Added Thomas Algorithm in Haskell (#321)

Author: jiegillet

contents/thomas_algorithm/code/haskell/thomas.hs

@@ -0,0 +1,18 @@
+import Data.List (zip4)
+import Data.Ratio
+
+thomas :: Fractional a => [a] -> [a] -> [a] -> [a] -> [a]
+thomas a b c = init . scanr back 0 . tail . scanl forward (0, 0) . zip4 a b c
+  where
+    forward (c', d') (a, b, c, d) =
+      let denominator = b - a * c'
+       in (c / denominator, (d - a * d') / denominator)
+    back (c, d) x = d - c * x
+
+main :: IO ()
+main = do
+  let a = [0, 2, 3] :: [Ratio Int]
+      b = [1, 3, 6]
+      c = [4, 5, 0]
+      d = [7, 5, 3]
+  print $ thomas a b c d

contents/thomas_algorithm/thomas_algorithm.md

@@ -22,7 +22,7 @@ In the end, we will update $$c$$ and $$d$$ to be $$c'$$ and $$d'$$ like so:
 $$
 \begin{align}
 c'_i &= \frac{c_i}{b_i - a_i \times c'_{i-1}} \\
-d'_i &= \frac{d_i - a_i*d'_{i-1}}{b_i - a_i \times c'_{i-1}}
+d'_i &= \frac{d_i - a_i \times d'_{i-1}}{b_i - a_i \times c'_{i-1}}
 \end{align}
 $$
 
@@ -44,6 +44,8 @@ $$
 [import, lang:"c_cpp"](code/c/thomas.c)
 {% sample lang="py" %}
 [import, lang:"python"](code/python/thomas.py)
+{% sample lang="hs" %}
+[import, lang:"haskell"](code/haskell/thomas.hs)
 {% endmethod %}
 
 This is a much simpler implementation than Gaussian Elimination and only has one for loop before back-substitution, which is why it has a better complexity case.
@@ -70,4 +72,3 @@ $$
 \newcommand{\bfomega}{\boldsymbol{\omega}}
 \newcommand{\bftau}{\boldsymbol{\tau}}
 $$
-