/// <summary>
/// Get definite integral using composite trapezium rule
/// </summary>
/// <param name="f">Integrand</param>
/// <param name="a">Lower bound</param>
/// <param name="b">Upper bound</param>
/// <param name="eps">Error</param>
/// <returns>Result</returns>
public static double CompositeTrapeziumRule(Program.Function f, double a, double b, double eps)
{
if (b < a)
{
throw new Exception("Upper integral bound is less than lower");
}
if (a == b)
{
return(0);
}
// (?) All the program works only with constant numper of integral steps
double n = 200; // 1 + 1 / math.Sqrt(eps);
double bounds = (f(a) + f(b)) / 2;
double prevResult, nextResult = 0;
do
{
prevResult = nextResult;
nextResult = bounds;
double h = (b - a) / n;
for (int i = 1; i < n; i++)
{
nextResult += f(a + i * h);
}
nextResult *= h;
n *= 2;
}
//while (Math.Abs(nextResult - prevResult) > eps); /* Uncomment this and comment line below to use error checking */
while (false);
return(nextResult);
}
double B; // Upper bound of interval
/// <summary>
/// Create polinomial instance
/// </summary>
/// <param name="f">Function to approximate</param>
/// <param name="basisFunctions">Basis to use</param>
/// <param name="rule">Rule to use for integration</param>
/// <param name="solveMethod">Method to solve linear system</param>
/// <param name="a">Lower bound of interval</param>
/// <param name="b">Upper bound of interval</param>
/// <param name="degree">Polinomial degree</param>
public Polinomial(Program.Function f, Basis basisFunctions, Integral.Rule rule, LinearSystem.SolveMethod solveMethod, double a, double b, int degree)
{
// Initialize fields
function = f;
basis = basisFunctions;
integralRule = rule;
A = a;
B = b;
// Fill matrix with integrals - bind linear system
double[,] matrix = new double[degree, degree + 1];
for (int i = 0; i < degree; i++)
{
for (int j = i; j <= degree; j++)
{
if (j < degree)
{
matrix[i, j] = matrix[j, i] = rule(
delegate(double t)
{
return(basis[i](t) * basis[j](t));
}
, -1, 1, 0.001);
}
else
{
matrix[i, j] = rule(
delegate(double t)
{
return(basis[i](t) * f((b + a) / 2 + t * (b - a) / 2));
}
, -1, 1, 0.001);
}
}
}
// Solve linear system
coefficients = solveMethod(matrix).ToArray();
}
