Chebyshev coefficients: Difference between revisions
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}
</lang>
=={{header|C#|C sharp}}==
{{trans|C++}}
<lang csharp>using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
namespace Chebyshev {
class Program {
struct ChebyshevApprox {
public readonly List<double> coeffs;
public readonly Tuple<double, double> domain;
public ChebyshevApprox(Func<double, double> func, int n, Tuple<double, double> domain) {
coeffs = ChebCoef(func, n, domain);
this.domain = domain;
}
public double Call(double x) {
return ChebEval(coeffs, domain, x);
}
}
static double AffineRemap(Tuple<double, double> from, double x, Tuple<double, double> to) {
return to.Item1 + (x - from.Item1) * (to.Item2 - to.Item1) / (from.Item2 - from.Item1);
}
static List<double> ChebCoef(List<double> fVals) {
int n = fVals.Count;
double theta = Math.PI / n;
List<double> retval = new List<double>();
for (int i = 0; i < n; i++) {
retval.Add(0.0);
}
for (int ii = 0; ii < n; ii++) {
double f = fVals[ii] * 2.0 / n;
double phi = (ii + 0.5) * theta;
double c1 = Math.Cos(phi);
double s1 = Math.Sin(phi);
double c = 1.0;
double s = 0.0;
for (int j = 0; j < n; j++) {
retval[j] += f * c;
// update c -> cos(j*phi) for next value of j
double cNext = c * c1 - s * s1;
s = c * s1 + s * c1;
c = cNext;
}
}
return retval;
}
static List<double> ChebCoef(Func<double, double> func, int n, Tuple<double, double> domain) {
double remap(double x) {
return AffineRemap(new Tuple<double, double>(-1.0, 1.0), x, domain);
}
double theta = Math.PI / n;
List<double> fVals = new List<double>();
for (int i = 0; i < n; i++) {
fVals.Add(0.0);
}
for (int ii = 0; ii < n; ii++) {
fVals[ii] = func(remap(Math.Cos((ii + 0.5) * theta)));
}
return ChebCoef(fVals);
}
static double ChebEval(List<double> coef, double x) {
double a = 1.0;
double b = x;
double c;
double retval = 0.5 * coef[0] + b * coef[1];
var it = coef.GetEnumerator();
it.MoveNext();
it.MoveNext();
while (it.MoveNext()) {
double pc = it.Current;
c = 2.0 * b * x - a;
retval += pc * c;
a = b;
b = c;
}
return retval;
}
static double ChebEval(List<double> coef, Tuple<double, double> domain, double x) {
return ChebEval(coef, AffineRemap(domain, x, new Tuple<double, double>(-1.0, 1.0)));
}
static void Main() {
const int N = 10;
ChebyshevApprox fApprox = new ChebyshevApprox(Math.Cos, N, new Tuple<double, double>(0.0, 1.0));
Console.WriteLine("Coefficients: ");
foreach (var c in fApprox.coeffs) {
Console.WriteLine("\t{0: 0.00000000000000;-0.00000000000000;zero}", c);
}
Console.WriteLine("\nApproximation:\n x func(x) approx diff");
const int nX = 20;
const int min = 0;
const int max = 1;
for (int i = 0; i < nX; i++) {
double x = AffineRemap(new Tuple<double, double>(0, nX), i, new Tuple<double, double>(min, max));
double f = Math.Cos(x);
double approx = fApprox.Call(x);
Console.WriteLine("{0:0.000} {1:0.00000000000000} {2:0.00000000000000} {3:E}", x, f, approx, approx - f);
}
}
}
}</lang>
{{out}}
<pre>Coefficients:
1.64716947539031
-0.23229937161517
-0.05371511462205
0.00245823526698
0.00028211905743
-0.00000772222916
-0.00000058985565
0.00000001152143
0.00000000065963
-0.00000000001002
Approximation:
x func(x) approx diff
0.000 1.00000000000000 1.00000000000047 4.689582E-013
0.050 0.99875026039497 0.99875026039487 -9.370282E-014
0.100 0.99500416527803 0.99500416527849 4.622969E-013
0.150 0.98877107793604 0.98877107793600 -4.662937E-014
0.200 0.98006657784124 0.98006657784078 -4.604095E-013
0.250 0.96891242171065 0.96891242171041 -2.322587E-013
0.300 0.95533648912561 0.95533648912587 2.609024E-013
0.350 0.93937271284738 0.93937271284784 4.606315E-013
0.400 0.92106099400289 0.92106099400308 1.980638E-013
0.450 0.90044710235268 0.90044710235243 -2.473577E-013
0.500 0.87758256189037 0.87758256188991 -4.586331E-013
0.550 0.85252452205951 0.85252452205926 -2.461364E-013
0.600 0.82533561490968 0.82533561490988 1.961764E-013
0.650 0.79608379854906 0.79608379854951 4.536371E-013
0.700 0.76484218728449 0.76484218728474 2.553513E-013
0.750 0.73168886887382 0.73168886887359 -2.267075E-013
0.800 0.69670670934717 0.69670670934672 -4.467537E-013
0.850 0.65998314588498 0.65998314588494 -4.485301E-014
0.900 0.62160996827066 0.62160996827111 4.444223E-013
0.950 0.58168308946388 0.58168308946379 -8.992806E-014</pre>
=={{header|D}}==
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