81 lines
2.4 KiB
Python
81 lines
2.4 KiB
Python
"""This submodule contains tools for working with numpy.poly1d objects."""
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# External Dependencies
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from __future__ import division, absolute_import
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from itertools import combinations
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import numpy as np
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# Internal Dependencies
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from .misctools import isclose
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def polyroots(p, realroots=False, condition=lambda r: True):
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"""
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Returns the roots of a polynomial with coefficients given in p.
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p[0] * x**n + p[1] * x**(n-1) + ... + p[n-1]*x + p[n]
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INPUT:
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p - Rank-1 array-like object of polynomial coefficients.
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realroots - a boolean. If true, only real roots will be returned and the
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condition function can be written assuming all roots are real.
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condition - a boolean-valued function. Only roots satisfying this will be
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returned. If realroots==True, these conditions should assume the roots
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are real.
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OUTPUT:
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A list containing the roots of the polynomial.
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NOTE: This uses np.isclose and np.roots"""
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roots = np.roots(p)
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if realroots:
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roots = [r.real for r in roots if isclose(r.imag, 0)]
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roots = [r for r in roots if condition(r)]
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duplicates = []
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for idx, (r1, r2) in enumerate(combinations(roots, 2)):
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if isclose(r1, r2):
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duplicates.append(idx)
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return [r for idx, r in enumerate(roots) if idx not in duplicates]
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def polyroots01(p):
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"""Returns the real roots between 0 and 1 of the polynomial with
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coefficients given in p,
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p[0] * x**n + p[1] * x**(n-1) + ... + p[n-1]*x + p[n]
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p can also be a np.poly1d object. See polyroots for more information."""
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return polyroots(p, realroots=True, condition=lambda tval: 0 <= tval <= 1)
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def rational_limit(f, g, t0):
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"""Computes the limit of the rational function (f/g)(t)
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as t approaches t0."""
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assert isinstance(f, np.poly1d) and isinstance(g, np.poly1d)
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assert g != np.poly1d([0])
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if g(t0) != 0:
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return f(t0)/g(t0)
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elif f(t0) == 0:
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return rational_limit(f.deriv(), g.deriv(), t0)
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else:
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raise ValueError("Limit does not exist.")
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def real(z):
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try:
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return np.poly1d(z.coeffs.real)
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except AttributeError:
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return z.real
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def imag(z):
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try:
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return np.poly1d(z.coeffs.imag)
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except AttributeError:
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return z.imag
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def poly_real_part(poly):
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"""Deprecated."""
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return np.poly1d(poly.coeffs.real)
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def poly_imag_part(poly):
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"""Deprecated."""
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return np.poly1d(poly.coeffs.imag)
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