9 September 2021 10:05:56.949 AM ELLIPSOID_MONTE_CARLO_TEST FORTRAN90 version Test ELLIPSOID_MONTE_CARLO. TEST01 Use ELLIPSOID_SAMPLE to estimate integrals in a 2D ellipse x' * A * x <= r^2. Ellipsoid radius R = 2.00000 Ellipsoid center V: 1: 0.0000000 2: 0.0000000 Ellipsoid matrix A: Col 1 2 Row 1: 9. 1. 2: 1. 4. Ellipsoid volume = 2.12410 N 1 X Y X^2 XY Y^2 X^3 1 2.12410 -0.267768 0.911869 0.337552E-01 -0.114952 0.391461 -0.425523E-02 2 2.12410 -0.150980 0.538341 0.676523E-01 -0.978572E-02 0.150688 -0.129004E-01 4 2.12410 -0.730586E-01 0.116794 0.324902E-01 -0.623061E-01 0.187538 -0.120453E-02 8 2.12410 0.943424E-01 -0.818091E-01 0.164068E-01 -0.253701E-01 0.198494 0.145788E-02 16 2.12410 -0.414102E-01 0.219774 0.272431E-01 -0.174732E-01 0.148956 -0.166594E-02 32 2.12410 -0.743588E-01 -0.724010E-01 0.463675E-01 -0.213791E-01 0.119968 -0.258892E-02 64 2.12410 -0.529918E-02 -0.706354E-01 0.314517E-01 -0.284603E-01 0.148325 0.195947E-03 128 2.12410 0.167193E-01 -0.138514E-01 0.288876E-01 -0.142619E-01 0.162431 0.311038E-03 256 2.12410 -0.145484E-01 -0.438191E-02 0.272378E-01 -0.285268E-01 0.165608 -0.617590E-03 512 2.12410 0.108037E-01 0.171287E-01 0.302710E-01 -0.219363E-01 0.141459 0.269070E-03 1024 2.12410 0.604567E-02 -0.292858E-01 0.299290E-01 -0.209717E-01 0.144698 0.869128E-05 2048 2.12410 -0.146805E-01 0.397604E-02 0.288831E-01 -0.215105E-01 0.142554 -0.429265E-03 4096 2.12410 0.569517E-02 -0.110576E-01 0.300213E-01 -0.232665E-01 0.143184 0.180859E-03 8192 2.12410 -0.471302E-02 -0.621235E-03 0.293280E-01 -0.222492E-01 0.141558 -0.116796E-03 16384 2.12410 0.966117E-05 -0.340078E-02 0.296975E-01 -0.226769E-01 0.141765 -0.258648E-04 32768 2.12410 -0.154020E-02 0.637811E-02 0.294153E-01 -0.224156E-01 0.141743 -0.422286E-04 65536 2.12410 0.513801E-05 -0.125394E-02 0.295835E-01 -0.225675E-01 0.142731 -0.921092E-05 TEST02 Use ELLIPSOID_SAMPLE to estimate integrals in a 2D ellipse (x-v)' * A * (x-v) <= r^2. Ellipsoid radius R = 0.500000 Ellipsoid center V: 1: 2.0000000 2: 3.0000000 Ellipsoid matrix A: Col 1 2 Row 1: 9. 1. 2: 1. 4. Ellipsoid volume = 0.132757 N 1 X Y X^2 XY Y^2 X^3 1 0.132757 0.269919 0.401949 0.548798 0.817239 1.21699 1.11581 2 0.132757 0.263878 0.409270 0.524513 0.813507 1.26173 1.04259 4 0.132757 0.266712 0.399318 0.535899 0.802234 1.20156 1.07690 8 0.132757 0.264613 0.399480 0.527542 0.796033 1.20322 1.05195 16 0.132757 0.264762 0.399775 0.528091 0.797220 1.20472 1.05345 32 0.132757 0.264158 0.398631 0.525704 0.793143 1.19756 1.04638 64 0.132757 0.265779 0.396881 0.532193 0.794490 1.18704 1.06587 128 0.132757 0.265283 0.397291 0.530221 0.793789 1.18948 1.05999 256 0.132757 0.265403 0.398685 0.530707 0.796938 1.19782 1.06146 512 0.132757 0.265304 0.398430 0.530310 0.796130 1.19635 1.06026 1024 0.132757 0.265636 0.398163 0.531631 0.796604 1.19472 1.06420 2048 0.132757 0.265558 0.398454 0.531323 0.796948 1.19648 1.06329 4096 0.132757 0.265493 0.398247 0.531061 0.796348 1.19523 1.06250 8192 0.132757 0.265545 0.398180 0.531269 0.796369 1.19482 1.06313 16384 0.132757 0.265483 0.398284 0.531022 0.796390 1.19545 1.06238 32768 0.132757 0.265497 0.398224 0.531076 0.796310 1.19510 1.06255 65536 0.132757 0.265486 0.398319 0.531035 0.796468 1.19565 1.06243 TEST03 Use ELLIPSOID_SAMPLE to estimate integrals in a 3D ellipse (x-v)' * A * (x-v) <= r^2. Ellipsoid radius R = 0.500000 Ellipsoid center V: 1: 1.0000000 2: 2.0000000 3: 3.0000000 Ellipsoid matrix A: Col 1 2 3 Row 1: 9. 6. 3. 2: 6. 5. 4. 3: 3. 4. 9. Ellipsoid volume = 0.872665E-01 N 1 X Y Z X^2 YZ Z^3 1 0.872665E-01 0.662139E-01 0.211661 0.254222 0.502402E-01 4.35678 2.15746 2 0.872665E-01 0.792857E-01 0.184235 0.260167 0.765521E-01 3.48437 2.31926 4 0.872665E-01 0.776727E-01 0.188522 0.259064 0.799986E-01 3.65722 2.30203 8 0.872665E-01 0.975630E-01 0.155929 0.266648 0.122196 2.74087 2.50652 16 0.872665E-01 0.908765E-01 0.168825 0.263083 0.104262 3.05422 2.40509 32 0.872665E-01 0.807355E-01 0.185236 0.259418 0.835290E-01 3.54003 2.30723 64 0.872665E-01 0.902338E-01 0.170179 0.262098 0.101148 3.06529 2.37707 128 0.872665E-01 0.847279E-01 0.178782 0.260557 0.917069E-01 3.33879 2.33801 256 0.872665E-01 0.868023E-01 0.175704 0.261403 0.943174E-01 3.24516 2.35797 512 0.872665E-01 0.860331E-01 0.176641 0.261303 0.933822E-01 3.28006 2.35653 1024 0.872665E-01 0.866614E-01 0.175717 0.261401 0.951386E-01 3.25361 2.35987 2048 0.872665E-01 0.881746E-01 0.172891 0.262302 0.980400E-01 3.17444 2.38458 4096 0.872665E-01 0.869063E-01 0.175029 0.261733 0.954300E-01 3.23481 2.36895 8192 0.872665E-01 0.870195E-01 0.174931 0.261693 0.958459E-01 3.23258 2.36808 16384 0.872665E-01 0.873421E-01 0.174452 0.261779 0.965650E-01 3.21854 2.37051 32768 0.872665E-01 0.874249E-01 0.174274 0.261840 0.966207E-01 3.21287 2.37201 65536 0.872665E-01 0.872783E-01 0.174488 0.261827 0.962894E-01 3.21974 2.37165 ELLIPSOID_MONTE_CARLO_TEST Normal end of execution. 9 September 2021 10:05:57.061 AM