hypercube_exactness_test

hypercube_exactness_test, a Fortran90 code which calls hypercube_exactness() to investigate the polynomial exactness of a quadrature rule over the interior of the hypercube in M dimensions.

Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT license

Related Data and Programs:

hypercube_exactness, a Fortran90 code which measures the monomial exactness of an M-dimensional quadrature rule over the interior of the unit hypercube in M dimensions.

Source Code:

• hypercube_exactness_tst.sh, runs all the tests.
• hypercube_exactness_test.txt, the output file.

CC_D1_O2 is a Clenshaw-Curtis order 2 rule for 1D.

• cc_d1_o2_x.txt, the abscissas of the rule.
• cc_d1_o2_w.txt, the weights of the rule.
• cc_d1_o2_r.txt, defines the region for the rule.
• cc_d1_o2_exact.txt, the results of the exactness test, up to degree 5.

CC_D1_O3 is a Clenshaw-Curtis order 3 rule for 1D. If you are paying attention, you may be surprised to see that a Clenshaw Curtis rule of odd order has one more degree of accuracy than you'd expect!

• cc_d1_o3_x.txt, the abscissas of the rule.
• cc_d1_o3_w.txt, the weights of the rule.
• cc_d1_o3_r.txt, defines the region for the rule.
• cc_d1_o3_exact.txt, the results of the exactness test, up to degree 5.

CC_D2_O3x3 is a Clenshaw-Curtis 3x3 product rule for 2D.

• cc_d2_o3x3_x.txt, the abscissas of the rule.
• cc_d2_o3x3_w.txt, the weights of the rule.
• cc_d2_o3x3_r.txt, defines the region for the rule.
• cc_d2_o3x3_exact.txt, the results of the exactness test, up to degree 8.

CCGL_D2_O3x2 is a product rule for 2D whose factors are a Clenshaw-Curtis of order 3 and a Gauss-Legendre rule of order 2.

• ccgl_d2_o3x2_x.txt, the abscissas of the rule.
• ccgl_d2_o3x2_w.txt, the weights of the rule.
• ccgl_d2_o3x2_r.txt, defines the region for the rule.
• ccgl_d2_o3x2_exact.txt, the results of the exactness test, up to degree 5.