public static double Integrate(IFunction func, double start, double end, int step)
{
var d = (end - start) / step;
var sum = (func.F(start) + func.F(end)) / 2;
for (var i = 1; i < step; i++)
{
sum += func.F(start + i * d);
}
return(d * sum);
}
private void DrawFunction()
{
double step = 0.01;
double.TryParse(APointTextBox.Text, out double a);
double.TryParse(BPointTextBox.Text, out double b);
var xAxis = new List <double>();
var yAxis = new List <double>();
while (a <= b)
{
xAxis.Add(a);
yAxis.Add(_selectedFunction.F(a));
a += step;
}
DrawHelper.DrawGraph(Chart, yAxis.ToArray(), xAxis.ToArray(), _selectedFunction.ToString(), Color.Red, clearChart: true);
}
public double Integrate(IFunction function, long steps, double startX, double endX)
{
double result = 0.0, d = (endX - startX) / ((double)steps);
long step = 0;
for (double x = startX; x <= endX; x += d)
{
double y = function.F(x);
if (0 < step && step < steps)
{
double tmpResult = d * y;
result += tmpResult;
}
else
{
double tmpResult = d * y * 0.5;
result += tmpResult;
}
step++;
}
return result;
}
public double Integrate(IFunction function, long steps, double startX, double endX)
{
double result = 0.0, d = (endX - startX) / ((double)steps);
long step = 0;
for (double x = startX; x <= endX; x += d)
{
double y = function.F(x);
if (0 < step && step < steps)
{
double tmpResult = d * y;
result += tmpResult;
}
else
{
double tmpResult = d * y * 0.5;
result += tmpResult;
}
step++;
}
return(result);
}
private void runButton_Click(object sender, EventArgs e)
{
if (!IsFildsValid())
{
return;
}
int n;
try {
n = Convert.ToInt32(nTextBox.Text);
} catch {
errorLabel.Text = "Invalid data";
return;
}
int m = 500;
double[] accurateY = new double[m + 1];
double[] accurateX = new double[m + 1];
for (int i = 0; i < m + 1; i++)
{
accurateX[i] = i * 2 * Math.PI / m;
accurateY[i] = _function.F(accurateX[i]);
}
double[] y = new double[2 * n + 1];
double[] t = new double[2 * n + 1];
double[] a = new double[n + 1];
double[] b = new double[n];
for (int j = 0; j < 2 * n + 1; j++)
{
t[j] = (2 * Math.PI * j) / (2 * n + 1);
y[j] = _function.F(t[j]);
}
//a[k]
for (int k = 0; k < n + 1; k++)
{
double sum = 0;
for (int j = 0; j < 2 * n + 1; j++)
{
sum += y[j] * Math.Cos(2 * Math.PI * j * k / (2 * n + 1));
}
a[k] = (2 * sum) / (2 * n + 1);
}
//b[k]
for (int k = 0; k < n; k++)
{
double sum = 0;
for (int j = 0; j < 2 * n + 1; j++)
{
sum += y[j] * Math.Sin(2 * Math.PI * j * (k + 1) / (2 * n + 1));
}
b[k] = (2 * sum) / (2 * n + 1);
}
double[] q = new double[m + 1];
for (int i = 0; i < m + 1; i++)
{
q[i] = Q(accurateX[i], n, a, b);
}
mainChart.Series.Clear();
DrawHelper.DrawGraph(mainChart, accurateY, accurateX, m, "accurate", Color.Green);
DrawHelper.DrawGraph(mainChart, q, accurateX, m, "trigonometric", Color.Blue);
}
private void runButton_Click(object sender, EventArgs e)
{
double a, b, h1, h2;
int n, m;
try
{
a = Convert.ToDouble(aTextBox.Text);
b = Convert.ToDouble(bTextBox.Text);
n = Convert.ToInt32(nTextBox.Text);
}
catch
{
MessageBox.Show("incorrect input.", "Error");
return;
}
m = 100 * n;
h1 = (b - a) / n;
h2 = (b - a) / m;
double[] x = new double[n + 1];
double[] alfa = new double[n + 1];
double[] beta = new double[n + 3];
double[] y = new double[m + 1];
double[] t = new double[m + 1];
for (int i = 0; i < n + 1; i++)
{
x[i] = a + i * h1;
alfa[i] = _function.F(x[i]);
}
for (int i = 0; i < m + 1; i++)
{
t[i] = a + i * h2;
y[i] = _function.F(t[i]);
}
double[] S1 = new double[n + 1];
double[] S3 = new double[m + 1];
for (int i = 0; i < n + 1; i++)
{
S1[i] = SumForS1(n, alfa, x[i], x, h1);
}
//matrix.
double[,] _A = new double[n + 3, n + 3];
double[] _b = new double[n + 3];
_A[0, 0] = -0.5;
_A[0, 2] = 0.5;
_A[n + 2, n] = -0.5;
_A[n + 2, n + 2] = 0.5;
_b[0] = h1 * 4 * a * a * a;
_b[n + 2] = h1 * 4 * b * b * b;
for (int i = 1; i < n + 2; i++)
{
_A[i, i - 1] = 1 / 6.0;
_A[i, i] = 2 / 3.0;
_A[i, i + 1] = 1 / 6.0;
_b[i] = _function.F(x[i - 1]);
}
beta = GaussMethod.Calculate(n + 3, _A, _b);
for (int i = 0; i < m + 1; i++)
{
S3[i] = SumForS3(n, beta, t[i], x, h1);
}
mainChart.Series.Clear();
DrawHelper.DrawGraph(mainChart, y, t, m - 1, "Exact", Color.Green);
DrawHelper.DrawGraph(mainChart, S1, x, n, "S1", Color.Indigo);
DrawHelper.DrawGraph(mainChart, S3, t, m, "S3", Color.Red);
}
private void runButton_Click(object sender, EventArgs e)
{
if (!IsFildsValid())
{
return;
}
double a, b, faultX, h1, h2;
int n, m;
try {
a = Convert.ToDouble(aTextBox.Text);
b = Convert.ToDouble(bTextBox.Text);
faultX = Convert.ToDouble(xTextBox.Text);
n = Convert.ToInt32(nTextBox.Text);
m = Convert.ToInt32(mTextBox.Text);
} catch {
errorLabel.Text = "Invalid data";
return;
}
h1 = (b - a) / n;
h2 = (b - a) / m;
double[] x = new double[n + 1];
double[] t = new double[m + 1];
double[] x_ch = new double[n + 1];
double[] y = new double[n + 1];
double[] accurate_y = new double[m + 1];
double[] y_ch = new double[n + 1];
for (int k = 0; k < n + 1; k++)
{
x[k] = a + k * h1;
y[k] = _function.F(x[k]);
}
for (int k = 0; k < m + 1; k++)
{
t[k] = a + k * h2;
accurate_y[k] = _function.F(t[k]);
}
for (int k = 0; k < n + 1; k++)
{
x_ch[k] = ((a + b) / 2) + ((b - a) / 2) * Math.Cos(((double)(2 * k + 1) / (double)(2 * (n + 1))) * Math.PI);
y_ch[k] = _function.F(x_ch[k]);
}
double[] p = new double[m + 1];
double[] p_ch = new double[m + 1];
for (int k = 0; k < m + 1; k++)
{
p[k] = _polynomialForm.CalcPolynomial(n + 1, x, y, t[k]);
}
for (int k = 0; k < m + 1; k++)
{
p_ch[k] = _polynomialForm.CalcPolynomial(n + 1, x_ch, y_ch, t[k]);
}
mainChart.Series.Clear();
DrawHelper.DrawGraph(mainChart, accurate_y, t, m, "accurate", Color.Green);
DrawHelper.DrawGraph(mainChart, p, t, m, "simple polynomial", Color.Blue);
DrawHelper.DrawGraph(mainChart, p_ch, t, m, "Chebyshev polynomial", Color.Pink);
double polynomialError = Math.Abs(_function.F(faultX) - _polynomialForm.CalcPolynomial(n, x, y, faultX));
funcErrorLabel.Text = String.Format("Error: \n{0:f13}", polynomialError);
}
