Chebyshev coefficients: Difference between revisions
Added XPL0 example.
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Line 2,465:
0.950 0.58168308946388 0.58168308946379 -8.992806E-014
1.000 0.54030230586814 0.54030230586859 4.468648E-013</pre>
=={{header|Wren}}==
{{trans|Kotlin}}
Line 2,554 ⟶ 2,555:
0.950 0.58168309 0.58168309 -8.99e-14
1.000 0.54030231 0.54030231 4.47e-13
</pre>
=={{header|XPL0}}==
{{trans|C}}
<syntaxhighlight lang "XPL0">include xpllib; \for Print and Pi
func real Map(X, MinX, MaxX, MinTo, MaxTo);
\Map X from range Min,Max to MinTo,MaxTo
real X, MinX, MaxX, MinTo, MaxTo;
return (X-MinX) / (MaxX-MinX) * (MaxTo-MinTo) + MinTo;
proc ChebCoef(N, Min, Max, Coef);
int N; real Min, Max, Coef;
int I, J;
real F;
[for I:= 0 to N-1 do Coef(I):= 0.0;
for I:= 0 to N-1 do
[F:= Cos(Map(Cos(Pi*(float(I)+0.5)/float(N)), -1.0, 1.0, Min, Max)) *
2.0/float(N);
for J:= 0 to N-1 do
Coef(J):= Coef(J) + F*Cos(Pi*float(J) * (float(I)+0.5) / float(N));
];
];
func real ChebApprox(X, N, Min, Max, Coef);
real X; int N; real Min, Max, Coef;
real A, B, C, Res;
int I;
[A:= 1.0;
B:= Map(X, Min, Max, -1.0, 1.0);
Res:= Coef(0)/2.0 + Coef(1)*B;
X:= 2.0*B;
for I:= 2 to N-1 do
[C:= X*B - A;
Res:= Res + Coef(I)*C;
A:= B;
B:= C;
];
return Res;
];
def N=10, MinV=0.0, MaxV=1.0;
real C(N);
int I;
real X, F, Approx;
[ChebCoef(N, MinV, MaxV, C);
Print("Coefficients:\n");
for I:= 0 to N-1 do
Print(" %2.15f\n", C(I));
Print("\nApproximation:\n X Cos(X) Approx Diff\n");
for I:= 0 to 20 do
[X:= Map(float(I), 0.0, 20.0, MinV, MaxV);
F:= Cos(X);
Approx:= ChebApprox(X, N, MinV, MaxV, C);
Print("%2.2f %2.14f %2.14f %0.1f\n", X, F, Approx, Approx-F);
];
]</syntaxhighlight>
{{out}}
<pre>
Coefficients:
1.647169475390310
-0.232299371615172
-0.053715114622048
0.002458235266982
0.000282119057434
-0.000007722229156
-0.000000589855646
0.000000011521428
0.000000000659630
-0.000000000010022
Approximation:
X Cos(X) Approx Diff
0.00 1.00000000000000 1.00000000000047 4.7E-013
0.05 0.99875026039497 0.99875026039487 -9.4E-014
0.10 0.99500416527803 0.99500416527849 4.6E-013
0.15 0.98877107793604 0.98877107793599 -4.7E-014
0.20 0.98006657784124 0.98006657784078 -4.6E-013
0.25 0.96891242171064 0.96891242171041 -2.3E-013
0.30 0.95533648912561 0.95533648912587 2.6E-013
0.35 0.93937271284738 0.93937271284784 4.6E-013
0.40 0.92106099400289 0.92106099400308 2.0E-013
0.45 0.90044710235268 0.90044710235243 -2.5E-013
0.50 0.87758256189037 0.87758256188991 -4.6E-013
0.55 0.85252452205951 0.85252452205926 -2.5E-013
0.60 0.82533561490968 0.82533561490987 2.0E-013
0.65 0.79608379854906 0.79608379854951 4.5E-013
0.70 0.76484218728449 0.76484218728474 2.5E-013
0.75 0.73168886887382 0.73168886887359 -2.3E-013
0.80 0.69670670934717 0.69670670934672 -4.5E-013
0.85 0.65998314588498 0.65998314588494 -4.4E-014
0.90 0.62160996827066 0.62160996827111 4.5E-013
0.95 0.58168308946388 0.58168308946379 -9.0E-014
1.00 0.54030230586814 0.54030230586859 4.5E-013
</pre>
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