product_rule_test

product_rule_test, a C++ code which calls product_rule(), which creates a multidimensional quadrature rule by using a product of distinct one-dimensional quadrature rules.

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:

product_rule, a C++ code which constructs a product quadrature rule from distinct 1D factor rules.

Source Code:

• product_rule_test.sh, runs all the tests.
• product_rule_test.txt, the output file.

As an example, we make a 2D product rule.

The first factor is a 1D Clenshaw Curtis rule of order 3:

• cc_d1_o3_x.txt, the abscissas of a 1D Clenshaw Curtis rule of order 3.
• cc_d1_o3_w.txt, the weights of a 1D Clenshaw Curtis rule of order 3.
• cc_d1_o3_r.txt, defines the range of the region.

The second factor is a 1D Gauss Legendre rule of order 2:

• gl_d1_o2_x.txt, the abscissas of a 1D Clenshaw Curtis rule of order 2.
• gl_d1_o2_w.txt, the weights of a 1D Clenshaw Curtis rule of order 2.
• gl_d1_o2_r.txt, defines the range of the region.

We give the command

product_rule factors.txt

• factors.txt, a file containing the list of factors.

The resulting product rule files:

• ccgl_d2_o3x2_x.txt, the abscissas of a 2D Clenshaw Curtis product rule of order 6.
• ccgl_d2_o3x2_w.txt, the weights of a 2D Clenshaw Curtis product rule of order 6.
• ccgl_d2_o3x2_r.txt, defines the range of the product region.