private static void triangle_unit_quad_test(int degree_max)
//****************************************************************************80
//
// Purpose:
//
// TRIANGLE_UNIT_QUAD_TEST tests the rules for the unit triangle.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 18 April 2008
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, int DEGREE_MAX, the maximum total degree of the
// monomials to check.
//
{
const int DIM_NUM = 2;
int[] expon = new int[DIM_NUM];
int h = 0;
int t = 0;
Console.WriteLine("");
Console.WriteLine("TRIANGLE_UNIT_QUAD_TEST");
Console.WriteLine(" For the unit triangle,");
Console.WriteLine(" we approximate monomial integrals with:");
Console.WriteLine(" TRIANGLE_UNIT_O01,");
Console.WriteLine(" TRIANGLE_UNIT_O03,");
Console.WriteLine(" TRIANGLE_UNIT_O03b,");
Console.WriteLine(" TRIANGLE_UNIT_O06,");
Console.WriteLine(" TRIANGLE_UNIT_O06b,");
Console.WriteLine(" TRIANGLE_UNIT_O07,");
Console.WriteLine(" TRIANGLE_UNIT_O12,");
bool more = false;
SubCompData data = new();
for (;;)
{
SubComp.subcomp_next(ref data, degree_max, DIM_NUM, ref expon, ref more, ref h, ref t);
Console.WriteLine("");
string cout = " Monomial exponents: ";
int dim;
for (dim = 0; dim < DIM_NUM; dim++)
{
cout += " " + expon[dim].ToString(CultureInfo.InvariantCulture).PadLeft(2);
}
Console.WriteLine(cout);
Console.WriteLine("");
int order = 1;
double[] w = new double[order];
double[] xy = new double[DIM_NUM * order];
QuadratureRule.triangle_unit_o01(ref w, ref xy);
double[] v = Monomial.monomial_value(DIM_NUM, order, expon, xy);
double quad = QuadratureRule.triangle_unit_volume() * typeMethods.r8vec_dot_product(order, w, v);
Console.WriteLine(" " + order.ToString(CultureInfo.InvariantCulture).PadLeft(6)
+ " " + quad.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
order = 3;
w = new double[order];
xy = new double[DIM_NUM * order];
QuadratureRule.triangle_unit_o03(ref w, ref xy);
v = Monomial.monomial_value(DIM_NUM, order, expon, xy);
quad = QuadratureRule.triangle_unit_volume() * typeMethods.r8vec_dot_product(order, w, v);
Console.WriteLine(" " + order.ToString(CultureInfo.InvariantCulture).PadLeft(6)
+ " " + quad.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
order = 3;
w = new double[order];
xy = new double[DIM_NUM * order];
QuadratureRule.triangle_unit_o03b(ref w, ref xy);
v = Monomial.monomial_value(DIM_NUM, order, expon, xy);
quad = QuadratureRule.triangle_unit_volume() * typeMethods.r8vec_dot_product(order, w, v);
Console.WriteLine(" " + order.ToString(CultureInfo.InvariantCulture).PadLeft(6)
+ " " + quad.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
order = 6;
w = new double[order];
xy = new double[DIM_NUM * order];
QuadratureRule.triangle_unit_o06(ref w, ref xy);
v = Monomial.monomial_value(DIM_NUM, order, expon, xy);
quad = QuadratureRule.triangle_unit_volume() * typeMethods.r8vec_dot_product(order, w, v);
Console.WriteLine(" " + order.ToString(CultureInfo.InvariantCulture).PadLeft(6)
+ " " + quad.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
order = 6;
w = new double[order];
xy = new double[DIM_NUM * order];
QuadratureRule.triangle_unit_o06b(ref w, ref xy);
v = Monomial.monomial_value(DIM_NUM, order, expon, xy);
quad = QuadratureRule.triangle_unit_volume() * typeMethods.r8vec_dot_product(order, w, v);
Console.WriteLine(" " + order.ToString(CultureInfo.InvariantCulture).PadLeft(6)
+ " " + quad.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
order = 7;
w = new double[order];
xy = new double[DIM_NUM * order];
QuadratureRule.triangle_unit_o07(ref w, ref xy);
v = Monomial.monomial_value(DIM_NUM, order, expon, xy);
quad = QuadratureRule.triangle_unit_volume() * typeMethods.r8vec_dot_product(order, w, v);
Console.WriteLine(" " + order.ToString(CultureInfo.InvariantCulture).PadLeft(6)
+ " " + quad.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
order = 12;
w = new double[order];
xy = new double[DIM_NUM * order];
QuadratureRule.triangle_unit_o12(ref w, ref xy);
v = Monomial.monomial_value(DIM_NUM, order, expon, xy);
quad = QuadratureRule.triangle_unit_volume() * typeMethods.r8vec_dot_product(order, w, v);
Console.WriteLine(" " + order.ToString(CultureInfo.InvariantCulture).PadLeft(6)
+ " " + quad.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
Console.WriteLine("");
quad = QuadratureRule.triangle_unit_monomial(expon);
Console.WriteLine(" " + " Exact"
+ " " + quad.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
if (!more)
{
break;
}
}
}
public static void square_quad_test(int degree_max)
//****************************************************************************80
//
// Purpose:
//
// SQUARE_QUAD_TEST tests the rules for a square in 2D.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 06 September 2014
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, int DEGREE_MAX, the maximum total degree of the
// monomials to check.
//
{
double[] a = { -1.0, -1.0 };
double[] b = { +1.0, +1.0 };
int[] expon = new int[2];
int h = 0;
int[] order_1d = new int[2];
int t = 0;
SubCompData data = new();
Console.WriteLine("");
Console.WriteLine("SQUARE_QUAD_TEST");
Console.WriteLine(" For a square in 2D,");
Console.WriteLine(" we approximate monomial integrals with:");
Console.WriteLine(" SQUARE_RULE, which returns M by N point rules..");
bool more = false;
for (;;)
{
SubComp.subcomp_next(ref data, degree_max, 2, ref expon, ref more, ref h, ref t);
Console.WriteLine("");
string cout = " Monomial exponents: ";
int i;
for (i = 0; i < 2; i++)
{
cout += " " + expon[i].ToString(CultureInfo.InvariantCulture).PadLeft(2);
}
Console.WriteLine(cout);
Console.WriteLine("");
int k;
int order;
double[] xy;
double[] v;
double quad;
double[] w;
for (k = 1; k <= 5; k++)
{
for (i = 0; i < 2; i++)
{
order_1d[i] = k;
}
order = order_1d[0] * order_1d[1];
w = new double[order];
xy = new double[2 * order];
square_rule(a, b, order_1d, ref w, ref xy);
v = Monomial.monomial_value(2, order, expon, xy);
quad = typeMethods.r8vec_dot_product(order, w, v);
Console.WriteLine(" " + order_1d[0].ToString(CultureInfo.InvariantCulture).PadLeft(6)
+ " " + order_1d[1].ToString(CultureInfo.InvariantCulture).PadLeft(6)
+ " " + quad.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
}
//
// Try a rule of mixed orders.
//
order_1d[0] = 3;
order_1d[1] = 5;
order = order_1d[0] * order_1d[1];
w = new double[order];
xy = new double[2 * order];
square_rule(a, b, order_1d, ref w, ref xy);
v = Monomial.monomial_value(2, order, expon, xy);
quad = typeMethods.r8vec_dot_product(order, w, v);
Console.WriteLine(" " + order_1d[0].ToString(CultureInfo.InvariantCulture).PadLeft(6)
+ " " + order_1d[1].ToString(CultureInfo.InvariantCulture).PadLeft(6)
+ " " + quad.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
Console.WriteLine("");
quad = square_monomial(a, b, expon);
Console.WriteLine(" " + " Exact"
+ " " + " "
+ " " + quad.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
if (!more)
{
break;
}
}
}
private static void pyramid_unit_quad_test(int degree_max)
//****************************************************************************80
//
// Purpose:
//
// PYRAMID__UNIT_QUAD_TEST tests the rules for the unit pyramid.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 19 April 2008
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, int DEGREE_MAX, the maximum total degree of the
// monomials to check.
//
{
const int DIM_NUM = 3;
int[] expon = new int[DIM_NUM];
int h = 0;
int t = 0;
Console.WriteLine("");
Console.WriteLine("PYRAMID__UNIT_QUAD_TEST");
Console.WriteLine(" For the unit pyramid,");
Console.WriteLine(" we approximate monomial integrals with:");
Console.WriteLine(" PYRAMID__UNIT_O01,");
Console.WriteLine(" PYRAMID__UNIT_O05,");
Console.WriteLine(" PYRAMID__UNIT_O06,");
Console.WriteLine(" PYRAMID__UNIT_O08,");
Console.WriteLine(" PYRAMID__UNIT_O08b,");
Console.WriteLine(" PYRAMID__UNIT_O09,");
Console.WriteLine(" PYRAMID__UNIT_O13,");
Console.WriteLine(" PYRAMID__UNIT_O18,");
Console.WriteLine(" PYRAMID__UNIT_O27,");
Console.WriteLine(" PYRAMID__UNIT_O48,");
bool more = false;
SubCompData data = new();
for (;;)
{
SubComp.subcomp_next(ref data, degree_max, DIM_NUM, ref expon, ref more, ref h, ref t);
if (expon[0] % 2 == 1 || expon[1] % 2 == 1)
{
continue;
}
Console.WriteLine("");
string cout = " Monomial exponents: ";
int dim;
for (dim = 0; dim < DIM_NUM; dim++)
{
cout += " " + expon[dim].ToString().PadLeft(2);
}
Console.WriteLine(cout);
Console.WriteLine("");
int order = 1;
double[] w = new double[order];
double[] xyz = new double[DIM_NUM * order];
FelippaRule.pyramid_unit_o01(ref w, ref xyz);
double[] v = Monomial.monomial_value(DIM_NUM, order, expon, xyz);
double quad = FelippaRule.pyramid_unit_volume() * typeMethods.r8vec_dot_product(order, w, v);
Console.WriteLine(" " + order.ToString().PadLeft(6)
+ " " + quad.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
order = 5;
w = new double[order];
xyz = new double[DIM_NUM * order];
FelippaRule.pyramid_unit_o05(ref w, ref xyz);
v = Monomial.monomial_value(DIM_NUM, order, expon, xyz);
quad = FelippaRule.pyramid_unit_volume() * typeMethods.r8vec_dot_product(order, w, v);
Console.WriteLine(" " + order.ToString().PadLeft(6)
+ " " + quad.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
order = 6;
w = new double[order];
xyz = new double[DIM_NUM * order];
FelippaRule.pyramid_unit_o06(ref w, ref xyz);
v = Monomial.monomial_value(DIM_NUM, order, expon, xyz);
quad = FelippaRule.pyramid_unit_volume() * typeMethods.r8vec_dot_product(order, w, v);
Console.WriteLine(" " + order.ToString().PadLeft(6)
+ " " + quad.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
order = 8;
w = new double[order];
xyz = new double[DIM_NUM * order];
FelippaRule.pyramid_unit_o08(ref w, ref xyz);
v = Monomial.monomial_value(DIM_NUM, order, expon, xyz);
quad = FelippaRule.pyramid_unit_volume() * typeMethods.r8vec_dot_product(order, w, v);
Console.WriteLine(" " + order.ToString().PadLeft(6)
+ " " + quad.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
order = 8;
w = new double[order];
xyz = new double[DIM_NUM * order];
FelippaRule.pyramid_unit_o08b(ref w, ref xyz);
v = Monomial.monomial_value(DIM_NUM, order, expon, xyz);
quad = FelippaRule.pyramid_unit_volume() * typeMethods.r8vec_dot_product(order, w, v);
Console.WriteLine(" " + order.ToString().PadLeft(6)
+ " " + quad.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
order = 9;
w = new double[order];
xyz = new double[DIM_NUM * order];
FelippaRule.pyramid_unit_o09(ref w, ref xyz);
v = Monomial.monomial_value(DIM_NUM, order, expon, xyz);
quad = FelippaRule.pyramid_unit_volume() * typeMethods.r8vec_dot_product(order, w, v);
Console.WriteLine(" " + order.ToString().PadLeft(6)
+ " " + quad.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
order = 13;
w = new double[order];
xyz = new double[DIM_NUM * order];
FelippaRule.pyramid_unit_o13(ref w, ref xyz);
v = Monomial.monomial_value(DIM_NUM, order, expon, xyz);
quad = FelippaRule.pyramid_unit_volume() * typeMethods.r8vec_dot_product(order, w, v);
Console.WriteLine(" " + order.ToString().PadLeft(6)
+ " " + quad.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
order = 18;
w = new double[order];
xyz = new double[DIM_NUM * order];
FelippaRule.pyramid_unit_o18(ref w, ref xyz);
v = Monomial.monomial_value(DIM_NUM, order, expon, xyz);
quad = FelippaRule.pyramid_unit_volume() * typeMethods.r8vec_dot_product(order, w, v);
Console.WriteLine(" " + order.ToString().PadLeft(6)
+ " " + quad.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
order = 27;
w = new double[order];
xyz = new double[DIM_NUM * order];
FelippaRule.pyramid_unit_o27(ref w, ref xyz);
v = Monomial.monomial_value(DIM_NUM, order, expon, xyz);
quad = FelippaRule.pyramid_unit_volume() * typeMethods.r8vec_dot_product(order, w, v);
Console.WriteLine(" " + order.ToString().PadLeft(6)
+ " " + quad.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
order = 48;
w = new double[order];
xyz = new double[DIM_NUM * order];
FelippaRule.pyramid_unit_o48(ref w, ref xyz);
v = Monomial.monomial_value(DIM_NUM, order, expon, xyz);
quad = FelippaRule.pyramid_unit_volume() * typeMethods.r8vec_dot_product(order, w, v);
Console.WriteLine(" " + order.ToString().PadLeft(6)
+ " " + quad.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
Console.WriteLine("");
quad = FelippaRule.pyramid_unit_monomial(expon);
Console.WriteLine(" " + " Exact"
+ " " + quad.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
if (!more)
{
break;
}
}
}
private static void test02(int degree_max)
//****************************************************************************80
//
// Purpose:
//
// TEST02 tests the rules for the unit wedge.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 20 August 2014
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, int DEGREE_MAX, the maximum total degree of the
// monomials to check.
//
{
const int dim_num = 3;
int[] expon = new int[3];
int h = 0;
int[] line_order_array =
{
1, 2, 2, 3, 2, 3, 4
}
;
int t = 0;
const int test_num = 7;
int[] triangle_order_array =
{
1, 3, -3, 6, -6, 7, 12
}
;
Console.WriteLine("");
Console.WriteLine("TEST02");
Console.WriteLine(" For the unit wedge,");
Console.WriteLine(" we approximate monomial integrals with WEDG_UNIT_RULE.");
bool more = false;
SubCompData data = new();
for (;;)
{
SubComp.subcomp_next(ref data, degree_max, dim_num, ref expon, ref more, ref h, ref t);
if (expon[2] % 2 == 1)
{
if (!more)
{
break;
}
continue;
}
Console.WriteLine("");
Console.WriteLine(" Monomial exponents: "
+ expon[0].ToString(CultureInfo.InvariantCulture).PadLeft(2) + " "
+ expon[1].ToString(CultureInfo.InvariantCulture).PadLeft(2) + " "
+ expon[2].ToString(CultureInfo.InvariantCulture).PadLeft(2) + "");
Console.WriteLine("");
int test;
double quad;
for (test = 0; test < test_num; test++)
{
int line_order = line_order_array[test];
int triangle_order = triangle_order_array[test];
int order = line_order * Math.Abs(triangle_order);
double[] w = new double[order];
double[] xyz = new double[dim_num * order];
QuadratureRule.wedge_rule(line_order, triangle_order, ref w, ref xyz);
double[] v = Monomial.monomial_value(dim_num, order, expon, xyz);
quad = QuadratureRule.wedge_volume() * typeMethods.r8vec_dot_product(order, w, v);
Console.WriteLine(triangle_order.ToString(CultureInfo.InvariantCulture).PadLeft(6) + " "
+ line_order.ToString(CultureInfo.InvariantCulture).PadLeft(6) + " "
+ quad.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
}
Console.WriteLine("");
quad = QuadratureRule.wedge_integral(expon);
Console.WriteLine(" Exact "
+ quad.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
if (!more)
{
break;
}
}
}
public static void subcomp_next_test()
//****************************************************************************80
//
// Purpose:
//
// SUBCOMP_NEXT_TEST tests SUBCOMP_NEXT.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 09 November 2005
//
// Author:
//
// John Burkardt
//
{
const int n = 6;
const int k = 3;
int[] a = new int[k];
bool more = false;
int h = 0;
int t = 0;
SubCompData data = new();
Console.WriteLine("");
Console.WriteLine("SUBCOMP_NEXT_TEST");
Console.WriteLine(" SUBCOMP_NEXT generates subcompositions.");
Console.WriteLine("");
Console.WriteLine(" Seek all subcompositions of N = " + n + "");
Console.WriteLine(" using K = " + k + " parts.");
Console.WriteLine("");
Console.WriteLine(" # Sum");
Console.WriteLine("");
int rank = 0;
for (;;)
{
SubComp.subcomp_next(ref data, n, k, ref a, ref more, ref h, ref t);
int total = 0;
int i;
for (i = 0; i < k; i++)
{
total += a[i];
}
rank += 1;
string cout = " " + rank.ToString().PadLeft(4)
+ " " + total.ToString().PadLeft(4)
+ " ";
for (i = 0; i < k; i++)
{
cout += a[i].ToString().PadLeft(4);
}
Console.WriteLine(cout);
if (!more)
{
break;
}
}
}