Tue Oct 19 17:25:41 2021 truncated_normal_rule_test(): Python version: 3.6.9 Test truncated_normal_rule(). r8_mop_test r8_mop evaluates (-1.0)^I4 as an R8. I4 r8_mop(I4) 28 1.0 -48 1.0 -57 -1.0 65 -1.0 -28 1.0 -32 1.0 98 1.0 34 1.0 -21 -1.0 -83 -1.0 r8_mop_test Normal end of execution. r8vec_write_test: Python version: 3.6.9 Test r8vec_write, which writes an R8VEC to a file. Created file "r8vec_write_test.txt". r8vec_write_test: Normal end of execution. rule_write_test: Python version: 3.6.9 rule_write writes a quadrature rule to three files. Creating quadrature files. Common header is "rule_write_test". Weight file will be "rule_write_test_w.txt". Abscissa file will be "rule_write_test_x.txt". Region file will be "rule_write_test_r.txt". The quadrature rule has been written to files. rule_write_test: Normal end of execution. normal_01_cdf_test Python version: 3.6.9 normal_01_cdf evaluates the CDF; X CDF CDF (exact) (computed) 0 0.5 0.5 0.1 0.539827837277029 0.5398278372805048 0.2 0.579259709439103 0.5792597094424672 0.3 0.6179114221889526 0.6179114221891665 0.4 0.6554217416103242 0.6554217416083834 0.5 0.6914624612740131 0.6914624612735877 0.6 0.725746882249927 0.7257468822526401 0.7 0.758036347776927 0.7580363477802913 0.8 0.7881446014166033 0.7881446014178579 0.9 0.8159398746532405 0.8159398746539517 1 0.8413447460685429 0.8413447460717163 1.5 0.9331927987311419 0.9331927987330156 2 0.9772498680518208 0.9772498680509744 2.5 0.993790334674224 0.9937903346744605 3 0.9986501019683699 0.9986501019683744 3.5 0.9997673709209645 0.9997673709209559 4 0.9999683287581669 0.9999683287581664 normal_01_cdf_test: Normal end of execution. normal_01_moment_test Python version: 3.6.9 normal_01_moment evaluates moments of the Normal 01 PDF; Order Moment 0 1 1 0 2 1 3 0 4 3 5 0 6 15 7 0 8 105 9 0 10 945 normal_01_moment_test: Normal end of execution. normal_01_pdf_test Python version: 3.6.9 normal_01_pdf evaluates the PDF; X PDF -2 0.05399096651318806 -1.9 0.0656158147746766 -1.8 0.07895015830089415 -1.7 0.09404907737688695 -1.6 0.1109208346794555 -1.5 0.1295175956658917 -1.4 0.1497274656357449 -1.3 0.1713685920478074 -1.2 0.194186054983213 -1.1 0.2178521770325506 -1 0.2419707245191434 -0.9 0.2660852498987548 -0.8 0.2896915527614827 -0.7 0.3122539333667613 -0.6 0.3332246028917997 -0.5 0.3520653267642995 -0.4 0.3682701403033233 -0.3 0.3813878154605241 -0.2 0.3910426939754559 -0.1 0.3969525474770118 0 0.3989422804014327 0.1 0.3969525474770118 0.2 0.3910426939754559 0.3 0.3813878154605241 0.4 0.3682701403033233 0.5 0.3520653267642995 0.6 0.3332246028917997 0.7 0.3122539333667613 0.8 0.2896915527614827 0.9 0.2660852498987548 1 0.2419707245191434 1.1 0.2178521770325506 1.2 0.194186054983213 1.3 0.1713685920478074 1.4 0.1497274656357449 1.5 0.1295175956658917 1.6 0.1109208346794555 1.7 0.09404907737688695 1.8 0.07895015830089415 1.9 0.0656158147746766 2 0.05399096651318806 normal_01_pdf_test: Normal end of execution. normal_ms_moment_test Python version: 3.6.9 normal_ms_moment evaluates moments of the Normal MS distribution. Mu = 0, Sigma = 1 Order Moment 0 1 1 1 0 0 2 1 1 3 0 0 4 3 3 5 0 0 6 15 15 7 0 0 8 105 105 Mu = 2, Sigma = 1 Order Moment 0 1 1 1 2 2 2 5 5 3 14 14 4 43 43 5 142 142 6 499 499 7 1850 1850 8 7193 7193 Mu = 10, Sigma = 2 Order Moment 0 1 1 1 10 10 2 104 104 3 1120 1120 4 12448 12448 5 142400 142400 6 1.67296e+06 1.67296e+06 7 2.01472e+07 2.01472e+07 8 2.48315e+08 2.48315e+08 Mu = 0, Sigma = 2 Order Moment 0 1 1 1 0 0 2 4 4 3 0 0 4 48 48 5 0 0 6 960 960 7 0 0 8 26880 26880 normal_ms_moment_test: Normal end of execution. truncated_normal_a_moment_test Python version: 3.6.9 truncated_normal_a_moment evaluates moments of the lower Truncated Normal distribution. Test = 0, Mu = 0, Sigma = 1, A = 0 Order Moment 0 1 1 0.797885 2 1 3 1.59577 4 3 5 6.38308 6 15 7 38.2985 8 105 Test = 1, Mu = 0, Sigma = 1, A = -10 Order Moment 0 1 1 7.6946e-23 2 1 3 7.84849e-21 4 3 5 8.00854e-19 6 15 7 8.17511e-17 8 105 Test = 2, Mu = 0, Sigma = 1, A = 10 Order Moment 0 1 1 10.0981 2 101.981 3 1030.01 4 10404 5 105101 6 1.06183e+06 7 1.07287e+07 8 1.08414e+08 Test = 3, Mu = 0, Sigma = 2, A = -10 Order Moment 0 1 1 2.97344e-06 2 3.99997 3 0.000321132 4 47.9967 5 0.0348725 6 959.636 7 3.81038 8 26840.1 Test = 4, Mu = 0, Sigma = 2, A = 10 Order Moment 0 1 1 10.373 2 107.73 3 1120.28 4 11665.8 5 121655 6 1.27062e+06 7 1.32927e+07 8 1.39307e+08 Test = 5, Mu = -5, Sigma = 1, A = -10 Order Moment 0 1 1 -5 2 26 3 -140 4 777.997 5 -4449.97 6 26139.7 7 -157397 8 969947 truncated_normal_a_moment_test: Normal end of execution. truncated_normal_ab_moment_test Python version: 3.6.9 truncated_normal_ab_moment evaluates moments of the Truncated Normal distribution. Test = 0, Mu = 0, Sigma = 1, A = -1, B = 1 Order Moment 0 1 1 0 2 0.291125 3 0 4 0.1645 5 0 6 0.113627 7 0 8 0.086514 Test = 1, Mu = 0, Sigma = 1, A = 0, B = 1 Order Moment 0 1 1 0.459862 2 0.291125 3 0.21085 4 0.1645 5 0.134523 6 0.113627 7 0.0982649 8 0.086514 Test = 2, Mu = 0, Sigma = 1, A = -1, B = 0 Order Moment 0 1 1 -0.459862 2 0.291125 3 -0.21085 4 0.1645 5 -0.134523 6 0.113627 7 -0.0982649 8 0.086514 Test = 3, Mu = 0, Sigma = 2, A = -1, B = 1 Order Moment 0 1 1 0 2 0.322357 3 0 4 0.190636 5 0 6 0.135077 7 0 8 0.104524 Test = 4, Mu = 1, Sigma = 1, A = 0, B = 2 Order Moment 0 1 1 1 2 1.29113 3 1.87338 4 2.91125 5 4.73375 6 7.94801 7 13.6665 8 23.9346 Test = 5, Mu = 0, Sigma = 1, A = 0.5, B = 2 Order Moment 0 1 1 1.04299 2 1.23812 3 1.63828 4 2.35698 5 3.60741 6 5.77795 7 9.57285 8 16.2735 Test = 6, Mu = 0, Sigma = 1, A = -2, B = 2 Order Moment 0 1 1 0 2 0.773741 3 0 4 1.41619 5 0 6 3.46081 7 0 8 9.74509 Test = 7, Mu = 0, Sigma = 1, A = -4, B = 4 Order Moment 0 1 1 0 2 0.998929 3 0 4 2.97966 5 0 6 14.6242 7 0 8 97.9836 Test = 8, Mu = 5, Sigma = 0.5, A = 4, B = 7 Order Moment 0 1 1 5.02756 2 25.4978 3 130.441 4 673.075 5 3502.72 6 18382.1 7 97269.7 8 518913 truncated_normal_ab_moment_test: Normal end of execution. truncated_normal_b_moment_test Python version: 3.6.9 truncated_normal_b_moment evaluates moments of the upper Truncated Normal distribution. Test = 0, Mu = 0, Sigma = 1, B = 0 Order Moment 0 1 1 -0.797885 2 1 3 -1.59577 4 3 5 -6.38308 6 15 7 -38.2985 8 105 Test = 1, Mu = 0, Sigma = 1, B = 10 Order Moment 0 1 1 -7.6946e-23 2 1 3 -7.84849e-21 4 3 5 -8.00854e-19 6 15 7 -8.17511e-17 8 105 Test = 2, Mu = 0, Sigma = 1, B = -10 Order Moment 0 1 1 -10.0981 2 101.981 3 -1030.01 4 10404 5 -105101 6 1.06183e+06 7 -1.07287e+07 8 1.08414e+08 Test = 3, Mu = 0, Sigma = 2, B = 10 Order Moment 0 1 1 -2.97344e-06 2 3.99997 3 -0.000321132 4 47.9967 5 -0.0348725 6 959.636 7 -3.81038 8 26840.1 Test = 4, Mu = 0, Sigma = 2, B = -10 Order Moment 0 1 1 -10.373 2 107.73 3 -1120.28 4 11665.8 5 -121655 6 1.27062e+06 7 -1.32927e+07 8 1.39307e+08 Test = 5, Mu = 5, Sigma = 1, B = 10 Order Moment 0 1 1 5 2 26 3 140 4 777.997 5 4449.97 6 26139.7 7 157397 8 969947 truncated_normal_b_moment_test: Normal end of execution. moment_method_test Python version: 3.6.9 moment_method uses the method of moments for a quadrature rule. Computed Correct I X X 0 -2.85697 -2.85697 1 -1.35563 -1.35563 2 3.5938e-16 0 3 1.35563 1.35563 4 2.85697 2.85697 Computed Correct I W W 0 0.0112574 0.0112574 1 0.222076 0.222076 2 0.533333 0.533333 3 0.222076 0.222076 4 0.0112574 0.0112574 moment_method_test: Normal end of execution. option0_test: Python version: 3.6.9 Get a quadrature rule for the untruncated normal distribution. truncated_normal_rule Python version: 3.6.9 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. HEADER is used to generate 3 files: header_w.txt - the weight file header_x.txt - the abscissa file. header_r.txt - the region file, listing A and B. OPTION = 0 N = 5 MU = 1 SIGMA = 2 A = -oo B = +oo HEADER = "option0" Creating quadrature files. Common header 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. option0_test: Normal end of execution. option1_test: Python version: 3.6.9 Get a quadrature rule for the lower truncated normal distribution. truncated_normal_rule Python version: 3.6.9 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. HEADER is used to generate 3 files: header_w.txt - the weight file header_x.txt - the abscissa file. header_r.txt - the region file, listing A and B. OPTION = 1 N = 9 MU = 2 SIGMA = 0.5 A = 0 B = +oo HEADER = "option1" Creating quadrature files. Common header 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. option1_test: Normal end of execution. option2_test: Python version: 3.6.9 Get a quadrature rule for the upper truncated normal distribution. truncated_normal_rule Python version: 3.6.9 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. HEADER is used to generate 3 files: header_w.txt - the weight file header_x.txt - the abscissa file. header_r.txt - the region file, listing A and B. OPTION = 2 N = 9 MU = 2 SIGMA = 0.5 A = -oo B = 3 HEADER = "option2" Creating quadrature files. Common header 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. option2_test: Normal end of execution. option3_test: Python version: 3.6.9 Get a quadrature rule for the truncated normal distribution. truncated_normal_rule Python version: 3.6.9 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. HEADER is used to generate 3 files: header_w.txt - the weight file header_x.txt - the abscissa file. header_r.txt - the region file, listing A and B. OPTION = 3 N = 5 MU = 100 SIGMA = 25 A = 50 B = 150 HEADER = "option3" Creating quadrature files. Common header 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. option3_test: Normal end of execution. truncated_normal_rule_test(): Normal end of execution. Tue Oct 19 17:25:42 2021