Thu Sep 13 07:38:41 2018 ELLIPSOID_MONTE_CARLO_TESTS Python version: 3.6.5 Test the ELLIPSOID_MONTE_CARLO library. ELLIPSOID_MONTE_CARLO_TEST01 Use ELLIPSOID_SAMPLE to estimate integrals in a 2D ellipse x * A * x <= r^2. Ellipsoid radius R = 2 Ellipsoid center V: 0: 0 1: 0 Ellipsoid matrix A: Col: 0 1 Row 0 : 9 1 1 : 1 4 Ellipsoid volume = 2.1241 N 1 X Y X^2 XY Y^2 X^3 1 2.1241 0.321476 -0.299022 0.0486544 -0.0452561 0.0420951 0.00736369 2 2.1241 -0.27652 0.499696 0.0478767 -0.0370767 0.183433 -0.00932549 4 2.1241 -0.0612209 0.144295 0.0130204 0.0199415 0.0882489 -0.00185697 8 2.1241 0.0317852 0.0869245 0.0214724 -0.00735015 0.072673 -0.000699755 16 2.1241 0.00154063 0.0268314 0.0330817 -0.00946018 0.165506 0.000300543 32 2.1241 -0.0165851 -0.142963 0.0342288 -0.0367537 0.155094 -0.000345318 64 2.1241 -0.0387006 0.0566138 0.0242695 -0.0206398 0.136156 -0.000714845 128 2.1241 0.0379064 0.00648654 0.031136 -0.0242917 0.151621 0.000651244 256 2.1241 -0.00153402 0.0122716 0.0296746 -0.0252856 0.151463 0.000143204 512 2.1241 0.00152787 -0.0115445 0.030106 -0.0208186 0.138797 0.000188673 1024 2.1241 0.00311013 0.00155926 0.0290905 -0.0207969 0.138277 6.51272e-05 2048 2.1241 0.000532402 -0.0134502 0.0301181 -0.0230603 0.139695 0.000111932 4096 2.1241 0.00134544 -0.014149 0.0295652 -0.0227881 0.141501 0.00011408 8192 2.1241 -0.00300381 -0.00458822 0.0294594 -0.0228104 0.142268 -8.20529e-05 16384 2.1241 0.00173254 0.00273916 0.0290031 -0.0226607 0.143008 5.54886e-05 32768 2.1241 -0.00216533 0.00108515 0.0296114 -0.0224396 0.141952 -4.72238e-05 65536 2.1241 0.000332428 -0.00397407 0.0295669 -0.0224907 0.142094 2.96863e-05 ELLIPSOID_MONTE_CARLO_TEST01 Normal end of execution. ELLIPSOID_MONTE_CARLO_TEST02 Use ELLIPSOID_SAMPLE to estimate integrals in a 2D ellipse (x-v) * A * (x-v) <= r^2. Ellipsoid radius R = 0.5 Ellipsoid center V: 0: 2 1: 3 Ellipsoid matrix A: Col: 0 1 Row 0 : 9 1 1 : 1 4 Ellipsoid volume = 0.132757 N 1 X Y X^2 XY Y^2 X^3 1 0.132757 0.270536 0.393597 0.551308 0.802087 1.16694 1.12348 2 0.132757 0.261192 0.406077 0.513931 0.799048 1.24237 1.01132 4 0.132757 0.264556 0.400524 0.527251 0.798257 1.20868 1.05088 8 0.132757 0.26601 0.399628 0.533097 0.800717 1.20324 1.06851 16 0.132757 0.265537 0.398689 0.531252 0.797413 1.19797 1.06312 32 0.132757 0.265254 0.396036 0.530123 0.791151 1.18201 1.05974 64 0.132757 0.264908 0.399154 0.528702 0.796414 1.20065 1.05536 128 0.132757 0.266105 0.398371 0.533517 0.798424 1.19601 1.06989 256 0.132757 0.265489 0.398461 0.531046 0.796752 1.19655 1.06246 512 0.132757 0.265537 0.398089 0.531239 0.796169 1.19427 1.06304 1024 0.132757 0.265562 0.398294 0.531334 0.796652 1.1955 1.06332 2048 0.132757 0.265521 0.398059 0.531177 0.796054 1.19409 1.06286 4096 0.132757 0.265534 0.398048 0.531226 0.796071 1.19403 1.063 8192 0.132757 0.265466 0.398198 0.530953 0.796166 1.19493 1.06218 16384 0.132757 0.26554 0.398312 0.531248 0.796617 1.19562 1.06306 32768 0.132757 0.265479 0.398287 0.531006 0.796384 1.19546 1.06234 65536 0.132757 0.265518 0.398207 0.531162 0.796343 1.19499 1.06281 ELLIPSOID_MONTE_CARLO_TEST02 Normal end of execution. ELLIPSOID_MONTE_CARLO_TEST03 Use ELLIPSOID_SAMPLE to estimate integrals in a 3D ellipse (x-v) * A * (x-v) <= r^2. Ellipsoid radius R = 0.5 Ellipsoid center V: 0: 1 1: 2 2: 3 Ellipsoid matrix A: Col: 0 1 2 Row 0 : 9 6 3 1 : 6 5 4 2 : 3 4 9 Ellipsoid volume = 0.0872665 N 1 X Y Z X^2 YZ Z^3 1 0.0872665 0.117213 0.126728 0.274806 0.157435 1.82498 2.72512 2 0.0872665 0.102801 0.151943 0.267913 0.122241 2.49722 2.53422 4 0.0872665 0.104695 0.145739 0.267095 0.129378 2.3161 2.50943 8 0.0872665 0.0663363 0.210721 0.251955 0.0576277 4.27288 2.11125 16 0.0872665 0.0804799 0.186209 0.258233 0.0820292 3.54544 2.27084 32 0.0872665 0.0861435 0.175429 0.261995 0.0969454 3.28051 2.38262 64 0.0872665 0.0865357 0.175285 0.261551 0.0971515 3.26421 2.3663 128 0.0872665 0.0868618 0.175465 0.26168 0.0949801 3.24808 2.36578 256 0.0872665 0.0867801 0.175521 0.261463 0.0960104 3.25462 2.36324 512 0.0872665 0.0844921 0.178821 0.260793 0.0908591 3.34656 2.34398 1024 0.0872665 0.0891028 0.17146 0.262575 0.100054 3.13318 2.39189 2048 0.0872665 0.0860152 0.176521 0.261304 0.0938764 3.28072 2.35758 4096 0.0872665 0.0868008 0.17528 0.26166 0.0956624 3.24697 2.36747 8192 0.0872665 0.0870079 0.174965 0.261696 0.0958474 3.23437 2.36824 16384 0.0872665 0.0874084 0.174291 0.261855 0.0965594 3.2139 2.37227 32768 0.0872665 0.087374 0.174352 0.261853 0.0965529 3.21614 2.37241 65536 0.0872665 0.0874281 0.174271 0.261855 0.0966558 3.21347 2.37242 ELLIPSOID_MONTE_CARLO_TEST03 Normal end of execution. ELLIPSOID_SAMPLE_TEST Python version: 3.6.5 ELLIPSOID_SAMPLE samples the ellipsoid (X-V)' * A * (X-V) <= R * R. M = 3 A: Col: 0 1 2 Row 0 : 9 3 3 1 : 3 5 3 2 : 3 3 3 V: 0: 2 1: 3 2: 1 Ellipsoid sample points: Row: 0 1 2 Col 0 : 2.02302 2.73643 1.36035 1 : 2.19014 3.35763 0.323971 2 : 1.89653 2.49215 1.9117 3 : 2.02026 2.67354 1.44008 4 : 2.07738 2.86244 0.882691 5 : 2.13513 3.21093 0.434481 6 : 1.9996 3.11616 0.681972 7 : 2.0739 3.26926 0.651658 8 : 2.02292 2.94646 0.989642 9 : 2.0201 2.9251 1.09169 10 : 2.0805 3.14827 0.834059 11 : 2.03401 3.47311 0.242594 12 : 2.08054 3.57974 0.254499 13 : 1.92173 3.30598 0.769034 14 : 1.94536 3.42553 0.50902 15 : 1.83532 2.92959 1.2434 16 : 1.81012 2.71389 1.7339 17 : 2.01387 3.46813 0.501857 18 : 2.09828 2.97856 0.718395 19 : 1.82056 3.02479 1.30373 ELLIPSOID_SAMPLE_TEST Normal end of execution. ELLIPSOID_VOLUME_TEST Python version: 3.6.5 ELLIPSOID_VOLUME computes the volume of the ellipsoid (X-V)' * A * (X-V) <= R * R. M = 3 A: Col: 0 1 2 Row 0 : 9 3 3 1 : 3 5 3 2 : 3 3 3 V: 0: 2 1: 3 2: 1 Volume = 0.698132 ELLIPSOID_VOLUME_TEST Normal end of execution. HYPERSPHERE_UNIT_VOLUME_TEST Python version: 3.6.5 HYPERSPHERE_UNIT_VOLUME computes the volume of the unit hypersphere in M dimensions. M Volume 1 2 2 3.14159 3 4.18879 4 4.9348 5 5.26379 6 5.16771 7 4.72477 8 4.05871 9 3.29851 10 2.55016 HYPERSPHERE_UNIT_VOLUME_TEST Normal end of execution. I4VEC_TRANSPOSE_PRINT_TEST Python version: 3.6.5 I4VEC_TRANSPOSE_PRINT prints an I4VEC with 5 entries to a row, and an optional title. My array: 1 2 3 4 5 6 7 8 9 10 11 12 I4VEC_TRANSPOSE_PRINT_TEST: Normal end of execution. I4VEC_PRINT_TEST Python version: 3.6.5 I4VEC_PRINT prints an I4VEC. Here is an I4VEC: 0 91 1 92 2 93 3 94 I4VEC_PRINT_TEST: Normal end of execution. I4VEC_UNIFORM_AB_TEST Python version: 3.6.5 I4VEC_UNIFORM_AB computes pseudorandom values in an interval [A,B]. The lower endpoint A = -100 The upper endpoint B = 200 The initial seed is 123456789 The random vector: 0 -35 1 187 2 149 3 69 4 25 5 -81 6 -23 7 -67 8 -87 9 90 10 -82 11 35 12 20 13 127 14 139 15 -100 16 170 17 5 18 -72 19 -96 I4VEC_UNIFORM_AB_TEST: Normal end of execution. MONOMIAL_VALUE_TEST Python version: 3.6.5 Use monomial_value() to evaluate some monomials in dimensions 1 through 3. Spatial dimension M = 1 Exponents: -1 V(X) X(0) 0.111111 9.0000 0.125 8.0000 0.2 5.0000 0.333333 3.0000 -1 -1.0000 Spatial dimension M = 2 Exponents: -1 -2 V(X) X(0) X(1) -0.0277778 -1.0000 6.0000 -0.111111 -1.0000 3.0000 0.00680272 3.0000 7.0000 0.03125 8.0000 -2.0000 0.0277778 9.0000 2.0000 Spatial dimension M = 3 Exponents: -3 -3 5 V(X) X(0) X(1) X(2) 0.0625 8.0000 -1.0000 -2.0000 -0.00137174 1.0000 9.0000 -1.0000 0.000244141 2.0000 8.0000 1.0000 1.21363 6.0000 5.0000 8.0000 0.158766 3.0000 9.0000 5.0000 MONOMIAL_VALUE_TEST Normal end of execution. R8_NORMAL_01_TEST Python version: 3.6.5 R8_NORMAL_01 generates normally distributed random values. Using initial random number seed = 123456789 1.679040 -0.566060 1.212934 1.269381 -1.666087 -2.242464 0.039675 0.673068 -0.275127 2.164005 0.297785 2.044536 1.398819 -1.242985 -0.067084 -0.794396 -0.523768 -0.350567 0.131700 0.537380 R8_NORMAL_01_TEST Normal end of execution. R8_UNIFORM_01_TEST Python version: 3.6.5 R8_UNIFORM_01 produces a sequence of random values. Using random seed 123456789 SEED R8_UNIFORM_01(SEED) 469049721 0.218418 2053676357 0.956318 1781357515 0.829509 1206231778 0.561695 891865166 0.415307 141988902 0.066119 553144097 0.257578 236130416 0.109957 94122056 0.043829 1361431000 0.633966 Verify that the sequence can be restarted. Set the seed back to its original value, and see that we generate the same sequence. SEED R8_UNIFORM_01(SEED) 469049721 0.218418 2053676357 0.956318 1781357515 0.829509 1206231778 0.561695 891865166 0.415307 141988902 0.066119 553144097 0.257578 236130416 0.109957 94122056 0.043829 1361431000 0.633966 R8_UNIFORM_01_TEST Normal end of execution. R8MAT_PRINT_TEST Python version: 3.6.5 R8MAT_PRINT prints an R8MAT. Here is an R8MAT: Col: 0 1 2 3 4 Row 0 : 11 12 13 14 15 1 : 21 22 23 24 25 2 : 31 32 33 34 35 3 : 41 42 43 44 45 Col: 5 Row 0 : 16 1 : 26 2 : 36 3 : 46 R8MAT_PRINT_TEST: Normal end of execution. R8MAT_PRINT_SOME_TEST Python version: 3.6.5 R8MAT_PRINT_SOME prints some of an R8MAT. Here is an R8MAT: Col: 3 4 5 Row 0 : 14 15 16 1 : 24 25 26 2 : 34 35 36 R8MAT_PRINT_SOME_TEST: Normal end of execution. R8MAT_UNIFORM_AB_TEST Python version: 3.6.5 R8MAT_UNIFORM_AB computes a random R8MAT. -1 <= X <= 5 Initial seed is 123456789 Random R8MAT: Col: 0 1 2 3 Row 0 : 0.31051 -0.603288 -0.629637 -0.98897 1 : 4.73791 0.545467 1.69723 4.38502 2 : 3.97706 -0.340259 1.40784 1.10451 3 : 2.37017 -0.737026 3.52804 -0.432731 4 : 1.49184 2.80379 3.78372 -0.918299 R8MAT_UNIFORM_AB_TEST: Normal end of execution. R8PO_FA_TEST Python version: 3.6.5 R8PO_FA factors a positive definite symmetric linear system, Matrix order N = 5 The matrix A: Col: 0 1 2 3 4 Row 0 : 1 1 1 1 1 1 : 1 2 2 2 2 2 : 1 2 3 3 3 3 : 1 2 3 4 4 4 : 1 2 3 4 5 The factor R (a R8UT matrix): Col: 0 1 2 3 4 Row 0 : 1 1 1 1 1 1 : 0 1 1 1 1 2 : 0 0 1 1 1 3 : 0 0 0 1 1 4 : 0 0 0 0 1 The product R' * R: Col: 0 1 2 3 4 Row 0 : 1 1 1 1 1 1 : 1 2 2 2 2 2 : 1 2 3 3 3 3 : 1 2 3 4 4 4 : 1 2 3 4 5 R8PO_FA_TEST: Normal end of execution. R8PO_SL_TEST Python version: 3.6.5 R8PO_SL solves a linear system with an R8PO matrix after it has been factored by R8PO_FA. Matrix order N = 5 Matrix A: Col: 0 1 2 3 4 Row 0 : 2 -1 0 0 0 1 : 0 2 -1 0 0 2 : 0 0 2 -1 0 3 : 0 0 0 2 -1 4 : 0 0 0 0 2 Right hand side b: 0: 0 1: 0 2: 0 3: 0 4: 6 Solution x: 0: 1 1: 2 2: 3 3: 4 4: 5 R8PO_SL_TEST Normal end of execution. R8VEC_NORMAL_01_TEST Python version: 3.6.5 R8VEC_NORMAL_01 returns a vector of Normal 01 values SEED = 123456789 Vector: 0: 1.67904 1: -0.56606 2: 1.21293 3: 1.26938 4: -1.66609 5: -2.24246 6: 0.0396749 7: 0.673068 8: -0.275127 9: 2.164 R8VEC_NORMAL_01_TEST: Normal end of execution. R8VEC_PRINT_TEST Python version: 3.6.5 R8VEC_PRINT prints an R8VEC. Here is an R8VEC: 0: 123.456 1: 5e-06 2: -1e+06 3: 3.14159 R8VEC_PRINT_TEST: Normal end of execution. R8VEC_UNIFORM_01_TEST Python version: 3.6.5 R8VEC_UNIFORM_01 computes a random R8VEC. Initial seed is 123456789 Random R8VEC: 0: 0.218418 1: 0.956318 2: 0.829509 3: 0.561695 4: 0.415307 5: 0.0661187 6: 0.257578 7: 0.109957 8: 0.043829 9: 0.633966 R8VEC_UNIFORM_01_TEST: Normal end of execution. UNIFORM_IN_SPHERE01_MAP_TEST Python version: 3.6.5 UNIFORM_IN_SPHERE01_MAP computes points uniformly distributed inside the M-dimensional unit sphere. Random points inside unit 3-sphere Row: 0 1 2 Col 0 : 0.497518 -0.16773 0.359406 1 : 0.756069 0.330465 -0.384785 2 : 0.280276 -0.114567 0.901126 3 : 0.523193 -0.251279 0.401636 4 : -0.0681996 -0.80761 -0.532481 5 : 0.152427 -0.236512 -0.65837 6 : -0.609231 -0.374499 -0.606816 7 : 0.42781 0.522948 -0.0155662 8 : 0.0146253 -0.230002 -0.122921 9 : 0.231257 -0.039156 0.11065 UNIFORM_IN_SPHERE01_MAP_TEST Normal end of execution. ELLIPSOID_MONTE_CARLO_TESTS Normal end of execution. Thu Sep 13 07:38:57 2018