17 September 2021 11:53:50.274 PM TEST_INT_2D_TEST FORTRAN90 version Test the TEST_INT_2D library. TEST01 Use a Monte Carlo rule. Repeatedly multiply the number of points by 4. Problem Points Approx Error 1 1 1.26403 0.380908 1 4 1.29846 0.346477 1 16 1.37632 0.268611 1 64 1.62914 0.157967E-01 1 256 1.54327 0.101668 1 1024 1.55402 0.909099E-01 1 4096 1.60923 0.357060E-01 1 16384 1.61734 0.275979E-01 1 65536 1.63856 0.637087E-02 1 262144 1.64729 0.235840E-02 1 1048576 1.64230 0.263597E-02 1 4194304 1.64523 0.298621E-03 1 Exact 1.64493 2 1 4.66302 0.307851 2 4 4.26030 0.948673E-01 2 16 4.50093 0.145763 2 64 4.40727 0.520954E-01 2 256 4.34709 0.808320E-02 2 1024 4.33800 0.171700E-01 2 4096 4.35246 0.271344E-02 2 16384 4.33908 0.160903E-01 2 65536 4.34801 0.715782E-02 2 262144 4.35173 0.344431E-02 2 1048576 4.35369 0.148655E-02 2 4194304 4.35495 0.220450E-03 2 Exact 4.35517 3 1 3.11350 0.106969E-01 3 4 2.81187 0.312328 3 16 2.86675 0.257443 3 64 3.14477 0.205784E-01 3 256 3.09116 0.330340E-01 3 1024 3.07976 0.444332E-01 3 4096 3.11078 0.134109E-01 3 16384 3.10808 0.161134E-01 3 65536 3.11703 0.716200E-02 3 262144 3.12249 0.170326E-02 3 1048576 3.12273 0.146668E-02 3 4194304 3.12473 0.535907E-03 3 Exact 3.12419 4 1 3.03423 0.455222 4 4 2.34632 0.232688 4 16 2.35874 0.220272 4 64 2.60212 0.231123E-01 4 256 2.56616 0.128448E-01 4 1024 2.54317 0.358344E-01 4 4096 2.56569 0.133208E-01 4 16384 2.56366 0.153509E-01 4 65536 2.57270 0.630556E-02 4 262144 2.57723 0.177749E-02 4 1048576 2.57724 0.176309E-02 4 4194304 2.57916 0.153436E-03 4 Exact 2.57901 5 1 0.457031 0.125865E-01 5 4 0.368406 0.760383E-01 5 16 0.353274 0.911704E-01 5 64 0.440510 0.393405E-02 5 256 0.448441 0.399624E-02 5 1024 0.439900 0.454452E-02 5 4096 0.443780 0.664290E-03 5 16384 0.442074 0.237054E-02 5 65536 0.442861 0.158349E-02 5 262144 0.443820 0.624366E-03 5 1048576 0.444272 0.172251E-03 5 4194304 0.444546 0.101923E-03 5 Exact 0.444444 6 1 3.60022 1.73721 6 4 2.22490 0.361883 6 16 2.49066 0.627648 6 64 2.06812 0.205100 6 256 1.85054 0.124787E-01 6 1024 1.85653 0.648603E-02 6 4096 1.87415 0.111309E-01 6 16384 1.85097 0.120421E-01 6 65536 1.85589 0.712474E-02 6 262144 1.86077 0.224480E-02 6 1048576 1.86139 0.162291E-02 6 4194304 1.86276 0.260619E-03 6 Exact 1.86302 7 1 0.859011 0.325677 7 4 0.587914 0.545802E-01 7 16 0.570619 0.372861E-01 7 64 0.544216 0.108823E-01 7 256 0.542229 0.889605E-02 7 1024 0.546642 0.133086E-01 7 4096 0.534673 0.133945E-02 7 16384 0.532435 0.898429E-03 7 65536 0.533709 0.375917E-03 7 262144 0.532937 0.396811E-03 7 1048576 0.533382 0.488628E-04 7 4194304 0.533244 0.893102E-04 7 Exact 0.533333 8 1 0.327331E-08 2.66686 8 4 0.334292 2.33256 8 16 2.78919 0.122338 8 64 2.07469 0.592168 8 256 2.41847 0.248381 8 1024 2.77749 0.110636 8 4096 2.71912 0.522608E-01 8 16384 2.68242 0.155629E-01 8 65536 2.66255 0.430425E-02 8 262144 2.66945 0.259724E-02 8 1048576 2.67681 0.995579E-02 8 4194304 2.66940 0.254531E-02 8 Exact 2.66686 TEST02 Use a product of composite midpoint rules. Repeatedly multiply the number of points by 4. Problem Points Approx Error 1 1 1.33333 0.311601 1 4 1.45348 0.191454 1 16 1.53772 0.107218 1 64 1.58771 0.572219E-01 1 256 1.61522 0.297147E-01 1 1024 1.62975 0.151861E-01 1 4096 1.63725 0.768884E-02 1 16384 1.64106 0.387183E-02 1 65536 1.64299 0.194364E-02 1 262144 1.64396 0.973972E-03 1 1048576 1.64445 0.487579E-03 1 4194304 1.64469 0.243951E-03 1 Exact 1.64493 2 1 4.00000 0.355172 2 4 4.13118 0.223990 2 16 4.24756 0.107616 2 64 4.30870 0.464758E-01 2 256 4.33633 0.188448E-01 2 1024 4.34784 0.732937E-02 2 4096 4.35240 0.277035E-02 2 16384 4.35415 0.102654E-02 2 65536 4.35480 0.375125E-03 2 262144 4.35504 0.135750E-03 2 1048576 4.35512 0.487891E-04 2 4194304 4.35515 0.174506E-04 2 Exact 4.35517 3 1 2.82843 0.295767 3 4 2.99156 0.132631 3 16 3.06968 0.545143E-01 3 64 3.10297 0.212282E-01 3 256 3.11620 0.799722E-02 3 1024 3.12124 0.295064E-02 3 4096 3.12312 0.107402E-02 3 16384 3.12381 0.387428E-03 3 65536 3.12406 0.138903E-03 3 262144 3.12414 0.495910E-04 3 1048576 3.12418 0.176534E-04 3 4194304 3.12419 0.627153E-05 3 Exact 3.12419 4 1 2.30940 0.269606 4 4 2.45488 0.124128 4 16 2.52699 0.520150E-01 4 64 2.55850 0.205095E-01 4 256 2.57122 0.778749E-02 4 1024 2.57612 0.288779E-02 4 4096 2.57795 0.105464E-02 4 16384 2.57863 0.381286E-03 4 65536 2.57887 0.136909E-03 4 262144 2.57896 0.489305E-04 4 1048576 2.57899 0.174310E-04 4 4194304 2.57900 0.619568E-05 4 Exact 2.57901 5 1 0.500000 0.555556E-01 5 4 0.466506 0.220619E-01 5 16 0.452899 0.845413E-02 5 64 0.447604 0.315960E-02 5 256 0.445605 0.116077E-02 5 1024 0.444866 0.421460E-03 5 4096 0.444596 0.151795E-03 5 16384 0.444499 0.543670E-04 5 65536 0.444464 0.193968E-04 5 262144 0.444451 0.690166E-05 5 1048576 0.444447 0.245107E-05 5 4194304 0.444445 0.869327E-06 5 Exact 0.444444 6 1 1.00000 0.863016 6 4 1.00000 0.863016 6 16 1.75000 0.113016 6 64 1.82812 0.348912E-01 6 256 1.85449 0.852402E-02 6 1024 1.86060 0.242050E-02 6 4096 1.86242 0.600894E-03 6 16384 1.86285 0.161965E-03 6 65536 1.86298 0.389263E-04 6 262144 1.86301 0.100730E-04 6 1048576 1.86301 0.253260E-05 6 4194304 1.86302 0.634197E-06 6 Exact 1.86302 7 1 0.00000 0.533333 7 4 0.353553 0.179780 7 16 0.472530 0.608035E-01 7 64 0.512636 0.206978E-01 7 256 0.526236 0.709774E-02 7 1024 0.530883 0.245080E-02 7 4096 0.532482 0.851190E-03 7 16384 0.533036 0.297003E-03 7 65536 0.533229 0.104001E-03 7 262144 0.533297 0.365153E-04 7 1048576 0.533320 0.128458E-04 7 4194304 0.533329 0.452548E-05 7 Exact 0.533333 8 1 0.277725 2.38913 8 4 5.52171 2.85485 8 16 2.82579 0.158932 8 64 2.70698 0.401213E-01 8 256 2.67670 0.984254E-02 8 1024 2.66930 0.244856E-02 8 4096 2.66747 0.611384E-03 8 16384 2.66701 0.152799E-03 8 65536 2.66689 0.381967E-04 8 262144 2.66687 0.954899E-05 8 1048576 2.66686 0.238724E-05 8 4194304 2.66686 0.596808E-06 8 Exact 2.66686 TEST03 Use a product of Gauss-Legendre rules. The 1D rules essentially double in order. Problem Points Approx Error 1 1 1.33333 0.311601 1 9 1.58123 0.637073E-01 1 49 1.63077 0.141646E-01 1 225 1.64160 0.333146E-02 1 961 1.64413 0.807489E-03 1 3969 1.64474 0.198756E-03 1 16129 1.64488 0.493032E-04 1 65025 1.64492 0.122778E-04 1 Exact 1.64493 2 1 4.00000 0.355172 2 9 4.30864 0.465302E-01 2 49 4.34990 0.526763E-02 2 225 4.35456 0.611658E-03 2 961 4.35510 0.733017E-04 2 3969 4.35516 0.896068E-05 2 16129 4.35517 0.110734E-05 2 65025 4.35517 0.137619E-06 2 Exact 4.35517 3 1 2.82843 0.295767 3 9 3.10384 0.203550E-01 3 49 3.12224 0.195471E-02 3 225 3.12398 0.218752E-03 3 961 3.12417 0.259885E-04 3 3969 3.12419 0.317026E-05 3 16129 3.12419 0.391572E-06 3 65025 3.12419 0.486577E-07 3 Exact 3.12419 4 1 2.30940 0.269606 4 9 2.55776 0.212471E-01 4 49 2.57694 0.206741E-02 4 225 2.57878 0.231912E-03 4 961 2.57898 0.275674E-04 4 3969 2.57900 0.336332E-05 4 16129 2.57901 0.415432E-06 4 65025 2.57901 0.516230E-07 4 Exact 2.57901 5 1 0.500000 0.555556E-01 5 9 0.447801 0.335694E-02 5 49 0.444773 0.328619E-03 5 225 0.444481 0.369473E-04 5 961 0.444449 0.439436E-05 5 3969 0.444445 0.536199E-06 5 16129 0.444445 0.662327E-07 5 65025 0.444444 0.823038E-08 5 Exact 0.444444 6 1 1.00000 0.863016 6 9 2.06173 0.198712 6 49 1.86290 0.113944E-03 6 225 1.86838 0.536441E-02 6 961 1.86276 0.251951E-03 6 3969 1.86315 0.137089E-03 6 16129 1.86300 0.122869E-04 6 65025 1.86302 0.537063E-05 6 Exact 1.86302 7 1 0.00000 0.533333 7 9 0.443145 0.901887E-01 7 49 0.504725 0.286088E-01 7 225 0.523695 0.963804E-02 7 961 0.530005 0.332792E-02 7 3969 0.532170 0.116284E-02 7 16129 0.532925 0.408720E-03 7 65025 0.533189 0.144081E-03 7 Exact 0.533333 8 1 0.277725 2.38913 8 9 1.91043 0.756428 8 49 2.67050 0.364122E-02 8 225 2.66686 0.141251E-09 8 961 2.66686 0.888178E-15 8 3969 2.66686 0.577316E-14 8 16129 2.66686 0.137668E-13 8 65025 2.66686 0.577316E-13 8 Exact 2.66686 TEST_INT_2D_TEST Normal end of execution. 17 September 2021 11:53:52.518 PM