28 February 2022 09:13:16 AM TOMS655_TEST C version Test the TOMS655 library. ---------------------------------------- TEST01 Test CIQFS. Interpolatory quadrature formula Type Interval Weight function Name 1 (-1,+1) 1.0 Legendre Machine precision = 2.22045e-16 Knots Mult Weights 1 0.95105651629515353 2 0.22240110861588505 -0.0073134471884532138 2 0.58778525229247314 2 0.48363063741586088 -0.017871860197559892 3 6.123233995736766e-17 2 0.58793650793650787 -7.6050277186823266e-17 4 -0.58778525229247303 2 0.48363063741586082 0.017871860197559951 5 -0.95105651629515353 2 0.22240110861588536 0.0073134471884532008 Comparison of moments Order of precision 10 Errors : Absolute Relative ---------+------------------------- Minimum : 0.000e+00 0.000e+00 Maximum : 2.498e-16 2.498e-16 Weights ratio 0.667 Error in 10th power 3.867e-03 Error constant 0.000 Moments: True from QF Error Relative 1 2.0000000000e+00 2.0000000000e+00 0.000e+00 0.000e+00 2 0.0000000000e+00 -2.2204460493e-16 2.220e-16 2.220e-16 3 6.6666666667e-01 6.6666666667e-01 2.220e-16 1.332e-16 4 0.0000000000e+00 -2.2204460493e-16 2.220e-16 2.220e-16 5 4.0000000000e-01 4.0000000000e-01 1.110e-16 7.930e-17 6 0.0000000000e+00 -2.2204460493e-16 2.220e-16 2.220e-16 7 2.8571428571e-01 2.8571428571e-01 1.110e-16 8.635e-17 8 0.0000000000e+00 -1.9428902931e-16 1.943e-16 1.943e-16 9 2.2222222222e-01 2.2222222222e-01 1.388e-16 1.135e-16 10 0.0000000000e+00 -2.4980018054e-16 2.498e-16 2.498e-16 11 1.8181818182e-01 1.7795138889e-01 3.867e-03 3.272e-03 12 0.0000000000e+00 -2.4980018054e-16 2.498e-16 2.498e-16 13 1.5384615385e-01 1.4291914683e-01 1.093e-02 9.470e-03 ---------------------------------------- TEST02 Test CIQF, CIQFS, CGQF and CGQFS with all classical weight functions. Knots and weights of Gauss quadrature formula computed by CGQF. Interpolatory quadrature formula Type Interval Weight function Name 1 (a,b) 1.0 Legendre Parameters A -0.500000 B 2.000000 Machine precision = 2.22045e-16 Knots Mult Weights 1 -0.38272480742333004 1 0.29615860632023655 2 0.076913362367896254 1 0.59828583812420855 3 0.74999999999999989 1 0.71111111111111125 4 1.4230866376321039 1 0.59828583812420899 5 1.8827248074233298 1 0.29615860632023638 Comparison of moments Order of precision 10 Errors : Absolute Relative ---------+------------------------- Minimum : 0.000e+00 0.000e+00 Maximum : 1.998e-15 1.998e-15 Weights ratio 0.714 Error in 10th power 3.413e-02 Error constant 0.000 Moments: True from QF Error Relative 1 2.5000000000e+00 2.5000000000e+00 -1.776e-15 -5.075e-16 2 0.0000000000e+00 -5.5511151231e-17 5.551e-17 5.551e-17 3 1.3020833333e+00 1.3020833333e+00 -6.661e-16 -2.894e-16 4 0.0000000000e+00 -2.7755575616e-16 2.776e-16 2.776e-16 5 1.2207031250e+00 1.2207031250e+00 -4.441e-16 -2.000e-16 6 0.0000000000e+00 -7.7715611724e-16 7.772e-16 7.772e-16 7 1.3623918806e+00 1.3623918806e+00 -2.220e-16 -9.399e-17 8 0.0000000000e+00 -1.5543122345e-15 1.554e-15 1.554e-15 9 1.6556845771e+00 1.6556845771e+00 0.000e+00 0.000e+00 10 0.0000000000e+00 -1.9984014443e-15 1.998e-15 1.998e-15 11 2.1166422150e+00 2.0825114260e+00 3.413e-02 1.095e-02 12 0.0000000000e+00 -3.1086244690e-15 3.109e-15 3.109e-15 13 2.7984452362e+00 2.6530429698e+00 1.454e-01 3.828e-02 Weights of Gauss quadrature formula computed from the knots by CIQF. Interpolatory quadrature formula Type Interval Weight function Name 1 (a,b) 1.0 Legendre Parameters A -0.500000 B 2.000000 Machine precision = 2.22045e-16 Knots Mult Weights 1 -0.38272480742333004 2 0.29615860632023622 3.3728379694473028e-33 2 0.076913362367896254 2 0.5982858381242081 3.687623125937935e-32 3 0.74999999999999989 2 0.71111111111111114 -9.6164787288126241e-17 4 1.4230866376321039 2 0.59828583812420855 8.7989865281877796e-32 5 1.8827248074233298 2 0.29615860632023616 -4.1100262959702906e-17 Comparison of moments Order of precision 10 Errors : Absolute Relative ---------+------------------------- Minimum : 0.000e+00 0.000e+00 Maximum : 2.665e-15 2.665e-15 Weights ratio 0.714 Error in 10th power 3.413e-02 Error constant 0.000 Moments: True from QF Error Relative 1 2.5000000000e+00 2.5000000000e+00 0.000e+00 0.000e+00 2 0.0000000000e+00 -1.1102230246e-16 1.110e-16 1.110e-16 3 1.3020833333e+00 1.3020833333e+00 4.441e-16 1.929e-16 4 0.0000000000e+00 -3.8857805862e-16 3.886e-16 3.886e-16 5 1.2207031250e+00 1.2207031250e+00 8.882e-16 4.000e-16 6 0.0000000000e+00 -9.9920072216e-16 9.992e-16 9.992e-16 7 1.3623918806e+00 1.3623918806e+00 1.554e-15 6.579e-16 8 0.0000000000e+00 -1.6653345369e-15 1.665e-15 1.665e-15 9 1.6556845771e+00 1.6556845771e+00 2.220e-15 8.361e-16 10 0.0000000000e+00 -2.6645352591e-15 2.665e-15 2.665e-15 11 2.1166422150e+00 2.0825114260e+00 3.413e-02 1.095e-02 12 0.0000000000e+00 -4.4408920985e-15 4.441e-15 4.441e-15 13 2.7984452362e+00 2.6530429698e+00 1.454e-01 3.828e-02 Knots and weights of Gauss quadrature formula computed by CGQF. Interpolatory quadrature formula Type Interval Weight function Name 2 (a,b) ((b-x)*(x-a))^(-0.5) Chebyshev Parameters A -0.500000 B 2.000000 Machine precision = 2.22045e-16 Knots Mult Weights 1 -0.43882064536894183 1 0.62831853071795774 2 0.01526843463440819 1 0.62831853071795873 3 0.75 1 0.62831853071795929 4 1.4847315653655919 1 0.62831853071795962 5 1.9388206453689418 1 0.62831853071795862 Comparison of moments Order of precision 10 Errors : Absolute Relative ---------+------------------------- Minimum : 4.441e-16 1.286e-16 Maximum : 7.105e-15 3.997e-15 Weights ratio 0.759 Error in 10th power 5.715e-02 Error constant 0.000 Moments: True from QF Error Relative 1 3.1415926536e+00 3.1415926536e+00 -8.882e-16 -2.145e-16 2 0.0000000000e+00 1.7763568394e-15 -1.776e-15 -1.776e-15 3 2.4543692606e+00 2.4543692606e+00 4.441e-16 1.286e-16 4 0.0000000000e+00 1.9984014443e-15 -1.998e-15 -1.998e-15 5 2.8762139773e+00 2.8762139773e+00 1.776e-15 4.583e-16 6 0.0000000000e+00 2.6645352591e-15 -2.665e-15 -2.665e-15 7 3.7450702829e+00 3.7450702829e+00 3.997e-15 8.423e-16 8 0.0000000000e+00 3.5527136788e-15 -3.553e-15 -3.553e-15 9 5.1202132774e+00 5.1202132774e+00 7.105e-15 1.161e-15 10 0.0000000000e+00 3.9968028887e-15 -3.997e-15 -3.997e-15 11 7.2002999214e+00 7.1431546839e+00 5.715e-02 6.969e-03 12 0.0000000000e+00 6.2172489379e-15 -6.217e-15 -6.217e-15 13 1.0312929575e+01 1.0045061274e+01 2.679e-01 2.368e-02 Weights of Gauss quadrature formula computed from the knots by CIQF. Interpolatory quadrature formula Type Interval Weight function Name 2 (a,b) ((b-x)*(x-a))^(-0.5) Chebyshev Parameters A -0.500000 B 2.000000 Machine precision = 2.22045e-16 Knots Mult Weights 1 -0.43882064536894183 2 0.62831853071795774 -8.7196712450215769e-17 2 0.01526843463440819 2 0.62831853071795907 -1.6407443524653312e-31 3 0.75 2 0.62831853071795951 -8.5419973901991823e-17 4 1.4847315653655919 2 0.62831853071795962 -8.7196712450215979e-17 5 1.9388206453689418 2 0.62831853071795907 -9.9103068477365945e-33 Comparison of moments Order of precision 10 Errors : Absolute Relative ---------+------------------------- Minimum : 4.441e-16 1.146e-16 Maximum : 3.553e-15 3.109e-15 Weights ratio 0.759 Error in 10th power 5.715e-02 Error constant 0.000 Moments: True from QF Error Relative 1 3.1415926536e+00 3.1415926536e+00 -1.776e-15 -4.289e-16 2 0.0000000000e+00 2.1094237468e-15 -2.109e-15 -2.109e-15 3 2.4543692606e+00 2.4543692606e+00 -4.441e-16 -1.286e-16 4 0.0000000000e+00 1.7763568394e-15 -1.776e-15 -1.776e-15 5 2.8762139773e+00 2.8762139773e+00 4.441e-16 1.146e-16 6 0.0000000000e+00 2.4424906542e-15 -2.442e-15 -2.442e-15 7 3.7450702829e+00 3.7450702829e+00 1.332e-15 2.808e-16 8 0.0000000000e+00 2.6645352591e-15 -2.665e-15 -2.665e-15 9 5.1202132774e+00 5.1202132774e+00 3.553e-15 5.805e-16 10 0.0000000000e+00 3.1086244690e-15 -3.109e-15 -3.109e-15 11 7.2002999214e+00 7.1431546839e+00 5.715e-02 6.969e-03 12 0.0000000000e+00 3.5527136788e-15 -3.553e-15 -3.553e-15 13 1.0312929575e+01 1.0045061274e+01 2.679e-01 2.368e-02 Knots and weights of Gauss quadrature formula computed by CGQF. Interpolatory quadrature formula Type Interval Weight function Name 3 (a,b) ((b-x)*(x-a))^alpha Gegenbauer Parameters A -0.500000 B 2.000000 alpha 0.500000 Machine precision = 2.22045e-16 Knots Mult Weights 1 -0.33253175473054863 1 0.20453077171808579 2 0.12500000000000022 1 0.61359231515425683 3 0.75000000000000011 1 0.8181230868723417 4 1.3749999999999998 1 0.61359231515425661 5 1.8325317547305486 1 0.20453077171808542 Comparison of moments Order of precision 10 Errors : Absolute Relative ---------+------------------------- Minimum : 4.163e-16 1.286e-16 Maximum : 1.998e-15 1.110e-15 Weights ratio 0.711 Error in 10th power 2.232e-02 Error constant 0.000 Moments: True from QF Error Relative 1 2.4543692606e+00 2.4543692606e+00 -4.441e-16 -1.286e-16 2 0.0000000000e+00 -4.1633363423e-16 4.163e-16 4.163e-16 3 9.5873799243e-01 9.5873799243e-01 -4.441e-16 -2.267e-16 4 0.0000000000e+00 -4.9960036108e-16 4.996e-16 4.996e-16 5 7.4901405658e-01 7.4901405658e-01 -7.772e-16 -4.443e-16 6 0.0000000000e+00 -6.1062266354e-16 6.106e-16 6.106e-16 7 7.3145903963e-01 7.3145903963e-01 -1.332e-15 -7.694e-16 8 0.0000000000e+00 -6.6613381478e-16 6.661e-16 6.661e-16 9 8.0003332460e-01 8.0003332460e-01 -1.998e-15 -1.110e-15 10 0.0000000000e+00 -7.2164496601e-16 7.216e-16 7.216e-16 11 9.3753905226e-01 9.1521669388e-01 2.232e-02 1.152e-02 12 0.0000000000e+00 -8.3266726847e-16 8.327e-16 8.327e-16 13 1.1509966043e+00 1.0637998919e+00 8.720e-02 4.054e-02 Weights of Gauss quadrature formula computed from the knots by CIQF. Interpolatory quadrature formula Type Interval Weight function Name 3 (a,b) ((b-x)*(x-a))^alpha Gegenbauer Parameters A -0.500000 B 2.000000 alpha 0.500000 Machine precision = 2.22045e-16 Knots Mult Weights 1 -0.33253175473054863 2 0.2045307717180859 -2.8384346500721368e-17 2 0.12500000000000022 2 0.61359231515425661 -4.2576519751082002e-17 3 0.75000000000000011 2 0.81812308687234192 -5.2664014366543454e-17 4 1.3749999999999998 2 0.61359231515425627 -4.2576519751081866e-17 5 1.8325317547305486 2 0.2045307717180854 -2.838434650072125e-17 Comparison of moments Order of precision 10 Errors : Absolute Relative ---------+------------------------- Minimum : 0.000e+00 0.000e+00 Maximum : 2.220e-15 1.998e-15 Weights ratio 0.711 Error in 10th power 2.232e-02 Error constant 0.000 Moments: True from QF Error Relative 1 2.4543692606e+00 2.4543692606e+00 0.000e+00 0.000e+00 2 0.0000000000e+00 -6.9388939039e-16 6.939e-16 6.939e-16 3 9.5873799243e-01 9.5873799243e-01 -2.220e-16 -1.134e-16 4 0.0000000000e+00 -9.9920072216e-16 9.992e-16 9.992e-16 5 7.4901405658e-01 7.4901405658e-01 -7.772e-16 -4.443e-16 6 0.0000000000e+00 -1.3322676296e-15 1.332e-15 1.332e-15 7 7.3145903963e-01 7.3145903963e-01 -1.443e-15 -8.336e-16 8 0.0000000000e+00 -1.5543122345e-15 1.554e-15 1.554e-15 9 8.0003332460e-01 8.0003332460e-01 -2.220e-15 -1.234e-15 10 0.0000000000e+00 -1.9984014443e-15 1.998e-15 1.998e-15 11 9.3753905226e-01 9.1521669388e-01 2.232e-02 1.152e-02 12 0.0000000000e+00 -2.5535129566e-15 2.554e-15 2.554e-15 13 1.1509966043e+00 1.0637998919e+00 8.720e-02 4.054e-02 Knots and weights of Gauss quadrature formula computed by CGQF. Interpolatory quadrature formula Type Interval Weight function Name 4 (a,b) (b-x)^alpha*(x-a)^beta Jacobi Parameters A -0.500000 B 2.000000 alpha 0.500000 beta 2.000000 Machine precision = 2.22045e-16 Knots Mult Weights 1 -0.15303633066793587 1 0.076617129890421465 2 0.35753707671627766 1 0.5365906798597585 3 0.94535638653559406 1 1.2551248538055733 4 1.485888088482969 1 1.3472898724319176 5 1.8642547789330952 1 0.54899372611754638 Comparison of moments Order of precision 10 Errors : Absolute Relative ---------+------------------------- Minimum : 8.882e-16 4.069e-16 Maximum : 3.553e-15 7.968e-16 Weights ratio 0.790 Error in 10th power 1.458e-02 Error constant 0.000 Moments: True from QF Error Relative 1 3.7646162621e+00 3.7646162621e+00 -3.553e-15 -7.456e-16 2 1.5685901092e+00 1.5685901092e+00 -1.110e-15 -4.322e-16 3 1.6042398844e+00 1.6042398844e+00 -1.332e-15 -5.116e-16 4 1.2168913653e+00 1.2168913653e+00 -1.332e-15 -6.010e-16 5 1.3068727691e+00 1.3068727691e+00 -1.332e-15 -5.775e-16 6 1.1830538206e+00 1.1830538206e+00 -8.882e-16 -4.069e-16 7 1.3082283602e+00 1.3082283602e+00 -1.110e-15 -4.810e-16 8 1.2899102613e+00 1.2899102613e+00 -1.776e-15 -7.757e-16 9 1.4545503852e+00 1.4545503852e+00 -1.776e-15 -7.237e-16 10 1.5080928191e+00 1.5080928191e+00 -1.998e-15 -7.968e-16 11 1.7246139873e+00 1.7100388000e+00 1.458e-02 5.349e-03 12 1.8481104500e+00 1.8258707245e+00 2.224e-02 7.809e-03 13 2.1359361290e+00 2.0673751409e+00 6.856e-02 2.186e-02 Weights of Gauss quadrature formula computed from the knots by CIQF. Interpolatory quadrature formula Type Interval Weight function Name 4 (a,b) (b-x)^alpha*(x-a)^beta Jacobi Parameters A -0.500000 B 2.000000 alpha 0.500000 beta 2.000000 Machine precision = 2.22045e-16 Knots Mult Weights 1 -0.15303633066793587 2 0.076617129890421368 8.0169897973760331e-33 2 0.35753707671627766 2 0.53659067985975828 -3.7233457973722988e-17 3 0.94535638653559406 2 1.2551248538055706 -8.7091781967138696e-17 4 1.485888088482969 2 1.3472898724319171 -1.8697402965227462e-16 5 1.8642547789330952 2 0.54899372611754571 -1.5237636877761369e-16 Comparison of moments Order of precision 10 Errors : Absolute Relative ---------+------------------------- Minimum : 4.441e-16 9.321e-17 Maximum : 3.109e-15 1.239e-15 Weights ratio 0.790 Error in 10th power 1.458e-02 Error constant 0.000 Moments: True from QF Error Relative 1 3.7646162621e+00 3.7646162621e+00 4.441e-16 9.321e-17 2 1.5685901092e+00 1.5685901092e+00 6.661e-16 2.593e-16 3 1.6042398844e+00 1.6042398844e+00 6.661e-16 2.558e-16 4 1.2168913653e+00 1.2168913653e+00 6.661e-16 3.005e-16 5 1.3068727691e+00 1.3068727691e+00 1.332e-15 5.775e-16 6 1.1830538206e+00 1.1830538206e+00 1.554e-15 7.120e-16 7 1.3082283602e+00 1.3082283602e+00 1.998e-15 8.658e-16 8 1.2899102613e+00 1.2899102613e+00 1.998e-15 8.727e-16 9 1.4545503852e+00 1.4545503852e+00 2.665e-15 1.086e-15 10 1.5080928191e+00 1.5080928191e+00 3.109e-15 1.239e-15 11 1.7246139873e+00 1.7100388000e+00 1.458e-02 5.349e-03 12 1.8481104500e+00 1.8258707245e+00 2.224e-02 7.809e-03 13 2.1359361290e+00 2.0673751409e+00 6.856e-02 2.186e-02 Knots and weights of Gauss quadrature formula computed by CGQF. Interpolatory quadrature formula Type Interval Weight function Name 5 (a,oo) (x-a)^alpha*exp(-b*(x-a)) Gen Laguerre Parameters A -0.500000 B 2.000000 alpha 0.500000 Machine precision = 2.22045e-16 Knots Mult Weights 1 -0.28430059642607391 1 0.13097405507334794 2 0.37987684921184894 1 0.14587060425199255 3 1.552232681414158 1 0.034570386911402198 4 3.3733518897712789 1 0.0018997892129372692 5 6.2288391760287887 1 1.3698879195062412e-05 Comparison of moments Order of precision 10 Errors : Absolute Relative ---------+------------------------- Minimum : 2.776e-17 2.247e-17 Maximum : 3.411e-13 5.361e-16 Weights ratio 0.239 Error in 10th power 1.193e+01 Error constant 0.000 Moments: True from QF Error Relative 1 3.1332853433e-01 3.1332853433e-01 5.551e-17 4.227e-17 2 2.3499640075e-01 2.3499640075e-01 -2.776e-17 -2.247e-17 3 2.9374550093e-01 2.9374550093e-01 -1.665e-16 -1.287e-16 4 5.1405462663e-01 5.1405462663e-01 -2.220e-16 -1.467e-16 5 1.1566229099e+00 1.1566229099e+00 -4.441e-16 -2.059e-16 6 3.1807130023e+00 3.1807130023e+00 -1.776e-15 -4.249e-16 7 1.0337317257e+01 1.0337317257e+01 -5.329e-15 -4.700e-16 8 3.8764939715e+01 3.8764939715e+01 -2.132e-14 -5.361e-16 9 1.6475099379e+02 1.6475099379e+02 -8.527e-14 -5.144e-16 10 7.8256722051e+02 7.8256722051e+02 -3.411e-13 -4.353e-16 11 4.1084779077e+03 4.0965502339e+03 1.193e+01 2.902e-03 12 2.3623747969e+04 2.3227152817e+04 3.966e+02 1.679e-02 13 1.4764842481e+05 1.3988052727e+05 7.768e+03 5.261e-02 Weights of Gauss quadrature formula computed from the knots by CIQF. Interpolatory quadrature formula Type Interval Weight function Name 5 (a,oo) (x-a)^alpha*exp(-b*(x-a)) Gen Laguerre Parameters A -0.500000 B 2.000000 alpha 0.500000 Machine precision = 2.22045e-16 Knots Mult Weights 1 -0.28430059642607391 2 0.13097405507334794 0 2 0.37987684921184894 2 0.14587060425199269 0 3 1.552232681414158 2 0.034570386911402178 0 4 3.3733518897712789 2 0.0018997892129372711 0 5 6.2288391760287887 2 1.3698879195062407e-05 0 Comparison of moments Order of precision 10 Errors : Absolute Relative ---------+------------------------- Minimum : 5.551e-17 4.227e-17 Maximum : 5.684e-13 1.097e-15 Weights ratio 0.239 Error in 10th power 1.193e+01 Error constant 0.000 Moments: True from QF Error Relative 1 3.1332853433e-01 3.1332853433e-01 -5.551e-17 -4.227e-17 2 2.3499640075e-01 2.3499640075e-01 -1.388e-16 -1.124e-16 3 2.9374550093e-01 2.9374550093e-01 -1.665e-16 -1.287e-16 4 5.1405462663e-01 5.1405462663e-01 -2.220e-16 -1.467e-16 5 1.1566229099e+00 1.1566229099e+00 -8.882e-16 -4.118e-16 6 3.1807130023e+00 3.1807130023e+00 -2.665e-15 -6.373e-16 7 1.0337317257e+01 1.0337317257e+01 -1.243e-14 -1.097e-15 8 3.8764939715e+01 3.8764939715e+01 -4.263e-14 -1.072e-15 9 1.6475099379e+02 1.6475099379e+02 -1.705e-13 -1.029e-15 10 7.8256722051e+02 7.8256722051e+02 -5.684e-13 -7.254e-16 11 4.1084779077e+03 4.0965502339e+03 1.193e+01 2.902e-03 12 2.3623747969e+04 2.3227152817e+04 3.966e+02 1.679e-02 13 1.4764842481e+05 1.3988052727e+05 7.768e+03 5.261e-02 Knots and weights of Gauss quadrature formula computed by CGQF. Interpolatory quadrature formula Type Interval Weight function Name 6 (-oo,oo) |x-a|^alpha*exp(-b*(x-a)^2) Gen Hermite Parameters A -0.500000 B 2.000000 alpha 0.500000 Machine precision = 2.22045e-16 Knots Mult Weights 1 -1.9846400902538133 1 0.012302854647083833 2 -1.2388124270822396 1 0.20061059263754044 3 -0.50000000000000022 1 0.30281023613813191 4 0.23881242708224004 1 0.20061059263754014 5 0.98464009025381238 1 0.012302854647083803 Comparison of moments Order of precision 10 Errors : Absolute Relative ---------+------------------------- Minimum : 2.776e-17 2.240e-17 Maximum : 3.331e-15 3.331e-15 Weights ratio 0.422 Error in 10th power 1.644e-01 Error constant 0.000 Moments: True from QF Error Relative 1 7.2863713071e-01 7.2863713071e-01 5.551e-16 3.211e-16 2 0.0000000000e+00 -2.5673907444e-16 2.567e-16 2.567e-16 3 2.7323892402e-01 2.7323892402e-01 1.110e-16 8.720e-17 4 0.0000000000e+00 -1.4571677198e-16 1.457e-16 1.457e-16 5 2.3908405851e-01 2.3908405851e-01 -2.776e-17 -2.240e-17 6 0.0000000000e+00 -4.1633363423e-16 4.163e-16 4.163e-16 7 3.2874058046e-01 3.2874058046e-01 -1.665e-16 -1.253e-16 8 0.0000000000e+00 -1.2212453271e-15 1.221e-15 1.221e-15 9 6.1638858835e-01 6.1638858835e-01 -3.331e-16 -2.061e-16 10 0.0000000000e+00 -3.3306690739e-15 3.331e-15 3.331e-15 11 1.4639228973e+00 1.2995526071e+00 1.644e-01 6.671e-02 12 0.0000000000e+00 -8.6597395921e-15 8.660e-15 8.660e-15 13 4.2087783299e+00 2.8321771492e+00 1.377e+00 2.643e-01 Weights of Gauss quadrature formula computed from the knots by CIQF. Interpolatory quadrature formula Type Interval Weight function Name 6 (-oo,oo) |x-a|^alpha*exp(-b*(x-a)^2) Gen Hermite Parameters A -0.500000 B 2.000000 alpha 0.500000 Machine precision = 2.22045e-16 Knots Mult Weights 1 -1.9846400902538133 2 0.012302854647083838 1.6245898753159158e-35 2 -1.2388124270822396 2 0.20061059263754036 5.3232725458077471e-34 3 -0.50000000000000022 2 0.30281023613813207 1.642085241956142e-17 4 0.23881242708224004 2 0.20061059263754016 -5.3232725458077419e-34 5 0.98464009025381238 2 0.012302854647083803 -1.6245898753159249e-35 Comparison of moments Order of precision 10 Errors : Absolute Relative ---------+------------------------- Minimum : 2.776e-17 2.240e-17 Maximum : 3.497e-15 3.497e-15 Weights ratio 0.422 Error in 10th power 1.644e-01 Error constant 0.000 Moments: True from QF Error Relative 1 7.2863713071e-01 7.2863713071e-01 4.441e-16 2.569e-16 2 0.0000000000e+00 -1.4571677198e-16 1.457e-16 1.457e-16 3 2.7323892402e-01 2.7323892402e-01 1.665e-16 1.308e-16 4 0.0000000000e+00 -1.1796119637e-16 1.180e-16 1.180e-16 5 2.3908405851e-01 2.3908405851e-01 -2.776e-17 -2.240e-17 6 0.0000000000e+00 -4.4408920985e-16 4.441e-16 4.441e-16 7 3.2874058046e-01 3.2874058046e-01 -2.220e-16 -1.671e-16 8 0.0000000000e+00 -1.3045120539e-15 1.305e-15 1.305e-15 9 6.1638858835e-01 6.1638858835e-01 -3.331e-16 -2.061e-16 10 0.0000000000e+00 -3.4972025276e-15 3.497e-15 3.497e-15 11 1.4639228973e+00 1.2995526071e+00 1.644e-01 6.671e-02 12 0.0000000000e+00 -9.1038288019e-15 9.104e-15 9.104e-15 13 4.2087783299e+00 2.8321771492e+00 1.377e+00 2.643e-01 Knots and weights of Gauss quadrature formula computed by CGQF. Interpolatory quadrature formula Type Interval Weight function Name 7 (a,b) |x-(a+b)/2.0|^alpha Exponential Parameters A -0.500000 B 2.000000 alpha 0.500000 Machine precision = 2.22045e-16 Knots Mult Weights 1 -0.39148162917747831 1 0.29332908318369361 2 0.038501428978160779 1 0.47745248689814068 3 0.75000000000000022 1 0.32182684108615661 4 1.4614985710218396 1 0.47745248689814029 5 1.8914816291774779 1 0.29332908318369405 Comparison of moments Order of precision 10 Errors : Absolute Relative ---------+------------------------- Minimum : 1.665e-16 9.169e-17 Maximum : 1.998e-15 1.998e-15 Weights ratio 0.651 Error in 10th power 2.854e-02 Error constant 0.000 Moments: True from QF Error Relative 1 1.8633899812e+00 1.8633899812e+00 -6.661e-16 -2.326e-16 2 0.0000000000e+00 3.3306690739e-16 -3.331e-16 -3.331e-16 3 1.2478057910e+00 1.2478057910e+00 -2.220e-16 -9.878e-17 4 0.0000000000e+00 1.6653345369e-16 -1.665e-16 -1.665e-16 5 1.2407159854e+00 1.2407159854e+00 -2.220e-16 -9.910e-17 6 0.0000000000e+00 -2.2204460493e-16 2.220e-16 2.220e-16 7 1.4216537333e+00 1.4216537333e+00 2.220e-16 9.169e-17 8 0.0000000000e+00 -8.8817841970e-16 8.882e-16 8.882e-16 9 1.7536847038e+00 1.7536847038e+00 6.661e-16 2.419e-16 10 0.0000000000e+00 -1.9984014443e-15 1.998e-15 1.998e-15 11 2.2635875933e+00 2.2350506441e+00 2.854e-02 8.744e-03 12 0.0000000000e+00 -3.5527136788e-15 3.553e-15 3.553e-15 13 3.0128770049e+00 2.8869326844e+00 1.259e-01 3.139e-02 Weights of Gauss quadrature formula computed from the knots by CIQF. Interpolatory quadrature formula Type Interval Weight function Name 7 (a,b) |x-(a+b)/2.0|^alpha Exponential Parameters A -0.500000 B 2.000000 alpha 0.500000 Machine precision = 2.22045e-16 Knots Mult Weights 1 -0.39148162917747831 2 0.29332908318369372 4.0707587742840522e-17 2 0.038501428978160779 2 0.47745248689814052 -6.4202040326854086e-32 3 0.75000000000000022 2 0.32182684108615639 -3.0075161219879185e-17 4 1.4614985710218396 2 0.47745248689813979 6.4202040326853987e-32 5 1.8914816291774779 2 0.29332908318369399 -4.0707587742840559e-17 Comparison of moments Order of precision 10 Errors : Absolute Relative ---------+------------------------- Minimum : 1.110e-16 9.878e-17 Maximum : 2.442e-15 2.442e-15 Weights ratio 0.651 Error in 10th power 2.854e-02 Error constant 0.000 Moments: True from QF Error Relative 1 1.8633899812e+00 1.8633899812e+00 4.441e-16 1.551e-16 2 0.0000000000e+00 -1.1102230246e-16 1.110e-16 1.110e-16 3 1.2478057910e+00 1.2478057910e+00 2.220e-16 9.878e-17 4 0.0000000000e+00 -2.2204460493e-16 2.220e-16 2.220e-16 5 1.2407159854e+00 1.2407159854e+00 2.220e-16 9.910e-17 6 0.0000000000e+00 -6.6613381478e-16 6.661e-16 6.661e-16 7 1.4216537333e+00 1.4216537333e+00 1.332e-15 5.501e-16 8 0.0000000000e+00 -1.2212453271e-15 1.221e-15 1.221e-15 9 1.7536847038e+00 1.7536847038e+00 2.220e-15 8.064e-16 10 0.0000000000e+00 -2.4424906542e-15 2.442e-15 2.442e-15 11 2.2635875933e+00 2.2350506441e+00 2.854e-02 8.744e-03 12 0.0000000000e+00 -4.2188474936e-15 4.219e-15 4.219e-15 13 3.0128770049e+00 2.8869326844e+00 1.259e-01 3.139e-02 Knots and weights of Gauss quadrature formula computed by CGQF. Interpolatory quadrature formula Type Interval Weight function Name 8 (a,oo) (x-a)^alpha*(x+b)^beta Rational Parameters A -0.500000 B 2.000000 alpha 0.500000 beta -16.000000 Machine precision = 2.22045e-16 Knots Mult Weights 1 -0.43541078852037896 1 2.6216877717069182e-05 2 -0.21664377601574747 1 1.6250543349707077e-05 3 0.25596297684363967 1 1.2927396984510141e-06 4 1.2864478502358694 1 1.1152074844159653e-08 5 4.1096437374566168 1 2.8799054822892495e-12 Comparison of moments Order of precision 10 Errors : Absolute Relative ---------+------------------------- Minimum : 0.000e+00 0.000e+00 Maximum : 6.776e-21 6.776e-21 Weights ratio 0.000 Error in 10th power 8.249e-07 Error constant 0.000 Moments: True from QF Error Relative 1 4.3771315720e-05 4.3771315720e-05 -6.776e-21 -6.776e-21 2 7.2952192867e-06 7.2952192867e-06 2.541e-21 2.541e-21 3 2.1885657860e-06 2.1885657860e-06 0.000e+00 0.000e+00 4 9.9912785883e-07 9.9912785883e-07 -4.235e-22 -4.235e-22 5 6.4229648067e-07 6.4229648067e-07 -7.412e-22 -7.412e-22 6 5.5778378585e-07 5.5778378585e-07 -7.412e-22 -7.412e-22 7 6.3981081318e-07 6.3981081318e-07 -8.470e-22 -8.470e-22 8 9.5971621977e-07 9.5971621977e-07 -8.470e-22 -8.470e-22 9 1.8825202772e-06 1.8825202772e-06 -6.353e-22 -6.353e-22 10 4.8774389001e-06 4.8774389001e-06 8.470e-22 8.470e-22 11 1.7071036150e-05 1.6246154931e-05 8.249e-07 8.249e-07 12 8.4135821027e-05 6.4161911508e-05 1.997e-05 1.997e-05 13 6.3101865770e-04 2.7691346669e-04 3.541e-04 3.539e-04 Weights of Gauss quadrature formula computed from the knots by CIQF. Interpolatory quadrature formula Type Interval Weight function Name 8 (a,oo) (x-a)^alpha*(x+b)^beta Rational Parameters A -0.500000 B 2.000000 alpha 0.500000 beta -16.000000 Machine precision = 2.22045e-16 Knots Mult Weights 1 -0.43541078852037896 2 2.6216877717069182e-05 -8.186225983670371e-22 2 -0.21664377601574747 2 1.6250543349707097e-05 6.7656477710677604e-22 3 0.25596297684363967 2 1.2927396984510164e-06 -4.6767663452359094e-38 4 1.2864478502358694 2 1.1152074844159656e-08 -5.1629379760698297e-40 5 4.1096437374566168 2 2.8799054822892507e-12 -2.364810082427408e-43 Comparison of moments Order of precision 10 Errors : Absolute Relative ---------+------------------------- Minimum : 8.470e-22 8.470e-22 Maximum : 2.711e-20 2.710e-20 Weights ratio 0.000 Error in 10th power 8.249e-07 Error constant 0.000 Moments: True from QF Error Relative 1 4.3771315720e-05 4.3771315720e-05 -2.711e-20 -2.710e-20 2 7.2952192867e-06 7.2952192867e-06 -5.082e-21 -5.082e-21 3 2.1885657860e-06 2.1885657860e-06 -2.965e-21 -2.965e-21 4 9.9912785883e-07 9.9912785883e-07 -2.118e-21 -2.118e-21 5 6.4229648067e-07 6.4229648067e-07 -1.694e-21 -1.694e-21 6 5.5778378585e-07 5.5778378585e-07 -1.482e-21 -1.482e-21 7 6.3981081318e-07 6.3981081318e-07 -1.376e-21 -1.376e-21 8 9.5971621977e-07 9.5971621977e-07 -1.482e-21 -1.482e-21 9 1.8825202772e-06 1.8825202772e-06 -1.482e-21 -1.482e-21 10 4.8774389001e-06 4.8774389001e-06 -8.470e-22 -8.470e-22 11 1.7071036150e-05 1.6246154931e-05 8.249e-07 8.249e-07 12 8.4135821027e-05 6.4161911508e-05 1.997e-05 1.997e-05 13 6.3101865770e-04 2.7691346669e-04 3.541e-04 3.539e-04 ---------------------------------------- TEST03 Test CEIQFS. Integral of sin(x) on -1, 1 by Fejer type rule with 5 points of multiplicity 2. Quadrature formula: -0.0000000000000001 Exact value : 0.0000000000000000 Error : 1.188e-16 ---------------------------------------- TEST04 Test CEIQF. Integral of sin(x) from -0.500000 to 2.000000 by Fejer type rule with 5 points of multiplicity 2. Quadrature formula: 1.2937294066147371 Exact value : 1.2937293984375151 Error : 8.177e-09 ---------------------------------------- TEST05 Test CLIQFS. Interpolatory quadrature formula Type Interval Weight function Name 1 (-1,+1) 1.0 Legendre Machine precision = 2.22045e-16 Knots Mult Weights 1 0.95105651629515353 1 0.16778122846668317 2 0.58778525229247314 1 0.52555210486664983 3 6.123233995736766e-17 1 0.61333333333333362 4 -0.58778525229247303 1 0.52555210486664961 5 -0.95105651629515353 1 0.16778122846668336 Comparison of moments Order of precision 5 Errors : Absolute Relative ---------+------------------------- Minimum : 2.776e-17 2.776e-17 Maximum : 5.551e-16 3.331e-16 Weights ratio 0.667 Error in 5th power 1.110e-16 Error constant 0.000 Moments: True from QF Error Relative 1 2.0000000000e+00 2.0000000000e+00 4.441e-16 1.480e-16 2 0.0000000000e+00 2.7755575616e-17 -2.776e-17 -2.776e-17 3 6.6666666667e-01 6.6666666667e-01 5.551e-16 3.331e-16 4 0.0000000000e+00 -8.3266726847e-17 8.327e-17 8.327e-17 5 4.0000000000e-01 4.0000000000e-01 4.441e-16 3.172e-16 6 0.0000000000e+00 -1.1102230246e-16 1.110e-16 1.110e-16 7 2.8571428571e-01 2.9166666667e-01 -5.952e-03 -4.630e-03 8 0.0000000000e+00 -1.2490009027e-16 1.249e-16 1.249e-16 ---------------------------------------- TEST06 Test CLIQF and EIQFS. Interpolatory quadrature formula Type Interval Weight function Name 1 (a,b) 1.0 Legendre Parameters A -0.500000 B 2.000000 Machine precision = 2.22045e-16 Knots Mult Weights 1 1.9388206453689418 1 0.20972653558335388 2 1.4847315653655915 1 0.65694013108331228 3 0.75000000000000011 1 0.76666666666666683 4 0.015268434634408745 1 0.65694013108331206 5 -0.43882064536894183 1 0.20972653558335438 Comparison of moments Order of precision 5 Errors : Absolute Relative ---------+------------------------- Minimum : 1.943e-16 1.943e-16 Maximum : 1.554e-15 6.999e-16 Weights ratio 0.714 Error in 5th power 8.327e-16 Error constant 0.000 Moments: True from QF Error Relative 1 2.5000000000e+00 2.5000000000e+00 8.882e-16 2.538e-16 2 0.0000000000e+00 -1.9428902931e-16 1.943e-16 1.943e-16 3 1.3020833333e+00 1.3020833333e+00 8.882e-16 3.858e-16 4 0.0000000000e+00 -5.5511151231e-16 5.551e-16 5.551e-16 5 1.2207031250e+00 1.2207031250e+00 1.554e-15 6.999e-16 6 0.0000000000e+00 -8.3266726847e-16 8.327e-16 8.327e-16 7 1.3623918806e+00 1.3907750448e+00 -2.838e-02 -1.201e-02 8 0.0000000000e+00 -1.5543122345e-15 1.554e-15 1.554e-15 Integral of sin(x) from -0.500000 to 2.000000 by Fejer type rule with 5 points of multiplicity 1. Quadrature formula: 1.2937046571063413 Exact value : 1.2937293984375151 Error : 2.474e-05 ---------------------------------------- TEST07 Test CEGQF. Integral of x*sin(x) from -0.500000 to 2.000000 by Gauss-exponential rule with 12 points Quadrature formula: 0.6837561162217042 Exact value : 0.6837561162217043 Error : 1.110e-16 ---------------------------------------- TEST08 Test CEGQFS. Integral of x*sin(x) from -1 to +1 by Gauss-exponential rule with 12 points. Quadrature formula: 0.0000000000000000 Exact value : 0.0000000000000000 Error : 2.082e-17 TEST09 Call CGQFS to compute generalized Hermite rules. NT = 15 ALPHA = 1.000000 Interpolatory quadrature formula Type Interval Weight function Name 6 (-oo,oo) |x-a|^alpha*exp(-b*(x-a)^2) Gen Hermite alpha 1.000000 Machine precision = 2.22045e-16 Knots Mult Weights 1 -4.5926220079551996 1 2.9948067642554377e-09 2 -3.7675145053479846 1 1.919262837577024e-06 3 -3.0693157841808327 1 0.00016455571024870811 4 -2.4323439824622972 1 0.0040399515839194084 5 -1.830860590688635 1 0.037756369726656018 6 -1.2504344003802288 1 0.15020237158948324 7 -0.67898764333748718 1 0.24533482913204793 8 -4.4954222270085497e-17 1 0.12500000000000008 9 0.67898764333748785 1 0.2453348291320481 10 1.250434400380229 1 0.15020237158948338 11 1.8308605906886348 1 0.037756369726656254 12 2.4323439824622946 1 0.0040399515839194284 13 3.0693157841808332 1 0.00016455571024870882 14 3.7675145053479873 1 1.9192628375770181e-06 15 4.592622007955196 1 2.9948067642554397e-09 TEST10 Call CDGQF to compute a quadrature formula. KIND = 1 ALPHA = 0.000000 BETA = 0.000000 Index Abscissas Weights 0 -0.987992518020486 0.03075324199611693 1 -0.9372733924007061 0.07036604748810849 2 -0.8482065834104269 0.1071592204671715 3 -0.72441773136017 0.139570677926155 4 -0.5709721726085385 0.1662692058169941 5 -0.3941513470775634 0.1861610000155613 6 -0.2011940939974347 0.198431485327112 7 -1.675838770760716e-16 0.2025782419255613 8 0.2011940939974347 0.1984314853271111 9 0.3941513470775637 0.1861610000155626 10 0.5709721726085392 0.1662692058169944 11 0.7244177313601701 0.1395706779261534 12 0.848206583410427 0.1071592204671729 13 0.9372733924007057 0.07036604748810786 14 0.9879925180204853 0.03075324199611744 TEST10 Call CDGQF to compute a quadrature formula. KIND = 2 ALPHA = 0.000000 BETA = 0.000000 Index Abscissas Weights 0 -0.9945218953682731 0.2094395102393206 1 -0.9510565162951536 0.2094395102393177 2 -0.8660254037844385 0.2094395102393196 3 -0.7431448254773944 0.2094395102393191 4 -0.5877852522924731 0.2094395102393199 5 -0.4067366430758003 0.20943951023932 6 -0.2079116908177589 0.2094395102393191 7 4.33393098835631e-17 0.2094395102393193 8 0.2079116908177593 0.2094395102393198 9 0.4067366430758002 0.2094395102393194 10 0.5877852522924731 0.2094395102393196 11 0.743144825477394 0.2094395102393204 12 0.8660254037844384 0.2094395102393211 13 0.9510565162951534 0.2094395102393198 14 0.9945218953682728 0.2094395102393178 TEST10 Call CDGQF to compute a quadrature formula. KIND = 3 ALPHA = 0.000000 BETA = 0.000000 Index Abscissas Weights 0 -0.987992518020486 0.03075324199611693 1 -0.9372733924007061 0.07036604748810849 2 -0.8482065834104269 0.1071592204671715 3 -0.72441773136017 0.139570677926155 4 -0.5709721726085385 0.1662692058169941 5 -0.3941513470775634 0.1861610000155613 6 -0.2011940939974347 0.198431485327112 7 -1.675838770760716e-16 0.2025782419255613 8 0.2011940939974347 0.1984314853271111 9 0.3941513470775637 0.1861610000155626 10 0.5709721726085392 0.1662692058169944 11 0.7244177313601701 0.1395706779261534 12 0.848206583410427 0.1071592204671729 13 0.9372733924007057 0.07036604748810786 14 0.9879925180204853 0.03075324199611744 TEST10 Call CDGQF to compute a quadrature formula. KIND = 4 ALPHA = 0.000000 BETA = 0.000000 Index Abscissas Weights 0 -0.987992518020486 0.03075324199611693 1 -0.9372733924007061 0.07036604748810849 2 -0.8482065834104269 0.1071592204671715 3 -0.72441773136017 0.139570677926155 4 -0.5709721726085385 0.1662692058169941 5 -0.3941513470775634 0.1861610000155613 6 -0.2011940939974347 0.198431485327112 7 -1.675838770760716e-16 0.2025782419255613 8 0.2011940939974347 0.1984314853271111 9 0.3941513470775637 0.1861610000155626 10 0.5709721726085392 0.1662692058169944 11 0.7244177313601701 0.1395706779261534 12 0.848206583410427 0.1071592204671729 13 0.9372733924007057 0.07036604748810786 14 0.9879925180204853 0.03075324199611744 TEST10 Call CDGQF to compute a quadrature formula. KIND = 5 ALPHA = 0.000000 BETA = 0.000000 Index Abscissas Weights 0 0.09330781201728104 0.2182348859400854 1 0.492691740301881 0.3422101779228836 2 1.215595412070946 0.2630275779416809 3 2.269949526203739 0.1264258181059313 4 3.667622721751437 0.040206864921001 5 5.425336627413552 0.008563877803611831 6 7.56591622661307 0.001212436147214254 7 10.12022856801912 0.0001116743923442514 8 13.13028248217572 6.459926762022903e-06 9 16.65440770832996 2.226316907096256e-07 10 20.77647889944877 4.227430384979374e-09 11 25.62389422672879 3.921897267041077e-11 12 31.40751916975393 1.456515264073139e-13 13 38.53068330648603 1.483027051113284e-16 14 48.0260855726858 1.600594906211132e-20 TEST10 Call CDGQF to compute a quadrature formula. KIND = 6 ALPHA = 0.000000 BETA = 0.000000 Index Abscissas Weights 0 -4.49999070730939 1.522475804253516e-09 1 -3.669950373404451 1.059115547711071e-06 2 -2.967166927905604 0.0001000044412324996 3 -2.325732486173856 0.002778068842912774 4 -1.719992575186489 0.03078003387254618 5 -1.136115585210921 0.1584889157959359 6 -0.5650695832555758 0.4120286874988984 7 -1.638469319558613e-16 0.5641003087264176 8 0.5650695832555758 0.4120286874988981 9 1.136115585210921 0.1584889157959361 10 1.719992575186488 0.03078003387254607 11 2.325732486173858 0.002778068842912767 12 2.967166927905603 0.0001000044412325003 13 3.669950373404451 1.059115547711071e-06 14 4.499990707309388 1.522475804253535e-09 TEST10 Call CDGQF to compute a quadrature formula. KIND = 7 ALPHA = 0.000000 BETA = 0.000000 Index Abscissas Weights 0 -0.987992518020486 0.03075324199611693 1 -0.9372733924007061 0.07036604748810849 2 -0.8482065834104269 0.1071592204671715 3 -0.72441773136017 0.139570677926155 4 -0.5709721726085385 0.1662692058169941 5 -0.3941513470775634 0.1861610000155613 6 -0.2011940939974347 0.198431485327112 7 -1.675838770760716e-16 0.2025782419255613 8 0.2011940939974347 0.1984314853271111 9 0.3941513470775637 0.1861610000155626 10 0.5709721726085392 0.1662692058169944 11 0.7244177313601701 0.1395706779261534 12 0.848206583410427 0.1071592204671729 13 0.9372733924007057 0.07036604748810786 14 0.9879925180204853 0.03075324199611744 TEST10 Call CDGQF to compute a quadrature formula. KIND = 8 ALPHA = 1.000000 BETA = -33.000000 Index Abscissas Weights 0 0.01361683909815457 0.0002011020498189966 1 0.04663820034482355 0.0004495038907551643 2 0.1015058265688505 0.000280283477240797 3 0.1827118416726538 6.939527832882217e-05 4 0.2975340241767022 7.430450609904131e-06 5 0.4575406384763867 3.428803023873866e-07 6 0.6813618059551224 6.444586110015326e-09 7 0.9999999999999997 4.439192701910398e-11 8 1.467649039408975 9.487478523343267e-14 9 2.185598209002824 4.87083120074614e-17 10 3.360960154950583 4.014002150239429e-21 11 5.473099011237577 2.707472673069508e-26 12 9.851651218481582 4.323502217203897e-33 13 21.44165067705037 1.11235953674529e-42 14 73.43848251357539 1.554638299716062e-58 CGQF_TEST Call CGQF to compute a quadrature formula. KIND = 1 ALPHA = 0.000000 BETA = 0.000000 A = 0.000000 B = 1.000000 Index Abscissas Weights 0 0.006003740989756978 0.01537662099805846 1 0.03136330379964697 0.03518302374405424 2 0.07589670829478656 0.05357961023358577 3 0.137791134319915 0.06978533896307748 4 0.2145139136957308 0.08313460290849703 5 0.3029243264612183 0.09308050000778066 6 0.3994029530012826 0.099215742663556 7 0.4999999999999999 0.1012891209627807 8 0.6005970469987174 0.09921574266355553 9 0.6970756735387819 0.09308050000778129 10 0.7854860863042696 0.0831346029084972 11 0.862208865680085 0.06978533896307669 12 0.9241032917052134 0.05357961023358644 13 0.9686366962003529 0.03518302374405393 14 0.9939962590102427 0.01537662099805872 CGQF_TEST Call CGQF to compute a quadrature formula. KIND = 2 ALPHA = 0.000000 BETA = 0.000000 A = 0.000000 B = 1.000000 Index Abscissas Weights 0 0.002739052315863466 0.2094395102393206 1 0.02447174185242318 0.2094395102393177 2 0.06698729810778076 0.2094395102393196 3 0.1284275872613028 0.2094395102393191 4 0.2061073738537634 0.2094395102393199 5 0.2966316784620998 0.20943951023932 6 0.3960441545911206 0.2094395102393191 7 0.5 0.2094395102393193 8 0.6039558454088796 0.2094395102393198 9 0.7033683215379001 0.2094395102393194 10 0.7938926261462366 0.2094395102393196 11 0.871572412738697 0.2094395102393204 12 0.9330127018922192 0.2094395102393211 13 0.9755282581475767 0.2094395102393198 14 0.9972609476841364 0.2094395102393178 CGQF_TEST Call CGQF to compute a quadrature formula. KIND = 3 ALPHA = 1.000000 BETA = 0.000000 A = 0.000000 B = 1.000000 Index Abscissas Weights 0 0.01343391168429087 0.0002976851600462624 1 0.04456000204221316 0.001685909750963313 2 0.09215187438911482 0.004626096209989247 3 0.1544855096861577 0.009011961557897748 4 0.2293073003349492 0.01417291039984417 5 0.3139127832172615 0.01906084001900511 6 0.4052440132408413 0.02256156306349567 7 0.4999999999999999 0.02383273434418376 8 0.5947559867591586 0.02256156306349566 9 0.6860872167827383 0.0190608400190051 10 0.7706926996650507 0.01417291039984414 11 0.8455144903138425 0.009011961557897687 12 0.9078481256108852 0.004626096209989248 13 0.9554399979577866 0.001685909750963313 14 0.986566088315709 0.0002976851600462641 CGQF_TEST Call CGQF to compute a quadrature formula. KIND = 4 ALPHA = 1.500000 BETA = 0.500000 A = 0.000000 B = 1.000000 Index Abscissas Weights 0 0.009052268678253095 0.001694054925014199 1 0.03588190242074035 0.006356465380570267 2 0.07951920924723888 0.0128410600141245 3 0.1383870248066182 0.01958162794332472 4 0.2103577154467254 0.02500289961544036 5 0.2928300768709262 0.02791857605910341 6 0.3828233492143044 0.02780542929499534 7 0.4770849509094544 0.02488207576686375 8 0.5722080382812496 0.01998099955114914 9 0.6647546437376434 0.01426401852300561 10 0.7513799469119047 0.008875654967793177 11 0.8289532028579742 0.004642514438517171 12 0.8946710174575663 0.001906331216006745 13 0.9461591980875512 0.0005311344429374076 14 0.9815624550718498 6.669871051616858e-05 CGQF_TEST Call CGQF to compute a quadrature formula. KIND = 5 ALPHA = 1.000000 BETA = 0.000000 A = 1.000000 B = 1.000000 Index Abscissas Weights 0 1.229680505425134 0.07050242866378946 1 1.772144910375411 0.2495589090404948 2 2.631053099067446 0.325533115492133 3 3.815144590012253 0.2277270881393439 4 5.33716407733756 0.09618805798309657 5 7.214642764559242 0.02563428489418442 6 9.471163981346713 0.004356647202893064 7 12.13833196575081 0.0004674557699509067 8 15.25891002162424 3.079923831296578e-05 9 18.89205343816948 1.188390467804052e-06 10 23.12262017483362 2.493135570944067e-08 11 28.07931149904756 2.52956064020392e-10 12 33.9749735523974 1.019777669698137e-12 13 41.21658371149658 1.122070523608304e-15 14 50.84622170855656 1.309337137637658e-19 CGQF_TEST Call CGQF to compute a quadrature formula. KIND = 6 ALPHA = 1.000000 BETA = 0.000000 A = 0.000000 B = 0.500000 Index Abscissas Weights 0 -6.494948330503399 5.989613528510874e-09 1 -5.328070109900482 3.838525675154047e-06 2 -4.340668009194345 0.0003291114204974162 3 -3.439853848354766 0.008079903167838815 4 -2.589227878166283 0.07551273945331202 5 -1.768381287875588 0.3004047431789664 6 -0.9602335338916201 0.4906696582640958 7 -6.357487082028953e-17 0.2500000000000001 8 0.9602335338916211 0.4906696582640961 9 1.768381287875588 0.3004047431789667 10 2.589227878166283 0.07551273945331249 11 3.439853848354762 0.008079903167838855 12 4.340668009194346 0.0003291114204974176 13 5.328070109900485 3.838525675154035e-06 14 6.494948330503394 5.989613528510878e-09 CGQF_TEST Call CGQF to compute a quadrature formula. KIND = 7 ALPHA = 1.000000 BETA = 0.000000 A = 0.000000 B = 1.000000 Index Abscissas Weights 0 0.005651789332335289 0.007156800921516081 1 0.02954252401542823 0.01560299383311647 2 0.07156967392135666 0.02168842472715644 3 0.1301508326592595 0.02447326046578071 4 0.2030889370900901 0.02353234658681994 5 0.2877261840588361 0.0190081637904241 6 0.3814013485142831 0.01158488467518626 7 0.5000000000000001 0.003906250000000003 8 0.618598651485717 0.01158488467518621 9 0.7122738159411638 0.01900816379042413 10 0.7969110629099098 0.02353234658681987 11 0.86984916734074 0.0244732604657808 12 0.9284303260786436 0.02168842472715626 13 0.9704574759845717 0.01560299383311682 14 0.9943482106676649 0.007156800921515924 CGQF_TEST Call CGQF to compute a quadrature formula. KIND = 8 ALPHA = 1.000000 BETA = -33.000000 A = 0.000000 B = 1.000000 Index Abscissas Weights 0 0.01361683909815457 0.0002011020498189966 1 0.04663820034482355 0.0004495038907551643 2 0.1015058265688505 0.000280283477240797 3 0.1827118416726538 6.939527832882217e-05 4 0.2975340241767022 7.430450609904131e-06 5 0.4575406384763867 3.428803023873866e-07 6 0.6813618059551224 6.444586110015326e-09 7 0.9999999999999997 4.439192701910398e-11 8 1.467649039408975 9.487478523343267e-14 9 2.185598209002824 4.87083120074614e-17 10 3.360960154950583 4.014002150239429e-21 11 5.473099011237577 2.707472673069508e-26 12 9.851651218481582 4.323502217203897e-33 13 21.44165067705037 1.11235953674529e-42 14 73.43848251357539 1.554638299716062e-58 WM_TESTER: WM_TEST computes moments for rule 1 with ALPHA = 0, BETA = 0 Order Moment 0 2 1 0 2 0.666667 3 0 4 0.4 WM_TESTER: WM_TEST computes moments for rule 2 with ALPHA = 0, BETA = 0 Order Moment 0 3.14159 1 0 2 1.5708 3 0 4 1.1781 WM_TESTER: WM_TEST computes moments for rule 3 with ALPHA = 0.5, BETA = 0 Order Moment 0 1.5708 1 0 2 0.392699 3 0 4 0.19635 WM_TESTER: WM_TEST computes moments for rule 4 with ALPHA = 0.25, BETA = 0.75 Order Moment 0 1.66608 1 0.27768 2 0.45123 3 0.156195 4 0.238631 WM_TESTER: WM_TEST computes moments for rule 5 with ALPHA = 2, BETA = 0 Order Moment 0 2 1 6 2 24 3 120 4 720 WM_TESTER: WM_TEST computes moments for rule 6 with ALPHA = 1, BETA = 0 Order Moment 0 1 1 0 2 1 3 0 4 2 WM_TESTER: WM_TEST computes moments for rule 7 with ALPHA = 2, BETA = 0 Order Moment 0 0.666667 1 0 2 0.4 3 0 4 0.285714 WM_TESTER: WM_TEST computes moments for rule 8 with ALPHA = -0.5, BETA = -6 Order Moment 0 0.773126 1 0.0859029 2 0.0368155 3 0.0368155 4 0.0859029 WM_TESTER: WM_TEST computes moments for rule 9 with ALPHA = 0, BETA = 0 Order Moment 0 4.65705e-310 1 0 2 0.0368155 3 0 4 0.0859029 TOMS655_TEST Normal end of execution. 28 February 2022 09:13:16 AM