spectral-norm OCaml #2 program

(* The Computer Language Benchmarks Game
 * https://salsa.debian.org/benchmarksgame-team/benchmarksgame/
 *
 * Contributed by Sebastien Loisel
 * Cleanup by Troestler Christophe
 * Modified by Mauricio Fernandez
 *)

let eval_A i j = 1. /. float((i+j)*(i+j+1)/2+i+1)

let eval_A_times_u u v =
  let n = Array.length v - 1 in
  for i = 0 to  n do
    let vi = ref 0. in
      for j = 0 to n do vi := !vi +. eval_A i j *. u.(j) done;
      v.(i) <- !vi
  done

let eval_At_times_u u v =
  let n = Array.length v -1 in
  for i = 0 to n do
    let vi = ref 0. in
      for j = 0 to n do vi := !vi +. eval_A j i *. u.(j) done;
      v.(i) <- !vi
  done

let eval_AtA_times_u u v =
  let w = Array.make (Array.length u) 0.0 in
  eval_A_times_u u w; eval_At_times_u w v


let () =
  let n = try int_of_string(Array.get Sys.argv 1) with _ ->  2000 in
  let u = Array.make n 1.0  and  v = Array.make n 0.0 in
  for i = 0 to 9 do
    eval_AtA_times_u u v; eval_AtA_times_u v u
  done;

  let vv = ref 0.0  and  vBv = ref 0.0 in
  for i=0 to n-1 do
    vv := !vv +. v.(i) *. v.(i);
    vBv := !vBv +. u.(i) *. v.(i)
  done;
  Printf.printf "%0.9f\n" (sqrt(!vBv /. !vv))
    

NOTES:
64-bit Ubuntu quad core
The OCaml native-code compiler, version 4.10.0


Tue, 05 May 2020 23:21:53 GMT

MAKE:
mv spectralnorm.ocaml-2.ocaml spectralnorm.ocaml-2.ml
/opt/src/ocaml-4.10.0/bin/ocamlopt -noassert -unsafe -fPIC -nodynlink -inline 100 -O3 unix.cmxa bigarray.cmxa -ccopt -march=core2 spectralnorm.ocaml-2.ml -o spectralnorm.ocaml-2.ocaml_run
rm spectralnorm.ocaml-2.ml

2.80s to complete and log all make actions

COMMAND LINE:
./spectralnorm.ocaml-2.ocaml_run 5500

PROGRAM OUTPUT:
1.274224153