On Sun, Oct 7, 2018 at 7:14 PM Alan Braslau wrote:

On Sun, 7 Oct 2018 17:25:35 +0200 "Mikael P. Sundqvist" wrote:

...

ContourPlot[2 x^5 + x y + y^5 == 0, {x, 0, 2}, {y, -2, 1/2}]

Brut force:

\startTEXpage \startMPcode {doublefun} pen savedpen ; savedpen := currentpen ; pickup pencircle scaled .01 ; path p ; p := for i=0 upto 1000 : for j=0 upto 1000 : hide(x := 2i/1000 ; y := 2.5j/1000 - 2 ;) if abs(2*(x**5)+x*y+y**5) < .002i/1000 : (x,y) .. fi endfor endfor cycle ; draw subpath (0,length p - 1) of p ; setbounds currentpicture to (0,-2)--(2,-2)--(2,.5)--(0,.5)--cycle ; currentpicture := currentpicture xsized 5cm ; pickup savedpen ;

picture pic ; pic := currentpicture ; drawarrow llcorner pic--lrcorner pic ; drawarrow llcorner pic--ulcorner pic ; label.rt ("$x$", lrcorner pic) ; label.top("$y$", ulcorner pic) ; for x=0 step .5 until 2 : label.bot(decimal x,(x/2)[llcorner pic,lrcorner pic]) ; endfor for y=0 step .5 until 2.5 : label.lft(decimal (y-2),(y/2.5)[llcorner pic,ulcorner pic]) ; endfor \stopMPcode \stopTEXpage

Alan

Thanks both to luigi and to Alan! I'm impressed by your brute force method, Alan! In particular it learned me the "hide" command. I feel a bit ashamed. Earlier today I answered something else giving a reference to the metafun manual. Now I'm here not reading it carefully enough myself. In the helpers section it is clearly written how to import and plot data. Thus, I exported the data from the Mathematica plot (that file is pasted below in case anyone wants to try this themselves, sorry in advance for the big amount of text it generates in this email) and then importing it just worked fine. I like Alan's method very much, but it takes some time during compilation, so I will probably stick with importing. Working code below (where one can see that Alan's method is indeed working fine, at least with this example). Again, thanks to both luigi and Alan! \starttext \startTEXpage[offset=2bp] \startMPcode{doublefun} pen savedpen ; savedpen := currentpen ; pickup pencircle scaled .01 ; lua("MP = { } MP.data = table.load('mmadata.txt')") ; numeric n ; lua("mp.print('n := ',\#MP.data)") ; path mycurve; mycurve := lua("mp.pair(MP.data[1])") for i=2 upto n : .. lua("mp.pair(MP.data[" & decimal i & "])") endfor; draw mycurve withcolor darkred withpen pencircle scaled 0.04; path p ; p := for i=0 upto 1000 : for j=0 upto 1000 : hide(x := 2i/1000 ; y := 2.5j/1000 - 2 ;) if abs(2*(x**5)+x*y+y**5) < .002i/1000 : (x,y) .. fi endfor endfor cycle ; draw subpath (0,length p - 1) of p ; setbounds currentpicture to (0,-2)--(2,-2)--(2,.5)--(0,.5)--cycle ; currentpicture := currentpicture xsized 5cm ; pickup savedpen ; picture pic ; pic := currentpicture ; drawarrow llcorner pic--lrcorner pic ; drawarrow llcorner pic--ulcorner pic ; label.rt ("$x$", lrcorner pic) ; label.top("$y$", ulcorner pic) ; for x=0 step .5 until 2 : label.bot(decimal x,(x/2)[llcorner pic,lrcorner pic]) ; endfor for y=0 step .5 until 2.5 : label.lft(decimal (y-2),(y/2.5)[llcorner pic,ulcorner pic]) ; endfor \stopMPcode \stopTEXpage \stoptext %%% mmadata.txt %%% return {{1.7781332646374535, -2.0}, {1.7768209908069152, -1.9983615165933983}, {1.775510204081634, -1.9967215415115265}, {1.7664030082433901, -1.985873790716172}, {1.7568733335567501, -1.9744897959183674}, {1.7559890220139953, -1.973381069421283}, {1.7551020408163278, -1.9722667987462739}, {1.7455791311458495, -1.9608832289248324}, {1.7356495451060165, -1.9489795918367347}, {1.7351734376993888, -1.9483801416512756}, {1.7346938775510217, -1.9477751961654046}, {1.7247720468786834, -1.9358716760955252}, {1.714463398255413, -1.9234693877551021}, {1.7142857142857155, -1.9232445076564075}, {1.7093814232165505, -1.9173390239186459}, {1.7039827159442558, -1.910837931600294}, {1.6938775510204094, -1.8986359463002893}, {1.6935950869756253, -1.8983122637294494}, 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{0.2040816326530612, -0.0034693311989266035}, {0.19827874791776576, -0.002950475713535316}, {0.18962026246209016, -0.002770590289735809}, {0.18367346938775508, -0.002276228754648394}, {0.17695870487613444, -0.0018106259931288168}, {0.16994475754904617, -0.0018547673494080982}, {0.16326530612244897, -0.0014210391046479282}, {0.15592141581127092, -0.001024218743682052}, {0.1500574537158482, -0.001203693059272969}, {0.14285714285714285, -0.0008329879260291356}, {0.13509232585153358, -0.0004980603756430477}, {0.1299958383315521, -0.0007705082080104071}, {0.12244897959183673, -0.00044962729960941125}, {0.11441150696269169, -0.00015724084622331484}, {0.10979505323831777, -0.0005112854929206802}, {0.10204081632653061, -0.00021683572040633557}, {0.093829631052776, 0.00005989995953862605}, {0.08948471441215075, -0.0003890049439967871}, {0.08163265306122448, -0.00008881812385440856}, {0.07330397446341344, 0.00020676661460917144}, {0.06908320845627795, -0.00038068330720514645}, {0.061224489795918366, -0.00002810596445531298}, {0.05279149292677095, 0.000337164453779645}, {0.0485800339458205, -0.0004994473636443092}, {0.04081632653061224, 0}, {0.03222508810558834, 0.000534966398625247}, {0.027827852574969683, -0.0009294699955751749}, {0.02040816326530612, 0}, {0.011337910781976428, 0.0011337339715074921}, {0, -0.010204027425056751}, {0., 0.002538576406170707}} %%% End of file

On Sun, 7 Oct 2018, Hans Hagen wrote:

On 10/7/2018 7:14 PM, Alan Braslau wrote:

...

On Sun, 7 Oct 2018 17:25:35 +0200 "Mikael P. Sundqvist" wrote:

...

ContourPlot[2 x^5 + x y + y^5 == 0, {x, 0, 2}, {y, -2, 1/2}]

Brut force: [...]

as this takes some time here's a cheat:

\starttext

\startbuffer[demo] [...] \stopbuffer

\startTEXpage \typesetbuffer[demo] \stopTEXpage \stoptext

a next run the already prepared buffer will be taken unles it has been changed.

I thought that this will also be a good usecase of showing Lua+MP interaction. I wrote the code below following the metafun manual, but I cannot get it to compile. What am I missing? \startluacode local f = function(x, y) return 2*x^5 + x*y + y^5 end local abs = math.abs contour = { } function contour.generate(x_min, x_max, y_min, y_max) local pts = { } local length = 1000 local eps = 1e-3 for xi = x_min, x_max, (x_max - x_min)/length do for yi = y_min, y_max, (y_max - y_min)/length do if abs(f(xi,yi)) < eps then pts[#pts + 1] = {xi, yi} end end end return pts end contour.data = contour.generate(0, 2, -1, 0.5) function contour.n() mp.print(#contour.data) end function contour.point(i) mp.pair(contour.data[i]) end \stopluacode \starttext \startMPpage[instance=doublefun] pen savedpen ; savedpen := currentpen ; pickup pencircle scaled .01 ; p := for i = 1 upto lua.contour.n() : lua.contour.point(i) .. endfor cycle; draw subpath (0,length p - 1) of p ; setbounds currentpicture to (0,-2)--(2,-2)--(2,.5)--(0,.5)--cycle ; currentpicture := currentpicture xsized 5cm ; pickup savedpen ; picture pic ; pic := currentpicture ; drawarrow llcorner pic--lrcorner pic ; drawarrow llcorner pic--ulcorner pic ; label.rt ("$x$", lrcorner pic) ; label.top("$y$", ulcorner pic) ; for x=0 step .5 until 2 : label.bot(decimal x,(x/2)[llcorner pic,lrcorner pic]) ; endfor ; for y=0 step .5 until 2.5 : label.lft(decimal (y-2),(y/2.5)[llcorner pic,ulcorner pic]) ; endfor ; \stopMPpage \stoptext I get an error: ! Missing argument to lua. <to be read again> contour <*> ...caled .01 ; p := for i = 1 upto lua.contour .n() : lua.contour.point(i... That macro has more parameters than you thought. I'll continue by pretending that each missing argument is either zero or null. Thanks, Aditya

On Mon, 8 Oct 2018, Alan Braslau wrote:

On Mon, 8 Oct 2018 16:00:10 -0400 (EDT) Aditya Mahajan wrote:

...

On Sun, 7 Oct 2018, Hans Hagen wrote:

...

On 10/7/2018 7:14 PM, Alan Braslau wrote:

...

On Sun, 7 Oct 2018 17:25:35 +0200 "Mikael P. Sundqvist" wrote:

...

ContourPlot[2 x^5 + x y + y^5 == 0, {x, 0, 2}, {y, -2, 1/2}]

Brut force: [...]

as this takes some time here's a cheat:

\starttext

\startbuffer[demo] [...] \stopbuffer

\startTEXpage \typesetbuffer[demo] \stopTEXpage \stoptext

a next run the already prepared buffer will be taken unles it has been changed.

I thought that this will also be a good usecase of showing Lua+MP interaction. I wrote the code below following the metafun manual, but I cannot get it to compile. What am I missing?

You need to put it into the mp namespace:

Thanks. The metafun manual is confusing in this regard and I got the impression that any lua namespace could be used.

(then eps should be made a linear function of xi)

Oh, I missed that. Thanks.

(and, indeed this is much faster than calculating in MP)

Yes. Iterating over 10^6 values on a 1GHz computer should roughly take 1ms in any reasonable programming language. Metapost for loops work with macro expansion, which can be very expensive for large loops. Aditya

On Mon, 8 Oct 2018, Aditya Mahajan wrote:

On Mon, 8 Oct 2018, Alan Braslau wrote:

...

On Mon, 8 Oct 2018 16:00:10 -0400 (EDT) Aditya Mahajan wrote:

...

On Sun, 7 Oct 2018, Hans Hagen wrote:

...

On 10/7/2018 7:14 PM, Alan Braslau wrote:

...

On Sun, 7 Oct 2018 17:25:35 +0200 "Mikael P. Sundqvist" wrote:

...

ContourPlot[2 x^5 + x y + y^5 == 0, {x, 0, 2}, {y, -2, 1/2}]

Here is a proof of concept implementation in Lua + MP so that you can use: \ContourPlot [ function=2*x^5 + x*y + y^5, x={0, 2}, y={-2, 0.5}, n=1000, % Number of discretization points ] The code is fairly fast. But be careful. As with all ConTeXt key-value assignment, `x = { ...}` is different from `x={...}`. I am being a bit lazy here, and haven't adapted the metapost code to draw the axes to adapt to the function. \define\ContourPlot {\dosingleargument\doContourPlot} \def\doContourPlot[#1]% {\setvariables[ContourPlot][#1]% \ctxlua{userdata.contourplot( function(x,y) return \getvariable{ContourPlot}{function} end, {\getvariable{ContourPlot}{x}}, {\getvariable{ContourPlot}{y}}, \getvariable{ContourPlot}{n})}% \useMPgraphic{doublefun::ContourPlot}} \startluacode userdata = userdata or { } local abs = math.abs local data = { } local eps = 1e-3 function userdata.contourplot(f, xlim, ylim, length) local n = 0 data = { } for x = xlim[1], xlim[2], (xlim[2] - xlim[1])/length do for y = ylim[1], ylim[2], (ylim[2] - ylim[1])/length do if abs(f(x,y)) < eps*x then n = n + 1 data[n] = {x, y} end end end end function mp.ContourPath() mp.path(data) end \stopluacode \startuseMPgraphic{doublefun::ContourPlot} draw lua.mp.ContourPath() withpen pencircle scaled .01 ; % This needs to be fixed to adapt to the function. setbounds currentpicture to (0,-2)--(2,-2)--(2,.5)--(0,.5)--cycle ; currentpicture := currentpicture xsized 5cm ; picture pic ; pic := currentpicture ; drawarrow llcorner pic--lrcorner pic ; drawarrow llcorner pic--ulcorner pic ; label.rt ("$x$", lrcorner pic) ; label.top("$y$", ulcorner pic) ; for x=0 step .5 until 2 : label.bot(decimal x,(x/2)[llcorner pic,lrcorner pic]) ; endfor ; for y=0 step .5 until 2.5 : label.lft(decimal (y-2),(y/2.5)[llcorner pic,ulcorner pic]) ; endfor ; \stopuseMPgraphic \starttext \ContourPlot [ function=2*x^5 + x*y + y^5, x={0, 2}, y={-2, 0.5}, n=1000, ] \stoptext \endinput \starttext \startMPpage[instance=doublefun] pen savedpen ; savedpen := currentpen ; pickup pencircle scaled .01 ; p := for i = 1 upto lua.contour.n() : lua.contour.point(i) .. endfor cycle; draw subpath (0,length p - 1) of p ; setbounds currentpicture to (0,-2)--(2,-2)--(2,.5)--(0,.5)--cycle ; currentpicture := currentpicture xsized 5cm ; pickup savedpen ; picture pic ; pic := currentpicture ; drawarrow llcorner pic--lrcorner pic ; drawarrow llcorner pic--ulcorner pic ; label.rt ("$x$", lrcorner pic) ; label.top("$y$", ulcorner pic) ; for x=0 step .5 until 2 : label.bot(decimal x,(x/2)[llcorner pic,lrcorner pic]) ; endfor ; for y=0 step .5 until 2.5 : label.lft(decimal (y-2),(y/2.5)[llcorner pic,ulcorner pic]) ; endfor ; \stopMPpage \stoptext

On Tue, 9 Oct 2018, Alan Braslau wrote:

On Mon, 8 Oct 2018 17:56:24 -0400 (EDT) Aditya Mahajan wrote:

...

Here is a proof of concept implementation in Lua + MP so that you can use:

\ContourPlot [ function=2*x^5 + x*y + y^5, x={0, 2}, y={-2, 0.5}, n=1000, % Number of discretization points ]

The code is fairly fast. But be careful. As with all ConTeXt key-value assignment, `x = { ...}` is different from `x={...}`. I am being a bit lazy here, and haven't adapted the metapost code to draw the axes to adapt to the function.

Hans and I played with Aditya's demonstration, to complete the example. It demonstrates some fun lua+MP+ConTeXt tricks:

Looking at lua-mplib.mpvi, isn't it better to use MP namespace (instead of mp) for user defined functions? The metafun manual says that one can omit the prefix `lua` and simply use `mp` or `MP`. That does not seem to work. Aditya

Wow! This is cool! I must admit I do not get how the connections between MetaPost and Lua works, but it seem to work fine. Challenge: To do this for a more complicated closed and self-intersecting curve like the Bernoulli lemniscate, say (x^2+y^2)^2=x^2-y^2 (a good domain could be -1.5 wrote:

On 10/8/2018 11:25 PM, Aditya Mahajan wrote:

...

On Mon, 8 Oct 2018, Alan Braslau wrote:

...

On Mon, 8 Oct 2018 16:00:10 -0400 (EDT) Aditya Mahajan wrote:

...

On Sun, 7 Oct 2018, Hans Hagen wrote:

...

On 10/7/2018 7:14 PM, Alan Braslau wrote:

...

On Sun, 7 Oct 2018 17:25:35 +0200 "Mikael P. Sundqvist" wrote:

> ContourPlot[2 x^5 + x y + y^5 == 0, {x, 0, 2}, {y, -2, 1/2}]

Brut force: [...]

as this takes some time here's a cheat:

\starttext

\startbuffer[demo] [...] \stopbuffer

\startTEXpage \typesetbuffer[demo] \stopTEXpage \stoptext

a next run the already prepared buffer will be taken unles it has been changed.

I thought that this will also be a good usecase of showing Lua+MP interaction. I wrote the code below following the metafun manual, but I cannot get it to compile. What am I missing?

You need to put it into the mp namespace:

Thanks. The metafun manual is confusing in this regard and I got the impression that any lua namespace could be used.

...

(then eps should be made a linear function of xi)

Oh, I missed that. Thanks.

...

(and, indeed this is much faster than calculating in MP)

Yes. Iterating over 10^6 values on a 1GHz computer should roughly take

hm, my 3.4 gig laptop cpu needs 0.18 sec for the slightly more that i million steps ... it depends on the function too

...

1ms in any reasonable programming language. Metapost for loops work with macro expansion, which can be very expensive for large loops.

generalized:

\startluacode ----- abs = math.abs

local contour = { } local data = { } local origin = { 0, 0 } local length = 0

local function generate(f, x_min, x_max, y_min, y_max) local points = { } local length = 1000 local eps = 1e-3 local spe = -eps local n = 0 local code = "return function(x,y) return " .. f .. " end" local action = load(code) if action then action = action() end for xi = x_min, x_max, (x_max - x_min)/length do for yi = y_min, y_max, (y_max - y_min)/length do -- if abs(action(xi,yi)) < eps then -- 10% gain with: local v = action(xi,yi) if v < eps and v > spe then n = n + 1 points[n] = { xi, yi } end end end return points, n end

function mp.Countour(...) data, length = generate(...) end

function mp.ContourN() mp.print(length) end

function mp.ContourPoint(i) mp.pair(data[i] or origin) end

function mp.ContourPath(f,...) if f then data, length = generate(f,...) end mp.path(length > 0 and data or origin) end

\stopluacode

\starttext \startMPpage[instance=doublefun] % lua.mp.Countour("2*x^5 + x*y + y^5", 0, 2, -1, 0.5) ; % draw lua.mp.ContourPath() withpen pencircle scaled .01 ; draw lua.mp.ContourPath("2*x^5 + x*y + y^5", 0, 2, -1, 0.5) withpen pencircle scaled .01 ; setbounds currentpicture to (0,-2) -- (2,-2) -- (2,.5) -- (0,.5) -- cycle ; currentpicture := currentpicture xsized 5cm ; picture pic ; pic := currentpicture ; drawarrow llcorner pic -- lrcorner pic ; drawarrow llcorner pic -- ulcorner pic ; label.rt ("$x$", lrcorner pic) ; label.top("$y$", ulcorner pic) ; for x=0 step .5 until 2 : label.bot(decimal x,(x/2)[llcorner pic,lrcorner pic]) ; endfor ; for y=0 step .5 until 2.5 : label.lft(decimal (y-2),(y/2.5)[llcorner pic,ulcorner pic]) ; endfor ; \stopMPpage \stoptext

----------------------------------------------------------------- Hans Hagen | PRAGMA ADE Ridderstraat 27 | 8061 GH Hasselt | The Netherlands tel: 038 477 53 69 | www.pragma-ade.nl | www.pragma-pod.nl -----------------------------------------------------------------

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