Home License -- for personal use only. Not for government, academic, research, commercial, or other organizational use. 13-May-2025 10:31:43 alpert_rule_test(): MATLAB/Octave version 9.11.0.2358333 (R2021b) Update 7 Test the ALPERT_RULE library. MONTE_CARLO_REGULAR_TEST Test the Monte Carlo rule on the regular integrand. N Estimate Error 33 0.0588157 0.0681113 65 0.290735 0.30003 129 -0.0595525 0.0502569 257 -0.0601013 0.0508056 513 -0.189512 0.180216 1025 -0.00123228 0.0080634 2049 -0.0333955 0.0240998 4097 0.0104379 0.0197336 8193 0.022549 0.0318447 16385 0.00325925 0.0125549 32769 -0.00241494 0.00688074 65537 -0.0207149 0.0114192 131073 -0.0176524 0.00835676 262145 -0.0147761 0.00548037 524289 -0.00924213 5.3551e-05 1048577 -0.0106062 0.00131049 Exact: -0.00929568 MONTE_CARLO_LOG_TEST Test the Monte Carlo rule on the log singular integrand. N Estimate Error 33 0.0249273 0.0376984 65 -0.000370568 0.0124005 129 -0.00235424 0.0104169 257 -0.0151101 0.00233904 513 -0.0165841 0.00381297 1025 -0.0125882 0.000182918 2049 -0.0111362 0.00163494 4097 0.00326717 0.0160383 8193 -0.00204541 0.0107257 16385 -0.00939644 0.00337467 32769 -0.00757668 0.00519442 65537 -0.0082757 0.00449541 131073 -0.0134086 0.000637445 262145 -0.0139345 0.00116339 524289 -0.0125988 0.000172313 1048577 -0.0127591 1.19879e-05 Exact: -0.0127711 MONTE_CARLO_POWER_TEST Test the Monte Carlo rule on the power singular integrand. N Estimate Error 33 -0.35666 0.435981 65 1.82054 1.74122 129 0.633228 0.553907 257 0.0668812 0.0124398 513 0.353575 0.274254 1025 0.241563 0.162242 2049 0.0110543 0.0682667 4097 0.0515653 0.0277557 8193 0.0256403 0.0536807 16385 0.0443422 0.0349788 32769 0.064894 0.014427 65537 0.0771954 0.00212557 131073 0.0676466 0.0116744 262145 0.0747497 0.00457133 524289 0.0782687 0.0010523 1048577 0.0878841 0.00856308 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 1.45971e-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 2.16338e-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 4.23989e-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 1.63514e-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 1.16199e-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 2.84679e-10 Exact: 0.079321 alpert_rule_test(): Normal end of execution. 13-May-2025 10:31:43