13 July 2021 02:56:01 PM alpert_rule_test(): GCC version 7.5.0 Test alpert_rule(). MONTE_CARLO_REGULAR_TEST Test the Monte Carlo rule on the regular integrand. N Estimate Error 33 0.0726524 0.0819481 65 -0.000266206 0.00902948 129 0.178291 0.187586 257 0.135114 0.144409 513 0.0382964 0.047592 1025 0.0240217 0.0333174 2049 -0.0363538 0.0270582 4097 -0.0282882 0.0189925 8193 -0.0274368 0.0181411 16385 0.00186061 0.0111563 32769 0.0136433 0.0229389 65537 -0.00623016 0.00306552 131073 -0.010295 0.000999325 262145 -0.00699581 0.00229987 524289 -0.0108866 0.00159094 1048577 -0.00918838 0.000107307 Exact: -0.00929568 MONTE_CARLO_LOG_TEST Test the Monte Carlo rule on the log singular integrand. N Estimate Error 33 -0.228146 0.215375 65 0.00587318 0.0186443 129 0.0497586 0.0625297 257 0.0964866 0.109258 513 0.0221565 0.0349276 1025 -0.0334722 0.0207011 2049 0.0171524 0.0299235 4097 -0.0330124 0.0202413 8193 -0.00335703 0.00941407 16385 -0.00998029 0.00279082 32769 -0.0106336 0.0021375 65537 -0.014243 0.00147191 131073 -0.0162687 0.0034976 262145 -0.0104547 0.0023164 524289 -0.0146355 0.00186434 1048577 -0.0119328 0.000838322 Exact: -0.0127711 MONTE_CARLO_POWER_TEST Test the Monte Carlo rule on the power singular integrand. N Estimate Error 33 0.642806 0.563485 65 -0.00649485 0.0858159 129 0.275387 0.196066 257 0.057494 0.021827 513 0.0418089 0.0375121 1025 0.0847778 0.00545684 2049 -0.0288245 0.108146 4097 0.0801184 0.000797372 8193 0.00613614 0.0731849 16385 0.0947588 0.0154378 32769 0.105905 0.026584 65537 0.0891585 0.00983749 131073 0.0905591 0.0112381 262145 0.071792 0.00752896 524289 0.0718595 0.00746152 1048577 0.0799518 0.000630812 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 0.106785 0.119556 65 0.0259598 0.0387309 129 -0.00317143 0.00959968 257 -0.00976066 0.00301044 513 -0.0115398 0.00123129 1025 -0.0121956 0.000575547 2049 -0.0124892 0.000281953 4097 -0.012631 0.000140123 Exact: -0.0127711 TRAPEZOID_POWER_TEST Test the trapezoidal rule on the power-singular integrand. N Estimate Error 33 2.30103 2.22171 65 -0.0847227 0.164044 129 -0.00245137 0.0817724 257 0.0295214 0.0497996 513 0.0455685 0.0337525 1025 0.0557052 0.0236158 2049 0.0626641 0.0166569 4097 0.0675496 0.0117714 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 1.45973e-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 7.70167e-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 2.16424e-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 1 1 16 18 0.0588235 0.0412452 0.0540163 1 2 1 1 32 34 0.030303 -0.0585047 0.0457336 1 2 1 1 64 66 0.0153846 -0.0107057 0.00206539 1 2 1 1 128 130 0.00775194 -0.0124222 0.000348888 2 3 2 2 16 20 0.0526316 0.0465206 0.0592917 2 3 2 2 32 36 0.0285714 -0.0108302 0.00194095 2 3 2 2 64 68 0.0149254 -0.00409752 0.00867359 2 3 2 2 128 132 0.00763359 -0.0125088 0.000262288 3 4 3 2 16 21 0.0526316 0.0618049 0.074576 3 4 3 2 32 37 0.0285714 0.000459112 0.0132302 3 4 3 2 64 69 0.0149254 -0.0121884 0.000582729 3 4 3 2 128 133 0.00763359 -0.0127824 1.13258e-05 4 5 4 3 16 23 0.047619 0.0598335 0.0726046 4 5 4 3 32 39 0.027027 0.00731479 0.0200859 4 5 4 3 64 71 0.0144928 -0.0125993 0.00017183 4 5 4 3 128 135 0.0075188 -0.0127943 2.32273e-05 5 6 5 3 16 24 0.047619 0.0144266 0.0271977 5 6 5 3 32 40 0.027027 0.0114131 0.0241842 5 6 5 3 64 72 0.0144928 -0.0131021 0.000331028 5 6 5 3 128 136 0.0075188 -0.0127737 2.55889e-06 6 8 7 5 16 27 0.0416667 0.0608432 0.0736143 6 8 7 5 32 43 0.025 0.0136405 0.0264116 6 8 7 5 64 75 0.0138889 -0.0129275 0.000156429 6 8 7 5 128 139 0.00735294 -0.0127702 9.4815e-07 7 10 10 6 16 32 0.0384615 0.0241135 0.0368846 7 10 10 6 32 48 0.0238095 -0.0152253 0.00245414 7 10 10 6 64 80 0.0135135 -0.0127659 5.22334e-06 7 10 10 6 128 144 0.00724638 -0.0127711 1.0156e-10 8 12 11 7 16 35 0.0344828 0.0309983 0.0437694 8 12 11 7 32 51 0.0222222 -0.0138375 0.00106644 8 12 11 7 64 83 0.012987 -0.0127712 9.2525e-08 8 12 11 7 128 147 0.0070922 -0.0127711 4.2399e-11 9 14 14 9 16 40 0.030303 0.0411346 0.0539057 9 14 14 9 32 56 0.0204082 -0.0122271 0.000544027 9 14 14 9 64 88 0.0123457 -0.012771 7.31058e-08 9 14 14 9 128 152 0.00689655 -0.0127711 1.63497e-12 10 16 15 10 16 43 0.0285714 0.0332425 0.0460136 10 16 15 10 32 59 0.0196078 -0.0126612 0.000109918 10 16 15 10 64 91 0.0120482 -0.0127711 2.22928e-08 10 16 15 10 128 155 0.00680272 -0.0127711 1.15801e-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 2 2 16 20 0.0526316 -0.0274236 0.106745 2 2 2 2 32 36 0.0285714 0.302254 0.222933 2 2 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 3 2 16 22 0.05 -0.266472 0.345793 4 3 3 2 32 38 0.0277778 0.147106 0.0677852 4 3 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 4 3 16 24 0.0454545 -0.265049 0.34437 6 4 4 3 32 40 0.0263158 0.0859191 0.0065981 6 4 4 3 64 72 0.0142857 0.0759639 0.00335713 7 6 6 4 16 28 0.0416667 -0.202176 0.281497 7 6 6 4 32 44 0.025 0.0436246 0.0356964 7 6 6 4 64 76 0.0138889 0.0794586 0.000137591 8 8 8 5 16 32 0.037037 -0.339485 0.418806 8 8 8 5 32 48 0.0232558 0.069808 0.00951302 8 8 8 5 64 80 0.0133333 0.0793247 3.71329e-06 9 10 10 6 16 36 0.0333333 -0.403544 0.482865 9 10 10 6 32 52 0.0217391 0.0826427 0.00332171 9 10 10 6 64 84 0.0128205 0.0793167 4.29831e-06 10 12 12 8 16 40 0.030303 0.118805 0.0394842 10 12 12 8 32 56 0.0204082 0.0809902 0.00166916 10 12 12 8 64 88 0.0123457 0.0793235 2.45276e-06 11 14 14 9 16 44 0.0277778 -0.000343625 0.0796646 11 14 14 9 32 60 0.0192308 0.0791337 0.000187326 11 14 14 9 64 92 0.0119048 0.079321 2.4056e-08 12 16 16 10 16 48 0.025641 0.092208 0.012887 12 16 16 10 32 64 0.0181818 0.0793329 1.19136e-05 12 16 16 10 64 96 0.0114943 0.079321 2.84679e-10 Exact: 0.079321 ALPERT_RULE_TEST Normal end of execution. 13 July 2021 02:56:01 PM