1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
|
open Gsl
let _ =
Error.init ()
let zeta2 = Math.pi *. Math.pi /. 6.
let zeta_terms n =
let t = Array.make n 0. in
let sum = ref 0. in
for i=0 to pred n do
let np1 = float (i + 1) in
t.(i) <- 1. /. (np1 *. np1) ;
sum := !sum +. t.(i)
done ;
(t, !sum)
let print_res sum nbterms sum_accel sum_plain nbterms_accel =
Printf.printf "term-by-term sum = % .16f using %d terms\n"
sum nbterms ;
Printf.printf "term-by-term sum = % .16f using %d terms\n"
sum_plain nbterms_accel ;
Printf.printf "exact value = % .16f\n" zeta2 ;
Printf.printf "accelerated sum = % .16f using %d terms\n"
sum_accel.Fun.res nbterms_accel ;
Printf.printf "estimated error = % .16f\n"
sum_accel.Fun.err ;
Printf.printf "actual error = % .16f\n"
(sum_accel.Fun.res -. zeta2)
let _ =
let n = 20 in
let (t, sum) = zeta_terms n in
let ws = Sum.make n in
let res = Sum.accel t ws in
let { Sum.sum_plain = sum_plain ;
Sum.terms_used = nbterms_used } = Sum.get_info ws in
print_res sum n res sum_plain nbterms_used ;
print_newline ();
print_endline "\"truncated\" version:" ;
let ws = Sum.Trunc.make n in
let res = Sum.Trunc.accel t ws in
let { Sum.Trunc.sum_plain = sum_plain ;
Sum.Trunc.terms_used = nbterms_used } =
Sum.Trunc.get_info ws in
print_res sum n res sum_plain nbterms_used
|
