private static void square_minimal_rule_error_max_test()
//****************************************************************************80
//
// Purpose:
//
// SQUARE_MINIMAL_RULE_ERROR_MAX_TEST tests SQUARE_MINIMAL_RULE_ERROR_MAX.
//
// Licensing:
//
// This code is distributed under the GNU GPL license.
//
// Modified:
//
// 22 February 2018
//
// Author:
//
// John Burkardt.
//
// Reference:
//
// Mattia Festa, Alvise Sommariva,
// Computing almost minimal formulas on the square,
// Journal of Computational and Applied Mathematics,
// Volume 17, Number 236, November 2012, pages 4296-4302.
//
{
int degree;
Console.WriteLine("");
Console.WriteLine("SQUARE_MINIMAL_RULE_ERROR_MAX_TEST");
Console.WriteLine(" SQUARE_MINIMAL_RULE_ERROR_MAX computes the maximum");
Console.WriteLine(" error for a rule that should be exact for all monomials");
Console.WriteLine(" up to a given value of DEGREE.");
int degree_max = MinimalRule.square_minimal_rule_degree_max();
Console.WriteLine("");
Console.WriteLine(" Degree Monomials Error Max");
Console.WriteLine("");
for (degree = 0; degree <= degree_max; degree++)
{
double error_max = MinimalRule.square_minimal_rule_error_max(degree);
int m_num = (degree + 1) * (degree + 2) / 2;
Console.WriteLine(" " + degree.ToString().PadLeft(4)
+ " " + m_num.ToString().PadLeft(4)
+ " " + error_max + "");
}
}
private static void square_minimal_rule_order_test()
//****************************************************************************80
//
// Purpose:
//
// SQUARE_MINIMAL_RULE_ORDER_TEST tests SQUARE_MINIMAL_RULE_ORDER.
//
// Licensing:
//
// This code is distributed under the GNU GPL license.
//
// Modified:
//
// 22 February 2018
//
// Author:
//
// John Burkardt.
//
// Reference:
//
// Mattia Festa, Alvise Sommariva,
// Computing almost minimal formulas on the square,
// Journal of Computational and Applied Mathematics,
// Volume 17, Number 236, November 2012, pages 4296-4302.
//
{
int degree;
Console.WriteLine("");
Console.WriteLine("SQUARE_MINIMAL_RULE_ORDER_TEST");
Console.WriteLine(" Print the order (number of points) for each");
Console.WriteLine(" minimal square rule.");
int degree_max = MinimalRule.square_minimal_rule_degree_max();
Console.WriteLine("");
Console.WriteLine(" Degree Order");
Console.WriteLine("");
for (degree = 0; degree <= degree_max; degree++)
{
int order = MinimalRule.square_minimal_rule_order(degree);
Console.WriteLine(" " + degree
+ " " + order + "");
}
}
private static void square_minimal_rule_print_test(int degree)
//****************************************************************************80
//
// Purpose:
//
// SQUARE_MINIMAL_RULE_PRINT_TEST tests SQUARE_MINIMAL_RULE_PRINT.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 22 February 2018
//
// Author:
//
// John Burkardt
//
{
int j;
Console.WriteLine("");
Console.WriteLine("SQUARE_MINIMAL_RULE_PRINT_TEST");
Console.WriteLine(" SQUARE_MINIMAL_RULE_PRINT prints a quadrature rule");
Console.WriteLine(" for the symmetric unit square.");
Console.WriteLine(" Minimal quadrature rule for a square.");
Console.WriteLine(" Polynomial exactness degree DEGREE = " + degree + "");
//
// Retrieve and print a symmetric quadrature rule.
//
double[] xyw = MinimalRule.square_minimal_rule(degree);
int order = MinimalRule.square_minimal_rule_order(degree);
Console.WriteLine("");
Console.WriteLine(" Number of nodes N = " + order + "");
Console.WriteLine("");
Console.WriteLine(" J X Y W");
Console.WriteLine("");
for (j = 0; j < order; j++)
{
Console.WriteLine(" " + j.ToString().PadLeft(4)
+ " " + xyw[0 + j * 3].ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + xyw[1 + j * 3].ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + xyw[2 + j * 3].ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
}
double d = 0.0;
for (j = 0; j < order; j++)
{
d += xyw[2 + j * 3];
}
Console.WriteLine("");
Console.WriteLine(" Sum " + d.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
double area = Integrals.squaresym_area();
Console.WriteLine(" Area " + area.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
}
