public LagrangePolynomial(double[] nodes, Function function) {
Polynomial result = new Polynomial(EMPTY);
_nodes = (double[]) nodes.Clone();
if (CheckForRepeats(_nodes))
throw new Exception("Points mustn't be repeated");
for (int i = 0; i < _nodes.Length; i++) {
result += function(nodes[i]) * Basis(i);
}
_coefficients = result.Coefficients;
}
static void Main(string[] args) {
try {
Console.SetWindowSize(80, 40);
double[] array1 = { 12.6, 14.5, 0, 7 };
Polynomial polyA = new Polynomial(array1);
Console.WriteLine("polyA = " + polyA);
double[] array2 = { 0, -20, 23 };
Polynomial polyB = new Polynomial(array2);
Console.WriteLine("polyB = " + polyB);
Console.WriteLine();
Console.WriteLine();
Console.WriteLine("polyA + polyB = " + (polyA + polyB));
Console.WriteLine("polyA - polyB = " + (polyA - polyB));
Console.WriteLine("polyA * polyB = " + (polyA * polyB));
Console.WriteLine();
Console.WriteLine("polyA + 69 = " + (polyA + 69));
Console.WriteLine("69 + polyB = " + (69 + polyB));
Console.WriteLine("polyA - 69 = " + (polyA - 69));
Console.WriteLine("69 - polyB = " + (69 - polyB));
Console.WriteLine();
Console.WriteLine("polyA * 3 = " + (polyA * 3));
Console.WriteLine("3 * polyB = " + (3 * polyB));
Console.WriteLine("polyA / 2 = " + (polyA / 2));
Console.WriteLine("polyB / 2 = " + (polyB / 2));
Console.WriteLine();
Console.WriteLine();
Console.WriteLine();
double[] points1 = { -1.5, -0.75, 0, 0.75, 1.5 };
Polynomial polyC = new LagrangePolynomial(points1, Math.Tan);
Console.WriteLine("For f(x)=tg(x) in points:");
foreach (double point in points1) {
Console.WriteLine(" x = " + point);
}
Console.WriteLine("Interpolation formula is:");
Console.WriteLine(polyC);
Console.WriteLine();
double[,] points2 = //{ { 0, 0, 0 } }
{ { -1.5, -14.1014 },
{ -0.75, -0.931596 },
{ 0, 0 },
{ 0.75, 0.931596 },
{ 1.5, 14.1014 } };
polyC = new LagrangePolynomial(points2);
Console.WriteLine("The same polynomial, but it's set up with 2D array in the same points:");
Console.WriteLine(polyC);
Console.WriteLine();
Point[] points3 = { new Point(-1.5, -14.1014),
new Point(-0.75, -0.931596),
new Point(0, 0),
new Point(0.75, 0.931596),
new Point(1.5, 14.1014) };
Console.WriteLine("The same again, but points are set up as Point objects:");
polyC = new LagrangePolynomial(points3);
Console.WriteLine(polyC);
Console.WriteLine();
Console.WriteLine();
LagrangePolynomial polyD = new LagrangePolynomial(-5, 0.5, 20, Math.Sin);
Console.WriteLine("Just trying to get result in the point pi/2 from polinomial by f(x)=sin(x):");
Console.WriteLine(polyD.GetResult(Math.PI / 2).ToString("0.#######"));
Console.ReadKey();
} catch (Exception e) {
Console.ForegroundColor = ConsoleColor.Red;
Console.WriteLine(e);
Console.ReadKey();
}
}
public LagrangePolynomial(double firstNode, double step, int count, Function function) {
if (step == 0)
throw new Exception("Points mustn't be repeated");
_nodes = new double[count];
_nodes[0] = firstNode;
for (int i = 1; i < count; i++)
_nodes[i] = _nodes[i - 1] + step;
Polynomial result = new Polynomial(EMPTY);
for (int i = 0; i < count; i++) {
result += function(_nodes[i]) * Basis(i);
}
_coefficients = result.Coefficients;
}
public LagrangePolynomial(double[,] points) { //points[i, 0] - should store X coordinates, points[i, 1] - Y coordinates
if (points.GetLength(1) != 2)
throw new Exception("Points should belong to the two-dimensional plane.");
int count = points.GetLength(0);
_nodes = new double[count];
for (int i = 0; i < count; i++) {
_nodes[i] = points[i, 0];
}
if (CheckForRepeats(_nodes))
throw new Exception("Points mustn't be repeated");
Polynomial result = new Polynomial(EMPTY);
for (int i = 0; i < count; i++) {
result += points[i, 1] * Basis(i);
}
_coefficients = result.Coefficients;
}
public LagrangePolynomial(Point[] points) {
_nodes = new double[points.Length];
for (int i = 0; i < points.Length; i++) {
_nodes[i] = points[i].X;
}
if (CheckForRepeats(_nodes))
throw new Exception("Points mustn't be repeated");
Polynomial result = new Polynomial(EMPTY);
for (int i = 0; i < points.Length; i++) {
result += points[i].Y * Basis(i);
}
_coefficients = result.Coefficients;
}
public Polynomial Basis(int index) {
Polynomial poly = new Polynomial(NOT_EMPTY);
for (int i = 0; i < _nodes.Length; i++) {
if (i != index) {
double[] polyCoefficients = { _nodes[i], -1 };
poly *= (new Polynomial(polyCoefficients)) / (_nodes[index] - _nodes[i]);
}
}
return poly;
}
public Polynomial(Polynomial poly) { // create copy of poly
_coefficients = poly.Coefficients;
}