Tue May 20 21:17:33 2025 alpert_rule_test(): python version: 3.10.12 numpy version: 1.26.4 Test alpert_rule(). integral_log_test(): integral_log() returns the value of the integral of the log-singular test function over [0,1]. integral_log = -0.0127711 integral_power_test(): integral_power() returns the value of the integral of the power-singular test function over [0,1]. integral_power = 0.079321 integral_regular_test(): integral_regular() returns the value of the integral of the regular test function over [0,1]. integral_regular = -0.00929568 integrand_log_test(): integrand_log() evaluates the log-singular test function. X F(X) 0 0.1 -0.819582 1 0.2 0.216049 2 0.3 0.326882 3 0.4 0.289404 4 0.5 0.375732 5 0.6 0.19033 6 0.7 -0.408104 7 0.8 -0.779193 8 0.9 -0.27192 integrand_power_test(): integrand_power() evaluates the power-singular test function. X F(X) 0 0.1 1.41053 1 0.2 -2.34867 2 0.3 -2.55866 3 0.4 0.0137197 4 0.5 2.19295 5 0.6 1.65734 6 0.7 -0.715092 7 0.8 -2.08769 8 0.9 -0.965806 integrand_regular_test(): integrand_regular() evaluates the regular test function. X F(X) 0 0.1 0.528144 1 0.2 -1.52428 2 0.3 -1.77221 3 0.4 0.07787 4 0.5 1.83576 5 0.6 1.42042 6 0.7 -0.676473 7 0.8 -1.97253 8 0.9 -0.933434 r8vec_linspace2_test(): r8vec_linspace2() returns evenly spaced values between A and B omitting the endpoints. The linspace2 vector: 0: 12 1: 14 2: 16 3: 18 monte_carlo_regular_test(): Test the Monte Carlo rule on the regular integrand. N Estimate Error 33 -0.115493 0.106197 65 -0.0529568 0.0436611 129 -0.00249708 0.0067986 257 0.0662871 0.0755828 513 -0.077175 0.0678793 1025 0.042839 0.0521347 2049 -0.0415463 0.0322507 4097 -0.0248319 0.0155362 8193 -0.0258022 0.0165065 16385 -0.00861749 0.000678191 32769 -0.023048 0.0137523 65537 -0.00147 0.00782568 131073 -0.0114659 0.00217022 262145 -0.00470839 0.00458729 524289 -0.010325 0.00102933 1048577 -0.00925344 4.22473e-05 Exact: -0.00929568 monte_carlo_log_test(): Test the Monte Carlo rule on the log singular integrand. N Estimate Error 33 -0.0180885 0.0053174 65 0.0234335 0.0362047 129 -0.00802999 0.00474112 257 0.00907561 0.0218467 513 -0.0437064 0.0309353 1025 0.00217782 0.0149489 2049 -0.0304697 0.0176986 4097 -0.0057486 0.0070225 8193 -0.0179383 0.00516719 16385 -0.0144843 0.00171318 32769 -0.0188105 0.00603941 65537 -0.0103885 0.0023826 131073 -0.0109225 0.00184859 262145 -0.0136926 0.000921529 524289 -0.0130832 0.000312112 1048577 -0.0132707 0.000499642 Exact: -0.0127711 monte_carlo_power_test(): Test the Monte Carlo rule on the power singular integrand. N Estimate Error 33 -0.305359 0.38468 65 0.467177 0.387856 129 -0.380776 0.460097 257 0.0577411 0.0215799 513 0.0811908 0.00186977 1025 0.0505817 0.0287393 2049 0.121118 0.0417965 4097 0.108105 0.028784 8193 0.0995499 0.0202289 16385 0.0733416 0.00597939 32769 0.0624993 0.0168217 65537 0.0976615 0.0183405 131073 0.088782 0.00946103 262145 0.066377 0.012944 524289 0.0675272 0.0117938 1048577 0.0847431 0.00542214 Exact: 0.079321 trapezoid_regular_test(): Test the trapezoidal rule on the regular integrand. N Estimate Error 33 1.75055 1.75985 65 -0.000120503 0.00917518 129 -0.00732275 0.00197293 257 -0.008818 0.000477683 513 -0.00917718 0.000118502 1025 -0.00926611 2.9569e-05 2049 -0.00928829 7.38872e-06 4097 -0.00929384 1.84696e-06 Exact: -0.00929568 trapezoid_log_test(): Test the trapezoidal rule on the log-singular integrand. N Estimate Error 33 0.195807 0.208578 65 -0.00158735 0.0111838 129 -0.0154339 0.00266282 257 -0.0127499 2.11606e-05 513 -0.0124405 0.000330599 1025 -0.01256 0.000211067 2049 -0.0126605 0.000110625 4097 -0.0127155 5.56122e-05 Exact: -0.0127711 trapezoid_power_test(): Test the trapezoidal rule on the power-singular integrand. N Estimate Error 33 2.05764 1.97832 65 -0.0162439 0.0955649 129 0.0445193 0.0348017 257 0.0487851 0.0305359 513 0.0558982 0.0234228 1025 0.0623896 0.0169314 2049 0.0672789 0.0120421 4097 0.0707927 0.00852834 Exact: 0.079321 alpert_regular_test(): Test the Alpert rule on the regular integrand. Rule Order J A N N+2J H Estimate Error 1 3 1 1 16 18 0.0588235 -0.0500628 0.0407671 1 3 1 1 32 34 0.030303 0.20575 0.215045 1 3 1 1 64 66 0.0153846 -0.010612 0.00131633 2 4 2 2 16 20 0.0526316 -0.141581 0.132286 2 4 2 2 32 36 0.0285714 0.0378063 0.047102 2 4 2 2 64 68 0.0149254 -0.0114231 0.00212739 3 5 2 2 16 20 0.0526316 -0.131604 0.122308 3 5 2 2 32 36 0.0285714 0.0259184 0.0352141 3 5 2 2 64 68 0.0149254 -0.0101763 0.00088057 4 6 3 3 16 22 0.047619 -0.137677 0.128381 4 6 3 3 32 38 0.027027 -0.00188668 0.007409 4 6 3 3 64 70 0.0144928 -0.0100067 0.00071098 5 7 3 3 16 22 0.047619 -0.142989 0.133693 5 7 3 3 32 38 0.027027 -0.0019785 0.00731718 5 7 3 3 64 70 0.0144928 -0.0102435 0.000947865 6 8 4 4 16 24 0.0434783 -0.136958 0.127662 6 8 4 4 32 40 0.025641 -0.020842 0.0115464 6 8 4 4 64 72 0.0140845 -0.00981928 0.000523596 7 12 6 5 16 28 0.04 -0.14334 0.134044 7 12 6 5 32 44 0.0243902 -0.0220527 0.012757 7 12 6 5 64 76 0.0136986 -0.00927675 1.89357e-05 8 16 8 7 16 32 0.0344828 -0.352522 0.343227 8 16 8 7 32 48 0.0222222 -0.00991724 0.000621561 8 16 8 7 64 80 0.012987 -0.00929594 2.608e-07 9 20 10 9 16 36 0.030303 0.0744691 0.0837647 9 20 10 9 32 52 0.0204082 -0.00766321 0.00163247 9 20 10 9 64 84 0.0123457 -0.00929541 2.75663e-07 10 24 12 10 16 40 0.0285714 -0.0758624 0.0665667 10 24 12 10 32 56 0.0196078 -0.00932891 3.32283e-05 10 24 12 10 64 88 0.0120482 -0.00929568 1.4597e-10 11 28 14 12 16 44 0.025641 -0.00866733 0.000628352 11 28 14 12 32 60 0.0181818 -0.00929862 2.93684e-06 11 28 14 12 64 92 0.0114943 -0.00929568 7.70181e-11 12 32 16 14 16 48 0.0232558 -0.00955747 0.00026179 12 32 16 14 32 64 0.0169492 -0.00929608 3.93839e-07 12 32 16 14 64 96 0.010989 -0.00929568 2.16431e-12 Exact: -0.00929568 alpert_log_test(): Test the Alpert rule on the log integrand. Rule Order J A N N+2J H Estimate Error 1 2.0 1 1 16 18 0.0588235 0.0412452 0.0540163 1 2.0 1 1 32 34 0.030303 -0.0585047 0.0457336 1 2.0 1 1 64 66 0.0153846 -0.0107057 0.00206539 1 2.0 1 1 128 130 0.00775194 -0.0124222 0.000348888 2 3.0 2 2 16 20 0.0526316 0.0465206 0.0592917 2 3.0 2 2 32 36 0.0285714 -0.0108302 0.00194095 2 3.0 2 2 64 68 0.0149254 -0.00409752 0.00867359 2 3.0 2 2 128 132 0.00763359 -0.0125088 0.000262288 3 4.0 3 2 16 21 0.0526316 0.0618049 0.074576 3 4.0 3 2 32 37 0.0285714 0.000459112 0.0132302 3 4.0 3 2 64 69 0.0149254 -0.0121884 0.000582729 3 4.0 3 2 128 133 0.00763359 -0.0127824 1.13258e-05 4 5.0 4 3 16 23 0.047619 0.0598335 0.0726046 4 5.0 4 3 32 39 0.027027 0.00731479 0.0200859 4 5.0 4 3 64 71 0.0144928 -0.0125993 0.00017183 4 5.0 4 3 128 135 0.0075188 -0.0127943 2.32273e-05 5 6.0 5 3 16 24 0.047619 0.0144266 0.0271977 5 6.0 5 3 32 40 0.027027 0.0114131 0.0241842 5 6.0 5 3 64 72 0.0144928 -0.0131021 0.000331028 5 6.0 5 3 128 136 0.0075188 -0.0127737 2.55889e-06 6 8.0 7 5 16 27 0.0416667 0.0608432 0.0736143 6 8.0 7 5 32 43 0.025 0.0136405 0.0264116 6 8.0 7 5 64 75 0.0138889 -0.0129275 0.000156429 6 8.0 7 5 128 139 0.00735294 -0.0127702 9.4815e-07 7 10.0 10 6 16 32 0.0384615 0.0241135 0.0368846 7 10.0 10 6 32 48 0.0238095 -0.0152253 0.00245414 7 10.0 10 6 64 80 0.0135135 -0.0127659 5.22334e-06 7 10.0 10 6 128 144 0.00724638 -0.0127711 1.01559e-10 8 12.0 11 7 16 35 0.0344828 0.0309983 0.0437694 8 12.0 11 7 32 51 0.0222222 -0.0138375 0.00106644 8 12.0 11 7 64 83 0.012987 -0.0127712 9.2525e-08 8 12.0 11 7 128 147 0.0070922 -0.0127711 4.23994e-11 9 14.0 14 9 16 40 0.030303 0.0411346 0.0539057 9 14.0 14 9 32 56 0.0204082 -0.0122271 0.000544027 9 14.0 14 9 64 88 0.0123457 -0.012771 7.31058e-08 9 14.0 14 9 128 152 0.00689655 -0.0127711 1.63545e-12 10 16.0 15 10 16 43 0.0285714 0.0332425 0.0460136 10 16.0 15 10 32 59 0.0196078 -0.0126612 0.000109918 10 16.0 15 10 64 91 0.0120482 -0.0127711 2.22928e-08 10 16.0 15 10 128 155 0.00680272 -0.0127711 1.16671e-13 Exact: -0.0127711 alpert_power_test(): Test the Alpert rule on the power integrand. Rule Order J A N N+2J H Estimate Error 1 1.5 1 1 16 18 0.0588235 0.0591092 0.0202119 1 1.5 1 1 32 34 0.030303 0.612287 0.532966 1 1.5 1 1 64 66 0.0153846 0.0856299 0.00630886 2 2.0 2 2 16 20 0.0526316 -0.0274236 0.106745 2 2.0 2 2 32 36 0.0285714 0.302254 0.222933 2 2.0 2 2 64 68 0.0149254 0.0670261 0.0122949 3 2.5 2 2 16 20 0.0526316 -0.214188 0.293509 3 2.5 2 2 32 36 0.0285714 0.178532 0.099211 3 2.5 2 2 64 68 0.0149254 0.0349942 0.0443268 4 3.0 3 2 16 22 0.05 -0.266472 0.345793 4 3.0 3 2 32 38 0.0277778 0.147106 0.0677852 4 3.0 3 2 64 70 0.0147059 0.0737758 0.00554521 5 3.5 3 2 16 22 0.05 -0.268635 0.347956 5 3.5 3 2 32 38 0.0277778 0.124609 0.0452876 5 3.5 3 2 64 70 0.0147059 0.0766103 0.00271075 6 4.0 4 3 16 24 0.0454545 -0.265049 0.34437 6 4.0 4 3 32 40 0.0263158 0.0859191 0.0065981 6 4.0 4 3 64 72 0.0142857 0.0759639 0.00335713 7 6.0 6 4 16 28 0.0416667 -0.202176 0.281497 7 6.0 6 4 32 44 0.025 0.0436246 0.0356964 7 6.0 6 4 64 76 0.0138889 0.0794586 0.000137591 8 8.0 8 5 16 32 0.037037 -0.339485 0.418806 8 8.0 8 5 32 48 0.0232558 0.069808 0.00951302 8 8.0 8 5 64 80 0.0133333 0.0793247 3.71329e-06 9 10.0 10 6 16 36 0.0333333 -0.403544 0.482865 9 10.0 10 6 32 52 0.0217391 0.0826427 0.00332171 9 10.0 10 6 64 84 0.0128205 0.0793167 4.29831e-06 10 12.0 12 8 16 40 0.030303 0.118805 0.0394842 10 12.0 12 8 32 56 0.0204082 0.0809902 0.00166916 10 12.0 12 8 64 88 0.0123457 0.0793235 2.45276e-06 11 14.0 14 9 16 44 0.0277778 -0.000343625 0.0796646 11 14.0 14 9 32 60 0.0192308 0.0791337 0.000187326 11 14.0 14 9 64 92 0.0119048 0.079321 2.4056e-08 12 16.0 16 10 16 48 0.025641 0.092208 0.012887 12 16.0 16 10 32 64 0.0181818 0.0793329 1.19136e-05 12 16.0 16 10 64 96 0.0114943 0.079321 2.8468e-10 Exact: 0.079321 alpert_rule_test(): Normal end of execution. Tue May 20 21:17:34 2025