void Solve(int partSumOrder, int iterCount, int nodesCount)
{
var chunksCount = (int)nupChunksCount.Value;
var(segment, y0, f, yExact) = Example3();
var nodes = Range(0, nodesCount).Select(j => segment.Start + segment.Length * j / (nodesCount - 1)).ToArray();
if (yExact != null)
{
//nodes = Range(0, nodesCount).Select(j => 1.0*j / nodesCount).ToArray();
exactSolutionPlot.DiscreteFunctions = new[] { new DiscreteFunction2D(x => yExact(x), nodes) };
exactSolutionPlot.Refresh();
}
//nodes = Range(0, nodesCount).Select(j => segment.Start + segment.Length * j / nodesCount).ToArray();
var cosSystem = new CosSystem();
var sobCosSystem = new SobolevCosSystem();
var solverIter = new CosSpectralSolverIter(1000);
var problem = new CauchyProblem(f, y0, segment);
var df = solverIter.Solve(problem, chunksCount, partSumOrder, iterCount, nodesCount);
//df.X = df.X.Select(x => x).ToArray();
numSolutionPlotIter.Colors = Colors;
numSolutionPlotIter.DiscreteFunctions = df.Select(d => d[0]).ToArray();
numSolutionPlotIter.Refresh();
//numSolutionPlotIter2.DiscreteFunctions = df[1];
//numSolutionPlotIter2.Refresh();
}
private static ISpectralOdeOperator <double[][]> CreateOperator(int quadratureNodesCount)
{
// Used to calculate coeffs that are represented as integrals
var quadratureNodes = new Segment(0, 1).GetUniformPartition(quadratureNodesCount);
var cosSystem = new CosSystem();
var sobCosSystem = new SobolevCosSystem();
var op = new CosSpectralOdeOperator(Natural.NumbersWithZero.Select(k => cosSystem.Get(k)),
Natural.NumbersWithZero.Select(k => sobCosSystem.Get(k)), quadratureNodes);
return(op);
}
public void CosSytemOrthonormality()
{
var cosSystem = new CosSystem();
for (int i = 0; i < 100; i++)
{
var i1 = i;
var v = Integrals.Trapezoid(x => cosSystem.Get(i1)(x) * cosSystem.Get(i1)(x), 0, 1, 10000);
Assert.AreEqual(1, v, 0.0000001);
}
var val = Integrals.Trapezoid(x => cosSystem.Get(0)(x) * cosSystem.Get(5)(x), 0, 1, 10000);
Assert.AreEqual(0, val, 0.0000001);
val = Integrals.Trapezoid(x => cosSystem.Get(4)(x) * cosSystem.Get(5)(x), 0, 1, 10000);
Assert.AreEqual(0, val, 0.0000001);
}
void SolveSystem(int partSumOrder, int iterCount, int nodesCount)
{
var chunksCount = (int)nupChunksCount.Value;
var(segment, initVals, f, h, yExact) = ExampleSystem6();
var nodes = Range(0, nodesCount).Select(j => segment.Start + segment.Length * j / (nodesCount - 1)).ToArray();
if (yExact != null)
{
exactSolutionPlot.DiscreteFunctions =
yExact.Select(y => new DiscreteFunction2D(y, nodes)).ToArray();
exactSolutionPlot.Refresh();
}
var cosSystem = new CosSystem();
var sobCosSystem = new SobolevCosSystem();
var solverIter = new CosSpectralSolverIter(1000);
var problem = new CauchyProblem(f, initVals, segment);
var solution = solverIter.Solve(problem, chunksCount, partSumOrder, iterCount, nodesCount);
var dfs = new List <DiscreteFunction2D>();
foreach (var s in solution)
{
dfs.AddRange(s);
}
numSolutionPlotIter.Colors = Colors;
numSolutionPlotIter.DiscreteFunctions = dfs.ToArray();
numSolutionPlotIter.Refresh();
//var deltas = solution.Zip(yExact, (df, y) => Abs(df.Y.Last() - y(df.X.Last()))).ToArray();
//var deltas = solution.Zip(yExact, (df, y) =>
// {
// var eDf = new DiscreteFunction2D(y, df.X);
// return Sqrt((df - eDf).Y.Average(v => v * v));
// }
// ).ToArray();
//Trace.WriteLine($"iter={iterCount}; N={partSumOrder}; dy1={deltas[0]};dy2={deltas[1]}");
}
