feat (exm): van der pol example

exm/vdp.ml

@@ -0,0 +1,59 @@
+
+open Hsim.Types
+open Solvers
+
+let of_array a = Bigarray.Array1.of_array Bigarray.Float64 Bigarray.c_layout a
+
+type state = { lx : Zls.carray; i : bool }
+
+let mu = 5.0
+let x0 = 1.0
+let y0 = 1.0
+
+let fder _ y yd =
+  yd.{0} <- y.{1}; yd.{1} <- (mu *. (1.0 -. (y.{0} *. y.{0})) *. y.{1}) -. y.{0}
+let fzero _ _ _ = ()
+let fout _ y     = of_array [| y.{0}; y.{1} |]
+let step { i; lx } _ =
+  let lx = if i then of_array [| x0; y0 |] else lx in
+  of_array [| lx.{0}; lx.{1} |], { lx; i = false }
+
+let cget s     = s.lx
+let cset s lx = { s with lx }
+let zset s _   = s
+let yd         = Zls.cmake 2
+let zout       = Zls.cmake 1
+let zsize      = 1
+let s_init     = { lx = of_array [| x0; y0 |]; i = true }
+let reset _ _  = s_init
+let jump _     = true
+
+let van_der_pol () =
+  HNode { state = s_init;
+          fder = (fun _ _ y -> fder 0.0 y yd; yd);
+          fzer = (fun _ _ y -> fzero 0.0 y zout; zout);
+          fout = (fun s _ y -> fout s y);
+          step;
+          horizon = (fun _ -> max_float);
+          cset; cget; zset; zsize; reset; jump }
+
+(* let van_der_pol_prop_record () = *)
+(*   let s_init =  *)
+(*       { lx = of_array [| x0; y0 |]; i = true } in *)
+(*   { name = "van_der_pol_prop"; *)
+(*     s = s_init; *)
+(*     fder = (fun s a y -> fder 0.0 y yd; yd); *)
+(*     fzero = (fun s a y -> fzero 0.0 y zout; zout); *)
+(*     fout = (fun s { lx } y -> 1.0 /. (abs_float (s.lx.{0} -. lx.{0}))); *)
+(*     fstep = (fun s { lx } -> *)
+(*       let v, s = fstep s () in *)
+(*       s.lx.{0} -. lx.{0}, s); *)
+(*     horizon = (fun s -> max_float); *)
+(*     cset; cget; zset; csize; zsize; reset; jump } *)
+(* let van_der_pol_with_assert () = *)
+(*   Fun_hybrid *)
+(*     { body = van_der_pol_record (); *)
+(*       assertions = *)
+(*         [Fun_hybrid { body = *)
+(*                         van_der_pol_prop_record (); *)
+(*                       assertions = [] }] } *)