CODEWITHSUNDEEP
haskellrecursionnumerical-methods
user1324521
user1324521

Reputation: 9

Haskell: Numerically integrating using recursion

I'm giving Haskell a go at the moment and struggling to rewrite loops in terms of recursions.

I am trying to write a basic integrator which takes some function f(x) and integrates it over the range [a, b] via the Midpoint Method. The integrating function takes three parameters N, a, and b, where N is the number of rectangles being used to approximate the integral.

Wolfram Alpha link

When I try to compile this with GHCI I get a lot of abstract error messages and I don't really know where to start. Lots of 'Out of Scopes' and several 'Multiple Declarations of Main.a [or b]'.

Thanks

MPInt 1 a b = DELTA 1 -- Base case
MPInt N a b = (MPInt (N-1) a b) + DELTA
     where 
     dX = (b - a) / N
     DELTA = dX * f (a + dX * (N+0.5))

f :: (Num a) => a -> a
f x = x^2

Upvotes: 1

Views: 617

Answers (1)

jwodder
jwodder

Reputation: 57590

  • You've named your function MPInt. Only the names of modules, classes, types, and constructors can begin with capital letters; values (including functions) must begin with lowercase letters (or an underscore, or certain punctuation marks). The same problem also applies to N and DELTA.

  • You use DELTA in the definition of the first case of MPInt, yet it's defined as part of the second case. A where clause only applies to the expression immediately before it (in this case, the MPInt N a b = ... definition). (Also, this first use of DELTA treats it as a function, yet the second use and its definition have it as a numeric value).

Upvotes: 10

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