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