Tue Oct 19 11:21:58 2021 alpert_rule_test(): Python version: 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_log_test(): Normal end of execution. 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_power_test(): Normal end of execution. integral_regular_test: integral_regular returns the value of the integral of the regular test function over [0,1]. integral_regular = -0.00929568 integral_regular_test(): Normal end of execution. 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_log_test(): Normal end of execution. 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_power_test(): Normal end of execution. 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 integrand_regular_test(): Normal end of execution. 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 r8vec_linspace2_test Normal end of execution. r8vec_print_test(): 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. monte_carlo_regular_test(): Test the Monte Carlo rule on the regular integrand. N Estimate Error 33 0.164843 0.174139 65 0.0310297 0.0403254 129 0.0566138 0.0659095 257 0.042213 0.0515087 513 0.0300427 0.0393384 1025 -0.00791537 0.00138031 2049 -0.0430115 0.0337158 4097 -0.00629279 0.00300289 8193 0.00590703 0.0152027 16385 -0.0197529 0.0104572 32769 -0.0125129 0.00321719 65537 -0.00197897 0.00731671 131073 -0.0158123 0.00651664 262145 -0.00878104 0.000514647 524289 -0.00994363 0.000647946 1048577 -0.010128 0.000832331 Exact: -0.00929568 monte_carlo_regular_test(): Normal end of execution. monte_carlo_log_test(): Test the Monte Carlo rule on the log singular integrand. N Estimate Error 33 0.100454 0.113226 65 -0.161512 0.148741 129 -0.022399 0.00962794 257 -0.0745181 0.061747 513 -0.00609822 0.00667289 1025 -0.00696899 0.00580212 2049 -0.00742192 0.00534918 4097 -0.0188074 0.00603631 8193 -0.0298161 0.017045 16385 -0.00509735 0.00767375 32769 -0.0179534 0.00518226 65537 -0.0143478 0.00157668 131073 -0.0153445 0.0025734 262145 -0.0107729 0.00199818 524289 -0.0113569 0.00141417 1048577 -0.0133855 0.00061438 Exact: -0.0127711 monte_carlo_log_test(): Normal end of execution. monte_carlo_power_test(): Test the Monte Carlo rule on the power singular integrand. N Estimate Error 33 0.236799 0.157478 65 -0.272526 0.351847 129 0.0176745 0.0616465 257 -0.161823 0.241144 513 0.163731 0.0844099 1025 -0.0178334 0.0971544 2049 0.019097 0.060224 4097 0.105742 0.0264207 8193 0.0517692 0.0275518 16385 0.0931565 0.0138355 32769 0.0639881 0.0153329 65537 0.156858 0.0775374 131073 0.0674336 0.0118874 262145 0.0719605 0.00736055 524289 0.0754508 0.00387021 1048577 0.0724033 0.00691773 Exact: 0.079321 monte_carlo_power_test(): Normal end of execution. 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_regular_test(): Normal end of execution. 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_log_test(): Normal end of execution. 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 trapezoid_power_test(): Normal end of execution. 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_regular_test(): Normal end of execution. 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 1.16667e-13 Exact: -0.0127711 alpert_log_test(): Normal end of execution. 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_power_test(): Normal end of execution. alpert_rule_test(): Normal end of execution. Tue Oct 19 11:21:59 2021