/// <summary> /// Integrates a given function within the given integral. /// </summary> /// <param name="f">The function to integrate.</param> /// <param name="a">The lower limit.</param> /// <param name="b">The higher limit.</param> /// <returns> /// The integral of <paramref name="function"/> over the interval from <paramref name="a"/> to <paramref name="b"/> /// </returns> public double Integrate(Sharp3D.Math.Core.MathFunctions.UnaryFunction <double> f, double a, double b) { if (a == b) { return(0); } if (a > b) { return(-Integrate(f, b, a)); } // Start with the crudest estimate int n = 1; double estimate = ((f(a) + f(b)) * (b - a)) / 2.0; double newEstimate = 0; int i = 1; do { switch (_method) { case Method.Default: newEstimate = defaultIteration(f, a, b, estimate, n); n *= 2; break; case Method.MidPoint: newEstimate = midPointIteration(f, a, b, estimate, n); n *= 3; break; } // Check accuracy if (System.Math.Abs(newEstimate - estimate) <= _accuracy) { return(newEstimate); } estimate = newEstimate; i++; }while (i < _maxSteps); throw new MathException("Max number of iterations reached."); }
/// <summary> /// Integrates a given function within the given integral. /// </summary> /// <param name="f">The function to integrate.</param> /// <param name="a">The lower limit.</param> /// <param name="b">The higher limit.</param> /// <returns> /// The integral of <paramref name="function"/> over the interval from <paramref name="a"/> to <paramref name="b"/> /// </returns> public double Integrate(Sharp3D.Math.Core.MathFunctions.UnaryFunction <double> f, double a, double b) { if (a > b) { return(-Integrate(f, b, a)); } double sum = 0; double stepSize = (b - a) / _stepCount; double stepSizeDiv3 = stepSize / 3; for (int i = 0; i < _stepCount; i = i + 2) { sum += (f(a + i * stepSize) + 4 * f(a + (i + 1) * stepSize) + f(a + (i + 2) * stepSize)) * stepSizeDiv3; } return(sum); }
/// <summary> /// Integrates a given function within the given integral. /// </summary> /// <param name="f">The function to integrate.</param> /// <param name="a">The lower limit.</param> /// <param name="b">The higher limit.</param> /// <returns> /// The integral of <paramref name="function"/> over the interval from <paramref name="a"/> to <paramref name="b"/> /// </returns> public float Integrate(Sharp3D.Math.Core.MathFunctions.UnaryFunction <float> f, float a, float b) { if (a > b) { return(-Integrate(f, b, a)); } float sum = 0; float stepSize = (float)((b - a) / _stepCount); float stepSizeDiv3 = stepSize / 3.0f; for (int i = 0; i < _stepCount; i = i + 2) { sum += (f(a + i * stepSize) + 4.0f * f(a + (i + 1) * stepSize) + f(a + (i + 2) * stepSize)) * stepSizeDiv3; } return(sum); }
/// <summary> /// Integrates a given function within the given integral. /// </summary> /// <param name="f">The function to integrate.</param> /// <param name="a">The lower limit.</param> /// <param name="b">The higher limit.</param> /// <returns> /// The integral of <paramref name="function"/> over the interval from <paramref name="a"/> to <paramref name="b"/> /// </returns> public double Integrate(Sharp3D.Math.Core.MathFunctions.UnaryFunction <double> f, double a, double b) { // Check the _romD field is initialized correctly. if ((_romD == null) || (_romD.GetLength(1) == _order)) { _romD = new double[1, _order]; } if (a > b) { return(Integrate(f, b, a)); } double h = (b - a); _romD[0, 0] = 0.5 * h * (f(a) + f(b)); for (int i = 2, ipower = 1; i <= _order; i++, ipower *= 2, h /= 2) { // Approximation using the trapezoid rule. double sum = 0; for (int j = 1; j <= ipower; j++) { sum += f(a + h * (j - 0.5)); } // Richardson extrapolation _romD[1, 0] = 0.5 * (_romD[0, 0] + (h * sum)); for (int k = 1, kpower = 4; k < i; k++, kpower *= 4) { _romD[1, k] = (kpower * _romD[1, k - 1] - _romD[0, k - 1]) / (kpower - 1); } // Save the extrapolated values for the next iteration for (int j = 0; j < i; j++) { _romD[0, j] = _romD[1, j]; } } return(_romD[0, _order - 1]); }