09 May 2025 9:46:20.740 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 1.15110 0.493833 1 4 1.63101 0.139201E-01 1 16 1.44538 0.199553 1 64 1.50106 0.143871 1 256 1.61766 0.272741E-01 1 1024 1.62456 0.203712E-01 1 4096 1.58936 0.555752E-01 1 16384 1.64168 0.325449E-02 1 65536 1.64081 0.412042E-02 1 262144 1.64547 0.536053E-03 1 1048576 1.64866 0.372121E-02 1 4194304 1.64194 0.299357E-02 1 Exact 1.64493 2 1 4.12938 0.225795 2 4 4.13127 0.223900 2 16 4.36406 0.888311E-02 2 64 4.61243 0.257257 2 256 4.27609 0.790803E-01 2 1024 4.30991 0.452598E-01 2 4096 4.36826 0.130916E-01 2 16384 4.35959 0.442159E-02 2 65536 4.35427 0.899386E-03 2 262144 4.35416 0.101707E-02 2 1048576 4.35467 0.499287E-03 2 4194304 4.35490 0.272313E-03 2 Exact 4.35517 3 1 3.02175 0.102441 3 4 3.28653 0.162334 3 16 3.06911 0.550882E-01 3 64 3.28974 0.165549 3 256 3.07260 0.515934E-01 3 1024 3.10070 0.234965E-01 3 4096 3.11558 0.861904E-02 3 16384 3.12555 0.136021E-02 3 65536 3.12825 0.405772E-02 3 262144 3.12230 0.189234E-02 3 1048576 3.12558 0.138586E-02 3 4194304 3.12449 0.297503E-03 3 Exact 3.12419 4 1 5.60909 3.03008 4 4 2.44245 0.136559 4 16 2.73191 0.152902 4 64 2.66498 0.859715E-01 4 256 2.52977 0.492374E-01 4 1024 2.52290 0.561043E-01 4 4096 2.57826 0.744017E-03 4 16384 2.59173 0.127194E-01 4 65536 2.58353 0.452140E-02 4 262144 2.57503 0.397703E-02 4 1048576 2.57922 0.214114E-03 4 4194304 2.57890 0.111914E-03 4 Exact 2.57901 5 1 0.449284 0.484004E-02 5 4 0.320271 0.124173 5 16 0.393277 0.511679E-01 5 64 0.453355 0.891048E-02 5 256 0.437444 0.700002E-02 5 1024 0.451616 0.717106E-02 5 4096 0.448248 0.380324E-02 5 16384 0.443494 0.950235E-03 5 65536 0.444714 0.269956E-03 5 262144 0.443834 0.610040E-03 5 1048576 0.444319 0.125453E-03 5 4194304 0.444486 0.415305E-04 5 Exact 0.444444 6 1 0.472595 1.39042 6 4 2.38313 0.520112 6 16 1.92364 0.606236E-01 6 64 1.89846 0.354449E-01 6 256 1.82715 0.358618E-01 6 1024 1.87179 0.876988E-02 6 4096 1.87270 0.968721E-02 6 16384 1.87555 0.125327E-01 6 65536 1.86358 0.563500E-03 6 262144 1.86483 0.181553E-02 6 1048576 1.86170 0.131761E-02 6 4194304 1.86345 0.430180E-03 6 Exact 1.86302 7 1 0.476207 0.571268E-01 7 4 0.482434 0.508994E-01 7 16 0.491258 0.420757E-01 7 64 0.547451 0.141177E-01 7 256 0.519213 0.141208E-01 7 1024 0.537146 0.381291E-02 7 4096 0.526746 0.658740E-02 7 16384 0.533736 0.402533E-03 7 65536 0.534069 0.735860E-03 7 262144 0.533435 0.101519E-03 7 1048576 0.533181 0.152422E-03 7 4194304 0.533146 0.187301E-03 7 Exact 0.533333 8 1 0.209689E-07 2.66686 8 4 4.87093 2.20407 8 16 1.68866 0.978197 8 64 2.98460 0.317742 8 256 2.67835 0.114910E-01 8 1024 2.44425 0.222602 8 4096 2.72664 0.597819E-01 8 16384 2.69426 0.274090E-01 8 65536 2.67465 0.779591E-02 8 262144 2.65256 0.142936E-01 8 1048576 2.67055 0.368940E-02 8 4194304 2.66175 0.510306E-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. 09 May 2025 9:46:22.411 PM