1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
|
-----------------------------------------------------------------------------
-- |
-- 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.
@disp = putStr . disps 2
\> disp $ 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.
@disp = putStr . dispf 3
\> disp (1/3 + ident 4)
4x4
1.333 0.333 0.333 0.333
0.333 1.333 0.333 0.333
0.333 0.333 1.333 0.333
0.333 0.333 0.333 1.333
@
-}
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 = 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.
@disp = putStr . vecdisp ('dispf' 2)
\> disp ('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 :: 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)
|
