private static void test01()
//****************************************************************************80
//
// Purpose:
//
// TEST01 uses BALL01_SAMPLE 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[3];
int[] e_test =
{
0, 0, 0,
2, 0, 0,
0, 2, 0,
0, 0, 2,
4, 0, 0,
2, 2, 0,
0, 0, 4
};
int i;
int j;
double[] result = new double[7];
Console.WriteLine("");
Console.WriteLine("TEST01");
Console.WriteLine(" Estimate integrals over the interior of the unit ball");
Console.WriteLine(" using the Monte Carlo method.");
int seed = 123456789;
Console.WriteLine("");
Console.WriteLine(" N 1 X^2 Y^2 " +
" Z^2 X^4 X^2Y^2 Z^4");
Console.WriteLine("");
int n = 1;
string cout;
while (n <= 65536)
{
double[] x = MonteCarlo.ball01_sample(n, ref seed);
cout = " " + n.ToString().PadLeft(8);
for (j = 0; j < 7; j++)
{
for (i = 0; i < 3; i++)
{
e[i] = e_test[i + j * 3];
}
double[] value = Monomial.monomial_value(3, n, e, x);
result[j] = MonteCarlo.ball01_volume() * typeMethods.r8vec_sum(n, value) / n;
cout += " " + result[j].ToString(CultureInfo.InvariantCulture).PadLeft(14);
}
Console.WriteLine(cout);
n = 2 * n;
}
Console.WriteLine("");
cout = " Exact";
for (j = 0; j < 7; j++)
{
for (i = 0; i < 3; i++)
{
e[i] = e_test[i + j * 3];
}
result[j] = MonteCarlo.ball01_monomial_integral(e);
cout += " " + result[j].ToString(CultureInfo.InvariantCulture).PadLeft(14);
}
Console.WriteLine(cout);
}
private static void Main(string[] args)
//****************************************************************************80
//
// Purpose:
//
// MAIN is the main program for PYRAMID_EXACTNESS.
//
// Discussion:
//
// This program investigates the polynomial exactness of a quadrature
// rule for the pyramid.
//
// The integration region is:
//
// - ( 1 - Z ) <= X <= 1 - Z
// - ( 1 - Z ) <= Y <= 1 - Z
// 0 <= Z <= 1.
//
// When Z is zero, the integration region is a square lying in the (X,Y)
// plane, centered at (0,0,0) with "radius" 1. As Z increases to 1, the
// radius of the square diminishes, and when Z reaches 1, the square has
// contracted to the single point (0,0,1).
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 28 July 2009
//
// Author:
//
// John Burkardt
//
{
int degree;
int degree_max;
bool error = false;
int last = 0;
string quad_filename;
Console.WriteLine("");
Console.WriteLine("PYRAMID_EXACTNESS");
Console.WriteLine(" Investigate the polynomial exactness of a quadrature");
Console.WriteLine(" rule for the pyramid.");
//
// Get the quadrature file root name:
//
try
{
quad_filename = args[0];
}
catch
{
Console.WriteLine("");
Console.WriteLine("PYRAMID_EXACTNESS:");
Console.WriteLine(" Enter the \"root\" name of the quadrature files.");
quad_filename = Console.ReadLine();
}
//
// Create the names of:
// the quadrature X file;
// the quadrature W file;
//
string quad_w_filename = quad_filename + "_w.txt";
string quad_x_filename = quad_filename + "_x.txt";
//
// The second command line argument is the maximum degree.
//
try
{
degree_max = typeMethods.s_to_i4(args[1], ref last, ref error);
}
catch
{
Console.WriteLine("");
Console.WriteLine("PYRAMID_EXACTNESS:");
Console.WriteLine(" Please enter the maximum total degree to check.");
degree_max = Convert.ToInt32(Console.ReadLine());
}
//
// Summarize the input.
//
Console.WriteLine("");
Console.WriteLine("PYRAMID_EXACTNESS: User input:");
Console.WriteLine(" Quadrature rule X file = \"" + quad_x_filename + "\".");
Console.WriteLine(" Quadrature rule W file = \"" + quad_w_filename + "\".");
Console.WriteLine(" Maximum total degree to check = " + degree_max + "");
//
// Read the X file.
//
TableHeader th = typeMethods.r8mat_header_read(quad_x_filename);
int dim_num = th.m;
int order = th.n;
Console.WriteLine("");
Console.WriteLine(" Spatial dimension = " + dim_num + "");
Console.WriteLine(" Number of points = " + order + "");
if (dim_num != 3)
{
Console.WriteLine("");
Console.WriteLine("PYRAMID_EXACTNESS - Fatal error!");
Console.WriteLine(" The quadrature abscissas must be 3 dimensional.");
return;
}
double[] x = typeMethods.r8mat_data_read(quad_x_filename, dim_num, order);
//
// Read the W file.
//
th = typeMethods.r8mat_header_read(quad_w_filename);
int dim_num2 = th.m;
int order2 = th.n;
if (dim_num2 != 1)
{
Console.WriteLine("");
Console.WriteLine("PYRAMID_EXACTNESS - Fatal error!");
Console.WriteLine(" The quadrature weight file should have exactly");
Console.WriteLine(" one value on each line.");
return;
}
if (order2 != order)
{
Console.WriteLine("");
Console.WriteLine("PYRAMID_EXACTNESS - Fatal error!");
Console.WriteLine(" The quadrature weight file should have exactly");
Console.WriteLine(" the same number of lines as the abscissa file.");
return;
}
double[] w = typeMethods.r8mat_data_read(quad_w_filename, 1, order);
//
// Explore the monomials.
//
int[] expon = new int[dim_num];
Console.WriteLine("");
Console.WriteLine(" Error Degree Exponents");
Console.WriteLine("");
for (degree = 0; degree <= degree_max; degree++)
{
bool more = false;
int h = 0;
int t = 0;
for (;;)
{
Comp.comp_next(degree, dim_num, ref expon, ref more, ref h, ref t);
double[] v = Monomial.monomial_value(dim_num, order, expon, x);
double quad = Pyramid.pyra_unit_volume() * typeMethods.r8vec_dot_product(order, w, v);
double exact = Pyramid.pyra_unit_monomial(expon);
double quad_error = Math.Abs(quad - exact);
string cout = " " + quad_error.ToString(CultureInfo.InvariantCulture).PadLeft(12)
+ " " + degree.ToString().PadLeft(2)
+ " ";
int dim;
for (dim = 0; dim < dim_num; dim++)
{
cout += expon[dim].ToString().PadLeft(3);
}
Console.WriteLine(cout);
if (!more)
{
break;
}
}
Console.WriteLine("");
Console.WriteLine("");
Console.WriteLine("PYRAMID_EXACTNESS:");
Console.WriteLine(" Normal end of execution.");
Console.WriteLine("");
}
}
private static void test01()
//****************************************************************************80
//
// Purpose:
//
// TEST01 compares exact and estimated integrals in 3D.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 16 January 2014
//
// Author:
//
// John Burkardt
//
{
const int m = 3;
const int n = 4192;
int test;
const int test_num = 20;
Console.WriteLine("");
Console.WriteLine("TEST01");
Console.WriteLine(" Estimate monomial integrals using Monte Carlo");
Console.WriteLine(" over the interior of the unit simplex in M dimensions.");
//
// Get sample points.
//
int seed = 123456789;
double[] x = Integrals.simplex01_sample(m, n, ref seed);
Console.WriteLine("");
Console.WriteLine(" Number of sample points used is " + n + "");
//
// Randomly choose exponents.
//
Console.WriteLine("");
Console.WriteLine(" We randomly choose the exponents.");
Console.WriteLine("");
Console.WriteLine(" Ex Ey Ez MC-Estimate Exact Error");
Console.WriteLine("");
for (test = 1; test <= test_num; test++)
{
int[] e = UniformRNG.i4vec_uniform_ab_new(m, 0, 4, ref seed);
double[] value = Monomial.monomial_value(m, n, e, x);
double result = Integrals.simplex01_volume(m) * typeMethods.r8vec_sum(n, value)
/ n;
double exact = Integrals.simplex01_monomial_integral(m, e);
double error = Math.Abs(result - exact);
Console.WriteLine(" " + e[0].ToString().PadLeft(2)
+ " " + e[1].ToString().PadLeft(2)
+ " " + e[2].ToString().PadLeft(2)
+ " " + result.ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + exact.ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + error.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
}
}
public static void line_fekete_monomial(int m, double a, double b, int n, double[] x,
ref int nf, ref double[] xf, ref double[] wf)
//****************************************************************************80
//
// Purpose:
//
// LINE_FEKETE_MONOMIAL: approximate Fekete points in an interval [A,B].
//
// Discussion:
//
// We use the uniform weight and the monomial basis:
//
// P(j) = x^(j-1)
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 13 April 2014
//
// Author:
//
// John Burkardt
//
// Reference:
//
// Alvise Sommariva, Marco Vianello,
// Computing approximate Fekete points by QR factorizations of Vandermonde
// matrices,
// Computers and Mathematics with Applications,
// Volume 57, 2009, pages 1324-1336.
//
// Parameters:
//
// Input, int M, the number of basis polynomials.
//
// Input, double A, B, the endpoints of the interval.
//
// Input, int N, the number of sample points.
// M <= N.
//
// Input, double X(N), the coordinates of the sample points.
//
// Output, int &NF, the number of Fekete points.
// If the computation is successful, NF = M.
//
// Output, double XF(NF), the coordinates of the Fekete points.
//
// Output, double WF(NF), the weights of the Fekete points.
//
{
int j;
if (n < m)
{
Console.WriteLine("");
Console.WriteLine("LINE_FEKETE_MONOMIAL - Fatal error!");
Console.WriteLine(" N < M.");
return;
}
//
// Form the moments.
//
double[] mom = Monomial.line_monomial_moments(a, b, m);
//
// Form the rectangular Vandermonde matrix V for the polynomial basis.
//
double[] v = new double[m * n];
for (j = 0; j < n; j++)
{
v[0 + j * m] = 1.0;
int i;
for (i = 1; i < m; i++)
{
v[i + j * m] = v[i - 1 + j * m] * x[j];
}
}
//
// Solve the system for the weights W.
//
double[] w = QRSolve.qr_solve(m, n, v, mom);
//
// Extract the data associated with the nonzero weights.
//
nf = 0;
for (j = 0; j < n; j++)
{
if (w[j] == 0.0)
{
continue;
}
if (nf >= m)
{
continue;
}
xf[nf] = x[j];
wf[nf] = w[j];
nf += 1;
}
}
private static void test01(int nv, double[] v)
//****************************************************************************80
//
// Purpose:
//
// TEST01 estimates integrals over a polygon in 2D.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 09 May 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 j;
double result;
string cout;
Console.WriteLine("");
Console.WriteLine("TEST01");
Console.WriteLine(" Use POLYGON_SAMPLE to estimate integrals");
Console.WriteLine(" over the interior of a polygon in 2D.");
int seed = 123456789;
Console.WriteLine("");
Console.WriteLine(" N" +
" 1" +
" X^2 " +
" Y^2" +
" X^4" +
" X^2Y^2" +
" Y^4" +
" X^6");
int n = 1;
while (n <= 65536)
{
double[] x = MonteCarlo.polygon_sample(nv, v, n, ref seed);
cout = " " + n.ToString(CultureInfo.InvariantCulture).PadLeft(8);
for (j = 0; j < 7; j++)
{
e[0] = e_test[0 + j * 2];
e[1] = e_test[1 + j * 2];
double[] value = Monomial.monomial_value(2, n, e, x);
result = MonteCarlo.polygon_area(nv, v) * typeMethods.r8vec_sum(n, value) / n;
cout += " " + result.ToString(CultureInfo.InvariantCulture).PadLeft(14);
}
Console.WriteLine(cout);
n = 2 * n;
}
Console.WriteLine("");
cout = " Exact";
for (j = 0; j < 7; j++)
{
e[0] = e_test[0 + j * 2];
e[1] = e_test[1 + j * 2];
result = MonteCarlo.polygon_monomial_integral(nv, v, e);
cout += " " + result.ToString(CultureInfo.InvariantCulture).PadLeft(14);
}
Console.WriteLine(cout);
}
private static void test01()
//****************************************************************************80
//
// Purpose:
//
// TEST01 compares exact and estimated monomial integrals.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 14 April 2014
//
// Author:
//
// John Burkardt
//
{
const int e_max = 6;
int e3;
int[] expon = new int[3];
const int m = 3;
const int n = 500000;
Console.WriteLine("");
Console.WriteLine("TEST01");
Console.WriteLine(" Compare exact and estimated integrals ");
Console.WriteLine(" over the unit pyramid in 3D.");
//
// Get sample points.
//
int seed = 123456789;
double[] x = Integrals.pyramid01_sample(n, ref seed);
Console.WriteLine("");
Console.WriteLine(" Number of sample points used is " + n + "");
Console.WriteLine("");
Console.WriteLine(" E1 E2 E3 MC-Estimate Exact Error");
Console.WriteLine("");
//
// Check all monomials, with only even dependence on X or Y,
// up to total degree E_MAX.
//
for (e3 = 0; e3 <= e_max; e3++)
{
expon[2] = e3;
int e2;
for (e2 = 0; e2 <= e_max - e3; e2 += 2)
{
expon[1] = e2;
int e1;
for (e1 = 0; e1 <= e_max - e3 - e2; e1 += 2)
{
expon[0] = e1;
double[] value = Monomial.monomial_value(m, n, expon, x);
double q = Integrals.pyramid01_volume() * typeMethods.r8vec_sum(n, value) / n;
double exact = Integrals.pyramid01_monomial_integral(expon);
double error = Math.Abs(q - exact);
Console.WriteLine(" " + expon[0].ToString().PadLeft(2)
+ " " + expon[1].ToString().PadLeft(2)
+ " " + expon[2].ToString().PadLeft(2)
+ " " + q.ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + exact.ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + error.ToString(CultureInfo.InvariantCulture).PadLeft(12) + "");
}
}
}
}
private static void test05()
//****************************************************************************80
//
// Purpose:
//
// TEST05 tests KEAST_RULE.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 03 July 2008
//
// Author:
//
// John Burkardt
//
{
int degree;
const int degree_max = 3;
const int dim_num = 3;
int[] expon = new int[3];
Console.WriteLine("");
Console.WriteLine("TEST05");
Console.WriteLine(" Demonstrate the KEAST rules on a sequence of");
Console.WriteLine(" monomial integrands X^A Y^B Z^C");
Console.WriteLine(" on the unit tetrahedron.");
int rule_num = KeastRule.keast_rule_num();
Console.WriteLine("");
Console.WriteLine(" Rule Order Quad");
Console.WriteLine("");
for (degree = 0; degree <= degree_max; degree++)
{
bool more = false;
int h = 0;
int t = 0;
for (;;)
{
Comp.comp_next(degree, dim_num, ref expon, ref more, ref h, ref t);
Console.WriteLine("");
Console.WriteLine(" F(X,Y,Z)"
+ " = X^" + expon[0]
+ " * Y^" + expon[1]
+ " * Z^" + expon[2] + "");
Console.WriteLine("");
int rule;
for (rule = 1; rule <= rule_num; rule++)
{
int order_num = KeastRule.keast_order_num(rule);
double[] xyz = new double[3 * order_num];
double[] w = new double[order_num];
KeastRule.keast_rule(rule, order_num, ref xyz, ref w);
double[] mono = Monomial.monomial_value(dim_num, order_num, xyz, expon);
double quad = typeMethods.r8vec_dot(order_num, w, mono);
Console.WriteLine(" " + rule.ToString().PadLeft(8)
+ " " + order_num.ToString().PadLeft(8)
+ " " + quad.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
}
if (!more)
{
break;
}
}
}
}
private static void Main(string[] args)
//****************************************************************************80
//
// Purpose:
//
// MAIN is the main program for WEDGE_EXACTNESS.
//
// Discussion:
//
// This program investigates the polynomial exactness of a quadrature
// rule for the unit wedge.
//
// The interior of the unit wedge in 3D is defined by the constraints:
// 0 <= X
// 0 <= Y
// X + Y <= 1
// -1 <= Z <= +1
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 24 August 2014
//
// Author:
//
// John Burkardt
//
{
int degree;
int degree_max;
string quad_filename;
Console.WriteLine("");
Console.WriteLine("WEDGE_EXACTNESS");
Console.WriteLine(" Investigate the polynomial exactness of a quadrature");
Console.WriteLine(" rule for the unit wedge.");
//
// Get the quadrature file root name:
//
try
{
quad_filename = args[0];
}
catch
{
Console.WriteLine("");
Console.WriteLine("WEDGE_EXACTNESS:");
Console.WriteLine(" Enter the \"root\" name of the quadrature files.");
quad_filename = Console.ReadLine();
}
//
// Create the names of:
// the quadrature X file;
// the quadrature W file;
//
string quad_w_filename = quad_filename + "_w.txt";
string quad_x_filename = quad_filename + "_x.txt";
//
// The second command line argument is the maximum degree.
//
try
{
degree_max = Convert.ToInt32(args[1]);
}
catch
{
Console.WriteLine("");
Console.WriteLine("WEDGE_EXACTNESS:");
Console.WriteLine(" Please enter the maximum total degree to check.");
degree_max = Convert.ToInt32(Console.ReadLine());
}
//
// Summarize the input.
//
Console.WriteLine("");
Console.WriteLine("WEDGE_EXACTNESS: User input:");
Console.WriteLine(" Quadrature rule X file = \"" + quad_x_filename + "\".");
Console.WriteLine(" Quadrature rule W file = \"" + quad_w_filename + "\".");
Console.WriteLine(" Maximum total degree to check = " + degree_max + "");
//
// Read the X file.
//
TableHeader hd = typeMethods.r8mat_header_read(quad_x_filename);
int dim_num = hd.m;
int order = hd.n;
Console.WriteLine("");
Console.WriteLine(" Spatial dimension = " + dim_num + "");
Console.WriteLine(" Number of points = " + order + "");
if (dim_num != 3)
{
Console.WriteLine("");
Console.WriteLine("WEDGE_EXACTNESS - Fatal error!");
Console.WriteLine(" The quadrature abscissas must be 3 dimensional.");
return;
}
double[] x = typeMethods.r8mat_data_read(quad_x_filename, dim_num, order);
//
// Read the W file.
//
hd = typeMethods.r8mat_header_read(quad_w_filename);
int dim_num2 = hd.m;
int order2 = hd.n;
if (dim_num2 != 1)
{
Console.WriteLine("");
Console.WriteLine("WEDGE_EXACTNESS - Fatal error!");
Console.WriteLine(" The quadrature weight file should have exactly");
Console.WriteLine(" one value on each line.");
return;
}
if (order2 != order)
{
Console.WriteLine("");
Console.WriteLine("WEDGE_EXACTNESS - Fatal error!");
Console.WriteLine(" The quadrature weight file should have exactly");
Console.WriteLine(" the same number of lines as the abscissa file.");
return;
}
double[] w = typeMethods.r8mat_data_read(quad_w_filename, 1, order);
//
// Explore the monomials.
//
int[] expon = new int[dim_num];
Console.WriteLine("");
Console.WriteLine(" Error Degree Exponents");
Console.WriteLine("");
for (degree = 0; degree <= degree_max; degree++)
{
bool more = false;
int h = 0;
int t = 0;
for (;;)
{
Comp.comp_next(degree, dim_num, ref expon, ref more, ref h, ref t);
double[] v = Monomial.monomial_value(dim_num, order, expon, x);
double quad = Integrals.wedge01_volume() * typeMethods.r8vec_dot_product(order, w, v);
double exact = Integrals.wedge01_integral(expon);
double quad_error = Math.Abs(quad - exact);
string cout = " " + quad_error.ToString(CultureInfo.InvariantCulture).PadLeft(12)
+ " " + degree.ToString().PadLeft(2)
+ " ";
int dim;
for (dim = 0; dim < dim_num; dim++)
{
cout += expon[dim].ToString().PadLeft(3);
}
Console.WriteLine(cout);
if (!more)
{
break;
}
}
Console.WriteLine("");
}
Console.WriteLine("");
Console.WriteLine("WEDGE_EXACTNESS:");
Console.WriteLine(" Normal end of execution.");
Console.WriteLine("");
}
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);
}
private static void test01()
//****************************************************************************80
//
// Purpose:
//
// TEST01 uses TETRAHEDRON_SAMPLE_01 to compare exact and estimated integrals.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 15 January 2014
//
// Author:
//
// John Burkardt
//
{
int[] e = new int[3];
int i;
const int m = 3;
const int n = 4192;
Console.WriteLine("");
Console.WriteLine("TEST01");
Console.WriteLine(" Estimate monomial integrals using Monte Carlo");
Console.WriteLine(" over the interior of the unit tetrahedron in 3D.");
//
// Get sample points.
//
int seed = 123456789;
double[] x = Integrals.tetrahedron01_sample(n, ref seed);
Console.WriteLine("");
Console.WriteLine(" Number of sample points used is " + n + "");
//
// Run through the exponents.
//
Console.WriteLine("");
Console.WriteLine(" Ex Ey Ez MC-Estimate Exact Error");
Console.WriteLine("");
for (i = 0; i <= 3; i++)
{
e[0] = i;
int j;
for (j = 0; j <= 3; j++)
{
e[1] = j;
int k;
for (k = 0; k <= 3; k++)
{
e[2] = k;
double[] value = Monomial.monomial_value(m, n, e, x);
double result = Integrals.tetrahedron01_volume() * typeMethods.r8vec_sum(n, value)
/ n;
double exact = Integrals.tetrahedron01_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)
+ " " + e[2].ToString(CultureInfo.InvariantCulture).PadLeft(2)
+ " " + result.ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + exact.ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + error.ToString(CultureInfo.InvariantCulture).PadLeft(10) + "");
}
}
}
}