Numerical integration/Adaptive Simpson's method: Difference between revisions
Numerical integration/Adaptive Simpson's method (view source)
Revision as of 15:00, 17 May 2023
, 1 year agoAdded Pascal before →{{header|Perl}}
(→{{header|D}}: Do not needlessly recompute f.) |
(Added Pascal before →{{header|Perl}}) |
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<pre>$ ocaml adaptive_simpson_task.ml
estimated definite integral of sin(x) for x from 0 to 1: 0.459697694132</pre>
=={{header|Pascal}}==
{{works with|Free Pascal Compiler|3.2.2}}
<syntaxhighlight lang="pascal">
program adaptive_simpson_task;
type function_real_to_real = function(value : real) : real;
var fa, fb, m, fm, whole : real;
function quad_asr (f : function_real_to_real;
a, b, tol : real;
depth : integer) : real;
procedure quad_asr_simpsons_ ( f: function_real_to_real;
a, fa, b, fb: real;
var m, fm, quadval: real);
begin
m := (a + b) / 2;
fm := f(m);
quadval := ((b - a) / 6) * (fa + (4 * fm) + fb)
end;
function quad_asr_ (f : function_real_to_real;
a, fa, b, fb : real;
tol, whole, m, fm : real;
depth : integer) : real;
var
lm, flm, left : real;
rm, frm, right : real;
delta, tol_ : real;
begin
quad_asr_simpsons_ (f, a, fa, m, fm, lm, flm, left);
quad_asr_simpsons_ (f, m, fm, b, fb, rm, frm, right);
delta := left + right - whole;
tol_ := tol / 2;
if (depth <= 0) or (tol_ = tol) or (abs(delta) <= 15 * tol) then
quad_asr_ := left + right + (delta / 15)
else
quad_asr_ := (quad_asr_ (f, a, fa, m, fm, tol_,
left , lm, flm, depth - 1)
+ quad_asr_ (f, m, fm, b, fb, tol_,
right, rm, frm, depth - 1))
end;
begin
fa := f(a);
fb := f(b);
quad_asr_simpsons_ (f, a, fa, b, fb, m, fm, whole);
quad_asr := quad_asr_ (f, a, fa, b, fb, tol, whole, m, fm, depth)
end;
function sine (x : real) : real;
begin
sine := sin (x);
end;
begin
writeln ('estimated definite integral of sin(x) ',
'for x from 0 to 1: ', quad_asr (@sine, 0, 1, 1e-9, 1000))
end.
</syntaxhighlight>
{{out}}
<pre>estimated definite integral of sin(x) for x from 0 to 1: 4.5969769413178579E-001</pre>
=={{header|Perl}}==
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