Plot.hs

-----------------------------------------------------------------------------
-- |
-- 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 using gnuplot and imageMagick.
-- 
-- This module is deprecated. It will be replaced by improved drawing tools based
-- on the Gnuplot package by Henning Thielemann.
-----------------------------------------------------------------------------

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(outer)
import Numeric.GSL.Vector(FunCodeS(Max,Min),toScalarR)
import Data.List(intersperse)
import System
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 ()