Thiele's interpolation formula: Difference between revisions
Python solution
(Added zkl) |
(Python solution) |
||
Line 883:
#"{$atan}"
4*$atan.InvokeReturnAsIs(1)</lang>
=={{header|Python}}==
{{trans|Go}}
<lang python>#!/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)))</lang>
{{out}}
<pre>
3.14159265358979
3.14159265358979
3.14159265358980
</pre>
=={{header|Racket}}==
| |||