19 January 2020 09:01:50 AM
CUBE_EXACTNESS_TEST
C version
Test the CUBE_EXACTNESS library.
TEST01
Product Gauss-Legendre rules for the 3D Legendre integral.
Density function rho(x) = 1.
Region: -1 <= x <= +1.
-1 <= y <= +1.
-1 <= z <= +1.
Level: L
Exactness: 2*L+1
Order: N = (L+1)*(L+1)*(L+1)
Quadrature rule for the 3D Legendre integral.
Number of points in rule is 1
D I J K Relative Error
0
0 0 0 0.0000000000000000
1
1 0 0 0.0000000000000000
0 1 0 0.0000000000000000
0 0 1 0.0000000000000000
2
2 0 0 1.0000000000000000
1 1 0 0.0000000000000000
0 2 0 1.0000000000000000
1 0 1 0.0000000000000000
0 1 1 0.0000000000000000
0 0 2 1.0000000000000000
Quadrature rule for the 3D Legendre integral.
Number of points in rule is 8
D I J K Relative Error
0
0 0 0 0.0000000000000000
1
1 0 0 0.0000000000000000
0 1 0 0.0000000000000000
0 0 1 0.0000000000000000
2
2 0 0 0.0000000000000000
1 1 0 0.0000000000000000
0 2 0 0.0000000000000000
1 0 1 0.0000000000000000
0 1 1 0.0000000000000000
0 0 2 0.0000000000000000
3
3 0 0 0.0000000000000000
2 1 0 0.0000000000000000
1 2 0 0.0000000000000000
0 3 0 0.0000000000000000
2 0 1 0.0000000000000001
1 1 1 0.0000000000000000
0 2 1 0.0000000000000001
1 0 2 0.0000000000000000
0 1 2 0.0000000000000000
0 0 3 0.0000000000000001
4
4 0 0 0.4444444444444446
3 1 0 0.0000000000000000
2 2 0 0.0000000000000002
1 3 0 0.0000000000000000
0 4 0 0.4444444444444446
3 0 1 0.0000000000000000
2 1 1 0.0000000000000000
1 2 1 0.0000000000000000
0 3 1 0.0000000000000000
2 0 2 0.0000000000000002
1 1 2 0.0000000000000000
0 2 2 0.0000000000000002
1 0 3 0.0000000000000000
0 1 3 0.0000000000000000
0 0 4 0.4444444444444446
Quadrature rule for the 3D Legendre integral.
Number of points in rule is 27
D I J K Relative Error
0
0 0 0 0.0000000000000002
1
1 0 0 0.0000000000000000
0 1 0 0.0000000000000000
0 0 1 0.0000000000000000
2
2 0 0 0.0000000000000002
1 1 0 0.0000000000000000
0 2 0 0.0000000000000002
1 0 1 0.0000000000000000
0 1 1 0.0000000000000000
0 0 2 0.0000000000000003
3
3 0 0 0.0000000000000000
2 1 0 0.0000000000000000
1 2 0 0.0000000000000000
0 3 0 0.0000000000000000
2 0 1 0.0000000000000000
1 1 1 0.0000000000000000
0 2 1 0.0000000000000000
1 0 2 0.0000000000000000
0 1 2 0.0000000000000000
0 0 3 0.0000000000000001
4
4 0 0 0.0000000000000001
3 1 0 0.0000000000000000
2 2 0 0.0000000000000005
1 3 0 0.0000000000000000
0 4 0 0.0000000000000001
3 0 1 0.0000000000000000
2 1 1 0.0000000000000000
1 2 1 0.0000000000000000
0 3 1 0.0000000000000000
2 0 2 0.0000000000000005
1 1 2 0.0000000000000000
0 2 2 0.0000000000000005
1 0 3 0.0000000000000000
0 1 3 0.0000000000000000
0 0 4 0.0000000000000001
5
5 0 0 0.0000000000000000
4 1 0 0.0000000000000000
3 2 0 0.0000000000000000
2 3 0 0.0000000000000000
1 4 0 0.0000000000000000
0 5 0 0.0000000000000000
4 0 1 0.0000000000000000
3 1 1 0.0000000000000000
2 2 1 0.0000000000000000
1 3 1 0.0000000000000000
0 4 1 0.0000000000000000
3 0 2 0.0000000000000000
2 1 2 0.0000000000000000
1 2 2 0.0000000000000000
0 3 2 0.0000000000000000
2 0 3 0.0000000000000001
1 1 3 0.0000000000000000
0 2 3 0.0000000000000000
1 0 4 0.0000000000000000
0 1 4 0.0000000000000000
0 0 5 0.0000000000000000
6
6 0 0 0.1599999999999997
5 1 0 0.0000000000000000
4 2 0 0.0000000000000004
3 3 0 0.0000000000000000
2 4 0 0.0000000000000004
1 5 0 0.0000000000000000
0 6 0 0.1599999999999997
5 0 1 0.0000000000000000
4 1 1 0.0000000000000000
3 2 1 0.0000000000000000
2 3 1 0.0000000000000000
1 4 1 0.0000000000000000
0 5 1 0.0000000000000000
4 0 2 0.0000000000000004
3 1 2 0.0000000000000000
2 2 2 0.0000000000000006
1 3 2 0.0000000000000000
0 4 2 0.0000000000000004
3 0 3 0.0000000000000000
2 1 3 0.0000000000000000
1 2 3 0.0000000000000000
0 3 3 0.0000000000000000
2 0 4 0.0000000000000004
1 1 4 0.0000000000000000
0 2 4 0.0000000000000004
1 0 5 0.0000000000000000
0 1 5 0.0000000000000000
0 0 6 0.1599999999999998
Quadrature rule for the 3D Legendre integral.
Number of points in rule is 64
D I J K Relative Error
0
0 0 0 0.0000000000000002
1
1 0 0 0.0000000000000000
0 1 0 0.0000000000000000
0 0 1 0.0000000000000001
2
2 0 0 0.0000000000000008
1 1 0 0.0000000000000000
0 2 0 0.0000000000000007
1 0 1 0.0000000000000000
0 1 1 0.0000000000000000
0