Wed Sep 12 21:11:24 2018 CIRCLE_MONTE_CARLO_TEST Python version: 3.6.5 Test the CIRCLE_MONTE_CARLO library. CIRCLE01_LENGTH_TEST Python version: 3.6.5 CIRCLE01_LENGTH returns the length of the unit circle. CIRCLE01_LENGTH() = 6.28319 CIRCLE01_LENGTH_TEST Normal end of execution. CIRCLE01_MONOMIAL_INTEGRAL_TEST Python version: 3.6.5 CIRCLE01_MONOMIAL_INTEGRAL returns the value of the integral of a monomial over the unit circle in 2D. Compare with a Monte Carlo estimate. Number of sample points used is 4192 If any exponent is odd, the integral is zero. We restrict this test to randomly chosen even exponents. Ex Ey MC-Estimate Exact Error 10 6 0.00812931 0.00862864 0.0005 0 6 2.01266 1.9635 0.049 10 6 0.00812931 0.00862864 0.0005 6 10 0.00825513 0.00862864 0.00037 6 6 0.0290444 0.0306796 0.0016 6 4 0.0699347 0.0736311 0.0037 2 6 0.242124 0.245437 0.0033 8 2 0.168632 0.171806 0.0032 2 4 0.382608 0.392699 0.01 8 8 0.00632997 0.00671117 0.00038 6 4 0.0699347 0.0736311 0.0037 4 8 0.0415049 0.0429515 0.0014 8 8 0.00632997 0.00671117 0.00038 10 0 1.57835 1.54625 0.032 0 10 1.59896 1.54625 0.053 4 8 0.0415049 0.0429515 0.0014 2 2 0.76166 0.785398 0.024 8 2 0.168632 0.171806 0.0032 2 6 0.242124 0.245437 0.0033 2 8 0.171575 0.171806 0.00023 CIRCLE01_MONOMIAL_INTEGRAL_TEST Normal end of execution. CIRCLE01_SAMPLE_ERGODIC_TEST Python version: 3.6.5 CIRCLE01_SAMPLE_ERGODIC ergodically samples the unit circle. Use it to estimate integrals. N 1 X^2 Y^2 X^4 X^2Y^2 Y^4 X^6 1 6.283185307 6.283185307 0 6.283185307 0 0 6.283185307 2 6.283185307 4.849716988 1.43346832 4.070321825 0.7793951631 0.6540731564 3.646554649 4 6.283185307 3.018369913 3.264815394 2.250524732 0.7678451818 2.496970212 1.902971277 8 6.283185307 3.049675381 3.233509926 2.300804618 0.7488707628 2.484639164 1.958708144 16 6.283185307 3.117519265 3.165666042 2.379081125 0.7384381403 2.427227902 2.016396847 32 6.283185307 3.219061499 3.064123808 2.43707687 0.781984629 2.282139179 2.047919031 64 6.283185307 3.16392701 3.119258297 2.383917095 0.780009915 2.339248382 1.993699361 128 6.283185307 3.16441952 3.118765787 2.385001988 0.7794175322 2.339348255 1.995559912 256 6.283185307 3.156056777 3.12712853 2.371065206 0.7849915706 2.34213696 1.977888379 512 6.283185307 3.140118921 3.143066386 2.355499644 0.7846192776 2.358447108 1.963715413 1024 6.283185307 3.141618707 3.1415666 2.356986312 0.7846323959 2.356934204 1.964665182 2048 6.283185307 3.143281658 3.139903649 2.357892798 0.78538886 2.354514789 1.965158523 4096 6.283185307 3.141457119 3.141728188 2.356083522 0.7853735969 2.356354591 1.96343864 8192 6.283185307 3.141500541 3.141684766 2.356149808 0.785350733 2.356334033 1.963507282 16384 6.283185307 3.141591557 3.14159375 2.35624137 0.7853501875 2.356243562 1.963566493 32768 6.283185307 3.141695988 3.141489319 2.35629807 0.7853979182 2.356091401 1.963597306 65536 6.283185307 3.141585849 3.141599458 2.356188483 0.7853973656 2.356202093 1.963491738 Exact 6.283185307 3.141592654 3.141592654 2.35619449 0.7853981634 2.35619449 1.963495408 CIRCLE01_SAMPLE_ERGODIC_TEST Normal end of execution. CIRCLE01_SAMPLE_RANDOM_TEST Python version: 3.6.5 CIRCLE01_SAMPLE_RANDOM randomly samples the unit circle. Use it to estimate integrals. N 1 X^2 Y^2 X^4 X^2Y^2 Y^4 X^6 1 6.283185307 0.2441759833 6.039009324 0.009489121827 0.2346868615 5.804322462 0.0003687644944 2 6.283185307 3.032904838 3.250280469 2.70173798 0.3311668577 2.919113611 2.499061463 4 6.283185307 3.223276534 3.059908773 2.587560159 0.6357163745 2.424192399 2.257590427 8 6.283185307 3.320589438 2.962595869 2.554310612 0.7662788261 2.196317043 2.075681364 16 6.283185307 3.576016729 2.707168578 2.86746481 0.7085519185 1.99861666 2.427010708 32 6.283185307 3.303758059 2.979427248 2.466899098 0.8368589614 2.142568287 2.014183101 64 6.283185307 3.01501375 3.268171557 2.19253144 0.8224823104 2.445689247 1.757483001 128 6.283185307 3.033001233 3.250184074 2.222242799 0.8107584348 2.439425639 1.8094348 256 6.283185307 3.251565255 3.031620052 2.43497141 0.8165938449 2.215026207 2.010591353 512 6.283185307 3.200200768 3.08298454 2.421901192 0.7782995753 2.304684964 2.027136805 1024 6.283185307 3.223621478 3.059563829 2.439255739 0.784365739 2.27519809 2.04694632 2048 6.283185307 3.156622804 3.126562504 2.378266232 0.778356572 2.348205932 1.988959415 4096 6.283185307 3.139525253 3.143660054 2.377734178 0.7617910749 2.381868979 1.99752215 8192 6.283185307 3.135938816 3.147246491 2.358198263 0.777740553 2.369505938 1.967432887 16384 6.283185307 3.14294352 3.140241787 2.364130277 0.7788132431 2.361428544 1.972746407 32768 6.283185307 3.145215612 3.137969695 2.365205002 0.7800106101 2.357959085 1.973305917 65536 6.283185307 3.142542786 3.140642522 2.35866479 0.7838779959 2.356764526 1.965931937 Exact 6.283185307 3.141592654 3.141592654 2.35619449 0.7853981634 2.35619449 1.963495408 CIRCLE01_SAMPLE_RANDOM_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_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_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_GAMMA_TEST: Python version: 3.6.5 R8_GAMMA evaluates the Gamma function. X GAMMA(X) R8_GAMMA(X) -0.5 -3.544907701811032 -3.544907701811032 -0.01 -100.5871979644108 -100.5871979644108 0.01 99.4325851191506 99.4325851191506 0.1 9.513507698668732 9.513507698668731 0.2 4.590843711998803 4.590843711998803 0.4 2.218159543757688 2.218159543757688 0.5 1.772453850905516 1.772453850905516 0.6 1.489192248812817 1.489192248812817 0.8 1.164229713725303 1.164229713725303 1 1 1 1.1 0.9513507698668732 0.9513507698668732 1.2 0.9181687423997607 0.9181687423997607 1.3 0.8974706963062772 0.8974706963062772 1.4 0.8872638175030753 0.8872638175030754 1.5 0.8862269254527581 0.8862269254527581 1.6 0.8935153492876903 0.8935153492876903 1.7 0.9086387328532904 0.9086387328532904 1.8 0.9313837709802427 0.9313837709802427 1.9 0.9617658319073874 0.9617658319073874 2 1 1 3 2 2 4 6 6 10 362880 362880 20 1.21645100408832e+17 1.216451004088321e+17 30 8.841761993739702e+30 8.841761993739751e+30 R8_GAMMA_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_TRANSPOSE_PRINT_TEST Python version: 3.6.5 R8MAT_TRANSPOSE_PRINT prints an R8MAT. Here is an R8MAT, transposed: Row: 0 1 2 3 Col 0 : 11 21 31 41 1 : 12 22 32 42 2 : 13 23 33 43 R8MAT_TRANSPOSE_PRINT_TEST: Normal end of execution. R8MAT_TRANSPOSE_PRINT_SOME_TEST Python version: 3.6.5 R8MAT_TRANSPOSE_PRINT_SOME prints some of an R8MAT, transposed. R8MAT, rows 0:2, cols 3:5: Row: 0 1 2 Col 3 : 14 24 34 4 : 15 25 35 5 : 16 26 36 R8MAT_TRANSPOSE_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. 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. CIRCLE_MONTE_CARLO_TEST: Normal end of execution. Wed Sep 12 21:11:26 2018