Chebyshev coefficients: Difference between revisions
no edit summary
Thundergnat (talk | contribs) m (syntax highlighting fixup automation) |
No edit summary |
||
| (11 intermediate revisions by 7 users not shown) | |||
Line 9:
Calculate coefficients: cosine function, '''10''' coefficients, interval '''0 1'''
<br><br>
=={{header|11l}}==
{{trans|Python}}
<syntaxhighlight lang="11l">F test_func(Float x)
R cos(x)
Line 96 ⟶ 95:
0.950 0.5816830895 0.5816830895 -8.98e-14
</pre>
=={{header|ALGOL 60}}==
{{works with|GNU Marst|Any - tested with release 2.7}}
{{Trans|ALGOL W}}...which is{{Trans|Java}}
<syntaxhighlight lang="algol60">
begin comment Chebyshev coefficients ;
real PI;
procedure chebyshevCoef( func, min, max, coef, N )
; value min, max, N
; real procedure func
; real min, max
; real array coef
; integer N
;
begin
real procedure map( x, min x, max x, min to, max to )
; value x, min x, max x, min to, max to
; real x, min x, max x, min to, max to
;
begin
map := ( x - min x ) / ( max x - min x ) * ( max to - min to ) + min to
end map ;
integer i, j;
for i := 0 step 1 until N - 1 do begin
real m, f;
m := map( cos( PI * ( i + 0.5 ) / N ), -1, 1, min, max );
f := func( m ) * 2 / N;
for j := 0 step 1 until N - 1 do begin
coef[ j ] := coef[ j ] + f * cos( PI * j * ( i + 0.5 ) / N )
end j
end i
end chebyshevCoef ;
PI := arctan( 1 ) * 4;
begin
integer N;
N := 10;
begin
real array c [ 0 : N - 1 ];
integer i;
chebyshevCoef( cos, 0, 1, c, N );
outstring( 1, "Coefficients:\n" );
for i := 0 step 1 until N - 1 do begin
if c[ i ] >= 0 then outstring( 1, " " );
outstring( 1, " " );outreal( 1, c[ i ] );outstring( 1, "\n" )
end i
end
end
end
</syntaxhighlight>
{{out}}
<pre>
Coefficients:
1.64716947539
-0.232299371615
-0.053715114622
0.00245823526698
0.000282119057434
-7.72222915635e-006
-5.89855645675e-007
1.15214277563e-008
6.59630183808e-010
-1.00219138544e-011
</pre>
=={{header|ALGOL 68}}==
{{Trans|Java}}... using nested procedures and returning the coefficient array instead of using a reference parameter.
<syntaxhighlight lang="algol68">
BEGIN # Chebyshev Coefficients #
PROC chebyshev coef = ( PROC( REAL )REAL func, REAL min, max, INT n )[]REAL:
BEGIN
PROC map = ( REAL x, min x, max x, min to, max to )REAL:
( x - min x ) / ( max x - min x ) * ( max to - min to ) + min to;
[ 0 : n - 1 ]REAL coef; FOR i FROM LWB coef TO UPB coef DO coef[ i ] := 0 OD;
FOR i FROM 0 TO UPB coef DO
REAL m = map( cos( pi * ( i + 0.5 ) / n ), -1, 1, min, max );
REAL f = func( m ) * 2 / n;
FOR j FROM 0 TO UPB coef DO
coef[ j ] +:= f * cos( pi * j * ( i + 0.5 ) / n )
OD
OD;
coef
END # chebyshev coef # ;
BEGIN
INT n = 10;
REAL min := 0, max := 1;
[]REAL c = chebyshev coef( cos, min, max, n );
print( ( "Coefficients:", newline ) );
FOR i FROM LWB c TO UPB c DO
print( ( fixed( c[ i ], -18, 14 ), newline ) )
OD
END
END
</syntaxhighlight>
{{out}}
<pre>
Coefficients:
1.64716947539031
-0.23229937161517
-0.05371511462205
0.00245823526698
0.00028211905743
-0.00000772222916
-0.00000058985565
0.00000001152143
0.00000000065963
-0.00000000001002
</pre>
=={{header|ALGOL W}}==
{{Trans|Java}}... using nested procedures. In Algol W, procedures can't find the bounds of array parameters, so an extra parameter is reuired for the chebyshevCoef procedure.
<syntaxhighlight lang="algolw">
begin % Chebyshev coefficients %
procedure chebyshevCoef ( real procedure func
; real value min, max
; real array coef ( * )
; integer value N
) ;
begin
real procedure map ( real value x, min_x, max_x, min_to, max_to ) ;
( x - min_x ) / ( max_x - min_x ) * ( max_to - min_to ) + min_to;
for i := 0 until N - 1 do begin
real m, f;
m := map( cos( PI * ( i + 0.5 ) / N ), -1, 1, min, max );
f := func( m ) * 2 / N;
for j := 0 until N - 1 do begin
coef( j ) := coef( j ) + f * cos( PI * j * ( i + 0.5 ) / N )
end for_j
end for_i
end chebyshevCoef ;
begin
integer N;
N := 10;
begin
real array c ( 0 :: N - 1 );
chebyshevCoef( cos, 0, 1, c, N );
write( "Coefficients:" );
for i := 0 until N - 1 do write( r_format := "S", r_w := 14, c( i ) )
end
end
end.
</syntaxhighlight>
{{out}}
<pre>
Coefficients:
1.6471694'+00
-2.3229937'-01
-5.3715114'-02
2.4582352'-03
2.8211905'-04
-7.7222291'-06
-5.8985564'-07
1.1521427'-08
6.5963014'-10
-1.0021983'-11
</pre>
=={{header|BASIC}}==
==={{header|Applesoft BASIC}}===
The [[#MSX-BASIC|MSX-BASIC]] solution works without any changes.
==={{header|BASIC256}}===
{{trans|FreeBASIC}}
Given the limitations of the language, only 8 coefficients are calculated
<syntaxhighlight lang=
dim cheby(n)
dim coef(n)
Line 128 ⟶ 295:
6 : -5.89855645106e-07
7 : 1.15214275009e-08</pre>
==={{header|Chipmunk Basic}}===
{{trans|FreeBASIC}}
{{works with|Chipmunk Basic|3.6.4}}
<syntaxhighlight lang="qbasic">100 cls
110 rem pi = 4 * atn(1)
120 a = 0
130 b = 1
140 n = 10
150 dim cheby(n)
160 dim coef(n)
170 for i = 0 to n-1
180 coef(i) = cos(cos(pi/n*(i+1/2))*(b-a)/2+(b+a)/2)
190 next i
200 for i = 0 to n-1
210 w = 0
220 for j = 0 to n-1
230 w = w+coef(j)*cos(pi/n*i*(j+1/2))
240 next j
250 cheby(i) = w*2/n
260 print i;" : ";cheby(i)
270 next i
280 end</syntaxhighlight>
{{out}}
<pre>0 : 1.647169
1 : -0.232299
2 : -0.053715
3 : 2.458235E-03
4 : 2.821191E-04
5 : -7.722229E-06
6 : -5.898556E-07
7 : 1.152143E-08
8 : 6.596304E-10
9 : -1.002234E-11</pre>
==={{header|FreeBASIC}}===
<syntaxhighlight lang="freebasic">Const pi As Double = 4 * Atn(1)
Dim As Integer i, j
Dim As Double w, a = 0, b = 1, n = 10
Dim As Double cheby(n), coef(n)
For i = 0 To n-1
coef(i) = Cos(Cos(pi/n*(i+1/2))*(b-a)/2+(b+a)/2)
Next i
For i = 0 To n-1
w = 0
For j = 0 To n-1
w += coef(j) * Cos(pi/n*i*(j+1/2))
Next j
cheby(i) = w*2/n
Print i; " : "; cheby(i)
Next i
Sleep</syntaxhighlight>
{{out}}
<pre> 0 : 1.647169475390314
1 : -0.2322993716151719
2 : -0.05371511462204768
3 : 0.002458235266981634
4 : 0.0002821190574339161
5 : -7.7222291556156e-006
6 : -5.898556451056081e-007
7 : 1.152142750093788e-008
8 : 6.596299062522348e-010
9 : -1.002201654998203e-011</pre>
==={{header|Gambas}}===
{{trans|FreeBASIC}}
<syntaxhighlight lang="vbnet">Public coef[10] As Float
Public Sub Main()
Dim i As Integer, j As Integer
Dim w As Float, a As Float = 0, b As Float = 1, n As Float = 10
For i = 0 To n - 1
coef[i] = Cos(Cos(Pi / n * (i + 1 / 2)) * (b - a) / 2 + (b + a) / 2)
Next
For i = 0 To n - 1
w = 0
For j = 0 To n - 1
w += coef[j] * Cos(Pi / n * i * (j + 1 / 2))
Next
cheby[i] = w * 2 / n
Print i; " : "; cheby[i]
Next
End</syntaxhighlight>
{{out}}
<pre>0 : 1,64716947539031
1 : -0,232299371615172
2 : -0,053715114622048
3 : 0,002458235266982
4 : 0,000282119057434
5 : -7,7222291556156E-6
6 : -5,89855645105608E-7
7 : 1,15214275009379E-8
8 : 6,59629906252235E-10
9 : -1,0022016549982E-11</pre>
==={{header|GW-BASIC}}===
{{trans|FreeBASIC}}
{{works with|PC-BASIC|any}}
<syntaxhighlight lang="qbasic">100 CLS
110 PI# = 4 * ATN(1)
120 A# = 0
130 B# = 1
140 N# = 10
150 DIM CHEBY(N#)
160 DIM COEF(N#)
170 FOR I = 0 TO N#-1
180 COEF(I) = COS(COS(PI#/N#*(I+1/2))*(B#-A#)/2+(B#+A#)/2)
190 NEXT I
200 FOR I = 0 TO N#-1
210 W# = 0
220 FOR J = 0 TO N#-1
230 W# = W# + COEF(J) * COS(PI#/N#*I*(J+1/2))
240 NEXT J
250 CHEBY(I) = W# * 2 / N#
260 PRINT I; " : "; CHEBY(I)
270 NEXT I
280 END</syntaxhighlight>
{{out}}
<pre>0 : 1.647169
1 : -.2322993
2 : -5.371515E-02
3 : 2.458321E-03
4 : 2.820671E-04
5 : -7.766486E-06
6 : -5.857175E-07
7 : 9.834766E-08
8 : -1.788139E-07
9 : -9.089708E-08</pre>
==={{header|Minimal BASIC}}===
{{trans|FreeBASIC}}
{{works with|BASICA}}
<syntaxhighlight lang="qbasic">110 LET P = 4 * ATN(1)
120 LET A = 0
130 LET B = 1
140 LET N = 10
170 FOR I = 0 TO N-1
180 LET K(I) = COS(COS(P/N*(I+1/2))*(B-A)/2+(B+A)/2)
190 NEXT I
200 FOR I = 0 TO N-1
210 LET W = 0
220 FOR J = 0 TO N-1
230 LET W = W + K(J) * COS(P/N*I*(J+1/2))
240 NEXT J
250 LET C(I) = W * 2 / N
260 PRINT I; " : "; C(I)
270 NEXT I
280 END</syntaxhighlight>
{{out}}
<pre> 0 : 1.6471695
1 : -.23229937
2 : -5.3715115E-2
3 : 2.4582353E-3
4 : 2.8211906E-4
5 : -7.7222291E-6
6 : -5.8985565E-7
7 : 1.1521437E-8
8 : 6.5962449E-10
9 : -1.0018986E-11</pre>
==={{header|MSX Basic}}===
{{trans|FreeBASIC}}
{{works with|MSX BASIC|any}}
<syntaxhighlight lang="qbasic">100 CLS : rem 10 HOME for Applesoft BASIC
110 PI = 4 * ATN(1)
120 A = 0
130 B = 1
140 N = 10
150 DIM CHEBY(N)
160 DIM COEF(N)
170 FOR I = 0 TO N-1
180 COEF(I) = COS(COS(PI/N*(I+1/2))*(B-A)/2+(B+A)/2)
190 NEXT I
200 FOR I = 0 TO N-1
210 W = 0
220 FOR J = 0 TO N-1
230 W = W + COEF(J) * COS(PI/N*I*(J+1/2))
240 NEXT J
250 CHEBY(I) = W * 2 / N
260 PRINT I; " : "; CHEBY(I)
270 NEXT I
280 END</syntaxhighlight>
==={{header|QBasic}}===
Line 133 ⟶ 487:
{{works with|QuickBasic|4.5}}
{{trans|FreeBASIC}}
<syntaxhighlight lang="qbasic">pi = 4 * ATN(1)
a = 0: b = 1: n = 10
DIM cheby!(n)
Line 152 ⟶ 506:
END</syntaxhighlight>
{{out}}
<pre> 0 : 1.647169470787048000000
1 : -0.232299402356147800000
2 : -0.053715050220489500000
Line 162 ⟶ 515:
7 : 0.000000053614126471757
8 : 0.000000079823998078155
9 : -0.000000070922546058227</pre>
==={{header|
{{trans|FreeBASIC}}
<syntaxhighlight lang="qbasic">100 cls
120 let a = 0
130 let b = 1
140 let n = 10
150 array c
160 array k
170 for i = 0 to n-1
180 let k[i] = cos(cos(pi/n*(i+1/2))*(b-a)/2+(b+a)/2)
190 next i
200 for i = 0 to n-1
210 let w = 0
220 for j = 0 to n-1
230 let w = w + k[j] * cos(pi/n*i*(j+1/2))
240 next j
250 let c[i] = w * 2 / n
260 print i; " : "; c[i]
270 next i
280 end</syntaxhighlight>
{{out}}
<pre>0 : 1.6471694753903137
1 : -0.23229937161517186
2 : -0.05371511462204768
3 : 0.0024582352669816343
4 : 0.0002821190574339161
5 : -0.0000077222291556156
6 : -5.898556451056081e-7
7 : 1.1521427500937876e-8
8 : 6.59629917354465e-10
9 : -1.0022016549982027e-11</pre>
==={{header|Run BASIC}}===
{{trans|FreeBASIC}}
{{works with|Just BASIC}}
{{works with|Liberty BASIC}}
<syntaxhighlight lang="vb">pi = 4 * atn(1)
a = 0
b = 1
n = 10
dim cheby(n)
dim coef(n)
for i = 0 to n-1
coef(i) = cos(cos(pi/n*(i+1/2))*(b-a)/2+(b+a)/2)
next i
for i = 0 to n-1
w = 0
w
cheby(i) = w * 2 / n
==={{header|Yabasic}}===
{{trans|FreeBASIC}}
<syntaxhighlight lang="yabasic">a = 0: b = 1: n = 10
dim cheby(n)
dim coef(n)
Line 226 ⟶ 603:
8 : 6.5963e-10
9 : -1.0022e-11</pre>
=={{header|C}}==
C99.
<syntaxhighlight lang=
#include <string.h>
#include <math.h>
Line 297 ⟶ 673:
return 0;
}</syntaxhighlight>
=={{header|C sharp|C#}}==
{{trans|C++}}
<syntaxhighlight lang="csharp">using System;
using System.Collections.Generic;
using System.Linq;
Line 444 ⟶ 819:
0.900 0.62160996827066 0.62160996827111 4.444223E-013
0.950 0.58168308946388 0.58168308946379 -8.992806E-014</pre>
=={{header|C++}}==
Based on the C99 implementation above. The main improvement is that, because C++ containers handle memory for us, we can use a more functional style.
Line 452 ⟶ 826:
The wrapper class ChebyshevApprox_ supports very terse user code.
<syntaxhighlight lang=
#include <iostream>
#include <iomanip>
Line 555 ⟶ 929:
}
</syntaxhighlight>
=={{header|D}}==
This imperative code retains some of the style of the original C version.
<syntaxhighlight lang="d">import std.math: PI, cos;
/// Map x from range [min, max] to [min_to, max_to].
Line 698 ⟶ 1,071:
0.900 0.62160996827066445648 0.62160996827066445674 2.71e-19
0.950 0.58168308946388349416 0.58168308946388349403 -1.63e-19</pre>
=={{header|EasyLang}}==
<syntaxhighlight lang="text">
numfmt 12 0
a = 0
b = 1
Line 706 ⟶ 1,079:
len coef[] n
len cheby[] n
for i
coef[i + 1] = cos (180 / pi * (cos (180 / n * (i + 1 / 2)) * (b - a) / 2 + (b + a) / 2))
.
for i
w = 0
for j
w += coef[j + 1] * cos (180 / n * i * (j + 1 / 2))
.
cheby[i + 1] = w * 2 / n
print cheby[i + 1]
.
</syntaxhighlight>
=={{header|Go}}==
Line 724 ⟶ 1,098:
Two variances here from the WP presentation and most mathematical presentations follow other examples on this page and so keep output directly comparable. One variance is that the Kronecker delta factor is dropped, which has the effect of doubling the first coefficient. This simplifies both coefficient generation and polynomial evaluation. A further variance is that there is no scaling for the range of function values. The result is that coefficients are not necessarily bounded by 1 (2 for the first coefficient) but by the maximum function value over the argument range from min to max (or twice that for the first coefficient.)
<syntaxhighlight lang="go">package main
import (
Line 815 ⟶ 1,189:
1.0 0.54030231 0.54030231 -4.476e-13
</pre>
=={{header|Groovy}}==
{{trans|Java}}
<syntaxhighlight lang="groovy">class ChebyshevCoefficients {
static double map(double x, double min_x, double max_x, double min_to, double max_to) {
return (x - min_x) / (max_x - min_x) * (max_to - min_to) + min_to
Line 859 ⟶ 1,232:
6.59630183807991E-10
-1.0021913854352249E-11</pre>
=={{header|J}}==
From 'J for C Programmers: Calculating Chebyshev Coefficients [[http://www.jsoftware.com/learning/a_first_look_at_j_programs.htm#_Toc191734318]]
<syntaxhighlight lang=
chebft =: adverb define
:
Line 870 ⟶ 1,242:
</syntaxhighlight>
Calculate coefficients:
<syntaxhighlight lang=
10 (2&o.) chebft 0 1
1.64717 _0.232299 _0.0537151 0.00245824 0.000282119 _7.72223e_6 _5.89856e_7 1.15214e_8 6.59629e_10 _1.00227e_11
</syntaxhighlight>
=={{header|Java}}==
Partial translation of [[Chebyshev_coefficients#C|C]] via [[Chebyshev_coefficients#D|D]]
{{works with|Java|8}}
<syntaxhighlight lang="java">import static java.lang.Math.*;
import java.util.function.Function;
Line 927 ⟶ 1,298:
6.59630183807991E-10
-1.0021913854352249E-11</pre>
=={{header|jq}}==
'''Adapted from [[#Wren|Wren]]'''
Line 934 ⟶ 1,304:
'''Preliminaries'''
<syntaxhighlight lang="jq">def lpad($len): tostring | ($len - length) as $l | (" " * $l) + .;
def rpad($len; $fill): tostring | ($len - length) as $l | . + ($fill * $l)[:$l];
Line 952 ⟶ 1,322:
end;</syntaxhighlight>
'''Chebyshev Coefficients'''
<syntaxhighlight lang="jq">def mapRange($x; $min; $max; $minTo; $maxTo):
(($x - $min)/($max - $min))*($maxTo - $minTo) + $minTo;
Line 1,032 ⟶ 1,402:
1.00 0.54030230 0.54030230 4.47e-13
</pre>
=={{header|Julia}}==
{{works with|Julia|0.6}}
{{trans|Go}}
<syntaxhighlight lang="julia">mutable struct Cheb
c::Vector{Float64}
min::Float64
Line 1,113 ⟶ 1,482:
0.9 0.62160997 0.62160997 -4.449e-13
1.0 0.54030231 0.54030231 -4.476e-13</pre>
=={{header|Kotlin}}==
{{trans|C}}
<syntaxhighlight lang="scala">// version 1.1.2
typealias DFunc = (Double) -> Double
Line 1,204 ⟶ 1,572:
1.000 0.54030231 0.54030231 4.5e-13
</pre>
=={{header|Lua}}==
{{trans|Java}}
<syntaxhighlight lang="lua">function map(x, min_x, max_x, min_to, max_to)
return (x - min_x) / (max_x - min_x) * (max_to - min_to) + min_to
end
Line 1,257 ⟶ 1,624:
6.5963018380799e-010
-1.0021913854352e-011</pre>
=={{header|Microsoft Small Basic}}==
{{trans|Perl}}
<syntaxhighlight lang="smallbasic">' N Chebyshev coefficients for the range 0 to 1 - 18/07/2018
pi=Math.pi
a=0
Line 1,293 ⟶ 1,659:
9 : -0,0000000000100189955816952521
</pre>
=={{header|МК-61/52}}==
{{trans|BASIC}}
<syntaxhighlight lang="mk-61">0 ПA 1 ПB 8 ПC 0 ПD ИПC ИПD
- x#0 44 пи ИПC / ИПD 1 ^ 2
/ + * cos ИПB ИПA - 2 / *
ИПB ИПA + 2 / + cos KПD ИПD 1
+ ПD БП 08 0 ПD ИПC ИПD - x#0
95 0 ПB ПE ИПC ИПE - x#0 83 пи
ИПC / ИПD * ИПE 1 ^ 2 / +
* cos KИПE * ИПB + ПB ИПE 1 +
ПE БП 54 ИПB 2 * ИПC / С/П ИПD
1 + ПD БП 46 С/П</syntaxhighlight>
=={{header|Nim}}==
{{trans|Go}}
<syntaxhighlight lang=
type Cheb = object
Line 1,371 ⟶ 1,748:
0.9 0.62160997 0.62160997 -4.450e-13
1.0 0.54030231 0.54030231 -4.476e-13</pre>
=={{header|Perl}}==
{{trans|C}}
<syntaxhighlight lang="perl">use constant PI => 2 * atan2(1, 0);
sub chebft {
Line 1,403 ⟶ 1,779:
+6.5962992e-10
-1.0021994e-11</pre>
=={{header|Phix}}==
{{trans|Go}}
<!--<syntaxhighlight lang=
<span style="color: #008080;">function</span> <span style="color: #000000;">Cheb</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">cmin</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">cmax</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">ncoeff</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">nnodes</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ncoeff</span><span style="color: #0000FF;">),</span>
Line 1,478 ⟶ 1,853:
1.0 0.54030231 0.54030231 -4.477e-13
</pre>
=={{header|Python}}==
{{trans|C++}}
<syntaxhighlight lang="python">import math
def test_func(x):
Line 1,569 ⟶ 1,943:
0.900 0.6216099683 0.6216099683 4.46e-13
0.950 0.5816830895 0.5816830895 -8.99e-14</pre>
=={{header|Racket}}==
{{trans|C}}
<syntaxhighlight lang="racket">#lang typed/racket
(: chebft (Real Real Nonnegative-Integer (Real -> Real) -> (Vectorof Real)))
(define (chebft a b n func)
Line 1,610 ⟶ 1,983:
6.596299173544651e-010
-1.0022016549982027e-011)</pre>
=={{header|Raku}}==
(formerly Perl 6)
{{trans|C}}
<syntaxhighlight lang="raku" line>sub chebft ( Code $func, Real \a, Real \b, Int \n ) {
my \bma = ½ × (b - a);
Line 1,621 ⟶ 1,993:
my @pi-n = ( ^n »+» ½ ) »×» (π/n);
my @f = ( @
my @sums = (^n).map: { [+] @f »×« ( @pi-n »×» $_ )».cos };
Line 1,656 ⟶ 2,028:
The numeric precision is dependent on the number of decimal digits specified in the value of '''pi'''.
<syntaxhighlight lang="rexx">/*REXX program calculates N Chebyshev coefficients for the range 0 ──► 1 (inclusive)*/
numeric digits length( pi() ) - length(.) /*DIGITS default is nine, but use 71. */
parse arg a b N . /*obtain optional arguments from the CL*/
Line 1,722 ⟶ 2,094:
19 Chebyshev coefficient is: 2.859065292763079576513213370136E-29
</pre>
=={{header|Ruby}}==
<syntaxhighlight lang="ruby">def mapp(x, min_x, max_x, min_to, max_to)
return (x - min_x) / (max_x - min_x) * (max_to - min_to) + min_to
end
Line 1,765 ⟶ 2,136:
6.59630183807991e-10
-1.0021913854352249e-11</pre>
=={{header|Scala}}==
{{Out}}Best seen running in your browser either by [https://scalafiddle.io/sf/DqRNe2A/0 ScalaFiddle (ES aka JavaScript, non JVM)] or [https://scastie.scala-lang.org/M5Ye6h8ZRkmTCNzexUh3uw Scastie (remote JVM)].
<syntaxhighlight lang=
object ChebyshevCoefficients extends App {
Line 1,799 ⟶ 2,169:
}</syntaxhighlight>
=={{header|Sidef}}==
{{trans|Raku}}
<syntaxhighlight lang="ruby">func chebft (callback, a, b, n) {
var bma = (0.5 * b-a)
var bpa = (0.5 * b+a)
var pi_n = ((
var f = (pi_n
var sums = (
sums
}
for v in (chebft(func(v){v.cos}, 0, 1, 10)
say ("%+.10e" % v)
}</syntaxhighlight>
Line 1,836 ⟶ 2,205:
{{trans|Kotlin}}
<syntaxhighlight lang="swift">import Foundation
typealias DFunc = (Double) -> Double
Line 1,932 ⟶ 2,301:
0.950 0.58168309 0.58168309 -9.0e-14
1.000 0.54030231 0.54030231 4.5e-13</pre>
=={{header|VBScript}}==
{{trans|Microsoft Small Basic}}
To run in console mode with cscript.
<syntaxhighlight lang="vb">' N Chebyshev coefficients for the range 0 to 1
Dim coef(10),cheby(10)
pi=4*Atn(1)
Line 1,965 ⟶ 2,333:
9 : -1,0022016549982E-11
</pre>
=={{header|Visual Basic .NET}}==
{{trans|C#}}
<syntaxhighlight lang="vbnet">Module Module1
Structure ChebyshevApprox
Line 2,114 ⟶ 2,481:
{{trans|Kotlin}}
{{libheader|Wren-fmt}}
<syntaxhighlight lang=
var mapRange = Fn.new { |x, min, max, minTo, maxTo| (x - min)/(max - min)*(maxTo - minTo) + minTo }
Line 2,200 ⟶ 2,567:
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>
=={{header|zkl}}==
{{trans|C}}{{trans|Perl}}
<syntaxhighlight lang="zkl">var [const] PI=(1.0).pi;
fcn chebft(a,b,n,func){
bma,bpa,fac := 0.5*(b - a), 0.5*(b + a), 2.0/n;
| |||