Überarbeitungsverlauf[Zurück]
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6 |
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Geht einigermaßen mit Lua.
\begin{filecontents*}{1.dat}
spalteB spalteA
1 2
3 2
-4 15
5 12
-30 10
20 1
30 2
5 8
-4 3
6 4
7 12
8 1
45 9
-3 45
2 45
4 23
6 56
-8 23
12 12
56 12
6 4
-7 66
76 2
3 12
-2 7
4 3
6 2
-8 1
-12 1
-56 1
-64 3
-7 77
-76 43
1 34
5 23
7 23
12 2
45 2
\end{filecontents*}
\documentclass{article}
\usepackage{pgfplots}
\usepgfplotslibrary{statistics}
\usepackage{luacode}
\begin{luacode*}
-- http://lua-users.org/wiki/SplitJoin
function string:split(sep)
local sep, fields = sep or ":", {}
local pattern = string.format("([^%s]+)", sep)
self:gsub(pattern, function(c) fields[#fields+1] = c end)
return fields
end
function read_table(fname)
local tab = {}
for line in io.lines(fname) do
local fields = line:split(' ')
local _x, _y = fields[1], fields[2]
local x, y = tonumber(_x), tonumber(_y)
if x and y then
tab[#tab+1] = { x = x, y = y }
end
end
return tab
end
function generate_table(tab)
tex.sprint("{\r")
tex.sprint("x y\r")
for i = 1, #tab do
tex.sprint(tab[i].x .. " " .. tab[i].y .. "\r")
end
tex.sprint("}")
end
function generate_hist(tab,xmin,xmax,Nx,ymin,ymax,Ny)
local xstep = (xmax - xmin) / (Nx-1)
local ystep = (ymax - ymin) / (Ny-1)
tex.sprint("{\r")
tex.sprint("x y z\r")
for x = xmin,xmax,xstep do
for y = ymin,ymax,ystep do
local bins = 0
for i = 1,#tab do
if (x-xstep/2 <= tab[i].x and tab[i].x < x+xstep/2) and
(y-ystep/2 <= tab[i].y and tab[i].y < y+ystep/2) then
bins = bins + 1
end
end
tex.sprint(x .. " " .. y .. " " .. bins .. "\r")
end
tex.sprint("\r")
end
tex.sprint("}")
end
\end{luacode*}
\newcommand\readtable[4]{%
\directlua{tab = read_table("\luaescapestring{#1}")}
\expandafter\pgfplotstableread\directlua{generate_hist(tab,#2,#3)}#4
}
\begin{document}
\readtable{1.dat}{-100,100,10}{0,80,10}\histtable
\begin{tikzpicture}
\begin{axis}
\addplot[
matrix plot*,mesh/rows=10,mesh/cols=10,
point meta=explicit,
shader=faceted,colormap/cool
] table[meta=z] {\histtable};
\addplot[only marks,mark=o] table {1.dat};
\end{axis}
\end{tikzpicture}
\end{document}
![alt text][1]
---
Bevor ein Minimalbeispiel da war habe ich gaußverteilte Zufallszahlen geplottet.
\documentclass{article}
\usepackage{pgfplots}
\usepgfplotslibrary{statistics}
\usepackage{luacode}
\begin{luacode*}
-- Initialize the random number generator according to
-- http://lua-users.org/wiki/MathLibraryTutorial
math.randomseed( tonumber(tostring(os.time()):reverse():sub(1,6)) )
-- standard Box-Muller transform
-- https://en.wikipedia.org/wiki/Box-Muller_transform
function gauss_random(mu, sigma)
-- State variables
local generate = false
local z0 = 0.0
local z1 = 0.0
-- Parameters
mu = mu or 0.0
sigma = sigma or 1.0
function random()
generate = not generate
if (not generate) then
return z1*sigma + mu;
end
local u1, u2
repeat
u1 = math.random()
u2 = math.random()
until ( u1 > 1e-16 )
z0 = math.sqrt(-2.0 * math.log(u1)) * math.cos(2*math.pi * u2)
z1 = math.sqrt(-2.0 * math.log(u1)) * math.sin(2*math.pi * u2)
return z0*sigma + mu
end
return random
end
function generate(N)
local tab = {}
local gauss = gauss_random()
for i = 1, N do
tab[i] = { x = gauss(), y = gauss() }
end
return tab
end
function generate_table(tab)
tex.sprint("{\r")
tex.sprint("x y z\r")
for i = 1, #tab do
tex.sprint(tab[i].x .. " " .. tab[i].y .. " 0\r")
end
tex.sprint("}")
end
function generate_hist(tab,xmin,xmax,Nx,ymin,ymax,Ny)
local xstep = (xmax - xmin) / (Nx-1)
local ystep = (ymax - ymin) / (Ny-1)
tex.sprint("{\r")
tex.sprint("x y z\r")
for x = xmin,xmax,xstep do
for y = ymin,ymax,ystep do
local bins = 0
for i = 1,#tab do
if (x-xstep/2 <= tab[i].x and tab[i].x < x+xstep/2) and
(y-ystep/2 <= tab[i].y and tab[i].y < y+ystep/2) then
bins = bins + 1
end
end
tex.sprint(x .. " " .. y .. " " .. bins .. "\r")
end
tex.sprint("\r")
end
tex.sprint("}")
end
\end{luacode*}
\newcommand\generatetable[5]{%
\directlua{tab = generate(#1)}
\expandafter\pgfplotstableread\directlua{generate_table(tab)}#4
\expandafter\pgfplotstableread\directlua{generate_hist(tab,#2,#3)}#5
}
\begin{document}
\generatetable{400}{-4,4,10}{-4,4,10}\pointtable\histtable
\begin{tikzpicture}
\begin{axis}
\addplot[
matrix plot,mesh/rows=10,mesh/cols=10,
point meta=explicit,
shader=faceted,colormap/cool
] table[meta=z] {\histtable};
\addplot[only marks,mark=o] table {\pointtable};
\end{axis}
\end{tikzpicture}
\end{document}
![alt text][2]
[1]: http://texwelt.de/wissen/upfiles/test_197.png
[2]: http://texwelt.de/wissen/upfiles/test_196.png
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Geht einigermaßen mit Lua.
\begin{filecontents*}{1.dat}
spalteB spalteA
1 2
3 2
-4 15
5 12
-30 10
20 1
30 2
5 8
-4 3
6 4
7 12
8 1
45 9
-3 45
2 45
4 23
6 56
-8 23
12 12
56 12
6 4
-7 66
76 2
3 12
-2 7
4 3
6 2
-8 1
-12 1
-56 1
-64 3
-7 77
-76 43
1 34
5 23
7 23
12 2
45 2
\end{filecontents*}
\documentclass{article}
\usepackage{pgfplots}
\usepgfplotslibrary{statistics}
\usepackage{luacode}
\begin{luacode*}
-- http://lua-users.org/wiki/SplitJoin
function string:split(sep)
local sep, fields = sep or ":", {}
local pattern = string.format("([^%s]+)", sep)
self:gsub(pattern, function(c) fields[#fields+1] = c end)
return fields
end
function read_table(fname)
local tab = {}
for line in io.lines(fname) do
local fields = line:split(' ')
local _x, _y = table.unpack(line:split(' '))
fields[1], fields[2]
local x, y = tonumber(_x), tonumber(_y)
if x and y then
tab[#tab+1] = { x = x, y = y }
end
end
return tab
end
function generate_table(tab)
tex.sprint("{\r")
tex.sprint("x y\r")
for i = 1, #tab do
tex.sprint(tab[i].x .. " " .. tab[i].y .. "\r")
end
tex.sprint("}")
end
function generate_hist(tab,xmin,xmax,Nx,ymin,ymax,Ny)
local xstep = (xmax - xmin) / (Nx-1)
local ystep = (ymax - ymin) / (Ny-1)
tex.sprint("{\r")
tex.sprint("x y z\r")
for x = xmin,xmax,xstep do
for y = ymin,ymax,ystep do
local bins = 0
for i = 1,#tab do
if (x-xstep/2 <= tab[i].x and tab[i].x < x+xstep/2) and
(y-ystep/2 <= tab[i].y and tab[i].y < y+ystep/2) then
bins = bins + 1
end
end
tex.sprint(x .. " " .. y .. " " .. bins .. "\r")
end
tex.sprint("\r")
end
tex.sprint("}")
end
\end{luacode*}
\newcommand\readtable[4]{%
\directlua{tab = read_table("\luaescapestring{#1}")}
\expandafter\pgfplotstableread\directlua{generate_hist(tab,#2,#3)}#4
}
\begin{document}
\readtable{1.dat}{-100,100,10}{0,80,10}\histtable
\begin{tikzpicture}
\begin{axis}
\addplot[
matrix plot*,mesh/rows=10,mesh/cols=10,
point meta=explicit,
shader=faceted,colormap/cool
] table[meta=z] {\histtable};
\addplot[only marks,mark=o] table {1.dat};
\end{axis}
\end{tikzpicture}
\end{document}
![alt text][1]
---
Bevor ein Minimalbeispiel da war habe ich gaußverteilte Zufallszahlen geplottet.
\documentclass{article}
\usepackage{pgfplots}
\usepgfplotslibrary{statistics}
\usepackage{luacode}
\begin{luacode*}
-- Initialize the random number generator according to
-- http://lua-users.org/wiki/MathLibraryTutorial
math.randomseed( tonumber(tostring(os.time()):reverse():sub(1,6)) )
-- standard Box-Muller transform
-- https://en.wikipedia.org/wiki/Box-Muller_transform
function gauss_random(mu, sigma)
-- State variables
local generate = false
local z0 = 0.0
local z1 = 0.0
-- Parameters
local mu = mu or 0.0
local sigma = sigma or 1.0
function random()
generate = not generate
if (not generate) then
return z1*sigma + mu;
end
local u1, u2
repeat
u1 = math.random()
u2 = math.random()
until ( u1 > 1e-16 )
z0 = math.sqrt(-2.0 * math.log(u1)) * math.cos(2*math.pi * u2)
z1 = math.sqrt(-2.0 * math.log(u1)) * math.sin(2*math.pi * u2)
return z0*sigma + mu
end
return random
end
function generate(N)
local tab = {}
local gauss = gauss_random()
for i = 1, N do
tab[i] = { x = gauss(), y = gauss() }
end
return tab
end
function generate_table(tab)
tex.sprint("{\r")
tex.sprint("x y z\r")
for i = 1, #tab do
tex.sprint(tab[i].x .. " " .. tab[i].y .. " 0\r")
end
tex.sprint("}")
end
function generate_hist(tab,xmin,xmax,Nx,ymin,ymax,Ny)
local xstep = (xmax - xmin) / (Nx-1)
local ystep = (ymax - ymin) / (Ny-1)
tex.sprint("{\r")
tex.sprint("x y z\r")
for x = xmin,xmax,xstep do
for y = ymin,ymax,ystep do
local bins = 0
for i = 1,#tab do
if (x-xstep/2 <= tab[i].x and tab[i].x < x+xstep/2) and
(y-ystep/2 <= tab[i].y and tab[i].y < y+ystep/2) then
bins = bins + 1
end
end
tex.sprint(x .. " " .. y .. " " .. bins .. "\r")
end
tex.sprint("\r")
end
tex.sprint("}")
end
\end{luacode*}
\newcommand\generatetable[5]{%
\directlua{tab = generate(#1)}
\expandafter\pgfplotstableread\directlua{generate_table(tab)}#4
\expandafter\pgfplotstableread\directlua{generate_hist(tab,#2,#3)}#5
}
\begin{document}
\generatetable{400}{-4,4,10}{-4,4,10}\pointtable\histtable
\begin{tikzpicture}
\begin{axis}
\addplot[
matrix plot,mesh/rows=10,mesh/cols=10,
point meta=explicit,
shader=faceted,colormap/cool
] table[meta=z] {\histtable};
\addplot[only marks,mark=o] table {\pointtable};
\end{axis}
\end{tikzpicture}
\end{document}
![alt text][2]
[1]: http://texwelt.de/wissen/upfiles/test_197.png
[2]: http://texwelt.de/wissen/upfiles/test_196.png
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4 |
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Geht einigermaßen mit Lua.
\begin{filecontents*}{1.dat}
spalteB spalteA
1 2
3 2
-4 15
5 12
-30 10
20 1
30 2
5 8
-4 3
6 4
7 12
8 1
45 9
-3 45
2 45
4 23
6 56
-8 23
12 12
56 12
6 4
-7 66
76 2
3 12
-2 7
4 3
6 2
-8 1
-12 1
-56 1
-64 3
-7 77
-76 43
1 34
5 23
7 23
12 2
45 2
\end{filecontents*}
\documentclass{article}
\usepackage{pgfplots}
\usepgfplotslibrary{statistics}
\usepackage{luacode}
\begin{luacode*}
-- Initialize the random number generator according to
-- http://lua-users.org/wiki/MathLibraryTutorial
math.randomseed( tonumber(tostring(os.time()):reverse():sub(1,6)) )
-- standard Box-Muller transform
-- https://en.wikipedia.org/wiki/Box-Muller_transform
http://lua-users.org/wiki/SplitJoin
function gauss_random(mu, sigma)
-- State variables
string:split(sep)
local generate = false
sep, fields = sep or ":", {}
local z0 = 0.0
pattern = string.format("([^%s]+)", sep)
self:gsub(pattern, function(c) fields[#fields+1] = c end)
return fields
end
function read_table(fname)
local z1 = 0.0
-- Parameters
tab = {}
for line in io.lines(fname) do
local mu = mu or 0.0
_x, _y = table.unpack(line:split(' '))
local sigma = sigma or 1.0
x, y = tonumber(_x), tonumber(_y)
if x and y then
tab[#tab+1] = { x = x, y = y }
end
end
return tab
end
function random()
generate = not generate
if (not generate) then
return z1*sigma + mu;
end
local u1, u2
repeat
u1 = math.random()
u2 = math.random()
until ( u1 > 1e-16 )
z0 = math.sqrt(-2.0 * math.log(u1)) * math.cos(2*math.pi * u2)
z1 = math.sqrt(-2.0 * math.log(u1)) * math.sin(2*math.pi * u2)
return z0*sigma + mu
end
return random
end
function generate(N)
local gauss = gauss_random()
generate_table(tab)
tex.sprint("{\r")
tex.sprint("x y\r")
for i = 1, N #tab do
table[i] = { x = gauss(), y = gauss() }
end
return table
end
function generate_table(table)
tex.sprint("{\r")
tex.sprint("x y z\r")
for i = 1, #table do
tex.sprint(table[i].x tex.sprint(tab[i].x .. " " .. table[i].y tab[i].y .. " 0\r")
"\r")
end
tex.sprint("}")
end
function generate_hist(table,xmin,xmax,Nx,ymin,ymax,Ny)
generate_hist(tab,xmin,xmax,Nx,ymin,ymax,Ny)
local xstep = (xmax - xmin) / (Nx-1)
local ystep = (ymax - ymin) / (Ny-1)
tex.sprint("{\r")
tex.sprint("x y z\r")
for x = xmin,xmax,xstep do
for y = ymin,ymax,ystep do
local bins = 0
for i = 1,#table 1,#tab do
if (x-xstep/2 <= table[i].x tab[i].x and table[i].x tab[i].x < x+xstep/2) and
(y-ystep/2 <= table[i].y tab[i].y and table[i].y tab[i].y < y+ystep/2) then
bins = bins + 1
end
end
tex.sprint(x .. " " .. y .. " " .. bins .. "\r")
end
tex.sprint("\r")
end
tex.sprint("}")
end
\end{luacode*}
\newcommand\readtable[4]{%
\directlua{tab = read_table("\luaescapestring{#1}")}
\expandafter\pgfplotstableread\directlua{generate_hist(tab,#2,#3)}#4
}
\begin{document}
\readtable{1.dat}{-100,100,10}{0,80,10}\histtable
\begin{tikzpicture}
\begin{axis}
\addplot[
matrix plot*,mesh/rows=10,mesh/cols=10,
point meta=explicit,
shader=faceted,colormap/cool
] table[meta=z] {\histtable};
\addplot[only marks,mark=o] table {1.dat};
\end{axis}
\end{tikzpicture}
\end{document}
![alt text][1]
---
Bevor ein Minimalbeispiel da war habe ich gaußverteilte Zufallszahlen geplottet.
\documentclass{article}
\usepackage{pgfplots}
\usepgfplotslibrary{statistics}
\usepackage{luacode}
\begin{luacode*}
-- Initialize the random number generator according to
-- http://lua-users.org/wiki/MathLibraryTutorial
math.randomseed( tonumber(tostring(os.time()):reverse():sub(1,6)) )
-- standard Box-Muller transform
-- https://en.wikipedia.org/wiki/Box-Muller_transform
function gauss_random(mu, sigma)
-- State variables
local generate = false
local z0 = 0.0
local z1 = 0.0
-- Parameters
local mu = mu or 0.0
local sigma = sigma or 1.0
function random()
generate = not generate
if (not generate) then
return z1*sigma + mu;
end
local u1, u2
repeat
u1 = math.random()
u2 = math.random()
until ( u1 > 1e-16 )
z0 = math.sqrt(-2.0 * math.log(u1)) * math.cos(2*math.pi * u2)
z1 = math.sqrt(-2.0 * math.log(u1)) * math.sin(2*math.pi * u2)
return z0*sigma + mu
end
return random
end
function generate(N)
tab = {}
local gauss = gauss_random()
for i = 1, N do
tab[i] = { x = gauss(), y = gauss() }
end
return tab
end
function generate_table(tab)
tex.sprint("{\r")
tex.sprint("x y z\r")
for i = 1, #tab do
tex.sprint(tab[i].x .. " " .. tab[i].y .. " 0\r")
end
tex.sprint("}")
end
function generate_hist(tab,xmin,xmax,Nx,ymin,ymax,Ny)
local xstep = (xmax - xmin) / (Nx-1)
local ystep = (ymax - ymin) / (Ny-1)
tex.sprint("{\r")
tex.sprint("x y z\r")
for x = xmin,xmax,xstep do
for y = ymin,ymax,ystep do
local bins = 0
for i = 1,#tab do
if (x-xstep/2 <= tab[i].x and tab[i].x < x+xstep/2) and
(y-ystep/2 <= tab[i].y and tab[i].y < y+ystep/2) then
bins = bins + 1
end
end
tex.sprint(x .. " " .. y .. " " .. bins .. "\r")
end
tex.sprint("\r")
end
tex.sprint("}")
end
\end{luacode*}
\newcommand\generatetable[5]{%
\directlua{tab = generate(#1)}
\expandafter\pgfplotstableread\directlua{generate_table(tab)}#4
\expandafter\pgfplotstableread\directlua{generate_hist(tab,#2,#3)}#5
}
\begin{document}
\generatetable{400}{-4,4,10}{-4,4,10}\pointtable\histtable
\begin{tikzpicture}
\begin{axis}
\addplot[
matrix plot,mesh/rows=10,mesh/cols=10,
point meta=explicit,
shader=faceted,colormap/cool
] table[meta=z] {\histtable};
\addplot[only marks,mark=o] table {\pointtable};
\end{axis}
\end{tikzpicture}
\end{document}
![alt text][1]
text][2]
[1]: http://texwelt.de/wissen/upfiles/test_197.png
[2]: http://texwelt.de/wissen/upfiles/test_196.png
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3 |
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Geht einigermaßen mit Lua.
\documentclass{article}
\usepackage{pgfplots}
\usepgfplotslibrary{statistics}
\usepackage{luacode}
\begin{luacode*}
-- Initialize the random number generator according to
-- http://lua-users.org/wiki/MathLibraryTutorial
math.randomseed( tonumber(tostring(os.time()):reverse():sub(1,6)) )
-- standard Box-Muller transform
-- https://en.wikipedia.org/wiki/Box-Muller_transform
function gauss_random(mu, sigma)
-- State variables
local generate = false
local z0 = 0.0
local z1 = 0.0
-- Parameters
local mu = mu or 0.0
local sigma = sigma or 1.0
function random()
generate = not generate
if (not generate) then
return z1*sigma + mu;
end
local u1, u2
repeat
u1 = math.random()
u2 = math.random()
until ( u1 > 1e-16 )
z0 = math.sqrt(-2.0 * math.log(u1)) * math.cos(2*math.pi * u2)
z1 = math.sqrt(-2.0 * math.log(u1)) * math.sin(2*math.pi * u2)
return z0*sigma + mu
end
return random
end
function generate(N)
local gauss = gauss_random()
for i = 1, N do
table[i] = { x = gauss(), y = gauss() }
end
return table
end
function generate_table(table)
tex.sprint("{\r")
tex.sprint("x y z\r")
for i = 1, #table do
tex.sprint(table[i].x .. " " .. table[i].y .. " 0\r")
end
tex.sprint("}")
end
function generate_hist(table,xmin,xmax,Nx,ymin,ymax,Nx)
local xmin = xmin or -4
local xmax = xmax or 4
local Nx = Nx or 20
local ymin = ymin or -4
local ymax = ymax or 4
local Ny = Ny or 20
generate_hist(table,xmin,xmax,Nx,ymin,ymax,Ny)
local xstep = (xmax - xmin) / (Nx-1)
local ystep = (ymax - ymin) / (Ny-1)
tex.sprint("{\r")
tex.sprint("x y z\r")
for x = xmin,xmax,xstep do
for y = ymin,ymax,ystep do
local bins = 0
for i = 1,#table do
if (x-xstep/2 <= table[i].x and table[i].x < x+xstep/2) and
(y-ystep/2 <= table[i].y and table[i].y < y+ystep/2) then
bins = bins + 1
end
end
tex.sprint(x .. " " .. y .. " " .. bins .. "\r")
end
tex.sprint("\r")
end
tex.sprint("}")
end
\end{luacode*}
\newcommand\generatetable[4]{%
\newcommand\generatetable[5]{%
\directlua{tab = generate(#1)}
\expandafter\pgfplotstableread\directlua{generate_table(tab)}#3
\expandafter\pgfplotstableread\directlua{generate_hist(tab)}#4
\expandafter\pgfplotstableread\directlua{generate_table(tab)}#4
\expandafter\pgfplotstableread\directlua{generate_hist(tab,#2,#3)}#5
}
\begin{document}
\generatetable{400}{}\pointtable\histtable
\generatetable{400}{-4,4,10}{-4,4,10}\pointtable\histtable
\begin{tikzpicture}
\begin{axis}
\addplot[matrix plot,mesh/rows=20,mesh/cols=20,point meta=explicit] \addplot[
matrix plot,mesh/rows=10,mesh/cols=10,
point meta=explicit,
shader=faceted,colormap/cool
] table[meta=z] {\histtable};
\addplot[only marks,mark=x] marks,mark=o] table {\pointtable};
\end{axis}
\end{tikzpicture}
\end{document}
![alt text][1]
[1]: http://texwelt.de/wissen/upfiles/test_195.pnghttp://texwelt.de/wissen/upfiles/test_196.png
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2 |
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Geht einigermaßen mit Lua. Beim Histogramm ist noch irgendwas komisch, weil die Punkte auch in benachbarten Feldern mitgezählt werden.
Lua.
\documentclass{article}
\usepackage{pgfplots}
\usepgfplotslibrary{statistics}
\usepackage{luacode}
\begin{luacode*}
-- Initialize the random number generator according to
-- http://lua-users.org/wiki/MathLibraryTutorial
math.randomseed( tonumber(tostring(os.time()):reverse():sub(1,6)) )
-- standard Box-Muller transform
-- https://en.wikipedia.org/wiki/Box-Muller_transform
function gauss_random(mu, sigma)
-- State variables
local generate = false
local z0 = 0.0
local z1 = 0.0
-- Parameters
local mu = mu or 0.0
local sigma = sigma or 1.0
function random()
generate = not generate
if (not generate) then
return z1 * sigma z1*sigma + mu;
end
local u1, u2
repeat
u1 = math.random()
u2 = math.random()
until ( u1 > 1e-16 )
z0 = math.sqrt(-2.0 * math.log(u1)) * math.cos(2*math.pi * u2)
z1 = math.sqrt(-2.0 * math.log(u1)) * math.sin(2*math.pi * u2)
return z0*sigma + mu
end
return random
end
function generate(N)
local gauss = gauss_random()
for i = 1, N do
table[i] = { x = gauss(), y = gauss() }
end
return table
end
function generate_table(table)
tex.sprint("{\r")
tex.sprint("x y z\r")
for i = 1, #table do
tex.sprint(table[i].x .. " " .. table[i].y .. " 0\r")
end
tex.sprint("}")
end
function generate_hist(table,xmin,xmax,Nx,ymin,ymax,Nx)
local xmin = xmin or -4
local xmax = xmax or 4
local Nx = Nx or 20
local ymin = ymin or -4
local ymax = ymax or 4
local Ny = Ny or 20
local xstep = (xmax - xmin) / (Nx-1)
local ystep = (ymax - ymin) / (Ny-1)
tex.sprint("{\r")
tex.sprint("x y z\r")
for x = xmin,xmax,xstep do
for y = ymin,ymax,ystep do
local bins = 0
for i = 1,#table do
if (x (x-xstep/2 <= table[i].x and table[i].x < x+xstep) x+xstep/2) and
(y (y-ystep/2 <= table[i].y and table[i].y < y+ystep) y+ystep/2) then
bins = bins + 1
end
end
tex.sprint(x .. " " .. y .. " " .. bins .. "\r")
end
tex.sprint("\r")
end
tex.sprint("}")
end
\end{luacode*}
\newcommand\generatetable[4]{%
\directlua{tab = generate(#1)}
\expandafter\pgfplotstableread\directlua{generate_table(tab)}#3
\expandafter\pgfplotstableread\directlua{generate_hist(tab)}#4
}
\begin{document}
\generatetable{100}{}\pointtable\histtable
\generatetable{400}{}\pointtable\histtable
\begin{tikzpicture}
\begin{axis}[view={0}{90}]
\addplot3[surf,mesh/rows=20,mesh/cols=20,z buffer=sort] table \begin{axis}
\addplot[matrix plot,mesh/rows=20,mesh/cols=20,point meta=explicit] table[meta=z] {\histtable};
\addplot3[only marks,mark=o] \addplot[only marks,mark=x] table {\pointtable};
\end{axis}
\end{tikzpicture}
\end{document}
![alt text][1]
[1]: http://texwelt.de/wissen/upfiles/test_194.pnghttp://texwelt.de/wissen/upfiles/test_195.png
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Geht einigermaßen mit Lua. Beim Histogramm ist noch irgendwas komisch, weil die Punkte auch in benachbarten Feldern mitgezählt werden.
\documentclass{article}
\usepackage{pgfplots}
\usepgfplotslibrary{statistics}
\usepackage{luacode}
\begin{luacode*}
-- Initialize the random number generator according to
-- http://lua-users.org/wiki/MathLibraryTutorial
math.randomseed( tonumber(tostring(os.time()):reverse():sub(1,6)) )
-- standard Box-Muller transform
-- https://en.wikipedia.org/wiki/Box-Muller_transform
function gauss_random(mu, sigma)
-- State variables
local generate = false
local z0 = 0.0
local z1 = 0.0
-- Parameters
local mu = mu or 0.0
local sigma = sigma or 1.0
function random()
generate = not generate
if (not generate) then
return z1 * sigma + mu;
end
repeat
u1 = math.random()
u2 = math.random()
until ( u1 > 1e-16 )
z0 = math.sqrt(-2.0 * math.log(u1)) * math.cos(2*math.pi * u2)
z1 = math.sqrt(-2.0 * math.log(u1)) * math.sin(2*math.pi * u2)
return z0*sigma + mu
end
return random
end
function generate(N)
local gauss = gauss_random()
for i = 1, N do
table[i] = { x = gauss(), y = gauss() }
end
return table
end
function generate_table(table)
tex.sprint("{\r")
tex.sprint("x y z\r")
for i = 1, #table do
tex.sprint(table[i].x .. " " .. table[i].y .. " 0\r")
end
tex.sprint("}")
end
function generate_hist(table,xmin,xmax,Nx,ymin,ymax,Nx)
local xmin = xmin or -4
local xmax = xmax or 4
local Nx = Nx or 20
local ymin = ymin or -4
local ymax = ymax or 4
local Ny = Ny or 20
local xstep = (xmax - xmin) / (Nx-1)
local ystep = (ymax - ymin) / (Ny-1)
tex.sprint("{\r")
tex.sprint("x y z\r")
for x = xmin,xmax,xstep do
for y = ymin,ymax,ystep do
local bins = 0
for i = 1,#table do
if (x <= table[i].x and table[i].x < x+xstep) and
(y <= table[i].y and table[i].y < y+ystep) then
bins = bins + 1
end
end
tex.sprint(x .. " " .. y .. " " .. bins .. "\r")
end
end
tex.sprint("}")
end
\end{luacode*}
\newcommand\generatetable[4]{%
\directlua{tab = generate(#1)}
\expandafter\pgfplotstableread\directlua{generate_table(tab)}#3
\expandafter\pgfplotstableread\directlua{generate_hist(tab)}#4
}
\begin{document}
\generatetable{100}{}\pointtable\histtable
\begin{tikzpicture}
\begin{axis}[view={0}{90}]
\addplot3[surf,mesh/rows=20,mesh/cols=20,z buffer=sort] table {\histtable};
\addplot3[only marks,mark=o] table {\pointtable};
\end{axis}
\end{tikzpicture}
\end{document}
![alt text][1]
[1]: http://texwelt.de/wissen/upfiles/test_194.png
