Conditioning of evaluating tan()¶
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import numpy as np
import matplotlib.pyplot as pt
Let us estimate the sensitivity of evaluating the $\tan$ function:
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x = np.linspace(-5, 5, 1000)
pt.ylim([-10, 10])
pt.plot(x, np.tan(x))
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x = np.pi/2 - 0.0001
#x = 0.1
x
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np.tan(x)
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dx = 0.00005
np.tan(x+dx)
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Condition number estimates¶
From evaluation data¶
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#clear
np.abs(np.tan(x+dx) - np.tan(x))/np.abs(np.tan(x)) / (np.abs(dx) / np.abs(x))
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Using the derivative estimate¶
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import sympy as sp
xsym = sp.Symbol("x")
f = sp.tan(xsym)
df = f.diff(xsym)
df
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Evaluate the derivative estimate. Use .subs(xsym, x) to substitute in the value of x.
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#clear
(xsym*df/f).subs(xsym, x)
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