April 3 2023 9:35:09.802 AM sphere_triangle_quad_test(): FORTRAN90 version Test sphere_triangle_quad(). TEST01 Approximate the integral of a function on a random spherical triangle. QUAD_01 uses centroids of spherical triangles. QUAD_02 uses vertices of spherical triangles. QUAD_03 uses midsides of spherical triangles. Vertices of random spherical triangle: V1: 0.795416 -0.223966 -0.563163 V2: -0.696321 -0.284310 0.659018 V3: 0.901719 0.397757 -0.169386 QUAD_01 QUAD_02 QUAD_03 P(X,Y,Z) = 1 3.06905 3.06905 3.06905 P(X,Y,Z) = X 3.04241 1.02385 1.51463 P(X,Y,Z) = Y -0.335970 -0.113063 -0.677827 P(X,Y,Z) = Z -0.223529 -0.752233E-01 0.705114 P(X,Y,Z) = X^2 3.01600 1.97509 1.03742 P(X,Y,Z) = Y^2 Z^2 0.195098E-03 0.568326E-01 0.692846E-01 P(X,Y,Z) = X^2 Y^2 Z^2 0.191725E-03 0.314860E-01 0.748156E-02 P(X,Y,Z) = Y^2 Z^4 0.103493E-05 0.208925E-01 0.308005E-01 P(X,Y,Z) = Z^6 0.458117E-06 0.116464 0.554106 P(X,Y,Z) = X Y^2 Z^4 0.102594E-05 -0.663518E-02 0.115693E-01 P(X,Y,Z) = X^2 Y^4 Z^2 0.229758E-05 0.252144E-02 0.127823E-02 P(X,Y,Z) = X^6 Y^2 0.349039E-01 0.109428 0.540225E-02 P(X,Y,Z) = Z^8 0.243015E-08 0.467480E-01 0.448050 P(X,Y,Z) = X^6 Z^4 0.819592E-04 0.485087E-01 0.164461E-01 P(X,Y,Z) = X^4 Y^6 Z^2 0.270575E-07 0.148405E-03 0.358269E-04 P(X,Y,Z) = X^2 Y^4 Z^8 0.342959E-12 0.131797E-03 0.122125E-03 P(X,Y,Z) = X^16 2.66940 0.224836 0.243061 TEST02 Approximate an integral on a random spherical triangle. QUAD_MC1 uses a Monte Carlo method with è points. QUAD_MC2 uses a Monte Carlo method with ' points. QUAD_MC3 uses a Monte Carlo method with  † points. Vertices of random spherical triangle: V1: 0.795416 -0.223966 -0.563163 V2: -0.696321 -0.284310 0.659018 V3: 0.901719 0.397757 -0.169386 QUAD_MC1 QUAD_MC2 QUAD_MC3 P(X,Y,Z) = 1 3.06905 3.06905 3.06905 P(X,Y,Z) = X 1.49039 1.45444 1.45637 P(X,Y,Z) = Y -1.07421 -1.04610 -1.04440 P(X,Y,Z) = Z 1.26596 1.30980 1.32544 P(X,Y,Z) = X^2 1.29010 1.27525 1.27829 P(X,Y,Z) = Y^2 Z^2 0.192870 0.177030 0.182439 P(X,Y,Z) = X^2 Y^2 Z^2 0.247888E-01 0.252832E-01 0.248802E-01 P(X,Y,Z) = Y^2 Z^4 0.837552E-01 0.861373E-01 0.851929E-01 P(X,Y,Z) = Z^6 0.531964 0.479835 0.482496 P(X,Y,Z) = X Y^2 Z^4 0.442363E-02 0.506373E-02 0.505596E-02 P(X,Y,Z) = X^2 Y^4 Z^2 0.668430E-02 0.717428E-02 0.725439E-02 P(X,Y,Z) = X^6 Y^2 0.558710E-01 0.555553E-01 0.568885E-01 P(X,Y,Z) = Z^8 0.374850 0.374319 0.377645 P(X,Y,Z) = X^6 Z^4 0.158417E-01 0.150701E-01 0.150134E-01 P(X,Y,Z) = X^4 Y^6 Z^2 0.639512E-03 0.723393E-03 0.713386E-03 P(X,Y,Z) = X^2 Y^4 Z^8 0.443024E-03 0.452401E-03 0.453963E-03 P(X,Y,Z) = X^16 0.379094 0.335969 0.339363 TEST03 SPHERE01_TRIANGLE_QUAD_ICOS1C approximates the integral of a function over a spherical triangle on the surface of the unit sphere using a centroid rule. We do not have an exact result, so we compare each estimate to the final one. Vertices of random spherical triangle: V1: 0.795416 -0.223966 -0.563163 V2: -0.696321 -0.284310 0.659018 V3: 0.901719 0.397757 -0.169386 FACTOR N RESULT P(X,Y,Z) = 1 1 1 3.0690548 0.51E-09 2 4 3.0690548 0.51E-09 4 16 3.0690548 0.51E-09 8 64 3.0690548 0.51E-09 16 256 3.0690548 0.51E-09 32 1024 3.0690548 0.51E-09 64 4096 3.0690548 0.51E-09 128 16384 3.0690548 0.51E-09 256 65536 3.0690548 0.51E-09 512 262144 3.0690548 0.48E-09 P(X,Y,Z) = X 1 1 3.0424097 1.6 2 4 1.4580608 0.71E-02 4 16 1.4909482 0.26E-01 8 64 1.4715879 0.64E-02 16 256 1.4633045 0.18E-02 32 1024 1.4646303 0.52E-03 64 4096 1.4650207 0.13E-03 128 16384 1.4651186 0.33E-04 256 65536 1.4651431 0.80E-05 512 262144 1.4651492 0.19E-05 P(X,Y,Z) = Y 1 1 -0.33596979 0.71 2 4 -0.57944949 0.47 4 16 -0.87749071 0.17 8 64 -1.0211533 0.27E-01 16 256 -1.0437687 0.43E-02 32 1024 -1.0469543 0.11E-02 64 4096 -1.0477565 0.27E-03 128 16384 -1.0479576 0.67E-04 256 65536 -1.0480079 0.17E-04 512 262144 -1.0480205 0.39E-05 P(X,Y,Z) = Z 1 1 -0.22352870 1.5 2 4 0.59222577 0.73 4 16 1.0353422 0.28 8 64 1.2736668 0.44E-01 16 256 1.3118673 0.62E-02 32 1024 1.3165379 0.15E-02 64 4096 1.3176986 0.39E-03 128 16384 1.3179895 0.97E-04 256 65536 1.3180622 0.24E-04 512 262144 1.3180804 0.57E-05 P(X,Y,Z) = X^2 1 1 3.0159959 1.7 2 4 2.1115250 0.83 4 16 1.6276516 0.35 8 64 1.3482269 0.67E-01 16 256 1.2877188 0.60E-02 32 1024 1.2831055 0.14E-02 64 4096 1.2820344 0.36E-03 128 16384 1.2817657 0.89E-04 256 65536 1.2816985 0.22E-04 512 262144 1.2816817 0.53E-05 P(X,Y,Z) = Y^2 Z^2 1 1 0.19509813E-03 0.18 2 4 0.11173650 0.70E-01 4 16 0.13602353 0.46E-01 8 64 0.17083063 0.11E-01 16 256 0.18130698 0.76E-03 32 1024 0.18196420 0.11E-03 64 4096 0.18204469 0.27E-04 128 16384 0.18206476 0.67E-05 256 65536 0.18206977 0.16E-05 512 262144 0.18207102 0.39E-06 P(X,Y,Z) = X^2 Y^2 Z^2 1 1 0.19172521E-03 0.25E-01 2 4 0.24531813E-01 0.42E-03 4 16 0.14437995E-01 0.11E-01 8 64 0.21325852E-01 0.36E-02 16 256 0.24844968E-01 0.10E-03 32 1024 0.24887410E-01 0.60E-04 64 4096 0.24932235E-01 0.15E-04 128 16384 0.24943617E-01 0.38E-05 256 65536 0.24946472E-01 0.94E-06 512 262144 0.24947186E-01 0.22E-06 P(X,Y,Z) = Y^2 Z^4 1 1 0.10349286E-05 0.85E-01 2 4 0.69416427E-01 0.16E-01 4 16 0.65374258E-01 0.20E-01 8 64 0.83372516E-01 0.19E-02 16 256 0.85063380E-01 0.17E-03 32 1024 0.85240746E-01 0.53E-05 64 4096 0.85236962E-01 0.15E-05 128 16384 0.85235812E-01 0.40E-06 256 65536 0.85235513E-01 0.99E-07 512 262144 0.85235437E-01 0.24E-07 P(X,Y,Z) = Z^6 1 1 0.45811711E-06 0.48 2 4 0.27142163 0.21 4 16 0.44202683 0.39E-01 8 64 0.47344443 0.78E-02 16 256 0.48108927 0.15E-03 32 1024 0.48137563 0.14E-03 64 4096 0.48127204 0.35E-04 128 16384 0.48124549 0.89E-05 256 65536 0.48123881 0.22E-05 512 262144 0.48123714 0.52E-06 P(X,Y,Z) = X Y^2 Z^4 1 1 0.10259435E-05 0.51E-02 2 4 -0.30978950E-01 0.36E-01 4 16 -0.16349055E-01 0.21E-01 8 64 -0.26907206E-02 0.78E-02 16 256 0.42501142E-02 0.82E-03 32 1024 0.49464238E-02 0.12E-03 64 4096 0.50382632E-02 0.31E-04 128 16384 0.50613268E-02 0.77E-05 256 65536 0.50670991E-02 0.19E-05 512 262144 0.50685425E-02 0.45E-06 P(X,Y,Z) = X^2 Y^4 Z^2 1 1 0.22975787E-05 0.73E-02 2 4 0.37393700E-02 0.35E-02 4 16 0.44025568E-02 0.29E-02 8 64 0.54554699E-02 0.18E-02 16 256 0.71749539E-02 0.90E-04 32 1024 0.72419156E-02 0.23E-04 64 4096 0.72590136E-02 0.58E-05 128 16384 0.72633723E-02 0.15E-05 256 65536 0.72644650E-02 0.36E-06 512 262144 0.72647384E-02 0.85E-07 P(X,Y,Z) = X^6 Y^2 1 1 0.34903913E-01 0.22E-01 2 4 0.36376861E-01 0.21E-01 4 16 0.86349310E-01 0.29E-01 8 64 0.62460997E-01 0.54E-02 16 256 0.56921836E-01 0.11E-03 32 1024 0.57113046E-01 0.86E-04 64 4096 0.57048756E-01 0.22E-04 128 16384 0.57032572E-01 0.54E-05 256 65536 0.57028515E-01 0.13E-05 512 262144 0.57027500E-01 0.32E-06 P(X,Y,Z) = Z^8 1 1 0.24301541E-08 0.38 2 4 0.17056594 0.21 4 16 0.38192803 0.21E-02 8 64 0.38658868 0.67E-02 16 256 0.38071940 0.85E-03 32 1024 0.38009166 0.22E-03 64 4096 0.37992485 0.57E-04 128 16384 0.37988231 0.14E-04 256 65536 0.37987163 0.35E-05 512 262144 0.37986896 0.84E-06 P(X,Y,Z) = X^6 Z^4 1 1 0.81959164E-04 0.15E-01 2 4 0.82961901E-02 0.66E-02 4 16 0.15349878E-01 0.42E-03 8 64 0.18722066E-01 0.38E-02 16 256 0.15052578E-01 0.12E-03 32 1024 0.14907323E-01 0.27E-04 64 4096 0.14927618E-01 0.65E-05 128 16384 0.14932485E-01 0.16E-05 256 65536 0.14933703E-01 0.40E-06 512 262144 0.14934008E-01 0.95E-07 P(X,Y,Z) = X^4 Y^6 Z^2 1 1 0.27057501E-07 0.71E-03 2 4 0.12572515E-03 0.58E-03 4 16 0.25652759E-03 0.45E-03 8 64 0.70544929E-03 0.12E-05 16 256 0.76287761E-03 0.56E-04 32 1024 0.70378115E-03 0.29E-05 64 4096 0.70592719E-03 0.72E-06 128 16384 0.70646742E-03 0.18E-06 256 65536 0.70660279E-03 0.44E-07 512 262144 0.70663665E-03 0.11E-07 P(X,Y,Z) = X^2 Y^4 Z^8 1 1 0.34295905E-12 0.46E-03 2 4 0.92039795E-03 0.46E-03 4 16 0.37315648E-03 0.83E-04 8 64 0.24128599E-03 0.21E-03 16 256 0.41495547E-03 0.41E-04 32 1024 0.45543599E-03 0.64E-06 64 4096 0.45594791E-03 0.13E-06 128 16384 0.45604413E-03 0.32E-07 256 65536 0.45606832E-03 0.79E-08 512 262144 0.45607437E-03 0.19E-08 P(X,Y,Z) = X^16 1 1 2.6693986 2.3 2 4 1.4495431 1.1 4 16 0.48851698 0.15 8 64 0.33008811 0.98E-02 16 256 0.34689830 0.70E-02 32 1024 0.34127742 0.14E-02 64 4096 0.34023746 0.35E-03 128 16384 0.33997729 0.86E-04 256 65536 0.33991220 0.21E-04 512 262144 0.33989593 0.51E-05 TEST03 SPHERE01_TRIANGLE_QUAD_ICOS1M approximate the integral of a function over a spherical triangle on the surface of the unit sphere using a midpoint rule. We do not have an exact result, so we compare each estimate to the final one. Vertices of random spherical triangle: V1: 0.795416 -0.223966 -0.563163 V2: -0.696321 -0.284310 0.659018 V3: 0.901719 0.397757 -0.169386 FACTOR N RESULT P(X,Y,Z) = 1 1 3 3.0690548 0.51E-09 2 12 3.0690548 0.51E-09 4 48 3.0690548 0.51E-09 8 192 3.0690548 0.51E-09 16 768 3.0690548 0.51E-09 32 3072 3.0690548 0.51E-09 64 12288 3.0690548 0.51E-09 128 49152 3.0690548 0.51E-09 256 196608 3.0690548 0.51E-09 512 786432 3.0690548 0.48E-09 P(X,Y,Z) = X 1 3 1.5146333 0.49E-01 2 12 1.3391288 0.13 4 48 1.4161789 0.49E-01 8 192 1.4488356 0.16E-01 16 768 1.4577767 0.74E-02 32 3072 1.4632315 0.19E-02 64 12288 1.4646693 0.48E-03 128 49152 1.4650307 0.12E-03 256 196608 1.4651211 0.30E-04 512 786432 1.4651437 0.71E-05 P(X,Y,Z) = Y 1 3 -0.67782654 0.37 2 12 -0.69417318 0.35 4 48 -0.86528596 0.18 8 192 -1.0080416 0.40E-01 16 768 -1.0396664 0.84E-02 32 3072 -1.0459044 0.21E-02 64 12288 -1.0474925 0.53E-03 128 49152 -1.0478915 0.13E-03 256 196608 -1.0479913 0.33E-04 512 786432 -1.0480163 0.78E-05 P(X,Y,Z) = Z 1 3 0.70511380 0.61 2 12 0.81458139 0.50 4 48 1.0349595 0.28 8 192 1.2585004 0.60E-01 16 768 1.3067144 0.11E-01 32 3072 1.3152153 0.29E-02 64 12288 1.3173659 0.72E-03 128 49152 1.3179062 0.18E-03 256 196608 1.3180414 0.44E-04 512 786432 1.3180752 0.11E-04 P(X,Y,Z) = X^2 1 3 1.0374204 0.24 2 12 1.6738428 0.39 4 48 1.5465109 0.26 8 192 1.3502163 0.69E-01 16 768 1.2911961 0.95E-02 32 3072 1.2840310 0.24E-02 64 12288 1.2822682 0.59E-03 128 49152 1.2818243 0.15E-03 256 196608 1.2817131 0.36E-04 512 786432 1.2816853 0.87E-05 P(X,Y,Z) = Y^2 Z^2 1 3 0.69284636E-01 0.11 2 12 0.18328390 0.12E-02 4 48 0.14519673 0.37E-01 8 192 0.17212931 0.99E-02 16 768 0.18104870 0.10E-02 32 3072 0.18188145 0.19E-03 64 12288 0.18202418 0.47E-04 128 49152 0.18205964 0.12E-04 256 196608 0.18206849 0.29E-05 512 786432 0.18207070 0.69E-06 P(X,Y,Z) = X^2 Y^2 Z^2 1 3 0.74815556E-02 0.17E-01 2 12 0.40138510E-01 0.15E-01 4 48 0.22979464E-01 0.20E-02 8 192 0.21748208E-01 0.32E-02 16 768 0.24642828E-01 0.30E-03 32 3072 0.24838585E-01 0.11E-03 64 12288 0.24919550E-01 0.28E-04 128 49152 0.24940414E-01 0.70E-05 256 196608 0.24945669E-01 0.17E-05 512 786432 0.24946985E-01 0.41E-06 P(X,Y,Z) = Y^2 Z^4 1 3 0.30800538E-01 0.54E-01 2 12 0.98762668E-01 0.14E-01 4 48 0.57898290E-01 0.27E-01 8 192 0.83586236E-01 0.16E-02 16 768 0.85149295E-01 0.86E-04 32 3072 0.85258738E-01 0.23E-04 64 12288 0.85241980E-01 0.66E-05 128 49152 0.85237100E-01 0.17E-05 256 196608 0.85235837E-01 0.42E-06 512 786432 0.85235518E-01 0.10E-06 P(X,Y,Z) = Z^6 1 3 0.55410577 0.73E-01 2 12 0.30254841 0.18 4 48 0.44923740 0.32E-01 8 192 0.47756410 0.37E-02 16 768 0.48244476 0.12E-02 32 3072 0.48171451 0.48E-03 64 12288 0.48135930 0.12E-03 128 49152 0.48126747 0.31E-04 256 196608 0.48124432 0.76E-05 512 786432 0.48123852 0.18E-05 P(X,Y,Z) = X Y^2 Z^4 1 3 0.11569346E-01 0.65E-02 2 12 0.18816669E-01 0.14E-01 4 48 -0.11699406E-01 0.17E-01 8 192 -0.16460618E-02 0.67E-02 16 768 0.39374641E-02 0.11E-02 32 3072 0.48384069E-02 0.23E-03 64 12288 0.50109084E-02 0.58E-04 128 49152 0.50544659E-02 0.15E-04 256 196608 0.50653825E-02 0.36E-05 512 786432 0.50681133E-02 0.85E-06 P(X,Y,Z) = X^2 Y^4 Z^2 1 3 0.12782343E-02 0.60E-02 2 12 0.89719313E-02 0.17E-02 4 48 0.83042444E-02 0.10E-02 8 192 0.58443121E-02 0.14E-02 16 768 0.71187318E-02 0.15E-03 32 3072 0.72249530E-02 0.40E-04 64 12288 0.72546139E-02 0.10E-04 128 49152 0.72622615E-02 0.26E-05 256 196608 0.72641866E-02 0.63E-06 512 786432 0.72646687E-02 0.15E-06 P(X,Y,Z) = X^6 Y^2 1 3 0.54022453E-02 0.52E-01 2 12 0.41621761E-01 0.15E-01 4 48 0.70345381E-01 0.13E-01 8 192 0.62562909E-01 0.55E-02 16 768 0.57214615E-01 0.19E-03 32 3072 0.57160413E-01 0.13E-03 64 12288 0.57061163E-01 0.34E-04 128 49152 0.57035708E-01 0.85E-05 256 196608 0.57029301E-01 0.21E-05 512 786432 0.57027696E-01 0.50E-06 P(X,Y,Z) = Z^8 1 3 0.44804993 0.68E-01 2 12 0.17963896 0.20 4 48 0.35779942 0.22E-01 8 192 0.38604801 0.62E-02 16 768 0.38214345 0.23E-02 32 3072 0.38050427 0.64E-03 64 12288 0.38003093 0.16E-03 128 49152 0.37990902 0.41E-04 256 196608 0.37987832 0.10E-04 512 786432 0.37987063 0.24E-05 P(X,Y,Z) = X^6 Z^4 1 3 0.16446099E-01 0.15E-02 2 12 0.15182542E-01 0.25E-03 4 48 0.71815261E-02 0.78E-02 8 192 0.16523417E-01 0.16E-02 16 768 0.14864535E-01 0.70E-04 32 3072 0.14874167E-01 0.60E-04 64 12288 0.14919145E-01 0.15E-04 128 49152 0.14930360E-01 0.37E-05 256 196608 0.14933172E-01 0.92E-06 512 786432 0.14933875E-01 0.22E-06 P(X,Y,Z) = X^4 Y^6 Z^2 1 3 0.35826866E-04 0.67E-03 2 12 0.51708151E-03 0.19E-03 4 48 0.65595034E-03 0.51E-04 8 192 0.50819874E-03 0.20E-03 16 768 0.73429503E-03 0.28E-04 32 3072 0.70163764E-03 0.50E-05 64 12288 0.70537299E-03 0.13E-05 128 49152 0.70632771E-03 0.32E-06 256 196608 0.70656779E-03 0.79E-07 512 786432 0.70662789E-03 0.19E-07 P(X,Y,Z) = X^2 Y^4 Z^8 1 3 0.12212520E-03 0.33E-03 2 12 0.13094135E-02 0.85E-03 4 48 0.47634334E-03 0.20E-04 8 192 0.37603274E-03 0.80E-04 16 768 0.42676231E-03 0.29E-04 32 3072 0.45514102E-03 0.94E-06 64 12288 0.45585603E-03 0.22E-06 128 49152 0.45602068E-03 0.55E-07 256 196608 0.45606243E-03 0.14E-07 512 786432 0.45607290E-03 0.33E-08 P(X,Y,Z) = X^16 1 3 0.24306136 0.97E-01 2 12 0.65894922 0.32 4 48 0.60302990 0.26 8 192 0.35542325 0.16E-01 16 768 0.35140892 0.12E-01 32 3072 0.34256519 0.27E-02 64 12288 0.34056180 0.67E-03 128 49152 0.34005851 0.17E-03 256 196608 0.33993251 0.41E-04 512 786432 0.33990101 0.98E-05 TEST05 SPHERE01_TRIANGLE_QUAD_ICOS1V approximates the integral of a function over a spherical triangle on the surface of the unit sphere using a vertex rule. We do not have an exact result, so we compare each estimate to the final one. Vertices of random spherical triangle: V1: 0.795416 -0.223966 -0.563163 V2: -0.696321 -0.284310 0.659018 V3: 0.901719 0.397757 -0.169386 FACTOR N RESULT P(X,Y,Z) = 1 1 3 3.0690548 0.51E-09 2 12 3.0690548 0.51E-09 4 48 3.0690548 0.51E-09 8 192 3.0690548 0.51E-09 16 768 3.0690548 0.51E-09 32 3072 3.0690548 0.51E-09 64 12288 3.0690548 0.51E-09 128 49152 3.0690548 0.51E-09 256 196608 3.0690548 0.51E-09 512 786432 3.0690548 0.48E-09 P(X,Y,Z) = X 1 3 1.0238514 0.44 2 12 1.0316791 0.43 4 48 1.2416257 0.22 8 192 1.3779194 0.87E-01 16 768 1.4414767 0.24E-01 32 3072 1.4590637 0.61E-02 64 12288 1.4636170 0.15E-02 128 49152 1.4647669 0.38E-03 256 196608 1.4650551 0.95E-04 512 786432 1.4651272 0.23E-04 P(X,Y,Z) = Y 1 3 -0.11306273 0.93 2 12 -0.74007307 0.31 4 48 -0.89914013 0.15 8 192 -0.98000267 0.68E-01 16 768 -1.0276643 0.20E-01 32 3072 -1.0427748 0.52E-02 64 12288 -1.0467016 0.13E-02 128 49152 -1.0476932 0.33E-03 256 196608 -1.0479417 0.82E-04 512 786432 -1.0480039 0.19E-04 P(X,Y,Z) = Z 1 3 -0.75223326E-01 1.4 2 12 0.93275388 0.39 4 48 1.1381190 0.18 8 192 1.2318404 0.86E-01 16 768 1.2916667 0.26E-01 32 3072 1.3112717 0.68E-02 64 12288 1.3163693 0.17E-02 128 49152 1.3176563 0.43E-03 256 196608 1.3179789 0.11E-03 512 786432 1.3180596 0.25E-04 P(X,Y,Z) = X^2 1 3 1.9750865 0.69 2 12 1.0140237 0.27 4 48 1.2178480 0.64E-01 8 192 1.3130626 0.31E-01 16 768 1.3009017 0.19E-01 32 3072 1.2867816 0.51E-02 64 12288 1.2829678 0.13E-02 128 49152 1.2820000 0.32E-03 256 196608 1.2817571 0.80E-04 512 786432 1.2816963 0.19E-04 P(X,Y,Z) = Y^2 Z^2 1 3 0.56832555E-01 0.13 2 12 0.77617823E-01 0.10 4 48 0.18719190 0.51E-02 8 192 0.18239532 0.32E-03 16 768 0.18059807 0.15E-02 32 3072 0.18163024 0.44E-03 64 12288 0.18196245 0.11E-03 128 49152 0.18204428 0.27E-04 256 196608 0.18206465 0.67E-05 512 786432 0.18206974 0.16E-05 P(X,Y,Z) = X^2 Y^2 Z^2 1 3 0.31486035E-01 0.65E-02 2 12 0.13749622E-01 0.11E-01 4 48 0.35232780E-01 0.10E-01 8 192 0.28108426E-01 0.32E-02 16 768 0.23967181E-01 0.98E-03 32 3072 0.24698249E-01 0.25E-03 64 12288 0.24881908E-01 0.65E-04 128 49152 0.24930833E-01 0.17E-04 256 196608 0.24943263E-01 0.41E-05 512 786432 0.24946383E-01 0.98E-06 P(X,Y,Z) = Y^2 Z^4 1 3 0.20892460E-01 0.64E-01 2 12 0.34135797E-01 0.51E-01 4 48 0.99839030E-01 0.15E-01 8 192 0.82640672E-01 0.26E-02 16 768 0.85485105E-01 0.25E-03 32 3072 0.85305479E-01 0.70E-04 64 12288 0.85256554E-01 0.21E-04 128 49152 0.85240935E-01 0.55E-05 256 196608 0.85236808E-01 0.14E-05 512 786432 0.85235762E-01 0.33E-06 P(X,Y,Z) = Z^6 1 3 0.11646444 0.36 2 12 0.54057498 0.59E-01 4 48 0.45127201 0.30E-01 8 192 0.48891840 0.77E-02 16 768 0.48667765 0.54E-02 32 3072 0.48269293 0.15E-02 64 12288 0.48161859 0.38E-03 128 49152 0.48133325 0.96E-04 256 196608 0.48126082 0.24E-04 512 786432 0.48124265 0.57E-05 P(X,Y,Z) = X Y^2 Z^4 1 3 -0.66351753E-02 0.12E-01 2 12 0.71491014E-02 0.21E-02 4 48 0.26892267E-01 0.22E-01 8 192 0.66302221E-02 0.16E-02 16 768 0.35026674E-02 0.16E-02 32 3072 0.45188583E-02 0.55E-03 64 12288 0.49291307E-02 0.14E-03 128 49152 0.50339014E-02 0.35E-04 256 196608 0.50602338E-02 0.87E-05 512 786432 0.50668257E-02 0.21E-05 P(X,Y,Z) = X^2 Y^4 Z^2 1 3 0.25214372E-02 0.47E-02 2 12 0.17534720E-02 0.55E-02 4 48 0.80878156E-02 0.82E-03 8 192 0.91883223E-02 0.19E-02 16 768 0.69903895E-02 0.27E-03 32 3072 0.71760843E-02 0.89E-04 64 12288 0.72415609E-02 0.23E-04 128 49152 0.72589382E-02 0.59E-05 256 196608 0.72633520E-02 0.15E-05 512 786432 0.72644599E-02 0.35E-06 P(X,Y,Z) = X^6 Y^2 1 3 0.10942767 0.52E-01 2 12 0.14609328E-01 0.42E-01 4 48 0.29853754E-01 0.27E-01 8 192 0.54462428E-01 0.26E-02 16 768 0.58619457E-01 0.16E-02 32 3072 0.57295087E-01 0.27E-03 64 12288 0.57097924E-01 0.71E-04 128 49152 0.57045090E-01 0.18E-04 256 196608 0.57031658E-01 0.44E-05 512 786432 0.57028286E-01 0.11E-05 P(X,Y,Z) = Z^8 1 3 0.46748006E-01 0.33 2 12 0.42558335 0.46E-01 4 48 0.31203149 0.68E-01 8 192 0.37173242 0.81E-02 16 768 0.38557764 0.57E-02 32 3072 0.38169887 0.18E-02 64 12288 0.38034635 0.48E-03 128 49152 0.37998898 0.12E-03 256 196608 0.37989838 0.30E-04 512 786432 0.37987565 0.71E-05 P(X,Y,Z) = X^6 Z^4 1 3 0.48508696E-01 0.34E-01 2 12 0.21026762E-01 0.61E-02 4 48 0.10823045E-01 0.41E-02 8 192 0.67314157E-02 0.82E-02 16 768 0.14047509E-01 0.89E-03 32 3072 0.14777712E-01 0.16E-03 64 12288 0.14893830E-01 0.40E-04 128 49152 0.14923990E-01 0.10E-04 256 196608 0.14931577E-01 0.25E-05 512 786432 0.14933476E-01 0.59E-06 P(X,Y,Z) = X^4 Y^6 Z^2 1 3 0.14840502E-03 0.56E-03 2 12 0.59483385E-04 0.65E-03 4 48 0.42602231E-03 0.28E-03 8 192 0.62112420E-03 0.86E-04 16 768 0.54976815E-03 0.16E-03 32 3072 0.69545584E-03 0.11E-04 64 12288 0.70372628E-03 0.29E-05 128 49152 0.70590960E-03 0.74E-06 256 196608 0.70646285E-03 0.18E-06 512 786432 0.70660164E-03 0.43E-07 P(X,Y,Z) = X^2 Y^4 Z^8 1 3 0.13179690E-03 0.32E-03 2 12 0.15380922E-03 0.30E-03 4 48 0.12325080E-02 0.78E-03 8 192 0.84853036E-03 0.39E-03 16 768 0.51863904E-03 0.63E-04 32 3072 0.45454955E-03 0.15E-05 64 12288 0.45558610E-03 0.49E-06 128 49152 0.45595071E-03 0.13E-06 256 196608 0.45604478E-03 0.31E-07 512 786432 0.45606848E-03 0.74E-08 P(X,Y,Z) = X^16 1 3 0.22483589 0.12 2 12 0.17674348 0.16 4 48 0.43276350 0.93E-01 8 192 0.48863952 0.15 16 768 0.36219129 0.22E-01 32 3072 0.34639491 0.65E-02 64 12288 0.34153296 0.16E-02 128 49152 0.34030206 0.41E-03 256 196608 0.33999345 0.10E-03 512 786432 0.33991624 0.24E-04 TEST06 SPHERE01_TRIANGLE_QUAD_ICOS2V approximates the integral of a function over a spherical triangle on the surface of the unit sphere using a vertex rule. We do not have an exact result, so we compare each estimate to the final one. Vertices of random spherical triangle: V1: 0.795416 -0.223966 -0.563163 V2: -0.696321 -0.284310 0.659018 V3: 0.901719 0.397757 -0.169386 FACTOR N RESULT P(X,Y,Z) = 1 1 3 3.0690548 0.30E-09 2 12 3.0690548 0.30E-09 4 48 3.0690548 0.30E-09 8 192 3.0690548 0.30E-09 16 768 3.0690548 0.30E-09 32 3072 3.0690548 0.30E-09 64 12288 3.0690548 0.30E-09 128 49152 3.0690548 0.30E-09 256 196608 3.0690548 0.30E-09 512 786432 3.0690548 0.28E-09 P(X,Y,Z) = X 1 3 1.0238514 0.44 2 12 1.0316791 0.43 4 48 1.3266931 0.14 8 192 1.4296819 0.35E-01 16 768 1.4562829 0.89E-02 32 3072 1.4629299 0.22E-02 64 12288 1.4645957 0.56E-03 128 49152 1.4650124 0.14E-03 256 196608 1.4651165 0.34E-04 512 786432 1.4651426 0.81E-05 P(X,Y,Z) = Y 1 3 -0.11306273 0.93 2 12 -0.74007307 0.31 4 48 -0.95042145 0.98E-01 8 192 -1.0254543 0.23E-01 16 768 -1.0424257 0.56E-02 32 3072 -1.0466229 0.14E-02 64 12288 -1.0476741 0.35E-03 128 49152 -1.0479370 0.87E-04 256 196608 -1.0480027 0.22E-04 512 786432 -1.0480192 0.51E-05 P(X,Y,Z) = Z 1 3 -0.75223326E-01 1.4 2 12 0.93275388 0.39 4 48 1.1516180 0.17 8 192 1.2690057 0.49E-01 16 768 1.3056284 0.12E-01 32 3072 1.3149559 0.31E-02 64 12288 1.3173028 0.78E-03 128 49152 1.3178905 0.20E-03 256 196608 1.3180375 0.48E-04 512 786432 1.3180742 0.11E-04 P(X,Y,Z) = X^2 1 3 1.9750865 0.69 2 12 1.0140237 0.27 4 48 1.2005759 0.81E-01 8 192 1.2609140 0.21E-01 16 768 1.2763565 0.53E-02 32 3072 1.2803319 0.13E-02 64 12288 1.2813391 0.34E-03 128 49152 1.2815918 0.84E-04 256 196608 1.2816550 0.21E-04 512 786432 1.2816708 0.49E-05 P(X,Y,Z) = Y^2 Z^2 1 3 0.56832555E-01 0.13 2 12 0.77617823E-01 0.10 4 48 0.14619357 0.36E-01 8 192 0.19374097 0.12E-01 16 768 0.18493249 0.29E-02 32 3072 0.18277469 0.70E-03 64 12288 0.18224688 0.18E-03 128 49152 0.18211528 0.44E-04 256 196608 0.18208240 0.11E-04 512 786432 0.18207418 0.26E-05 P(X,Y,Z) = X^2 Y^2 Z^2 1 3 0.31486035E-01 0.65E-02 2 12 0.13749622E-01 0.11E-01 4 48 0.27482796E-01 0.25E-02 8 192 0.28703510E-01 0.38E-02 16 768 0.25574439E-01 0.63E-03 32 3072 0.25104926E-01 0.16E-03 64 12288 0.24986842E-01 0.39E-04 128 49152 0.24957281E-01 0.98E-05 256 196608 0.24949888E-01 0.24E-05 512 786432 0.24948040E-01 0.58E-06 P(X,Y,Z) = Y^2 Z^4 1 3 0.20892460E-01 0.64E-01 2 12 0.34135797E-01 0.51E-01 4 48 0.40642538E-01 0.45E-01 8 192 0.87667355E-01 0.24E-02 16 768 0.86280136E-01 0.10E-02 32 3072 0.85465675E-01 0.23E-03 64 12288 0.85291717E-01 0.56E-04 128 49152 0.85249415E-01 0.14E-04 256 196608 0.85238908E-01 0.34E-05 512 786432 0.85236286E-01 0.82E-06 P(X,Y,Z) = Z^6 1 3 0.11646444 0.36 2 12 0.54057498 0.59E-01 4 48 0.54617852 0.65E-01 8 192 0.45620862 0.25E-01 16 768 0.47391746 0.73E-02 32 3072 0.47944930 0.18E-02 64 12288 0.48079128 0.44E-03 128 49152 0.48112534 0.11E-03 256 196608 0.48120878 0.27E-04 512 786432 0.48122963 0.65E-05 P(X,Y,Z) = X Y^2 Z^4 1 3 -0.66351753E-02 0.12E-01 2 12 0.71491014E-02 0.21E-02 4 48 0.65105600E-02 0.14E-02 8 192 0.10793517E-01 0.57E-02 16 768 0.61026233E-02 0.10E-02 32 3072 0.53146691E-02 0.25E-03 64 12288 0.51299301E-02 0.61E-04 128 49152 0.50842212E-02 0.15E-04 256 196608 0.50728213E-02 0.37E-05 512 786432 0.50699730E-02 0.89E-06 P(X,Y,Z) = X^2 Y^4 Z^2 1 3 0.25214372E-02 0.47E-02 2 12 0.17534720E-02 0.55E-02 4 48 0.12204383E-01 0.49E-02 8 192 0.80152249E-02 0.75E-03 16 768 0.75158286E-02 0.25E-03 32 3072 0.73277464E-02 0.63E-04 64 12288 0.72805985E-02 0.16E-04 128 49152 0.72687745E-02 0.39E-05 256 196608 0.72658159E-02 0.97E-06 512 786432 0.72650761E-02 0.23E-06 P(X,Y,Z) = X^6 Y^2 1 3 0.10942767 0.52E-01 2 12 0.14609328E-01 0.42E-01 4 48 0.80200288E-01 0.23E-01 8 192 0.59063454E-01 0.20E-02 16 768 0.57513361E-01 0.49E-03 32 3072 0.57150827E-01 0.12E-03 64 12288 0.57058159E-01 0.31E-04 128 49152 0.57034915E-01 0.77E-05 256 196608 0.57029100E-01 0.19E-05 512 786432 0.57027646E-01 0.45E-06 P(X,Y,Z) = Z^8 1 3 0.46748006E-01 0.33 2 12 0.42558335 0.46E-01 4 48 0.47845688 0.99E-01 8 192 0.36394196 0.16E-01 16 768 0.37339401 0.65E-02 32 3072 0.37833126 0.15E-02 64 12288 0.37948688 0.38E-03 128 49152 0.37977294 0.95E-04 256 196608 0.37984430 0.23E-04 512 786432 0.37986213 0.56E-05 P(X,Y,Z) = X^6 Z^4 1 3 0.48508696E-01 0.34E-01 2 12 0.21026762E-01 0.61E-02 4 48 0.89657101E-02 0.60E-02 8 192 0.12703251E-01 0.22E-02 16 768 0.14511716E-01 0.42E-03 32 3072 0.14825674E-01 0.11E-03 64 12288 0.14906871E-01 0.27E-04 128 49152 0.14927292E-01 0.68E-05 256 196608 0.14932405E-01 0.17E-05 512 786432 0.14933683E-01 0.40E-06 P(X,Y,Z) = X^4 Y^6 Z^2 1 3 0.14840502E-03 0.56E-03 2 12 0.59483385E-04 0.65E-03 4 48 0.12643502E-02 0.56E-03 8 192 0.76457080E-03 0.58E-04 16 768 0.73367771E-03 0.27E-04 32 3072 0.71365720E-03 0.70E-05 64 12288 0.70840764E-03 0.18E-05 128 49152 0.70708830E-03 0.44E-06 256 196608 0.70675806E-03 0.11E-06 512 786432 0.70667547E-03 0.26E-07 P(X,Y,Z) = X^2 Y^4 Z^8 1 3 0.13179690E-03 0.32E-03 2 12 0.15380922E-03 0.30E-03 4 48 0.17336717E-03 0.28E-03 8 192 0.53740966E-03 0.81E-04 16 768 0.46221650E-03 0.61E-05 32 3072 0.45823338E-03 0.22E-05 64 12288 0.45660231E-03 0.53E-06 128 49152 0.45620718E-03 0.13E-06 256 196608 0.45610905E-03 0.32E-07 512 786432 0.45608455E-03 0.77E-08 P(X,Y,Z) = X^16 1 3 0.22483589 0.12 2 12 0.17674348 0.16 4 48 0.20910459 0.13 8 192 0.33175412 0.81E-02 16 768 0.33729858 0.26E-02 32 3072 0.33924610 0.64E-03 64 12288 0.33972967 0.16E-03 128 49152 0.33985031 0.40E-04 256 196608 0.33988045 0.99E-05 512 786432 0.33988799 0.24E-05 sphere_triangle_quad_test(): Normal end of execution. April 3 2023 9:41:13.114 AM