private static void bernstein_matrix_test()
//****************************************************************************80
//
// Purpose:
//
// BERNSTEIN_MATRIX_TEST tests BERNSTEIN_MATRIX.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 26 January 2016
//
// Author:
//
// John Burkardt
//
{
Console.WriteLine("");
Console.WriteLine("BERNSTEIN_MATRIX_TEST");
Console.WriteLine(" BERNSTEIN_MATRIX returns a matrix A which transforms a");
Console.WriteLine(" polynomial coefficient vector from the power basis to");
Console.WriteLine(" the Bernstein basis.");
int n = 5;
double[] a = BernsteinPolynomial.bernstein_matrix(n);
typeMethods.r8mat_print(n, n, a, " Bernstein matrix A of order 5:");
}
private static void bernstein_matrix_inverse_test()
//****************************************************************************80
//
// Purpose:
//
// BERNSTEIN_MATRIX_INVERSE_TEST tests BERNSTEIN_MATRIX_INVERSE.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 26 January 2016
//
// Author:
//
// John Burkardt
//
{
Console.WriteLine("");
Console.WriteLine("BERNSTEIN_MATRIX_INVERSE_TEST");
Console.WriteLine(" BERNSTEIN_MATRIX_INVERSE computes the inverse of the");
Console.WriteLine(" Bernstein matrix A.");
Console.WriteLine("");
Console.WriteLine(" N ||A|| ||inv(A)|| ||I-A*inv(A)||");
Console.WriteLine("");
for (int n = 5; n <= 15; n++)
{
double[] a = BernsteinPolynomial.bernstein_matrix(n);
double a_norm_frobenius = typeMethods.r8mat_norm_fro(n, n, a);
double[] b = BernsteinPolynomial.bernstein_matrix_inverse(n);
double b_norm_frobenius = typeMethods.r8mat_norm_fro(n, n, b);
double[] c = typeMethods.r8mat_mm_new(n, n, n, a, b);
double error_norm_frobenius = typeMethods.r8mat_is_identity(n, c);
Console.WriteLine(" " + n.ToString().PadLeft(4)
+ " " + a_norm_frobenius.ToString().PadLeft(14)
+ " " + b_norm_frobenius.ToString().PadLeft(14)
+ " " + error_norm_frobenius.ToString().PadLeft(14) + "");
}
}
private static void bernstein_matrix_determinant_test()
//****************************************************************************80
//
// Purpose:
//
// BERNSTEIN_MATRIX_DETERMINANT_TEST tests BERNSTEIN_MATRIX_DETERMINANT.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 26 January 2016
//
// Author:
//
// John Burkardt
//
{
Console.WriteLine("");
Console.WriteLine("BERNSTEIN_MATRIX_DETERMINANT_TEST");
Console.WriteLine(" BERNSTEIN_MATRIX_DETERMINANT computes the determinant of");
Console.WriteLine(" the Bernstein matrix.");
Console.WriteLine("");
Console.WriteLine(" N ||A|| det(A)");
Console.WriteLine(" computed");
Console.WriteLine("");
for (int n = 5; n <= 15; n++)
{
double[] a = BernsteinPolynomial.bernstein_matrix(n);
double a_norm_frobenius = typeMethods.r8mat_norm_fro(n, n, a);
double d1 = BernsteinPolynomial.bernstein_matrix_determinant(n);
Console.WriteLine(" " + n.ToString().PadLeft(4)
+ " " + a_norm_frobenius.ToString().PadLeft(14)
+ " " + d1.ToString().PadLeft(14) + "");
}
}
private static void bernstein_matrix_test2()
//****************************************************************************80
//
// Purpose:
//
// BERNSTEIN_MATRIX_TEST2 tests BERNSTEIN_MATRIX.
//
// Discussion:
//
// Here we use the Bernstein matrix to describe a Bernstein polynomial
// in terms of the standard monomials.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 27 January 2016
//
// Author:
//
// John Burkardt
//
{
Console.WriteLine("");
Console.WriteLine("TEST06");
Console.WriteLine(" BERNSTEIN_MATRIX returns a matrix A which");
Console.WriteLine(" transforms a polynomial coefficient vector");
Console.WriteLine(" from the the Bernstein basis to the power basis.");
Console.WriteLine(" We can use this to get explicit values of the");
Console.WriteLine(" 4-th degree Bernstein polynomial coefficients as");
Console.WriteLine("");
Console.WriteLine(" b(4,K)(X) = C4 * x^4");
Console.WriteLine(" + C3 * x^3");
Console.WriteLine(" + C2 * x^2");
Console.WriteLine(" + C1 * x");
Console.WriteLine(" + C0 * 1");
int n = 5;
Console.WriteLine("");
Console.WriteLine(" K C4 C3 C2" +
" C1 C0");
Console.WriteLine("");
double[] a = BernsteinPolynomial.bernstein_matrix(n);
double[] x = new double[n];
for (int k = 0; k < n; k++)
{
for (int i = 0; i < n; i++)
{
x[i] = 0.0;
}
x[k] = 1.0;
double[] ax = typeMethods.r8mat_mv_new(n, n, a, x);
string cout = " " + k.ToString().PadLeft(4) + " ";
for (int i = 0; i < n; i++)
{
cout += " " + ax[i].ToString().PadLeft(14);
}
Console.WriteLine(cout);
}
}
