-----------------------------------------------------------------------------
-- |
-- Module      :  Data.Packed.IO
-- Copyright   :  (c) Alberto Ruiz 2010
--
-- Maintainer  :  Alberto Ruiz
-- Stability   :  provisional
--
-- Display, formatting and IO functions for numeric 'Vector' and 'Matrix'
--
-----------------------------------------------------------------------------

module Data.Packed.IO (
dispf, disps, dispcf, vecdisp, latexFormat, format,
) where

import Data.Packed
import Text.Printf(printf)
import Data.List(intersperse)
import Data.Complex
import Numeric.Vectorized(vectorScan,saveMatrix)
import Control.Applicative((<$>)) import Data.Packed.Internal {- | Creates a string from a matrix given a separator and a function to show each entry. Using this function the user can easily define any desired display function: @import Text.Printf(printf)@ @disp = putStr . format \" \" (printf \"%.2f\")@ -} format :: (Element t) => String -> (t -> String) -> Matrix t -> String format sep f m = table sep . map (map f) . toLists$ 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 $ident 2) "\\begin{bmatrix}\n1 & 0\n\\\\\n0 & 1\n\\end{bmatrix}" -} latexFormat :: String -- ^ type of braces: \"matrix\", \"bmatrix\", \"pmatrix\", etc. -> String -- ^ Formatted matrix, with elements separated by spaces and newlines -> String latexFormat del tab = "\\begin{"++del++"}\n" ++ f tab ++ "\\end{"++del++"}" where f = unlines . intersperse "\\\\" . map unwords . map (intersperse " & " . words) . tail . lines -- | Pretty print a complex number with at most n decimal digits. showComplex :: Int -> Complex Double -> String showComplex d (a:+b) | isZero a && isZero b = "0" | isZero b = sa | isZero a && isOne b = s2++"i" | isZero a = sb++"i" | isOne b = sa++s3++"i" | otherwise = sa++s1++sb++"i" where sa = shcr d a sb = shcr d b s1 = if b<0 then "" else "+" s2 = if b<0 then "-" else "" s3 = if b<0 then "-" else "+" shcr d a | lookslikeInt a = printf "%.0f" a | otherwise = printf ("%."++show d++"f") a lookslikeInt x = show (round x :: Int) ++".0" == shx || "-0.0" == shx where shx = show x isZero x = show x elem ["0.0","-0.0"] isOne x = show x elem ["1.0","-1.0"] -- | Pretty print a complex matrix with at most n decimal digits. dispcf :: Int -> Matrix (Complex Double) -> String dispcf d m = sdims m ++ "\n" ++ format " " (showComplex d) m -------------------------------------------------------------------- -- | reads a matrix from a string containing a table of numbers. readMatrix :: String -> Matrix Double readMatrix = fromLists . map (map read). map words . filter (not.null) . lines -------------------------------------------------------------------------------- apparentCols :: FilePath -> IO Int apparentCols s = f . dropWhile null . map words . lines <$> readFile s
where
f [] = 0
f (x:_) = length x

-- | load a matrix from an ASCII file formatted as a 2D table.
loadMatrix :: FilePath -> IO (Matrix Double)
if (dim v mod c /= 0)