The following asks for 2 sets of data (with corresponding x and y values), calculates a linear equation that matches the data as closely as possible, then allows you to "play around" with the equation by substituting x values.
import Data.Char slope :: [Float] -> [Float] -> Float slope xs ys | xN /= yN = error $ "x len: " ++ show xN ++ " y len: " ++ show yN | otherwise = (xN * (sum $ coorProds xs ys) - xSum * ySum) / (xN * (sum $ squares xs) - (xSum * xSum)) where (xN,yN) = (fromIntegral $ length xs, fromIntegral $ length ys) (xSum,ySum) = (sum xs, sum ys) intercept :: [Float] -> [Float] -> Float intercept xs ys | xN /= yN = error $ "x len: " ++ show xN ++ " y len: " ++ show yN | otherwise = (ySum - (b * xSum)) / xN where b = slope xs ys (xN,yN) = (fromIntegral $ length xs, fromIntegral $ length ys) (xSum,ySum) = (sum xs, sum ys) getEquation :: [Float] -> [Float] -> ((Float -> Float),Float,Float) getEquation xs ys = (\x -> (inter + (b * x)) , inter, b) where inter = intercept xs ys b = slope xs ys coorProds :: [Float] -> [Float] -> [Float] coorProds xs ys = map (\(x,y) -> x * y) $ zip xs ys squares :: [Float] -> [Float] squares = map (\x -> x * x) cutIntoPair :: String -> (String,String) cutIntoPair = (\(x,y)-> (x,drop 1 y)) . break (== ' ') isFloat :: String -> Bool isFloat = all (\c -> isDigit c || c == '.') toFloat :: String -> Float toFloat s | isFloat s = read s :: Float | otherwise = error $ show s ++ " is not a number" getPairs :: IO ([Float],[Float]) getPairs = do i <- getLine let (x,y) = cutIntoPair i if isFloat x then do (xs,ys) <- getPairs return ((toFloat x : xs), (toFloat y : ys)) else return ([],[]) useEquation :: (Float -> Float) -> IO () useEquation e = do putStr "When x = "; x <- getLine putStrLn $ "y = " ++ (show $ e (toFloat x)) ++ "\n" useEquation e showEquation :: Float -> Float -> String showEquation i b = "y = " ++ show i ++ " + " ++ show b ++ "x" main = do putStrLn $ "Enter x and y values seperated by a space\n\t" ++ "Then type a non-number to continue" (xs,ys) <- getPairs let (linEq,i,b) = getEquation xs ys putStrLn $ showEquation i b putStrLn "Enter x values to get their calculated y values" useEquation linEq I'm looking for general feedback, and suggestions regarding the following points:
getEquationhas a couple issues.- I was able to write it point-free when the function only returned the equation, but now that I'm wrapping everything in a tuple, so I can also return the calculated slope and intercept values (to show the equation later), it's not behaving as I expected. I tried writing it as a section, like
(inter + (b *), but that attempts to apply+to the function(b*), which obviously results in a "No instance" error. My solution was to just wrap it in a lambda, but that's quite ugly, in my opinion. - Is there a better way of dealing with the need to have the slope and intercept after the function is "constructed" than passing them back with the equation? The optimal solution would the ability to extract them out of the function, but I'm pretty sure that's not possible.
- I was able to write it point-free when the function only returned the equation, but now that I'm wrapping everything in a tuple, so I can also return the calculated slope and intercept values (to show the equation later), it's not behaving as I expected. I tried writing it as a section, like
cutIntoPairlooks ugly too. It splits a string at the first space, then returns the 2 parts. Break leaves the space in the second slot though, so to remove it, I resorted to passing the result to a lambda that leaves the first part of the tuple the same, but drops the first char of the second slot. I'd like to know if there is a cleaner way to go about this task.The slope and intercept functions are slightly messy, but I had to cram a lot of math into the space. Tips on how to format it neater would be appreciated.
To use it, type x and y values separated by a space, pressing enter between sets. When you're done entering, type a non-number, like so:
2 4 4 8 12 24 k
