fold

With using python library numpy, it is possible to use the function cumprod to evaluate cumulative products, e.g. a = np.array([1,2,3,4,2]) np.cumprod(a) gives array([ 1, 2, 6, 24, 48]) It is indeed possible to apply this function only along one axis. I would like to do the same with matrices (represented as numpy arrays), e.g. if I have S0 = np.array([[1, 0], [0, 1]]) Sx = np.array([[0, 1], [1, 0]]) Sy = np.array([[0, -1j], [1j, 0]]) Sz = np.array([[1, 0], [0, -1]]) and b = np.array([S0, Sx, Sy, Sz]) then I would like to have a cumprod -like function which gives np.array([S0, S0.dot(Sx), S0

UPDATE - Solution Thanks to jacobm for his help, I came up with a solution. // Folding Recursion let reverse_list_3 theList = List.fold_left (fun element recursive_call -> recursive_call::element) [] theList;; I'm learning about the different ways of recursion in OCaml (for class) and for some exercise, I'm writing a function to reverse a list using different recursion styles. // Forward Recursion let rec reverse_list_forward theList = match theList with [] -> [] | (head::tail) -> (reverse_list_1 tail) @ [head];; // Tail Recursion let rec reverse_list_tail theList result = match theList with [

I am trying to transform the following HList Some(C(15)) :: None :: Some(B(55)) :: None :: Some(A(195)) :: HNil to C(15) :: B(55) :: A(195) :: HNil Here is what I have at the moment : import shapeless._ case class A(value: Int) case class B(value: Int) case class C(value: Int) trait folderLP extends Poly2 { implicit def default[T, L <: HList] = at[T, L]((acc, t) => acc) } object folder extends folderLP { implicit def none[T, L <: HList] = at[None.type, L]((t, acc) => acc) implicit def someDiameter[T, L <: HList] = at[Some[C], L]((t, acc) => t.get :: acc) implicit def someRatio[T, L <: HList] =

let us say we have a tree... data Tree a = Node a [Tree a] deriving (Show) and that tree has some nodes t = Node 1 [Node 2 [Node 3 []], Node 4 [], Node 5 [Node 6 []]] the following function will collect the paths in a tree. paths :: Tree a -> [[a]] paths (Node n []) = [[n]] paths (Node n ns) = map ((:) n . concat . paths) ns like so: *Main> paths t [[1,2,3],[1,4],[1,5,6]] But now how could we fold these paths? Obviously we could do this. Which folds after finding the paths. wastefullFold :: (a -> b -> b) -> b -> Tree a -> [b] wastefullFold f z (Node n ns) = map (foldr f z) $ paths (Node n ns)

I want to write a function that goes through a list updating an accumulator until that accumulator reaches a certain condition or I get to the end of the list. For example, a product function that stops as soon as its accumulator reaches zero. I know how to code it by writing the recursion by hand: {-# LANGUAGE BangPatterns #-} prod :: [Integer] -> Integer prod xs = go 1 xs where go 0 _ = 0 go !acc [] = acc go !acc (x:xs) = go (acc * x) xs but is there a way to code this using folds and other higher order functions? One thing that comes to mind is defining mult 0 _ = 0 mult x y = x * y and

I've been studying folds for the past few days. I can implement simple functions with them, like length , concat and filter . What I'm stuck at is trying to implement with foldr functions like delete , take and find . I have implemented these with explicit recursion but it doesn't seem obvious to me how to convert these types of functions to right folds. I have studied the tutorials by Graham Hutton and Bernie Pope. Imitating Hutton's dropWhile , I was able to implement delete with foldr but it fails on infinite lists. From reading Implement insert in haskell with foldr , How can this function

I need to break from foldl. Here is a dummy example how to break from fold when I count sum of values in a list and meet too big value (i.e. 10) L = [1,2,3,4,10,5,6,7], Res = try lists:foldl( fun(I, Value) -> if (I < 10) -> Value + I; true -> throw({too_big_value, Value}) end end, 0, L) catch throw:{too_big_value, Value} -> Value end, Res. I know this example is artificial but are there any nice method to break out fold (I know that fold always scan the whole structure)? Please note, that i need to retrieve correct data even if i break from fold. In this case i should get data from previous