Numerical integration: Difference between revisions
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=={{header|jq}}==
{{works with|jq}}
'''Also works with gojq, the Go implementation of jq.'''
The five different integration methods are each presented as independent functions
to facilitate reuse.
<syntaxhighlight lang=jq>
def integrate_left($a; $b; $n; f):
(($b - $a) / $n) as $h
| reduce range(0;$n) as $i (0;
($a + $i * $h) as $x
| . + ($x|f) )
| . * $h;
def integrate_mid($a; $b; $n; f):
(($b - $a) / $n) as $h
| reduce range(0;$n) as $i (0;
($a + $i * $h) as $x
| . + (($x + $h/2) | f) )
| . * $h;
def integrate_right($a; $b; $n; f):
(($b - $a) / $n) as $h
| reduce range(1; $n + 1) as $i (0;
($a + $i * $h) as $x
| . + ($x|f) )
| . * $h;
def integrate_trapezium($a; $b; $n; f):
(($b - $a) / $n) as $h
| reduce range(0;$n) as $i (0;
($a + $i * $h) as $x
| . + ( ($x|f) + (($x + $h)|f)) / 2 )
| . * $h;
def integrate_simpson($a; $b; $n; f):
(($b - $a) / $n) as $h
| reduce range(0;$n) as $i (0;
($a + $i * $h) as $x
| . + ((( ($x|f) + 4 * (($x + ($h/2))|f) + (($x + $h)|f)) / 6)) )
| . * $h;
def demo($a; $b; $n; f):
"Left = \(integrate_left($a;$b;$n;f))",
"Mid = \(integrate_mid ($a;$b;$n;f))",
"Right = \(integrate_right($a;$b;$n;f))",
"Trapezium = \(integrate_trapezium($a;$b;$n;f))",
"Simpson = \(integrate_simpson($a;$b;$n;f))",
"" ;
demo(0; 1; 100; .*.*. ),
demo(1; 100; 1000; 1 / . ),
demo(0; 5000; 5000000; . ),
demo(0; 6000; 6000000; . )
</syntaxhighlight>
{{output}}
<pre>
Left = 0.24502500000000005
Mid = 0.24998750000000006
Right = 0.25502500000000006
Trapezium = 0.250025
Simpson = 0.25
Left = 4.65499105751468
Mid = 4.604762548678376
Right = 4.55698105751468
Trapezium = 4.605986057514676
Simpson = 4.605170384957133
Left = 12499997.5
Mid = 12500000
Right = 12500002.5
Trapezium = 12500000
Simpson = 12500000
Left = 17999997.000000004
Mid = 17999999.999999993
Right = 18000003.000000004
Trapezium = 17999999.999999993
Simpson = 17999999.999999993
</pre>
=={{header|Julia}}==
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