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|
-----------------------------------------------------------------------------
-- |
-- Module : Graphics.Plot
-- Copyright : (c) Alberto Ruiz 2005
-- License : GPL-style
--
-- Maintainer : Alberto Ruiz (aruiz at um dot es)
-- Stability : provisional
-- Portability : uses gnuplot and ImageMagick
--
-- Very basic (and provisional) drawing tools.
--
-----------------------------------------------------------------------------
module Graphics.Plot(
mplot,
plot, parametricPlot,
splot, mesh, mesh', meshdom,
matrixToPGM, imshow,
gnuplotX
) where
import Data.Packed.Vector
import Data.Packed.Matrix
import Numeric.LinearAlgebra.Linear(outer)
import Numeric.GSL.Vector(FunCodeS(Max,Min),toScalarR)
import Data.List(intersperse)
import System
import Data.IORef
import System.Exit
import Foreign hiding (rotate)
size = dim
-- | Loads a real matrix from a formatted ASCII text file
--fromFile :: FilePath -> IO Matrix
--fromFile filename = readFile filename >>= return . readMatrix read
-- | Saves a real matrix to a formatted ascii text file
toFile :: FilePath -> Matrix Double -> IO ()
toFile filename matrix = writeFile filename (unlines . map unwords. map (map show) . toLists $ matrix)
------------------------------------------------------------------------
-- | From vectors x and y, it generates a pair of matrices to be used as x and y arguments for matrix functions.
meshdom :: Vector Double -> Vector Double -> (Matrix Double , Matrix Double)
meshdom r1 r2 = (outer r1 (constant 1 (size r2)), outer (constant 1 (size r1)) r2)
gnuplotX :: String -> IO ()
gnuplotX command = do {system cmdstr; return()} where
cmdstr = "echo \""++command++"\" | gnuplot -persist"
datafollows = "\\\"-\\\""
prep = (++"e\n\n") . unlines . map (unwords . (map show))
{- | Draws a 3D surface representation of a real matrix.
> > mesh (hilb 20)
In certain versions you can interactively rotate the graphic using the mouse.
-}
mesh :: Matrix Double -> IO ()
mesh m = gnuplotX (command++dat) where
command = "splot "++datafollows++" matrix with lines\n"
dat = prep $ toLists $ m
mesh' :: Matrix Double -> IO ()
mesh' m = do
writeFile "splot-gnu-command" "splot \"splot-tmp.txt\" matrix with lines; pause -1";
toFile "splot-tmp.txt" m
putStr "Press [Return] to close the graphic and continue... "
system "gnuplot -persist splot-gnu-command"
system "rm splot-tmp.txt splot-gnu-command"
return ()
{- | Draws the surface represented by the function f in the desired ranges and number of points, internally using 'mesh'.
> > let f x y = cos (x + y)
> > splot f (0,pi) (0,2*pi) 50
-}
splot :: (Matrix Double->Matrix Double->Matrix Double) -> (Double,Double) -> (Double,Double) -> Int -> IO ()
splot f rx ry n = mesh' z where
(x,y) = meshdom (linspace n rx) (linspace n ry)
z = f x y
{- | plots several vectors against the first one -}
mplot :: [Vector Double] -> IO ()
mplot m = gnuplotX (commands++dats) where
commands = if length m == 1 then command1 else commandmore
command1 = "plot "++datafollows++" with lines\n" ++ dat
commandmore = "plot " ++ plots ++ "\n"
plots = concat $ intersperse ", " (map cmd [2 .. length m])
cmd k = datafollows++" using 1:"++show k++" with lines"
dat = prep $ toLists $ fromColumns m
dats = concat (replicate (length m-1) dat)
mplot' m = do
writeFile "plot-gnu-command" (commands++endcmd)
toFile "plot-tmp.txt" (fromColumns m)
putStr "Press [Return] to close the graphic and continue... "
system "gnuplot plot-gnu-command"
system "rm plot-tmp.txt plot-gnu-command"
return ()
where
commands = if length m == 1 then command1 else commandmore
command1 = "plot \"plot-tmp.txt\" with lines\n"
commandmore = "plot " ++ plots ++ "\n"
plots = concat $ intersperse ", " (map cmd [2 .. length m])
cmd k = "\"plot-tmp.txt\" using 1:"++show k++" with lines"
endcmd = "pause -1"
-- apply several functions to one object
mapf fs x = map ($ x) fs
{- | Draws a list of functions over a desired range and with a desired number of points
> > plot [sin, cos, sin.(3*)] (0,2*pi) 1000
-}
plot :: [Vector Double->Vector Double] -> (Double,Double) -> Int -> IO ()
plot fs rx n = mplot (x: mapf fs x)
where x = linspace n rx
{- | Draws a parametric curve. For instance, to draw a spiral we can do something like:
> > parametricPlot (\t->(t * sin t, t * cos t)) (0,10*pi) 1000
-}
parametricPlot :: (Vector Double->(Vector Double,Vector Double)) -> (Double, Double) -> Int -> IO ()
parametricPlot f rt n = mplot [fx, fy]
where t = linspace n rt
(fx,fy) = f t
-- | writes a matrix to pgm image file
matrixToPGM :: Matrix Double -> String
matrixToPGM m = header ++ unlines (map unwords ll) where
c = cols m
r = rows m
header = "P2 "++show c++" "++show r++" "++show (round maxgray :: Int)++"\n"
maxgray = 255.0
maxval = toScalarR Max $ flatten $ m
minval = toScalarR Min $ flatten $ m
scale = if (maxval == minval)
then 0.0
else maxgray / (maxval - minval)
f x = show ( round ( scale *(x - minval) ) :: Int )
ll = map (map f) (toLists m)
-- | imshow shows a representation of a matrix as a gray level image using ImageMagick's display.
imshow :: Matrix Double -> IO ()
imshow m = do
system $ "echo \""++ matrixToPGM m ++"\"| display -antialias -resize 300 - &"
return ()
|
