Tue Oct 19 11:34:06 2021 FASTGL_TEST Python version: 3.6.9 Test FASTGL. BESSELJZERO_TEST: Python version: 3.6.9 BESSELJZERO returns the K-th zero of J0(X). K X(K) J0(X(K)) 1 2.404825557695773 -9.586882554916807e-17 2 5.520078110286311 -1.649512978984192e-17 3 8.653727912911013 -8.704431814720906e-17 4 11.79153443901428 -2.648198437547529e-16 5 14.93091770848779 3.116350654874824e-17 6 18.07106396791092 2.018692387036633e-17 7 21.21163662987926 2.344109152846459e-16 8 24.3524715307493 -2.86928989515932e-16 9 27.49347913204025 3.768179511787033e-16 10 30.63460646843198 -4.60131523227105e-17 11 33.77582021357357 -1.703433687342173e-16 12 36.91709835366404 4.757064369962872e-16 13 40.05842576462824 -3.73517749785528e-16 14 43.19979171317673 2.233264506649664e-16 15 46.34118837166181 -4.222004282041191e-16 16 49.48260989739781 3.531900590014637e-17 17 52.624051841115 -4.895448801427226e-16 18 55.76551075501998 5.281022674030892e-16 19 58.90698392608094 -8.448828973789405e-17 20 62.04846919022717 -8.623133105851914e-17 21 65.18996480020687 -8.060939453919353e-16 22 68.33146932985679 -7.839972438305659e-16 23 71.47298160359372 6.426179603201589e-16 24 74.61450064370183 -3.873292258284105e-16 25 77.75602563038805 1.742313368754129e-17 26 80.89755587113763 1.253796306490628e-16 27 84.03909077693818 5.45730056874019e-16 28 87.18062984364116 4.857397268575678e-16 29 90.32217263721049 -6.741558543062515e-16 30 93.46371878194476 -6.800166403610428e-16 BESSELJZERO_TEST: Normal end of execution. BESSELJ1SQUARED_TEST: Python version: 3.6.9 BESSELJ1SQUARED returns the square of the Bessel J1(X) function at the K-th zero of J0(X). K X(K) J1(X(K))^2 BESSELJ1SQUARED 1 2.404825557695773 0.2695141239419168 0.2695141239419169 2 5.520078110286311 0.1157801385822038 0.1157801385822037 3 8.653727912911013 0.07368635113640826 0.07368635113640822 4 11.79153443901428 0.05403757319811629 0.05403757319811628 5 14.93091770848779 0.04266142901724307 0.04266142901724309 6 18.07106396791092 0.03524210349099611 0.0352421034909961 7 21.21163662987926 0.03002107010305466 0.03002107010305467 8 24.3524715307493 0.02614739149530809 0.02614739149530809 9 27.49347913204025 0.0231591218246914 0.02315912182469139 10 30.63460646843198 0.02078382912226784 0.02078382912226786 11 33.77582021357357 0.01885045066931767 0.01885045066931767 12 36.91709835366404 0.01724615756966501 0.01724615756966501 13 40.05842576462824 0.0158935181059236 0.0158935181059236 14 43.19979171317673 0.01473762609647219 0.01473762609647219 15 46.34118837166181 0.01373846514538712 0.01373846514538712 16 49.48260989739781 0.01286618173761514 0.01286618173761513 17 52.624051841115 0.01209805154862679 0.0120980515486268 18 55.76551075501998 0.01141647122449161 0.01141647122449161 19 58.90698392608094 0.01080759279118021 0.0108075927911802 20 62.04846919022717 0.01026037292628077 0.01026037292628076 21 65.18996480020687 0.009765897139791058 0.009765897139791051 22 68.33146932985679 0.009316890387627164 0.009316890387627166 23 71.47298160359372 0.008907356754001994 0.008907356754001991 24 74.61450064370183 0.008532310161358086 0.008532310161358083 25 77.75602563038805 0.00818757036270815 0.008187570362708157 26 80.89755587113763 0.007869606469720772 0.007869606469720769 27 84.03909077693818 0.007575415577297648 0.007575415577297647 28 87.18062984364116 0.007302427631477642 0.007302427631477641 29 90.32217263721049 0.007048430150990362 0.007048430150990362 30 93.46371878194476 0.006811508131014092 0.006811508131014086 BESSELJ1SQUARED_TEST: Normal end of execution. GLPAIR_TEST Python version: 3.6.9 Estimate integral ( 0 <= x <= 1 ) ln(x) dx. Nodes Estimate 1 -0.6931471805599453 10 -0.9942637022162133 100 -0.9999374873224512 1000 -0.9999993692484898 10000 -0.9999999936868078 100000 -0.9999999999368618 1000000 -0.9999999999993812 Exact -1.0 GLPAIR_TEST: Normal end of execution. GLPAIRS_TEST: Python version: 3.6.9 integral ( -1 <= x <= 1 ) cos(1000 x) dx Nodes Estimate 500 -0.2538816332422891 520 0.001592120992016624 540 0.001653759028178648 560 0.001653759081049292 580 0.001653759081048851 600 0.001653759081066034 Exact 0.001653759081064005 GLPAIRS_TEST: Normal end of execution. GLPAIRTABULATED_TEST: Python version: 3.6.9 integral ( -1 <= x <= 1 ) exp(x) dx Nodes Estimate 1 2 2 2.342696087909731 3 2.350336928680012 4 2.350402092156377 5 2.350402386462826 6 2.350402387286035 7 2.350402387287601 8 2.350402387287603 9 2.350402387287603 Exact 2.350402387287603 GLPAIRTABULATED_TEST: Normal end of execution. LEGENDRE_THETA_TEST: Python version: 3.6.9 LEGENDRE_THETA returns the K-th theta value for a Gauss Legendre rule of order L. Gauss Legendre rule of order 1 K Theta Cos(Theta) 1 1.5708 6.12323e-17 Gauss Legendre rule of order 2 K Theta Cos(Theta) 1 2.18628 -0.57735 2 0.955317 0.57735 Gauss Legendre rule of order 3 K Theta Cos(Theta) 1 2.45687 -0.774597 2 1.5708 6.12323e-17 3 0.684719 0.774597 Gauss Legendre rule of order 4 K Theta Cos(Theta) 1 2.6083 -0.861136 2 1.91769 -0.339981 3 1.2239 0.339981 4 0.533296 0.861136 Gauss Legendre rule of order 5 K Theta Cos(Theta) 1 2.70496 -0.90618 2 2.13942 -0.538469 3 1.5708 6.12323e-17 4 1.00218 0.538469 5 0.436635 0.90618 Gauss Legendre rule of order 6 K Theta Cos(Theta) 1 2.77199 -0.93247 2 2.29323 -0.661209 3 1.81174 -0.238619 4 1.32985 0.238619 5 0.848367 0.661209 6 0.369607 0.93247 Gauss Legendre rule of order 7 K Theta Cos(Theta) 1 2.82119 -0.949108 2 2.40615 -0.741531 3 1.9887 -0.405845 4 1.5708 6.12323e-17 5 1.15289 0.405845 6 0.735447 0.741531 7 0.320405 0.949108 Gauss Legendre rule of order 8 K Theta Cos(Theta) 1 2.85884 -0.96029 2 2.49256 -0.796666 3 2.12414 -0.525532 4 1.75528 -0.183435 5 1.38632 0.183435 6 1.01746 0.525532 7 0.649037 0.796666 8 0.282757 0.96029 Gauss Legendre rule of order 9 K Theta Cos(Theta) 1 2.88857 -0.96816 2 2.56081 -0.836031 3 2.23112 -0.613371 4 1.90102 -0.324253 5 1.5708 6.12323e-17 6 1.24057 0.324253 7 0.910474 0.613371 8 0.580787 0.836031 9 0.253022 0.96816 Gauss Legendre rule of order 10 K Theta Cos(Theta) 1 2.91265 -0.973907 2 2.61607 -0.865063 3 2.31775 -0.67941 4 2.01905 -0.433395 5 1.72023 -0.148874 6 1.42137 0.148874 7 1.12254 0.433395 8 0.823839 0.67941 9 0.52552 0.865063 10 0.228944 0.973907 LEGENDRE_THETA_TEST: Normal end of execution. LEGENDRE_WEIGHT_TEST: Python version: 3.6.9 LEGENDRE_WEIGHT returns the K-th weight for a Gauss Legendre rule of order L. Gauss Legendre rule of order 1 K Weight 1 2 Gauss Legendre rule of order 2 K Weight 1 1 2 1 Gauss Legendre rule of order 3 K Weight 1 0.555556 2 0.888889 3 0.555556 Gauss Legendre rule of order 4 K Weight 1 0.347855 2 0.652145 3 0.652145 4 0.347855 Gauss Legendre rule of order 5 K Weight 1 0.236927 2 0.478629 3 0.568889 4 0.478629 5 0.236927 Gauss Legendre rule of order 6 K Weight 1 0.171324 2 0.360762 3 0.467914 4 0.467914 5 0.360762 6 0.171324 Gauss Legendre rule of order 7 K Weight 1 0.129485 2 0.279705 3 0.38183 4 0.417959 5 0.38183 6 0.279705 7 0.129485 Gauss Legendre rule of order 8 K Weight 1 0.101229 2 0.222381 3 0.313707 4 0.362684 5 0.362684 6 0.313707 7 0.222381 8 0.101229 Gauss Legendre rule of order 9 K Weight 1 0.0812744 2 0.180648 3 0.260611 4 0.312347 5 0.330239 6 0.312347 7 0.260611 8 0.180648 9 0.0812744 Gauss Legendre rule of order 10 K Weight 1 0.0666713 2 0.149451 3 0.219086 4 0.269267 5 0.295524 6 0.295524 7 0.269267 8 0.219086 9 0.149451 10 0.0666713 LEGENDRE_WEIGHT_TEST: Normal end of execution. FASTGL_TEST: Normal end of execution. Tue Oct 19 11:34:19 2021