/*
* /// <summary>
* ///
* /// </summary>
* /// <param name="odeRightSide">Array of functions f_i(x,y_1,y_2,...,y_m) that represents ODE system right side, i. e.
* /// y_i'(x)=f_i(x,y1,y2,...,ym), i=1,...,m.
* /// </param>
* /// <param name="initialValues">y_i(a), i=1,...,m</param>
* /// <param name="coeffsCount"></param>
* /// <param name="quadratureNodes">Some implementations may require nodes for calculating integrals</param>
* /// <returns></returns>
* //public void SetParams(DynFunc<double>[] odeRightSide, double[] initialValues,
* // int coeffsCount, double[] quadratureNodes = null)
* //{
* //}
*
* //protected abstract ISpectralOdeOperator<double[][]> CreateSpectralOdeOperator();
* //protected abstract Segment GetOrthogonalitySegment();
* //protected abstract double[][] GetInitialCoeffs();
* //protected abstract double[] InvFourierSobolevTransform(double[] coeffs, double[] nodes);
*/
/// <summary>
/// Solves Cauchy problem on orthogonality segment, which is determined by orthogonal system used in GetCoeffsOperator().
/// </summary>
/// <param name="rightSides"></param>
/// <param name="initialValues"></param>
/// <param name="iterCount"></param>
/// <param name="initialCoeffs">Initial point for iteration method. It size should be equationsCount x partialSumOrder</param>
/// <param name="nodes">Calculated approximate solution is discretized on nodes. Nodes should be inside orthogonality segment</param>
/// <returns>Approximate solution on nodes</returns>
protected DiscreteFunction2D[] SolveOnOrthogonalitySegment(DynFunc <double>[] rightSides, double[] initialValues,
int iterCount, double[][] initialCoeffs, double[] nodes)
{
if (initialCoeffs.Length != rightSides.Length)
{
throw new ArgumentException("rightSides length should equal to initialCoeffs length");
}
// \eta(a)+\sum_{j=0}^{partialSumOrder-1}d_j\phi_{1,1+j}(t)
var partialSumOrder = initialCoeffs[0].Length;
_spectralOdeOperator.SetParams(rightSides, initialValues, partialSumOrder);
var result = FixedPointIteration.FindFixedPoint(c => _spectralOdeOperator.GetValue(c), initialCoeffs, iterCount);
return(result.Select((coeffs, j) =>
new DiscreteFunction2D(
nodes,
_ift.Transform(new[] { initialValues[j] }.Concat(coeffs).ToArray(), nodes)))
.ToArray());
}
public void FindTest()
{
var result = FixedPointIteration.FindFixedPoint((double x) => 0.5 * (9.0 / x + x), 1, 30);
NUnit.Framework.Assert.AreEqual(3, result, 0.01);
}
public void FindWithEpsTest()
{
var result = FixedPointIteration.FindFixedPoint((double x) => 0.5 * (9.0 / x + x), 1, 0.001, (x, y) => Math.Abs(x - y), 1000);
NUnit.Framework.Assert.AreEqual(3, result, 0.001);
}
