%D \module
%D   [       file=meta-imp-functions,
%D        version=2022.05.17,
%D          title=\METAPOST\ Graphics,
%D       subtitle=All kind of functions,
%D         author=Mikael Sundqvist & Hans Hagen,
%D           date=\currentdate,
%D      copyright={PRAGMA ADE \& \CONTEXT\ Development Team}]
%C
%C This module is part of the \CONTEXT\ macro||package and is
%C therefore copyrighted by \PRAGMA. See mreadme.pdf for
%C details.

% \useMPlibrary[functions]

% todo: as with contours, cache

\registerctxluafile{meta-imp-functions}{autosuffix}

\startMPextensions
    newscriptindex mfid_processfunction ; mfid_processfunction := scriptindex("processfunction") ;

    presetparameters "function" [ name = "unknown", smoothen = false, maxpath = 65536 ] ;

    def lmt_processfunction = applyparameters "function" "lmt_do_processfunction" enddef ;

    vardef lmt_do_processfunction =
        if getparameter "function" "smoothen" :
            for k within (runscript mfid_processfunction) : pathpoint .. endfor nocycle
        else :
            (runscript mfid_processfunction)
        fi
    enddef ;
\stopMPextensions

\continueifinputfile{meta-imp-functions.mkxl}

\starttext

\startluacode
    mp.registeraction {
        name   = "ms2",
        action = function(t, x, y)
            return -y, x
        end
    }
\stopluacode

\startMPpage
    path p ; p := lmt_processfunction [
        name = "rungekutta"
        lua  = "ms2",
        x    = 1,
        y    = 0,
        tmax = 6pi,
        dt   = 0.001,
        eps  = 0.00001,
    ] xysized (5cm,5cm) ;
    draw       p withcolor red withpen pencircle scaled 1 ;
    path q ; q := for i within p : pathpoint .. endfor nocycle ;
    draw       q withcolor green withpen pencircle scaled 1/2 ;
\stopMPpage

%

\startluacode
    mp.registeraction {
        name   = "ms3",
        action = function(t, x, y)
            return 1, -t*y*y
        end
    }
\stopluacode

\startMPpage
    path p ; p := lmt_processfunction [
        name = "rungekutta"
        lua  = "ms3",
        x    = 0,
        y    = 2,
        tmax = 10,
        dt   = 0.001,
        eps  = 0.00001,
    ] xysized (5cm,5cm) ;
    draw       p withcolor red withpen pencircle scaled  6 ;
\stopMPpage

%

\startluacode
    mp.registeraction {
        name   = "ms4",
        action = function(t, x, y)
            return 1, -y
        end
    }
\stopluacode

\startMPpage
    path p ; p := lmt_processfunction [
        name = "rungekutta"
        lua  = "ms4",
        x    = 0,
        y    = 1,
        tmax = 10,
        dt   = 0.001,
        eps  = 0.00001,
    ] scaled 5cm ;
    draw       p withcolor red withpen pencircle scaled  6 ;
\stopMPpage

%

\startluacode
    mp.registeraction {
        name   = "ms5",
        action = function(t, x, y)
            return x + y + x*x + y*y, x - y - x*x + y*y
        end
    }
\stopluacode

\startMPpage
    path b ; numeric s;

    s := 1cm ;
    b := ((-2.5,-2.5) -- (1.5,-2.5) -- (1.5,1.5) -- (-2.5,1.5) -- cycle) scaled s ;

    for i = -3.05 step 0.1 until 2.5 :
        for j = -3.05 step 0.1 until 2.5 :
            draw lmt_processfunction [
                name = "rungekutta",
                lua  = "ms5",
                x    = i,
                y    = j,
                tmax = 10,
                dt   = 0.1,
                eps  = 0.001,
                smoothen = true,
                maxpath  = 500, % crazy large paths .. so kind of bad spec here
            ]
                scaled s
                withpen pencircle scaled  0.1
                withcolor (uniformdeviate(1),uniformdeviate(1),uniformdeviate(1))
            ;
        endfor ;
    endfor ;

    % so how much slack ?

    draw b withpen pencircle scaled 2 ;
    clip currentpicture to b ;

\stopMPpage

% https://wolfram.com/xid/0dekz2-wla

\startluacode
    mp.registeraction {
        name   = "mma1",
        action = function(t, x, y)
            return 1, y*math.cos(x+y)
        end
    }
\stopluacode

\startMPpage
    path p ; p := lmt_processfunction [
        name = "rungekutta"
        lua  = "mma1",
        x    = 0,
        y    = 1,
        tmax = 30,
        dt   = 0.001,
        eps  = 0.00001,
    ] xysized(10cm,5cm) ;
    draw p withcolor red withpen pencircle scaled  2 ;
    drawpoints p withcolor blue withpen pencircle scaled 2 ;
\stopMPpage

% https://wolfram.com/xid/0dekz2-gpx

\startluacode
    mp.registeraction {
        name   = "mma2",
        action = function(t, x, y)
            return -y-x*x, 2*x-y*y*y
        end
    }
\stopluacode

\startMPpage
    path p ; p := lmt_processfunction [
        name = "rungekutta"
        lua  = "mma2",
        x    = 1,
        y    = 1,
        tmax = 20,
        dt   = 0.001,
        eps  = 0.00001,
    ] xysized(10cm,10cm) ;
    draw p withcolor red withpen pencircle scaled  2 ;
    drawpoints p withcolor blue withpen pencircle scaled 2 ;
\stopMPpage

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% https://wolfram.com/xid/0dekz2-xixft

\startluacode
    mp.registeraction {
        name   = "mma3",
        action = function(t, x, y)
            return y, -0.1 * y - math.sin(x) + 0.5 * math.cos(t)
        end
    }
\stopluacode

\startMPpage
    path p ; p := lmt_processfunction [
        name    = "rungekutta"
        lua     = "mma3",
        x       = 0,
        y       = 0,
        tmax    = 100,
        dt      = 0.001,
        eps     = 0.00001,
    ] xysized(10cm,10cm) ;
    draw p withcolor red withpen pencircle scaled  2 ;
    drawpoints p withcolor blue withpen pencircle scaled 2 ;
\stopMPpage

% https://wolfram.com/xid/0dekz2-dmilmp
% Stiff! Not working!

% \startluacode
%     mp.registeraction {
%         name   = "mma4",
%         action = function(t, x, y)
%             return y, - x + 1000 * (1 - x * x) * y
%         end
%     }
% \stopluacode

% \startMPpage % [instance=decimalfun]
%     path p ; p := lmt_processfunction [
%         name = "rungekutta"
%         lua  = "mma4",
%         x    = 2,
%         y    = 0,
%         tmax = 2000,
%         dt   = 0.01,
%         eps  = 0.0001
%     ] xynormalized(10cm,10cm) ;
%     draw p
%         withpen pencircle scaled 2
%         withcolor red
%     ;
%     %     drawpoints p withcolor blue withpen pencircle scaled 2 ;
% \stopMPpage

% https://wolfram.com/xid/0dekz2-d1orb
% Discontinuous right-hand side

\startluacode
    mp.registeraction {
        name   = "mma5",
        action = function(t, x, y)
            return 1, - math.cos(y) + math.floor(t)
        end
    }
\stopluacode

\startMPpage
    save n ; n := 0 ;
    for i = "xy", "tx", "ty" :
        path p ; p := lmt_processfunction [
            name    = "rungekutta",
            type    = i,
            lua     = "mma5",
            x       = 0,
            y       = 1,
            tmax    = 3,
            dt      = 0.001,
            eps     = 0.0001,
        ] xysized(10cm,10cm) shifted (n*11cm,0) ;
        draw p withcolor red withpen pencircle scaled  2 ;
        drawpoints p withcolor blue withpen pencircle scaled 2 ;
        n := n + 1 ;
    endfor ;
\stopMPpage

\startluacode
    mp.registeraction {
        name   = "mma6",
        action = function(t, x, y)
            return y, -x
        end
    }
\stopluacode

\startMPpage
    save n ; n := 0 ;
    for i = "xy", "tx", "ty" :
        path p ; p := lmt_processfunction [
            name    = "rungekutta",
            kind    = i,
            lua     = "mma6",
            x       = 1,
            y       = 0,
            tmin    = 0,
            tmax    = 6.28,
            dt      = 0.001,
            eps     = 0.0000001,
        ] xysized(10cm,10cm) shifted (n*11cm,0) ;
        draw p withcolor red withpen pencircle scaled  2 ;
        drawpoints p withcolor blue withpen pencircle scaled 2 ;
        n := n + 1 ;
    endfor ;
\stopMPpage

\startMPpage
    save n ; n := 0 ;
    for i = "xy", "tx", "ty" :
        path p ; p  := lmt_processfunction [
            name     = "rungekutta",
            kind     = i,
            lua      = "mma6",
            x        = 1,
            y        = 0,
            tmin     = 0,
            tmax     = 6,
            stepsize = "fixed",
            dt       = 0.5,
            maxpath  = 3,
        ] xysized(10cm,10cm) shifted (n*11cm,0) ;
        draw p withcolor red withpen pencircle scaled  2 ;
        drawpoints p withcolor blue withpen pencircle scaled 2 ;
        n := n + 1 ;
    endfor ;
\stopMPpage

\stoptext