examples/ocaml/x29.ml

(*
       Sample plots using date / time formatting for axes

  Copyright (C) 2007 Andrew Ross
  Copyright (C) 2008 Hezekiah M. Carty

  This file is part of PLplot.

    PLplot is free software; you can redistribute it and/or modify
  it under the terms of the GNU Library General Public License as published
  by the Free Software Foundation; either version 2 of the License, or
  (at your option) any later version.

  PLplot is distributed in the hope that it will be useful,
  but WITHOUT ANY WARRANTY; without even the implied warranty of
  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  GNU Library General Public License for more details.

  You should have received a copy of the GNU Library General Public License
  along with PLplot; if not, write to the Free Software
  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA

*)

open Plplot
open Printf

let pi = atan 1.0 *. 4.0

(* Plot a model diurnal cycle of temperature *)
let plot1 () =
  (* Data points every 10 minutes for 1 day *)
  let npts = 73 in

  let xmin = 0.0 in
  let xmax = 60.0 *. 60.0 *. 24.0 in (* Number of seconds in a day *)
  let ymin = 10.0 in
  let ymax = 20.0 in

  let x =
    Array.init npts (fun i -> xmax *. float_of_int i /. float_of_int npts)
  in
  let y =
    Array.init npts (
      fun i ->
        15.0 -. 5.0 *. cos (2.0 *. pi *. (float_of_int i /. float_of_int npts))
    )
  in

  (* Set x error bars to +/- 5 minute *)
  let xerr1 = Array.map (fun xi -> xi -. 60.0 *. 5.0) x in
  let xerr2 = Array.map (fun xi -> xi +. 60.0 *. 5.0) x in
  (* Set y error bars to +/- 0.1 deg C *)
  let yerr1 = Array.map (fun yi -> yi -. 0.1) y in
  let yerr2 = Array.map (fun yi -> yi +. 0.1) y in

  pladv 0;

  (* Rescale major ticks marks by 0.5 *)
  plsmaj 0.0 0.5;
  (* Rescale minor ticks and error bar marks by 0.5 *)
  plsmin 0.0 0.5;

  plvsta ();
  plwind xmin xmax ymin ymax;

  (* Draw a box with ticks spaced every 3 hour in X and 1 degree C in Y. *)
  plcol0 1;
  (* Set time format to be hours:minutes *)
  pltimefmt "%H:%M";
  plbox "bcnstd" (3.0 *. 60.0 *. 60.0) 3 "bcnstv" 1.0 5;

  plcol0 3;
  pllab "Time (hours:mins)" "Temperature (degC)" "#frPLplot Example 29 - Daily temperature";

  plcol0 4;

  plline x y;

  plcol0 2;
  plerrx xerr1 xerr2 y;
  plcol0 3;
  plerry x yerr1 yerr2;

  (* Rescale major / minor tick marks back to default *)
  plsmin 0.0 1.0;
  plsmaj 0.0 1.0;
  ()

(* Plot the number of hours of daylight as a function of day for a year *)
let plot2 () =
  (* Latitude for London *)
  let lat = 51.5 in

  let npts = 365 in

  let xmin = 0.0 in
  let xmax = float_of_int npts *. 60.0 *. 60.0 *. 24.0 in
  let ymin = 0.0 in
  let ymax = 24.0 in

  let x = Array.make npts 0.0 in
  let y = Array.make npts 0.0 in
  (* Formula for hours of daylight from
   * "A Model Comparison for Daylength as a Function of Latitude and
   * Day of the Year", 1995, Ecological Modelling, 80, pp 87-95. *)
  for j = 0 to npts - 1 do
    x.(j) <- float_of_int j *. 60.0 *. 60.0 *. 24.0;
    let p =
      asin (0.39795 *. cos (0.2163108 +. 2.0 *.
        atan (0.9671396 *. tan (0.00860 *. (float_of_int j -. 186.0))))
      )
    in
    let d =
      24.0 -. (24.0 /. pi) *. acos (( sin (0.8333 *. pi /. 180.0) +.
        sin (lat *. pi /. 180.0) *. sin p) /.
        (cos (lat *. pi /. 180.0) *. cos p)
      )
    in
    y.(j) <- d;
  done;

  plcol0 1;
  (* Set time format to be abbreviated month name followed by day of month *)
  pltimefmt "%b %d";
  plprec 1 1;
  plenv xmin xmax ymin ymax 0 40;


  plcol0 3;
  pllab "Date" "Hours of daylight" "#frPLplot Example 29 - Hours of daylight at 51.5N";

  plcol0 4;

  plline x y;

  plprec 0 0;
  ()

let plot3 () =
  (* Calculate seconds since the Unix epoch for 2005-12-01 UTC. *)
  (* Adopt the known result for POSIX-compliant systems. *)
  let tstart = 1133395200.0 in

  let npts = 62 in

  let xmin = tstart in
  let xmax = xmin +. float_of_int npts *. 60.0 *. 60.0 *. 24.0 in
  let ymin = 0.0 in
  let ymax = 5.0 in

  let x =
    Array.init npts (fun i -> xmin +. float_of_int i *. 60.0 *. 60.0 *. 24.0)
  in
  let y =
    Array.init npts (
      fun i ->
        1.0 +. sin (2.0 *. pi *. float_of_int i /. 7.0) +.
        exp (float_of_int (min i (npts - i)) /. 31.0)
    )
  in

  pladv 0;

  plvsta ();
  plwind xmin xmax ymin ymax;

  plcol0 1;
  (* Set time format to be ISO 8601 standard YYYY-MM-DD. Note that this is
     equivalent to %f for C99 compliant implementations of strftime. *)
  pltimefmt "%Y-%m-%d";
  (* Draw a box with ticks spaced every 14 days in X and 1 hour in Y. *)
  plbox "bcnstd" (14.0 *. 24.0 *. 60.0 *. 60.0) 14 "bcnstv" 1.0 4;

  plcol0 3;
  pllab "Date" "Hours of television watched" "#frPLplot Example 29 - Hours of television watched in Dec 2005 / Jan 2006";

  plcol0 4;

  (* Rescale symbol size (used by plpoin) by 0.5 *)
  plssym 0.0 0.5;
  plpoin x y 2;
  plline x y;
  ()

let plot4 () =
  (* TAI-UTC (seconds) as a function of time. *)

  (* Continuous time unit is Besselian years from whatever epoch is
   * chosen below.  Could change to seconds (or days) from the
   * epoch, but then would have to adjust xlabel_step below. *)
  let scale = 365.242198781 in
  (* MJD epoch (see <https://en.wikipedia.org/wiki/Julian_day>).
   * This is only set for illustrative purposes, and is overwritten
   * below for the time-representation reasons given in the
   * discussion below. *)
  let epoch_year  = ref 1858 in
  let epoch_month = ref 11 in
  let epoch_day   = ref 17 in
  let epoch_hour  = ref 0 in
  let epoch_min   = ref 0 in
  let epoch_sec   = ref 0. in
  (* To illustrate the time-representation issues of using the MJD
   * epoch, in 1985, MJD was roughly 46000 days which corresponds to
   * 4e9 seconds.  Thus, for the -DPL_DOUBLE=ON case where PLFLT is
   * a double which can represent continuous time to roughly 16
   * decimal digits of precision the time-representation error is
   * roughly ~400 nanoseconds.  Therefore the MJD epoch would be
   * acceptable for the plots below in the -DPL_DOUBLE=ON case.
   * However, that epoch is obviously not acceptable for the
   * -DPL_DOUBLE=OFF case where PLFLT is a float which can represent
   * continuous time to only ~7 decimal digits of precision
   * corresponding to a time representation error of 400 seconds (!)
   * in 1985.  For this reason, we do not use the MJD epoch below
   * and instead choose the best epoch for each case to minimize
   * time-representation issues. *)

  let xmin = ref 0.0 in
  let xmax = ref 0.0 in
  let npts = ref 0 in
  let ymin = ref 0.0 in
  let ymax = ref 0.0 in
  let time_format = ref "" in
  let if_TAI_time_format = ref false in
  let title_suffix = ref "" in
  let xtitle = ref "" in
  let xlabel_step = ref 0.0 in

  for kind = 0 to 6 do
    let () =
      match kind with
      | 0 ->
          (* Choose midpoint to maximize time-representation precision. *)
          epoch_year  := 1985;
          epoch_month := 0;
          epoch_day   := 2;
          epoch_hour  := 0;
          epoch_min   := 0;
          epoch_sec   := 0.;
          plconfigtime scale 0. 0. 0x0 true !epoch_year !epoch_month !epoch_day !epoch_hour !epoch_min !epoch_sec;
          xmin := plctime 1950 0 2 0 0 0.0;
          xmax := plctime 2020 0 2 0 0 0.0;
          npts := 70 * 12 + 1;
          ymin := 0.0;
          ymax := 36.0;
          time_format := "%Y%";
          if_TAI_time_format := true;
          title_suffix := "from 1950 to 2020";
          xtitle := "Year";
          xlabel_step := 10.0;
      | 1
      | 2 ->
          (* Choose midpoint to maximize time-representation precision. *)
          epoch_year  := 1961;
          epoch_month := 7;
          epoch_day   := 1;
          epoch_hour  := 0;
          epoch_min   := 0;
          epoch_sec   := 1.64757;
          plconfigtime scale 0. 0. 0x0 true !epoch_year !epoch_month !epoch_day !epoch_hour !epoch_min !epoch_sec;
          xmin := plctime 1961 7 1 0 0 (1.64757 -. 0.20);
          xmax := plctime 1961 7 1 0 0 (1.64757 +. 0.20);
          npts := 1001;
          ymin := 1.625;
          ymax := 1.725;
          time_format := "%S%2%";
          title_suffix := "near 1961-08-01 (TAI)";
          xlabel_step := 0.05 /. (scale *. 86400.0);
          if kind = 1 then (
            if_TAI_time_format := true;
            xtitle := "Seconds (TAI)";
          )
          else (
            if_TAI_time_format := false;
            xtitle := "Seconds (TAI) labelled with corresponding UTC";
          )
      | 3
      | 4 ->
          (* Choose midpoint to maximize time-representation precision. *)
          epoch_year  := 1963;
          epoch_month := 10;
          epoch_day   := 1;
          epoch_hour  := 0;
          epoch_min   := 0;
          epoch_sec   := 2.6972788;
          plconfigtime scale 0. 0. 0x0 true !epoch_year !epoch_month !epoch_day !epoch_hour !epoch_min !epoch_sec;
          xmin := plctime 1963 10 1 0 0 (2.6972788 -. 0.20);
          xmax := plctime 1963 10 1 0 0 (2.6972788 +. 0.20);
          npts := 1001;
          ymin := 2.55;
          ymax := 2.75;
          time_format := "%S%2%";
          title_suffix := "near 1963-11-01 (TAI)";
          xlabel_step := 0.05 /. (scale *. 86400.0);
          if kind = 3 then (
            if_TAI_time_format := true;
            xtitle := "Seconds (TAI)";
          )
          else (
            if_TAI_time_format := false;
            xtitle := "Seconds (TAI) labelled with corresponding UTC";
          )
      | 5
      | 6 ->
          (* Choose midpoint to maximize time-representation precision. *)
          epoch_year  := 2009;
          epoch_month := 0;
          epoch_day   := 1;
          epoch_hour  := 0;
          epoch_min   := 0;
          epoch_sec   := 34.;
          plconfigtime scale 0. 0. 0x0 true !epoch_year !epoch_month !epoch_day !epoch_hour !epoch_min !epoch_sec;
          xmin := plctime 2009 0 1 0 0 (34.0 -. 5.0);
          xmax := plctime 2009 0 1 0 0 (34.0 +. 5.0);
          npts := 1001;
          ymin := 32.5;
          ymax := 34.5;
          time_format := "%S%2%";
          title_suffix := "near 2009-01-01 (TAI)";
          xlabel_step := 1.0 /. (scale *. 86400.0);
          if kind = 5 then (
            if_TAI_time_format := true;
            xtitle := "Seconds (TAI)";
          )
          else (
            if_TAI_time_format := false;
            xtitle := "Seconds (TAI) labelled with corresponding UTC";
          )
      | _ -> failwith "Bad plot kind"
    in

    let x = Array.make 1001 0.0 in
    let y = Array.make 1001 0.0 in

    (* Printf.printf "%s%d\n" "npts = " !npts; *)
    for i = 0 to !npts - 1 do
      x.(i) <-
        !xmin +. float_of_int i *. (!xmax -. !xmin) /. (float_of_int (!npts - 1));
      let tai = x.(i) in
      (*Printf.printf "%g\n" tai; *)
      plconfigtime scale 0. 0. 0x0 true !epoch_year !epoch_month !epoch_day !epoch_hour !epoch_min !epoch_sec;
      let tai_year, tai_month, tai_day, tai_hour, tai_min, tai_sec = plbtime tai in
      (* Calculate residual using tai as the epoch to nearly maximize time-representation precision. *)
      plconfigtime scale 0. 0. 0x0 true tai_year tai_month tai_day tai_hour tai_min tai_sec;
      (* Calculate continuous tai with new epoch. *)
      let tai_new = plctime tai_year tai_month tai_day tai_hour tai_min tai_sec in
      (* Calculate broken-down utc (with leap seconds inserted) from continuous tai with new epoch. *)
      plconfigtime scale 0. 0. 0x2 true tai_year tai_month tai_day tai_hour tai_min tai_sec;
      let utc_year, utc_month, utc_day, utc_hour, utc_min, utc_sec = plbtime tai_new in
      (* Calculate continuous utc from broken-down utc using same epoch as for the continuous tai. *)
      plconfigtime scale 0. 0. 0x0 true tai_year tai_month tai_day tai_hour tai_min tai_sec;
      let utc = plctime utc_year utc_month utc_day utc_hour utc_min utc_sec in
      (* Convert residuals to seconds. *)
      y.(i) <- (tai_new -. utc) *. scale *. 86400.0;
    done;

    pladv 0;
    plvsta ();
    plwind !xmin !xmax !ymin !ymax;
    plcol0 1;
    plconfigtime scale 0. 0.
      (if !if_TAI_time_format then 0x0 else 0x2)
    true !epoch_year !epoch_month !epoch_day !epoch_hour !epoch_min !epoch_sec;
    pltimefmt !time_format;
    plbox "bcnstd" !xlabel_step 0 "bcnstv" 0.0 0;
    plcol0 3;
    let title = sprintf "#frPLplot Example 29 - TAI-UTC %s" !title_suffix in
    pllab !xtitle "TAI-UTC (sec)" title;

    plcol0 4;

    plline (Array.sub x 0 !npts) (Array.sub y 0 !npts);
  done;
  ()

(*--------------------------------------------------------------------------*\
 * Draws several plots which demonstrate the use of date / time formats for
 * the axis labels.
\*--------------------------------------------------------------------------*)
let () =
  (* Parse command line arguments *)
  plparseopts Sys.argv [PL_PARSE_FULL];

  (* Initialize plplot *)
  plinit ();

  plot1 ();

  plot2 ();

  plot3 ();

  plot4 ();

  (* Don't forget to call plend() to finish off! *)
  plend();
  ()