"""Return the truth value of (x1 < x2) element-wise."""
from __future__ import annotations
from typing import Any, Optional
import numpy
import numpoly
from ..baseclass import PolyLike
from ..dispatch import implements
[docs]@implements(numpy.less)
def less(
x1: PolyLike,
x2: PolyLike,
out: Optional[numpy.ndarray] = None,
**kwargs: Any,
) -> numpy.ndarray:
"""
Return the truth value of (x1 < x2) element-wise.
Args:
x1, x2:
Input arrays. 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:
Output array, element-wise comparison of `x1` and `x2`. Typically of
type bool, unless ``dtype=object`` is passed. This is a scalar if both
`x1` and `x2` are scalars.
Example:
>>> q0, q1 = numpoly.variable(2)
>>> numpoly.less(3, 4)
True
>>> numpoly.less(4*q0, 3*q0)
False
>>> numpoly.less(q0, q1)
True
>>> numpoly.less(q0**2, q0)
False
>>> numpoly.less([1, q0, q0**2, q0**3], q1)
array([ True, True, False, False])
>>> numpoly.less(q0+1, q0-1)
False
>>> numpoly.less(q0, q0)
False
"""
x1, x2 = numpoly.align_polynomials(x1, x2)
coefficients1 = x1.coefficients
coefficients2 = x2.coefficients
if out is None:
out = numpy.less(coefficients1[0], coefficients2[0], **kwargs)
if not out.shape:
return less(x1.ravel(), x2.ravel(), out=out.ravel()).item()
options = numpoly.get_options()
for idx in numpoly.glexsort(
x1.exponents.T, graded=options["sort_graded"], reverse=options["sort_reverse"]
):
indices = (coefficients1[idx] != 0) | (coefficients2[idx] != 0)
indices &= coefficients1[idx] != coefficients2[idx]
out[indices] = numpy.less(coefficients1[idx], coefficients2[idx], **kwargs)[
indices
]
return out