20 November 2015 07:49:16 AM TOMS655_PRB 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 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 Parameters A -0.5 B 2 Machine precision = 2.22e-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 Parameters A -0.5 B 2 Machine precision = 2.22e-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 Parameters A -0.5 B 2 Machine precision = 2.22e-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 Parameters A -0.5 B 2 Machine precision = 2.22e-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 Parameters A -0.5 B 2 alpha 0.5 Machine precision = 2.22e-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 Parameters A -0.5 B 2 alpha 0.5 Machine precision = 2.22e-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 Parameters A -0.5 B 2 alpha 0.5 beta 2 Machine precision = 2.22e-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 : 8.88e-16 4.07e-16 Maximum : 3.55e-15 7.97e-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 -3.55e-15 -7.46e-16 2 1.568590109 1.568590109 -1.11e-15 -4.32e-16 3 1.604239884 1.604239884 -1.33e-15 -5.12e-16 4 1.216891365 1.216891365 -1.33e-15 -6.01e-16 5 1.306872769 1.306872769 -1.33e-15 -5.78e-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 -1.78e-15 -7.76e-16 9 1.454550385 1.454550385 -1.78e-15 -7.24e-16 10 1.508092819 1.508092819 -2e-15 -7.97e-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 Parameters A -0.5 B 2 alpha 0.5 beta 2 Machine precision = 2.22e-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 : 4.44e-16 9.32e-17 Maximum : 3.11e-15 1.24e-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 4.44e-16 9.32e-17 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 6.66e-16 3e-16 5 1.306872769 1.306872769 1.33e-15 5.78e-16 6 1.183053821 1.183053821 1.55e-15 7.12e-16 7 1.30822836 1.30822836 2e-15 8.66e-16 8 1.289910261 1.289910261 2e-15 8.73e-16 9 1.454550385 1.454550385 2.66e-15 1.09e-15 10 1.508092819 1.508092819 3.11e-15 1.24e-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 Parameters A -0.5 B 2 alpha 0.5 Machine precision = 2.22e-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 : 2.78e-17 2.25e-17 Maximum : 3.41e-13 5.36e-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 5.55e-17 4.23e-17 2 0.2349964007 0.2349964007 -2.78e-17 -2.25e-17 3 0.2937455009 0.2937455009 -1.67e-16 -1.29e-16 4 0.5140546266 0.5140546266 -2.22e-16 -1.47e-16 5 1.15662291 1.15662291 -4.44e-16 -2.06e-16 6 3.180713002 3.180713002 -1.78e-15 -4.25e-16 7 10.33731726 10.33731726 -5.33e-15 -4.7e-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 Parameters A -0.5 B 2 alpha 0.5 Machine precision = 2.22e-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 : 5.55e-17 4.23e-17 Maximum : 5.68e-13 1.1e-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 -1.39e-16 -1.12e-16 3 0.2937455009 0.2937455009 -1.67e-16 -1.29e-16 4 0.5140546266 0.5140546266 -2.22e-16 -1.47e-16 5 1.15662291 1.15662291 -8.88e-16 -4.12e-16 6 3.180713002 3.180713002 -2.66e-15 -6.37e-16 7 10.33731726 10.33731726 -1.24e-14 -1.1e-15 8 38.76493972 38.76493972 -4.26e-14 -1.07e-15 9 164.7509938 164.7509938 -1.71e-13 -1.03e-15 10 782.5672205 782.5672205 -5.68e-13 -7.25e-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 Parameters A -0.5 B 2 alpha 0.5 Machine precision = 2.22e-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 Parameters A -0.5 B 2 alpha 0.5 Machine precision = 2.22e-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 Parameters A -0.5 B 2 alpha 0.5 Machine precision = 2.22e-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 Parameters A -0.5 B 2 alpha 0.5 Machine precision = 2.22e-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 Parameters A -0.5 B 2 alpha 0.5 beta -16 Machine precision = 2.22e-16 Knots Mult Weights 1 -0.43541078852037896 1 2.6216877717069348e-05 2 -0.21664377601574747 1 1.6250543349707175e-05 3 0.25596297684363967 1 1.2927396984510223e-06 4 1.2864478502358694 1 1.1152074844159717e-08 5 4.1096437374566168 1 2.8799054822892664e-12 Comparison of moments Order of precision 10 Errors : Absolute Relative ---------+------------------------- Minimum : 4.24e-22 4.24e-22 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 2.54e-21 2.54e-21 3 2.188565786e-06 2.188565786e-06 4.24e-22 4.24e-22 4 9.991278588e-07 9.991278588e-07 -4.24e-22 -4.24e-22 5 6.422964807e-07 6.422964807e-07 -7.41e-22 -7.41e-22 6 5.577837858e-07 5.577837858e-07 -6.35e-22 -6.35e-22 7 6.398108132e-07 6.398108132e-07 -6.35e-22 -6.35e-22 8 9.597162198e-07 9.597162198e-07 -4.24e-22 -4.24e-22 9 1.882520277e-06 1.882520277e-06 -6.35e-22 -6.35e-22 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 Parameters A -0.5 B 2 alpha 0.5 beta -16 Machine precision = 2.22e-16 Knots Mult Weights 1 -0.43541078852037896 2 2.6216877717069348e-05 -8.1862259836704228e-22 2 -0.21664377601574747 2 1.6250543349707192e-05 6.7656477710678018e-22 3 0.25596297684363967 2 1.2927396984510242e-06 -4.6767663452359381e-38 4 1.2864478502358694 2 1.1152074844159722e-08 -5.1629379760698615e-40 5 4.1096437374566168 2 2.8799054822892688e-12 -2.3648100824274224e-43 Comparison of moments Order of precision 10 Errors : Absolute Relative ---------+------------------------- Minimum : 8.47e-22 8.47e-22 Maximum : 2.03e-20 2.03e-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 -2.03e-20 -2.03e-20 2 7.295219287e-06 7.295219287e-06 -3.39e-21 -3.39e-21 3 2.188565786e-06 2.188565786e-06 -2.12e-21 -2.12e-21 4 9.991278588e-07 9.991278588e-07 -1.69e-21 -1.69e-21 5 6.422964807e-07 6.422964807e-07 -1.59e-21 -1.59e-21 6 5.577837858e-07 5.577837858e-07 -1.38e-21 -1.38e-21 7 6.398108132e-07 6.398108132e-07 -1.06e-21 -1.06e-21 8 9.597162198e-07 9.597162198e-07 -1.27e-21 -1.27e-21 9 1.882520277e-06 1.882520277e-06 -1.48e-21 -1.48e-21 10 4.8774389e-06 4.8774389e-06 -8.47e-22 -8.47e-22 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 Parameters A -0.5 B 2 Machine precision = 2.22e-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 Parameters A -0.5 B 2 Machine precision = 2.22e-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 ---------------------------------------- TEST03 Test CEIQFS. Integral of sin(x) on -1, 1 by Fejer type rule with 5 points of multiplicity 2. Quadrature formula: -1.188285581044113e-16 Exact value : 0 Error :1.188285581044113e-16 ---------------------------------------- TEST04 Test CEIQF. Integral of sin(x) from -0.5 to 2 by Fejer type rule with 5 points of multiplicity 2. Quadrature formula: 1.293729406614737 Exact value : 1.293729398437515 Error :8.177222010630203e-09 ---------------------------------------- TEST05 Test CLIQFS. Interpolatory quadrature formula Type Interval Weight function Name 1 (-1,+1) 1.0 Legendre Machine precision = 2.220446049250313e-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 Parameters A -0.5 B 2 Machine precision = 2.22e-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 -0.5 to 2 by Fejer type rule with 5 points of multiplicity 1. Quadrature formula: 1.293704657106341 Exact value : 1.293729398437515 Error :2.474133117380539e-05 ---------------------------------------- TEST07 Test CEGQF. Integral of x*sin(x) from -0.5 to 2 by Gauss-exponential rule with 12 points Quadrature formula: 0.6837561162217042 Exact value : 0.6837561162217043 Error :1.110223024625157e-16 ---------------------------------------- TEST08 Test CEGQFS. Integral of x*sin(x) from -1 to +1 by Gauss-exponential rule with 12 points. Quadrature formula: 2.081668171172169e-17 Exact value : 0 Error :2.081668171172169e-17 TEST09 Call CGQFS to compute generalized Hermite rules. NT = 15 ALPHA = 1 Interpolatory quadrature formula Type Interval Weight function Name 6 (-oo,+oo) |x-a|^alpha*exp(-b*(x-a)^2) Gen Hermite alpha 1 Machine precision = 2.220446049250313e-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 BETA = 0 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 BETA = 0 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 BETA = 0 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 BETA = 0 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 BETA = 0 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 BETA = 0 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 BETA = 0 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 BETA = -33 Index Abscissas Weights 0 0.01361683909815457 0.000201102049818997 1 0.04663820034482355 0.0004495038907551653 2 0.1015058265688505 0.0002802834772407977 3 0.1827118416726538 6.939527832882232e-05 4 0.2975340241767022 7.430450609904147e-06 5 0.4575406384763867 3.428803023873871e-07 6 0.6813618059551224 6.444586110015338e-09 7 0.9999999999999997 4.439192701910406e-11 8 1.467649039408975 9.487478523343283e-14 9 2.185598209002824 4.870831200746148e-17 10 3.360960154950583 4.014002150239437e-21 11 5.473099011237577 2.707472673069512e-26 12 9.851651218481582 4.323502217203904e-33 13 21.44165067705037 1.112359536745292e-42 14 73.43848251357539 1.554638299716064e-58 TEST10 Call CDGQF to compute a quadrature formula. KIND = 9 ALPHA = 0 BETA = 0 Index Abscissas Weights 0 -0.98078528040323 0.007473109420323872 1 -0.9238795325112866 0.02875472451595655 2 -0.831469612302545 0.06060491230690969 3 -0.7071067811865472 0.09817477042468067 4 -0.5555702330196022 0.1357446285424526 5 -0.3826834323650897 0.1675948163334056 6 -0.1950903220161284 0.1888764314290379 7 -2.370585341265966e-17 0.1963495408493621 8 0.1950903220161282 0.1888764314290382 9 0.3826834323650899 0.1675948163334048 10 0.555570233019602 0.1357446285424525 11 0.7071067811865477 0.09817477042468109 12 0.8314696123025451 0.06060491230690995 13 0.9238795325112865 0.02875472451595668 14 0.9807852804032302 0.007473109420323862 CGQF_TEST CGQF computes a quadrature formula with nondefault values of parameters A and B. KIND = 1 ALPHA = 0 BETA = 0 A = 0 B = 1 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 CGQF computes a quadrature formula with nondefault values of parameters A and B. KIND = 2 ALPHA = 0 BETA = 0 A = 0 B = 1 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 CGQF computes a quadrature formula with nondefault values of parameters A and B. KIND = 3 ALPHA = 1 BETA = 0 A = 0 B = 1 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 CGQF computes a quadrature formula with nondefault values of parameters A and B. KIND = 4 ALPHA = 1.5 BETA = 0.5 A = 0 B = 1 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 CGQF computes a quadrature formula with nondefault values of parameters A and B. KIND = 5 ALPHA = 1 BETA = 0 A = 1 B = 1 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 CGQF computes a quadrature formula with nondefault values of parameters A and B. KIND = 6 ALPHA = 1 BETA = 0 A = 0 B = 0.5 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 CGQF computes a quadrature formula with nondefault values of parameters A and B. KIND = 7 ALPHA = 1 BETA = 0 A = 0 B = 1 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 CGQF computes a quadrature formula with nondefault values of parameters A and B. KIND = 8 ALPHA = 1 BETA = -33 A = 0 B = 1 Index Abscissas Weights 0 0.01361683909815457 0.000201102049818997 1 0.04663820034482355 0.0004495038907551653 2 0.1015058265688505 0.0002802834772407977 3 0.1827118416726538 6.939527832882232e-05 4 0.2975340241767022 7.430450609904147e-06 5 0.4575406384763867 3.428803023873871e-07 6 0.6813618059551224 6.444586110015338e-09 7 0.9999999999999997 4.439192701910406e-11 8 1.467649039408975 9.487478523343283e-14 9 2.185598209002824 4.870831200746148e-17 10 3.360960154950583 4.014002150239437e-21 11 5.473099011237577 2.707472673069512e-26 12 9.851651218481582 4.323502217203904e-33 13 21.44165067705037 1.112359536745292e-42 14 73.43848251357539 1.554638299716064e-58 CGQF_TEST CGQF computes a quadrature formula with nondefault values of parameters A and B. KIND = 9 ALPHA = 0 BETA = 0 A = 0 B = 1 Index Abscissas Weights 0 0.009607359798385007 0.001868277355080968 1 0.03806023374435669 0.007188681128989138 2 0.08426519384872749 0.01515122807672742 3 0.1464466094067264 0.02454369260617017 4 0.2222148834901989 0.03393615713561315 5 0.3086582838174552 0.0418987040833514 6 0.4024548389919358 0.04721910785725947 7 0.5 0.04908738521234052 8 0.5975451610080641 0.04721910785725955 9 0.691341716182545 0.0418987040833512 10 0.777785116509801 0.03393615713561312 11 0.8535533905932738 0.02454369260617027 12 0.9157348061512726 0.01515122807672749 13 0.9619397662556433 0.007188681128989171 14 0.9903926402016151 0.001868277355080966 WM_TESTER: WM_TEST computes moments for rule 1 with ALPHA = 0, BETA = 0 Order Moment 0 2 1 0 2 0.6666666666666666 3 0 4 0.4 WM_TESTER: WM_TEST computes moments for rule 2 with ALPHA = 0, BETA = 0 Order Moment 0 3.141592653589793 1 0 2 1.570796326794897 3 0 4 1.178097245096172 WM_TESTER: WM_TEST computes moments for rule 3 with ALPHA = 0.5, BETA = 0 Order Moment 0 1.570796326794897 1 0 2 0.3926990816987241 3 0 4 0.1963495408493621 WM_TESTER: WM_TEST computes moments for rule 4 with ALPHA = 0.25, BETA = 0.75 Order Moment 0 1.666081101809387 1 0.2776801836348979 2 0.451230298406709 3 0.15619510329463 4 0.2386314078112403 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 0.6666666666666666 1 0 2 0.4 3 0 4 0.2857142857142857 WM_TESTER: WM_TEST computes moments for rule 8 with ALPHA = -0.5, BETA = -6 Order Moment 0 0.7731263170943633 1 0.08590292412159592 2 0.03681553890925539 3 0.03681553890925539 4 0.08590292412159591 WM_TESTER: WM_TEST computes moments for rule 9 with ALPHA = 0, BETA = 0 Order Moment 0 1.570796326794897 1 0 2 0.3926990816987241 3 0 4 0.1963495408493621 TOMS655_PRB Normal end of execution. 20 November 2015 07:49:16 AM