public static double Integrate(Func <double, double> func,
double a, double b, double alpha, double beta, int n)
{
var Mu = Mathematics.GetMuArray(n, a, b, alpha, beta);
double[] X = new double[n];
double h = (b - a) / (n - 1);
for (int i = 0; i < n; i++)
{
X[i] = a + h * i;
}
double[,] matrix = new double[n, n];
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
matrix[i, j] = Math.Pow(X[j], i);
}
}
var A = Mathematics.GausMethod(matrix, Mu);
double integralSum = 0;
for (int i = 0; i < n; i++)
{
integralSum += func(X[i]) * A[i];
}
return(integralSum);
}
public static double GetOptStepRichardson(Func <Func <double, double>,
double, double, double, double, int, int, double> method, Func <double, double> func,
double a, double b, double alpha, double beta, int n, int r, int ada, double epsilon)
{
double startStep = (b - a);
double[,] A = new double[r + 1, r + 1];
double[] B = new double[r + 1];
double[] X = new double[r + 1];
do
{
for (int i = 0; i < A.GetLength(0); i++)
{
double step = startStep / Math.Pow(2, i);
for (int j = 0; j < A.GetLength(0); j++)
{
if (j == 0)
{
A[i, j] = -1;
}
else
{
A[i, j] = Math.Pow(step, ada + j - 1);
}
}
B[i] = -method(func, a, b, alpha, beta, n, Mathematics.GetGoodNum(a, b, step));
}
X = Mathematics.GausMethod(A, B);
startStep /= 2;
} while (Math.Abs(X[0] + B[r]) > epsilon);
return(startStep / Math.Pow(2, r - 1));
}
static void Main(string[] args)
{
Stopwatch SW = new Stopwatch();
double accRunge;
double richOptStep;
int segmNum = 100;
double integralSum;
int n;
double a = 1.1d;
double b = 2.5d;
double alpha = 0.4d;
double beta = 0;
SW.Start();
SW.Stop();
//SW.Restart();
//n = 2;
//integralSum = GaussMethod.CompoundIntegrate(Function, a, b, alpha, beta, n, segmNum);
//SW.Stop();
//output("CQF (Gauss)", integralSum, n, SW.ElapsedTicks);
//richOptStep = Mathematics.GetOptStepRichardson(GaussMethod.CompoundIntegrate, Function, a, b, alpha, beta, n, 2, n - 1, 1e-6);
//Console.WriteLine("Optimal step (Richardson): " + richOptStep);
//Console.WriteLine(" => Optimal n: " + Mathematics.GetGoodNum(a, b, richOptStep));
SW.Restart();
n = 3;
integralSum = NewtonCotesMethod.CompoundIntegrate(Function, a, b, alpha, beta, n, segmNum);
SW.Stop();
output("CQF (Newton-Cotes)", integralSum, n, SW.ElapsedTicks);
accRunge = Mathematics.AccuracyRunge(integralSum, NewtonCotesMethod.CompoundIntegrate(Function, a, b, alpha, beta, n, segmNum * 2), n - 1);
var optStep = Mathematics.GetOptStep(a, b, segmNum, accRunge, n - 1, 1e-6);
Console.WriteLine("Optimal step (Runge): " + optStep);
Console.WriteLine(" => Optimal n: " + Mathematics.GetGoodNum(a, b, optStep));
richOptStep = Mathematics.GetOptStepRichardson(NewtonCotesMethod.CompoundIntegrate, Function, a, b, alpha, beta, n, 2, n - 1, 1e-6);
Console.WriteLine("Optimal step (Richardson): " + richOptStep);
Console.WriteLine(" => Optimal n: " + Mathematics.GetGoodNum(a, b, richOptStep));
Console.WriteLine("Error (Runge): " + accRunge);
}
public static double Integrate(Func <double, double> func,
double a, double b, double alpha, double beta, int n)
{
var Mu = Mathematics.GetMuArray(2 * n, a, b, alpha, beta);
var SLAE = new double[n, n];
var bSLAE = new double[n];
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
SLAE[i, j] = Mu[j + i];
}
bSLAE[i] = -Mu[n + i];
}
var acoefs = Mathematics.GausMethod(SLAE, bSLAE);
var polcoefs = new double[acoefs.Length + 1];
for (int i = 0; i < polcoefs.Length - 1; i++)
{
polcoefs[i] = acoefs[i];
}
polcoefs[polcoefs.Length - 1] = 1;
var nodes = GetSquarePolynomialRoots(polcoefs);
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
SLAE[i, j] = Math.Pow(nodes[j], i);
}
bSLAE[i] = Mu[i];
}
var intcoefs = Mathematics.GausMethod(SLAE, bSLAE);
double result = 0;
for (int i = 0; i < n; i++)
{
result += intcoefs[i] * func(nodes[i]);
}
return(result);
}
