Tamas K Papp wrote:
Hi,
Having read some tutorials, I would like to start using Haskell "for real", but I have some questions about data structures.
The mathematical description of the problem is the following: assume there is a function V(a,b,theta), where a and b can have two values, High or Low, and theta is a number between zero and n (n is given). The range of V is the real numbers.
Then there is an algorithm (called value iteration, but that's not important) that takes V and produces a function of the same type, called V'. The algorithm uses a mapping that is not elementwise, ie more than the corresponding values of V are needed to compute a particular V'(a,b,theta) -- things like V(other a,b,theta) and V(a,b,theta+1), where
data State = Low | High other :: State -> State other High = Low other Low = High
Question 1: V can be represented as a 3-dimensional array, where the first two indices are of type State, the third is Int (<= n). What data structure do you suggest in Haskell to store V? Is there a multidimensional array or something like this?
Read http://haskell.org/haskellwiki/Modern_array_libraries It sounds like you need Data.Array (lazy) or Data.Array.Unboxed (strict)
Let's call this structure TypeV.
Question 2: I would like to write
valueit :: TypeV -> TypeV valueit V = mapondescartesproduct [Low,High] [Low,High] [0..n] mapV where -- mapV would calculate the new V' using V -- mapV :: State -> State -> Int -> Double
to fill the new data structure. How to do this sensibly?
Your definition is almost clear. mapV takes the i :: (State,State,Int) index of an entry in V' and takes the whole old array V and computes the value at location i in V'. data State = Low | High deriving (Eq,Ord,Ix) -- assuming Ix is derivable... type TypeV = Array (State,State,Int) Double -- or UArray instead of Array mapV :: TypeV -> (State,State,Int) -> Double mapV = undefined valueit :: TypeV -> TypeV valueit oldV = listArray (minI,maxI) [ mapV oldV i | i <- range (minI,maxI) ] where minI = (Low,Low,0) maxI = (High,High,n) -- or move mapV to where clause; it can still use oldV valueit :: TypeV -> TypeV valueit oldV = listArray (minI,maxI) [ mapV i | i <- range (minI,maxI) ] where minI = (Low,Low,0) maxI = (High,High,n) mapV :: (State,State,Int) -> Double mapV = undefined
Thanks,
Tamas