Thu Sep 13 14:53:09 2018 QUADRULE_TEST Python version: 3.6.5 Test the QUADRULE library. HYPER_2F1_VALUES_TEST: Python version: 3.6.5 HYPER_2F1_VALUES stores values of the hypergeometric function 2F1 A B C X F -2 3 6.700000 0.250000 0.7235612934899779 0 1 6.700000 0.250000 0.9791110934527796 0 1 6.700000 0.250000 1.021657814008856 2 3 6.700000 0.250000 1.405156320011213 -2 3 6.700000 0.550000 0.4696143163982161 0 1 6.700000 0.550000 0.9529619497744632 0 1 6.700000 0.550000 1.051281421394799 2 3 6.700000 0.550000 2.399906290477786 -2 3 6.700000 0.850000 0.2910609592841472 0 1 6.700000 0.850000 0.9253696791037318 0 1 6.700000 0.850000 1.0865504094807 2 3 6.700000 0.850000 5.738156552618904 3 6 -5.500000 0.250000 15090.66974870461 1 6 -0.500000 0.250000 -104.3117006736435 1 6 0.500000 0.250000 21.17505070776881 3 6 4.500000 0.250000 4.194691581903192 3 6 -5.500000 0.550000 10170777974.04881 1 6 -0.500000 0.550000 -24708.63532248916 1 6 0.500000 0.550000 1372.230454838499 3 6 4.500000 0.550000 58.09272870639465 3 6 -5.500000 0.850000 5.868208761512417e+18 1 6 -0.500000 0.850000 -446350101.47296 1 6 0.500000 0.850000 5383505.756129573 3 6 4.500000 0.850000 20396.91377601966 HYPER_2F1_VALUES_TEST: Normal end of execution. PSI_VALUES_TEST: Python version: 3.6.5 PSI_VALUES stores values of the PSI function. X PSI(X) 0.100000 -10.4237549404110794 0.200000 -5.2890398965921879 0.300000 -3.5025242222001332 0.400000 -2.5613845445851160 0.500000 -1.9635100260214231 0.600000 -1.5406192138931900 0.700000 -1.2200235536979349 0.800000 -0.9650085667061385 0.900000 -0.7549269499470515 1.000000 -0.5772156649015329 1.100000 -0.4237549404110768 1.200000 -0.2890398965921883 1.300000 -0.1691908888667997 1.400000 -0.0613845445851161 1.500000 0.0364899739785765 1.600000 0.1260474527734763 1.700000 0.2085478748734940 1.800000 0.2849914332938615 1.900000 0.3561841611640597 2.000000 0.4227843350984671 PSI_VALUES_TEST: Normal end of execution. R8_EPSILON_TEST Python version: 3.6.5 R8_EPSILON produces the R8 roundoff unit. R = R8_EPSILON() = 2.220446e-16 ( 1 + R ) - 1 = 2.220446e-16 ( 1 + (R/2) ) - 1 = 0.000000e+00 R8_EPSILON_TEST Normal end of execution. R8_FACTORIAL_TEST Python version: 3.6.5 R8_FACTORIAL evaluates the factorial function. N Exact Computed 0 1 1 1 1 1 2 2 2 3 6 6 4 24 24 5 120 120 6 720 720 7 5040 5040 8 40320 40320 9 362880 362880 10 3628800 3628800 11 39916800 39916800 12 479001600 479001600 13 6227020800 6227020800 14 87178291200 87178291200 15 1307674368000 1307674368000 16 20922789888000 20922789888000 17 355687428096000 355687428096000 18 6402373705728000 6402373705728000 19 1.21645100408832e+17 1.21645100408832e+17 20 2.43290200817664e+18 2.43290200817664e+18 25 1.551121004333099e+25 1.551121004333099e+25 50 3.041409320171338e+64 3.041409320171338e+64 100 9.332621544394415e+157 9.33262154439441e+157 150 5.713383956445855e+262 5.71338395644585e+262 R8_FACTORIAL_TEST Normal end of execution. R8_FACTORIAL2_TEST Python version: 3.6.5 R8_FACTORIAL2 evaluates the double factorial function. N Exact Computed 0 1 1 1 1 1 2 2 2 3 3 3 4 8 8 5 15 15 6 48 48 7 105 105 8 384 384 9 945 945 10 3840 3840 11 10395 10395 12 46080 46080 13 135135 135135 14 645120 645120 15 2027025 2027025 R8_FACTORIAL2_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. R8_HUGE_TEST Python version: 3.6.5 R8_HUGE returns a "huge" R8; R8_HUGE = 1.79769e+308 R8_HUGE_TEST Normal end of execution. R8_HYPER_2F1_TEST Python version: 3.6.5 R8_HYPER_2F1 evaluates the hypergeometric 2F1 function. A B C X 2F1 2F1 DIFF (tabulated) (computed) -2.5 3.3 6.7 0.25 0.723561 0.723561 2.22045e-16 -0.5 1.1 6.7 0.25 0.979111 0.979111 1.11022e-16 0.5 1.1 6.7 0.25 1.02166 1.02166 0 2.5 3.3 6.7 0.25 1.40516 1.40516 4.44089e-16 -2.5 3.3 6.7 0.55 0.469614 0.469614 5.55112e-17 -0.5 1.1 6.7 0.55 0.952962 0.952962 3.33067e-16 0.5 1.1 6.7 0.55 1.05128 1.05128 8.88178e-16 2.5 3.3 6.7 0.55 2.39991 2.39991 1.77636e-15 -2.5 3.3 6.7 0.85 0.291061 0.291061 2.22045e-16 -0.5 1.1 6.7 0.85 0.92537 0.92537 0 0.5 1.1 6.7 0.85 1.08655 1.08655 0 2.5 3.3 6.7 0.85 5.73816 5.73816 3.97016e-13 3.3 6.7 -5.5 0.25 15090.7 15090.7 1.09139e-11 1.1 6.7 -0.5 0.25 -104.312 -104.312 2.84217e-14 1.1 6.7 0.5 0.25 21.1751 21.1751 1.06581e-14 3.3 6.7 4.5 0.25 4.19469 4.19469 8.88178e-16 3.3 6.7 -5.5 0.55 1.01708e+10 1.01708e+10 1.14441e-05 1.1 6.7 -0.5 0.55 -24708.6 -24708.6 1.81899e-11 1.1 6.7 0.5 0.55 1372.23 1372.23 2.27374e-12 3.3 6.7 4.5 0.55 58.0927 58.0927 2.84217e-14 3.3 6.7 -5.5 0.85 5.86821e+18 5.86821e+18 36864 1.1 6.7 -0.5 0.85 -4.4635e+08 -4.4635e+08 4.76837e-07 1.1 6.7 0.5 0.85 5.38351e+06 5.38351e+06 8.3819e-09 3.3 6.7 4.5 0.85 20396.9 20396.9 1.45519e-11 R8_HYPER_2F1_TEST Normal end of execution. R8_PSI_TEST: Python version: 3.6.5 R8_PSI evaluates the PSI function. X PSI(X) R8_PSI(X) 0.1 -10.42375494041108 -10.42375494041108 0.2 -5.289039896592188 -5.289039896592188 0.3 -3.502524222200133 -3.502524222200133 0.4 -2.561384544585116 -2.561384544585116 0.5 -1.963510026021423 -1.963510026021424 0.6 -1.54061921389319 -1.540619213893191 0.7 -1.220023553697935 -1.220023553697935 0.8 -0.9650085667061385 -0.9650085667061382 0.9 -0.7549269499470515 -0.7549269499470511 1 -0.5772156649015329 -0.5772156649015329 1.1 -0.4237549404110768 -0.4237549404110768 1.2 -0.2890398965921883 -0.2890398965921884 1.3 -0.1691908888667997 -0.1691908888667995 1.4 -0.06138454458511615 -0.06138454458511624 1.5 0.03648997397857652 0.03648997397857652 1.6 0.1260474527734763 0.1260474527734763 1.7 0.208547874873494 0.208547874873494 1.8 0.2849914332938615 0.2849914332938615 1.9 0.3561841611640597 0.3561841611640596 2 0.4227843350984671 0.4227843350984672 R8_PSI_TEST Normal end of execution. R8VEC_DIFF_NORM_LI_TEST Python version: 3.6.5 R8VEC_DIFF_NORM_LI: L-infinity norm of the difference of two R8VEC's. Vector V1: 0: -5.63163 1: 9.12635 2: 6.59018 3: 1.23391 4: -1.69386 Vector V2: 0: -8.67763 1: -4.84844 2: -7.80086 3: -9.12342 4: 2.67931 L-Infinity norm of V1-V2: 14.391 R8VEC_DIFF_NORM_LI_TEST Normal end of execution. R8VEC_INDICATOR1_TEST Python version: 3.6.5 R8VEC_INDICATOR1 returns the 1-based indicator matrix. The 1-based indicator vector: 0: 1 1: 2 2: 3 3: 4 4: 5 5: 6 6: 7 7: 8 8: 9 9: 10 R8VEC_INDICATOR1_TEST Normal end of execution. R8VEC_LINSPACE_TEST Python version: 3.6.5 R8VEC_LINSPACE returns evenly spaced values between A and B. The linspace vector: 0: 10 1: 12.5 2: 15 3: 17.5 4: 20 R8VEC_LINSPACE_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_REVERSE_TEST Python version: 3.6.5 R8VEC_REVERSE reverses an R8VEC. Original array: 0: 1 1: 2 2: 3 3: 4 4: 5 Reversed array: 0: 5 1: 4 2: 3 3: 2 4: 1 R8VEC_REVERSE_TEST: Normal end of execution. R8VEC_UNIFORM_AB_TEST Python version: 3.6.5 R8VEC_UNIFORM_AB computes a random R8VEC. -1 <= X <= 5 Initial seed is 123456789 Random R8VEC: 0: 0.31051 1: 4.73791 2: 3.97706 3: 2.37017 4: 1.49184 5: -0.603288 6: 0.545467 7: -0.340259 8: -0.737026 9: 2.80379 R8VEC_UNIFORM_AB_TEST: Normal end of execution. BASHFORTH_SET_TEST Python version: 3.6.5 BASHFORTH_SET sets the abscissas and weights for an Adams-Bashforth quadrature rule. Order W X 1 1 -0 2 1.5 -0 -0.5 -1 3 1.91667 -0 -1.33333 -1 0.416667 -2 4 2.29167 -0 -2.45833 -1 1.54167 -2 -0.375 -3 5 2.64028 -0 -3.85278 -1 3.63333 -2 -1.76944 -3 0.348611 -4 6 2.97014 -0 -5.50208 -1 6.93194 -2 -5.06806 -3 1.99792 -4 -0.329861 -5 7 3.28573 -0 -7.39563 -1 11.6658 -2 -11.3799 -3 6.7318 -4 -2.22341 -5 0.315592 -6 8 3.58996 -0 -9.52521 -1 18.0545 -2 -22.0278 -3 17.3797 -4 -8.61213 -5 2.44516 -6 -0.304225 -7 9 3.88482 -0 -11.8842 -1 26.3108 -2 -38.5404 -3 38.0204 -4 -25.1247 -5 10.7015 -6 -2.66317 -7 0.294868 -8 10 4.1718 -0 -14.4669 -1 36.642 -2 -62.6463 -3 74.1793 -4 -61.2836 -5 34.8074 -6 -12.9943 -7 2.87765 -8 -0.286975 -9 BASHFORTH_SET_TEST: Normal end of execution. CHEBYSHEV_SET_TEST Python version: 3.6.5 CHEBYSHEV_SET sets a Chebyshev quadrature rule over [-1,1] Index X W 0 0 2 0 -0.5773502691896258 1 1 0.5773502691896258 1 0 -0.7071067811865475 0.6666666666666666 1 0 0.6666666666666666 2 0.7071067811865475 0.6666666666666666 0 -0.7946544722917661 0.5 1 -0.1875924740850799 0.5 2 0.1875924740850799 0.5 3 0.7946544722917661 0.5 0 -0.8324974870009819 0.4 1 -0.3745414095535811 0.4 2 0 0.4 3 0.3745414095535811 0.4 4 0.8324974870009819 0.4 0 -0.8662468181078206 0.3333333333333333 1 -0.4225186537611115 0.3333333333333333 2 -0.2666354015167047 0.3333333333333333 3 0.2666354015167047 0.3333333333333333 4 0.4225186537611115 0.3333333333333333 5 0.8662468181078206 0.3333333333333333 0 -0.883861700758049 0.2857142857142857 1 -0.5296567752851569 0.2857142857142857 2 -0.3239118105199076 0.2857142857142857 3 0 0.2857142857142857 4 0.3239118105199076 0.2857142857142857 5 0.5296567752851569 0.2857142857142857 6 0.883861700758049 0.2857142857142857 0 -0.9115893077284345 0.2222222222222222 1 -0.601018655380238 0.2222222222222222 2 -0.52876178305788 0.2222222222222222 3 -0.1679061842148039 0.2222222222222222 4 0 0.2222222222222222 5 0.1679061842148039 0.2222222222222222 6 0.52876178305788 0.2222222222222222 7 0.601018655380238 0.2222222222222222 8 0.9115893077284345 0.2222222222222222 CHEBYSHEV_SET_TEST: Normal end of execution. CHEBYSHEV1_COMPUTE_TEST Python version: 3.6.5 CHEBYSHEV1_COMPUTE computes a Chebyshev Type 1 quadrature rule over [-1,1]. Index X W 0 6.123233995736766e-17 3.141592653589793 0 -0.7071067811865475 1.570796326794897 1 0.7071067811865476 1.570796326794897 0 -0.8660254037844387 1.047197551196598 1 6.123233995736766e-17 1.047197551196598 2 0.8660254037844387 1.047197551196598 0 -0.9238795325112867 0.7853981633974483 1 -0.3826834323650897 0.7853981633974483 2 0.3826834323650898 0.7853981633974483 3 0.9238795325112867 0.7853981633974483 0 -0.9510565162951535 0.6283185307179586 1 -0.587785252292473 0.6283185307179586 2 6.123233995736766e-17 0.6283185307179586 3 0.5877852522924731 0.6283185307179586 4 0.9510565162951535 0.6283185307179586 0 -0.9659258262890682 0.5235987755982988 1 -0.7071067811865475 0.5235987755982988 2 -0.2588190451025206 0.5235987755982988 3 0.2588190451025207 0.5235987755982988 4 0.7071067811865476 0.5235987755982988 5 0.9659258262890683 0.5235987755982988 0 -0.9749279121818237 0.4487989505128276 1 -0.7818314824680295 0.4487989505128276 2 -0.4338837391175581 0.4487989505128276 3 6.123233995736766e-17 0.4487989505128276 4 0.4338837391175582 0.4487989505128276 5 0.7818314824680298 0.4487989505128276 6 0.9749279121818236 0.4487989505128276 0 -0.9807852804032304 0.3926990816987241 1 -0.8314696123025453 0.3926990816987241 2 -0.555570233019602 0.3926990816987241 3 -0.1950903220161282 0.3926990816987241 4 0.1950903220161283 0.3926990816987241 5 0.5555702330196023 0.3926990816987241 6 0.8314696123025452 0.3926990816987241 7 0.9807852804032304 0.3926990816987241 0 -0.984807753012208 0.3490658503988659 1 -0.8660254037844385 0.3490658503988659 2 -0.6427876096865394 0.3490658503988659 3 -0.3420201433256685 0.3490658503988659 4 6.123233995736766e-17 0.3490658503988659 5 0.3420201433256688 0.3490658503988659 6 0.6427876096865394 0.3490658503988659 7 0.8660254037844387 0.3490658503988659 8 0.984807753012208 0.3490658503988659 0 -0.9876883405951377 0.3141592653589793 1 -0.8910065241883678 0.3141592653589793 2 -0.7071067811865475 0.3141592653589793 3 -0.4539904997395467 0.3141592653589793 4 -0.1564344650402306 0.3141592653589793 5 0.1564344650402309 0.3141592653589793 6 0.4539904997395468 0.3141592653589793 7 0.7071067811865476 0.3141592653589793 8 0.8910065241883679 0.3141592653589793 9 0.9876883405951378 0.3141592653589793 CHEBYSHEV1_COMPUTE_TEST: Normal end of execution. CHEBYSHEV1_INTEGRAL_TEST Python version: 3.6.5 CHEBYSHEV1_INTEGRAL evaluates Integral ( -1 < x < +1 ) x^n / (1-x*x) dx N Value 0 3.141592653589793 1 0 2 1.570796326794897 3 0 4 1.178097245096172 5 0 6 0.9817477042468102 7 0 8 0.8590292412159591 9 0 10 0.7731263170943631 CHEBYSHEV1_INTEGRAL_TEST Normal end of execution. CHEBYSHEV1_SET_TEST Python version: 3.6.5 CHEBYSHEV1_SET sets a Chebyshev Type 1 quadrature rule over [-1,1] Index X W 0 0 3.141592653589793 0 -0.7071067811865475 1.570796326794897 1 0.7071067811865476 1.570796326794897 0 -0.8660254037844387 1.047197551196598 1 0 1.047197551196598 2 0.8660254037844387 1.047197551196598 0 -0.9238795325112867 0.7853981633974483 1 -0.3826834323650897 0.7853981633974483 2 0.3826834323650898 0.7853981633974483 3 0.9238795325112867 0.7853981633974483 0 -0.9510565162951535 0.6283185307179586 1 -0.587785252292473 0.6283185307179586 2 0 0.6283185307179586 3 0.5877852522924731 0.6283185307179586 4 0.9510565162951535 0.6283185307179586 0 -0.9659258262890682 0.5235987755982988 1 -0.7071067811865475 0.5235987755982988 2 -0.2588190451025206 0.5235987755982988 3 0.2588190451025207 0.5235987755982988 4 0.7071067811865476 0.5235987755982988 5 0.9659258262890683 0.5235987755982988 0 -0.9749279121818237 0.4487989505128276 1 -0.7818314824680295 0.4487989505128276 2 -0.4338837391175581 0.4487989505128276 3 0 0.4487989505128276 4 0.4338837391175582 0.4487989505128276 5 0.7818314824680298 0.4487989505128276 6 0.9749279121818236 0.4487989505128276 0 -0.9807852804032304 0.3926990816987241 1 -0.8314696123025453 0.3926990816987241 2 -0.555570233019602 0.3926990816987241 3 -0.1950903220161282 0.3926990816987241 4 0.1950903220161283 0.3926990816987241 5 0.5555702330196023 0.3926990816987241 6 0.8314696123025452 0.3926990816987241 7 0.9807852804032304 0.3926990816987241 0 -0.984807753012208 0.3490658503988659 1 -0.8660254037844385 0.3490658503988659 2 -0.6427876096865394 0.3490658503988659 3 -0.3420201433256688 0.3490658503988659 4 0 0.3490658503988659 5 0.3420201433256688 0.3490658503988659 6 0.6427876096865394 0.3490658503988659 7 0.8660254037844387 0.3490658503988659 8 0.984807753012208 0.3490658503988659 0 -0.9876883405951377 0.3141592653589793 1 -0.8910065241883678 0.3141592653589793 2 -0.7071067811865475 0.3141592653589793 3 -0.4539904997395467 0.3141592653589793 4 -0.1564344650402306 0.3141592653589793 5 0.1564344650402309 0.3141592653589793 6 0.4539904997395468 0.3141592653589793 7 0.7071067811865476 0.3141592653589793 8 0.8910065241883679 0.3141592653589793 9 0.9876883405951378 0.3141592653589793 CHEBYSHEV1_SET_TEST: Normal end of execution. CHEBYSHEV2_COMPUTE_TEST Python version: 3.6.5 CHEBYSHEV2_COMPUTE computes a Chebyshev Type 2 quadrature rule over [-1,1]. Index X W 0 6.123233995736766e-17 1.570796326794897 0 -0.4999999999999998 0.7853981633974484 1 0.5000000000000001 0.7853981633974481 0 -0.7071067811865475 0.3926990816987243 1 6.123233995736766e-17 0.7853981633974483 2 0.7071067811865476 0.392699081698724 0 -0.8090169943749473 0.2170787134227061 1 -0.3090169943749473 0.5683194499747424 2 0.3090169943749475 0.5683194499747423 3 0.8090169943749475 0.217078713422706 0 -0.8660254037844387 0.1308996938995747 1 -0.4999999999999998 0.3926990816987242 2 6.123233995736766e-17 0.5235987755982988 3 0.5000000000000001 0.392699081698724 4 0.8660254037844387 0.1308996938995747 0 -0.900968867902419 0.08448869089158863 1 -0.6234898018587335 0.2743330560697779 2 -0.2225209339563143 0.4265764164360819 3 0.2225209339563144 0.4265764164360819 4 0.6234898018587336 0.2743330560697778 5 0.9009688679024191 0.08448869089158857 0 -0.9238795325112867 0.05750944903191316 1 -0.7071067811865475 0.1963495408493621 2 -0.3826834323650897 0.335189632666811 3 6.123233995736766e-17 0.3926990816987241 4 0.3826834323650898 0.335189632666811 5 0.7071067811865476 0.196349540849362 6 0.9238795325112867 0.05750944903191313 0 -0.9396926207859083 0.04083294770910712 1 -0.7660444431189779 0.1442256007956728 2 -0.4999999999999998 0.2617993877991495 3 -0.1736481776669303 0.338540227093519 4 0.1736481776669304 0.338540227093519 5 0.5000000000000001 0.2617993877991494 6 0.766044443118978 0.1442256007956727 7 0.9396926207859084 0.04083294770910708 0 -0.9510565162951535 0.02999954037160818 1 -0.8090169943749473 0.108539356711353 2 -0.587785252292473 0.2056199086476263 3 -0.3090169943749473 0.2841597249873712 4 6.123233995736766e-17 0.3141592653589793 5 0.3090169943749475 0.2841597249873711 6 0.5877852522924731 0.2056199086476263 7 0.8090169943749475 0.108539356711353 8 0.9510565162951535 0.02999954037160816 0 -0.9594929736144974 0.02266894250185884 1 -0.8412535328311811 0.08347854093418908 2 -0.654860733945285 0.1631221774548166 3 -0.4154150130018863 0.2363135602034873 4 -0.142314838273285 0.2798149423030966 5 0.1423148382732851 0.2798149423030965 6 0.4154150130018864 0.2363135602034873 7 0.6548607339452851 0.1631221774548166 8 0.8412535328311812 0.08347854093418902 9 0.9594929736144974 0.02266894250185884 CHEBYSHEV2_COMPUTE_TEST: Normal end of execution. CHEBYSHEV2_INTEGRAL_TEST Python version: 3.6.5 CHEBYSHEV2_INTEGRAL evaluates Integral ( -1 < x < +1 ) x^n * (1-x*x) dx N Value 0 3.141592653589793 1 0 2 0.3926990816987241 3 0 4 0.03272492347489368 5 0 6 0.001917475984857051 7 0 8 8.590292412159592e-05 9 0 10 3.107021271759111e-06 CHEBYSHEV2_INTEGRAL_TEST Normal end of execution. CHEBYSHEV2_SET_TEST Python version: 3.6.5 CHEBYSHEV2_SET sets a Chebyshev Type 2 quadrature rule over [-1,1] Index X W 0 0 1.570796326794897 0 -0.5 0.7853981633974484 1 0.5 0.7853981633974481 0 -0.7071067811865475 0.3926990816987243 1 0 0.7853981633974483 2 0.7071067811865476 0.392699081698724 0 -0.8090169943749473 0.2170787134227061 1 -0.3090169943749473 0.5683194499747424 2 0.3090169943749475 0.5683194499747423 3 0.8090169943749475 0.217078713422706 0 -0.8660254037844387 0.1308996938995747 1 -0.5 0.3926990816987242 2 0 0.5235987755982988 3 0.5 0.392699081698724 4 0.8660254037844387 0.1308996938995747 0 -0.900968867902419 0.08448869089158863 1 -0.6234898018587335 0.2743330560697779 2 -0.2225209339563143 0.4265764164360819 3 0.2225209339563144 0.4265764164360819 4 0.6234898018587336 0.2743330560697778 5 0.9009688679024191 0.08448869089158857 0 -0.9238795325112867 0.05750944903191316 1 -0.7071067811865475 0.1963495408493621 2 -0.3826834323650897 0.335189632666811 3 0 0.3926990816987241 4 0.3826834323650898 0.335189632666811 5 0.7071067811865476 0.196349540849362 6 0.9238795325112867 0.05750944903191313 0 -0.9396926207859083 0.04083294770910712 1 -0.7660444431189779 0.1442256007956728 2 -0.5 0.2617993877991495 3 -0.1736481776669303 0.338540227093519 4 0.1736481776669304 0.338540227093519 5 0.5 0.2617993877991494 6 0.766044443118978 0.1442256007956727 7 0.9396926207859084 0.04083294770910708 0 -0.9510565162951535 0.02999954037160818 1 -0.8090169943749473 0.108539356711353 2 -0.587785252292473 0.2056199086476263 3 -0.3090169943749473 0.2841597249873712 4 0 0.3141592653589793 5 0.3090169943749475 0.2841597249873711 6 0.5877852522924731 0.2056199086476263 7 0.8090169943749475 0.108539356711353 8 0.9510565162951535 0.02999954037160816 0 -0.9594929736144974 0.02266894250185884 1 -0.8412535328311811 0.08347854093418908 2 -0.654860733945285 0.1631221774548166 3 -0.4154150130018863 0.2363135602034873 4 -0.142314838273285 0.2798149423030966 5 0.1423148382732851 0.2798149423030965 6 0.4154150130018864 0.2363135602034873 7 0.6548607339452851 0.1631221774548166 8 0.8412535328311812 0.08347854093418902 9 0.9594929736144974 0.02266894250185884 CHEBYSHEV2_SET_TEST: Normal end of execution. CHEBYSHEV3_COMPUTE_TEST Python version: 3.6.5 CHEBYSHEV3_COMPUTE computes a Chebyshev Type 3 quadrature rule over [-1,1]. Index X W 0 0 3.141592653589793 0 1 1.570796326794897 1 -1 1.570796326794897 0 1 0.7853981633974483 1 6.123233995736766e-17 1.570796326794897 2 -1 0.7853981633974483 0 1 0.5235987755982988 1 0.5000000000000001 1.047197551196598 2 -0.4999999999999998 1.047197551196598 3 -1 0.5235987755982988 0 1 0.3926990816987241 1 0.7071067811865476 0.7853981633974483 2 6.123233995736766e-17 0.7853981633974483 3 -0.7071067811865475 0.7853981633974483 4 -1 0.3926990816987241 0 1 0.3141592653589793 1 0.8090169943749475 0.6283185307179586 2 0.3090169943749475 0.6283185307179586 3 -0.3090169943749473 0.6283185307179586 4 -0.8090169943749473 0.6283185307179586 5 -1 0.3141592653589793 0 1 0.2617993877991494 1 0.8660254037844387 0.5235987755982988 2 0.5000000000000001 0.5235987755982988 3 6.123233995736766e-17 0.5235987755982988 4 -0.4999999999999998 0.5235987755982988 5 -0.8660254037844387 0.5235987755982988 6 -1 0.2617993877991494 0 1 0.2243994752564138 1 0.9009688679024191 0.4487989505128276 2 0.6234898018587336 0.4487989505128276 3 0.2225209339563144 0.4487989505128276 4 -0.2225209339563143 0.4487989505128276 5 -0.6234898018587335 0.4487989505128276 6 -0.900968867902419 0.4487989505128276 7 -1 0.2243994752564138 0 1 0.1963495408493621 1 0.9238795325112867 0.3926990816987241 2 0.7071067811865476 0.3926990816987241 3 0.3826834323650898 0.3926990816987241 4 6.123233995736766e-17 0.3926990816987241 5 -0.3826834323650897 0.3926990816987241 6 -0.7071067811865475 0.3926990816987241 7 -0.9238795325112867 0.3926990816987241 8 -1 0.1963495408493621 0 1 0.1745329251994329 1 0.9396926207859084 0.3490658503988659 2 0.766044443118978 0.3490658503988659 3 0.5000000000000001 0.3490658503988659 4 0.1736481776669304 0.3490658503988659 5 -0.1736481776669303 0.3490658503988659 6 -0.4999999999999998 0.3490658503988659 7 -0.7660444431189779 0.3490658503988659 8 -0.9396926207859083 0.3490658503988659 9 -1 0.1745329251994329 CHEBYSHEV3_COMPUTE_TEST: Normal end of execution. CHEBYSHEV3_INTEGRAL_TEST Python version: 3.6.5 CHEBYSHEV3_INTEGRAL evaluates Integral ( -1 < x < +1 ) x^n / (1-x*x) dx N Value 0 3.141592653589793 1 0 2 1.570796326794897 3 0 4 1.178097245096172 5 0 6 0.9817477042468102 7 0 8 0.8590292412159591 9 0 10 0.7731263170943631 CHEBYSHEV3_INTEGRAL_TEST Normal end of execution. CHEBYSHEV3_SET_TEST Python version: 3.6.5 CHEBYSHEV3_SET sets a Chebyshev Type 3 quadrature rule over [-1,1]. Index X W 0 0 3.141592653589793 0 -1 1.570796326794897 1 1 1.570796326794897 0 -1 0.7853981633974483 1 0 1.570796326794897 2 1 0.7853981633974483 0 -1 0.5235987755982988 1 -0.5 1.047197551196598 2 0.5 1.047197551196598 3 1 0.5235987755982988 0 -1 0.3926990816987241 1 -0.7071067811865475 0.7853981633974483 2 0 0.7853981633974483 3 0.7071067811865476 0.7853981633974483 4 1 0.3926990816987241 0 -1 0.3141592653589793 1 -0.8090169943749473 0.6283185307179586 2 -0.3090169943749473 0.6283185307179586 3 0.3090169943749475 0.6283185307179586 4 0.8090169943749475 0.6283185307179586 5 1 0.3141592653589793 0 -1 0.2617993877991494 1 -0.8660254037844387 0.5235987755982988 2 -0.5 0.5235987755982988 3 0 0.5235987755982988 4 0.5000000000000001 0.5235987755982988 5 0.8660254037844387 0.5235987755982988 6 1 0.2617993877991494 0 -1 0.2243994752564138 1 -0.900968867902419 0.4487989505128276 2 -0.6234898018587335 0.4487989505128276 3 -0.2225209339563143 0.4487989505128276 4 0.2225209339563144 0.4487989505128276 5 0.6234898018587336 0.4487989505128276 6 0.9009688679024191 0.4487989505128276 7 1 0.2243994752564138 0 -1 0.1963495408493621 1 -0.9238795325112867 0.3926990816987241 2 -0.7071067811865475 0.3926990816987241 3 -0.3826834323650897 0.3926990816987241 4 0 0.3926990816987241 5 0.3826834323650898 0.3926990816987241 6 0.7071067811865476 0.3926990816987241 7 0.9238795325112867 0.3926990816987241 8 1 0.1963495408493621 0 -1 0.1745329251994329 1 -0.9396926207859083 0.3490658503988659 2 -0.7660444431189779 0.3490658503988659 3 -0.5 0.3490658503988659 4 -0.1736481776669303 0.3490658503988659 5 0.1736481776669304 0.3490658503988659 6 0.5000000000000001 0.3490658503988659 7 0.766044443118978 0.3490658503988659 8 0.9396926207859084 0.3490658503988659 9 1 0.1745329251994329 CHEBYSHEV3_SET_TEST: Normal end of execution. CLENSHAW_CURTIS_COMPUTE_TEST Python version: 3.6.5 CLENSHAW_CURTIS_COMPUTE computes a Clenshaw-Curtis quadrature rule over [-1,1]. Index X W 0 0 2 0 -1 1 1 1 1 0 -1 0.3333333333333334 1 6.123233995736766e-17 1.333333333333333 2 1 0.3333333333333334 0 -1 0.1111111111111111 1 -0.4999999999999998 0.8888888888888892 2 0.5000000000000001 0.8888888888888888 3 1 0.1111111111111111 0 -1 0.06666666666666668 1 -0.7071067811865475 0.5333333333333334 2 6.123233995736766e-17 0.7999999999999999 3 0.7071067811865476 0.5333333333333333 4 1 0.06666666666666668 0 -1 0.04000000000000001 1 -0.8090169943749473 0.3607430412000113 2 -0.3090169943749473 0.5992569587999887 3 0.3090169943749475 0.5992569587999889 4 0.8090169943749475 0.3607430412000112 5 1 0.04000000000000001 0 -1 0.02857142857142858 1 -0.8660254037844387 0.2539682539682539 2 -0.4999999999999998 0.4571428571428573 3 6.123233995736766e-17 0.5206349206349206 4 0.5000000000000001 0.4571428571428571 5 0.8660254037844387 0.2539682539682539 6 1 0.02857142857142858 0 -1 0.02040816326530613 1 -0.900968867902419 0.1901410072182084 2 -0.6234898018587335 0.3522424237181591 3 -0.2225209339563143 0.4372084057983264 4 0.2225209339563144 0.4372084057983264 5 0.6234898018587336 0.3522424237181591 6 0.9009688679024191 0.1901410072182084 7 1 0.02040816326530613 0 -1 0.01587301587301588 1 -0.9238795325112867 0.1462186492160182 2 -0.7071067811865475 0.2793650793650794 3 -0.3826834323650897 0.3617178587204898 4 6.123233995736766e-17 0.3936507936507936 5 0.3826834323650898 0.3617178587204897 6 0.7071067811865476 0.2793650793650794 7 0.9238795325112867 0.1462186492160181 8 1 0.01587301587301588 0 -1 0.01234567901234569 1 -0.9396926207859083 0.1165674565720372 2 -0.7660444431189779 0.2252843233381044 3 -0.4999999999999998 0.3019400352733687 4 -0.1736481776669303 0.3438625058041442 5 0.1736481776669304 0.3438625058041442 6 0.5000000000000001 0.3019400352733685 7 0.766044443118978 0.2252843233381044 8 0.9396926207859084 0.1165674565720371 9 1 0.01234567901234569 CLENSHAW_CURTIS_COMPUTE_TEST: Normal end of execution. CLENSHAW_CURTIS_SET_TEST Python version: 3.6.5 CLENSHAW_CURTIS_SET sets up a Clenshaw Curtis quadrature rule over [-1,1]. Index X W 0 0 2 0 -1 1 1 1 1 0 -1 0.3333333333333333 1 0 1.333333333333333 2 1 0.3333333333333333 0 -1 0.1111111111111111 1 -0.5 0.8888888888888888 2 0.5 0.8888888888888888 3 1 0.1111111111111111 0 -1 0.06666666666666667 1 -0.7071067811865476 0.5333333333333333 2 0 0.8 3 0.7071067811865476 0.5333333333333333 4 1 0.06666666666666667 0 -1 0.04 1 -0.8090169943749475 0.3607430412000112 2 -0.3090169943749475 0.5992569587999887 3 0.3090169943749475 0.5992569587999887 4 0.8090169943749373 0.3607430412000112 5 1 0.04 0 -1 0.02857142857142857 1 -0.8660254037844386 0.253968253968254 2 -0.5 0.4571428571428571 3 0 0.5206349206349207 4 0.5 0.4571428571428571 5 0.8660254037844386 0.253968253968254 6 1 0.02857142857142857 0 -1 0.02040816326530612 1 -0.9009688679024191 0.1901410072182083 2 -0.6234898018587335 0.3522424237181591 3 -0.2225209339563144 0.4372084057983264 4 0.2225209339563144 0.4372084057983264 5 0.6234898018587335 0.3522424237181591 6 0.9009688679024191 0.1901410072182083 7 1 0.02040816326530612 0 -1 0.01587301587301587 1 -0.9238795325112867 0.1462186492160182 2 -0.7071067811865476 0.2793650793650794 3 -0.3826834323650898 0.3617178587204898 4 0 0.3936507936507936 5 0.3826834323650898 0.3617178587204898 6 0.7071067811865476 0.2793650793650794 7 0.9238795325112867 0.1462186492160182 8 1 0.01587301587301587 0 -1 0.01234567901234568 1 -0.9396926207859084 0.1165674565720371 2 -0.766044443118979 0.2252843233381044 3 -0.5 0.3019400352733686 4 -0.1736481776669304 0.3438625058041442 5 0.1736481776669304 0.3438625058041442 6 0.5 0.3019400352733686 7 0.766044443118979 0.2252843233381044 8 0.9396926207859084 0.1165674565720371 9 1 0.01234567901234568 CLENSHAW_CURTIS_SET_TEST: Normal end of execution. FEJER1_COMPUTE_TEST Python version: 3.6.5 FEJER1_COMPUTE computes the abscissas and weights of a Fejer type 1 quadrature rule. Order W X 1 2 6.12323e-17 2 1 -0.707107 1 0.707107 3 0.444444 -0.866025 1.11111 6.12323e-17 0.444444 0.866025 4 0.264298 -0.92388 0.735702 -0.382683 0.735702 0.382683 0.264298 0.92388 5 0.167781 -0.951057 0.525552 -0.587785 0.613333 6.12323e-17 0.525552 0.587785 0.167781 0.951057 6 0.118661 -0.965926 0.377778 -0.707107 0.503561 -0.258819 0.503561 0.258819 0.377778 0.707107 0.118661 0.965926 7 0.0867162 -0.974928 0.287831 -0.781831 0.398242 -0.433884 0.454422 6.12323e-17 0.398242 0.433884 0.287831 0.781831 0.0867162 0.974928 8 0.0669829 -0.980785 0.222988 -0.83147 0.324153 -0.55557 0.385877 -0.19509 0.385877 0.19509 0.324153 0.55557 0.222988 0.83147 0.0669829 0.980785 9 0.0527366 -0.984808 0.179189 -0.866025 0.264037 -0.642788 0.330845 -0.34202 0.346384 6.12323e-17 0.330845 0.34202 0.264037 0.642788 0.179189 0.866025 0.0527366 0.984808 10 0.0429391 -0.987688 0.145875 -0.891007 0.220317 -0.707107 0.280879 -0.45399 0.309989 -0.156434 0.309989 0.156434 0.280879 0.45399 0.220317 0.707107 0.145875 0.891007 0.0429391 0.987688 FEJER1_COMPUTE_TEST: Normal end of execution. FEJER1_SET_TEST Python version: 3.6.5 FEJER1_SET sets the abscissas and weights of a Fejer type 1 quadrature rule. Order W X 1 2 0 2 1 -0.707107 1 0.707107 3 0.444444 -0.866025 1.11111 0 0.444444 0.866025 4 0.264298 -0.92388 0.735702 -0.382683 0.735702 0.382683 0.264298 0.92388 5 0.167781 -0.951057 0.525552 -0.587785 0.613333 0 0.525552 0.587785 0.167781 0.951057 6 0.118661 -0.965926 0.377778 -0.707107 0.503561 -0.258819 0.503561 0.258819 0.377778 0.707107 0.118661 0.965926 7 0.0867162 -0.974928 0.287831 -0.781831 0.398242 -0.433884 0.454422 0 0.398242 0.433884 0.287831 0.781831 0.0867162 0.974928 8 0.0669829 -0.980785 0.222988 -0.83147 0.324153 -0.55557 0.385877 -0.19509 0.385877 0.19509 0.324153 0.55557 0.222988 0.83147 0.0669829 0.980785 9 0.0527366 -0.984808 0.179189 -0.866025 0.264037 -0.642788 0.330845 -0.34202 0.346384 0 0.330845 0.34202 0.264037 0.642788 0.179189 0.866025 0.0527366 0.984808 10 0.0429391 -0.987688 0.145875 -0.891007 0.220317 -0.707107 0.280879 -0.45399 0.309989 -0.156434 0.309989 0.156434 0.280879 0.45399 0.220317 0.707107 0.145875 0.891007 0.0429391 0.987688 FEJER1_SET_TEST: Normal end of execution. FEJER2_COMPUTE_TEST Python version: 3.6.5 FEJER2_COMPUTE computes the abscissas and weights of a Fejer type 2 quadrature rule. Order W X 1 2 0 2 1 -0.5 1 0.5 3 0.666667 -0.707107 0.666667 6.12323e-17 0.666667 0.707107 4 0.425464 -0.809017 0.574536 -0.309017 0.574536 0.309017 0.425464 0.809017 5 0.311111 -0.866025 0.4 -0.5 0.577778 6.12323e-17 0.4 0.5 0.311111 0.866025 6 0.226915 -0.900969 0.326794 -0.62349 0.446291 -0.222521 0.446291 0.222521 0.326794 0.62349 0.226915 0.900969 7 0.177965 -0.92388 0.247619 -0.707107 0.393464 -0.382683 0.361905 6.12323e-17 0.393464 0.382683 0.247619 0.707107 0.177965 0.92388 8 0.13977 -0.939693 0.20637 -0.766044 0.314286 -0.5 0.339575 -0.173648 0.339575 0.173648 0.314286 0.5 0.20637 0.766044 0.13977 0.939693 9 0.114781 -0.951057 0.165433 -0.809017 0.27379 -0.587785 0.279011 -0.309017 0.333968 6.12323e-17 0.279011 0.309017 0.27379 0.587785 0.165433 0.809017 0.114781 0.951057 10 0.0944195 -0.959493 0.141135 -0.841254 0.226387 -0.654861 0.253051 -0.415415 0.285007 -0.142315 0.285007 0.142315 0.253051 0.415415 0.226387 0.654861 0.141135 0.841254 0.0944195 0.959493 FEJER2_COMPUTE_TEST: Normal end of execution. FEJER2_SET_TEST Python version: 3.6.5 FEJER2_SET sets the abscissas and weights of a Fejer type 2 quadrature rule. Order W X 1 2 0 2 1 -0.5 1 0.5 3 0.666667 -0.707107 0.666667 0 0.666667 0.707107 4 0.425464 -0.809017 0.574536 -0.309017 0.574536 0.309017 0.425464 0.809017 5 0.311111 -0.866025 0.4 -0.5 0.577778 0 0.4 0.5 0.311111 0.866025 6 0.226915 -0.900969 0.326794 -0.62349 0.446291 -0.222521 0.446291 0.222521 0.326794 0.62349 0.226915 0.900969 7 0.177965 -0.92388 0.247619 -0.707107 0.393464 -0.382683 0.361905 0 0.393464 0.382683 0.247619 0.707107 0.177965 0.92388 8 0.13977 -0.939693 0.20637 -0.766044 0.314286 -0.5 0.339575 -0.173648 0.339575 0.173648 0.314286 0.5 0.20637 0.766044 0.13977 0.939693 9 0.114781 -0.951057 0.165433 -0.809017 0.27379 -0.587785 0.279011 -0.309017 0.333968 0 0.279011 0.309017 0.27379 0.587785 0.165433 0.809017 0.114781 0.951057 10 0.0944195 -0.959493 0.141135 -0.841254 0.226387 -0.654861 0.253051 -0.415415 0.285007 -0.142315 0.285007 0.142315 0.253051 0.415415 0.226387 0.654861 0.141135 0.841254 0.0944195 0.959493 FEJER2_SET_TEST: Normal end of execution. GEGENBAUER_INTEGRAL_TEST Python version: 3.6.5 GEGENBAUER_INTEGRAL evaluates Integral ( -1 < x < +1 ) x^n * (1-x*x)^alpha dx N Value 0 1.748038369528081 1 0 2 0.4994395341508805 3 0 4 0.2724215640822983 5 0 6 0.1816143760548655 7 0 8 0.133821119198322 9 0 10 0.1047295715465127 GEGENBAUER_INTEGRAL_TEST Normal end of execution. GEGENBAUER_SS_COMPUTE_TEST Python version: 3.6.5 GEGENBAUER_SS_COMPUTE computes Gauss-Gegenbauer rules; Abscissas and weights for a generalized Gauss Gegenbauer rule with ALPHA = 0.5 # W X 0 1.570796326794897 0 0 0.7853981633974484 -0.5 1 0.7853981633974484 0.5 0 0.3926990816987239 -0.7071067811865475 1 0.7853981633974484 0 2 0.3926990816987239 0.7071067811865475 0 0.217078713422706 -0.8090169943749475 1 0.5683194499747424 -0.3090169943749475 2 0.5683194499747424 0.3090169943749474 3 0.217078713422706 0.8090169943749475 0 0.130899693899574 -0.8660254037844387 1 0.3926990816987242 -0.5 2 0.5235987755982989 0 3 0.3926990816987242 0.5 4 0.130899693899575 0.8660254037844387 0 0.08448869089158841 -0.9009688679024191 1 0.2743330560697777 -0.6234898018587335 2 0.4265764164360819 -0.2225209339563144 3 0.4265764164360819 0.2225209339563144 4 0.2743330560697777 0.6234898018587335 5 0.08448869089158884 0.900968867902419 0 0.05750944903191331 -0.9238795325112867 1 0.1963495408493619 -0.7071067811865475 2 0.3351896326668111 -0.3826834323650898 3 0.3926990816987242 0 4 0.3351896326668108 0.3826834323650898 5 0.1963495408493624 0.7071067811865476 6 0.05750944903191331 0.9238795325112867 0 0.04083294770910693 -0.9396926207859084 1 0.1442256007956728 -0.766044443118978 2 0.2617993877991495 -0.5 3 0.3385402270935191 -0.1736481776669303 4 0.3385402270935191 0.1736481776669303 5 0.2617993877991495 0.5 6 0.1442256007956728 0.766044443118978 7 0.04083294770910754 0.9396926207859084 0 0.02999954037160841 -0.9510565162951536 1 0.108539356711353 -0.8090169943749475 2 0.2056199086476264 -0.5877852522924731 3 0.2841597249873712 -0.3090169943749475 4 0.3141592653589794 0 5 0.2841597249873712 0.3090169943749475 6 0.2056199086476264 0.5877852522924731 7 0.108539356711353 0.8090169943749475 8 0.02999954037160841 0.9510565162951536 0 0.02266894250185901 -0.9594929736144974 1 0.08347854093418892 -0.8412535328311812 2 0.1631221774548165 -0.6548607339452851 3 0.2363135602034873 -0.4154150130018864 4 0.2798149423030965 -0.1423148382732851 5 0.2798149423030966 0.1423148382732851 6 0.2363135602034873 0.4154150130018864 7 0.1631221774548165 0.6548607339452851 8 0.08347854093418892 0.8412535328311812 9 0.02266894250185901 0.9594929736144974 GEGENBAUER_SS_COMPUTE_TEST: Normal end of execution. GEN_HERMITE_EK_COMPUTE_TEST Python version: 3.6.5 GEN_HERMITE_EK_COMPUTE computes a generalized Hermite quadrature rule using the Elhay-Kautsky algorithm. Using ALPHA = 0.5 Index X W 0 0 1.225416702465178 0 -0.8660254037844385 0.6127083512325888 1 0.8660254037844385 0.6127083512325888 0 -1.322875655532295 0.262589293385395 1 0 0.7002381156943873 2 1.322875655532295 0.2625892933853951 0 -1.752961966367865 0.07477218653431648 1 -0.6535475074298001 0.5379361646982723 2 0.6535475074297997 0.5379361646982722 3 1.752961966367866 0.07477218653431648 0 -2.099598150879758 0.02069085274024055 1 -1.044838554429487 0.3373854564216626 2 0 0.5092640841413727 3 1.044838554429487 0.3373854564216618 4 2.099598150879757 0.02069085274024059 0 -2.431196006814872 0.004758432285876828 1 -1.428264330850234 0.1432946705182552 2 -0.5471261076464521 0.4646552484284566 3 0.5471261076464519 0.4646552484284565 4 1.428264330850234 0.1432946705182554 5 2.431196006814872 0.004758432285876804 0 -2.719880088556293 0.001106289401968463 1 -1.747360778896521 0.05564733125066081 2 -0.8938582730216026 0.3522490969234104 3 0 0.4074112673130981 4 0.8938582730216028 0.3522490969234111 5 1.747360778896521 0.05564733125066098 6 2.719880088556293 0.00110628940196846 0 -2.999078968343316 0.0002288084584739164 1 -2.057439418477468 0.01787577463926721 2 -1.241738340943189 0.1866121206001918 3 -0.4801606747408059 0.4079916475346562 4 0.4801606747408056 0.4079916475346565 5 1.241738340943189 0.1866121206001918 6 2.057439418477468 0.01787577463926723 7 2.999078968343316 0.0002288084584739132 0 -3.251152326134132 4.824428349517108e-05 1 -2.331322119300714 0.005575754103643737 2 -1.537416408684744 0.08875797489986054 3 -0.7945417010067838 0.3467847917084952 4 0 0.343083172474188 5 0.794541701006784 0.3467847917084949 6 1.537416408684744 0.08875797489986068 7 2.331322119300714 0.005575754103643735 8 3.251152326134132 4.824428349517049e-05 0 -3.496605880747676 9.347334083394586e-06 1 -2.598397149544623 0.00153635644240256 2 -1.827991812365274 0.03517634314374584 3 -1.114905370566644 0.2117439807373517 4 -0.4330259998733383 0.3642423235750059 5 0.4330259998733384 0.3642423235750052 6 1.114905370566644 0.2117439807373521 7 1.827991812365275 0.03517634314374578 8 2.598397149544622 0.001536356442402556 9 3.496605880747678 9.347334083394711e-06 GEN_HERMITE_EK_COMPUTE_TEST: Normal end of execution. GEN_HERMITE_INTEGRAL_TEST Python version: 3.6.5 GEN_HERMITE_INTEGRAL evaluates Integral ( -oo < x < +oo ) exp(-x^2) x^n |x|^alpha dx Use ALPHA = 0.5 N Value 0 1.225416702465178 1 0 2 0.9190625268488832 3 0 4 1.608359421985546 5 0 6 4.422988410460251 7 0 8 16.58620653922594 9 0 10 78.78448106132322 GEN_HERMITE_INTEGRAL_TEST Normal end of execution. GEN_LAGUERRE_EK_COMPUTE_TEST Python version: 3.6.5 GEN_LAGUERRE_EK_COMPUTE computes a generalized Laguerre quadrature rule using the Elhay-Kautsky algorithm. Using ALPHA = 0.5 Index X W 0 1.5 0.8862269254527581 0 0.9188611699158102 0.7233630235462758 1 4.081138830084189 0.1628639019064827 0 0.6663259077023709 0.5671862778403113 1 2.800775054150256 0.305371768844547 2 7.032899038147373 0.01366887876790015 0 0.5235260767382689 0.4530087465586076 1 2.156648763269093 0.3816169601718002 2 5.137387546176711 0.05079462757224079 3 10.18243761381592 0.000806591150110032 0 0.4313988071478517 0.3704505700074587 1 1.759753698423697 0.4125843737694528 2 4.104465362828316 0.0977798200531807 3 7.746703779542557 0.005373415341171986 4 13.45767835205758 3.874628149393569e-05 0 0.3669498773083711 0.3094240968362605 1 1.488534292310453 0.417752149707022 2 3.434007968424071 0.1432858732209769 3 6.349067925680377 0.01533249102263385 4 10.54046985844834 0.0004306911960439421 5 16.82097007782838 1.623469821074069e-06 0 0.3193036339206303 0.263124514395892 1 1.290758622959153 0.409141869414102 2 2.958374458696649 0.1821177320927161 3 5.409031597244431 0.03005332430127097 4 8.804079578056783 0.001760894117540059 5 13.46853574325147 2.852947122115979e-05 6 20.24991636587088 6.166001541039125e-08 0 0.2826336481165994 0.227139361952472 1 1.139873801581615 0.3935945428036152 2 2.60152484340603 0.2129089708672277 3 4.724114537527792 0.0478774832031381 4 7.605256299231612 0.004542517474762657 5 11.41718207654583 0.0001624046001853259 6 16.49941079765582 1.642377413806098e-06 7 23.7300039959347 2.173943126630926e-09 0 0.2535325549744195 0.1985712548680197 1 1.02084427772039 0.3749207846631712 2 2.323096077022467 0.236074821000825 3 4.199350600657291 0.06709610500320433 4 6.713974316615028 0.009008508896644349 5 9.972009159539351 0.0005426607386359309 6 14.15405367127805 1.270536687910845e-05 7 19.61190281916595 8.484309239668572e-08 8 27.25123652302705 7.22864716439652e-11 0 0.2298729805186557 0.1754708150466604 1 0.9244815469866583 0.3552233888020722 2 2.099410462708799 0.2526835596756778 3 3.782880873707291 0.0863561026953325 4 6.019918027701461 0.01510977803486088 5 8.88034759799671 0.001328215628363561 6 12.47483240483621 5.418780021170328e-05 7 16.99084729354255 8.737475869187144e-07 8 22.79100289494894 4.01969988693978e-09 9 30.80640591705273 2.2922215302047e-12 GEN_LAGUERRE_EK_COMPUTE_TEST: Normal end of execution. GEN_LAGUERRE_INTEGRAL_TEST Python version: 3.6.5 GEN_LAGUERRE_INTEGRAL evaluates Integral ( 0 < x < +oo ) exp(-x) x^n x^alpha dx Use ALPHA = 0.5 N Value 0 0.8862269254527581 1 1.329340388179137 2 3.323350970447843 3 11.63172839656745 4 52.34277778455353 5 287.8852778150444 6 1871.254305797788 7 14034.40729348341 8 119292.461994609 9 1133278.388948786 10 11899423.08396225 GEN_LAGUERRE_INTEGRAL_TEST Normal end of execution. HERMITE_EK_COMPUTE_TEST Python version: 3.6.5 HERMITE_EK_COMPUTE computes a Hermite quadrature rule using the Elhay-Kautsky algorithm. Index X W 0 0 1.772453850905516 0 -0.7071067811865475 0.8862269254527578 1 0.7071067811865475 0.8862269254527578 0 -1.224744871391589 0.2954089751509195 1 0 1.181635900603677 2 1.224744871391589 0.2954089751509192 0 -1.650680123885784 0.0813128354472452 1 -0.5246476232752902 0.8049140900055129 2 0.5246476232752905 0.8049140900055127 3 1.650680123885784 0.0813128354472453 0 -2.020182870456086 0.01995324205904592 1 -0.9585724646138184 0.3936193231522413 2 0 0.9453087204829423 3 0.9585724646138184 0.3936193231522407 4 2.020182870456086 0.01995324205904592 0 -2.350604973674492 0.00453000990550884 1 -1.335849074013697 0.1570673203228568 2 -0.4360774119276161 0.7246295952243927 3 0.4360774119276162 0.7246295952243929 4 1.335849074013697 0.1570673203228564 5 2.350604973674492 0.004530009905508842 0 -2.651961356835233 0.0009717812450995198 1 -1.673551628767471 0.05451558281912718 2 -0.8162878828589647 0.425607252610128 3 0 0.810264617556807 4 0.8162878828589646 0.4256072526101278 5 1.673551628767472 0.05451558281912701 6 2.651961356835232 0.0009717812450995181 0 -2.930637420257241 0.000199604072211368 1 -1.981656756695844 0.01707798300741351 2 -1.15719371244678 0.2078023258148917 3 -0.3811869902073222 0.6611470125582416 4 0.3811869902073224 0.6611470125582413 5 1.157193712446781 0.2078023258148918 6 1.981656756695843 0.0170779830074135 7 2.930637420257244 0.0001996040722113682 0 -3.190993201781527 3.960697726326435e-05 1 -2.266580584531841 0.004943624275536949 2 -1.468553289216668 0.08847452739437661 3 -0.7235510187528373 0.4326515590025557 4 0 0.7202352156060514 5 0.7235510187528374 0.4326515590025553 6 1.468553289216667 0.08847452739437671 7 2.266580584531842 0.004943624275536965 8 3.190993201781528 3.96069772632642e-05 0 -3.436159118837737 7.640432855232626e-06 1 -2.532731674232791 0.001343645746781242 2 -1.756683649299881 0.03387439445548108 3 -1.036610829789514 0.2401386110823153 4 -0.3429013272237044 0.6108626337353246 5 0.3429013272237046 0.610862633735326 6 1.036610829789513 0.2401386110823147 7 1.756683649299881 0.03387439445548109 8 2.53273167423279 0.001343645746781238 9 3.436159118837737 7.640432855232587e-06 HERMITE_EK_COMPUTE_TEST: Normal end of execution. HERMITE_INTEGRAL_TEST Python version: 3.6.5 HERMITE_INTEGRAL evaluates Integral ( -oo < x < +oo ) exp(-x^2) x^m dx N Value 0 1.772453850905516 1 0 2 0.8862269254527579 3 0 4 1.329340388179137 5 0 6 3.323350970447842 7 0 8 11.63172839656745 9 0 10 52.34277778455352 HERMITE_INTEGRAL_TEST Normal end of execution. HERMITE_SET_TEST Python version: 3.6.5 HERMITE_SET sets a Hermite quadrature rule over (-oo,+oo). Index X W 0 0 1.772453850905516 0 -0.7071067811865476 0.8862269254527581 1 0.7071067811865476 0.8862269254527581 0 -1.224744871391589 0.2954089751509194 1 0 1.181635900603677 2 1.224744871391589 0.2954089751509194 0 -1.650680123885784 0.08131283544724517 1 -0.5246476232752904 0.8049140900055128 2 0.5246476232752904 0.8049140900055128 3 1.650680123885784 0.08131283544724517 0 -2.020182870456086 0.01995324205904591 1 -0.9585724646138185 0.3936193231522412 2 0 0.9453087204829419 3 0.9585724646138185 0.3936193231522412 4 2.020182870456086 0.01995324205904591 0 -2.350604973674492 0.004530009905508846 1 -1.335849074013697 0.1570673203228566 2 -0.4360774119276165 0.7246295952243925 3 0.4360774119276165 0.7246295952243925 4 1.335849074013697 0.1570673203228566 5 2.350604973674492 0.004530009905508846 0 -2.651961356835233 0.0009717812450995191 1 -1.673551628767471 0.05451558281912703 2 -0.8162878828589647 0.4256072526101278 3 0 0.8102646175568073 4 0.8162878828589647 0.4256072526101278 5 1.673551628767471 0.05451558281912703 6 2.651961356835233 0.0009717812450995191 0 -2.930637420257244 0.0001996040722113676 1 -1.981656756695843 0.01707798300741347 2 -1.15719371244678 0.2078023258148919 3 -0.3811869902073221 0.6611470125582413 4 0.3811869902073221 0.6611470125582413 5 1.15719371244678 0.2078023258148919 6 1.981656756695843 0.01707798300741347 7 2.930637420257244 0.0001996040722113676 0 -3.190993201781528 3.960697726326439e-05 1 -2.266580584531843 0.004943624275536947 2 -1.468553289216668 0.08847452739437657 3 -0.7235510187528376 0.4326515590025558 4 0 0.720235215606051 5 0.7235510187528376 0.4326515590025558 6 1.468553289216668 0.08847452739437657 7 2.266580584531843 0.004943624275536947 8 3.190993201781528 3.960697726326439e-05 0 -3.436159118837737 7.640432855232621e-06 1 -2.53273167423279 0.001343645746781233 2 -1.756683649299882 0.03387439445548106 3 -1.036610829789514 0.2401386110823147 4 -0.3429013272237046 0.6108626337353258 5 0.3429013272237046 0.6108626337353258 6 1.036610829789514 0.2401386110823147 7 1.756683649299882 0.03387439445548106 8 2.53273167423279 0.001343645746781233 9 3.436159118837737 7.640432855232621e-06 HERMITE_SET_TEST: Normal end of execution. HERMITE_GK16_SET_TEST Python version: 3.6.5 HERMITE_GK16_SET sets up a nested rule for the Hermite integration problem. Index X W 0 0 1.772453850905516 0 -1.224744871391589 0.2954089751509193 1 0 1.181635900603677 2 1.224744871391589 0.2954089751509193 0 -2.959210779063838 0.001233068065515345 1 -1.224744871391589 0.2455792853503139 2 -0.5240335474869576 0.232862517873861 3 0 0.813104108326135 4 0.5240335474869576 0.232862517873861 5 1.224744871391589 0.2455792853503139 6 2.959210779063838 0.001233068065515345 0 -2.959210779063838 0.0001670882630688235 1 -2.023230191100516 0.0141731178739791 2 -1.224744871391589 0.1681189289476777 3 -0.5240335474869576 0.4786942854911412 4 0 0.450147009753782 5 0.5240335474869576 0.4786942854911412 6 1.224744871391589 0.1681189289476777 7 2.023230191100516 0.0141731178739791 8 2.959210779063838 0.0001670882630688235 0 -4.499599398310388 3.746346994305176e-08 1 -3.667774215946338 -1.454284338706939e-06 2 -2.959210779063838 0.0001872381894927835 3 -2.023230191100516 0.01246651913280592 4 -1.835707975175187 0.00348407193468038 5 -1.224744871391589 0.1571829837665224 6 -0.8700408953529029 0.02515582570171293 7 -0.5240335474869576 0.4511980360235854 8 0 0.4731073350496539 9 0.5240335474869576 0.4511980360235854 10 0.8700408953529029 0.02515582570171293 11 1.224744871391589 0.1571829837665224 12 1.835707975175187 0.00348407193468038 13 2.023230191100516 0.01246651913280592 14 2.959210779063838 0.0001872381894927835 15 3.667774215946338 -1.454284338706939e-06 16 4.499599398310388 3.746346994305176e-08 0 -4.499599398310388 1.529571770532236e-09 1 -3.667774215946338 1.080276720662476e-06 2 -2.959210779063838 0.0001065658977285227 3 -2.266513262056788 0.005113317439088385 4 -2.023230191100516 -0.01123243848906923 5 -1.835707975175187 0.03205524309944588 6 -1.224744871391589 0.1136072989574827 7 -0.8700408953529029 0.1083886195500302 8 -0.5240335474869576 0.3692464336892085 9 0 0.5378816070051017 10 0.5240335474869576 0.3692464336892085 11 0.8700408953529029 0.1083886195500302 12 1.224744871391589 0.1136072989574827 13 1.835707975175187 0.03205524309944588 14 2.023230191100516 -0.01123243848906923 15 2.266513262056788 0.005113317439088385 16 2.959210779063838 0.0001065658977285227 17 3.667774215946338 1.080276720662476e-06 18 4.499599398310388 1.529571770532236e-09 0 -6.375939270982236 2.236564560704446e-15 1 -5.643257857885745 -2.630469645854894e-13 2 -5.036089944473094 9.067528823167982e-12 3 -4.499599398310388 1.405525202472248e-09 4 -3.667774215946338 1.088921969212812e-06 5 -2.959210779063838 0.0001054166239474666 6 -2.570558376584297 2.666515977893943e-05 7 -2.266513262056788 0.004838520820550261 8 -2.023230191100516 -0.009856627043461002 9 -1.835707975175187 0.02940942758035079 10 -1.579412134846767 0.003121021035268283 11 -1.224744871391589 0.1093932507186088 12 -0.8700408953529029 0.1159493098485312 13 -0.5240335474869576 0.3539388902958054 14 -0.1760641420820089 0.04985576189329316 15 0 0.4588883963675675 16 0.1760641420820089 0.04985576189329316 17 0.5240335474869576 0.3539388902958054 18 0.8700408953529029 0.1159493098485312 19 1.224744871391589 0.1093932507186088 20 1.579412134846767 0.003121021035268283 21 1.835707975175187 0.02940942758035079 22 2.023230191100516 -0.009856627043461002 23 2.266513262056788 0.004838520820550261 24 2.570558376584297 2.666515977893943e-05 25 2.959210779063838 0.0001054166239474666 26 3.667774215946338 1.088921969212812e-06 27 4.499599398310388 1.405525202472248e-09 28 5.036089944473094 9.067528823167982e-12 29 5.643257857885745 -2.630469645854894e-13 30 6.375939270982236 2.236564560704446e-15 0 -6.375939270982236 -1.76029328053725e-15 1 -5.643257857885745 4.721927866641769e-13 2 -5.036089944473094 -3.428157053034956e-11 3 -4.499599398310388 2.75478251389359e-09 4 -4.029220140504371 -2.390334338280351e-08 5 -3.667774215946338 1.224522096715844e-06 6 -2.959210779063838 9.871000919740917e-05 7 -2.570558376584297 0.0001475320490186277 8 -2.266513262056788 0.003758002660430479 9 -2.023230191100516 -0.004911857612387755 10 -1.835707975175187 0.0204350583591072 11 -1.579412134846767 0.01303287269902796 12 -1.224744871391589 0.09691344494458362 13 -0.8700408953529029 0.1372652119156755 14 -0.5240335474869576 0.3120865619469745 15 -0.1760641420820089 0.1841169604772579 16 0 0.2465664493282962 17 0.1760641420820089 0.1841169604772579 18 0.5240335474869576 0.3120865619469745 19 0.8700408953529029 0.1372652119156755 20 1.224744871391589 0.09691344494458362 21 1.579412134846767 0.01303287269902796 22 1.835707975175187 0.0204350583591072 23 2.023230191100516 -0.004911857612387755 24 2.266513262056788 0.003758002660430479 25 2.570558376584297 0.0001475320490186277 26 2.959210779063838 9.871000919740917e-05 27 3.667774215946338 1.224522096715844e-06 28 4.029220140504371 -2.390334338280351e-08 29 4.499599398310388 2.75478251389359e-09 30 5.036089944473094 -3.428157053034956e-11 31 5.643257857885745 4.721927866641769e-13 32 6.375939270982236 -1.76029328053725e-15 0 -6.375939270982236 1.86840148945106e-18 1 -5.643257857885745 9.659946627856324e-15 2 -5.036089944473094 5.489683694849946e-12 3 -4.499599398310388 8.15537218169169e-10 4 -4.029220140504371 3.792022239231953e-08 5 -3.667774215946338 4.373781804092699e-07 6 -3.349163953713195 4.846279973702046e-06 7 -2.959210779063838 6.332862080561789e-05 8 -2.570558376584297 0.0004878539930444377 9 -2.266513262056788 0.00145155804251559 10 -2.023230191100516 0.004096752772034405 11 -1.835707975175187 0.005592882891146918 12 -1.579412134846767 0.0277805089085351 13 -1.224744871391589 0.08024551814739089 14 -0.8700408953529029 0.163712215557358 15 -0.5240335474869576 0.2624487148878428 16 -0.1760641420820089 0.3398859558558522 17 0 0.0009126267536373792 18 0.1760641420820089 0.3398859558558522 19 0.5240335474869576 0.2624487148878428 20 0.8700408953529029 0.163712215557358 21 1.224744871391589 0.08024551814739089 22 1.579412134846767 0.0277805089085351 23 1.835707975175187 0.005592882891146918 24 2.023230191100516 0.004096752772034405 25 2.266513262056788 0.00145155804251559 26 2.570558376584297 0.0004878539930444377 27 2.959210779063838 6.332862080561789e-05 28 3.349163953713195 4.846279973702046e-06 29 3.667774215946338 4.373781804092699e-07 30 4.029220140504371 3.792022239231953e-08 31 4.499599398310388 8.15537218169169e-10 32 5.036089944473094 5.489683694849946e-12 33 5.643257857885745 9.659946627856324e-15 34 6.375939270982236 1.86840148945106e-18 HERMITE_GK16_SET_TEST: Normal end of execution. HERMITE_GK18_SET_TEST Python version: 3.6.5 HERMITE_GK18_SET sets up a nested rule for the Hermite integration problem. Index X W 0 0 1.772453850905516 0 -1.224744871391589 0.2954089751509193 1 0 1.181635900603677 2 1.224744871391589 0.2954089751509193 0 -2.959210779063838 0.0001670882630688235 1 -2.023230191100516 0.0141731178739791 2 -1.224744871391589 0.1681189289476777 3 -0.5240335474869576 0.4786942854911412 4 0 0.450147009753782 5 0.5240335474869576 0.4786942854911412 6 1.224744871391589 0.1681189289476777 7 2.023230191100516 0.0141731178739791 8 2.959210779063838 0.0001670882630688235 0 -4.499599398310388 1.529571770532236e-09 1 -3.667774215946338 1.080276720662476e-06 2 -2.959210779063838 0.0001065658977285227 3 -2.266513262056788 0.005113317439088385 4 -2.023230191100516 -0.01123243848906923 5 -1.835707975175187 0.03205524309944588 6 -1.224744871391589 0.1136072989574827 7 -0.8700408953529029 0.1083886195500302 8 -0.5240335474869576 0.3692464336892085 9 0 0.5378816070051017 10 0.5240335474869576 0.3692464336892085 11 0.8700408953529029 0.1083886195500302 12 1.224744871391589 0.1136072989574827 13 1.835707975175187 0.03205524309944588 14 2.023230191100516 -0.01123243848906923 15 2.266513262056788 0.005113317439088385 16 2.959210779063838 0.0001065658977285227 17 3.667774215946338 1.080276720662476e-06 18 4.499599398310388 1.529571770532236e-09 0 -6.853200069757519 1.90303509401305e-21 1 -6.124527854622158 1.87781893143729e-17 2 -5.52186520986835 1.822427515491294e-14 3 -4.986551454150765 4.566176367618686e-12 4 -4.499599398310388 4.22525843963111e-10 5 -4.057956316089741 1.659544880938982e-08 6 -3.667774215946338 2.959075202307441e-07 7 -3.31558461759329 3.309758709792034e-06 8 -2.959210779063838 3.226518598373974e-05 9 -2.597288631188366 0.0002349403664659752 10 -2.266513262056788 0.0009858275829964839 11 -2.023230191100516 0.001768022258182954 12 -1.835707975175187 0.004333498812272349 13 -1.561553427651873 0.01551310987485935 14 -1.224744871391589 0.04421164421898455 15 -0.870040895352903 0.09372082806552459 16 -0.524033547486958 0.1430993028968334 17 -0.214618180588171 0.1476557104026862 18 0 0.09688245529284255 19 0.214618180588171 0.1476557104026862 20 0.524033547486958 0.1430993028968334 21 0.870040895352903 0.09372082806552459 22 1.224744871391589 0.04421164421898455 23 1.561553427651873 0.01551310987485935 24 1.835707975175187 0.004333498812272349 25 2.023230191100516 0.001768022258182954 26 2.266513262056788 0.0009858275829964839 27 2.597288631188366 0.0002349403664659752 28 2.959210779063838 3.226518598373974e-05 29 3.31558461759329 3.309758709792034e-06 30 3.667774215946338 2.959075202307441e-07 31 4.057956316089741 1.659544880938982e-08 32 4.499599398310388 4.22525843963111e-10 33 4.986551454150765 4.566176367618686e-12 34 5.52186520986835 1.822427515491294e-14 35 6.124527854622158 1.87781893143729e-17 36 6.853200069757519 1.90303509401305e-21 HERMITE_GK18_SET_TEST: Normal end of execution. HERMITE_GK22_SET_TEST Python version: 3.6.5 HERMITE_GK22_SET sets up a nested rule for the Hermite integration problem. Index X W 0 0 1.772453850905516 0 -1.224744871391589 0.2954089751509193 1 0 1.181635900603677 2 1.224744871391589 0.2954089751509193 0 -2.959210779063838 0.0001670882630688235 1 -2.023230191100516 0.0141731178739791 2 -1.224744871391589 0.1681189289476777 3 -0.5240335474869576 0.4786942854911412 4 0 0.450147009753782 5 0.5240335474869576 0.4786942854911412 6 1.224744871391589 0.1681189289476777 7 2.023230191100516 0.0141731178739791 8 2.959210779063838 0.0001670882630688235 0 -4.499599398310388 1.529571770532236e-09 1 -3.667774215946338 1.080276720662476e-06 2 -2.959210779063838 0.0001065658977285227 3 -2.266513262056788 0.005113317439088385 4 -2.023230191100516 -0.01123243848906923 5 -1.835707975175187 0.03205524309944588 6 -1.224744871391589 0.1136072989574827 7 -0.8700408953529029 0.1083886195500302 8 -0.5240335474869576 0.3692464336892085 9 0 0.5378816070051017 10 0.5240335474869576 0.3692464336892085 11 0.8700408953529029 0.1083886195500302 12 1.224744871391589 0.1136072989574827 13 1.835707975175187 0.03205524309944588 14 2.023230191100516 -0.01123243848906923 15 2.266513262056788 0.005113317439088385 16 2.959210779063838 0.0001065658977285227 17 3.667774215946338 1.080276720662476e-06 18 4.499599398310388 1.529571770532236e-09 0 -7.251792998192644 6.641958938127579e-24 1 -6.54708325839754 8.604271725122073e-20 2 -5.9614610434045 1.140700785308509e-16 3 -5.437443360177798 4.08820161202506e-14 4 -4.95357434291298 5.818033931703204e-12 5 -4.499599398310388 4.007841416048347e-10 6 -4.070919267883068 1.491582104178314e-08 7 -3.667774215946338 3.153722658522649e-07 8 -3.296114596212218 3.811827917491775e-06 9 -2.959210779063838 2.889767802744787e-05 10 -2.630415236459871 0.0001890109098050979 11 -2.266513262056788 0.001406974240652468 12 -2.043834754429505 -0.01445284222069882 13 -2.023230191100516 0.01788525430336997 14 -1.835707975175187 0.0007054711101229627 15 -1.585873011819188 0.01654455267058608 16 -1.224744871391589 0.04510901033585913 17 -0.8700408953529029 0.09283382285101119 18 -0.5240335474869576 0.1459662938959264 19 -0.195324784415805 0.1656397404005296 20 0 0.05627934260432189 21 0.195324784415805 0.1656397404005296 22 0.5240335474869576 0.1459662938959264 23 0.8700408953529029 0.09283382285101119 24 1.224744871391589 0.04510901033585913 25 1.585873011819188 0.01654455267058608 26 1.835707975175187 0.0007054711101229627 27 2.023230191100516 0.01788525430336997 28 2.043834754429505 -0.01445284222069882 29 2.266513262056788 0.001406974240652468 30 2.630415236459871 0.0001890109098050979 31 2.959210779063838 2.889767802744787e-05 32 3.296114596212218 3.811827917491775e-06 33 3.667774215946338 3.153722658522649e-07 34 4.070919267883068 1.491582104178314e-08 35 4.499599398310388 4.007841416048347e-10 36 4.95357434291298 5.818033931703204e-12 37 5.437443360177798 4.08820161202506e-14 38 5.9614610434045 1.140700785308509e-16 39 6.54708325839754 8.604271725122073e-20 40 7.251792998192644 6.641958938127579e-24 HERMITE_GK22_SET_TEST: Normal end of execution. HERMITE_GK24_SET_TEST Python version: 3.6.5 HERMITE_GK24_SET sets up a nested rule for the Hermite integration problem. Index X W 0 0 1.772453850905516 0 -1.224744871391589 0.2954089751509193 1 0 1.181635900603677 2 1.224744871391589 0.2954089751509193 0 -2.959210779063838 0.0001670882630688235 1 -2.023230191100516 0.0141731178739791 2 -1.224744871391589 0.1681189289476777 3 -0.5240335474869576 0.4786942854911412 4 0 0.450147009753782 5 0.5240335474869576 0.4786942854911412 6 1.224744871391589 0.1681189289476777 7 2.023230191100516 0.0141731178739791 8 2.959210779063838 0.0001670882630688235 0 -4.499599398310388 1.529571770532236e-09 1 -3.667774215946338 1.080276720662476e-06 2 -2.959210779063838 0.0001065658977285227 3 -2.266513262056788 0.005113317439088385 4 -2.023230191100516 -0.01123243848906923 5 -1.835707975175187 0.03205524309944588 6 -1.224744871391589 0.1136072989574827 7 -0.8700408953529029 0.1083886195500302 8 -0.5240335474869576 0.3692464336892085 9 0 0.5378816070051017 10 0.5240335474869576 0.3692464336892085 11 0.8700408953529029 0.1083886195500302 12 1.224744871391589 0.1136072989574827 13 1.835707975175187 0.03205524309944588 14 2.023230191100516 -0.01123243848906923 15 2.266513262056788 0.005113317439088385 16 2.959210779063838 0.0001065658977285227 17 3.667774215946338 1.080276720662476e-06 18 4.499599398310388 1.529571770532236e-09 0 -10.16757499488187 5.461919474783181e-38 1 -7.231746029072501 8.754490987132388e-24 2 -6.535398426382995 9.926199715601491e-20 3 -5.954781975039809 1.226196149478644e-16 4 -5.434053000365068 4.21921851448196e-14 5 -4.952329763008589 5.869158852517349e-12 6 -4.499599398310388 4.000305754257769e-10 7 -4.071335874253583 1.486536435717965e-08 8 -3.667774215946338 3.160183632212892e-07 9 -3.295265921534226 3.838807619473985e-06 10 -2.959210779063838 2.868023180647778e-05 11 -2.633356763661946 0.0001847894656883574 12 -2.266513262056788 0.001509093332116388 13 -2.089340389294661 -0.003879955862387716 14 -2.023230191100516 0.00673547589010133 15 -1.835707975175187 0.001399662522915681 16 -1.583643465293944 0.01636168734938324 17 -1.224744871391589 0.0450612329041865 18 -0.8700408953529029 0.09287115844425754 19 -0.5240335474869576 0.1458632926321473 20 -0.196029453662011 0.1648809136874367 21 0 0.05795959861011811 22 0.196029453662011 0.1648809136874367 23 0.5240335474869576 0.1458632926321473 24 0.8700408953529029 0.09287115844425754 25 1.224744871391589 0.0450612329041865 26 1.583643465293944 0.01636168734938324 27 1.835707975175187 0.001399662522915681 28 2.023230191100516 0.00673547589010133 29 2.089340389294661 -0.003879955862387716 30 2.266513262056788 0.001509093332116388 31 2.633356763661946 0.0001847894656883574 32 2.959210779063838 2.868023180647778e-05 33 3.295265921534226 3.838807619473985e-06 34 3.667774215946338 3.160183632212892e-07 35 4.071335874253583 1.486536435717965e-08 36 4.499599398310388 4.000305754257769e-10 37 4.952329763008589 5.869158852517349e-12 38 5.434053000365068 4.21921851448196e-14 39 5.954781975039809 1.226196149478644e-16 40 6.535398426382995 9.926199715601491e-20 41 7.231746029072501 8.754490987132388e-24 42 10.16757499488187 5.461919474783181e-38 HERMITE_GK24_SET_TEST: Normal end of execution. HERMITE_1_SET_TEST Python version: 3.6.5 HERMITE_1_SET sets a unit density Hermite quadrature rule. The interval is (-oo,+oo). The density is 1.0. Index X W 0 0 1.772453850905516 0 -0.7071067811865476 1.461141182661139 1 0.7071067811865476 1.461141182661139 0 -1.224744871391589 1.323931175213644 1 0 1.181635900603677 2 1.224744871391589 1.323931175213644 0 -1.650680123885784 1.240225817695815 1 -0.5246476232752904 1.059964482894969 2 0.5246476232752904 1.059964482894969 3 1.650680123885784 1.240225817695815 0 -2.020182870456086 1.181488625535987 1 -0.9585724646138185 0.9865809967514283 2 0 0.9453087204829419 3 0.9585724646138185 0.9865809967514283 4 2.020182870456086 1.181488625535987 0 -2.350604973674492 1.136908332674525 1 -1.335849074013697 0.9355805576311808 2 -0.4360774119276165 0.8764013344362306 3 0.4360774119276165 0.8764013344362306 4 1.335849074013697 0.9355805576311808 5 2.350604973674492 1.136908332674525 0 -2.651961356835233 1.101330729610322 1 -1.673551628767471 0.8971846002251841 2 -0.8162878828589647 0.8286873032836393 3 0 0.8102646175568073 4 0.8162878828589647 0.8286873032836393 5 1.673551628767471 0.8971846002251841 6 2.651961356835233 1.101330729610322 0 -2.930637420257244 1.07193014424798 1 -1.981656756695843 0.8667526065633814 2 -1.15719371244678 0.7928900483864013 3 -0.3811869902073221 0.7645441286517292 4 0.3811869902073221 0.7645441286517292 5 1.15719371244678 0.7928900483864013 6 1.981656756695843 0.8667526065633814 7 2.930637420257244 1.07193014424798 0 -3.190993201781528 1.047003580976684 1 -2.266580584531843 0.8417527014786704 2 -1.468553289216668 0.7646081250945502 3 -0.7235510187528376 0.7303024527450922 4 0 0.720235215606051 5 0.7235510187528376 0.7303024527450922 6 1.468553289216668 0.7646081250945502 7 2.266580584531843 0.8417527014786704 8 3.190993201781528 1.047003580976684 0 -3.436159118837737 1.025451691365735 1 -2.53273167423279 0.8206661264048164 2 -1.756683649299882 0.7414419319435651 3 -1.036610829789514 0.7032963231049061 4 -0.3429013272237046 0.6870818539512734 5 0.3429013272237046 0.6870818539512734 6 1.036610829789514 0.7032963231049061 7 1.756683649299882 0.7414419319435651 8 2.53273167423279 0.8206661264048164 9 3.436159118837737 1.025451691365735 HERMITE_1_SET_TEST: Normal end of execution. HERMITE_PROBABILIST_SET_TEST Python version: 3.6.5 HERMITE_PROBABILIST_SET sets a Hermite quadrature rule. The integration interval is ( -oo, +oo ). The weight is exp ( - x * x / 2 ) / sqrt ( 2 * pi ). Index X W 0 0 1 0 -1 0.5 1 1 0.5 0 -1.732050807568877 0.1666666666666667 1 0 0.6666666666666666 2 1.732050807568877 0.1666666666666667 0 -2.334414218338977 0.04587585476806849 1 -0.7419637843027258 0.4541241452319315 2 0.7419637843027258 0.4541241452319315 3 2.334414218338977 0.04587585476806849 0 -2.856970013872806 0.01125741132772069 1 -1.355626179974266 0.2220759220056127 2 0 0.5333333333333333 3 1.355626179974266 0.2220759220056127 4 2.856970013872806 0.01125741132772069 0 -3.324257433552119 0.002555784402056247 1 -1.889175877753711 0.08861574604191452 2 -0.6167065901925941 0.4088284695560293 3 0.6167065901925941 0.4088284695560293 4 1.889175877753711 0.08861574604191452 5 3.324257433552119 0.002555784402056247 0 -3.750439717725742 0.0005482688559722178 1 -2.366759410734541 0.0307571239675865 2 -1.154405394739968 0.2401231786050127 3 0 0.4571428571428571 4 1.154405394739968 0.2401231786050127 5 2.366759410734541 0.0307571239675865 6 3.750439717725742 0.0005482688559722178 0 -4.144547186125894 0.0001126145383753678 1 -2.802485861287542 0.009635220120788266 2 -1.636519042435108 0.117239907661759 3 -0.5390798113513751 0.3730122576790774 4 0.5390798113513751 0.3730122576790774 5 1.636519042435108 0.117239907661759 6 2.802485861287542 0.009635220120788266 7 4.144547186125894 0.0001126145383753678 0 -4.512745863399783 2.234584400774658e-05 1 -3.20542900285647 0.002789141321231769 2 -2.07684797867783 0.04991640676521787 3 -1.023255663789133 0.2440975028949394 4 0 0.4063492063492063 5 1.023255663789133 0.2440975028949394 6 2.07684797867783 0.04991640676521787 7 3.20542900285647 0.002789141321231769 8 4.512745863399783 2.234584400774658e-05 0 -4.859462828332312 4.310652630718287e-06 1 -3.581823483551927 0.0007580709343122177 2 -2.484325841638955 0.01911158050077029 3 -1.465989094391158 0.1354837029802677 4 -0.4849357075154976 0.3446423349320191 5 0.4849357075154976 0.3446423349320191 6 1.465989094391158 0.1354837029802677 7 2.484325841638955 0.01911158050077029 8 3.581823483551927 0.0007580709343122177 9 4.859462828332312 4.310652630718287e-06 HERMITE_PROBABILIST_SET_TEST: Normal end of execution. IMTQLX_TEST Python version: 3.6.5 IMTQLX takes a symmetric tridiagonal matrix A and computes its eigenvalues LAM. It also accepts a vector Z and computes Q'*Z, where Q is the matrix that diagonalizes A. Computed eigenvalues: 0: 0.267949 1: 1 2: 2 3: 3 4: 3.73205 Exact eigenvalues: 0: 0.267949 1: 1 2: 2 3: 3 4: 3.73205 Vector Z: 0: 1 1: 1 2: 1 3: 1 4: 1 Vector Q*Z: 0: -2.1547 1: -1.8855e-16 2: 0.57735 3: 1.66533e-16 4: -0.154701 IMTQLX_TEST: Normal end of execution. JACOBI_EK_COMPUTE_TEST Python version: 3.6.5 JACOBI_EK_COMPUTE computes a generalized Jacobi quadrature rule using the Elhay-Kautsky algorithm. Using ALPHA = 1.5 Index X W 0 -0.25 1.570796326794896 0 -0.6076252185107651 0.933824464862914 1 0.2742918851774317 0.6369718619319824 0 -0.760157340487268 0.5261284436611056 1 -0.1528288638647804 0.8030739600082096 2 0.5379862043520485 0.2415939231255808 0 -0.8385964119177012 0.3144794551130207 1 -0.4056256275378191 0.678743654928424 2 0.1614690409023142 0.4757517664489192 3 0.682752998553206 0.1018214503045317 0 -0.8840882653201492 0.2001252566372697 1 -0.5629059317762043 0.5199632186774659 2 -0.1100274225210447 0.5356898968305487 3 0.3708136309492863 0.2672477173275187 4 0.7695413220014449 0.04777023732209325 0 -0.9127717928725458 0.1343056820427146 1 -0.6661693810819842 0.3902780567984853 2 -0.3028312803228947 0.499078675899895 3 0.1144215303885477 0.3697846812371453 4 0.5134534103439395 0.1528283716957896 5 0.8253260849735088 0.02452085912086582 0 -0.9320024628657495 0.09414510038510714 1 -0.7371931739434825 0.2943041944091259 2 -0.4418817729485141 0.4309263997770963 3 -0.0859506602240641 0.4009490239804647 4 0.2825323324996323 0.2463697069136382 5 0.6138099722388769 0.09055772921029319 6 0.8631857652433008 0.01354417211917143 0 -0.9455158043974037 0.06839190925948291 1 -0.7879673764819102 0.2248513392666883 2 -0.5444273641737976 0.3606436566319117 3 -0.2412867334092742 0.3883180543539711 4 0.08860534544266944 0.3008492695347081 5 0.4095019972429188 0.16405734578548 6 0.6866356906720186 0.0557415005793357 7 0.8900098006603341 0.007943251383318863 0 -0.9553706327691448 0.05117382374316969 1 -0.8254480244332432 0.1744634097524552 2 -0.6217762959622662 0.2984741580861981 3 -0.3624524217425484 0.3552731274654827 4 -0.07051816095979085 0.3200587357332041 5 0.2280875011498078 0.220229706982839 6 0.5068337773772098 0.1106616329196992 7 0.7409581449066003 0.03556668124983503 8 0.9096861124333756 0.004895050862014656 0 -0.962776688670377 0.03925058540055813 1 -0.8538674269792412 0.1374810592741681 2 -0.6813494824055374 0.2466379844126227 3 -0.4580176529455094 0.3155655291519008 4 -0.2004353100508689 0.3157558361063397 5 0.07229409169326702 0.2531373506672515 6 0.3399439927530339 0.1603930057544804 7 0.5826653601184614 0.07598607784811179 8 0.7824610233136923 0.02344462385831613 9 0.9245366386276249 0.003144274321147394 JACOBI_EK_COMPUTE_TEST: Normal end of execution. JACOBI_INTEGRAL_TEST Python version: 3.6.5 JACOBI_INTEGRAL evaluates Integral ( -1 < x < +1 ) x^n (1-x)^alpha (1+x)^beta dx Use ALPHA = 1.5 BETA = 0.5 N Value 0 1.570796326794896 1 -0.3926990816987241 2 0.392699081698724 3 -0.1963495408493619 4 0.1963495408493619 5 -0.1227184630308513 6 0.1227184630308513 7 -0.08590292412159588 8 0.08590292412159588 9 -0.06442719309119695 10 0.06442719309119677 JACOBI_INTEGRAL_TEST Normal end of execution. KRONROD_SET_TEST Python version: 3.6.5 KRONROD_SET sets up a Kronrod quadrature rule, This is used following a lower order Legendre rule. Legendre/Kronrod quadrature pair #0 W X 0 -0.9491079123427585 0.1294849661688697 1 -0.7415311855993945 0.2797053914892766 2 -0.4058451513773972 0.3818300505051189 3 0 0.4179591836734694 4 0.4058451513773972 0.3818300505051189 5 0.7415311855993945 0.2797053914892766 6 0.9491079123427585 0.1294849661688697 0 -0.9914553711208126 0.02293532201052922 1 -0.9491079123427585 0.06309209262997854 2 -0.8648644233597691 0.1047900103222502 3 -0.7415311855993943 0.1406532597155259 4 -0.5860872354676911 0.1690047266392679 5 -0.4058451513773972 0.1903505780647854 6 -0.207784955078985 0.2044329400752989 7 0 0.2094821410847278 8 0.207784955078985 0.2044329400752989 9 0.4058451513773972 0.1903505780647854 10 0.5860872354676911 0.1690047266392679 11 0.7415311855993943 0.1406532597155259 12 0.8648644233597691 0.1047900103222502 13 0.9491079123427585 0.06309209262997854 14 0.9914553711208126 0.02293532201052922 Legendre/Kronrod quadrature pair #1 W X 0 -0.9739065285171717 0.06667134430868814 1 -0.8650633666889845 0.1494513491505806 2 -0.6794095682990244 0.219086362515982 3 -0.4333953941292472 0.2692667193099963 4 -0.1488743389816312 0.2955242247147529 5 0.1488743389816312 0.2955242247147529 6 0.4333953941292472 0.2692667193099963 7 0.6794095682990244 0.219086362515982 8 0.8650633666889845 0.1494513491505806 9 0.9739065285171717 0.06667134430868814 0 -0.9956571630258081 0.01169463886737187 1 -0.9739065285171717 0.03255816230796473 2 -0.9301574913557082 0.054755896574352 3 -0.8650633666889845 0.07503967481091996 4 -0.7808177265864169 0.09312545458369761 5 -0.6794095682990244 0.1093871588022976 6 -0.5627571346686047 0.1234919762620659 7 -0.4333953941292472 0.1347092173114733 8 -0.2943928627014602 0.1427759385770601 9 -0.1488743389816312 0.1477391049013385 10 0 0.1494455540029169 11 0.1488743389816312 0.1477391049013385 12 0.2943928627014602 0.1427759385770601 13 0.4333953941292472 0.1347092173114733 14 0.5627571346686047 0.1234919762620659 15 0.6794095682990244 0.1093871588022976 16 0.7808177265864169 0.09312545458369761 17 0.8650633666889845 0.07503967481091996 18 0.9301574913557082 0.054755896574352 19 0.9739065285171717 0.03255816230796473 20 0.9956571630258081 0.01169463886737187 Legendre/Kronrod quadrature pair #2 W X 0 -0.9879925180204854 0.03075324199611727 1 -0.937273392400706 0.07036604748810812 2 -0.8482065834104272 0.1071592204671719 3 -0.7244177313601701 0.1395706779261543 4 -0.5709721726085388 0.1662692058169939 5 -0.3941513470775634 0.1861610000155622 6 -0.2011940939974345 0.1984314853271116 7 0 0.2025782419255613 8 0.2011940939974345 0.1984314853271116 9 0.3941513470775634 0.1861610000155622 10 0.5709721726085388 0.1662692058169939 11 0.7244177313601701 0.1395706779261543 12 0.8482065834104272 0.1071592204671719 13 0.937273392400706 0.07036604748810812 14 0.9879925180204854 0.03075324199611727 0 -0.9980022986933971 0.005377479872923349 1 -0.9879925180204854 0.01500794732931612 2 -0.9677390756791391 0.02546084732671532 3 -0.937273392400706 0.03534636079137585 4 -0.8972645323440819 0.04458975132476488 5 -0.8482065834104272 0.05348152469092809 6 -0.7904185014424659 0.06200956780067064 7 -0.72441773136017 0.06985412131872826 8 -0.650996741297417 0.07684968075772038 9 -0.5709721726085388 0.08308050282313302 10 -0.4850818636402397 0.08856444305621176 11 -0.3941513470775634 0.09312659817082532 12 -0.2991800071531688 0.09664272698362368 13 -0.2011940939974345 0.09917359872179196 14 -0.1011420669187175 0.1007698455238756 15 0 0.1013300070147915 16 0.1011420669187175 0.1007698455238756 17 0.2011940939974345 0.09917359872179196 18 0.2991800071531688 0.09664272698362368 19 0.3941513470775634 0.09312659817082532 20 0.4850818636402397 0.08856444305621176 21 0.5709721726085388 0.08308050282313302 22 0.650996741297417 0.07684968075772038 23 0.72441773136017 0.06985412131872826 24 0.7904185014424659 0.06200956780067064 25 0.8482065834104272 0.05348152469092809 26 0.8972645323440819 0.04458975132476488 27 0.937273392400706 0.03534636079137585 28 0.9677390756791391 0.02546084732671532 29 0.9879925180204854 0.01500794732931612 30 0.9980022986933971 0.005377479872923349 Legendre/Kronrod quadrature pair #3 W X 0 -0.9931285991850949 0.01761400713915212 1 -0.9639719272779138 0.04060142980038694 2 -0.9122344282513259 0.06267204833410907 3 -0.8391169718222188 0.08327674157670475 4 -0.7463319064601508 0.1019301198172404 5 -0.636053680726515 0.1181945319615184 6 -0.5108670019508271 0.1316886384491766 7 -0.3737060887154195 0.142096109318382 8 -0.2277858511416451 0.1491729864726037 9 -0.07652652113349734 0.1527533871307258 10 0.07652652113349734 0.1527533871307258 11 0.2277858511416451 0.1491729864726037 12 0.3737060887154195 0.142096109318382 13 0.5108670019508271 0.1316886384491766 14 0.636053680726515 0.1181945319615184 15 0.7463319064601508 0.1019301198172404 16 0.8391169718222188 0.08327674157670475 17 0.9122344282513259 0.06267204833410907 18 0.9639719272779138 0.04060142980038694 19 0.9931285991850949 0.01761400713915212 0 -0.9988590315882777 0.003073583718520532 1 -0.9931285991850949 0.008600269855642943 2 -0.9815078774502503 0.01462616925697125 3 -0.9639719272779138 0.02038837346126652 4 -0.9408226338317548 0.02588213360495116 5 -0.9122344282513259 0.0312873067770328 6 -0.878276811252282 0.0366001697582008 7 -0.8391169718222188 0.04166887332797369 8 -0.7950414288375512 0.04643482186749767 9 -0.7463319064601508 0.05094457392372869 10 -0.6932376563347514 0.05519510534828599 11 -0.636053680726515 0.05911140088063957 12 -0.5751404468197103 0.06265323755478117 13 -0.5108670019508271 0.06583459713361842 14 -0.4435931752387251 0.06864867292852161 15 -0.3737060887154196 0.07105442355344407 16 -0.301627868114913 0.07303069033278667 17 -0.2277858511416451 0.0745828754004992 18 -0.1526054652409227 0.07570449768455667 19 -0.07652652113349732 0.07637786767208074 20 0 0.07660071191799966 21 0.07652652113349732 0.07637786767208074 22 0.1526054652409227 0.07570449768455667 23 0.2277858511416451 0.0745828754004992 24 0.301627868114913 0.07303069033278667 25 0.3737060887154196 0.07105442355344407 26 0.4435931752387251 0.06864867292852161 27 0.5108670019508271 0.06583459713361842 28 0.5751404468197103 0.06265323755478117 29 0.636053680726515 0.05911140088063957 30 0.6932376563347514 0.05519510534828599 31 0.7463319064601508 0.05094457392372869 32 0.7950414288375512 0.04643482186749767 33 0.8391169718222188 0.04166887332797369 34 0.878276811252282 0.0366001697582008 35 0.9122344282513259 0.0312873067770328 36 0.9408226338317548 0.02588213360495116 37 0.9639719272779138 0.02038837346126652 38 0.9815078774502503 0.01462616925697125 39 0.9931285991850949 0.008600269855642943 40 0.9988590315882777 0.003073583718520532 KRONROD_SET_TEST: Normal end of execution. LAGUERRE_EK_COMPUTE_TEST Python version: 3.6.5 LAGUERRE_EK_COMPUTE computes a Laguerre quadrature rule using the Elhay-Kautsky algorithm. Index X W 0 1 1 0 0.5857864376269051 0.853553390593274 1 3.414213562373094 0.1464466094067262 0 0.4157745567834791 0.7110930099291731 1 2.294280360279042 0.2785177335692407 2 6.289945082937479 0.01038925650158614 0 0.3225476896193926 0.6031541043416337 1 1.745761101158347 0.3574186924377996 2 4.536620296921128 0.0388879085150054 3 9.395070912301131 0.000539294705561328 0 0.263560319718141 0.5217556105828089 1 1.413403059106517 0.3986668110831761 2 3.596425771040722 0.07594244968170767 3 7.085810005858837 0.003611758679922046 4 12.64080084427578 2.336997238577622e-05 0 0.2228466041792608 0.4589646739499636 1 1.188932101672624 0.4170008307721204 2 2.992736326059315 0.1133733820740448 3 5.775143569104511 0.01039919745314906 4 9.837467418382589 0.0002610172028149321 5 15.9828739806017 8.985479064296216e-07 0 0.1930436765603624 0.4093189517012744 1 1.026664895339192 0.4218312778617198 2 2.567876744950746 0.1471263486575055 3 4.900353084526484 0.02063351446871697 4 8.182153444562855 0.001074010143280748 5 12.73418029179781 1.586546434856422e-05 6 19.39572786226255 3.170315478995567e-08 0 0.1702796323051015 0.3691885893416387 1 0.9037017767993818 0.4187867808143421 2 2.251086629866132 0.1757949866371719 3 4.266700170287656 0.03334349226121559 4 7.045905402393467 0.002794536235225666 5 10.758516010181 9.076508773358223e-05 6 15.740678641278 8.485746716272525e-07 7 22.86313173688927 1.048001174871508e-09 0 0.1523222277318082 0.3361264217979625 1 0.8072200227422558 0.4112139804239848 2 2.005135155619348 0.1992875253708853 3 3.783473973331234 0.04746056276565157 4 6.204956777876612 0.005599626610794585 5 9.372985251687572 0.0003052497670932117 6 13.46623691109209 6.592123026075368e-06 7 18.8335977889917 4.110769330349561e-08 8 26.37407189092738 3.290874030350725e-11 0 0.1377934705404928 0.3084411157650208 1 0.729454549503172 0.4011199291552736 2 1.808342901740319 0.2180682876118088 3 3.401433697854901 0.06208745609867754 4 5.552496140063805 0.009501516975181085 5 8.330152746764496 0.0007530083885875395 6 11.84378583790006 2.825923349599567e-05 7 16.2792578313781 4.24931398496269e-07 8 21.99658581198076 1.839564823979623e-09 9 29.92069701227389 9.911827219609021e-13 LAGUERRE_EK_COMPUTE_TEST: Normal end of execution. LAGUERRE_INTEGRAL_TEST Python version: 3.6.5 LAGUERRE_INTEGRAL evaluates Integral ( 0 < x < oo ) x^n * exp(-x) dx N Value 0 1 1 1 2 2 3 6 4 24 5 120 6 720 7 5040 8 40320 9 362880 10 3628800 LAGUERRE_INTEGRAL_TEST Normal end of execution. LAGUERRE_SET_TEST Python version: 3.6.5 LAGUERRE_SET sets a Laguerre rule. I X W 0 1 1 0 0.585786437626905 0.8535533905932737 1 3.414213562373095 0.1464466094067262 0 0.4157745567834791 0.711093009929173 1 2.294280360279042 0.2785177335692409 2 6.289945082937479 0.01038925650158613 0 0.3225476896193923 0.6031541043416336 1 1.745761101158346 0.3574186924377997 2 4.536620296921128 0.03888790851500538 3 9.395070912301133 0.0005392947055613274 0 0.2635603197181409 0.5217556105828086 1 1.413403059106517 0.3986668110831759 2 3.596425771040722 0.0759424496817076 3 7.085810005858837 0.003611758679922048 4 12.64080084427578 2.336997238577623e-05 0 0.2228466041792607 0.4589646739499636 1 1.188932101672623 0.417000830772121 2 2.992736326059314 0.113373382074045 3 5.77514356910451 0.01039919745314907 4 9.837467418382589 0.0002610172028149321 5 15.9828739806017 8.985479064296212e-07 0 0.1930436765603624 0.4093189517012739 1 1.026664895339192 0.4218312778617198 2 2.567876744950746 0.1471263486575053 3 4.900353084526484 0.02063351446871694 4 8.182153444562861 0.001074010143280746 5 12.73418029179781 1.58654643485642e-05 6 19.39572786226254 3.17031547899558e-08 0 0.170279632305101 0.3691885893416375 1 0.9037017767993799 0.418786780814343 2 2.251086629866131 0.1757949866371718 3 4.266700170287659 0.03334349226121565 4 7.045905402393466 0.002794536235225673 5 10.758516010181 9.076508773358213e-05 6 15.740678641278 8.485746716272531e-07 7 22.86313173688927 1.04800117487151e-09 0 0.1523222277318083 0.3361264217979625 1 0.8072200227422558 0.4112139804239844 2 2.005135155619347 0.1992875253708856 3 3.783473973331233 0.0474605627656516 4 6.204956777876613 0.005599626610794583 5 9.372985251687576 0.0003052497670932106 6 13.46623691109209 6.592123026075352e-06 7 18.8335977889917 4.110769330349548e-08 8 26.37407189092738 3.290874030350708e-11 0 0.1377934705404924 0.3084411157650201 1 0.7294545495031705 0.4011199291552736 2 1.808342901740316 0.2180682876118094 3 3.4014336978549 0.06208745609867775 4 5.552496140063804 0.009501516975181101 5 8.330152746764497 0.0007530083885875388 6 11.84378583790007 2.825923349599566e-05 7 16.2792578313781 4.249313984962686e-07 8 21.99658581198076 1.839564823979631e-09 9 29.92069701227389 9.911827219609008e-13 LAGUERRE_SET_TEST: Normal end of execution. LAGUERRE_1_SET_TEST Python version: 3.6.5 LAGUERRE_1_SET sets a Laguerre rule. The density function is rho(x)=1. I X W 0 1 2.718281828459045 0 0.585786437626905 1.533326033119417 1 3.414213562373095 4.450957335054593 0 0.4157745567834791 1.077692859270921 1 2.294280360279042 2.762142961901588 2 6.289945082937479 5.601094625434427 0 0.3225476896193923 0.8327391238378892 1 1.745761101158346 2.048102438454297 2 4.536620296921128 3.631146305821517 3 9.395070912301133 6.48714508440766 0 0.2635603197181409 0.6790940422077504 1 1.413403059106517 1.638487873602747 2 3.596425771040722 2.769443242370837 3 7.085810005858837 4.315656900920894 4 12.64080084427578 7.219186354354445 0 0.2228466041792607 0.5735355074227382 1 1.188932101672623 1.369252590712305 2 2.992736326059314 2.260684593382672 3 5.77514356910451 3.350524582355455 4 9.837467418382589 4.886826800210821 5 15.9828739806017 7.849015945595828 0 0.1930436765603624 0.4964775975399723 1 1.026664895339192 1.177643060861198 2 2.567876744950746 1.918249781659806 3 4.900353084526484 2.771848636232111 4 8.182153444562861 3.841249122488515 5 12.73418029179781 5.380678207921533 6 19.39572786226254 8.40543248682831 0 0.170279632305101 0.4377234104929114 1 0.9037017767993799 1.033869347665598 2 2.251086629866131 1.669709765658776 3 4.266700170287659 2.376924701758599 4 7.045905402393466 3.208540913347926 5 10.758516010181 4.268575510825134 6 15.740678641278 5.818083368671918 7 22.86313173688927 8.906226215292222 0 0.1523222277318083 0.3914311243156399 1 0.8072200227422558 0.9218050285289631 2 2.005135155619347 1.480127909942915 3 3.783473973331233 2.086770807549261 4 6.204956777876613 2.772921389711971 5 9.372985251687576 3.591626068092266 6 13.46623691109209 4.648766002140204 7 18.8335977889917 6.212275419747135 8 26.37407189092738 9.363218237705798 0 0.1377934705404924 0.3540097386069963 1 0.7294545495031705 0.8319023010435806 2 1.808342901740316 1.330288561749328 3 3.4014336978549 1.863063903111131 4 5.552496140063804 2.450255558083011 5 8.330152746764497 3.122764155135185 6 11.84378583790007 3.934152695561524 7 16.2792578313781 4.99241487219303 8 21.99658581198076 6.572202485130799 9 29.92069701227389 9.784695840374624 LAGUERRE_1_SET_TEST: Normal end of execution. LEGENDRE_DR_COMPUTE_TEST Python version: 3.6.5 LEGENDRE_DR_COMPUTE computes a Legendre quadrature rule using the Davis-Rabinowitz algorithm. Index X W 0 0 2 0 -0.5773502691896258 0.9999999999999994 1 0.5773502691896258 0.9999999999999994 0 -0.7745966692414833 0.5555555555555558 1 0 0.8888888888888888 2 0.7745966692414833 0.5555555555555558 0 -0.8611363115940526 0.3478548451374539 1 -0.3399810435848563 0.6521451548625462 2 0.3399810435848563 0.6521451548625462 3 0.8611363115940526 0.3478548451374539 0 -0.906179845938664 0.2369268850561891 1 -0.5384693101056831 0.4786286704993666 2 0 0.5688888888888889 3 0.5384693101056831 0.4786286704993666 4 0.906179845938664 0.2369268850561891 0 -0.9324695142031521 0.1713244923791702 1 -0.6612093864662645 0.3607615730481386 2 -0.2386191860831969 0.467913934572691 3 0.2386191860831969 0.467913934572691 4 0.6612093864662645 0.3607615730481386 5 0.9324695142031521 0.1713244923791702 0 -0.9491079123427585 0.1294849661688699 1 -0.7415311855993945 0.2797053914892767 2 -0.4058451513773972 0.3818300505051191 3 0 0.4179591836734693 4 0.4058451513773972 0.3818300505051191 5 0.7415311855993945 0.2797053914892767 6 0.9491079123427585 0.1294849661688699 0 -0.9602898564975362 0.1012285362903764 1 -0.7966664774136267 0.2223810344533745 2 -0.525532409916329 0.3137066458778873 3 -0.1834346424956498 0.3626837833783618 4 0.1834346424956498 0.3626837833783618 5 0.525532409916329 0.3137066458778873 6 0.7966664774136267 0.2223810344533745 7 0.9602898564975362 0.1012285362903764 0 -0.9681602395076261 0.08127438836157443 1 -0.8360311073266358 0.1806481606948574 2 -0.6133714327005904 0.2606106964029354 3 -0.3242534234038089 0.3123470770400029 4 0 0.3302393550012598 5 0.3242534234038089 0.3123470770400029 6 0.6133714327005904 0.2606106964029354 7 0.8360311073266358 0.1806481606948574 8 0.9681602395076261 0.08127438836157443 0 -0.9739065285171717 0.06667134430868805 1 -0.8650633666889845 0.1494513491505806 2 -0.6794095682990244 0.2190863625159821 3 -0.4333953941292472 0.2692667193099965 4 -0.1488743389816312 0.295524224714753 5 0.1488743389816312 0.295524224714753 6 0.4333953941292472 0.2692667193099965 7 0.6794095682990244 0.2190863625159821 8 0.8650633666889845 0.1494513491505806 9 0.9739065285171717 0.06667134430868805 LEGENDRE_DR_COMPUTE_TEST: Normal end of execution. LEGENDRE_EK_COMPUTE_TEST Python version: 3.6.5 LEGENDRE_EK_COMPUTE computes a Legendre quadrature rule using the Elhay-Kautsky algorithm. Index X W 0 0 2 0 -0.5773502691896256 1 1 0.5773502691896256 1 0 -0.7745966692414832 0.5555555555555559 1 -6.466579952145703e-17 0.8888888888888886 2 0.7745966692414834 0.5555555555555554 0 -0.8611363115940526 0.3478548451374537 1 -0.3399810435848563 0.6521451548625463 2 0.3399810435848564 0.6521451548625459 3 0.8611363115940522 0.347854845137454 0 -0.9061798459386641 0.2369268850561892 1 -0.538469310105683 0.4786286704993667 2 -3.478412152580952e-17 0.5688888888888882 3 0.5384693101056829 0.478628670499367 4 0.9061798459386642 0.2369268850561892 0 -0.9324695142031522 0.1713244923791701 1 -0.6612093864662647 0.3607615730481389 2 -0.2386191860831971 0.4679139345726916 3 0.2386191860831969 0.4679139345726918 4 0.6612093864662648 0.3607615730481388 5 0.9324695142031524 0.1713244923791705 0 -0.9491079123427583 0.1294849661688696 1 -0.7415311855993943 0.2797053914892763 2 -0.4058451513773971 0.381830050505119 3 4.452841060583418e-17 0.4179591836734696 4 0.4058451513773971 0.3818300505051177 5 0.7415311855993941 0.2797053914892761 6 0.9491079123427584 0.1294849661688694 0 -0.9602898564975358 0.101228536290376 1 -0.7966664774136267 0.2223810344533742 2 -0.5255324099163291 0.3137066458778873 3 -0.1834346424956499 0.3626837833783611 4 0.1834346424956497 0.3626837833783627 5 0.5255324099163293 0.3137066458778878 6 0.7966664774136266 0.2223810344533745 7 0.9602898564975362 0.1012285362903759 0 -0.9681602395076263 0.08127438836157426 1 -0.836031107326636 0.1806481606948577 2 -0.6133714327005901 0.2606106964029359 3 -0.3242534234038091 0.3123470770400025 4 1.604668093316319e-16 0.3302393550012599 5 0.324253423403809 0.3123470770400033 6 0.6133714327005904 0.2606106964029349 7 0.836031107326636 0.180648160694857 8 0.9681602395076262 0.08127438836157452 0 -0.973906528517172 0.06667134430868817 1 -0.8650633666889845 0.1494513491505806 2 -0.6794095682990243 0.2190863625159822 3 -0.4333953941292472 0.2692667193099962 4 -0.1488743389816309 0.2955242247147525 5 0.148874338981631 0.2955242247147538 6 0.4333953941292469 0.2692667193099955 7 0.6794095682990243 0.2190863625159825 8 0.8650633666889844 0.14945134915058 9 0.973906528517172 0.06667134430868776 LEGENDRE_EK_COMPUTE_TEST: Normal end of execution. LEGENDRE_INTEGRAL_TEST Python version: 3.6.5 LEGENDRE_INTEGRAL evaluates Integral ( -1 < x < +1 ) x^n dx N Value 0 2 1 0 2 0.6666666666666666 3 0 4 0.4 5 0 6 0.2857142857142857 7 0 8 0.2222222222222222 9 0 10 0.1818181818181818 LEGENDRE_INTEGRAL_TEST Normal end of execution. LEGENDRE_SET_TEST Python version: 3.6.5 LEGENDRE_SET sets a Legendre quadrature rule. I X W 0 0 2 0 -0.5773502691896257 1 1 0.5773502691896257 1 0 -0.7745966692414834 0.5555555555555556 1 0 0.8888888888888888 2 0.7745966692414834 0.5555555555555556 0 -0.8611363115940526 0.3478548451374538 1 -0.3399810435848563 0.6521451548625461 2 0.3399810435848563 0.6521451548625461 3 0.8611363115940526 0.3478548451374538 0 -0.906179845938664 0.2369268850561891 1 -0.5384693101056831 0.4786286704993665 2 0 0.5688888888888889 3 0.5384693101056831 0.4786286704993665 4 0.906179845938664 0.2369268850561891 0 -0.9324695142031521 0.1713244923791704 1 -0.6612093864662645 0.3607615730481386 2 -0.2386191860831969 0.467913934572691 3 0.2386191860831969 0.467913934572691 4 0.6612093864662645 0.3607615730481386 5 0.9324695142031521 0.1713244923791704 0 -0.9491079123427585 0.1294849661688697 1 -0.7415311855993945 0.2797053914892766 2 -0.4058451513773972 0.3818300505051189 3 0 0.4179591836734694 4 0.4058451513773972 0.3818300505051189 5 0.7415311855993945 0.2797053914892766 6 0.9491079123427585 0.1294849661688697 0 -0.9602898564975363 0.1012285362903763 1 -0.7966664774136267 0.2223810344533745 2 -0.525532409916329 0.3137066458778873 3 -0.1834346424956498 0.362683783378362 4 0.1834346424956498 0.362683783378362 5 0.525532409916329 0.3137066458778873 6 0.7966664774136267 0.2223810344533745 7 0.9602898564975363 0.1012285362903763 0 -0.9681602395076261 0.08127438836157441 1 -0.8360311073266358 0.1806481606948574 2 -0.6133714327005904 0.2606106964029354 3 -0.3242534234038089 0.3123470770400029 4 0 0.3302393550012598 5 0.3242534234038089 0.3123470770400029 6 0.6133714327005904 0.2606106964029354 7 0.8360311073266358 0.1806481606948574 8 0.9681602395076261 0.08127438836157441 0 -0.9739065285171717 0.06667134430868814 1 -0.8650633666889845 0.1494513491505806 2 -0.6794095682990244 0.219086362515982 3 -0.4333953941292472 0.2692667193099963 4 -0.1488743389816312 0.2955242247147529 5 0.1488743389816312 0.2955242247147529 6 0.4333953941292472 0.2692667193099963 7 0.6794095682990244 0.219086362515982 8 0.8650633666889845 0.1494513491505806 9 0.9739065285171717 0.06667134430868814 LEGENDRE_SET_TEST: Normal end of execution. LOBATTO_COMPUTE_TEST Python version: 3.6.5 LOBATTO_COMPUTE computes a Lobatto rule I X W 0 -1 0.166667 1 -0.447214 0.833333 2 0.447214 0.833333 3 1 0.166667 0 -1 0.047619 1 -0.830224 0.276826 2 -0.468849 0.431745 3 0 0.487619 4 0.468849 0.431745 5 0.830224 0.276826 6 1 0.047619 0 -1 0.0222222 1 -0.919534 0.133306 2 -0.738774 0.224889 3 -0.477925 0.292043 4 -0.165279 0.32754 5 0.165279 0.32754 6 0.477925 0.292043 7 0.738774 0.224889 8 0.919534 0.133306 9 1 0.0222222 LOBATTO_COMPUTE_TEST: Normal end of execution. LOBATTO_SET_TEST Python version: 3.6.5 LOBATTO_SET sets a Lobatto rule I X W 0 -1 0.166667 1 -0.447214 0.833333 2 0.447214 0.833333 3 1 0.166667 0 -1 0.047619 1 -0.830224 0.276826 2 -0.468849 0.431745 3 0 0.487619 4 0.468849 0.431745 5 0.830224 0.276826 6 1 0.047619 0 -1 0.0222222 1 -0.919534 0.133306 2 -0.738774 0.224889 3 -0.477925 0.292043 4 -0.165279 0.32754 5 0.165279 0.32754 6 0.477925 0.292043 7 0.738774 0.224889 8 0.919534 0.133306 9 1 0.0222222 LOBATTO_SET_TEST: Normal end of execution. MOULTON_SET_TEST Python version: 3.6.5 MOULTON_SET sets the abscissas and weights for an Adams-Moulton quadrature rule. Order W X 1 1 1 2 0.5 1 0.5 0 3 0.416667 1 0.666667 0 -0.0833333 -1 4 0.375 1 0.791667 0 -0.208333 -1 0.0416667 -2 5 0.348611 1 0.897222 0 -0.366667 -1 0.147222 -2 -0.0263889 -3 6 0.329861 1 0.990972 0 -0.554167 -1 0.334722 -2 -0.120139 -3 0.01875 -4 7 0.315592 1 1.07659 0 -0.768204 -1 0.620106 -2 -0.334177 -3 0.104365 -4 -0.0142692 -5 8 0.304225 1 1.15616 0 -1.00692 -1 1.01796 -2 -0.732035 -3 0.34308 -4 -0.0938409 -5 0.0113674 -6 9 0.294868 1 1.23101 0 -1.2689 -1 1.54193 -2 -1.38699 -3 0.867046 -4 -0.355824 -5 0.0862197 -6 -0.00935654 -7 10 0.286975 1 1.30204 0 -1.55303 -1 2.20491 -2 -2.38145 -3 1.86151 -4 -1.0188 -5 0.370352 -6 -0.0803895 -7 0.00789255 -8 MOULTON_SET_TEST: Normal end of execution. NC_COMPUTE_WEIGHTS_TEST Python version: 3.6.5 NC_COMPUTE_WEIGHTS computes weights for a Newton-Cotes quadrature rule Index X W 0 0.5 1 0 0 0.5 1 1 0.5 0 0 0.1666666666666666 1 0.5 0.6666666666666667 2 1 0.1666666666666666 0 0 0.125 1 0.3333333333333333 0.375 2 0.6666666666666666 0.375 3 1 0.1250000000000003 0 0 0.07777777777777839 1 0.25 0.3555555555555561 2 0.5 0.1333333333333329 3 0.75 0.3555555555555583 4 1 0.07777777777777795 0 0 0.06597222222221788 1 0.2 0.2604166666666643 2 0.4 0.1736111111111285 3 0.6 0.1736111111110983 4 0.8 0.2604166666666687 5 1 0.0659722222222211 0 0 0.04880952380951875 1 0.1666666666666667 0.2571428571428811 2 0.3333333333333333 0.03214285714284415 3 0.5 0.3238095238095013 4 0.6666666666666666 0.03214285714278731 5 0.8333333333333334 0.2571428571428838 6 1 0.04880952380952142 0 0 0.04346064814816586 1 0.1428571428571428 0.2070023148149858 2 0.2857142857142857 0.07656250000019327 3 0.4285714285714285 0.1729745370369784 4 0.5714285714285714 0.1729745370371489 5 0.7142857142857143 0.07656250000005294 6 0.8571428571428571 0.2070023148148872 7 1 0.0434606481481824 0 0 0.03488536155206035 1 0.125 0.2076895943561112 2 0.25 -0.03273368606834737 3 0.375 0.3702292769000053 4 0.5 -0.1601410934754171 5 0.625 0.370229276900929 6 0.75 -0.03273368606535598 7 0.875 0.207689594355787 8 1 0.0348853615519884 0 0 0.03188616071413897 1 0.1111111111111111 0.1756808035706854 2 0.2222222222222222 0.01205357144226582 3 0.3333333333333333 0.2158928571161596 4 0.4444444444444444 0.06448660712112542 5 0.5555555555555556 0.06448660717715882 6 0.6666666666666666 0.215892857159794 7 0.7777777777777778 0.01205357143547303 8 0.8888888888888888 0.1756808035724458 9 1 0.03188616071432337 NC_COMPUTE_WEIGHTS_TEST Normal end of execution. NCC_COMPUTE_TEST Python version: 3.6.5 NCC_COMPUTE computes a Newton-Cotes Closed quadrature rule Index X W 0 0 2 0 -1 1 1 1 1 0 -1 0.3333333333333333 1 0 1.333333333333333 2 1 0.3333333333333333 0 -1 0.2500000000000004 1 -0.3333333333333333 0.7499999999999996 2 0.3333333333333333 0.75 3 1 0.25 0 -1 0.1555555555555557 1 -0.5 0.711111111111111 2 0 0.2666666666666666 3 0.5 0.711111111111111 4 1 0.1555555555555556 0 -1 0.1319444444444441 1 -0.6 0.5208333333333339 2 -0.2 0.3472222222222229 3 0.2 0.347222222222221 4 0.6 0.5208333333333326 5 1 0.1319444444444444 0 -1 0.09761904761904808 1 -0.6666666666666666 0.5142857142857133 2 -0.3333333333333333 0.06428571428570932 3 0 0.6476190476190524 4 0.3333333333333333 0.06428571428571317 5 0.6666666666666666 0.514285714285714 6 1 0.09761904761904755 0 -1 0.08692129629629897 1 -0.7142857142857143 0.4140046296296206 2 -0.4285714285714285 0.1531249999999869 3 -0.1428571428571428 0.3459490740740891 4 0.1428571428571428 0.3459490740740738 5 0.4285714285714285 0.1531250000000043 6 0.7142857142857143 0.4140046296296293 7 1 0.08692129629629636 0 -1 0.06977072310405794 1 -0.75 0.4153791887125269 2 -0.5 -0.0654673721340393 3 -0.25 0.7404585537919086 4 0 -0.3202821869488677 5 0.25 0.740458553791866 6 0.5 -0.0654673721340393 7 0.75 0.4153791887125232 8 1 0.06977072310405667 0 -1 0.06377232142857905 1 -0.7777777777777778 0.3513616071428758 2 -0.5555555555555556 0.02410714285722957 3 -0.3333333333333333 0.4317857142858179 4 -0.1111111111111111 0.1289732142857689 5 0.1111111111111111 0.1289732142858637 6 0.3333333333333333 0.4317857142856988 7 0.5555555555555556 0.02410714285714771 8 0.7777777777777778 0.3513616071428603 9 1 0.06377232142857162 NCC_COMPUTE_TEST Normal end of execution. NCC_SET_TEST Python version: 3.6.5 NCC_SET sets up a Newton-Cotes Closed quadrature rule Index X W 0 0 2 0 -1 1 1 1 1 0 -1 0.333333 1 0 1.33333 2 1 0.333333 0 -1 0.25 1 -0.333333 0.75 2 0.333333 0.75 3 1 0.25 0 -1 0.155556 1 -0.5 0.711111 2 0 0.266667 3 0.5 0.711111 4 1 0.155556 0 -1 0.131944 1 -0.6 0.520833 2 -0.2 0.347222 3 0.2 0.347222 4 0.6 0.520833 5 1 0.131944 0 -1 0.097619 1 -0.666667 0.514286 2 -0.333333 0.0642857 3 0 0.647619 4 0.333333 0.0642857 5 0.666667 0.514286 6 1 0.097619 0 -1 0.0869213 1 -0.714286 0.414005 2 -0.428571 0.153125 3 -0.142857 0.345949 4 0.142857 0.345949 5 0.428571 0.153125 6 0.714286 0.414005 7 1 0.0869213 0 -1 0.0697707 1 -0.75 0.415379 2 -0.5 -0.0654674 3 -0.25 0.740459 4 0 -0.320282 5 0.25 0.740459 6 0.5 -0.0654674 7 0.75 0.415379 8 1 0.0697707 0 -1 0.0637723 1 -0.777778 0.351362 2 -0.555556 0.0241071 3 -0.333333 0.431786 4 -0.111111 0.128973 5 0.111111 0.128973 6 0.333333 0.431786 7 0.555556 0.0241071 8 0.777778 0.351362 9 1 0.0637723 NCC_SET_TEST: Normal end of execution. NCO_COMPUTE_TEST Python version: 3.6.5 NCO_COMPUTE computes a Newton-Cotes Open quadrature rule Index X W 0 0 2 0 -1 1 1 1 1 0 -1 0.3333333333333333 1 0 1.333333333333333 2 1 0.3333333333333333 0 -1 0.2500000000000004 1 -0.3333333333333333 0.7499999999999996 2 0.3333333333333333 0.75 3 1 0.25 0 -1 0.1555555555555557 1 -0.5 0.711111111111111 2 0 0.2666666666666666 3 0.5 0.711111111111111 4 1 0.1555555555555556 0 -1 0.1319444444444441 1 -0.6 0.5208333333333339 2 -0.2 0.3472222222222229 3 0.2 0.347222222222221 4 0.6 0.5208333333333326 5 1 0.1319444444444444 0 -1 0.09761904761904808 1 -0.6666666666666666 0.5142857142857133 2 -0.3333333333333333 0.06428571428570932 3 0 0.6476190476190524 4 0.3333333333333333 0.06428571428571317 5 0.6666666666666666 0.514285714285714 6 1 0.09761904761904755 0 -1 0.08692129629629897 1 -0.7142857142857143 0.4140046296296206 2 -0.4285714285714285 0.1531249999999869 3 -0.1428571428571428 0.3459490740740891 4 0.1428571428571428 0.3459490740740738 5 0.4285714285714285 0.1531250000000043 6 0.7142857142857143 0.4140046296296293 7 1 0.08692129629629636 0 -1 0.06977072310405794 1 -0.75 0.4153791887125269 2 -0.5 -0.0654673721340393 3 -0.25 0.7404585537919086 4 0 -0.3202821869488677 5 0.25 0.740458553791866 6 0.5 -0.0654673721340393 7 0.75 0.4153791887125232 8 1 0.06977072310405667 0 -1 0.06377232142857905 1 -0.7777777777777778 0.3513616071428758 2 -0.5555555555555556 0.02410714285722957 3 -0.3333333333333333 0.4317857142858179 4 -0.1111111111111111 0.1289732142857689 5 0.1111111111111111 0.1289732142858637 6 0.3333333333333333 0.4317857142856988 7 0.5555555555555556 0.02410714285714771 8 0.7777777777777778 0.3513616071428603 9 1 0.06377232142857162 NCO_COMPUTE_TEST Normal end of execution. NCO_SET_TEST Python version: 3.6.5 NCO_SET sets up a Newton-Cotes Open quadrature rule Index X W 0 0 2 0 -0.333333 1 1 0.333333 1 0 -0.5 1.33333 1 0 -0.666667 2 0.5 1.33333 0 -0.6 0.916667 1 -0.2 0.0833333 2 0.2 0.0833333 3 0.6 0.916667 0 -0.666667 1.1 1 -0.333333 -1.4 2 0 2.6 3 0.333333 -1.4 4 0.666667 1.1 0 -0.714286 0.848611 1 -0.428571 -0.629167 2 -0.142857 0.780556 3 0.142857 0.780556 4 0.428571 -0.629167 5 0.714286 0.848611 0 -0.75 0.973545 1 -0.5 -2.01905 2 -0.25 4.64762 3 0 -5.20423 4 0.25 4.64762 5 0.5 -2.01905 6 0.75 0.973545 0 -0.777778 0.797768 1 -0.555556 -1.25134 2 -0.333333 2.21741 3 -0.111111 -0.763839 4 0.111111 -0.763839 5 0.333333 2.21741 6 0.555556 -1.25134 7 0.777778 0.797768 0 -0.8 0.891755 1 -0.6 -2.57716 2 -0.4 7.35009 3 -0.2 -12.1407 4 0 14.9519 5 0.2 -12.1407 6 0.4 7.35009 7 0.6 -2.57716 8 0.8 0.891755 0 -0.818182 0.758509 1 -0.636364 -1.81966 2 -0.454545 4.3193 3 -0.272727 -4.70834 4 -0.0909091 2.45019 5 0.0909091 2.45019 6 0.272727 -4.70834 7 0.454545 4.3193 8 0.636364 -1.81966 9 0.818182 0.758509 NCO_SET_TEST: Normal end of execution. NCOH_COMPUTE_TEST Python version: 3.6.5 NCOH_COMPUTE computes a Newton-Cotes Open Half quadrature rule Index X W 0 0 2 0 -0.5 1 1 0.5 1 0 -0.6666666666666666 0.75 1 0 0.5 2 0.6666666666666666 0.75 0 -0.75 0.5416666666666666 1 -0.25 0.4583333333333335 2 0.25 0.4583333333333335 3 0.75 0.5416666666666666 0 -0.8 0.4774305555555558 1 -0.4 0.1736111111111107 2 0 0.697916666666667 3 0.4 0.1736111111111112 4 0.8 0.4774305555555554 0 -0.8333333333333334 0.3859375 1 -0.5 0.2171874999999994 2 -0.1666666666666667 0.3968749999999941 3 0.1666666666666667 0.3968750000000001 4 0.5 0.2171875000000004 5 0.8333333333333334 0.3859374999999999 0 -0.8571428571428571 0.3580005787037045 1 -0.5714285714285714 0.0127604166666625 2 -0.2857142857142857 0.8102864583333247 3 0 -0.3620949074074109 4 0.2857142857142857 0.8102864583333318 5 0.5714285714285714 0.01276041666666561 6 0.8571428571428571 0.3580005787037041 0 -0.875 0.3055007853835972 1 -0.625 0.07371135085978964 2 -0.375 0.4875279017857209 3 -0.125 0.1332599619708654 4 0.125 0.1332599619709007 5 0.375 0.487527901785696 6 0.625 0.07371135085978775 7 0.875 0.3055007853835978 0 -0.8888888888888888 0.2902556501116099 1 -0.6666666666666666 -0.09096261160714961 2 -0.4444444444444444 1.012537667410742 3 -0.2222222222222222 -1.12557756696433 4 0 1.82749372209814 5 0.2222222222222222 -1.125577566964292 6 0.4444444444444444 1.012537667410705 7 0.6666666666666666 -0.09096261160714395 8 0.8888888888888888 0.2902556501116076 0 -0.9 0.2557278856819025 1 -0.7 -0.02652149772308931 2 -0.5 0.6604044811645895 3 -0.3 -0.3376966473075349 4 -0.1 0.4480857781842378 5 0.1 0.4480857781845167 6 0.3 -0.3376966473076202 7 0.5 0.6604044811646075 8 0.7 -0.02652149772306411 9 0.9 0.2557278856819051 NCOH_COMPUTE_TEST Normal end of execution. NCOH_SET_TEST Python version: 3.6.5 NCOH_SET sets up a Newton-Cotes Open half quadrature rule Index X W 0 0 2 0 -0.5 1 1 0.5 1 0 -0.6666666666666666 0.75 1 0 0.5 2 0.6666666666666666 0.75 0 -0.75 0.5416666666666666 1 -0.25 0.4583333333333333 2 0.25 0.4583333333333333 3 0.75 0.5416666666666666 0 -0.8 0.4774305555555556 1 -0.4 0.1736111111111111 2 0 0.6979166666666666 3 0.4 0.1736111111111111 4 0.8 0.4774305555555556 0 -0.8333333333333334 0.3859375 1 -0.5 0.2171875 2 -0.1666666666666667 0.396875 3 0.1666666666666667 0.396875 4 0.5 0.2171875 5 0.8333333333333334 0.3859375 0 -0.8571428571428571 0.3580005787037037 1 -0.5714285714285714 0.01276041666666667 2 -0.2857142857142857 0.8102864583333333 3 0 -0.3620949074074074 4 0.2857142857142857 0.8102864583333333 5 0.5714285714285714 0.01276041666666667 6 0.8571428571428571 0.3580005787037037 0 -0.875 0.3055007853835979 1 -0.625 0.07371135085978836 2 -0.375 0.4875279017857143 3 -0.125 0.1332599619708995 4 0.125 0.1332599619708995 5 0.375 0.4875279017857143 6 0.625 0.07371135085978836 7 0.875 0.3055007853835979 0 -0.8888888888888888 0.2902556501116071 1 -0.6666666666666666 -0.09096261160714286 2 -0.4444444444444444 1.012537667410714 3 -0.2222222222222222 -1.125577566964286 4 0 1.827493722098214 5 0.2222222222222222 -1.125577566964286 6 0.4444444444444444 1.012537667410714 7 0.6666666666666666 -0.09096261160714286 8 0.8888888888888888 0.2902556501116071 0 -0.9 0.2557278856819059 1 -0.7 -0.0265214977230765 2 -0.5 0.6604044811645723 3 -0.3 -0.3376966473076499 4 -0.1 0.4480857781842482 5 0.1 0.4480857781842482 6 0.3 -0.3376966473076499 7 0.5 0.6604044811645723 8 0.7 -0.0265214977230765 9 0.9 0.2557278856819059 NCOH_SET_TEST: Normal end of execution. PATTERSON_SET_TEST Python version: 3.6.5 PATTERSON_SET sets a Patterson quadrature rule. Index X W 0 0 2 0 -0.7745966692414834 0.5555555555555556 1 0 0.8888888888888888 2 0.7745966692414834 0.5555555555555556 0 -0.9604912687080203 0.1046562260264673 1 -0.7745966692414834 0.2684880898683334 2 -0.4342437493468025 0.4013974147759622 3 0 0.4509165386584741 4 0.4342437493468025 0.4013974147759622 5 0.7745966692414834 0.2684880898683334 6 0.9604912687080203 0.1046562260264673 0 -0.993831963212755 0.01700171962994026 1 -0.9604912687080203 0.05160328299707974 2 -0.888459232872257 0.09292719531512454 3 -0.7745966692414834 0.1344152552437842 4 -0.6211029467372264 0.1715119091363914 5 -0.4342437493468025 0.200628529376989 6 -0.2233866864289669 0.2191568584015875 7 0 0.2255104997982067 8 0.2233866864289669 0.2191568584015875 9 0.4342437493468025 0.200628529376989 10 0.6211029467372264 0.1715119091363914 11 0.7745966692414834 0.1344152552437842 12 0.888459232872257 0.09292719531512454 13 0.9604912687080203 0.05160328299707974 14 0.993831963212755 0.01700171962994026 PATTERSON_SET_TEST: Normal end of execution. RADAU_SET_TEST Python version: 3.6.5 RADAU_SET sets a Radau rule. I X W 0 -1 0.125 1 -0.5753189235216941 0.6576886399601195 2 0.1810662711185306 0.7763869376863438 3 0.8228240809745921 0.4409244223535367 0 -1 0.04081632653061224 1 -0.8538913426394822 0.2392274892253124 2 -0.538467724060109 0.3809498736442312 3 -0.1173430375431003 0.4471098290145665 4 0.3260306194376914 0.4247037790059556 5 0.7038428006630314 0.3182042314673015 6 0.9413671456804302 0.1489884711120206 0 -1 0.02 1 -0.9274843742335811 0.1202966705574816 2 -0.7638420424200026 0.2042701318790007 3 -0.5256460303700792 0.2681948378411787 4 -0.236234469390588 0.3058592877244226 5 0.07605919783797813 0.3135824572269384 6 0.3806648401447243 0.2906101648329183 7 0.6477666876740095 0.2391934317143797 8 0.8512252205816079 0.1643760127369215 9 0.971175180702247 0.07361700548675849 RADAU_SET_TEST: Normal end of execution. TIMESTAMP_TEST: Python version: 3.6.5 TIMESTAMP prints a timestamp of the current date and time. Thu Sep 13 14:53:09 2018 TIMESTAMP_TEST: Normal end of execution. QUADRULE_TEST: Normal end of execution. Thu Sep 13 14:53:09 2018