private static void test01(int nt)
//****************************************************************************80
//
// Purpose:
//
// TEST01 tests CIRCLE_RULE.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 06 April 2014
//
// Author:
//
// John Burkardt
//
{
int[] e = new int[2];
int e1;
Console.WriteLine("");
Console.WriteLine("TEST01");
Console.WriteLine(" CIRCLE_RULE can compute a rule Q(f) for the unit circle");
Console.WriteLine(" using NT equally spaced angles.");
Console.WriteLine(" Estimate integrals I(f) where f = x^e(1) * y^e(2)");
Console.WriteLine(" using " + nt + " points.");
//
// Compute the quadrature rule.
//
double[] w = new double[nt];
double[] t = new double[nt];
QuadratureRule.circle_rule(nt, ref w, ref t);
//
// Apply it to integrands.
//
Console.WriteLine("");
Console.WriteLine(" E(1) E(2) I(f) Q(f)");
Console.WriteLine("");
//
// Specify a monomial.
//
for (e1 = 0; e1 <= 6; e1 += 2)
{
e[0] = e1;
int e2;
for (e2 = e1; e2 <= 6; e2 += 2)
{
e[1] = e2;
double q = 0.0;
int i;
for (i = 0; i < nt; i++)
{
double x = Math.Cos(t[i]);
double y = Math.Sin(t[i]);
q += w[i] * Math.Pow(x, e[0]) * Math.Pow(y, e[1]);
}
q = 2.0 * Math.PI * q;
double exact = Integrals.circle01_monomial_integral(e);
Console.WriteLine(" " + e[0].ToString(CultureInfo.InvariantCulture).PadLeft(2)
+ " " + e[1].ToString(CultureInfo.InvariantCulture).PadLeft(2)
+ " " + exact.ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + q.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
}
}
}
private static void test01()
//****************************************************************************80
//
// Purpose:
//
// TEST01 uses CIRCLE01_SAMPLE with an increasing number of points.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 12 January 2014
//
// Author:
//
// John Burkardt
//
{
const int m = 2;
const int n = 4192;
int test;
const int test_num = 20;
Console.WriteLine("");
Console.WriteLine("TEST01");
Console.WriteLine(" Use CIRCLE01_SAMPLE to compare exact and");
Console.WriteLine(" estimated integrals along the circumference");
Console.WriteLine(" of the unit circle in 2D.");
//
// Get sample points.
//
int seed = 123456789;
double[] x = Integrals.circle01_sample(n, ref seed);
Console.WriteLine("");
Console.WriteLine(" Number of sample points used is " + n + "");
//
// Randomly choose X, Y exponents.
//
Console.WriteLine("");
Console.WriteLine(" If any exponent is odd, the integral is zero.");
Console.WriteLine(" We restrict this test to randomly chosen even exponents.");
Console.WriteLine("");
Console.WriteLine(" Ex Ey MC-Estimate Exact Error");
Console.WriteLine("");
for (test = 1; test <= test_num; test++)
{
int[] e = UniformRNG.i4vec_uniform_ab_new(m, 0, 5, ref seed);
int i;
for (i = 0; i < m; i++)
{
e[i] *= 2;
}
double[] value = Monomial.monomial_value(m, n, e, x);
double result = Integrals.circle01_length() * typeMethods.r8vec_sum(n, value)
/ n;
double exact = Integrals.circle01_monomial_integral(e);
double error = Math.Abs(result - exact);
Console.WriteLine(" " + e[0].ToString(CultureInfo.InvariantCulture).PadLeft(2)
+ " " + e[1].ToString(CultureInfo.InvariantCulture).PadLeft(2)
+ " " + result.ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + exact.ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + error.ToString(CultureInfo.InvariantCulture).PadLeft(10) + "");
}
}
private static void circle01_sample_random_test()
//****************************************************************************80
//
// Purpose:
//
// CIRCLE01_SAMPLE_RANDOM_TEST uses CIRCLE01_SAMPLE_RANDOM with an increasing number of points.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 02 January 2014
//
// Author:
//
// John Burkardt
//
{
int[] e = new int[2];
int[] e_test =
{
0, 0,
2, 0,
0, 2,
4, 0,
2, 2,
0, 4,
6, 0
}
;
int i;
int j;
Console.WriteLine("");
Console.WriteLine("CIRCLE0_SAMPLE_RANDOM_TEST");
Console.WriteLine(" CIRCLE01_SAMPLE_RANDOM randomly samples the unit circle.");
Console.WriteLine(" Use it to estimate integrals.");
int seed = 123456789;
Console.WriteLine("");
Console.WriteLine(" N 1 X^2 Y^2" +
" X^4 X^2Y^2 Y^4 X^6");
Console.WriteLine("");
int n = 1;
while (n <= 65536)
{
double[] x = MonteCarlo.circle01_sample_random(n, ref seed);
string cout = " " + n.ToString(CultureInfo.InvariantCulture).PadLeft(8);
for (j = 0; j < 7; j++)
{
for (i = 0; i < 2; i++)
{
e[i] = e_test[i + j * 2];
}
double[] value = Monomial.monomial_value(2, n, e, x);
double result = Integrals.circle01_length() * typeMethods.r8vec_sum(n, value) / n;
cout += " " + result.ToString(CultureInfo.InvariantCulture).PadLeft(14);
}
Console.WriteLine(cout);
n = 2 * n;
}
Console.WriteLine("");
string cout2 = " Exact";
for (j = 0; j < 7; j++)
{
for (i = 0; i < 2; i++)
{
e[i] = e_test[i + j * 2];
}
double exact = Integrals.circle01_monomial_integral(e);
cout2 += " " + exact.ToString(CultureInfo.InvariantCulture).PadLeft(14);
}
Console.WriteLine(cout2);
}
