25 August 2021 10:39:23.349 PM alpert_rule_test(): FORTRAN90 version. Test alpert_rule(). monte_carlo_regular_test(): Test the Monte Carlo rule on the regular integrand. N Estimate Error 33 -0.272207 0.262911 65 -0.546692E-01 0.453736E-01 129 0.269753E-01 0.362710E-01 257 -0.413678E-01 0.320721E-01 513 -0.734658E-01 0.641701E-01 1025 0.782886E-02 0.171245E-01 2049 -0.233476E-01 0.140519E-01 4097 -0.204800E-02 0.724768E-02 8193 -0.289038E-01 0.196081E-01 16385 -0.178483E-03 0.911720E-02 32769 -0.199480E-01 0.106523E-01 65537 -0.197357E-01 0.104400E-01 131073 -0.107327E-01 0.143701E-02 262145 -0.120640E-01 0.276829E-02 524289 -0.130527E-01 0.375706E-02 1048577 -0.107214E-01 0.142572E-02 Exact: -0.929568E-02 monte_carlo_log_test(): Test the Monte Carlo rule on the log singular integrand. N Estimate Error 33 -0.740818E-01 0.613107E-01 65 0.536852E-01 0.664563E-01 129 0.903414E-02 0.218052E-01 257 -0.234946E-02 0.104217E-01 513 0.670041E-02 0.194715E-01 1025 0.406280E-01 0.533992E-01 2049 -0.780049E-02 0.497062E-02 4097 -0.272775E-01 0.145064E-01 8193 -0.136253E-01 0.854219E-03 16385 -0.116613E-01 0.110981E-02 32769 -0.107706E-01 0.200048E-02 65537 -0.151027E-01 0.233163E-02 131073 -0.126921E-01 0.790027E-04 262145 -0.139313E-01 0.116016E-02 524289 -0.146517E-01 0.188059E-02 1048577 -0.112599E-01 0.151121E-02 Exact: -0.127711E-01 monte_carlo_power_test(): Test the Monte Carlo rule on the power singular integrand. N Estimate Error 33 -0.256734 0.336055 65 -0.280474E-01 0.107368 129 0.276658E-01 0.516552E-01 257 -0.309521 0.388842 513 0.155341 0.760195E-01 1025 -0.518512E-01 0.131172 2049 0.140956 0.616347E-01 4097 -0.569999E-03 0.798910E-01 8193 0.121288 0.419673E-01 16385 0.950467E-01 0.157257E-01 32769 0.112809 0.334877E-01 65537 0.838712E-01 0.455023E-02 131073 0.813592E-01 0.203818E-02 262145 0.680173E-01 0.113037E-01 524289 0.150179 0.708581E-01 1048577 0.705586E-01 0.876237E-02 Exact: 0.793210E-01 trapezoid_regular_test(): Test the trapezoidal rule on the regular integrand. N Estimate Error 33 1.75055 1.75985 65 -0.120503E-03 0.917518E-02 129 -0.732275E-02 0.197293E-02 257 -0.881800E-02 0.477683E-03 513 -0.917718E-02 0.118502E-03 1025 -0.926611E-02 0.295690E-04 2049 -0.928829E-02 0.738872E-05 4097 -0.929384E-02 0.184696E-05 Exact: -0.929568E-02 trapezoid_log_test(): Test the trapezoidal rule on the log-singular integrand. N Estimate Error 33 0.106785 0.119556 65 0.259598E-01 0.387309E-01 129 -0.317143E-02 0.959968E-02 257 -0.976066E-02 0.301044E-02 513 -0.115398E-01 0.123129E-02 1025 -0.121956E-01 0.575547E-03 2049 -0.124892E-01 0.281953E-03 4097 -0.126310E-01 0.140123E-03 Exact: -0.127711E-01 trapezoid_power_test(): Test the trapezoidal rule on the power-singular integrand. N Estimate Error 33 2.30103 2.22171 65 -0.847227E-01 0.164044 129 -0.245137E-02 0.817724E-01 257 0.295214E-01 0.497996E-01 513 0.455685E-01 0.337525E-01 1025 0.557052E-01 0.236158E-01 2049 0.626641E-01 0.166569E-01 4097 0.675496E-01 0.117714E-01 Exact: 0.793210E-01 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 0.588235E-01 -0.500628E-01 0.407671E-01 1 3 1 1 32 34 0.303030E-01 0.205750 0.215045 1 3 1 1 64 66 0.153846E-01 -0.106120E-01 0.131633E-02 2 4 2 2 16 20 0.526316E-01 -0.141581 0.132286 2 4 2 2 32 36 0.285714E-01 0.378063E-01 0.471020E-01 2 4 2 2 64 68 0.149254E-01 -0.114231E-01 0.212739E-02 3 5 2 2 16 20 0.526316E-01 -0.131604 0.122308 3 5 2 2 32 36 0.285714E-01 0.259184E-01 0.352141E-01 3 5 2 2 64 68 0.149254E-01 -0.101763E-01 0.880570E-03 4 6 3 3 16 22 0.476190E-01 -0.137677 0.128381 4 6 3 3 32 38 0.270270E-01 -0.188668E-02 0.740900E-02 4 6 3 3 64 70 0.144928E-01 -0.100067E-01 0.710980E-03 5 7 3 3 16 22 0.476190E-01 -0.142989 0.133693 5 7 3 3 32 38 0.270270E-01 -0.197850E-02 0.731718E-02 5 7 3 3 64 70 0.144928E-01 -0.102435E-01 0.947865E-03 6 8 4 4 16 24 0.434783E-01 -0.136958 0.127662 6 8 4 4 32 40 0.256410E-01 -0.208420E-01 0.115464E-01 6 8 4 4 64 72 0.140845E-01 -0.981928E-02 0.523596E-03 7 12 6 5 16 28 0.400000E-01 -0.143340 0.134044 7 12 6 5 32 44 0.243902E-01 -0.220527E-01 0.127570E-01 7 12 6 5 64 76 0.136986E-01 -0.927675E-02 0.189357E-04 8 16 8 7 16 32 0.344828E-01 -0.352522 0.343227 8 16 8 7 32 48 0.222222E-01 -0.991724E-02 0.621561E-03 8 16 8 7 64 80 0.129870E-01 -0.929594E-02 0.260800E-06 9 20 10 9 16 36 0.303030E-01 0.744691E-01 0.837647E-01 9 20 10 9 32 52 0.204082E-01 -0.766321E-02 0.163247E-02 9 20 10 9 64 84 0.123457E-01 -0.929541E-02 0.275663E-06 10 24 12 10 16 40 0.285714E-01 -0.758624E-01 0.665667E-01 10 24 12 10 32 56 0.196078E-01 -0.932891E-02 0.332283E-04 10 24 12 10 64 88 0.120482E-01 -0.929568E-02 0.145973E-09 11 28 14 12 16 44 0.256410E-01 -0.866733E-02 0.628352E-03 11 28 14 12 32 60 0.181818E-01 -0.929862E-02 0.293684E-05 11 28 14 12 64 92 0.114943E-01 -0.929568E-02 0.770167E-10 12 32 16 14 16 48 0.232558E-01 -0.955747E-02 0.261790E-03 12 32 16 14 32 64 0.169492E-01 -0.929608E-02 0.393839E-06 12 32 16 14 64 96 0.109890E-01 -0.929568E-02 0.216424E-11 Exact: -0.929568E-02 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 0.588235E-01 0.412452E-01 0.540163E-01 1 2 1 1 32 34 0.303030E-01 -0.585047E-01 0.457336E-01 1 2 1 1 64 66 0.153846E-01 -0.107057E-01 0.206539E-02 1 2 1 1 128 130 0.775194E-02 -0.124222E-01 0.348888E-03 2 3 2 2 16 20 0.526316E-01 0.465206E-01 0.592917E-01 2 3 2 2 32 36 0.285714E-01 -0.108302E-01 0.194095E-02 2 3 2 2 64 68 0.149254E-01 -0.409752E-02 0.867359E-02 2 3 2 2 128 132 0.763359E-02 -0.125088E-01 0.262288E-03 3 4 3 2 16 21 0.526316E-01 0.618049E-01 0.745760E-01 3 4 3 2 32 37 0.285714E-01 0.459112E-03 0.132302E-01 3 4 3 2 64 69 0.149254E-01 -0.121884E-01 0.582729E-03 3 4 3 2 128 133 0.763359E-02 -0.127824E-01 0.113258E-04 4 5 4 3 16 23 0.476190E-01 0.598335E-01 0.726046E-01 4 5 4 3 32 39 0.270270E-01 0.731479E-02 0.200859E-01 4 5 4 3 64 71 0.144928E-01 -0.125993E-01 0.171830E-03 4 5 4 3 128 135 0.751880E-02 -0.127943E-01 0.232273E-04 5 6 5 3 16 24 0.476190E-01 0.144266E-01 0.271977E-01 5 6 5 3 32 40 0.270270E-01 0.114131E-01 0.241842E-01 5 6 5 3 64 72 0.144928E-01 -0.131021E-01 0.331028E-03 5 6 5 3 128 136 0.751880E-02 -0.127737E-01 0.255889E-05 6 8 7 5 16 27 0.416667E-01 0.608432E-01 0.736143E-01 6 8 7 5 32 43 0.250000E-01 0.136405E-01 0.264116E-01 6 8 7 5 64 75 0.138889E-01 -0.129275E-01 0.156429E-03 6 8 7 5 128 139 0.735294E-02 -0.127702E-01 0.948150E-06 7 10 10 6 16 32 0.384615E-01 0.241135E-01 0.368846E-01 7 10 10 6 32 48 0.238095E-01 -0.152253E-01 0.245414E-02 7 10 10 6 64 80 0.135135E-01 -0.127659E-01 0.522334E-05 7 10 10 6 128 144 0.724638E-02 -0.127711E-01 0.101560E-09 8 12 11 7 16 35 0.344828E-01 0.309983E-01 0.437694E-01 8 12 11 7 32 51 0.222222E-01 -0.138375E-01 0.106644E-02 8 12 11 7 64 83 0.129870E-01 -0.127712E-01 0.925250E-07 8 12 11 7 128 147 0.709220E-02 -0.127711E-01 0.423990E-10 9 14 14 9 16 40 0.303030E-01 0.411346E-01 0.539057E-01 9 14 14 9 32 56 0.204082E-01 -0.122271E-01 0.544027E-03 9 14 14 9 64 88 0.123457E-01 -0.127710E-01 0.731058E-07 9 14 14 9 128 152 0.689655E-02 -0.127711E-01 0.163497E-11 10 16 15 10 16 43 0.285714E-01 0.332425E-01 0.460136E-01 10 16 15 10 32 59 0.196078E-01 -0.126612E-01 0.109918E-03 10 16 15 10 64 91 0.120482E-01 -0.127711E-01 0.222928E-07 10 16 15 10 128 155 0.680272E-02 -0.127711E-01 0.115801E-12 Exact: -0.127711E-01 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 0.588235E-01 0.591092E-01 0.202119E-01 1 1.5 1 1 32 34 0.303030E-01 0.612287 0.532966 1 1.5 1 1 64 66 0.153846E-01 0.856299E-01 0.630886E-02 2 2.0 2 2 16 20 0.526316E-01 -0.274236E-01 0.106745 2 2.0 2 2 32 36 0.285714E-01 0.302254 0.222933 2 2.0 2 2 64 68 0.149254E-01 0.670261E-01 0.122949E-01 3 2.5 2 2 16 20 0.526316E-01 -0.214188 0.293509 3 2.5 2 2 32 36 0.285714E-01 0.178532 0.992110E-01 3 2.5 2 2 64 68 0.149254E-01 0.349942E-01 0.443268E-01 4 3.0 3 2 16 22 0.500000E-01 -0.266472 0.345793 4 3.0 3 2 32 38 0.277778E-01 0.147106 0.677852E-01 4 3.0 3 2 64 70 0.147059E-01 0.737758E-01 0.554521E-02 5 3.5 3 2 16 22 0.500000E-01 -0.268635 0.347956 5 3.5 3 2 32 38 0.277778E-01 0.124609 0.452876E-01 5 3.5 3 2 64 70 0.147059E-01 0.766103E-01 0.271075E-02 6 4.0 4 3 16 24 0.454545E-01 -0.265049 0.344370 6 4.0 4 3 32 40 0.263158E-01 0.859191E-01 0.659810E-02 6 4.0 4 3 64 72 0.142857E-01 0.759639E-01 0.335713E-02 7 6.0 6 4 16 28 0.416667E-01 -0.202176 0.281497 7 6.0 6 4 32 44 0.250000E-01 0.436246E-01 0.356964E-01 7 6.0 6 4 64 76 0.138889E-01 0.794586E-01 0.137591E-03 8 8.0 8 5 16 32 0.370370E-01 -0.339485 0.418806 8 8.0 8 5 32 48 0.232558E-01 0.698080E-01 0.951302E-02 8 8.0 8 5 64 80 0.133333E-01 0.793247E-01 0.371329E-05 9 10.0 10 6 16 36 0.333333E-01 -0.403544 0.482865 9 10.0 10 6 32 52 0.217391E-01 0.826427E-01 0.332171E-02 9 10.0 10 6 64 84 0.128205E-01 0.793167E-01 0.429831E-05 10 12.0 12 8 16 40 0.303030E-01 0.118805 0.394842E-01 10 12.0 12 8 32 56 0.204082E-01 0.809902E-01 0.166916E-02 10 12.0 12 8 64 88 0.123457E-01 0.793235E-01 0.245276E-05 11 14.0 14 9 16 44 0.277778E-01 -0.343625E-03 0.796646E-01 11 14.0 14 9 32 60 0.192308E-01 0.791337E-01 0.187326E-03 11 14.0 14 9 64 92 0.119048E-01 0.793210E-01 0.240560E-07 12 16.0 16 10 16 48 0.256410E-01 0.922080E-01 0.128870E-01 12 16.0 16 10 32 64 0.181818E-01 0.793329E-01 0.119136E-04 12 16.0 16 10 64 96 0.114943E-01 0.793210E-01 0.284679E-09 Exact: 0.793210E-01 alpert_rule_test(): Normal end of execution. 25 August 2021 10:39:23.839 PM