28 September 2024 08:22:15 PM

nint_exactness_mixed():
  C++ version
  Investigate the polynomial exactness of
  a multidimensional quadrature rule
  for a region R = R1 x R2 x ... x RM.

  Individual rules may be for:

  Legendre:
  region: [-1,+1]
  weight: w(x)=1
  rules: Gauss-Legendre, Clenshaw-Curtis, Fejer2, Gauss-Patterson

  Jacobi:
  region: [-1,+1]
  weight: w(x)=(1-x)^alpha (1+x)^beta
  rules: Gauss-Jacobi

  Laguerre:
  region: [0,+oo)
  weight: w(x)=exp(-x)
  rules: Gauss-Laguerre

  Generalized Laguerre:
  region: [0,+oo)
  weight: w(x)=x^alpha exp(-x)
  rules: Generalized Gauss-Laguerre

  Hermite:
  region: (-oo,+o)
  weight: w(x)=exp(-x*x)
  rules: Gauss-Hermite

  Generalized Hermite:
  region: (-oo,+oo)
  weight: w(x)=|x|^alpha exp(-x*x)
  rules: generalized Gauss-Hermite

nint_exactness_mixed(): User input:
  Quadrature rule A file = "sparse_grid_mixed_d2_l2_ccxcc_a.txt".
  Quadrature rule B file = "sparse_grid_mixed_d2_l2_ccxcc_b.txt".
  Quadrature rule R file = "sparse_grid_mixed_d2_l2_ccxcc_r.txt".
  Quadrature rule W file = "sparse_grid_mixed_d2_l2_ccxcc_w.txt".
  Quadrature rule X file = "sparse_grid_mixed_d2_l2_ccxcc_x.txt".
  Maximum total degree to check = 7

  Spatial dimension = 2
  Number of points  = 25

  Analysis of integration region:

     0  Gauss Legendre.
     1  Gauss Legendre.

      Error    Degree  Exponents

   2.22045e-16      0    0  0

   5.55112e-17      1    1  0
   1.11022e-16      1    0  1

   3.33067e-16      2    2  0
             0      2    1  1
     4.996e-16      2    0  2

   1.66533e-16      3    3  0
             0      3    2  1
             0      3    1  2
   1.66533e-16      3    0  3

             0      4    4  0
             0      4    3  1
             0      4    2  2
             0      4    1  3
             0      4    0  4

   1.38778e-16      5    5  0
             0      5    4  1
             0      5    3  2
             0      5    2  3
             0      5    1  4
   1.38778e-16      5    0  5

     0.0666667      6    6  0
             0      6    5  1
      0.666667      6    4  2
             0      6    3  3
      0.666667      6    2  4
             0      6    1  5
     0.0666667      6    0  6

   8.32667e-17      7    7  0
             0      7    6  1
             0      7    5  2
             0      7    4  3
             0      7    3  4
             0      7    2  5
             0      7    1  6
   9.71445e-17      7    0  7


nint_exactness_mixed():
  Normal end of execution.

28 September 2024 08:22:15 PM