08-Dec-2022 20:38:57 alpert_rule_test(): MATLAB/Octave version 4.2.2 Test the ALPERT_RULE library. MONTE_CARLO_REGULAR_TEST Test the Monte Carlo rule on the regular integrand. N Estimate Error 33 0.470178 0.479474 65 -0.15931 0.150015 129 0.061013 0.0703087 257 0.202752 0.212047 513 -0.0108102 0.00151454 1025 -0.00593857 0.00335711 2049 0.00905842 0.0183541 4097 -0.0120535 0.00275777 8193 -0.0196532 0.0103575 16385 -0.0261508 0.0168551 32769 -0.0149466 0.00565091 65537 -0.00967399 0.000378306 131073 -0.0107059 0.00141023 262145 -0.00915313 0.000142555 524289 -0.00667904 0.00261665 1048577 -0.0102423 0.000946664 Exact: -0.00929568 MONTE_CARLO_LOG_TEST Test the Monte Carlo rule on the log singular integrand. N Estimate Error 33 0.110111 0.122882 65 -0.125635 0.112864 129 -0.0272235 0.0144524 257 -0.0947932 0.082022 513 0.00552783 0.0182989 1025 -0.0320244 0.0192533 2049 -0.0441593 0.0313882 4097 -0.0359601 0.023189 8193 0.0081499 0.020921 16385 -0.0149512 0.00218009 32769 -0.00988532 0.00288579 65537 -0.0123278 0.00044331 131073 -0.0150116 0.00224045 262145 -0.0115081 0.00126303 524289 -0.0104482 0.00232295 1048577 -0.0111176 0.00165355 Exact: -0.0127711 MONTE_CARLO_POWER_TEST Test the Monte Carlo rule on the power singular integrand. N Estimate Error 33 -0.452724 0.532045 65 0.768863 0.689542 129 -0.195486 0.274807 257 0.0022781 0.0770429 513 -0.00142704 0.080748 1025 -0.00964239 0.0889634 2049 0.154312 0.074991 4097 0.059534 0.019787 8193 0.0770348 0.00228624 16385 0.0529449 0.0263761 32769 0.0630651 0.0162559 65537 0.0637764 0.0155446 131073 0.102173 0.0228517 262145 0.0752178 0.00410319 524289 0.0802785 0.000957541 1048577 0.0786188 0.000702232 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 2.1643e-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 1.63543e-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 1.16665e-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. 08-Dec-2022 20:38:58