Thiele's interpolation formula: Difference between revisions
→{{header|jq}}
(Added FreeBASIC) |
|||
Line 848:
3.14159265358979
3.14159265358980</pre>
=={{header|jq}}==
'''Adapted from [[#Wren|Wren]]'''
'''Works with jq, the C implementation of jq'''
'''Works with gojq, the Go implementation of jq'''
<syntaxhighlight lang="jq">
def N: 32;
# Input: {x,y,r}
# Output: update r and set .result
def rho($i; $n):
if $n < 0 then .result = 0
elif $n == 0 then .result = .y[$i]
else (((N - 1 - $n) * (N - $n) / 2) + $i) as $idx
| if (.r[$idx] == null)
then
rho($i; $n - 1) | .result as $r1
| rho($i + 1; $n - 1) | .result as $r2
| rho($i + 1; $n - 2) | .result as $r3
| .r[$idx] = (.x[$i] - .x[$i + $n]) / ($r1 - $r2) + $r3
end
| .result = .r[$idx]
end;
# Input: {x,y,r}
# Output: update r and set .result
def thiele($xin; $n):
if $n > N - 1 then .result = 1
else
rho(0; $n) | .result as $r1
| rho(0; $n -2) | .result as $r2
| thiele($xin; $n + 1) | .result as $t
| .result = ($r1 - $r2) + ($xin - .x[$n]) / $t
end;
# Output: {xval, tsin, tcos, ttan}
def init($step):
reduce range(0; N) as $i ({};
($i * $step) as $x
| .xval[$i] = $x
| .tsin[$i] = ($x|sin)
| .tcos[$i] = ($x|cos)
| .ttan[$i] = .tsin[$i] / .tcos[$i] ) ;
init(0.05)
| ({r: [], x: .tsin, y: .xval} | 6 * thiele(0.5; 0).result),
({r: [], x: .tcos, y: .xval} | 3 * thiele(0.5; 0).result),
({r: [], x: .ttan, y: .xval} | 4 * thiele(1.0; 0).result)
</syntaxhighlight>
{{output}}
<pre>
3.141592653589793
3.1415926535897936
3.141592653589796
</pre>
=={{header|Julia}}==
| |||