HFit - fitting algorithms in Haskell

It's very interesting class of tasks - fitting of some figure using several input points with noise. The simplest method is Least Squares Algorithm.

Idea of algorithm is to find a and b of line equation a*x + b using sum's minimization of difference's squares: ∑(y_i - (a*x_i + b))². Result is 2 formulas:

\[ a=\frac{n \sum\limits_{i=1}^n x_i y_i - \sum\limits_{i=1}^n x_i \sum\limits_{i=1}^n y_i} {n \sum\limits_{i=1}^n x_i^2 - ({\sum\limits_{i=1}^n x_i})^2} \]

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\[ b=\frac{\sum\limits_{i=1}^n y_i - a \sum\limits_{i=1}^n x_i} {n} \]

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And when we know a and b we can generates (x0, y0) (x1, y1) points to create line…

Application initializes Tcl/Tk UI via sending Tcl code to wish interpreter:

...
  mainTcl <- readFile "ui.tcl"
  (Just si, Just so, Just sx, ph) <- createProcess (proc wish []) {
    std_in=CreatePipe, std_out=CreatePipe, std_err=CreatePipe, close_fds=False}
  hSetBuffering si NoBuffering
  hSetBuffering so NoBuffering
  hPutStrLn si mainTcl
...

Communication loop lives in separate process:

...
  forkIO $ ioLoop si so
  waitForProcess ph
  putStrLn "bye."
  where
    ioLoop si so = forever $ do
        resp <- (hGetLine so) `catchIOError` (\_ -> return "eof")
        case resp of
          "eof" -> exitSuccess
          _|resp `startsWith` "calc " ->
            putStrLn ("-> " ++ resp) >> 
            let res = calc resp in
            putStrLn ("<- " ++ res) >> hPutStrLn si res
          _ -> putStrLn resp >> return ()
...

and when new line is got from wish then it will be processed with calc function which gets request (here it's call resp from Wish, yep:) and parse coordinates like "1 2 3 4", ie. x0 y0 x1 y1 ... xn yn with parsePt (after splitting them into words):

...
-- Parse ["12", "34", "56", "78"] to [(12, 34), (56, 78)]
parsePt :: [String] -> [Pt]
parsePt [] = []
parsePt (k:v:t) = (read k, read v) : parsePt t
...

then done all calculation in Double domain. Result of calculation is Tcl command like "takeCalc x0 y0 x1 y1" with coordinates of found line 2 points:

    -> calc 119 285 194 235 379 64
    <- takeCalc 119  306  379  46

Wish will get this command and create line on canvas.

Actually it's initial state, so needs many improvement, adding new algorithms, etc…