Thu Sep 13 07:38:32 2018 ELLIPSE_MONTE_CARLO_TESTS Python version: 3.6.5 Test the ELLIPSE_MONTE_CARLO library. ELLIPSE_AREA1_TEST Python version: 3.6.5 ELLIPSE_AREA1 computes the area of an ellipse. R = 10 Matrix A in ellipse definition x*A*x=r^2 Col: 0 1 Row 0 : 5 1 1 : 1 2 Area = 104.72 ELLIPSE_AREA1_TEST Normal end of execution. ELLIPSE_AREA2_TEST Python version: 3.6.5 ELLIPSE_AREA2 computes the area of an ellipse. Ellipse: 5 * x^2 + 2 * xy + 2 * y^2 = 10 Area = 104.72 ELLIPSE_AREA2_TEST Normal end of execution. ELLIPSE_MONTE_CARLO_TEST Use ELLIPSE01_SAMPLE to estimate integrals in the ellipse x * A * x <= r^2. 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 ELLIPSE_MONTE_CARLO_TEST: Normal end of execution. ELLIPSE_SAMPLE_TEST Python version: 3.6.5 ELLIPSE_SAMPLE computes points uniformly distributed inside an ellipse x'*A*x=r^2. Random points inside ellipse Row: 0 1 Col 0 : 1.5858 -1.82229 1 : -0.980284 4.46526 2 : -2.00148 1.07972 3 : 0.188387 0.132934 4 : -0.397559 2.72314 5 : 0.00607196 2.30289 6 : -1.18765 -2.03451 7 : 0.920274 -2.26936 8 : -0.421153 -1.32974 9 : 0.549653 3.16931 ELLIPSE_SAMPLE_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. 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. ELLIPSE_MONTE_CARLO_TESTS Normal end of execution. Thu Sep 13 07:38:36 2018