Numerical integration/Adaptive Simpson's method: Difference between revisions
Numerical integration/Adaptive Simpson's method (view source)
Revision as of 18:18, 19 May 2023
, 1 year agoForth before →{{header|Fortran}}
(Added ObjectIcon ahead of OCaml →{{header|OCaml}}) |
(Forth before →{{header|Fortran}}) |
||
Line 793:
Simpson's rule integration of sin from 0 to 1 is: 0.4596976941573994
</pre>
=={{header|Forth}}==
{{works with|Gforth|0.7.3}}
<syntaxhighlight lang="forth">
\ -*- mode: forth -*-
\
\ The following was written for Gforth, using its implementation of
\ local variables and of f=
\
Defer f
: simpson-rule { F: a F: fa F: b F: fb -- m fm quadval }
a b f+ 0.5e0 f* \ -- m
fdup f \ -- m fm
fdup 4.0e0 f* fa f+ fb f+
b a f- 6.0e0 f/ f* \ -- m fm quadval
;
: recursive-simpson
{ F: a F: fa F: b F: fb F: tol F: whole F: m F: fm depth -- quadval }
a fa m fm simpson-rule { F: lm F: flm F: left }
m fm b fb simpson-rule { F: rm F: frm F: right }
left right f+ whole f- { F: delta }
tol 0.5e0 f* { F: tol_ }
depth 0 <=
tol_ tol f= or
delta fabs 15.0e0 tol f* f<= or
if
left right f+ delta 15.0e0 f/ f+
else
a fa m fm tol_ left lm flm depth 1 - recurse
m fm b fb tol_ right rm frm depth 1 - recurse
f+
then
;
: quad-asr { F: a F: b F: tol depth -- quadval }
a f { F: fa }
b f { F: fb }
a fa b fb simpson-rule { F: m F: fm F: whole }
a fa b fb tol whole m fm depth recursive-simpson
;
:noname fsin ; IS f
." estimate of ∫ sin x dx from 0 to 1: "
0.0e0 1.0e0 1.0e-12 100 quad-asr f.
cr
</syntaxhighlight>
{{out}}
<pre>$ gforth adaptive_simpson_task.fs -e bye
estimate of ∫ sin x dx from 0 to 1: 0.45969769413186</pre>
=={{header|Fortran}}==
| |||