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Implementation of operations involving polynomials.
import numpy as np
from numba import jit
from numba.core import types
from numba.core.extending import overload
from import numpy_support as np_support
def roots_impl(p):
# cast int vectors to float cf. numpy, this is a bit dicey as
# the roots could be complex which will fail anyway
ty = getattr(p, 'dtype', p)
if isinstance(ty, types.Integer):
cast_t = np.float64
cast_t = np_support.as_dtype(ty)
def roots_impl(p):
# impl based on numpy:
if len(p.shape) != 1:
raise ValueError("Input must be a 1d array.")
non_zero = np.nonzero(p)[0]
if len(non_zero) == 0:
return np.zeros(0, dtype=cast_t)
tz = len(p) - non_zero[-1] - 1
# pull out the coeffs selecting between possible zero pads
p = p[int(non_zero[0]):int(non_zero[-1]) + 1]
n = len(p)
if n > 1:
# construct companion matrix, ensure fortran order
# to give to eigvals, write to upper diag and then
# transpose.
A = np.diag(np.ones((n - 2,), cast_t), 1).T
A[0, :] = -p[1:] / p[0] # normalize
roots = np.linalg.eigvals(A)
roots = np.zeros(0, dtype=cast_t)
# add in additional zeros on the end if needed
if tz > 0:
return np.hstack((roots, np.zeros(tz, dtype=cast_t)))
return roots
return roots_impl
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