30 July 2014 08:02:17 AM
SQUARE_EXACTNESS_PRB
C++ version
Test the SQUARE_EXACTNESS library.
TEST01
Product Gauss-Legendre rules for the 2D Legendre integral.
Density function rho(x) = 1.
Region: -1 <= x <= +1.
Region: -1 <= y <= +1.
Level: L
Exactness: 2*L+1
Order: N = (L+1)*(L+1)
Quadrature rule for the 2D Legendre integral.
Number of points in rule is 1
D I J Relative Error
0
0 0 0
1
1 0 0
0 1 0
2
2 0 1
1 1 0
0 2 1
Quadrature rule for the 2D Legendre integral.
Number of points in rule is 4
D I J Relative Error
0
0 0 0
1
1 0 0
0 1 0
2
2 0 0
1 1 0
0 2 0
3
3 0 0
2 1 0
1 2 0
0 3 0
4
4 0 0.4444444444444445
3 1 0
2 2 0
1 3 0
0 4 0.4444444444444445
Quadrature rule for the 2D Legendre integral.
Number of points in rule is 9
D I J Relative Error
0
0 0 0
1
1 0 0
0 1 0
2
2 0 1.665334536937735e-16
1 1 0
0 2 1.665334536937735e-16
3
3 0 0
2 1 0
1 2 0
0 3 5.551115123125783e-17
4
4 0 2.775557561562891e-16
3 1 0
2 2 4.996003610813204e-16
1 3 0
0 4 2.775557561562891e-16
5
5 0 0
4 1 0
3 2 0
2 3 0
1 4 0
0 5 1.387778780781446e-17
6
6 0 0.1599999999999996
5 1 0
4 2 4.163336342344337e-16
3 3 0
2 4 4.163336342344337e-16
1 5 0
0 6 0.1599999999999996
Quadrature rule for the 2D Legendre integral.
Number of points in rule is 16
D I J Relative Error
0
0 0 2.220446049250313e-16
1
1 0 1.387778780781446e-17
0 1 1.387778780781446e-17
2
2 0 1.665334536937735e-16
1 1 0
0 2 3.33066907387547e-16
3
3 0 0
2 1 2.775557561562891e-17
1 2 1.387778780781446e-17
0 3 0
4
4 0 8.326672684688674e-16
3 1 0
2 2 4.996003610813204e-16
1 3 0
0 4 8.326672684688674e-16
5
5 0 0
4 1 1.387778780781446e-17
3 2 6.938893903907228e-18
2 3 1.387778780781446e-17
1 4 0
0 5 1.387778780781446e-17
6
6 0 9.71445146547012e-16
5 1 0
4 2 1.040834085586084e-15
3 3 0
2 4 1.040834085586084e-15
1 5 0
0 6 1.165734175856414e-15
7
7 0 0
6 1 1.387778780781446e-17
5 2 0
4 3 0
3 4 0
2 5 6.938893903907228e-18
1 6 0
0 7 1.387778780781446e-17
8
8 0 0.05224489795918474
7 1 0
6 2 1.165734175856414e-15
5 3 0
4 4 1.214306433183765e-15
3 5 0
2 6 1.020017403874363e-15
1 7 6.938893903907228e-18
0 8 0.05224489795918474
Quadrature rule for the 2D Legendre integral.
Number of points in rule is 25
D I J Relative Error
0
0 0 0
1
1 0 3.469446951953614e-17
0 1 3.469446951953614e-17
2
2 0 1.665334536937735e-16
1 1 6.938893903907228e-18
0 2 3.33066907387547e-16
3
3 0 1.387778780781446e-17
2 1 8.326672684688674e-17
1 2 0
0 3 2.775557561562891e-17
4
4 0 8.326672684688674e-16
3 1 0
2 2 8.743006318923108e-16
1 3 0
0 4 8.326672684688674e-16
5
5 0 0
4 1 1.387778780781446e-17
3 2 0
2 3 6.938893903907228e-18
1 4 6.938893903907228e-18
0 5 6.938893903907228e-18
6
6 0 7.771561172376096e-16
5 1 3.469446951953614e-18
4 2 1.040834085586084e-15
3 3 0
2 4 1.040834085586084e-15
1 5 0
0 6 9.71445146547012e-16
7
7 0 0
6 1 0
5 2 0
4 3 3.469446951953614e-18
3 4 0
2 5 6.938893903907228e-18
1 6 0
0 7 3.469446951953614e-17
8
8 0 9.992007221626409e-16
7 1 0
6 2 1.457167719820518e-15
5 3 3.469446951953614e-18
4 4 1.214306433183765e-15
3 5 3.469446951953614e-18
2 6 1.311450947838466e-15
1 7 0
0 8 8.743006318923108e-16
9
9 0 0
8 1 6.938893903907228e-18
7 2 0
6 3 0
5 4 0
4 5 0
3 6 0
2 7 0
1 8 3.469446951953614e-18
0 9 3.469446951953614e-17
10
10 0 0.01612496850592232
9 1 0
8 2 1.311450947838466e-15
7 3 0
6 4 1.578598363138894e-15
5 5 0
4 6 1.700029006457271e-15
3 7 0
2 8 1.311450947838466e-15
1 9 0
0 10 0.01612496850592232
Quadrature rule for the 2D Legendre integral.
Number of points in rule is 36
D I J Relative Error
0
0 0 2.220446049250313e-16
1
1 0 3.469446951953614e-18
0 1 1.040834085586084e-17
2
2 0 1.665334536937735e-16
1 1 1.040834085586084e-17
0 2 0
3
3 0 1.734723475976807e-17
2 1 3.469446951953614e-18
1 2 3.469446951953614e-18
0 3 1.040834085586084e-17
4
4 0 0
3 1 3.469446951953614e-18
2 2 0
1 3 3.469446951953614e-18
0 4 1.387778780781446e-16
5
5 0 0
4 1 1.387778780781446e-17
3 2 3.469446951953614e-18
2 3 2.081668171172169e-17
1 4 6.938893903907228e-18
0 5 3.469446951953614e-17
6
6 0 1.942890293094024e-16
5 1 3.469446951953614e-18
4 2 0
3 3 0
2 4 2.081668171172169e-16
1 5 0
0 6 0
7
7 0 0
6 1 6.938893903907228e-18
5 2 3.469446951953614e-18
4 3 3.469446951953614e-18
3 4 3.469446951953614e-18
2 5 1.040834085586084e-17
1 6 3.469446951953614e-18
0 7 3.469446951953614e-18
8
8 0 3.747002708109903e-16
7 1 0
6 2 1.457167719820518e-16
5 3 0
4 4 0
3 5 0
2 6 0
1 7 0
0 8 1.249000902703301e-16
9
9 0 0
8 1 6.938893903907228e-18
7 2 0
6 3 0
5 4 0
4 5 6.938893903907228e-18
3 6 0
2 7 3.469446951953614e-18
1 8 0
0 9 1.040834085586084e-17
10
10 0 0
9 1 5.204170427930421e-18
8 2 3.747002708109903e-16
7 3 0
6 4 1.214306433183765e-16
5 5 1.734723475976807e-18
4 6 1.214306433183765e-16
3 7 0
2 8 3.747002708109903e-16
1 9 5.204170427930421e-18
0 10 0
11
11 0 0
10 1 3.469446951953614e-18
9 2 1.734723475976807e-18
8 3 0
7 4 1.734723475976807e-18
6 5 3.469446951953614e-18
5 6 1.734723475976807e-18
4 7 5.204170427930421e-18
3 8 1.734723475976807e-18
2 9 3.469446951953614e-18
1 10 0
0 11 6.938893903907228e-18
12
12 0 0.004797511291018436
11 1 0
10 2 1.144917494144693e-16
9 3 0
8 4 3.122502256758253e-16
7 5 0
6 6 1.700029006457271e-16
5 7 0
4 8 1.561251128379126e-16
3 9 0
2 10 2.289834988289385e-16
1 11 0
0 12 0.004797511291018075
TEST02
Padua rule for the 2D Legendre integral.
Density function rho(x) = 1.
Region: -1 <= x <= +1.
Region: -1 <= y <= +1.
Level: L
Exactness: L+1 when L is 0,
L otherwise.
Order: N = (L+1)*(L+2)/2
Quadrature rule for the 2D Legendre integral.
Number of points in rule is 1
D I J Relative Error
0
0 0 0
1
1 0 0
0 1 0
2
2 0 1
1 1 0
0 2 1
Quadrature rule for the 2D Legendre integral.
Number of points in rule is 3
D I J Relative Error
0
0 0 0
1
1 0 0
0 1 0
2
2 0 2
1 1 0
0 2 0.5000000000000001
Quadrature rule for the 2D Legendre integral.
Number of points in rule is 6
D I J Relative Error
0
0 0 1.110223024625157e-16
1
1 0 1.110223024625157e-16
0 1 4.440892098500626e-16
2
2 0 4.996003610813204e-16
1 1 5.551115123125783e-17
0 2 3.33066907387547e-16
3
3 0 1.110223024625157e-16
2 1 0.6666666666666665
1 2 2.775557561562891e-17
0 3 0.3333333333333338
Quadrature rule for the 2D Legendre integral.
Number of points in rule is 10
D I J Relative Error
0
0 0 1.110223024625157e-16
1
1 0 8.326672684688674e-17
0 1 6.38378239159465e-16
2
2 0 0
1 1 6.800116025829084e-16
0 2 3.33066907387547e-16
3
3 0 2.775557561562891e-17
2 1 7.494005416219807e-16
1 2 4.163336342344337e-16
0 3 9.020562075079397e-16
4
4 0 0.1666666666666668
3 1 1.096345236817342e-15
2 2 0.2499999999999993
1 3 7.216449660063518e-16
0 4 0.04166666666666707
Quadrature rule for the 2D Legendre integral.
Number of points in rule is 15
D I J Relative Error
0
0 0 0
1
1 0 8.604228440844963e-16
0 1 3.05311331771918e-16
2
2 0 1.665334536937735e-16
1 1 1.942890293094024e-16
0 2 1.665334536937735e-16
3
3 0 2.498001805406602e-16
2 1 1.249000902703301e-16
1 2 4.163336342344337e-16
0 3 2.081668171172169e-17
4
4 0 1.249000902703301e-15
3 1 3.608224830031759e-16
2 2 1.124100812432971e-15
1 3 1.595945597898663e-16
0 4 1.387778780781446e-16
5
5 0 5.551115123125783e-17
4 1 0.03333333333333316
3 2 3.05311331771918e-16
2 3 0.05555555555555579
1 4 2.046973701652632e-16
0 5 0.01666666666666697
Quadrature rule for the 2D Legendre integral.
Number of points in rule is 21
D I J Relative Error
0
0 0 0
1
1 0 4.163336342344337e-16
0 1 7.28583859910259e-17
2
2 0 8.326672684688674e-16
1 1 1.908195823574488e-16
0 2 1.665334536937735e-16
3
3 0 7.771561172376096e-16
2 1 5.93275428784068e-16
1 2 2.0643209364124e-16
0 3 2.445960101127298e-16
4
4 0 8.326672684688674e-16
3 1 4.961309141293668e-16
2 2 1.249000902703301e-16
1 3 2.099015405931937e-16
0 4 0
5
5 0 7.494005416219807e-16
4 1 9.71445146547012e-16
3 2 2.203098814490545e-16
2 3 2.584737979205443e-16
1 4 1.023486850826316e-16
0 5 2.688821387764051e-16
6
6 0 0.008333333333334275
5 1 1.269817584415023e-15
4 2 0.02083333333333263
3 3 4.007211229506424e-16
2 4 0.02083333333333243
1 5 4.041905699025961e-16
0 6 0.006250000000000172
SQUARE_EXACTNESS_PRB
Normal end of execution.
30 July 2014 08:02:17 AM