"""First array elements raised to powers from second array, element-wise."""
from __future__ import annotations
from typing import Any
import numpy
import numpoly
from ..baseclass import ndpoly, PolyLike
from ..dispatch import implements
[docs]@implements(numpy.power)
def power(x1: PolyLike, x2: PolyLike, **kwargs: Any) -> ndpoly:
"""
First array elements raised to powers from second array, element-wise.
Raise each base in `x1` to the positionally-corresponding power in
`x2`. `x1` and `x2` must be broadcastable to the same shape. Note that an
integer type raised to a negative integer power will raise a ValueError.
Args:
x1:
The bases.
x2:
The exponents. If ``x1.shape != x2.shape``, they must be
broadcastable to a common shape (which becomes the shape of the
output).
out:
A location into which the result is stored. If provided, it must
have a shape that the inputs broadcast to. If not provided or
`None`, a freshly-allocated array is returned. A tuple (possible
only as a keyword argument) must have length equal to the number of
outputs.
where:
This condition is broadcast over the input. At locations where the
condition is True, the `out` array will be set to the ufunc result.
Elsewhere, the `out` array will retain its original value. Note
that if an uninitialized `out` array is created via the default
``out=None``, locations within it where the condition is False will
remain uninitialized.
kwargs:
Keyword args passed to numpy.ufunc.
Return:
The bases in `x1` raised to the exponents in `x2`.
This is a scalar if both `x1` and `x2` are scalars.
Example:
>>> q0 = numpoly.variable()
>>> (q0+1)**3
polynomial(q0**3+3*q0**2+3*q0+1)
>>> q0q1 = numpoly.variable(2)
>>> (q0q1+1)**[1, 2]
polynomial([q0+1, q1**2+2*q1+1])
"""
x1 = numpoly.aspolynomial(x1)
x2 = numpoly.aspolynomial(x2).tonumpy().astype(int)
if not x2.shape:
out = numpoly.ndpoly.from_attributes(
[(0,)], [numpy.ones(x1.shape, dtype=x1._dtype)], x1.names[:1]
)
for _ in range(x2.item()):
out = numpoly.multiply(out, x1, **kwargs)
elif x1.shape:
if x2.shape[-1] == 1:
if x1.shape[-1] == 1:
out = numpoly.power(x1.T[0].T, x2.T[0].T).T[numpy.newaxis].T
else:
out = numpoly.concatenate(
[power(x, x2.T[0])[numpy.newaxis] for x in x1.T], axis=0
).T
elif x1.shape[-1] == 1:
out = numpoly.concatenate(
[power(x1.T[0].T, x.T).T[numpy.newaxis] for x in x2.T], axis=0
).T
else:
out = numpoly.concatenate(
[power(x1_, x2_).T[numpy.newaxis] for x1_, x2_ in zip(x1.T, x2.T)],
axis=0,
).T
else:
out = numpoly.concatenate(
[power(x1, x.T).T[numpy.newaxis] for x in x2.T], axis=0
).T
return numpoly.polynomial(out)