Source file owl_plot.ml

# 1 "src/owl/misc/owl_plot.ml"
(*
 * OWL - an OCaml numerical library for scientific computing
 * Copyright (c) 2016-2018 Liang Wang <liang.wang@cl.cam.ac.uk>
 *)

(** Plot Module *)

(* types in plot module *)

type dsmat = Owl_dense_matrix.D.mat

type color = RED | GREEN | BLUE

type legend_typ = LINE | SCATTER | BOX

type legend_position = North | South | West | East | NorthWest | NorthEast | SouthWest | SouthEast


type legend_item = {
  mutable plot_type    : legend_typ;
  mutable line_style   : int;
  mutable line_color   : int * int * int;
  mutable marker       : string;
  mutable marker_color : int * int * int;
  mutable fill_pattern : int;
  mutable fill_color   : int * int * int;
}


type page = {
  mutable title           : string;
  mutable fgcolor         : int * int * int;
  mutable fontsize        : float;
  mutable is_3d           : bool;
  mutable no_axes         : bool;
  (* control axis labels *)
  mutable xlabel          : string;
  mutable ylabel          : string;
  mutable zlabel          : string;
  (* control axis ranges *)
  mutable xrange          : float * float;
  mutable yrange          : float * float;
  mutable zrange          : float * float;
  mutable auto_xrange     : bool;
  mutable auto_yrange     : bool;
  mutable auto_zrange     : bool;
  (* control tick labels *)
  mutable xticklabels     : (float * string) list;
  mutable yticklabels     : (float * string) list;
  mutable zticklabels     : (float * string) list;
  (* control axis log scale *)
  mutable xlogscale       : bool;
  mutable ylogscale       : bool;
  (* control grids *)
  mutable xgrid           : bool;
  mutable ygrid           : bool;
  mutable zgrid           : bool;
  (* viewing perspective for 3D plots
   * http://plplot.sourceforge.net/docbook-manual/plplot-html-5.12.0/plw3d.html *)
  mutable altitude        : float;
  mutable azimuth         : float;
  (* control legend *)
  mutable legend          : bool;
  mutable legend_position : legend_position;
  mutable legend_items    : legend_item array;
  mutable legend_names    : string array;
  (* cache the plot operations *)
  mutable plots           : (unit -> unit) array;
}


type handle = {
  mutable holdon       : bool;
  mutable output       : string;
  mutable bgcolor      : int * int * int;
  mutable pensize      : float;
  mutable page_size    : int * int;
  (* control the sub plots *)
  mutable shape        : int * int;
  mutable pages        : page array;
  mutable current_page : int;
}


type axis = X | Y | Z | XY | XZ | YZ | XYZ


(* Specification to configure a plot *)

type spec =
  | RGB         of int * int * int
  | LineStyle   of int
  | LineWidth   of float
  | Marker      of string
  | MarkerSize  of float
  | Fill
  | FillPattern of int
  | Contour
  | Altitude    of float
  | Azimuth     of float
  | ZLine       of axis
  | NoMagColor
  | Curtain
  | Faceted
  | Axis        of axis


let _get_rgb l default_val =
  let l = l
    |> List.filter (function RGB _ -> true | _ -> false)
    |> List.map (function RGB (r,g,b) -> (r,g,b) | _ -> default_val)
  in
  let k = List.length l in
  if k = 0 then default_val else List.nth l (k - 1)


let _get_line_style l default_val =
  let l = l
    |> List.filter (function LineStyle _ -> true | _ -> false)
    |> List.map (function LineStyle x -> x | _ -> default_val)
  in
  let k = List.length l in
  if k = 0 then default_val else List.nth l (k - 1)


let _get_line_width l default_val =
  let l = l
    |> List.filter (function LineWidth _ -> true | _ -> false)
    |> List.map (function LineWidth x -> x | _ -> default_val)
  in
  let k = List.length l in
  if k = 0 then default_val else List.nth l (k - 1)


let _get_marker l default_val =
  let l = l
    |> List.filter (function Marker _ -> true | _ -> false)
    |> List.map (function Marker x -> x | _ -> default_val)
  in
  let k = List.length l in
  if k = 0 then default_val else List.nth l (k - 1)


let _get_marker_size l default_val =
  let l = l
    |> List.filter (function MarkerSize _ -> true | _ -> false)
    |> List.map (function MarkerSize x -> x | _ -> default_val)
  in
  let k = List.length l in
  if k = 0 then default_val else List.nth l (k - 1)


let _get_fill l default_val =
  let l = l
    |> List.filter (function Fill -> true | _ -> false)
    |> List.map (function Fill -> true | _ -> default_val)
  in
  let k = List.length l in
  if k = 0 then default_val else List.nth l (k - 1)


let _get_fill_pattern l default_val =
  let l = l
    |> List.filter (function FillPattern _ -> true | _ -> false)
    |> List.map (function FillPattern x -> x | _ -> default_val)
  in
  let k = List.length l in
  if k = 0 then default_val else List.nth l (k - 1)


let _get_contour l default_val =
  let l = l
    |> List.filter (function Contour -> true | _ -> false)
    |> List.map (function Contour -> true | _ -> default_val)
  in
  let k = List.length l in
  if k = 0 then default_val else List.nth l (k - 1)


let _get_altitude l default_val =
  let l = l
    |> List.filter (function Altitude _ -> true | _ -> false)
    |> List.map (function Altitude x -> x | _ -> default_val)
  in
  let k = List.length l in
  if k = 0 then default_val else List.nth l (k - 1)


let _get_azimuth l default_val =
  let l = l
    |> List.filter (function Azimuth _ -> true | _ -> false)
    |> List.map (function Azimuth x -> x | _ -> default_val)
  in
  let k = List.length l in
  if k = 0 then default_val else List.nth l (k - 1)


let _get_zline l default_val =
  let l = l
    |> List.filter (function ZLine _ -> true | _ -> false)
    |> List.map (function
        | ZLine X  -> Plplot.PL_DRAW_LINEX
        | ZLine Y  -> Plplot.PL_DRAW_LINEY
        | ZLine XY -> Plplot.PL_DRAW_LINEXY
        | _        -> default_val
      )
  in
  let k = List.length l in
  if k = 0 then default_val else List.nth l (k - 1)


let _get_mag_color l default_val =
  let l = l
    |> List.filter (function NoMagColor -> true | _ -> false)
    |> List.map (function NoMagColor -> false | _ -> true)
  in
  let k = List.length l in
  if k = 0 then default_val else List.nth l (k - 1)


let _get_curtain l default_val =
  let l = l
    |> List.filter (function Curtain -> true | _ -> false)
    |> List.map (function Curtain -> true | _ -> false)
  in
  let k = List.length l in
  if k = 0 then default_val else List.nth l (k - 1)


let _get_faceted l default_val =
  let l = l
    |> List.filter (function Faceted -> true | _ -> false)
    |> List.map (function Faceted -> true | _ -> false)
  in
  let k = List.length l in
  if k = 0 then default_val else List.nth l (k - 1)


let _get_axis l default_val =
  let l = l
    |> List.filter (function Axis _ -> true | _ -> false)
    |> List.map (function Axis x -> x | _ -> default_val)
  in
  let k = List.length l in
  if k = 0 then default_val else List.nth l (k - 1)


(* module functions to simplify plotting *)


let _create_page () = {
  title           = "";
  fgcolor         = (255, 0, 0);
  fontsize        = -1.;
  is_3d           = false;
  no_axes         = false;
  xlabel          = "x";
  ylabel          = "y";
  zlabel          = "z";
  xrange          = (infinity, neg_infinity);
  yrange          = (infinity, neg_infinity);
  zrange          = (infinity, neg_infinity);
  auto_xrange     = true;
  auto_yrange     = true;
  auto_zrange     = true;
  xticklabels     = [];
  yticklabels     = [];
  zticklabels     = [];
  xlogscale       = false;
  ylogscale       = false;
  xgrid           = false;
  ygrid           = false;
  zgrid           = false;
  altitude        = 33.;
  azimuth         = 45.;
  legend          = false;
  legend_position = NorthEast;
  legend_items    = [||];
  legend_names    = [||];
  plots           = [||];
}


let _create_handle () = {
  holdon       = true;
  output       = "";
  bgcolor      = (0, 0, 0);
  pensize      = 0.;
  page_size    = (0,0);
  shape        = (1, 1);
  current_page = 0;
  pages        = [|_create_page ()|];
}


let create ?(m=1) ?(n=1) s =
  let pages = Array.make (m * n) None |> Array.map (fun _ -> _create_page ()) in
  let h = _create_handle () in
  h.shape <- (m, n);
  h.pages <- pages;
  h.output <- s;
  h


let _default_handle =
  let h = _create_handle () in
  h.holdon <- false;
  h


let _supported_device = [
    "aqt"; "xwin"; "pdf"; "ps"; "psc";
    "png"; "svg"; "xfig"; "psttf"; "psttc";
    "xcairo"; "pdfcairo"; "epscairo"; "pscairo"; "svgcairo";
    "pngcairo"; "memcairo"; "extcairo"
  ]


let _set_device h =
  try let x = Owl_utils.get_suffix h.output in
    Plplot.plsdev x;
    Plplot.plsfnam h.output;
  with exn -> ()


let _add_legend_item p plot_type line_style line_color marker marker_color fill_pattern fill_color =
  let item = {
    plot_type    = plot_type;
    line_style   = line_style;
    line_color   = line_color;
    marker       = marker;
    marker_color = marker_color;
    fill_pattern = fill_pattern;
    fill_color   = fill_color;
  }
  in
  p.legend_items <- Array.append p.legend_items [|item|]


let _plplot_position pos =
  let open Plplot in
  match pos with
  | North     -> [ PL_POSITION_TOP ]
  | South     -> [ PL_POSITION_BOTTOM ]
  | West      -> [ PL_POSITION_LEFT ]
  | East      -> [ PL_POSITION_RIGHT ]
  | NorthWest -> [ PL_POSITION_TOP; PL_POSITION_LEFT ]
  | NorthEast -> [ PL_POSITION_TOP; PL_POSITION_RIGHT ]
  | SouthWest -> [ PL_POSITION_BOTTOM; PL_POSITION_LEFT ]
  | SouthEast -> [ PL_POSITION_BOTTOM; PL_POSITION_RIGHT ]


let _draw_legend p =
  let open Plplot in
  let _ = plscmap0n 64 in
  let cbase = 16 in
  let opt = [ PL_LEGEND_BOUNDING_BOX ] in
  let position = _plplot_position p.legend_position @ [ PL_POSITION_INSIDE ] in
  let opt_array = Array.map (fun item ->
    match item.plot_type with
    | LINE -> [ PL_LEGEND_LINE; PL_LEGEND_SYMBOL ]
    | SCATTER -> [ PL_LEGEND_SYMBOL ]
    | BOX -> [ PL_LEGEND_COLOR_BOX ]
    ) p.legend_items in
  let text_colors = Array.map (fun _ -> 1) p.legend_items in
  let text = Array.mapi (fun i _ -> p.legend_names.(i)) p.legend_items in
  let line_colors = Array.mapi (fun i x ->
    let r, g, b = x.line_color in
    plscol0 (i + cbase) r g b; (i + cbase)
    ) p.legend_items in
  let line_styles = Array.map (fun x -> x.line_style) p.legend_items in
  let line_widths = Array.map (fun _ -> 1.) p.legend_items in
  let marker_colors = line_colors in
  let marker_scales = Array.map (fun _ -> 1.) p.legend_items in
  let marker_nums = Array.map (fun _ -> 3) p.legend_items in
  let markers = Array.map (fun x -> x.marker) p.legend_items in
  let box_colors = line_colors in
  let box_patterns = Array.map (fun x -> x.fill_pattern) p.legend_items in
  let box_scales = Array.map (fun x -> 0.8) p.legend_items in
  let box_linewidths = Array.map (fun x -> 1.) p.legend_items in
  let _ = pllegend opt position 0.05 0.05
    0.1 15 1 1 0 0
    opt_array 1.0 1.0 2.0
    1.0 text_colors text
    box_colors box_patterns box_scales box_linewidths
    line_colors line_styles line_widths
    marker_colors marker_scales marker_nums markers
  in ()


let _calculate_paper_size m n =
  let max_w, max_h = 900., 900. in
  let r0 = 4. /. 3. in
  let cur_w, cur_h = r0 *. (float_of_int n), float_of_int m in
  let r1 = max_w /. max_h in
  let r2 = cur_w /. cur_h in
  let w, h = match (r1 /. r2) < 1. with
    | true  -> max_w, max_w /. r2
    | false -> max_h *. r2, max_h
  in
  int_of_float w, int_of_float h


(* calculate the axis config based on a page config *)
let _config_2d_axis p =
  let base = 0 in
  if p.no_axes then -1 else
  let residual =
    if (p.xlogscale, p.ylogscale) = (true, false) then 10 else
    if (p.xlogscale, p.ylogscale) = (false, true) then 20 else
    if (p.xlogscale, p.ylogscale) = (true, true)  then 30 else
    if p.xticklabels |> List.length > 0
    || p.yticklabels |> List.length > 0
    then 70
    else 0
  in base + residual


let _initialise h =
  let open Plplot in
  (* configure before init *)
  _set_device h;
  let r, g, b = h.bgcolor in
  plscolbg r g b;
  (* init the plot *)
  let m, n = h.shape in
  if not (h.shape = (1,1)) then plssub n m;
  let x, y = match h.page_size = (0, 0) with
    | true  -> _calculate_paper_size m n
    | false -> h.page_size
  in
  plspage 0. 0. x y 0 0;
  plinit ();
  (* configure after init *)
  plwidth h.pensize


(* callback function of drawing customised tick labels *)
let _draw_ticklabels p axis value =
  let open Plplot in
  let l = match axis with
    | PL_X_AXIS -> p.xticklabels
    | PL_Y_AXIS -> p.yticklabels
    | PL_Z_AXIS -> p.zticklabels
  in
  try List.assoc value l
  with exn -> Printf.sprintf "%g" value


let _prepare_page p =
  let open Plplot in
  (* customise tick labels if necessary *)
  plslabelfunc (_draw_ticklabels p);
  (* configure an individual page *)
  let r, g, b = p.fgcolor in
  plscol0 2 r g b;
  plcol0 2;
  if p.fontsize > 0. then plschr p.fontsize 1.0;
  let xmin, xmax = p.xrange in
  let ymin, ymax = p.yrange in
  let zmin, zmax = p.zrange in
  let alt, az = p.altitude, p.azimuth in
  if not p.is_3d then (
    (* prepare a 2D plot *)
    plenv xmin xmax ymin ymax 0 (_config_2d_axis p)
  )
  else (
    (* prepare a 3D plot *)
    pladv 0;
    plvpor 0.0 1.0 0.0 0.9;
    plwind (-1.0) 1.0 (-1.0) 1.5;
    plw3d 1.0 1.0 1.2 xmin xmax ymin ymax zmin zmax alt az;
    plbox3 "bntu" p.xlabel 0.0 0
           "bntu" p.ylabel 0.0 0
           "bcdfntu" p.zlabel 0.0 4
  );
  (* set x-label, y-label, and title *)
  pllab p.xlabel p.ylabel p.title;
  (* reset foreground colour to index 1 *)
  plcol0 1;
  if p.legend then _draw_legend p


let _finalise () =
  (* play safe, reset pages in default_handle *)
  _default_handle.pages <- [|_create_page ()|];
  Plplot.plend ()


let output h =
  h.holdon <- false;
  _initialise h;
  Array.iteri (fun i p ->
    if i > 0 then Plplot.pladv i;
    _prepare_page p;
    Array.iter (fun f -> f ()) p.plots
  ) h.pages;
  _finalise ()


let set_output h s =
  let x = Owl_utils.get_suffix s in
  match (List.mem x _supported_device) with
  | true  -> h.output <- s
  | false -> Owl_log.error "unsupported file type."


let set_title h s = (h.pages.(h.current_page)).title <- s


let set_xlabel h s = (h.pages.(h.current_page)).xlabel <- s


let set_ylabel h s = (h.pages.(h.current_page)).ylabel <- s


let set_zlabel h s = (h.pages.(h.current_page)).zlabel <- s


let set_xrange h a b =
  (h.pages.(h.current_page)).auto_xrange <- false;
  (h.pages.(h.current_page)).xrange <- (a, b)


let set_yrange h a b =
  (h.pages.(h.current_page)).auto_yrange <- false;
  (h.pages.(h.current_page)).yrange <- (a, b)


let set_zrange h a b =
  (h.pages.(h.current_page)).auto_zrange <- false;
  (h.pages.(h.current_page)).zrange <- (a, b)


let set_xticklabels h l = (h.pages.(h.current_page)).xticklabels <- l


let set_yticklabels h l = (h.pages.(h.current_page)).yticklabels <- l


let set_zticklabels h l = (h.pages.(h.current_page)).zticklabels <- l


let set_foreground_color h r g b = (h.pages.(h.current_page)).fgcolor <- (r, g, b)


let set_background_color h r g b = h.bgcolor <- (r, g, b)


let set_font_size h x = (h.pages.(h.current_page)).fontsize <- x


let set_pen_size h x = h.pensize <- x


let set_page_size h x y = h.page_size <- (x, y)


let legend_on h ?(position=NorthEast) s =
  (h.pages.(h.current_page)).legend <- true;
  (h.pages.(h.current_page)).legend_position <- position;
  (h.pages.(h.current_page)).legend_names <- s


let legend_off h = (h.pages.(h.current_page)).legend <- false


(* TODO *)
let rgb = None


(*FIXME: plptex3 to write text inside the viewport of a 3D plot*)
let text ?(h=_default_handle) ?(spec=[]) x y ?(dx=0.) ?(dy=0.) s =
  let open Plplot in
  (* prepare the closure *)
  let p = h.pages.(h.current_page) in
  let color = _get_rgb spec p.fgcolor in
  let r, g, b = color in
  (* drawing function *)
  let f = (fun () ->
    (*save original color index*)
    let r', g', b' = plgcol0 1 in
    plscol0 1 r g b; plcol0 1;
    plptex x y dx dy 0. s;
    (* restore original settings *)
    plscol0 1 r' g' b'; plcol0 1
  )
  in
  (* add closure as a layer *)
  p.plots <- Array.append p.plots [|f|];
  if not h.holdon then output h


let _thinning x =
  let l = float_of_int (Array.length x) in
  let n = if l < 16. then l else 16. in
  let c = float_of_int (Array.length x) /. n in
  Array.init (int_of_float n) (fun i -> x.(int_of_float (float_of_int i *. c)))


let _union_range p r x =
  let a, b = r in
  let m, n = Owl_stats.minmax x in
  let c = if a < m then a else m in
  let d = if b > n then b else n in
  let e = (d -. c) *. p in
  c -. e, d +. e


let _adjust_range ?(margin=0.) h d axis =
  let p = h.pages.(h.current_page) in
  match axis with
  | X -> if p.auto_xrange then p.xrange <- _union_range margin p.xrange d
  | Y -> if p.auto_yrange then p.yrange <- _union_range margin p.yrange d
  | Z -> if p.auto_zrange then p.zrange <- _union_range margin p.zrange d
  | _ -> failwith "owl_plot:_adjust_range"


let plot ?(h=_default_handle) ?(spec=[]) x y =
  let open Plplot in
  let x = Owl_dense_matrix.D.to_array x in
  let y = Owl_dense_matrix.D.to_array y in
  _adjust_range h x X;
  _adjust_range h y Y;
  (* prepare the closure *)
  let p = h.pages.(h.current_page) in
  let color = _get_rgb spec p.fgcolor in
  let r, g, b = color in
  let marker = _get_marker spec "" in
  let marker_size = _get_marker_size spec 4. in
  let line_style = _get_line_style spec 1 in
  let line_width = _get_line_width spec (-1.) in
  let old_pensize = h.pensize in
  (* drawing function *)
  let f = (fun () ->
    let r', g', b' = plgcol0 1 in
    plscol0 1 r g b; plcol0 1;
    if line_width > (-1.) then plwidth line_width;
    let c' = plgchr () |> fst in
    plschr marker_size 1.;
    if line_style > 0 && line_style < 9 then
      pllsty line_style; plline x y;
    if marker <> "" then (
      let x', y' = _thinning x, _thinning y in
      plstring x' y' marker
    );
    (* restore original settings *)
    plschr c' 1.;
    plwidth old_pensize;
    pllsty 1;
    plscol0 1 r' g' b'; plcol0 1
  )
  in
  (* add closure as a layer *)
  p.plots <- Array.append p.plots [|f|];
  (* add legend item to page *)
  _add_legend_item p LINE line_style color marker color 0 color;
  if not h.holdon then output h


let plot_fun ?(h=_default_handle) ?(spec=[]) f a b =
  let x = Owl_dense_matrix.D.linspace a b 100 in
  let y = Owl_dense_matrix.D.map f x in
  plot ~h ~spec x y


let scatter ?(h=_default_handle) ?(spec=[]) x y =
  let open Plplot in
  let x = Owl_dense_matrix.D.to_array x in
  let y = Owl_dense_matrix.D.to_array y in
  _adjust_range h x X;
  _adjust_range h y Y;
  (* prepare the closure *)
  let p = h.pages.(h.current_page) in
  let color = _get_rgb spec p.fgcolor in
  let r, g, b = color in
  let marker = _get_marker spec "•" in
  let marker_size = _get_marker_size spec 4. in
  (* drawing function *)
  let f = (fun () ->
    let r', g', b' = plgcol0 1 in
    plscol0 1 r g b;
    plcol0 1;
    let c' = plgchr () |> fst in
    plschr marker_size 1.;
    plstring x y marker;
    (* restore original settings *)
    plschr c' 1.;
    plscol0 1 r' g' b';
    plcol0 1
  )
  in
  (* add closure as a layer *)
  p.plots <- Array.append p.plots [|f|];
  (* add legend item to page *)
  _add_legend_item p SCATTER 0 color marker color 0 color;
  if not h.holdon then output h


let histogram ?(h=_default_handle) ?(spec=[]) ?(bin=10) x =
  let open Plplot in
  let x = Owl_dense_matrix.D.to_array x in
  _adjust_range h x X;
  let xmin, xmax = Owl_stats.minmax x in
  let ymin, ymax = 0., Owl_stats.(histogram x bin |> Array.map float_of_int |> max)  *. 1.1 in
  _adjust_range h [|xmin; xmax|] X;
  _adjust_range h [|ymin; ymax|] Y;
  (* prepare the closure *)
  let p = h.pages.(h.current_page) in
  let color = _get_rgb spec p.fgcolor in
  let r, g, b = color in
  (* drawing function *)
  let f = (fun () ->
    let r', g', b' = plgcol0 1 in
    let _ = plscol0 1 r g b; plcol0 1 in
    plhist x xmin xmax bin [ PL_HIST_DEFAULT; PL_HIST_NOSCALING; PL_HIST_NOEXPAND ];
    (* restore original settings *)
    plscol0 1 r' g' b'; plcol0 1;
  )
  in
  (* add closure as a layer *)
  p.plots <- Array.append p.plots [|f|];
  (* add legend item to page *)
  _add_legend_item p BOX 1 color "" color 0 color;
  if not h.holdon then output h


let subplot h i j =
  let _, n = h.shape in
  h.current_page <- (n * i + j)


let stem ?(h=_default_handle) ?(spec=[]) x y =
  let open Plplot in
  let x = Owl_dense_matrix.D.to_array x in
  let y = Owl_dense_matrix.D.to_array y in
  _adjust_range h x X;
  _adjust_range h y Y;
  (* prepare the closure *)
  let p = h.pages.(h.current_page) in
  let color = _get_rgb spec p.fgcolor in
  let r, g, b = color in
  let marker = _get_marker spec "#[0x2299]" in
  let marker_size = _get_marker_size spec 4. in
  let line_style = _get_line_style spec 2 in
  let line_width = _get_line_width spec (-1.) in
  let old_pensize = h.pensize in
  (* drawing function *)
  let f = (fun () ->
    let r', g', b' = plgcol0 1 in
    plscol0 1 r g b; plcol0 1;
    if line_width > (-1.) then plwidth line_width;
    let c' = plgchr () |> fst in
    plschr marker_size 1.;
    if line_style > 0 && line_style < 9 then (
      pllsty line_style;
      Owl_utils.Array.iter2 (fun x' y' -> pljoin x' 0. x' y') x y
    );
    if not (marker = "") then plstring x y marker;
    (* restore original settings *)
    plschr c' 1.;
    plwidth old_pensize;
    pllsty 1;
    plscol0 1 r' g' b';
    plcol0 1
  )
  in
  (* add closure as a layer *)
  p.plots <- Array.append p.plots [|f|];
  (* add legend item to page *)
  _add_legend_item p LINE line_style color marker color 0 color;
  if not h.holdon then output h


let autocorr ?(h=_default_handle) ?(spec=[]) x =
  let z = Owl_dense_matrix.D.to_array x in
  let x' = Array.init (Array.length z) (fun i -> float_of_int i) in
  let y' = Array.mapi (fun i _ -> Owl_stats.autocorrelation ~lag:i z) x' in
  let x' = Owl_dense_matrix.D.of_arrays [|x'|] in
  let y' = Owl_dense_matrix.D.of_arrays [|y'|] in
  set_xlabel h "Lag";
  set_ylabel h "Autocorrelation";
  (* prepare the closure *)
  let p = h.pages.(h.current_page) in
  let r, g, b = _get_rgb spec p.fgcolor in
  let color = RGB (r, g, b) in
  let marker = Marker (_get_marker spec "•") in
  let marker_size = MarkerSize (_get_marker_size spec 4.) in
  let line_style = LineStyle (_get_line_style spec 1) in
  let line_width = LineWidth (_get_line_width spec (-1.)) in
  let spec = [ color; marker; marker_size; line_style; line_width ] in
  (* drawing function *)
  stem ~h ~spec x' y'


let draw_line ?(h=_default_handle) ?(spec=[]) x0 y0 x1 y1 =
  let open Plplot in
  let x = [|x0; x1|] in
  let y = [|y0; y1|] in
  _adjust_range h x X;
  _adjust_range h y Y;
  (* prepare the closure *)
  let p = h.pages.(h.current_page) in
  let color = _get_rgb spec p.fgcolor in
  let r, g, b = color in
  let line_style = _get_line_style spec 1 in
  let line_width = _get_line_width spec (-1.) in
  let old_pensize = h.pensize in
  (* drawing function *)
  let f = (fun () ->
    let r', g', b' = plgcol0 1 in
    plscol0 1 r g b;
    plcol0 1;
    if line_width > (-1.) then plwidth line_width;
    if line_style > 0 && line_style < 9 then (
      pllsty line_style;
      pljoin x0 y0 x1 y1
    );
    (* restore original settings *)
    plwidth old_pensize;
    pllsty 1;
    plscol0 1 r' g' b';
    plcol0 1
  )
  in
  (* add closure as a layer *)
  p.plots <- Array.append p.plots [|f|];
  if not h.holdon then output h


(* TODO *)
let plot_multi = None


let _draw_error_bar ?(w=0.) x y e =
  let open Plplot in
  let w = w /. 2. in
  (* draw vertical line *)
  let x' = [|x; x|] in
  let y' = [|y-.e; y+.e|] in
  plline x' y';
  (* draw upper bar *)
  let x' = [|x-.w; x+.w|] in
  let y' = [|y+.e; y+.e|] in
  plline x' y';
  (* draw lower line *)
  let x' = [|x-.w; x+.w|] in
  let y' = [|y-.e; y-.e|] in
  plline x' y'


let error_bar ?(h=_default_handle) ?(spec=[]) x y e =
  let open Plplot in
  let ymin = Owl_dense_matrix.D.(min'(y - e)) in
  let ymax = Owl_dense_matrix.D.(max'(y + e)) in
  let x = Owl_dense_matrix.D.to_array x in
  let y = Owl_dense_matrix.D.to_array y in
  let e = Owl_dense_matrix.D.to_array e in
  _adjust_range h x X;
  _adjust_range h [|ymin; ymax|] Y;
  (* prepare the closure *)
  let p = h.pages.(h.current_page) in
  let color = _get_rgb spec p.fgcolor in
  let r, g, b = color in
  let line_style = _get_line_style spec 1 in
  let line_width = _get_line_width spec (-1.) in
  let old_pensize = h.pensize in
  let w = let a, b = Owl_stats.minmax x in (a -. b) *. 0.02 in
  (* drawing function *)
  let f = (fun () ->
    let r', g', b' = plgcol0 1 in
    plscol0 1 r g b;
    plcol0 1;
    if line_width > (-1.) then plwidth line_width;
    pllsty line_style;
    Owl_utils.Array.iter3 (fun x0 y0 e0 ->
      _draw_error_bar ~w x0 y0 e0
    ) x y e;
    (* restore original settings *)
    plwidth old_pensize;
    pllsty 1;
    plscol0 1 r' g' b';
    plcol0 1
  ) in
  (* add closure as a layer *)
  p.plots <- Array.append p.plots [|f|];
  if not h.holdon then output h


let _draw_whiskers_box w x y =
  let open Plplot in
  let ymed, y1st, y3rd = Owl_stats.(median y, first_quartile y, third_quartile y) in
  let w = w /. 2. in
  let x' = [|x-.w; x-.w; x+.w; x+.w; x-.w|] in
  let y' = [|y1st; y3rd; y3rd; y1st; y1st|] in
  pllsty 1; plline x' y';
  let x' = [|x-.w; x+.w|] in
  let y' = [|ymed; ymed|] in
  pllsty 1; plline x' y';
  let ymin, ymax = Owl_stats.minmax y in
  let x' = [|x; x|] in
  let y' = [|ymin; y1st|] in
  pllsty 1; plline x' y';
  let x' = [|x; x|] in
  let y' = [|y3rd; ymax|] in
  pllsty 1; plline x' y'


let boxplot ?(h=_default_handle) ?(spec=[]) y =
  let open Plplot in
  let m, _ = Owl_dense_matrix.D.shape y in
  let x = Array.init m (fun i -> float_of_int i +. 1.) in
  let xmin, xmax = Owl_stats.minmax x in
  let w = 0.4 in
  let y0 = Owl_dense_matrix.D.to_array y in
  let y1 = Owl_dense_matrix.D.to_arrays y in
  _adjust_range h [|xmin-.w; xmax+.w|] X;
  _adjust_range h ~margin:0.1 y0 Y;
  (* prepare the closure *)
  let p = h.pages.(h.current_page) in
  let color = _get_rgb spec p.fgcolor in
  let r, g, b = color in
  (* drawing function *)
  let f = (fun () ->
    let r', g', b' = plgcol0 1 in
    plscol0 1 r g b;
    plcol0 1;
    Owl_utils.Array.iter2 (fun x' y' -> _draw_whiskers_box w x' y') x y1;
    (* restore original settings *)
    plscol0 1 r' g' b';
    plcol0 1;
    pllsty 1
  )
  in
  (* add closure as a layer *)
  p.plots <- Array.append p.plots [|f|];
  if not h.holdon then output h


let _draw_bar w x0 y0 =
  let open Plplot in
  let x = [|x0-.w; x0-.w; x0+.w; x0+.w|] in
  let y = [|0.; y0; y0; 0.|] in
  plfill x y;
  pllsty 1;
  plline x y


let draw_rect ?(h=_default_handle) ?(spec=[]) x0 y0 x1 y1 =
  let open Plplot in
  let x = [|x0; x0; x1; x1|] in
  let y = [|y1; y0; y0; y1|] in
  _adjust_range h x X;
  _adjust_range h y Y;
  (* prepare the closure *)
  let p = h.pages.(h.current_page) in
  let color = _get_rgb spec p.fgcolor in
  let r, g, b = color in
  let line_style = _get_line_style spec 1 in
  let fill_pattern = _get_fill_pattern spec 0 in
  (* drawing function *)
  let f = (fun () ->
    let r', g', b' = plgcol0 1 in
    plscol0 1 r g b;
    plcol0 1;
    pllsty line_style;
    plpsty fill_pattern;
    plfill x y;
    (* restore original settings *)
    plscol0 1 r' g' b';
    plcol0 1;
    pllsty 1
  )
  in
  (* add closure as a layer *)
  p.plots <- Array.append p.plots [|f|];
  if not h.holdon then output h


let bar ?(h=_default_handle) ?(spec=[]) y =
  let open Plplot in
  let w = 0.4 in
  let y = Owl_dense_matrix.D.to_array y in
  let x = Array.mapi (fun i _ -> float_of_int i +. 1.) y in
  let xmin, xmax = Owl_stats.minmax x in
  _adjust_range h [|xmin-.w; xmax+.w|] X;
  _adjust_range h y Y;
  (* prepare the closure *)
  let p = h.pages.(h.current_page) in
  let color = _get_rgb spec p.fgcolor in
  let r, g, b = color in
  let line_style = _get_line_style spec 1 in
  let fill_pattern = _get_fill_pattern spec 0 in
  (* drawing function *)
  let f = (fun () ->
    let r', g', b' = plgcol0 1 in
    plscol0 1 r g b;
    plcol0 1;
    pllsty line_style;
    plpsty fill_pattern;
    Owl_utils.Array.iter2 (fun x0 y0 -> _draw_bar w x0 y0) x y;
    (* restore original settings *)
    plscol0 1 r' g' b';
    plcol0 1;
    pllsty 1
  )
  in
  (* add closure as a layer *)
  p.plots <- Array.append p.plots [|f|];
  (* add legend item to page *)
  _add_legend_item p BOX line_style color "" color fill_pattern color;
  if not h.holdon then output h


let area ?(h=_default_handle) ?(spec=[]) x y=
  let open Plplot in
  let x = Owl_dense_matrix.D.to_array x in
  let y = Owl_dense_matrix.D.to_array y in
  let xmin, xmax = Owl_stats.minmax x in
  let x = Array.(append (append [|xmin|] x) [|xmax|]) in
  let y = Array.(append (append [|0.|] y) [|0.|]) in
  _adjust_range h x X;
  _adjust_range h y Y;
  (* prepare the closure *)
  let p = h.pages.(h.current_page) in
  let color = _get_rgb spec p.fgcolor in
  let r, g, b = color in
  let line_style = _get_line_style spec 1 in
  let fill_pattern = _get_fill_pattern spec 0 in
  (* drawing function *)
  let f = (fun () ->
    let r', g', b' = plgcol0 1 in
    plscol0 1 r g b;
    plcol0 1;
    pllsty line_style;
    plline x y;
    plpsty fill_pattern;
    plfill x y;
    (* restore original settings *)
    plscol0 1 r' g' b';
    plcol0 1;
    pllsty 1
  )
  in
  (* add closure as a layer *)
  p.plots <- Array.append p.plots [|f|];
  (* add legend item to page *)
  _add_legend_item p BOX line_style color "" color fill_pattern color;
  if not h.holdon then output h


let draw_polygon ?(h=_default_handle) ?(spec=[]) x y =
  let open Plplot in
  let x = Owl_dense_matrix.D.to_array x in
  let y = Owl_dense_matrix.D.to_array y in
  _adjust_range h x X;
  _adjust_range h y Y;
  (* prepare the closure *)
  let p = h.pages.(h.current_page) in
  let color = _get_rgb spec p.fgcolor in
  let r, g, b = color in
  let line_style = _get_line_style spec 1 in
  let fill_pattern = _get_fill_pattern spec 0 in
  (* drawing function *)
  let f = (fun () ->
    let r', g', b' = plgcol0 1 in
    plscol0 1 r g b;
    plcol0 1;
    pllsty line_style;
    plline x y;
    plpsty fill_pattern;
    plfill x y;
    (* restore original settings *)
    plscol0 1 r' g' b';
    plcol0 1;
    pllsty 1
  )
  in
  (* add closure as a layer *)
  p.plots <- Array.append p.plots [|f|];
  (* add legend item to page *)
  _add_legend_item p BOX line_style color "" color fill_pattern color;
  if not h.holdon then output h

let _ecdf_interleave x i =
  let m = Array.length x in
  let n = 2 * m in
  let y = Array.make n 0. in
  Array.iteri (fun j z ->
    let k = 2 * j + i in
    if k < n then y.(k) <- z;
    if k < n - 1 then y.(k + 1) <- z
  ) x;
  y


let ecdf ?(h=_default_handle) ?(spec=[]) x =
  let x0 = Owl_dense_matrix.D.to_array x in
  let x, y = Owl_stats.ecdf x0 in
  let x = _ecdf_interleave x 0 in
  let y = _ecdf_interleave y 1 in
  let n = Array.length x in
  let x = Owl_dense_matrix.D.of_array x n 1 in
  let y = Owl_dense_matrix.D.of_array y n 1 in
  plot ~h ~spec x y


let stairs ?(h=_default_handle) ?(spec=[]) x y =
  let x = Owl_dense_matrix.D.to_array x in
  let y = Owl_dense_matrix.D.to_array y in
  let x = _ecdf_interleave x 0 in
  let a = y.(0) in
  let y = _ecdf_interleave y 1 in
  let _ = y.(0) <- a in
  let n = Array.length x in
  let x = Owl_dense_matrix.D.of_array x n 1 in
  let y = Owl_dense_matrix.D.of_array y n 1 in
  plot ~h ~spec x y


let draw_circle ?(h=_default_handle) ?(spec=[]) x y rr =
  let open Plplot in
  let n = 1000 in
  let theta = (2. *. Owl_const.pi) /. (float_of_int n) in
  let x' = Array.init (n + 1) (fun i -> x +. Owl_maths.(sin (float_of_int i *. theta)) *. rr) in
  let y' = Array.init (n + 1) (fun i -> y +. Owl_maths.(cos (float_of_int i *. theta)) *. rr) in
  _adjust_range h ~margin:0.05 x' X;
  _adjust_range h ~margin:0.05 y' Y;
  (* prepare the closure *)
  let p = h.pages.(h.current_page) in
  let color = _get_rgb spec p.fgcolor in
  let r, g, b = color in
  let line_style = _get_line_style spec 1 in
  let line_width = _get_line_width spec (-1.) in
  let fill_pattern = _get_fill_pattern spec 0 in
  let old_pensize = h.pensize in
  (* drawing function *)
  let f = (fun () ->
    let r', g', b' = plgcol0 1 in
    plscol0 1 r g b;
    plcol0 1;
    if line_width > (-1.) then plwidth line_width;
    pllsty line_style;
    plpsty fill_pattern;
    plfill x' y';
    plline x' y';
    (* restore original settings *)
    plscol0 1 r' g' b';
    plcol0 1;
    plwidth old_pensize;
    pllsty 1
  )
  in
  (* add closure as a layer *)
  p.plots <- Array.append p.plots [|f|];
  if not h.holdon then output h


let _draw_arc fill n x =
  let open Plplot in
  let a = 2. *. Owl_const.pi in
  let theta = a /. n in
  let i = ref 0. in

  Array.iter (fun y ->
    let c = n *. y in
    let x' = Array.init (int_of_float c + 1) (fun j -> Owl_maths.(sin ((float_of_int j +. !i) *. theta))) in
    let y' = Array.init (int_of_float c + 1) (fun j -> Owl_maths.(cos ((float_of_int j +. !i) *. theta))) in
    let x' = Array.(append [|0.|] x') in
    let y' = Array.(append [|0.|] y') in
    plline x' y';

    (* generates a color theme *)
    let r', g', b' = plgcol0 1 in
    let rgb = mod_float ((!i +. 1.) *. 50.) 256. |> int_of_float in
    plscol0 1 rgb rgb rgb;
    plcol0 1;
    plpsty 3;
    plfill x' y';
    (* restore original settings *)
    plscol0 1 r' g' b';
    plcol0 1;

    i := !i +. c;
  ) x


(* TODO: improve the filling ... *)
let pie ?(h=_default_handle) ?(spec=[]) x =
  let open Plplot in
  _adjust_range h ~margin:0.1 [|-1.; 1.|] X;
  _adjust_range h ~margin:0.1 [|-1.; 1.|] Y;
  let x = Owl_dense_matrix.D.to_array x in
  let x = Owl_stats.normlise_pdf x in
  (* prepare the closure *)
  let p = h.pages.(h.current_page) in
  let color = _get_rgb spec p.fgcolor in
  let r, g, b = color in
  let fill = _get_fill spec false in
  let old_pensize = h.pensize in
  (* drawing function *)
  let f = (fun () ->
    let r', g', b' = plgcol0 1 in
    plscol0 1 r g b;
    plcol0 1;
    plwidth 1.;
    pllsty 1;
    plpsty 0;
    _draw_arc fill 1000. x;
    (* restore original settings *)
    plscol0 1 r' g' b'; plcol0 1;
    plwidth old_pensize;
    pllsty 1
  )
  in
  (* add closure as a layer *)
  p.plots <- Array.append p.plots [|f|];
  if not h.holdon then output h


let loglog ?(h=_default_handle) ?(spec=[]) ?x y =
  let open Plplot in
  let y = Owl_dense_matrix.D.to_array y in
  let n = Array.length y in
  let x = match x with
    | Some mtx -> Owl_dense_matrix.D.to_array mtx
    (* The range is [1..n] instead of [0..(n-1)] *)
    | None     ->
      Owl_dense_matrix.D.linspace 1. (float_of_int n) n
      |> Owl_dense_matrix.D.to_array
  in
  let axis = _get_axis spec XY in
  let x, y = match axis with
    | X -> (Array.map Owl_maths.log10 x, y)
    | Y -> (x, Array.map Owl_maths.log10 y)
    | _ -> (Array.map Owl_maths.log10 x, Array.map Owl_maths.log10 y)
  in
  _adjust_range h x X;
  _adjust_range h y Y;
  let p = h.pages.(h.current_page) in
  let _ = match axis with
    | X -> p.xlogscale <- true
    | Y -> p.ylogscale <- true
    | _ -> (p.xlogscale <- true; p.ylogscale <- true)
  in
  (* prepare the closure *)
  let color = _get_rgb spec p.fgcolor in
  let r, g, b = color in
  let marker = _get_marker spec "" in
  let marker_size = _get_marker_size spec 4. in
  let line_style = _get_line_style spec 1 in
  let line_width = _get_line_width spec (-1.) in
  let old_pensize = h.pensize in
  (* drawing function *)
  let f = (fun () ->
    let r', g', b' = plgcol0 1 in
    plscol0 1 r g b; plcol0 1;
    if line_width > (-1.) then plwidth line_width;
    let c' = plgchr () |> fst in
    plschr marker_size 1.;
    if line_style > 0 && line_style < 9 then
      pllsty line_style; plline x y;
    if marker <> "" then (
      let x', y' = _thinning x, _thinning y in
      plstring x' y' marker
    );
    (* restore original settings *)
    plschr c' 1.;
    plwidth old_pensize;
    pllsty 1;
    plscol0 1 r' g' b'; plcol0 1
  )
  in
  (* add closure as a layer *)
  p.plots <- Array.append p.plots [|f|];
  (* add legend item to page *)
  _add_legend_item p LINE line_style color marker color 0 color;
  if not h.holdon then output h


let semilogx ?(h=_default_handle) ?(spec=[]) ?x y =
  let spec = spec @ [Axis X] in
  match x with
  | Some arr -> loglog ~h ~spec ~x:arr y
  | None     -> loglog ~h ~spec y


let semilogy ?(h=_default_handle) ?(spec=[]) ?x y =
  let spec = spec @ [Axis Y] in
  match x with
  | Some arr -> loglog ~h ~spec ~x:arr y
  | None     -> loglog ~h ~spec y


let surf ?(h=_default_handle) ?(spec=[]) x y z =
  let open Plplot in
  let x = Owl_dense_matrix.D.(row x 0 |> to_array) in
  let y = Owl_dense_matrix.D.(col y 0 |> to_array) in
  let z = Owl_dense_matrix.D.transpose z in
  let z0 = Owl_dense_matrix.D.to_arrays z in
  let z1 = Owl_dense_matrix.D.to_array z in
  _adjust_range h x X;
  _adjust_range h y Y;
  _adjust_range h z1 Z;
  (* construct contour level *)
  let zmin, zmax = Owl_stats.minmax z1 in
  let clvl = Owl_dense_matrix.D.(linspace zmin zmax 10 |> to_array) in
  (* prepare the closure *)
  let p = h.pages.(h.current_page) in
  p.is_3d <- true;
  p.altitude <- _get_altitude spec p.altitude;
  p.azimuth <- _get_azimuth spec p.azimuth;
  (* assemble the specifications *)
  let mag_color = _get_mag_color spec true in
  let contour = _get_contour spec false in
  let curtain = _get_curtain spec false in
  let faceted = _get_faceted spec false in
  let opt = [ PL_DIFFUSE ] in
  let opt = opt @ if mag_color then [ PL_MAG_COLOR ] else [] in
  let opt = opt @ if contour then [ PL_BASE_CONT; PL_SURF_CONT ] else [] in
  let opt = opt @ if curtain then [ PL_DRAW_SIDES ] else [] in
  let opt = opt @ if faceted then [ PL_FACETED ] else [] in
  (* drawing function *)
  let f = (fun () ->
    plsurf3d x y z0 opt clvl;
    (* restore original settings, if any *)
  )
  in
  (* add closure as a layer *)
  p.plots <- Array.append p.plots [|f|];
  if not h.holdon then output h


let plot3d = surf


let mesh ?(h=_default_handle) ?(spec=[]) x y z =
  let open Plplot in
  let x = Owl_dense_matrix.D.(row x 0 |> to_array) in
  let y = Owl_dense_matrix.D.(col y 0 |> to_array) in
  let z = Owl_dense_matrix.D.transpose z in
  let z0 = Owl_dense_matrix.D.to_arrays z in
  let z1 = Owl_dense_matrix.D.to_array z in
  _adjust_range h x X;
  _adjust_range h y Y;
  _adjust_range h z1 Z;
  (* construct contour level *)
  let zmin, zmax = Owl_stats.minmax z1 in
  let clvl = Owl_dense_matrix.D.(linspace zmin zmax 10 |> to_array) in
  (* prepare the closure *)
  let p = h.pages.(h.current_page) in
  p.is_3d <- true;
  p.altitude <- _get_altitude spec p.altitude;
  p.azimuth <- _get_azimuth spec p.azimuth;
  let color = _get_rgb spec p.fgcolor in
  let r, g, b = color in
  (* assemble the specifications *)
  let mag_color = _get_mag_color spec true in
  let contour = _get_contour spec false in
  let curtain = _get_curtain spec false in
  let opt = [ PL_MESH ] in
  let opt = opt @ [ _get_zline spec PL_DRAW_LINEXY ] in
  let opt = opt @ if mag_color then [ PL_MAG_COLOR ] else [] in
  let opt = opt @ if contour then [ PL_BASE_CONT; PL_SURF_CONT ] else [] in
  let opt = opt @ if curtain then [ PL_DRAW_SIDES ] else [] in
  (* drawing function *)
  let f = (fun () ->
    (* only takes effect when NoMagColor is set *)
    let r', g', b' = plgcol0 1 in
    plscol0 1 r g b;
    plcol0 1;
    match contour with
    | true  -> plmeshc x y z0 opt clvl
    | false -> plmesh x y z0 opt
    ;
    (* restore original settings, if any *)
    plscol0 1 r' g' b';
    plcol0 1
  )
  in
  (* add closure as a layer *)
  p.plots <- Array.append p.plots [|f|];
  if not h.holdon then output h


let heatmap ?(h=_default_handle) x y z =
  let open Plplot in
  let x = Owl_dense_matrix.D.(row x 0 |> to_array) in
  let y = Owl_dense_matrix.D.(col y 0 |> to_array) in
  let z = Owl_dense_matrix.D.transpose z in
  let z0 = Owl_dense_matrix.D.to_arrays z in
  let z1 = Owl_dense_matrix.D.to_array z in
  _adjust_range h x X;
  _adjust_range h y Y;
  _adjust_range h z1 Z;
  (* construct contour level *)
  let xmin, xmax = Owl_stats.minmax x in
  let ymin, ymax = Owl_stats.minmax y in
  let zmin, zmax = Owl_stats.minmax z1 in
  let clvl = Owl_dense_matrix.D.(linspace zmin zmax 10 |> to_array) in
  (* prepare the closure *)
  let p = h.pages.(h.current_page) in
  let f = (fun () ->
    plshades z0 xmin xmax ymin ymax clvl 1.0 0 1.0 false
    (* restore original settings, if any *)
  ) in
  (* add closure as a layer *)
  p.plots <- Array.append p.plots [|f|];
  if not h.holdon then output h


let contour ?(h=_default_handle) x y z =
  let open Plplot in
  let m, n = Owl_dense_matrix.D.shape z in
  let x0 = Owl_dense_matrix.D.to_arrays x in
  let x1 = Owl_dense_matrix.D.to_array x in
  let y0 = Owl_dense_matrix.D.to_arrays y in
  let y1 = Owl_dense_matrix.D.to_array y in
  let z0 = Owl_dense_matrix.D.to_arrays z in
  let z1 = Owl_dense_matrix.D.to_array z in
  _adjust_range h x1 X;
  _adjust_range h y1 Y;
  (* construct contour level *)
  let zmin, zmax = Owl_stats.minmax z1 in
  let clvl = Owl_dense_matrix.D.(linspace zmin zmax 10 |> to_array) in
  (* prepare the closure *)
  let p = h.pages.(h.current_page) in
  let f = (fun () ->
    plset_pltr (pltr2 x0 y0);
    plcont z0 1 m 1 n clvl;
    plunset_pltr ()
    (* restore original settings, if any *)
  )
  in
  (* add closure as a layer *)
  p.plots <- Array.append p.plots [|f|];
  if not h.holdon then output h


let _draw_extended_line x0 y0 x1 y1 l r u d =
  (* Specify two points, draw a line between them, and extend on both ends with dash line *)
  let open Plplot in
  let x0, y0, x1, y1 = if x0 > x1 then x1, y1, x0, y0 else x0, y0, x1, y1 in
  let yl = if x0 = x1 then u else y0 -. (y1 -. y0) /. (x1 -. x0) *. (x0 -. l) in
  let yr = if x0 = x1 then d else y1 +. (y1 -. y0) /. (x1 -. x0) *. (r -. x1) in
  let xl = if x0 = x1 then x0 else l in
  let xr = if x0 = x1 then x0 else r in
  pllsty 1; pljoin x0 y0 x1 y1;
  pllsty 3; pljoin xl yl x0 y0;
  pllsty 3; pljoin x1 y1 xr yr;
  (* restore line style *)
  pllsty 1

let probplot ?(h=_default_handle) ?(spec=[]) ?(dist=(Owl_stats.gaussian_ppf ~mu:0. ~sigma:1.)) ?(noref=false) x =

    (* TODO: show y-axis as probability instead of invcdf; Choose suitable
      yticks for different distribution; support for censor data, frequency *)

    (* inputs *)
    let open Plplot in
    let x = Owl_dense_matrix.D.to_array x |> Owl_stats.sort ~inc:true in
    let y =
      let n = Array.length x in
      let qth = Owl_dense_matrix.D.linspace ((1. -. 0.5) /. float_of_int n)
        (( float_of_int n -. 0.5) /. float_of_int n) n in
      let q = Owl_dense_matrix.D.map dist qth in
      Owl_dense_matrix.D.to_array q
    in
    _adjust_range h x X;
    _adjust_range h y Y;
    (* parameters to draw the reference line *)
    let p1y, p1x = (Owl_stats.first_quartile y, Owl_stats.first_quartile x) in
    let p3y, p3x = (Owl_stats.third_quartile y, Owl_stats.third_quartile x) in
    let left, right = Owl_stats.minmax x in
    let up, down = Owl_stats.minmax y in
    (* prepare the closure *)
    let p = h.pages.(h.current_page) in
    let color = _get_rgb spec p.fgcolor in
    let r, g, b = color in
    let marker = _get_marker spec "#[0x002b]" in
    let marker_size = _get_marker_size spec 4. in
    (* drawing function *)
    let f = (fun () ->
      let r', g', b' = plgcol0 1 in
      plscol0 1 r g b;
      plcol0 1;
      let c' = plgchr () |> fst in
      plschr marker_size 1.;
      if not noref then _draw_extended_line p1x p1y p3x p3y left right up down;
      plstring x y marker;
      (* restore original settings *)
      plschr c' 1.;
      plscol0 1 r' g' b';
      plcol0 1
    )
    in
    (* add closure as a layer *)
    p.plots <- Array.append p.plots [|f|];
    (* add legend item to page *)
    _add_legend_item p SCATTER 0 color marker color 0 color;
    if not h.holdon then output h


let normplot ?(h=_default_handle) ?(spec=[]) ?(sigma=1.) x =
  (* TODO: replace yticklabels, including unseen tick labels,  with user-defined labels *)
  let dist = Owl_stats.gaussian_ppf ~mu:0. ~sigma in
  probplot ~h ~spec ~dist:dist x


let wblplot ?(h=_default_handle) ?(spec=[]) ?(lambda=1.) ?(k=1.) x =
  (* TODO: logscale and logfit *)
  (* inputs *)
  let open Plplot in
  let x = Owl_dense_matrix.D.to_array x |> Owl_stats.sort ~inc:true in
  let dist = Owl_stats.weibull_ppf ~shape:k ~scale:lambda in
  let y =
    let n = Array.length x in
    let qth = Owl_dense_matrix.D.linspace ((1. -. 0.5) /. float_of_int n)
      (( float_of_int n-. 0.5) /. float_of_int n) n in
    let q = Owl_dense_matrix.D.map dist qth in
    Owl_dense_matrix.D.to_array q
  in
  _adjust_range h x X;
  _adjust_range h y Y;
  (* parameters to draw the reference line *)
  let p1y, p1x = (Owl_stats.first_quartile y, Owl_stats.first_quartile x) in
  let p3y, p3x = (Owl_stats.third_quartile y, Owl_stats.third_quartile x) in
  let left, right = Owl_stats.minmax x in
  let up, down = Owl_stats.minmax y in
  (* prepare the closure; note the change to log sacle *)
  let p = h.pages.(h.current_page) in
  let color = _get_rgb spec p.fgcolor in
  let r, g, b = color in
  let marker = _get_marker spec "#[0x002b]" in
  let marker_size = _get_marker_size spec 4. in
  (* drawing function *)
  let f = (fun () ->
    let r', g', b' = plgcol0 1 in
    plscol0 1 r g b;
    plcol0 1;
    let c' = plgchr () |> fst in
    plschr marker_size 1.;
    _draw_extended_line p1x p1y p3x p3y left right up down;
    plstring x y marker;
    (* restore original settings *)
    plschr c' 1.;
    plscol0 1 r' g' b';
    plcol0 1
  )
  in
  (* add closure as a layer *)
  p.plots <- Array.append p.plots [|f|];
  (* add legend item to page *)
  _add_legend_item p SCATTER 0 color marker color 0 color;
  if not h.holdon then output h


let _ecdf_dist a b p =
  (* find the ecdf value of probability value p; (a, b) is the output of
    Stats.ecdf *)
  let rec _find_rec x lst i = match lst with
    | hd::tl -> if (hd > x) then i - 1 else _find_rec x tl (i+1)
    | _ -> (Array.length b) - 1
  in
  let ticks = Array.to_list b in
  let i = _find_rec p ticks 1 in
  a.(i)


let qqplot ?(h=_default_handle) ?(spec=[]) ?(pd=Owl_stats.gaussian_ppf ~mu:0. ~sigma:1.) ?x y =
  (* TODO: support matrix input; add support for `pvec` argument;
    plot the larger data input on x-axis *)
  let open Plplot in
  let y = Owl_dense_matrix.D.to_array y |> Owl_stats.sort ~inc:true in
  let n = Array.length y in
  let dist = match x with
    | Some arr ->
      (* if the second argument is a vector *)
      let x = Owl_dense_matrix.D.to_array arr in
      (* The empirical CDF of it is used as dist. *)
      let a, b = Owl_stats.ecdf x in
      (fun p -> _ecdf_dist a b p)
    | None     -> pd
  in
  let qth = Owl_dense_matrix.D.linspace ((1. -. 0.5) /. float_of_int n)
      (( float_of_int n-. 0.5) /. float_of_int n) n in
  let q = Owl_dense_matrix.D.map dist qth in
  let x = Owl_dense_matrix.D.to_array q in
  (* draw the figure *)
  _adjust_range h x X;
  _adjust_range h y Y;
  (* parameters to draw the reference line *)
  let p1y, p1x = (Owl_stats.first_quartile y, Owl_stats.first_quartile x) in
  let p3y, p3x = (Owl_stats.third_quartile y, Owl_stats.third_quartile x) in
  let left, right = Owl_stats.minmax x in
  let up, down = Owl_stats.minmax y in
  (* prepare the closure *)
  let p = h.pages.(h.current_page) in
  let color = _get_rgb spec p.fgcolor in
  let r, g, b = color in
  let marker = _get_marker spec "#[0x002b]" in
  let marker_size = _get_marker_size spec 4. in
  (* drawing function *)
  let f = (fun () ->
    let r', g', b' = plgcol0 1 in
    plscol0 1 r g b;
    plcol0 1;
    let c' = plgchr () |> fst in
    plschr marker_size 1.;
    _draw_extended_line p1x p1y p3x p3y left right up down;
    plstring x y marker;
    (* restore original settings *)
    plschr c' 1.;
    plscol0 1 r' g' b';
    plcol0 1
  )
  in
  (* add closure as a layer *)
  p.plots <- Array.append p.plots [|f|];
  (* add legend item to page *)
  _add_legend_item p SCATTER 0 color marker color 0 color;
  if not h.holdon then output h


(* TODO *)

let scatterhist = None


(* other plots *)

let image ?(h=_default_handle) x =
  let open Plplot in
  (* rotate the matrix 90 degree clockwise to be shown correctly as image *)
  let x = Owl_dense_matrix.D.rotate x 90 in
  (* compute necessary parameters *)
  let width, height = Owl_dense_matrix.D.shape x in
  let num_col = Owl_dense_matrix.D.max' x in
  let img = Owl_dense_matrix.D.to_arrays x in
  let width = float_of_int width in
  let height = float_of_int height in
  let num_col = int_of_float num_col in
  (* specify the boundary of imageplot *)
  let x = [|1.0; width|]  in
  let y = [|1.0; height|] in
  _adjust_range h x X;
  _adjust_range h y Y;
  (* keep the scale of original image instead of 4:3 *)
  h.page_size <- (int_of_float width, int_of_float height);
  (* prepare the closure *)
  let p = h.pages.(h.current_page) in
  let _ = p.no_axes <- true in
  let f = (fun () ->
    (* set gray_cmap *)
    let r = [|0.0; 1.0|] in
    let g = [|0.0; 1.0|] in
    let b = [|0.0; 1.0|] in
    let pos = [|0.0; 1.0|] in
    plscmap1n num_col;
    plscmap1l true pos r g b None;
    plimage img 1.0 width 1.0 height 0.0 0.0 1.0 width 1.0 height;
    (* possibly need to restore original settings *)
  )
  in
  p.plots <- Array.append p.plots [|f|];
  if not h.holdon then output h


let spy ?(h=_default_handle) ?(spec=[]) x =
  let xs = Owl_utils.Stack.make () in
  let ys = Owl_utils.Stack.make () in
  let m, n = Owl_dense_matrix.D.shape x in
  
  for i = 0 to m - 1 do
    for j = 0 to n - 1 do
      let a = Owl_dense_matrix.D.get x i j in
      if a <> 0. then (
        Owl_utils.Stack.push xs (float_of_int i);
        Owl_utils.Stack.push ys (float_of_int j);
      )
    done;
  done;

  let x = Owl_utils.Stack.to_array xs in
  let y = Owl_utils.Stack.to_array ys in
  let x = Owl_dense_matrix.D.of_arrays [|x|] in
  let y = Owl_dense_matrix.D.of_arrays [|y|] in
  scatter ~h ~spec x y



(* ends here *)