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1-----------------------------------------------------------------------------
2-- |
3-- Module : Numeric.IO
4-- Copyright : (c) Alberto Ruiz 2010
5-- License : GPL
6--
7-- Maintainer : Alberto Ruiz <aruiz@um.es>
8-- Stability : provisional
9-- Portability : portable
10--
11-- Display, formatting and IO functions for numeric 'Vector' and 'Matrix'
12--
13-----------------------------------------------------------------------------
14
15module Numeric.IO (
16 dispf, disps, dispcf, vecdisp, latexFormat, format,
17 loadMatrix, saveMatrix, fromFile, fileDimensions,
18 readMatrix, fromArray2D,
19 fscanfVector, fprintfVector, freadVector, fwriteVector
20) where
21
22import Data.Packed
23import Data.Packed.Internal
24import System.Process(readProcess)
25import Text.Printf(printf)
26import Data.List(intersperse)
27import Data.Complex
28
29{- | Creates a string from a matrix given a separator and a function to show each entry. Using
30this function the user can easily define any desired display function:
31
32@import Text.Printf(printf)@
33
34@disp = putStr . format \" \" (printf \"%.2f\")@
35
36-}
37format :: (Element t) => String -> (t -> String) -> Matrix t -> String
38format sep f m = table sep . map (map f) . toLists $ m
39
40{- | Show a matrix with \"autoscaling\" and a given number of decimal places.
41
42@disp = putStr . disps 2
43
44\> disp $ 120 * (3><4) [1..]
453x4 E3
46 0.12 0.24 0.36 0.48
47 0.60 0.72 0.84 0.96
48 1.08 1.20 1.32 1.44
49@
50-}
51disps :: Int -> Matrix Double -> String
52disps d x = sdims x ++ " " ++ formatScaled d x
53
54{- | Show a matrix with a given number of decimal places.
55
56@disp = putStr . dispf 3
57
58\> disp (1/3 + ident 4)
594x4
601.333 0.333 0.333 0.333
610.333 1.333 0.333 0.333
620.333 0.333 1.333 0.333
630.333 0.333 0.333 1.333
64@
65-}
66dispf :: Int -> Matrix Double -> String
67dispf d x = sdims x ++ "\n" ++ formatFixed (if isInt x then 0 else d) x
68
69sdims x = show (rows x) ++ "x" ++ show (cols x)
70
71formatFixed d x = format " " (printf ("%."++show d++"f")) $ x
72
73isInt = all lookslikeInt . toList . flatten
74
75formatScaled dec t = "E"++show o++"\n" ++ ss
76 where ss = format " " (printf fmt. g) t
77 g x | o >= 0 = x/10^(o::Int)
78 | otherwise = x*10^(-o)
79 o = floor $ maximum $ map (logBase 10 . abs) $ toList $ flatten t
80 fmt = '%':show (dec+3) ++ '.':show dec ++"f"
81
82{- | Show a vector using a function for showing matrices.
83
84@disp = putStr . vecdisp ('dispf' 2)
85
86\> disp ('linspace' 10 (0,1))
8710 |> 0.00 0.11 0.22 0.33 0.44 0.56 0.67 0.78 0.89 1.00
88@
89-}
90vecdisp :: (Element t) => (Matrix t -> String) -> Vector t -> String
91vecdisp f v
92 = ((show (dim v) ++ " |> ") ++) . (++"\n")
93 . unwords . lines . tail . dropWhile (not . (`elem` " \n"))
94 . f . trans . reshape 1
95 $ v
96
97-- | Tool to display matrices with latex syntax.
98latexFormat :: String -- ^ type of braces: \"matrix\", \"bmatrix\", \"pmatrix\", etc.
99 -> String -- ^ Formatted matrix, with elements separated by spaces and newlines
100 -> String
101latexFormat del tab = "\\begin{"++del++"}\n" ++ f tab ++ "\\end{"++del++"}"
102 where f = unlines . intersperse "\\\\" . map unwords . map (intersperse " & " . words) . tail . lines
103
104-- | Pretty print a complex number with at most n decimal digits.
105showComplex :: Int -> Complex Double -> String
106showComplex d (a:+b)
107 | isZero a && isZero b = "0"
108 | isZero b = sa
109 | isZero a && isOne b = s2++"i"
110 | isZero a = sb++"i"
111 | isOne b = sa++s3++"i"
112 | otherwise = sa++s1++sb++"i"
113 where
114 sa = shcr d a
115 sb = shcr d b
116 s1 = if b<0 then "" else "+"
117 s2 = if b<0 then "-" else ""
118 s3 = if b<0 then "-" else "+"
119
120shcr d a | lookslikeInt a = printf "%.0f" a
121 | otherwise = printf ("%."++show d++"f") a
122
123
124lookslikeInt x = show (round x :: Int) ++".0" == shx || "-0.0" == shx
125 where shx = show x
126
127isZero x = show x `elem` ["0.0","-0.0"]
128isOne x = show x `elem` ["1.0","-1.0"]
129
130-- | Pretty print a complex matrix with at most n decimal digits.
131dispcf :: Int -> Matrix (Complex Double) -> String
132dispcf d m = sdims m ++ "\n" ++ format " " (showComplex d) m
133
134--------------------------------------------------------------------
135
136-- | reads a matrix from a string containing a table of numbers.
137readMatrix :: String -> Matrix Double
138readMatrix = fromLists . map (map read). map words . filter (not.null) . lines
139
140{- | obtains the number of rows and columns in an ASCII data file
141 (provisionally using unix's wc).
142-}
143fileDimensions :: FilePath -> IO (Int,Int)
144fileDimensions fname = do
145 wcres <- readProcess "wc" ["-w",fname] ""
146 contents <- readFile fname
147 let tot = read . head . words $ wcres
148 c = length . head . dropWhile null . map words . lines $ contents
149 if tot > 0
150 then return (tot `div` c, c)
151 else return (0,0)
152
153-- | Loads a matrix from an ASCII file formatted as a 2D table.
154loadMatrix :: FilePath -> IO (Matrix Double)
155loadMatrix file = fromFile file =<< fileDimensions file
156
157-- | Loads a matrix from an ASCII file (the number of rows and columns must be known in advance).
158fromFile :: FilePath -> (Int,Int) -> IO (Matrix Double)
159fromFile filename (r,c) = reshape c `fmap` fscanfVector filename (r*c)
160