svgpathtoolss/svgpathtools/polytools.py

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2016-07-06 04:51:11 +00:00
"""This submodule contains tools for working with numpy.poly1d objects."""
# External Dependencies
from __future__ import division, absolute_import
from itertools import combinations
import numpy as np
# Internal Dependencies
from .misctools import isclose
def polyroots(p, realroots=False, condition=lambda r: True):
"""
Returns the roots of a polynomial with coefficients given in p.
p[0] * x**n + p[1] * x**(n-1) + ... + p[n-1]*x + p[n]
INPUT:
p - Rank-1 array-like object of polynomial coefficients.
realroots - a boolean. If true, only real roots will be returned and the
condition function can be written assuming all roots are real.
condition - a boolean-valued function. Only roots satisfying this will be
returned. If realroots==True, these conditions should assume the roots
are real.
OUTPUT:
A list containing the roots of the polynomial.
NOTE: This uses np.isclose and np.roots"""
roots = np.roots(p)
if realroots:
roots = [r.real for r in roots if isclose(r.imag, 0)]
roots = [r for r in roots if condition(r)]
duplicates = []
for idx, (r1, r2) in enumerate(combinations(roots, 2)):
if isclose(r1, r2):
duplicates.append(idx)
return [r for idx, r in enumerate(roots) if idx not in duplicates]
def polyroots01(p):
"""Returns the real roots between 0 and 1 of the polynomial with
coefficients given in p,
p[0] * x**n + p[1] * x**(n-1) + ... + p[n-1]*x + p[n]
p can also be a np.poly1d object. See polyroots for more information."""
return polyroots(p, realroots=True, condition=lambda tval: 0 <= tval <= 1)
def rational_limit(f, g, t0):
"""Computes the limit of the rational function (f/g)(t)
as t approaches t0."""
assert isinstance(f, np.poly1d) and isinstance(g, np.poly1d)
assert g != np.poly1d([0])
if g(t0) != 0:
return f(t0)/g(t0)
elif f(t0) == 0:
return rational_limit(f.deriv(), g.deriv(), t0)
else:
raise ValueError("Limit does not exist.")
def real(z):
try:
return np.poly1d(z.coeffs.real)
except AttributeError:
return z.real
def imag(z):
try:
return np.poly1d(z.coeffs.imag)
except AttributeError:
return z.imag
def poly_real_part(poly):
"""Deprecated."""
return np.poly1d(poly.coeffs.real)
def poly_imag_part(poly):
"""Deprecated."""
return np.poly1d(poly.coeffs.imag)