public static void roots_to_r8poly(int nroots, double[] roots, ref int nc, ref double[] c)
//****************************************************************************80
//
// Purpose:
//
// ROOTS_TO_R8POLY converts polynomial roots to polynomial coefficients.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 06 September 2004
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, int NROOTS, the number of roots specified.
//
// Input, double ROOTS[NROOTS], the roots.
//
// Output, integer *NC, the order of the polynomial, which will be NROOTS+1.
//
// Output, double C[*NC], the coefficients of the polynomial.
//
{
int i;
nc = nroots + 1;
//
// Initialize C to (0, 0, ..., 0, 1).
// Essentially, we are setting up a divided difference table.
//
double[] xtab = new double[nroots + 1];
for (i = 0; i < nc - 1; i++)
{
xtab[i] = roots[i];
}
xtab[nc - 1] = 0.0;
for (i = 0; i < nc - 1; i++)
{
c[i] = 0.0;
}
c[nc - 1] = 1.0;
//
// Convert to standard polynomial form by shifting the abscissas
// of the divided difference table to 0.
//
Dif.dif_shift_zero(nc, ref xtab, ref c);
}
private static void test01()
//****************************************************************************80
//
// Purpose:
//
// TEST01 tests DIF*;
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 01 June 2013
//
// Author:
//
// John Burkardt
//
{
const int MAXTAB = 10;
double[] diftab = new double[MAXTAB];
double[] diftab2 = new double[MAXTAB];
double[] diftab3 = new double[MAXTAB];
int i;
int ntab3 = 0;
double[] xtab = new double[MAXTAB];
double[] xtab2 = new double[MAXTAB];
double[] xtab3 = new double[MAXTAB];
double[] ytab = new double[MAXTAB];
Console.WriteLine("");
Console.WriteLine("TEST01");
Console.WriteLine(" DATA_TO_DIF_DISPLAY sets up a difference table");
Console.WriteLine(" and displays intermediate calculations;");
Console.WriteLine(" DIF_APPEND appends a new data point;");
Console.WriteLine(" DIF_ANTIDERIV computes the antiderivative;");
Console.WriteLine(" DIF_DERIV_TABLE computes the derivative;");
Console.WriteLine(" DIF_SHIFT_ZERO shifts all the abscissas to 0;");
Console.WriteLine(" DIF_VAL evaluates at a point;");
Console.WriteLine("");
//
// Set XTAB, YTAB to X, X^2.
//
int ntab = 4;
for (i = 0; i < ntab; i++)
{
xtab[i] = i + 1;
ytab[i] = xtab[i] * xtab[i];
}
Data.data_to_dif_display(ntab, xtab, ytab, ref diftab);
Dif.dif_print(ntab, xtab, diftab, " The divided difference polynomial:");
//
// Add (5,25) to the table.
//
Console.WriteLine("");
Console.WriteLine(" DIF_APPEND can add the data (5,25) to the table.");
Console.WriteLine("");
double xval = 5.0;
double yval = 25.0;
Dif.dif_append(ntab, xtab, diftab, xval, yval, ref ntab, ref xtab, ref diftab);
Dif.dif_print(ntab, xtab, diftab,
" The updated divided difference polynomial:");
//
// Evaluate the polynomial at 2.5.
//
Console.WriteLine("");
Console.WriteLine(" DIF_VAL can evaluate the table at a point.");
Console.WriteLine("");
xval = 2.5;
yval = Dif.dif_val(ntab, xtab, diftab, xval);
Console.WriteLine("");
Console.WriteLine(" DIF_VAL reports P(" + xval + ") = " + yval + "");
//
// Shift the base to zero.
//
Dif.dif_shift_zero(ntab, ref xtab, ref diftab);
Dif.dif_print(ntab, xtab, diftab,
" The divided difference table after DIF_SHIFT_ZERO:");
//
// Compute a table for the derivative.
//
int ntab2 = ntab - 1;
Dif.dif_deriv_table(ntab, xtab, diftab, ref xtab2, diftab2);
Dif.dif_print(ntab2, xtab2, diftab2,
" The divided difference table for the derivative:");
yval = Dif.dif_val(ntab2, xtab2, diftab2, xval);
Console.WriteLine("");
Console.WriteLine(" DIF_VAL reports P'(" + xval + ") = " + yval + "");
//
// Compute the antiderivative.
//
Dif.dif_antideriv(ntab, xtab, diftab, ref ntab3, xtab3, ref diftab3);
Dif.dif_print(ntab3, xtab3, diftab3,
" The divided difference table for the antiderivative:");
yval = Dif.dif_val(ntab3, xtab3, diftab3, xval);
Console.WriteLine("");
Console.WriteLine(" DIF_VAL reports (Anti)P(" + xval + ") = " + yval + "");
}
private static void test05()
//****************************************************************************80
//
// Purpose:
//
// TEST05 tests DATA_TO_DIF_DISPLAY, DIF_PRINT, DIF_SHIFT_ZERO, DIF_TO_R8POLY;
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 18 January 2007
//
// Author:
//
// John Burkardt
//
{
const int MAXTAB = 10;
double[] c = new double[MAXTAB];
double[] diftab1 = new double[MAXTAB];
double[] diftab2 = new double[MAXTAB];
int i;
double[] xtab1 = new double[MAXTAB];
double[] xtab2 = new double[MAXTAB];
double[] ytab1 = new double[MAXTAB];
double[] ytab2 = new double[MAXTAB];
Console.WriteLine("");
Console.WriteLine("TEST05");
Console.WriteLine(" DIF_TO_R8POLY converts a difference table to a polynomial;");
Console.WriteLine(" DIF_SHIFT_ZERO shifts a divided difference table to 0;");
Console.WriteLine("");
Console.WriteLine(" These are equivalent operations");
Console.WriteLine("");
//
// Set XTAB, YTAB to X, F(X)
//
const int ntab = 4;
for (i = 0; i < ntab; i++)
{
double x = i + 1;
xtab1[i] = x;
xtab2[i] = x;
ytab1[i] = -4.0 + x * (3.0 + x * (-2.0 + x));
ytab2[i] = ytab1[i];
}
//
// Compute and display the finite difference table.
//
Data.data_to_dif_display(ntab, xtab1, ytab1, ref diftab1);
Data.data_to_dif_display(ntab, xtab2, ytab2, ref diftab2);
//
// Examine the corresponding polynomial.
//
Dif.dif_print(ntab, xtab1, diftab1, " The divided difference table:");
//
// Shift to zero using DIF_SHIFT_ZERO.
//
Dif.dif_shift_zero(ntab, ref xtab1, ref diftab1);
typeMethods.r8poly_print(ntab, diftab1, " The polynomial using DIF_SHIFT_ZERO:");
//
// Shift to zero using DIF_TO_R8POLY.
//
Dif.dif_to_r8poly(ntab, xtab2, diftab2, ref c);
typeMethods.r8poly_print(ntab, c, " The polynomial using DIF_TO_R8POLY:");
}