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|
-----------------------------------------------------------------------------
-- |
-- Module : Numeric.IO
-- Copyright : (c) Alberto Ruiz 2010
-- License : GPL
--
-- Maintainer : Alberto Ruiz <aruiz@um.es>
-- Stability : provisional
-- Portability : portable
--
-- Display, formatting and IO functions for numeric 'Vector' and 'Matrix'
--
-----------------------------------------------------------------------------
module Numeric.IO (
dispf, disps, dispcf, vecdisp, latexFormat, format,
loadMatrix, saveMatrix, fromFile, fileDimensions,
readMatrix, fromArray2D,
fscanfVector, fprintfVector, freadVector, fwriteVector
) where
import Data.Packed
import Data.Packed.Internal
import System.Process(readProcess)
import Text.Printf(printf)
import Data.List(intersperse)
import Data.Complex
{- | Creates a string from a matrix given a separator and a function to show each entry. Using
this function the user can easily define any desired display function:
@import Text.Printf(printf)@
@disp = putStr . format \" \" (printf \"%.2f\")@
-}
format :: (Element t) => String -> (t -> String) -> Matrix t -> String
format sep f m = table sep . map (map f) . toLists $ m
{- | Show a matrix with \"autoscaling\" and a given number of decimal places.
>>> putStr . disps 2 $ 120 * (3><4) [1..]
3x4 E3
0.12 0.24 0.36 0.48
0.60 0.72 0.84 0.96
1.08 1.20 1.32 1.44
-}
disps :: Int -> Matrix Double -> String
disps d x = sdims x ++ " " ++ formatScaled d x
{- | Show a matrix with a given number of decimal places.
>>> dispf 2 (1/3 + ident 3)
"3x3\n1.33 0.33 0.33\n0.33 1.33 0.33\n0.33 0.33 1.33\n"
>>> putStr . dispf 2 $ (3><4)[1,1.5..]
3x4
1.00 1.50 2.00 2.50
3.00 3.50 4.00 4.50
5.00 5.50 6.00 6.50
>>> putStr . unlines . tail . lines . dispf 2 . asRow $ linspace 10 (0,1)
0.00 0.11 0.22 0.33 0.44 0.56 0.67 0.78 0.89 1.00
-}
dispf :: Int -> Matrix Double -> String
dispf d x = sdims x ++ "\n" ++ formatFixed (if isInt x then 0 else d) x
sdims x = show (rows x) ++ "x" ++ show (cols x)
formatFixed d x = format " " (printf ("%."++show d++"f")) $ x
isInt = all lookslikeInt . toList . flatten
formatScaled dec t = "E"++show o++"\n" ++ ss
where ss = format " " (printf fmt. g) t
g x | o >= 0 = x/10^(o::Int)
| otherwise = x*10^(-o)
o | rows t == 0 || cols t == 0 = 0
| otherwise = floor $ maximum $ map (logBase 10 . abs) $ toList $ flatten t
fmt = '%':show (dec+3) ++ '.':show dec ++"f"
{- | Show a vector using a function for showing matrices.
>>> putStr . vecdisp (dispf 2) $ linspace 10 (0,1)
10 |> 0.00 0.11 0.22 0.33 0.44 0.56 0.67 0.78 0.89 1.00
-}
vecdisp :: (Element t) => (Matrix t -> String) -> Vector t -> String
vecdisp f v
= ((show (dim v) ++ " |> ") ++) . (++"\n")
. unwords . lines . tail . dropWhile (not . (`elem` " \n"))
. f . trans . reshape 1
$ v
{- | Tool to display matrices with latex syntax.
>>> latexFormat "bmatrix" (dispf 2 $ ident 2)
"\\begin{bmatrix}\n1 & 0\n\\\\\n0 & 1\n\\end{bmatrix}"
-}
latexFormat :: String -- ^ type of braces: \"matrix\", \"bmatrix\", \"pmatrix\", etc.
-> String -- ^ Formatted matrix, with elements separated by spaces and newlines
-> String
latexFormat del tab = "\\begin{"++del++"}\n" ++ f tab ++ "\\end{"++del++"}"
where f = unlines . intersperse "\\\\" . map unwords . map (intersperse " & " . words) . tail . lines
-- | Pretty print a complex number with at most n decimal digits.
showComplex :: Int -> Complex Double -> String
showComplex d (a:+b)
| isZero a && isZero b = "0"
| isZero b = sa
| isZero a && isOne b = s2++"i"
| isZero a = sb++"i"
| isOne b = sa++s3++"i"
| otherwise = sa++s1++sb++"i"
where
sa = shcr d a
sb = shcr d b
s1 = if b<0 then "" else "+"
s2 = if b<0 then "-" else ""
s3 = if b<0 then "-" else "+"
shcr d a | lookslikeInt a = printf "%.0f" a
| otherwise = printf ("%."++show d++"f") a
lookslikeInt x = show (round x :: Int) ++".0" == shx || "-0.0" == shx
where shx = show x
isZero x = show x `elem` ["0.0","-0.0"]
isOne x = show x `elem` ["1.0","-1.0"]
-- | Pretty print a complex matrix with at most n decimal digits.
dispcf :: Int -> Matrix (Complex Double) -> String
dispcf d m = sdims m ++ "\n" ++ format " " (showComplex d) m
--------------------------------------------------------------------
-- | reads a matrix from a string containing a table of numbers.
readMatrix :: String -> Matrix Double
readMatrix = fromLists . map (map read). map words . filter (not.null) . lines
{- | obtains the number of rows and columns in an ASCII data file
(provisionally using unix's wc).
-}
fileDimensions :: FilePath -> IO (Int,Int)
fileDimensions fname = do
wcres <- readProcess "wc" ["-w",fname] ""
contents <- readFile fname
let tot = read . head . words $ wcres
c = length . head . dropWhile null . map words . lines $ contents
if tot > 0
then return (tot `div` c, c)
else return (0,0)
-- | Loads a matrix from an ASCII file formatted as a 2D table.
loadMatrix :: FilePath -> IO (Matrix Double)
loadMatrix file = fromFile file =<< fileDimensions file
-- | Loads a matrix from an ASCII file (the number of rows and columns must be known in advance).
fromFile :: FilePath -> (Int,Int) -> IO (Matrix Double)
fromFile filename (r,c) = reshape c `fmap` fscanfVector filename (r*c)
|
