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Diffstat (limited to 'tex/context/base/mkxl/meta-imp-functions.mkxl')
| -rw-r--r-- | tex/context/base/mkxl/meta-imp-functions.mkxl | 342 |
1 files changed, 342 insertions, 0 deletions
diff --git a/tex/context/base/mkxl/meta-imp-functions.mkxl b/tex/context/base/mkxl/meta-imp-functions.mkxl new file mode 100644 index 000000000..dd20ea8b8 --- /dev/null +++ b/tex/context/base/mkxl/meta-imp-functions.mkxl @@ -0,0 +1,342 @@ +%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 |