thomas python example

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

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+#Author: gammison
+
+#note this example is inplace and destructive
+def thomas(a:list,b:list,c:list,d:list):
+
+    #set the initial elements
+    c[0] = c[0] / b[0]
+    d[0] = d[0] / b[0]
+
+    n = len(d) #number of equations to solve
+    #range is exclusive, loop will run from 1 to n-1
+    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, will loop n-2 to 0 inclusive
+    for i in range(n-2,-1,-1):
+        d[i] = d[i] - c[i]*d[i+1]
+
+    return d
+
+    #Complexity:
+    #Two loops,each take O(n), and a few contant time operations => T(n) = 2*O(n)+c*O(1) = O(n)
+
+#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)