linear algebra moved

1 files changed, 141 insertions, 0 deletions

diff --git a/packages/base/src/Data/Packed/IO.hs b/packages/base/src/Data/Packed/IO.hs
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+++ b/packages/base/src/Data/Packed/IO.hs
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+-----------------------------------------------------------------------------
+-- |
+-- Module      :  Data.Packed.IO
+-- Copyright   :  (c) Alberto Ruiz 2010
+-- License     :  BSD3
+--
+-- Maintainer  :  Alberto Ruiz
+-- Stability   :  provisional
+--
+-- Display, formatting and IO functions for numeric 'Vector' and 'Matrix'
+--
+-----------------------------------------------------------------------------
+{-# OPTIONS_HADDOCK hide #-}
+
+module Data.Packed.IO (
+    dispf, disps, dispcf, vecdisp, latexFormat, format,
+    readMatrix, fromArray2D
+) where
+
+import Data.Packed
+import Data.Packed.Development
+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
+