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Ingy döt Net 2023-07-01 11:58:00 -04:00
parent 7387c8f97b
commit cb5bb5e222
199093 changed files with 3378972 additions and 0 deletions
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7
Task/Numerical-integration/OCaml/numerical-integration-1.ocaml Normal file
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let integrate f a b steps meth =
let h = (b -. a) /. float_of_int steps in
let rec helper i s =
if i >= steps then s
else helper (succ i) (s +. meth f (a +. h *. float_of_int i) h)
in
h *. helper 0 0.

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Task/Numerical-integration/OCaml/numerical-integration-2.ocaml Normal file
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let methods = [
( "rect_l", fun f x _ -> f x);
( "rect_m", fun f x h -> f (x +. h /. 2.) );
( "rect_r", fun f x h -> f (x +. h) );
( "trap", fun f x h -> (f x +. f (x +. h)) /. 2. );
( "simp", fun f x h -> (f x +. 4. *. f (x +. h /. 2.) +. f (x +. h)) /. 6. )
]

6
Task/Numerical-integration/OCaml/numerical-integration-3.ocaml Normal file
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let functions = [
( "cubic", (fun x -> x*.x*.x), 0.0, 1.0, 100);
( "recip", (fun x -> 1.0/.x), 1.0, 100.0, 1000);
( "x to 5e3", (fun x -> x), 0.0, 5000.0, 5_000_000);
( "x to 6e3", (fun x -> x), 0.0, 6000.0, 6_000_000)
]

7
Task/Numerical-integration/OCaml/numerical-integration-4.ocaml Normal file
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let () =
List.iter (fun (s,f,lo,hi,n) ->
Printf.printf "Testing function %s:\n" s;
List.iter (fun (name,meth) ->
Printf.printf " method %s gives %.15g\n" name (integrate f lo hi n meth)
) methods
) functions