26-Jul-2022 18:48:39 toms655_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2 Test toms655(). ---------------------------------------- test01(): Test ciqfs(). Interpolatory quadrature formula Type Interval Weight function Name 1 (-1,+1) 1.0 Legendre Machine precision = 2.220446e-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 0 Maximum : 2.5e-16 2.5e-16 Weights ratio 0.667 Error in 10th power 0.00387 Error constant 1.07e-09 Moments: True from QF Error Relative 1 2 2 0 0 2 0 -2.220446049e-16 2.22e-16 2.22e-16 3 0.6666666667 0.6666666667 2.22e-16 1.33e-16 4 0 -2.220446049e-16 2.22e-16 2.22e-16 5 0.4 0.4 1.11e-16 7.93e-17 6 0 -2.220446049e-16 2.22e-16 2.22e-16 7 0.2857142857 0.2857142857 1.11e-16 8.64e-17 8 0 -1.942890293e-16 1.94e-16 1.94e-16 9 0.2222222222 0.2222222222 1.39e-16 1.14e-16 10 0 -2.498001805e-16 2.5e-16 2.5e-16 11 0.1818181818 0.1779513889 0.00387 0.00327 12 0 -2.498001805e-16 2.5e-16 2.5e-16 13 0.1538461538 0.1429191468 0.0109 0.00947 ---------------------------------------- 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 Parameter A -5.000000e-01 B 2.000000 Machine precision = 2.220446e-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 0 Maximum : 2e-15 2e-15 Weights ratio 0.714 Error in 10th power 0.0341 Error constant 9.41e-09 Moments: True from QF Error Relative 1 2.5 2.5 -1.78e-15 -5.08e-16 2 0 -5.551115123e-17 5.55e-17 5.55e-17 3 1.302083333 1.302083333 -6.66e-16 -2.89e-16 4 0 -2.775557562e-16 2.78e-16 2.78e-16 5 1.220703125 1.220703125 -4.44e-16 -2e-16 6 0 -7.771561172e-16 7.77e-16 7.77e-16 7 1.362391881 1.362391881 -2.22e-16 -9.4e-17 8 0 -1.554312234e-15 1.55e-15 1.55e-15 9 1.655684577 1.655684577 0 0 10 0 -1.998401444e-15 2e-15 2e-15 11 2.116642215 2.082511426 0.0341 0.011 12 0 -3.108624469e-15 3.11e-15 3.11e-15 13 2.798445236 2.65304297 0.145 0.0383 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 Parameter A -5.000000e-01 B 2.000000 Machine precision = 2.220446e-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 0 Maximum : 2.66e-15 2.66e-15 Weights ratio 0.714 Error in 10th power 0.0341 Error constant 9.41e-09 Moments: True from QF Error Relative 1 2.5 2.5 0 0 2 0 -1.110223025e-16 1.11e-16 1.11e-16 3 1.302083333 1.302083333 4.44e-16 1.93e-16 4 0 -3.885780586e-16 3.89e-16 3.89e-16 5 1.220703125 1.220703125 8.88e-16 4e-16 6 0 -9.992007222e-16 9.99e-16 9.99e-16 7 1.362391881 1.362391881 1.55e-15 6.58e-16 8 0 -1.665334537e-15 1.67e-15 1.67e-15 9 1.655684577 1.655684577 2.22e-15 8.36e-16 10 0 -2.664535259e-15 2.66e-15 2.66e-15 11 2.116642215 2.082511426 0.0341 0.011 12 0 -4.440892099e-15 4.44e-15 4.44e-15 13 2.798445236 2.65304297 0.145 0.0383 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 Type 1 Parameter A -5.000000e-01 B 2.000000 Machine precision = 2.220446e-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 : 4.44e-16 1.29e-16 Maximum : 7.11e-15 4e-15 Weights ratio 0.759 Error in 10th power 0.0571 Error constant 1.57e-08 Moments: True from QF Error Relative 1 3.141592654 3.141592654 -8.88e-16 -2.14e-16 2 0 1.776356839e-15 -1.78e-15 -1.78e-15 3 2.454369261 2.454369261 4.44e-16 1.29e-16 4 0 1.998401444e-15 -2e-15 -2e-15 5 2.876213977 2.876213977 1.78e-15 4.58e-16 6 0 2.664535259e-15 -2.66e-15 -2.66e-15 7 3.745070283 3.745070283 4e-15 8.42e-16 8 0 3.552713679e-15 -3.55e-15 -3.55e-15 9 5.120213277 5.120213277 7.11e-15 1.16e-15 10 0 3.996802889e-15 -4e-15 -4e-15 11 7.200299921 7.143154684 0.0571 0.00697 12 0 6.217248938e-15 -6.22e-15 -6.22e-15 13 10.31292957 10.04506127 0.268 0.0237 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 Type 1 Parameter A -5.000000e-01 B 2.000000 Machine precision = 2.220446e-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 : 4.44e-16 1.15e-16 Maximum : 3.55e-15 3.11e-15 Weights ratio 0.759 Error in 10th power 0.0571 Error constant 1.57e-08 Moments: True from QF Error Relative 1 3.141592654 3.141592654 -1.78e-15 -4.29e-16 2 0 2.109423747e-15 -2.11e-15 -2.11e-15 3 2.454369261 2.454369261 -4.44e-16 -1.29e-16 4 0 1.776356839e-15 -1.78e-15 -1.78e-15 5 2.876213977 2.876213977 4.44e-16 1.15e-16 6 0 2.442490654e-15 -2.44e-15 -2.44e-15 7 3.745070283 3.745070283 1.33e-15 2.81e-16 8 0 2.664535259e-15 -2.66e-15 -2.66e-15 9 5.120213277 5.120213277 3.55e-15 5.8e-16 10 0 3.108624469e-15 -3.11e-15 -3.11e-15 11 7.200299921 7.143154684 0.0571 0.00697 12 0 3.552713679e-15 -3.55e-15 -3.55e-15 13 10.31292957 10.04506127 0.268 0.0237 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 Parameter A -5.000000e-01 B 2.000000 alpha 0.500000 Machine precision = 2.220446e-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 : 4.16e-16 1.29e-16 Maximum : 2e-15 1.11e-15 Weights ratio 0.711 Error in 10th power 0.0223 Error constant 6.15e-09 Moments: True from QF Error Relative 1 2.454369261 2.454369261 -4.44e-16 -1.29e-16 2 0 -4.163336342e-16 4.16e-16 4.16e-16 3 0.9587379924 0.9587379924 -4.44e-16 -2.27e-16 4 0 -4.996003611e-16 5e-16 5e-16 5 0.7490140566 0.7490140566 -7.77e-16 -4.44e-16 6 0 -6.106226635e-16 6.11e-16 6.11e-16 7 0.7314590396 0.7314590396 -1.33e-15 -7.69e-16 8 0 -6.661338148e-16 6.66e-16 6.66e-16 9 0.8000333246 0.8000333246 -2e-15 -1.11e-15 10 0 -7.21644966e-16 7.22e-16 7.22e-16 11 0.9375390523 0.9152166939 0.0223 0.0115 12 0 -8.326672685e-16 8.33e-16 8.33e-16 13 1.150996604 1.063799892 0.0872 0.0405 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 Parameter A -5.000000e-01 B 2.000000 alpha 0.500000 Machine precision = 2.220446e-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 0 Maximum : 2.22e-15 2e-15 Weights ratio 0.711 Error in 10th power 0.0223 Error constant 6.15e-09 Moments: True from QF Error Relative 1 2.454369261 2.454369261 0 0 2 0 -6.938893904e-16 6.94e-16 6.94e-16 3 0.9587379924 0.9587379924 -2.22e-16 -1.13e-16 4 0 -9.992007222e-16 9.99e-16 9.99e-16 5 0.7490140566 0.7490140566 -7.77e-16 -4.44e-16 6 0 -1.33226763e-15 1.33e-15 1.33e-15 7 0.7314590396 0.7314590396 -1.44e-15 -8.34e-16 8 0 -1.554312234e-15 1.55e-15 1.55e-15 9 0.8000333246 0.8000333246 -2.22e-15 -1.23e-15 10 0 -1.998401444e-15 2e-15 2e-15 11 0.9375390523 0.9152166939 0.0223 0.0115 12 0 -2.553512957e-15 2.55e-15 2.55e-15 13 1.150996604 1.063799892 0.0872 0.0405 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 Parameter A -5.000000e-01 B 2.000000 alpha 0.500000 beta 2.000000 Machine precision = 2.220446e-16 Knots Mult Weights 1 -0.15303633066793587 1 0.076617129890421423 2 0.35753707671627766 1 0.53659067985975828 3 0.94535638653559406 1 1.2551248538055719 4 1.485888088482969 1 1.3472898724319169 5 1.8642547789330952 1 0.54899372611754638 Comparison of moments Order of precision 10 Errors : Absolute Relative ---------+------------------------- Minimum : 6.66e-16 2.56e-16 Maximum : 2.22e-15 8.85e-16 Weights ratio 0.79 Error in 10th power 0.0146 Error constant 4.02e-09 Moments: True from QF Error Relative 1 3.764616262 3.764616262 -1.78e-15 -3.73e-16 2 1.568590109 1.568590109 -6.66e-16 -2.59e-16 3 1.604239884 1.604239884 -6.66e-16 -2.56e-16 4 1.216891365 1.216891365 -1.33e-15 -6.01e-16 5 1.306872769 1.306872769 -1.11e-15 -4.81e-16 6 1.183053821 1.183053821 -8.88e-16 -4.07e-16 7 1.30822836 1.30822836 -1.11e-15 -4.81e-16 8 1.289910261 1.289910261 -2e-15 -8.73e-16 9 1.454550385 1.454550385 -2e-15 -8.14e-16 10 1.508092819 1.508092819 -2.22e-15 -8.85e-16 11 1.724613987 1.7100388 0.0146 0.00535 12 1.84811045 1.825870725 0.0222 0.00781 13 2.135936129 2.067375141 0.0686 0.0219 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 Parameter A -5.000000e-01 B 2.000000 alpha 0.500000 beta 2.000000 Machine precision = 2.220446e-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 : 0 0 Maximum : 2.89e-15 1.15e-15 Weights ratio 0.79 Error in 10th power 0.0146 Error constant 4.02e-09 Moments: True from QF Error Relative 1 3.764616262 3.764616262 0 0 2 1.568590109 1.568590109 4.44e-16 1.73e-16 3 1.604239884 1.604239884 6.66e-16 2.56e-16 4 1.216891365 1.216891365 4.44e-16 2e-16 5 1.306872769 1.306872769 1.11e-15 4.81e-16 6 1.183053821 1.183053821 1.55e-15 7.12e-16 7 1.30822836 1.30822836 1.78e-15 7.7e-16 8 1.289910261 1.289910261 1.78e-15 7.76e-16 9 1.454550385 1.454550385 2.44e-15 9.95e-16 10 1.508092819 1.508092819 2.89e-15 1.15e-15 11 1.724613987 1.7100388 0.0146 0.00535 12 1.84811045 1.825870725 0.0222 0.00781 13 2.135936129 2.067375141 0.0686 0.0219 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 Parameter A -5.000000e-01 B 2.000000 alpha 0.500000 Machine precision = 2.220446e-16 Knots Mult Weights 1 -0.28430059642607391 1 0.13097405507334794 2 0.37987684921184894 1 0.14587060425199255 3 1.552232681414158 1 0.034570386911402191 4 3.3733518897712789 1 0.001899789212937269 5 6.2288391760287887 1 1.3698879195062409e-05 Comparison of moments Order of precision 10 Errors : Absolute Relative ---------+------------------------- Minimum : 0 0 Maximum : 3.41e-13 6.27e-16 Weights ratio 0.239 Error in 10th power 11.9 Error constant 3.29e-06 Moments: True from QF Error Relative 1 0.3133285343 0.3133285343 0 0 2 0.2349964007 0.2349964007 -5.55e-17 -4.49e-17 3 0.2937455009 0.2937455009 -1.67e-16 -1.29e-16 4 0.5140546266 0.5140546266 -1.11e-16 -7.33e-17 5 1.15662291 1.15662291 -6.66e-16 -3.09e-16 6 3.180713002 3.180713002 -1.33e-15 -3.19e-16 7 10.33731726 10.33731726 -7.11e-15 -6.27e-16 8 38.76493972 38.76493972 -2.13e-14 -5.36e-16 9 164.7509938 164.7509938 -8.53e-14 -5.14e-16 10 782.5672205 782.5672205 -3.41e-13 -4.35e-16 11 4108.477908 4096.550234 11.9 0.0029 12 23623.74797 23227.15282 397 0.0168 13 147648.4248 139880.5273 7.77e+03 0.0526 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 Parameter A -5.000000e-01 B 2.000000 alpha 0.500000 Machine precision = 2.220446e-16 Knots Mult Weights 1 -0.28430059642607391 2 0.13097405507334792 0 2 0.37987684921184894 2 0.14587060425199266 0 3 1.552232681414158 2 0.034570386911402171 0 4 3.3733518897712789 2 0.0018997892129372707 0 5 6.2288391760287887 2 1.3698879195062405e-05 0 Comparison of moments Order of precision 10 Errors : Absolute Relative ---------+------------------------- Minimum : 5.55e-17 4.23e-17 Maximum : 4.55e-13 1.07e-15 Weights ratio 0.239 Error in 10th power 11.9 Error constant 3.29e-06 Moments: True from QF Error Relative 1 0.3133285343 0.3133285343 -5.55e-17 -4.23e-17 2 0.2349964007 0.2349964007 -1.11e-16 -8.99e-17 3 0.2937455009 0.2937455009 -1.67e-16 -1.29e-16 4 0.5140546266 0.5140546266 -1.11e-16 -7.33e-17 5 1.15662291 1.15662291 -6.66e-16 -3.09e-16 6 3.180713002 3.180713002 -2.22e-15 -5.31e-16 7 10.33731726 10.33731726 -1.07e-14 -9.4e-16 8 38.76493972 38.76493972 -4.26e-14 -1.07e-15 9 164.7509938 164.7509938 -1.42e-13 -8.57e-16 10 782.5672205 782.5672205 -4.55e-13 -5.8e-16 11 4108.477908 4096.550234 11.9 0.0029 12 23623.74797 23227.15282 397 0.0168 13 147648.4248 139880.5273 7.77e+03 0.0526 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 Parameter A -5.000000e-01 B 2.000000 alpha 0.500000 Machine precision = 2.220446e-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 : 2.78e-17 2.24e-17 Maximum : 3.33e-15 3.33e-15 Weights ratio 0.422 Error in 10th power 0.164 Error constant 4.53e-08 Moments: True from QF Error Relative 1 0.7286371307 0.7286371307 5.55e-16 3.21e-16 2 0 -2.567390744e-16 2.57e-16 2.57e-16 3 0.273238924 0.273238924 1.11e-16 8.72e-17 4 0 -1.45716772e-16 1.46e-16 1.46e-16 5 0.2390840585 0.2390840585 -2.78e-17 -2.24e-17 6 0 -4.163336342e-16 4.16e-16 4.16e-16 7 0.3287405805 0.3287405805 -1.67e-16 -1.25e-16 8 0 -1.221245327e-15 1.22e-15 1.22e-15 9 0.6163885884 0.6163885884 -3.33e-16 -2.06e-16 10 0 -3.330669074e-15 3.33e-15 3.33e-15 11 1.463922897 1.299552607 0.164 0.0667 12 0 -8.659739592e-15 8.66e-15 8.66e-15 13 4.20877833 2.832177149 1.38 0.264 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 Parameter A -5.000000e-01 B 2.000000 alpha 0.500000 Machine precision = 2.220446e-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 : 2.78e-17 2.24e-17 Maximum : 3.5e-15 3.5e-15 Weights ratio 0.422 Error in 10th power 0.164 Error constant 4.53e-08 Moments: True from QF Error Relative 1 0.7286371307 0.7286371307 4.44e-16 2.57e-16 2 0 -1.45716772e-16 1.46e-16 1.46e-16 3 0.273238924 0.273238924 1.67e-16 1.31e-16 4 0 -1.179611964e-16 1.18e-16 1.18e-16 5 0.2390840585 0.2390840585 -2.78e-17 -2.24e-17 6 0 -4.440892099e-16 4.44e-16 4.44e-16 7 0.3287405805 0.3287405805 -2.22e-16 -1.67e-16 8 0 -1.304512054e-15 1.3e-15 1.3e-15 9 0.6163885884 0.6163885884 -3.33e-16 -2.06e-16 10 0 -3.497202528e-15 3.5e-15 3.5e-15 11 1.463922897 1.299552607 0.164 0.0667 12 0 -9.103828802e-15 9.1e-15 9.1e-15 13 4.20877833 2.832177149 1.38 0.264 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 Parameter A -5.000000e-01 B 2.000000 alpha 0.500000 Machine precision = 2.220446e-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 : 1.67e-16 9.17e-17 Maximum : 2e-15 2e-15 Weights ratio 0.651 Error in 10th power 0.0285 Error constant 7.86e-09 Moments: True from QF Error Relative 1 1.863389981 1.863389981 -6.66e-16 -2.33e-16 2 0 3.330669074e-16 -3.33e-16 -3.33e-16 3 1.247805791 1.247805791 -2.22e-16 -9.88e-17 4 0 1.665334537e-16 -1.67e-16 -1.67e-16 5 1.240715985 1.240715985 -2.22e-16 -9.91e-17 6 0 -2.220446049e-16 2.22e-16 2.22e-16 7 1.421653733 1.421653733 2.22e-16 9.17e-17 8 0 -8.881784197e-16 8.88e-16 8.88e-16 9 1.753684704 1.753684704 6.66e-16 2.42e-16 10 0 -1.998401444e-15 2e-15 2e-15 11 2.263587593 2.235050644 0.0285 0.00874 12 0 -3.552713679e-15 3.55e-15 3.55e-15 13 3.012877005 2.886932684 0.126 0.0314 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 Parameter A -5.000000e-01 B 2.000000 alpha 0.500000 Machine precision = 2.220446e-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 : 1.11e-16 9.88e-17 Maximum : 2.44e-15 2.44e-15 Weights ratio 0.651 Error in 10th power 0.0285 Error constant 7.86e-09 Moments: True from QF Error Relative 1 1.863389981 1.863389981 4.44e-16 1.55e-16 2 0 -1.110223025e-16 1.11e-16 1.11e-16 3 1.247805791 1.247805791 2.22e-16 9.88e-17 4 0 -2.220446049e-16 2.22e-16 2.22e-16 5 1.240715985 1.240715985 2.22e-16 9.91e-17 6 0 -6.661338148e-16 6.66e-16 6.66e-16 7 1.421653733 1.421653733 1.33e-15 5.5e-16 8 0 -1.221245327e-15 1.22e-15 1.22e-15 9 1.753684704 1.753684704 2.22e-15 8.06e-16 10 0 -2.442490654e-15 2.44e-15 2.44e-15 11 2.263587593 2.235050644 0.0285 0.00874 12 0 -4.218847494e-15 4.22e-15 4.22e-15 13 3.012877005 2.886932684 0.126 0.0314 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 Parameter A -5.000000e-01 B 2.000000 alpha 0.500000 beta -16.000000 Machine precision = 2.220446e-16 Knots Mult Weights 1 -0.43541078852037896 1 2.6216877717069308e-05 2 -0.21664377601574747 1 1.6250543349707155e-05 3 0.25596297684363967 1 1.2927396984510202e-06 4 1.2864478502358694 1 1.1152074844159701e-08 5 4.1096437374566168 1 2.8799054822892628e-12 Comparison of moments Order of precision 10 Errors : Absolute Relative ---------+------------------------- Minimum : 0 0 Maximum : 6.78e-21 6.78e-21 Weights ratio 4.38e-05 Error in 10th power 8.25e-07 Error constant 2.27e-13 Moments: True from QF Error Relative 1 4.377131572e-05 4.377131572e-05 6.78e-21 6.78e-21 2 7.295219287e-06 7.295219287e-06 1.69e-21 1.69e-21 3 2.188565786e-06 2.188565786e-06 4.24e-22 4.24e-22 4 9.991278588e-07 9.991278588e-07 -2.12e-22 -2.12e-22 5 6.422964807e-07 6.422964807e-07 -4.24e-22 -4.24e-22 6 5.577837858e-07 5.577837858e-07 -4.24e-22 -4.24e-22 7 6.398108132e-07 6.398108132e-07 -3.18e-22 -3.18e-22 8 9.597162198e-07 9.597162198e-07 -4.24e-22 -4.24e-22 9 1.882520277e-06 1.882520277e-06 0 0 10 4.8774389e-06 4.8774389e-06 1.69e-21 1.69e-21 11 1.707103615e-05 1.624615493e-05 8.25e-07 8.25e-07 12 8.413582103e-05 6.416191151e-05 2e-05 2e-05 13 0.0006310186577 0.0002769134667 0.000354 0.000354 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 Parameter A -5.000000e-01 B 2.000000 alpha 0.500000 beta -16.000000 Machine precision = 2.220446e-16 Knots Mult Weights 1 -0.43541078852037896 2 2.6216877717069314e-05 -8.1862259836704115e-22 2 -0.21664377601574747 2 1.6250543349707175e-05 6.7656477710677943e-22 3 0.25596297684363967 2 1.2927396984510225e-06 -4.6767663452359323e-38 4 1.2864478502358694 2 1.1152074844159711e-08 -5.162937976069855e-40 5 4.1096437374566168 2 2.8799054822892648e-12 -2.3648100824274188e-43 Comparison of moments Order of precision 10 Errors : Absolute Relative ---------+------------------------- Minimum : 1.16e-21 1.16e-21 Maximum : 2.71e-20 2.71e-20 Weights ratio 4.38e-05 Error in 10th power 8.25e-07 Error constant 2.27e-13 Moments: True from QF Error Relative 1 4.377131572e-05 4.377131572e-05 -2.71e-20 -2.71e-20 2 7.295219287e-06 7.295219287e-06 -5.93e-21 -5.93e-21 3 2.188565786e-06 2.188565786e-06 -3.39e-21 -3.39e-21 4 9.991278588e-07 9.991278588e-07 -1.91e-21 -1.91e-21 5 6.422964807e-07 6.422964807e-07 -1.48e-21 -1.48e-21 6 5.577837858e-07 5.577837858e-07 -1.27e-21 -1.27e-21 7 6.398108132e-07 6.398108132e-07 -1.16e-21 -1.16e-21 8 9.597162198e-07 9.597162198e-07 -1.27e-21 -1.27e-21 9 1.882520277e-06 1.882520277e-06 -1.69e-21 -1.69e-21 10 4.8774389e-06 4.8774389e-06 -1.69e-21 -1.69e-21 11 1.707103615e-05 1.624615493e-05 8.25e-07 8.25e-07 12 8.413582103e-05 6.416191151e-05 2e-05 2e-05 13 0.0006310186577 0.0002769134667 0.000354 0.000354 Knots and weights of Gauss quadrature formula computed by cgqf(). Interpolatory quadrature formula Type Interval Weight function Name 9 (a,b) ((b-x)*(x-a))^(+0.5) Chebyshev Type 2 Parameter A -5.000000e-01 B 2.000000 Machine precision = 2.220446e-16 Knots Mult Weights 1 -0.33253175473054863 1 0.20453077171808565 2 0.12500000000000022 1 0.61359231515425661 3 0.75000000000000011 1 0.81812308687234137 4 1.3749999999999998 1 0.61359231515425661 5 1.8325317547305486 1 0.20453077171808534 Comparison of moments Order of precision 10 Errors : Absolute Relative ---------+------------------------- Minimum : 0 0 Maximum : 1.67e-15 9.25e-16 Weights ratio 0.711 Error in 10th power 0.0223 Error constant 6.15e-09 Moments: True from QF Error Relative 1 2.454369261 2.454369261 0 0 2 0 -1.942890293e-16 1.94e-16 1.94e-16 3 0.9587379924 0.9587379924 0 0 4 0 -3.885780586e-16 3.89e-16 3.89e-16 5 0.7490140566 0.7490140566 -4.44e-16 -2.54e-16 6 0 -4.440892099e-16 4.44e-16 4.44e-16 7 0.7314590396 0.7314590396 -8.88e-16 -5.13e-16 8 0 -5.551115123e-16 5.55e-16 5.55e-16 9 0.8000333246 0.8000333246 -1.67e-15 -9.25e-16 10 0 -6.106226635e-16 6.11e-16 6.11e-16 11 0.9375390523 0.9152166939 0.0223 0.0115 12 0 -7.21644966e-16 7.22e-16 7.22e-16 13 1.150996604 1.063799892 0.0872 0.0405 Weights of Gauss quadrature formula computed from the knots by ciqf(). Interpolatory quadrature formula Type Interval Weight function Name 9 (a,b) ((b-x)*(x-a))^(+0.5) Chebyshev Type 2 Parameter A -5.000000e-01 B 2.000000 Machine precision = 2.220446e-16 Knots Mult Weights 1 -0.33253175473054863 2 0.20453077171808587 -2.8384346500721368e-17 2 0.12500000000000022 2 0.61359231515425638 -4.2576519751081983e-17 3 0.75000000000000011 2 0.8181230868723417 -5.2664014366543436e-17 4 1.3749999999999998 2 0.61359231515425616 -4.2576519751081854e-17 5 1.8325317547305486 2 0.20453077171808534 -2.8384346500721244e-17 Comparison of moments Order of precision 10 Errors : Absolute Relative ---------+------------------------- Minimum : 0 0 Maximum : 2.05e-15 2.05e-15 Weights ratio 0.711 Error in 10th power 0.0223 Error constant 6.15e-09 Moments: True from QF Error Relative 1 2.454369261 2.454369261 4.44e-16 1.29e-16 2 0 -7.21644966e-16 7.22e-16 7.22e-16 3 0.9587379924 0.9587379924 0 0 4 0 -1.054711873e-15 1.05e-15 1.05e-15 5 0.7490140566 0.7490140566 -6.66e-16 -3.81e-16 6 0 -1.387778781e-15 1.39e-15 1.39e-15 7 0.7314590396 0.7314590396 -1.22e-15 -7.05e-16 8 0 -1.609823386e-15 1.61e-15 1.61e-15 9 0.8000333246 0.8000333246 -2e-15 -1.11e-15 10 0 -2.053912596e-15 2.05e-15 2.05e-15 11 0.9375390523 0.9152166939 0.0223 0.0115 12 0 -2.609024108e-15 2.61e-15 2.61e-15 13 1.150996604 1.063799892 0.0872 0.0405 ---------------------------------------- ceiqfs_test(): ceiqfs() sets up a quadrature formula and evaluates it for a particular function f(x). 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 : 1.188286e-16 ---------------------------------------- test04(): ceiqf() sets up a quadrature formula and evaluates it on a particular function f(x). Integral of sin(x) from -0.500000 to 2.000000 by Fejer type rule with 5 points of multiplicity 2. Quadrature formula: 1.2937294066147369 Exact value : 1.2937293984375151 Error : 8.177222e-09 ---------------------------------------- test05() Test cliqfs(). Interpolatory quadrature formula Type Interval Weight function Name 1 (-1,+1) 1.0 Legendre Machine precision = 2.220446e-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 : 2.78e-17 2.78e-17 Maximum : 5.55e-16 3.33e-16 Weights ratio 0.667 Error in 5th power 1.11e-16 Error constant 9.25e-19 Moments: True from QF Error Relative 1 2 2 4.44e-16 1.48e-16 2 0 2.775557562e-17 -2.78e-17 -2.78e-17 3 0.6666666667 0.6666666667 5.55e-16 3.33e-16 4 0 -8.326672685e-17 8.33e-17 8.33e-17 5 0.4 0.4 4.44e-16 3.17e-16 6 0 -1.110223025e-16 1.11e-16 1.11e-16 7 0.2857142857 0.2916666667 -0.00595 -0.00463 8 0 -1.249000903e-16 1.25e-16 1.25e-16 ---------------------------------------- test06(): Test cliqf() and eiqfs(). Interpolatory quadrature formula Type Interval Weight function Name 1 (a,b) 1.0 Legendre Parameter A -5.000000e-01 B 2.000000 Machine precision = 2.220446e-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 : 1.94e-16 1.94e-16 Maximum : 1.55e-15 7e-16 Weights ratio 0.714 Error in 5th power 8.33e-16 Error constant 6.94e-18 Moments: True from QF Error Relative 1 2.5 2.5 8.88e-16 2.54e-16 2 0 -1.942890293e-16 1.94e-16 1.94e-16 3 1.302083333 1.302083333 8.88e-16 3.86e-16 4 0 -5.551115123e-16 5.55e-16 5.55e-16 5 1.220703125 1.220703125 1.55e-15 7e-16 6 0 -8.326672685e-16 8.33e-16 8.33e-16 7 1.362391881 1.390775045 -0.0284 -0.012 8 0 -1.554312234e-15 1.55e-15 1.55e-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 : 2.474133e-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 : 1.110223e-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 : 3.469447e-17 test09() Call cgqfs() for a generalized Gauss Hermite rule. 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 = 2.220446e-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(): cdgqf() computes a quadrature formula. KIND = 1 ALPHA = 0.000000 BETA = 0.000000 Index Abscissas Weights 1 -9.8799251802048604e-01 3.0753241996116926e-02 2 -9.3727339240070606e-01 7.0366047488108485e-02 3 -8.4820658341042687e-01 1.0715922046717154e-01 4 -7.2441773136016996e-01 1.3957067792615496e-01 5 -5.7097217260853850e-01 1.6626920581699406e-01 6 -3.9415134707756339e-01 1.8616100001556132e-01 7 -2.0119409399743468e-01 1.9843148532711199e-01 8 -1.6758387707607162e-16 2.0257824192556134e-01 9 2.0119409399743471e-01 1.9843148532711105e-01 10 3.9415134707756366e-01 1.8616100001556257e-01 11 5.7097217260853916e-01 1.6626920581699439e-01 12 7.2441773136017007e-01 1.3957067792615338e-01 13 8.4820658341042698e-01 1.0715922046717288e-01 14 9.3727339240070573e-01 7.0366047488107861e-02 15 9.8799251802048527e-01 3.0753241996117443e-02 test10(): cdgqf() computes a quadrature formula. KIND = 2 ALPHA = 0.000000 BETA = 0.000000 Index Abscissas Weights 1 -9.9452189536827307e-01 2.0943951023932061e-01 2 -9.5105651629515364e-01 2.0943951023931773e-01 3 -8.6602540378443849e-01 2.0943951023931962e-01 4 -7.4314482547739436e-01 2.0943951023931914e-01 5 -5.8778525229247314e-01 2.0943951023931986e-01 6 -4.0673664307580032e-01 2.0943951023932000e-01 7 -2.0791169081775887e-01 2.0943951023931914e-01 8 4.3339309883563101e-17 2.0943951023931931e-01 9 2.0791169081775929e-01 2.0943951023931981e-01 10 4.0673664307580015e-01 2.0943951023931945e-01 11 5.8778525229247314e-01 2.0943951023931962e-01 12 7.4314482547739402e-01 2.0943951023932036e-01 13 8.6602540378443837e-01 2.0943951023932114e-01 14 9.5105651629515342e-01 2.0943951023931975e-01 15 9.9452189536827285e-01 2.0943951023931784e-01 test10(): cdgqf() computes a quadrature formula. KIND = 3 ALPHA = 0.000000 BETA = 0.000000 Index Abscissas Weights 1 -9.8799251802048604e-01 3.0753241996116926e-02 2 -9.3727339240070606e-01 7.0366047488108485e-02 3 -8.4820658341042687e-01 1.0715922046717154e-01 4 -7.2441773136016996e-01 1.3957067792615496e-01 5 -5.7097217260853850e-01 1.6626920581699406e-01 6 -3.9415134707756339e-01 1.8616100001556132e-01 7 -2.0119409399743468e-01 1.9843148532711199e-01 8 -1.6758387707607162e-16 2.0257824192556134e-01 9 2.0119409399743471e-01 1.9843148532711105e-01 10 3.9415134707756366e-01 1.8616100001556257e-01 11 5.7097217260853916e-01 1.6626920581699439e-01 12 7.2441773136017007e-01 1.3957067792615338e-01 13 8.4820658341042698e-01 1.0715922046717288e-01 14 9.3727339240070573e-01 7.0366047488107861e-02 15 9.8799251802048527e-01 3.0753241996117443e-02 test10(): cdgqf() computes a quadrature formula. KIND = 4 ALPHA = 0.000000 BETA = 0.000000 Index Abscissas Weights 1 -9.8799251802048604e-01 3.0753241996116926e-02 2 -9.3727339240070606e-01 7.0366047488108485e-02 3 -8.4820658341042687e-01 1.0715922046717154e-01 4 -7.2441773136016996e-01 1.3957067792615496e-01 5 -5.7097217260853850e-01 1.6626920581699406e-01 6 -3.9415134707756339e-01 1.8616100001556132e-01 7 -2.0119409399743468e-01 1.9843148532711199e-01 8 -1.6758387707607162e-16 2.0257824192556134e-01 9 2.0119409399743471e-01 1.9843148532711105e-01 10 3.9415134707756366e-01 1.8616100001556257e-01 11 5.7097217260853916e-01 1.6626920581699439e-01 12 7.2441773136017007e-01 1.3957067792615338e-01 13 8.4820658341042698e-01 1.0715922046717288e-01 14 9.3727339240070573e-01 7.0366047488107861e-02 15 9.8799251802048527e-01 3.0753241996117443e-02 test10(): cdgqf() computes a quadrature formula. KIND = 5 ALPHA = 0.000000 BETA = 0.000000 Index Abscissas Weights 1 9.3307812017281042e-02 2.1823488594008542e-01 2 4.9269174030188095e-01 3.4221017792288355e-01 3 1.2155954120709456e+00 2.6302757794168086e-01 4 2.2699495262037392e+00 1.2642581810593134e-01 5 3.6676227217514366e+00 4.0206864921001000e-02 6 5.4253366274135519e+00 8.5638778036118308e-03 7 7.5659162266130702e+00 1.2124361472142537e-03 8 1.0120228568019117e+01 1.1167439234425141e-04 9 1.3130282482175721e+01 6.4599267620229030e-06 10 1.6654407708329963e+01 2.2263169070962561e-07 11 2.0776478899448765e+01 4.2274303849793740e-09 12 2.5623894226728787e+01 3.9218972670410767e-11 13 3.1407519169753932e+01 1.4565152640731388e-13 14 3.8530683306486033e+01 1.4830270511132836e-16 15 4.8026085572685801e+01 1.6005949062111317e-20 test10(): cdgqf() computes a quadrature formula. KIND = 6 ALPHA = 0.000000 BETA = 0.000000 Index Abscissas Weights 1 -4.4999907073093901e+00 1.5224758042535159e-09 2 -3.6699503734044510e+00 1.0591155477110709e-06 3 -2.9671669279056041e+00 1.0000444123249965e-04 4 -2.3257324861738558e+00 2.7780688429127737e-03 5 -1.7199925751864888e+00 3.0780033872546176e-02 6 -1.1361155852109208e+00 1.5848891579593585e-01 7 -5.6506958325557577e-01 4.1202868749889843e-01 8 -1.6384693195586128e-16 5.6410030872641759e-01 9 5.6506958325557577e-01 4.1202868749889815e-01 10 1.1361155852109210e+00 1.5848891579593610e-01 11 1.7199925751864880e+00 3.0780033872546068e-02 12 2.3257324861738580e+00 2.7780688429127672e-03 13 2.9671669279056032e+00 1.0000444123250034e-04 14 3.6699503734044514e+00 1.0591155477110705e-06 15 4.4999907073093883e+00 1.5224758042535350e-09 test10(): cdgqf() computes a quadrature formula. KIND = 7 ALPHA = 0.000000 BETA = 0.000000 Index Abscissas Weights 1 -9.8799251802048604e-01 3.0753241996116926e-02 2 -9.3727339240070606e-01 7.0366047488108485e-02 3 -8.4820658341042687e-01 1.0715922046717154e-01 4 -7.2441773136016996e-01 1.3957067792615496e-01 5 -5.7097217260853850e-01 1.6626920581699406e-01 6 -3.9415134707756339e-01 1.8616100001556132e-01 7 -2.0119409399743468e-01 1.9843148532711199e-01 8 -1.6758387707607162e-16 2.0257824192556134e-01 9 2.0119409399743471e-01 1.9843148532711105e-01 10 3.9415134707756366e-01 1.8616100001556257e-01 11 5.7097217260853916e-01 1.6626920581699439e-01 12 7.2441773136017007e-01 1.3957067792615338e-01 13 8.4820658341042698e-01 1.0715922046717288e-01 14 9.3727339240070573e-01 7.0366047488107861e-02 15 9.8799251802048527e-01 3.0753241996117443e-02 test10(): cdgqf() computes a quadrature formula. KIND = 8 ALPHA = 1.000000 BETA = -33.000000 Index Abscissas Weights 1 1.3616839098154570e-02 2.0110204981899703e-04 2 4.6638200344823549e-02 4.4950389075516529e-04 3 1.0150582656885053e-01 2.8028347724079770e-04 4 1.8271184167265378e-01 6.9395278328822320e-05 5 2.9753402417670222e-01 7.4304506099041468e-06 6 4.5754063847638665e-01 3.4288030238738712e-07 7 6.8136180595512241e-01 6.4445861100153378e-09 8 9.9999999999999967e-01 4.4391927019104055e-11 9 1.4676490394089752e+00 9.4874785233432834e-14 10 2.1855982090028236e+00 4.8708312007461483e-17 11 3.3609601549505834e+00 4.0140021502394373e-21 12 5.4730990112375766e+00 2.7074726730695125e-26 13 9.8516512184815817e+00 4.3235022172039042e-33 14 2.1441650677050369e+01 1.1123595367452922e-42 15 7.3438482513575394e+01 1.5546382997160635e-58 test10(): cdgqf() computes a quadrature formula. KIND = 9 ALPHA = 0.000000 BETA = 0.000000 Index Abscissas Weights 1 -9.8078528040322999e-01 7.4731094203238715e-03 2 -9.2387953251128663e-01 2.8754724515956551e-02 3 -8.3146961230254501e-01 6.0604912306909689e-02 4 -7.0710678118654724e-01 9.8174770424680674e-02 5 -5.5557023301960218e-01 1.3574462854245262e-01 6 -3.8268343236508967e-01 1.6759481633340559e-01 7 -1.9509032201612844e-01 1.8887643142903787e-01 8 -2.3705853412659656e-17 1.9634954084936210e-01 9 1.9509032201612816e-01 1.8887643142903821e-01 10 3.8268343236508995e-01 1.6759481633340481e-01 11 5.5557023301960196e-01 1.3574462854245248e-01 12 7.0710678118654768e-01 9.8174770424681090e-02 13 8.3146961230254512e-01 6.0604912306909946e-02 14 9.2387953251128652e-01 2.8754724515956682e-02 15 9.8078528040323021e-01 7.4731094203238620e-03 cgqf_tester(): cgqf() computes a quadrature formula with nondefault values of A and B. KIND = 1 ALPHA = 0.000000 BETA = 0.000000 A = 0.000000 B = 1.000000 Index Abscissas Weights 1 6.0037409897569782e-03 1.5376620998058463e-02 2 3.1363303799646969e-02 3.5183023744054243e-02 3 7.5896708294786563e-02 5.3579610233585769e-02 4 1.3779113431991502e-01 6.9785338963077481e-02 5 2.1451391369573075e-01 8.3134602908497029e-02 6 3.0292432646121831e-01 9.3080500007780662e-02 7 3.9940295300128265e-01 9.9215742663555997e-02 8 4.9999999999999989e-01 1.0128912096278067e-01 9 6.0059704699871741e-01 9.9215742663555526e-02 10 6.9707567353878186e-01 9.3080500007781286e-02 11 7.8548608630426964e-01 8.3134602908497196e-02 12 8.6220886568008503e-01 6.9785338963076690e-02 13 9.2410329170521344e-01 5.3579610233586442e-02 14 9.6863669620035286e-01 3.5183023744053930e-02 15 9.9399625901024269e-01 1.5376620998058721e-02 cgqf_tester(): cgqf() computes a quadrature formula with nondefault values of A and B. KIND = 2 ALPHA = 0.000000 BETA = 0.000000 A = 0.000000 B = 1.000000 Index Abscissas Weights 1 2.7390523158634661e-03 2.0943951023932061e-01 2 2.4471741852423179e-02 2.0943951023931773e-01 3 6.6987298107780757e-02 2.0943951023931962e-01 4 1.2842758726130282e-01 2.0943951023931914e-01 5 2.0610737385376343e-01 2.0943951023931986e-01 6 2.9663167846209981e-01 2.0943951023932000e-01 7 3.9604415459112058e-01 2.0943951023931914e-01 8 5.0000000000000000e-01 2.0943951023931931e-01 9 6.0395584540887959e-01 2.0943951023931981e-01 10 7.0336832153790008e-01 2.0943951023931945e-01 11 7.9389262614623657e-01 2.0943951023931962e-01 12 8.7157241273869701e-01 2.0943951023932036e-01 13 9.3301270189221919e-01 2.0943951023932114e-01 14 9.7552825814757671e-01 2.0943951023931975e-01 15 9.9726094768413642e-01 2.0943951023931784e-01 cgqf_tester(): cgqf() computes a quadrature formula with nondefault values of A and B. KIND = 3 ALPHA = 1.000000 BETA = 0.000000 A = 0.000000 B = 1.000000 Index Abscissas Weights 1 1.3433911684290867e-02 2.9768516004626244e-04 2 4.4560002042213165e-02 1.6859097509633132e-03 3 9.2151874389114818e-02 4.6260962099892470e-03 4 1.5448550968615771e-01 9.0119615578977477e-03 5 2.2930730033494923e-01 1.4172910399844170e-02 6 3.1391278321726146e-01 1.9060840019005106e-02 7 4.0524401324084131e-01 2.2561563063495674e-02 8 4.9999999999999989e-01 2.3832734344183763e-02 9 5.9475598675915864e-01 2.2561563063495656e-02 10 6.8608721678273832e-01 1.9060840019005099e-02 11 7.7069269966505072e-01 1.4172910399844143e-02 12 8.4551449031384251e-01 9.0119615578976870e-03 13 9.0784812561088524e-01 4.6260962099892479e-03 14 9.5543999795778656e-01 1.6859097509633130e-03 15 9.8656608831570902e-01 2.9768516004626412e-04 cgqf_tester(): cgqf() computes a quadrature formula with nondefault values of A and B. KIND = 4 ALPHA = 1.500000 BETA = 0.500000 A = 0.000000 B = 1.000000 Index Abscissas Weights 1 9.0522686782530948e-03 1.6940549250141993e-03 2 3.5881902420740353e-02 6.3564653805702667e-03 3 7.9519209247238876e-02 1.2841060014124496e-02 4 1.3838702480661819e-01 1.9581627943324725e-02 5 2.1035771544672538e-01 2.5002899615440364e-02 6 2.9283007687092621e-01 2.7918576059103414e-02 7 3.8282334921430439e-01 2.7805429294995337e-02 8 4.7708495090945441e-01 2.4882075766863746e-02 9 5.7220803828124955e-01 1.9980999551149136e-02 10 6.6475464373764337e-01 1.4264018523005611e-02 11 7.5137994691190468e-01 8.8756549677931774e-03 12 8.2895320285797425e-01 4.6425144385171709e-03 13 8.9467101745756628e-01 1.9063312160067453e-03 14 9.4615919808755122e-01 5.3113444293740762e-04 15 9.8156245507184980e-01 6.6698710516168583e-05 cgqf_tester(): cgqf() computes a quadrature formula with nondefault values of A and B. KIND = 5 ALPHA = 1.000000 BETA = 0.000000 A = 1.000000 B = 1.000000 Index Abscissas Weights 1 1.2296805054251339e+00 7.0502428663789460e-02 2 1.7721449103754114e+00 2.4955890904049483e-01 3 2.6310530990674463e+00 3.2553311549213299e-01 4 3.8151445900122534e+00 2.2772708813934389e-01 5 5.3371640773375599e+00 9.6188057983096570e-02 6 7.2146427645592421e+00 2.5634284894184425e-02 7 9.4711639813467130e+00 4.3566472028930643e-03 8 1.2138331965750808e+01 4.6745576995090672e-04 9 1.5258910021624239e+01 3.0799238312965784e-05 10 1.8892053438169484e+01 1.1883904678040519e-06 11 2.3122620174833624e+01 2.4931355709440674e-08 12 2.8079311499047563e+01 2.5295606402039204e-10 13 3.3974973552397401e+01 1.0197776696981372e-12 14 4.1216583711496575e+01 1.1220705236083044e-15 15 5.0846221708556556e+01 1.3093371376376583e-19 cgqf_tester(): cgqf() computes a quadrature formula with nondefault values of A and B. KIND = 6 ALPHA = 1.000000 BETA = 0.000000 A = 0.000000 B = 0.500000 Index Abscissas Weights 1 -6.4949483305033988e+00 5.9896135285108737e-09 2 -5.3280701099004819e+00 3.8385256751540472e-06 3 -4.3406680091943448e+00 3.2911142049741617e-04 4 -3.4398538483547663e+00 8.0799031678388152e-03 5 -2.5892278781662834e+00 7.5512739453312022e-02 6 -1.7683812878755882e+00 3.0040474317896643e-01 7 -9.6023353389162014e-01 4.9066965826409575e-01 8 -6.3574870820289532e-17 2.5000000000000011e-01 9 9.6023353389162114e-01 4.9066965826409609e-01 10 1.7683812878755885e+00 3.0040474317896670e-01 11 2.5892278781662830e+00 7.5512739453312494e-02 12 3.4398538483547623e+00 8.0799031678388551e-03 13 4.3406680091943457e+00 3.2911142049741758e-04 14 5.3280701099004855e+00 3.8385256751540353e-06 15 6.4949483305033944e+00 5.9896135285108778e-09 cgqf_tester(): cgqf() computes a quadrature formula with nondefault values of A and B. KIND = 7 ALPHA = 1.000000 BETA = 0.000000 A = 0.000000 B = 1.000000 Index Abscissas Weights 1 5.6517893323352886e-03 7.1568009215160809e-03 2 2.9542524015428229e-02 1.5602993833116469e-02 3 7.1569673921356658e-02 2.1688424727156437e-02 4 1.3015083265925953e-01 2.4473260465780706e-02 5 2.0308893709009013e-01 2.3532346586819936e-02 6 2.8772618405883610e-01 1.9008163790424103e-02 7 3.8140134851428309e-01 1.1584884675186258e-02 8 5.0000000000000011e-01 3.9062500000000035e-03 9 6.1859865148571702e-01 1.1584884675186207e-02 10 7.1227381594116379e-01 1.9008163790424134e-02 11 7.9691106290990976e-01 2.3532346586819866e-02 12 8.6984916734074003e-01 2.4473260465780803e-02 13 9.2843032607864362e-01 2.1688424727156264e-02 14 9.7045747598457166e-01 1.5602993833116823e-02 15 9.9434821066766488e-01 7.1568009215159240e-03 cgqf_tester(): cgqf() computes a quadrature formula with nondefault values of A and B. KIND = 8 ALPHA = 1.000000 BETA = -33.000000 A = 0.000000 B = 1.000000 Index Abscissas Weights 1 1.3616839098154570e-02 2.0110204981899703e-04 2 4.6638200344823549e-02 4.4950389075516529e-04 3 1.0150582656885053e-01 2.8028347724079770e-04 4 1.8271184167265378e-01 6.9395278328822320e-05 5 2.9753402417670222e-01 7.4304506099041468e-06 6 4.5754063847638665e-01 3.4288030238738712e-07 7 6.8136180595512241e-01 6.4445861100153378e-09 8 9.9999999999999967e-01 4.4391927019104055e-11 9 1.4676490394089752e+00 9.4874785233432834e-14 10 2.1855982090028236e+00 4.8708312007461483e-17 11 3.3609601549505834e+00 4.0140021502394373e-21 12 5.4730990112375766e+00 2.7074726730695125e-26 13 9.8516512184815817e+00 4.3235022172039042e-33 14 2.1441650677050369e+01 1.1123595367452922e-42 15 7.3438482513575394e+01 1.5546382997160635e-58 cgqf_tester(): cgqf() computes a quadrature formula with nondefault values of A and B. KIND = 9 ALPHA = 0.000000 BETA = 0.000000 A = 0.000000 B = 1.000000 Index Abscissas Weights 1 9.6073597983850068e-03 1.8682773550809679e-03 2 3.8060233744356686e-02 7.1886811289891377e-03 3 8.4265193848727493e-02 1.5151228076727422e-02 4 1.4644660940672638e-01 2.4543692606170169e-02 5 2.2221488349019891e-01 3.3936157135613154e-02 6 3.0865828381745519e-01 4.1898704083351397e-02 7 4.0245483899193579e-01 4.7219107857259468e-02 8 5.0000000000000000e-01 4.9087385212340524e-02 9 5.9754516100806410e-01 4.7219107857259551e-02 10 6.9134171618254503e-01 4.1898704083351203e-02 11 7.7778511650980098e-01 3.3936157135613119e-02 12 8.5355339059327384e-01 2.4543692606170273e-02 13 9.1573480615127256e-01 1.5151228076727486e-02 14 9.6193976625564326e-01 7.1886811289891706e-03 15 9.9039264020161510e-01 1.8682773550809655e-03 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 1.5708 1 0 2 0.392699 3 0 4 0.19635 toms655_test(): Normal end of execution. 26-Jul-2022 18:48:40