Resistor mesh: Difference between revisions

=={{header|Haskell}}==

Translation of Octave program. All mutations are expressed as monoidal operations.

<lang haskell>{-# LANGUAGE ParallelListComp #-}

import Numeric.LinearAlgebra (linearSolve, toDense, (!), flatten)

import Data.Monoid ((<>), Sum(..))

rMesh n (ar, ac) (br, bc)

| n < 2 = Nothing

| any (\x -> x < 1 || x > n) [ar, ac, br, bc] = Nothing

| otherwise = between a b <$> voltage

where

a = (ac - 1) + n*(ar - 1)

b = (bc - 1) + n*(br - 1)

between x y v = abs (v ! a - v ! b)

voltage = flatten <$> linearSolve matrixG current

matrixG = toDense $ concat [ element row col node

| row <- [1..n], col <- [1..n]

| node <- [0..] ]

element row col node =

let (Sum c, elements) =

(Sum 1, [((node, node-n), -1)]) `when` (row > 1) <>

(Sum 1, [((node, node+n), -1)]) `when` (row < n) <>

(Sum 1, [((node, node-1), -1)]) `when` (col > 1) <>

(Sum 1, [((node, node+1), -1)]) `when` (col < n)

in [((node, node), c)] <> elements

x `when` p = if p then x else mempty

current = toDense [ ((a, 0), -1) , ((b, 0), 1) , ((n^2-1, 0), 0) ]</lang>

{{Out}}

λ> rMesh 10 (2,2) (7,8)

Just 1.6089912417307304