Initial data commit

Task/Thieles-interpolation-formula/Python/thieles-interpolation-formula.py

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+#!/usr/bin/env python3
+
+import math
+
+def thieleInterpolator(x, y):
+    ρ = [[yi]*(len(y)-i) for i, yi in enumerate(y)]
+    for i in range(len(ρ)-1):
+        ρ[i][1] = (x[i] - x[i+1]) / (ρ[i][0] - ρ[i+1][0])
+    for i in range(2, len(ρ)):
+        for j in range(len(ρ)-i):
+            ρ[j][i] = (x[j]-x[j+i]) / (ρ[j][i-1]-ρ[j+1][i-1]) + ρ[j+1][i-2]
+    ρ0 = ρ[0]
+    def t(xin):
+        a = 0
+        for i in range(len(ρ0)-1, 1, -1):
+            a = (xin - x[i-1]) / (ρ0[i] - ρ0[i-2] + a)
+        return y[0] + (xin-x[0]) / (ρ0[1]+a)
+    return t
+
+# task 1: build 32 row trig table
+xVal = [i*.05 for i in range(32)]
+tSin = [math.sin(x) for x in xVal]
+tCos = [math.cos(x) for x in xVal]
+tTan = [math.tan(x) for x in xVal]
+# task 2: define inverses
+iSin = thieleInterpolator(tSin, xVal)
+iCos = thieleInterpolator(tCos, xVal)
+iTan = thieleInterpolator(tTan, xVal)
+# task 3: demonstrate identities
+print('{:16.14f}'.format(6*iSin(.5)))
+print('{:16.14f}'.format(3*iCos(.5)))
+print('{:16.14f}'.format(4*iTan(1)))