18 September 2013 08:37:19 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
TEST11
Call CGQF to compute 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
TEST11
Call CGQF to compute 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
TEST11
Call CGQF to compute 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
TEST11
Call CGQF to compute 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
TEST11
Call CGQF to compute 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
TEST11
Call CGQF to compute 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
TEST11
Call CGQF to compute 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
TEST11
Call CGQF to compute 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
TEST11
Call CGQF to compute 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
TOMS655_PRB
Normal end of execution.
18 September 2013 08:37:20 AM