thomas python example (#191)

Author: gammison

CONTRIBUTORS.md

@@ -13,6 +13,7 @@ Chinmaya Mahesh
 Unlambder
 Kjetil Johannessen
 CDsigma
+Gammison
 hsjoihs
 DominikRafacz
 lulucca12

chapters/matrix_methods/thomas/code/python/thomas.py

@@ -0,0 +1,42 @@
+# Author: gammison
+
+# note this example is inplace and destructive
+def thomas(a, b, c, d):
+    
+    #set the initial elements
+    c[0] = c[0] / b[0]
+    d[0] = d[0] / b[0]
+
+    n = len(d) #number of equations to solve
+    for i in range(1,n):
+        #scale factor for c and d
+        scale = 1 / (b[i] - c[i-1]*a[i])
+        
+        c[i] = c[i] * scale
+        d[i] = (d[i] -a[i] * d[i-1]) * scale
+
+    
+    # do the back substitution
+    for i in range(n-2,-1,-1):
+        d[i] = d[i] - c[i]*d[i+1]
+    
+    return d
+
+def main():
+    # example for matrix
+    # [1  4  0][x]   [7]
+    # [2  3  5][y] = [5]
+    # [0  3  6][z]   [3]
+    #                 [.8666]
+    # soln will equal [1.533]
+    #                 [-.266]
+    # note we index a from 1 and c from 0
+    a = [0, 2, 3]
+    b = [1, 3, 6]
+    c = [4, 5, 0]
+    d = [7, 5, 3]
+    soln = thomas(a, b, c, d)
+    print(soln)
+
+if __name__ == '__main__':
+    main()

chapters/matrix_methods/thomas/thomas.md

@@ -40,6 +40,8 @@ In code, this will look like this:
 {% method %}
 {% sample lang="jl" %}
 [import, lang:"julia"](code/julia/thomas.jl)
+{% sample lang="py" %}
+[import, lang:"python"](code/python/thomas.py)
 {% 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.