Numerical integration/Adaptive Simpson's method: Difference between revisions

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 Simpson's integration of sine from 0 to 1 = 0.459698
 </pre>
+=={{header|Python}}==
+{{works with|SWI-Prolog|9.1.2}}
+{{works with|GNU Prolog|1.5.0}}
+<syntaxhighlight lang="prolog">
+%%% -*- mode: prolog; prolog-indent-width: 2; -*-
+main :-
+  quad_asr(sine, 0.0, 1.0, 0.000000001, 1, QuadVal),
+  write('estimate of ∫ sin x dx from 0 to 1: '),
+  write(QuadVal),
+  write('\n'),
+  halt.
+sine(X, Y) :- Y is sin(X).
+quad_asr(F, A, B, Tol, Depth, QuadVal) :-
+  call(F, A, FA),
+  call(F, B, FB),
+  simpson_rule(F, A, FA, B, FB, M, FM, Whole),
+  recursive_simpson(F, A, FA, B, FB, Tol, Whole, M, FM, Depth,
+                    QuadVal).
+recursive_simpson(F, A, FA, B, FB, Tol, Whole, M, FM, Depth,
+                  QuadVal) :-
+  simpson_rule(F, A, FA, M, FM, LM, FLM, Left),
+  simpson_rule(F, M, FM, B, FB, RM, FRM, Right),
+  Delta is (Left + Right - Whole),
+  Tol_ is (0.5 * Tol),
+  ((Depth =< 0.0, Tol_ \= Tol, abs(Delta) =< 15.0 * Tol)
+  -> QuadVal is Left + Right + (Delta / 15.0)
+  ;  (Depth_ is Depth - 1,
+      recursive_simpson(F, A, FA, M, FM, Tol_, Left, LM, FLM,
+                        Depth_, QuadValLeft),
+      recursive_simpson(F, M, FM, B, FB, Tol_, Right, RM, FRM,
+                        Depth_, QuadValRight),
+      QuadVal is QuadValLeft + QuadValRight)).
+simpson_rule(F, A, FA, B, FB, M, FM, QuadVal) :-
+  M is (0.5 * (A + B)),
+  call(F, M, FM),
+  QuadVal is ((B - A) / 6.0) * (FA + (4.0 * FM) + FB).
+:- initialization(main).
+</syntaxhighlight>
+{{out}}
+The output varies by Prolog implementation:
+<pre>$ swipl adaptive_simpson_task_prolog.pl
+estimate of ∫ sin x dx from 0 to 1: 0.4596976941317858
+$ gplc adaptive_simpson_task_prolog.pl && ./adaptive_simpson_task_prolog
+estimate of ∫ sin x dx from 0 to 1: 0.45969769413178579</pre>
 =={{header|Python}}==