On Wed, Aug 30, 2006 at 03:11:35PM +0200, Tamas K Papp wrote:
[...]
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?
There are: http://haskell.org/onlinereport/array.html (There are other implementations with destructive updates and a more comfortable API, but pure Haskell98 is probably the best thing to start with.) The trick is that Int is not the only index data type, but tuples of index data types are, too. Do this: | type Point = (State, State, Int) | type TypeV = Array State Double | | matrix :: TypeV | matrix = array bounds values | where | ...
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
I think Array.ixmap is pretty much doing what you want, with slightly different typing. hth? matthias