scipy.interpolate.approximate_taylor_polynomial¶
-
scipy.interpolate.
approximate_taylor_polynomial
(f, x, degree, scale, order=None)[source]¶ Estimate the Taylor polynomial of f at x by polynomial fitting.
- Parameters
- fcallable
The function whose Taylor polynomial is sought. Should accept a vector of x values.
- xscalar
The point at which the polynomial is to be evaluated.
- degreeint
The degree of the Taylor polynomial
- scalescalar
The width of the interval to use to evaluate the Taylor polynomial. Function values spread over a range this wide are used to fit the polynomial. Must be chosen carefully.
- orderint or None, optional
The order of the polynomial to be used in the fitting; f will be evaluated
order+1
times. If None, use degree.
- Returns
- ppoly1d instance
The Taylor polynomial (translated to the origin, so that for example p(0)=f(x)).
Notes
The appropriate choice of “scale” is a trade-off; too large and the function differs from its Taylor polynomial too much to get a good answer, too small and round-off errors overwhelm the higher-order terms. The algorithm used becomes numerically unstable around order 30 even under ideal circumstances.
Choosing order somewhat larger than degree may improve the higher-order terms.