999968 MOMENT = 0.577913E+07 ORDER = 17, b = -0.00000 , MU = -2.00000 , S = 0.500000 ORDER = 17, H = 4.00000 , H_PDF = 0.133830E-03, H_CDF = 0.999968 MOMENT = -0.187928E+08 ORDER = 18, b = -0.00000 , MU = -2.00000 , S = 0.500000 ORDER = 18, H = 4.00000 , H_PDF = 0.133830E-03, H_CDF = 0.999968 MOMENT = 0.621469E+08 Moments: 1: 1.000000000000000 2: 2.000066917232235 3: 4.250133834464469 4: 9.500301127545054 5: 22.18820263093846 6: 53.87670638942198 7: 135.4886660675170 8: 351.7923917191670 9: 940.6899490564888 10: 2584.964681551312 11: 7286.481748479722 12: 21035.37520083773 13: 62108.57520999469 14: 187323.2760225026 15: 576499.4214774877 16: 1808630.309033735 17: 5779133.448608049 18: 18792788.13335104 19: 62146893.42328629 Hankel matrix H: Col 1 2 3 4 5 Row 1: 1. 2.00007 4.25013 9.50030 22.1882 2: 2.00007 4.25013 9.50030 22.1882 53.8767 3: 4.25013 9.50030 22.1882 53.8767 135.489 4: 9.50030 22.1882 53.8767 135.489 351.792 5: 22.1882 53.8767 135.489 351.792 940.690 6: 53.8767 135.489 351.792 940.690 2584.96 7: 135.489 351.792 940.690 2584.96 7286.48 8: 351.792 940.690 2584.96 7286.48 21035.4 9: 940.690 2584.96 7286.48 21035.4 62108.6 10: 2584.96 7286.48 21035.4 62108.6 187323. Col 6 7 8 9 10 Row 1: 53.8767 135.489 351.792 940.690 2584.96 2: 135.489 351.792 940.690 2584.96 7286.48 3: 351.792 940.690 2584.96 7286.48 21035.4 4: 940.690 2584.96 7286.48 21035.4 62108.6 5: 2584.96 7286.48 21035.4 62108.6 187323. 6: 7286.48 21035.4 62108.6 187323. 576499. 7: 21035.4 62108.6 187323. 576499. 0.180863E+07 8: 62108.6 187323. 576499. 0.180863E+07 0.577913E+07 9: 187323. 576499. 0.180863E+07 0.577913E+07 0.187928E+08 10: 576499. 0.180863E+07 0.577913E+07 0.187928E+08 0.621469E+08 Froebenius norm H-R'*R = 0.758516E-08 Cholesky factor R: Col 1 2 3 4 5 Row 1: 1. 2.00007 4.25013 9.50030 22.1882 2: 0. 0.499866 2.00003 6.37564 19.0027 3: 0. 0. 0.352748 2.11956 9.01426 4: 0. 0. 0. 0.302790 2.43440 5: 0. 0. 0. 0. 0.295097 6: 0. 0. 0. 0. 0. 7: 0. 0. 0. 0. 0. 8: 0. 0. 0. 0. 0. 9: 0. 0. 0. 0. 0. 10: 0. 0. 0. 0. 0. Col 6 7 8 9 10 Row 1: 53.8767 135.489 351.792 940.690 2584.96 2: 55.4781 161.655 474.290 1407.42 4233.89 3: 33.5963 117.730 400.296 1342.42 4481.97 4: 12.9700 58.0946 237.771 924.731 3491.16 5: 2.98781 19.2013 100.727 472.558 2072.54 6: 0.312730 3.84462 29.0813 175.560 931.797 7: 0. 0.351126 5.11340 44.7389 306.831 8: 0. 0. 0.412284 6.98179 69.7036 9: 0. 0. 0. 0.503269 9.76547 10: 0. 0. 0. 0. 0.636584 Jacobi matrix J: Col 1 2 3 4 5 Row 1: 2.00007 0.499866 0. 0. 0. 2: 0.499866 2.00107 0.705684 0. 0. 3: 0. 0.705684 2.00757 0.858375 0. 4: 0. 0. 0.858375 2.03119 0.974595 5: 0. 0. 0. 0.974595 2.08494 6: 0. 0. 0. 0. 1.05975 7: 0. 0. 0. 0. 0. 8: 0. 0. 0. 0. 0. 9: 0. 0. 0. 0. 0. Col 6 7 8 9 Row 1: 0. 0. 0. 0. 2: 0. 0. 0. 0. 3: 0. 0. 0. 0. 4: 0. 0. 0. 0. 5: 1.05975 0. 0. 0. 6: 2.16889 1.12278 0. 0. 7: 1.12278 2.26913 1.17418 0. 8: 0. 1.17418 2.37158 1.22068 9: 0. 0. 1.22068 2.46965 Eigenvector matrix V: Col 1 2 3 4 5 Row 1: 0.205816E-01 -0.988634E-01 -0.295503 0.540525 0.617497 2: -0.748698E-01 0.268565 0.512095 -0.408409 0.135787 3: 0.178448 -0.447134 -0.420023 -0.163712 -0.416442 4: -0.318030 0.490457 0.654721E-02 0.409225 -0.161319 5: 0.446358 -0.305202 0.363907 -0.274681E-01 0.353739 6: -0.509154 -0.355376E-01 -0.332626 -0.364352 0.156717 7: 0.479842 0.336392 -0.368378E-01 0.203273 -0.342104 8: -0.366187 -0.432129 0.353684 0.236438 -0.103491 9: 0.195371 0.288645 -0.323198 -0.340644 0.351247 Col 6 7 8 9 Row 1: -0.439003 0.185853 -0.416333E-01 0.355302E-02 2: -0.531101 0.415980 -0.139327 0.164720E-01 3: -0.143404 0.527266 -0.300583 0.515524E-01 4: 0.336851 0.340648 -0.468610 0.125186 5: 0.324560 -0.842136E-01 -0.524627 0.248267 6: -0.150571 -0.395438 -0.355152 0.407886 7: -0.364799 -0.255097 0.194411E-01 0.546214 8: 0.396908E-01 0.193514 0.362848 0.562836 9: 0.358483 0.363846 0.368110 0.371813 Creating quadrature files. "Root" file name is "option1". Weight file will be "option1_w.txt". Abscissa file will be "option1_x.txt". Region file will be "option1_r.txt". truncated_normal_rule(): Normal end of execution. 22 March 2023 7:08:32.874 PM 22 March 2023 7:08:32.876 PM truncated_normal_rule(): FORTRAN90 version For the (truncated) Gaussian probability density function pdf(x) = exp(-0.5*((x-MU)/SIGMA)^2) / SIGMA / sqrt ( 2 * pi ) compute an N-point quadrature rule for approximating Integral ( A <= x <= B ) f(x) pdf(x) dx The value of OPTION determines the truncation interval [A,B]: 0: (-oo,+oo) 1: [A,+oo) 2: (-oo,B] 3: [A,B] The user specifies OPTION, N, MU, SIGMA, A, B and FILENAME. FILENAME is used to generate 3 files: filename_w.txt - the weight file filename_x.txt - the abscissa file. filename_r.txt - the region file, listing A and B. Enter OPTION, 0/1/2/3: Enter N, the number of quadrature points: Enter MU, the mean value of the normal distribution: Enter SIGMA, the standard deviation of the normal distribution: Enter B, the right endpoint: Enter FILENAME, the "root name" of the quadrature files). OPTION = 2 N = 9 MU = 2.00000 SIGMA = 0.500000 A = -oo B = 3.00000 FILENAME = "option2". ORDER = 0, b = 3.00000 , MU = 2.00000 , S = 0.500000 ORDER = 0, H = 2.00000 , H_PDF = 0.539910E-01, H_CDF = 0.977250 MOMENT = 1.00000 ORDER = 1, b = 3.00000 , MU = 2.00000 , S = 0.500000 ORDER = 1, H = 2.00000 , H_PDF = 0.539910E-01, H_CDF = 0.977250 MOMENT = 1.97238 ORDER = 2, b = 3.00000 , MU = 2.00000 , S = 0.500000 ORDER = 2, H = 2.00000 , H_PDF = 0.539910E-01, H_CDF = 0.977250 MOMENT = 4.11188 ORDER = 3, b = 3.00000 , MU = 2.00000 , S = 0.500000 ORDER = 3, H = 2.00000 , H_PDF = 0.539910E-01, H_CDF = 0.977250 MOMENT = 8.96133 ORDER = 4, b = 3.00000 , MU = 2.00000 , S = 0.500000 ORDER = 4, H = 2.00000 , H_PDF = 0.539910E-01, H_CDF = 0.977250 MOMENT = 20.2607 ORDER = 5, b = 3.00000 , MU = 2.00000 , S = 0.500000 ORDER = 5, H = 2.00000 , H_PDF = 0.539910E-01, H_CDF = 0.977250 MOMENT = 47.2453 ORDER = 6, b = 3.00000 , MU = 2.00000 , S = 0.500000 ORDER = 6, H = 2.00000 , H_PDF = 0.539910E-01, H_CDF = 0.977250 MOMENT = 113.104 ORDER = 7, b = 3.00000 , MU = 2.00000 , S = 0.500000 ORDER = 7, H = 2.00000 , H_PDF = 0.539910E-01, H_CDF = 0.977250 MOMENT = 276.938 ORDER = 8, b = 3.00000 , MU = 2.00000 , S = 0.500000 ORDER = 8, H = 2.00000 , H_PDF = 0.539910E-01, H_CDF = 0.977250 MOMENT = 691.393 ORDER = 9, b = 3.00000 , MU = 2.00000 , S = 0.500000 ORDER = 9, H = 2.00000 , H_PDF = 0.539910E-01, H_CDF = 0.977250 MOMENT = 1755.42 ORDER = 10, b = 3.00000 , MU = 2.00000 , S = 0.500000 ORDER = 10, H = 2.00000 , H_PDF = 0.539910E-01, H_CDF = 0.977250 MOMENT = 4522.76 ORDER = 11, b = 3.00000 , MU = 2.00000 , S = 0.500000 ORDER = 11, H = 2.00000 , H_PDF = 0.539910E-01, H_CDF = 0.977250 MOMENT = 11802.9 ORDER = 12, b = 3.00000 , MU = 2.00000 , S = 0.500000 ORDER = 12, H = 2.00000 , H_PDF = 0.539910E-01, H_CDF = 0.977250 MOMENT = 31149.9 ORDER = 13, b = 3.00000 , MU = 2.00000 , S = 0.500000 ORDER = 13, H = 2.00000 , H_PDF = 0.539910E-01, H_CDF = 0.977250 MOMENT = 83028.0 ORDER = 14, b = 3.00000 , MU = 2.00000 , S = 0.500000 ORDER = 14, H = 2.00000 , H_PDF = 0.539910E-01, H_CDF = 0.977250 MOMENT = 223252. ORDER = 15, b = 3.00000 , MU = 2.00000 , S = 0.500000 ORDER = 15, H = 2.00000 , H_PDF = 0.539910E-01, H_CDF = 0.977250 MOMENT = 604977. ORDER = 16, b = 3.00000 , MU = 2.00000 , S = 0.500000 ORDER = 16, H = 2.00000 , H_PDF = 0.539910E-01, H_CDF = 0.977250 MOMENT = 0.165077E+07 ORDER = 17, b = 3.00000 , MU = 2.00000 , S = 0.500000 ORDER = 17, H = 2.00000 , H_PDF = 0.539910E-01, H_CDF = 0.977250 MOMENT = 0.453234E+07 ORDER = 18, b = 3.00000 , MU = 2.00000 , S = 0.500000 ORDER = 18, H = 2.00000 , H_PDF = 0.539910E-01, H_CDF = 0.977250 MOMENT = 0.125131E+08 Moments: 1: 1.000000000000000 2: 1.972376068660481 3: 4.111880343302405 4: 8.961333338879379 5: 20.26073078906856 6: 47.24525647851546 7: 113.1038111278635 8: 276.9376610269910 9: 691.3934536882151 10: 1755.421615911829 11: 4522.756662066391 12: 11802.90184224510 13: 31149.88794017103 14: 83027.99171207208 15: 223251.6501446842 16: 604976.8640265733 17: 1650774.194330571 18: 4532336.179472007 19: 12513103.68896266 Hankel matrix H: Col 1 2 3 4 5 Row 1: 1. 1.97238 4.11188 8.96133 20.2607 2: 1.97238 4.11188 8.96133 20.2607 47.2453 3: 4.11188 8.96133 20.2607 47.2453 113.104 4: 8.96133 20.2607 47.2453 113.104 276.938 5: 20.2607 47.2453 113.104 276.938 691.393 6: 47.2453 113.104 276.938 691.393 1755.42 7: 113.104 276.938 691.393 1755.42 4522.76 8: 276.938 691.393 1755.42 4522.76 11802.9 9: 691.393 1755.42 4522.76 11802.9 31149.9 10: 1755.42 4522.76 11802.9 31149.9 83028.0 Col 6 7 8 9 10 Row 1: 47.2453 113.104 276.938 691.393 1755.42 2: 113.104 276.938 691.393 1755.42 4522.76 3: 276.938 691.393 1755.42 4522.76 11802.9 4: 691.393 1755.42 4522.76 11802.9 31149.9 5: 1755.42 4522.76 11802.9 31149.9 83028.0 6: 4522.76 11802.9 31149.9 83028.0 223252. 7: 11802.9 31149.9 83028.0 223252. 604977. 8: 31149.9 83028.0 223252. 604977. 0.165077E+07 9: 83028.0 223252. 604977. 0.165077E+07 0.453234E+07 10: 223252. 604977. 0.165077E+07 0.453234E+07 0.125131E+08 Froebenius norm H-R'*R = 0.232396E-08 Cholesky factor R: Col 1 2 3 4 5 Row 1: 1. 1.97238 4.11188 8.96133 20.2607 2: 0. 0.470758 1.80806 5.49244 15.4718 3: 0. 0. 0.289977 1.60928 6.27684 4: 0. 0. 0. 0.203971 1.44766 5: 0. 0. 0. 0. 0.157780 6: 0. 0. 0. 0. 0. 7: 0. 0. 0. 0. 0. 8: 0. 0. 0. 0. 0. 9: 0. 0. 0. 0. 0. 10: 0. 0. 0. 0. 0. Col 6 7 8 9 10 Row 1: 47.2453 113.104 276.938 691.393 1755.42 2: 42.3113 114.399 308.371 832.134 2252.55 3: 21.2753 67.1884 203.923 604.463 1765.91 4: 6.77779 26.4928 93.8617 313.258 1005.70 5: 1.34134 7.23653 31.7332 123.692 447.505 6: 0.132036 1.29097 7.80905 37.6784 159.290 7: 0. 0.118225 1.29307 8.59877 44.9904 8: 0. 0. 0.112312 1.34660 9.69862 9: 0. 0. 0. 0.112445 1.45525 10: 0. 0. 0. 0. 0.118015 Jacobi matrix J: Col 1 2 3 4 5 Row 1: 1.97238 0.470758 0. 0. 0. 2: 0.470758 1.86837 0.615978 0. 0. 3: 0. 0.615978 1.70893 0.703407 0. 4: 0. 0. 0.703407 1.54771 0.773539 5: 0. 0. 0. 0.773539 1.40394 6: 0. 0. 0. 0. 0.836837 7: 0. 0. 0. 0. 0. 8: 0. 0. 0. 0. 0. 9: 0. 0. 0. 0. 0. Col 6 7 8 9 Row 1: 0. 0. 0. 0. 2: 0. 0. 0. 0. 3: 0. 0. 0. 0. 4: 0. 0. 0. 0. 5: 0.836837 0. 0. 0. 6: 1.27609 0.895399 0. 0. 7: 0.895399 1.15993 0.949983 0. 8: 0. 0.949983 1.05254 1.00119 9: 0. 0. 1.00119 0.952048 Eigenvector matrix V: Col 1 2 3 4 5 Row 1: -0.148703E-02 -0.196842E-01 0.100790 -0.281350 -0.490599 2: 0.779976E-02 0.774489E-01 -0.284651 0.510324 0.426331 3: -0.288128E-01 -0.204766 0.489296 -0.406234 0.163784 4: 0.835221E-01 0.394683 -0.492299 -0.105904 -0.407253 5: -0.194558 -0.542186 0.130935 0.428166 -0.157136 6: 0.364712 0.466942 0.335979 -0.481555E-01 0.346528 7: -0.540313 -0.960870E-01 -0.359976 -0.391687 0.258008 8: 0.598549 -0.334943 -0.120741 0.624718E-01 -0.217068 9: -0.413599 0.403100 0.390972 0.375771 -0.355549 Col 6 7 8 9 Row 1: -0.574818 0.477461 -0.298887 0.147950 2: -0.117308E-01 0.402820 -0.465096 0.303331 3: 0.437138 -0.371533E-01 -0.403217 0.413431 4: 0.179963 -0.387646 -0.163647 0.456491 5: -0.296472 -0.378062 0.121845 0.444238 6: -0.371137 -0.779093E-01 0.340693 0.392152 7: -0.155078E-01 0.258193 0.429785 0.312473 8: 0.336393 0.402190 0.377858 0.215081 9: 0.327003 0.284070 0.215821 0.108455 Creating quadrature files. "Root" file name is "option2". Weight file will be "option2_w.txt". Abscissa file will be "option2_x.txt". Region file will be "option2_r.txt". truncated_normal_rule(): Normal end of execution. 22 March 2023 7:08:32.880 PM 22 March 2023 7:08:32.882 PM truncated_normal_rule(): FORTRAN90 version For the (truncated) Gaussian probability density function pdf(x) = exp(-0.5*((x-MU)/SIGMA)^2) / SIGMA / sqrt ( 2 * pi ) compute an N-point quadrature rule for approximating Integral ( A <= x <= B ) f(x) pdf(x) dx The value of OPTION determines the truncation interval [A,B]: 0: (-oo,+oo) 1: [A,+oo) 2: (-oo,B] 3: [A,B] The user specifies OPTION, N, MU, SIGMA, A, B and FILENAME. FILENAME is used to generate 3 files: filename_w.txt - the weight file filename_x.txt - the abscissa file. filename_r.txt - the region file, listing A and B. Enter OPTION, 0/1/2/3: Enter N, the number of quadrature points: Enter MU, the mean value of the normal distribution: Enter SIGMA, the standard deviation of the normal distribution: Enter A, the left endpoint: Enter B, the right endpoint: Enter FILENAME, the "root name" of the quadrature files). OPTION = 3 N = 5 MU = 100.000 SIGMA = 25.0000 A = 50.0000 B = 150.000 FILENAME = "option3". Moments: 1: 1.000000000000000 2: 100.0000000000000 3: 10483.58831471845 4: 1145076.494415535 5: 129568497.7600003 6: 15112482585.63112 7: 1809207227068.942 8: 221506953202234.8 9: 0.2765093050095114E+17 10: 0.3510260372572320E+19 11: 0.4522018809010304E+21 Hankel matrix H: Col 1 2 3 4 5 Row 1: 1. 100. 10483.6 0.114508E+07 0.129568E+09 2: 100. 10483.6 0.114508E+07 0.129568E+09 0.151125E+11 3: 10483.6 0.114508E+07 0.129568E+09 0.151125E+11 0.180921E+13 4: 0.114508E+07 0.129568E+09 0.151125E+11 0.180921E+13 0.221507E+15 5: 0.129568E+09 0.151125E+11 0.180921E+13 0.221507E+15 0.276509E+17 6: 0.151125E+11 0.180921E+13 0.221507E+15 0.276509E+17 0.351026E+19 Col 6 Row 1: 0.151125E+11 2: 0.180921E+13 3: 0.221507E+15 4: 0.276509E+17 5: 0.351026E+19 6: 0.452202E+21 Froebenius norm H-R'*R = 0.345278E-03 Cholesky factor R: Col 1 2 3 4 5 Row 1: 1. 100. 10483.6 0.114508E+07 0.129568E+09 2: 0. 21.9906 4398.13 684875. 0.980250E+08 3: 0. 0. 565.103 169531. 0.349279E+08 4: 0. 0. 0. 14563.4 0.582538E+07 5: 0. 0. 0. 0. 370064. 6: 0. 0. 0. 0. 0. Col 6 Row 1: 0.151125E+11 2: 0.135494E+11 3: 0.616191E+10 4: 0.149208E+10 5: 0.185032E+09 6: 0.933226E+07 Jacobi matrix J: Col 1 2 3 4 5 Row 1: 100. 21.9906 0. 0. 0. 2: 21.9906 100.000 25.6974 0. 0. 3: 0. 25.6974 100.000 25.7713 0. 4: 0. 0. 25.7713 100.000 25.4105 5: 0. 0. 0. 25.4105 100.000 Eigenvector matrix V: Col 1 2 3 4 5 Row 1: 0.236407 0.492900 0.634289 -0.492900 0.236407 2: -0.467897 -0.530162 0.163180E-08 -0.530162 0.467897 3: 0.590175 0.661848E-01 -0.542794 -0.661848E-01 0.590175 4: -0.530162 0.467897 -0.281785E-08 0.467897 0.530162 5: 0.309524 -0.502662 0.550502 0.502662 0.309524 Creating quadrature files. "Root" file name is "option3". Weight file will be "option3_w.txt". Abscissa file will be "option3_x.txt". Region file will be "option3_r.txt". truncated_normal_rule(): Normal end of execution. 22 March 2023 7:08:32.883 PM