def divmod(
x1: PolyLike,
x2: PolyLike,
out: Union[None, ndpoly, Tuple[ndpoly, ...]] = None,
where: Optional[numpy.ndarray] = numpy.array(True),
**kwargs: Any,
) -> Tuple[ndpoly, ndpoly]:
"""
Return element-wise quotient and remainder simultaneously.
``numpoly.divmod(x, y)`` is equivalent to ``(x // y, x % y)``, but faster
because it avoids redundant work. It is used to implement the Python
built-in function ``divmod`` on arrays.
Args:
x1:
Dividend array.
x2:
Divisor array. 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.
Returns:
Element-wise quotient and remainder resulting from floor division.
Raises:
numpoly.baseclass.FeatureNotSupported:
If either `x1` or `x2` contains indeterminants, numerical division
is no longer possible and an error is raised instead. For
polynomial division-remainder see ``numpoly.poly_divmod``.
Examples:
>>> numpoly.divmod([1, 22, 444], 4)
(polynomial([0, 5, 111]), polynomial([1, 2, 0]))
"""
del out
x1, x2 = numpoly.align_polynomials(x1, x2)
if not x1.isconstant() or not x2.isconstant():
raise numpoly.FeatureNotSupported(DIVMOD_ERROR_MSG)
quotient, remainder = numpy.divmod(x1.tonumpy(),
x2.tonumpy(),
where=where,
**kwargs)
return numpoly.polynomial(quotient), numpoly.polynomial(remainder)
def test_zeros_like(func_interface):
"""Tests for numpoly.zeros_like."""
poly = numpoly.polynomial([1, X, 2])
assert_equal(func_interface.zeros_like(poly), [0, 0, 0])
assert_equal(numpoly.zeros_like([1, X, 2]), [0, 0, 0])
poly = numpoly.polynomial([1., X, 2])
assert_equal(func_interface.zeros_like(poly), [0., 0., 0.])
def test_full_like(func_interface):
"""Tests for numpoly.full_like."""
poly = numpoly.polynomial([1, X, 2])
assert_equal(func_interface.full_like(poly, X), [X, X, X])
assert_equal(numpoly.full_like([1, X, 2], X), [X, X, X])
poly = numpoly.polynomial([1., X, 2])
assert_equal(func_interface.full_like(poly, Y), [1. * Y, Y, Y])
def test_add(interface):
"""Tests for numpoly.add."""
assert_equal(interface.add(X, 3), 3 + X)
assert_equal(interface.add(polynomial([1, X, Y]), 4), [5, 4 + X, 4 + Y])
assert_equal(interface.add(polynomial([0, X]), polynomial([Y, 0])), [Y, X])
assert_equal(interface.add(polynomial([[1, X], [Y, X * Y]]), [2, X]),
[[3, 2 * X], [2 + Y, X + X * Y]])
def test_copyto(func_interface):
"""Tests for numpoly.copyto."""
poly = numpoly.polynomial([1, X, Y])
poly_ref = numpoly.polynomial([1, X, Y])
with raises(ValueError):
func_interface.copyto(poly.values, poly_ref, casting="safe")
with raises(ValueError):
numpoly.copyto(poly.values, [1, 2, 3], casting="safe")
with raises(ValueError):
numpoly.copyto(X, Y, casting="unsafe")
func_interface.copyto(poly, X)
assert_equal(poly, [X, X, X])
func_interface.copyto(poly.values, poly_ref, casting="unsafe")
assert_equal(poly, poly_ref)
func_interface.copyto(poly, 4)
assert_equal(poly, [4, 4, 4])
func_interface.copyto(poly.values, poly_ref.values, casting="unsafe")
assert_equal(poly, poly_ref)
poly = numpoly.polynomial([1, 2, 3])
func_interface.copyto(poly, [3, 2, 1], casting="unsafe")
assert_equal(poly, [3, 2, 1])
func_interface.copyto(poly.values,
numpoly.polynomial([1, 2, 3]),
casting="unsafe")
assert_equal(poly, [1, 2, 3])
out = numpy.zeros(3, dtype=float)
numpoly.copyto(out, poly, casting="unsafe")
assert_equal(out, [1., 2., 3.])
def test_ones_like(func_interface):
"""Tests for numpoly.ones_like."""
poly = numpoly.polynomial([1, X, 2])
assert_equal(func_interface.ones_like(poly), [1, 1, 1])
assert_equal(numpoly.ones_like([1, X, 2]), [1, 1, 1])
poly = numpoly.polynomial([1., X, 2])
assert_equal(func_interface.ones_like(poly), [1., 1., 1.])
def test_count_nonzero(func_interface):
"""Tests for numpoly.count_nonzero."""
poly1 = polynomial([[0, Y], [X, 1]])
poly2 = polynomial([[0, Y, X, 0, 0], [3, 0, 0, 2, 19]])
assert_equal(func_interface.count_nonzero(poly1), 3, type_=int)
assert_equal(func_interface.count_nonzero(poly1, axis=0), [1, 2])
assert_equal(func_interface.count_nonzero(poly2, axis=0), [1, 1, 1, 1, 1])
assert_equal(func_interface.count_nonzero(X), 1, type_=int)
def test_where(func_interface):
"""Tests for numpoly.where."""
poly1 = numpoly.polynomial([0, 4, 0])
poly2 = numpoly.polynomial([Y, 0, X])
assert_equal(func_interface.where([0, 1, 0], poly1, poly2), [Y, 4, X])
assert_equal(func_interface.where([1, 0, 1], poly1, poly2), [0, 0, 0])
assert_equal(func_interface.where(poly1)[0], [1])
assert_equal(func_interface.where(poly2)[0], [0, 2])
def test_numpy_allclose(func_interface):
poly1 = numpoly.polynomial([1e10 * X, 1e-7])
poly2 = numpoly.polynomial([1.00001e10 * X, 1e-8])
assert not func_interface.allclose(poly1, poly2)
poly1 = numpoly.polynomial([1e10 * X, 1e-8])
poly2 = numpoly.polynomial([1.00001e10 * X, 1e-9])
assert func_interface.allclose(poly1, poly2)
poly2 = numpoly.polynomial([1e10 * Y, 1e-8])
assert not func_interface.allclose(poly1, poly2)
def test_numpy_logical_and(func_interface):
poly1 = numpoly.polynomial([0, X])
poly2 = numpoly.polynomial([1, X])
poly3 = numpoly.polynomial([0, Y])
assert numpy.all(func_interface.logical_and(1, poly1) == [False, True])
assert numpy.all(1 and poly1 == [0, X])
assert numpy.all(func_interface.logical_and(1, poly2) == [True, True])
assert numpy.all(1 and poly2 == [1, X])
assert numpy.all(func_interface.logical_and(poly2, poly3) == [False, True])
def test_numpy_logical_or(func_interface):
poly1 = numpoly.polynomial([0, X])
poly2 = numpoly.polynomial([1, X])
poly3 = numpoly.polynomial([0, Y])
assert numpy.all(func_interface.logical_or(1, poly1) == [True, True])
assert numpy.all(1 or poly1 == [1, 1])
assert numpy.all(func_interface.logical_or(0, poly1) == [False, True])
assert numpy.all(0 or poly1 == [0, X])
assert numpy.all(func_interface.logical_or(poly2, poly3) == [True, True])
def test_numpy_isclose(func_interface):
poly1 = numpoly.polynomial([1e10 * X, 1e-7])
poly2 = numpoly.polynomial([1.00001e10 * X, 1e-8])
assert numpy.all(func_interface.isclose(poly1, poly2) == [True, False])
poly1 = numpoly.polynomial([1e10 * X, 1e-8])
poly2 = numpoly.polynomial([1.00001e10 * X, 1e-9])
assert numpy.all(func_interface.isclose(poly1, poly2) == [True, True])
poly2 = numpoly.polynomial([1e10 * Y, 1e-8])
assert numpy.all(func_interface.isclose(poly1, poly2) == [False, True])
def test_numpy_add(interface):
assert interface.add(X, 3) == 3 + X
assert numpy.all(
interface.add(polynomial([1, X, Y]), 4) == [5, 4 + X, 4 + Y])
assert numpy.all(
interface.add(polynomial([0, X]), polynomial([Y, 0])) == [Y, X])
assert numpy.all(
interface.add(polynomial([[1, X], [Y, X * Y]]), [2, X]) ==
[[3, 2 * X], [2 + Y, X + X * Y]])
def test_numpy_array_str(func_interface):
assert str(4 + 6 * X**2) == "4+6*X**2"
assert func_interface.array_str(4 + 6 * X**2) == "4+6*X**2"
assert str(polynomial([1., -5 * X, 3 - X**2])) == "[1.0 -5.0*X 3.0-X**2]"
assert func_interface.array_str(polynomial([1., -5 * X, 3 - X**2
])) == "[1.0 -5.0*X 3.0-X**2]"
assert str(polynomial([[[1, 2], [5, Y]]])) == """\
[[[1 2]
[5 Y]]]"""
assert func_interface.array_str(polynomial([[[1, 2], [5, Y]]])) == """\
def test_allclose(func_interface):
"""Tests for numpoly.allclose."""
poly1 = numpoly.polynomial([1e10 * X, 1e-7])
poly2 = numpoly.polynomial([1.00001e10 * X, 1e-8])
assert_equal(func_interface.allclose(poly1, poly2), False, type_=bool)
poly1 = numpoly.polynomial([1e10 * X, 1e-8])
poly2 = numpoly.polynomial([1.00001e10 * X, 1e-9])
assert_equal(func_interface.allclose(poly1, poly2), True, type_=bool)
poly2 = numpoly.polynomial([1e10 * Y, 1e-8])
assert_equal(func_interface.allclose(poly1, poly2), False, type_=bool)
def test_isclose(func_interface):
"""Tests for numpoly.isclose."""
poly1 = numpoly.polynomial([1e10 * X, 1e-7])
poly2 = numpoly.polynomial([1.00001e10 * X, 1e-8])
assert_equal(func_interface.isclose(poly1, poly2), [True, False])
poly1 = numpoly.polynomial([1e10 * X, 1e-8])
poly2 = numpoly.polynomial([1.00001e10 * X, 1e-9])
assert_equal(func_interface.isclose(poly1, poly2), [True, True])
poly2 = numpoly.polynomial([1e10 * Y, 1e-8])
assert_equal(func_interface.isclose(poly1, poly2), [False, True])
def test_logical_and(func_interface):
"""Tests for numpoly.logical_and."""
poly1 = numpoly.polynomial([0, X])
poly2 = numpoly.polynomial([1, X])
poly3 = numpoly.polynomial([0, Y])
assert_equal(func_interface.logical_and(1, poly1), [False, True])
assert_equal(1 and poly1, poly1)
assert_equal(func_interface.logical_and(1, poly2), [True, True])
assert_equal(1 and poly2, poly2)
assert_equal(func_interface.logical_and(poly2, poly3), [False, True])
def test_logical_or(func_interface):
"""Tests for numpoly.logical_or."""
poly1 = numpoly.polynomial([0, X])
poly2 = numpoly.polynomial([1, X])
poly3 = numpoly.polynomial([0, Y])
assert_equal(func_interface.logical_or(1, poly1), [True, True])
assert_equal(1 or poly1, 1, type_=int)
assert_equal(func_interface.logical_or(0, poly1), [False, True])
assert_equal(0 or poly1, poly1)
assert_equal(func_interface.logical_or(poly2, poly3), [True, True])
def test_poly_divide():
const = numpoly.polynomial([1, 2])
poly1 = numpoly.polynomial(X)
poly2 = numpoly.polynomial([1, X])
poly3 = numpoly.polynomial([[0, Y], [X, 1]])
assert numpy.all(numpoly.poly_divide(poly1, const) == [X, 0.5 * X])
assert numpy.all(numpoly.poly_divide(const, poly1) == [0, 0])
assert numpy.all(poly1.__truediv__(poly2) == [X, 1])
assert numpy.all(poly2.__rtruediv__(poly3) == [[0, 0], [X, 0]])
assert numpy.all(poly2.__div__(poly1) == [0, 1])
assert numpy.all(poly3.__rdiv__(poly2) == [[0, 0], [0, X]])
def test_not_equal(interface):
"""Tests for numpoly.not_equal."""
poly = polynomial([[0, 2 + Y], [X, 2]])
assert_equal(([X, 2 + Y] != poly), [[True, False], [False, True]])
assert_equal(interface.not_equal(numpoly.polynomial([X, 2 + Y]), poly),
[[True, False], [False, True]])
assert_equal((X != poly), [[True, True], [False, True]])
assert_equal(interface.not_equal(X, poly), [[True, True], [False, True]])
assert_equal(poly != poly.T, [[False, True], [True, False]])
assert_equal(interface.not_equal(poly, poly.T),
[[False, True], [True, False]])
def test_true_divide(func_interface):
"""Tests for numpoly.true_divide."""
poly = polynomial([[0, Y], [X, 1]])
assert_equal(func_interface.true_divide(poly, 2),
polynomial([[0, 0.5 * Y], [0.5 * X, 0.5]]))
assert_equal(func_interface.true_divide(poly, [1, 2]),
[[0, 0.5 * Y], [X, 0.5]])
assert_equal(func_interface.true_divide(poly, [[1, 2], [2, 1]]),
[[0, 0.5 * Y], [0.5 * X, 1]])
with raises(numpoly.FeatureNotSupported):
func_interface.true_divide(poly, X)
def test_numpy_divide(func_interface):
poly = polynomial([[0, Y], [X, 1]])
assert numpy.all(poly / 2 == polynomial([[0, 0.5 * Y], [0.5 * X, 0.5]]))
assert numpy.all(
func_interface.divide(poly, 2) == [[0, 0.5 * Y], [0.5 * X, 0.5]])
assert numpy.all(poly / [1, 2] == [[0, 0.5 * Y], [X, 0.5]])
assert numpy.all(
func_interface.divide(poly, [1, 2]) == [[0, 0.5 * Y], [X, 0.5]])
assert numpy.all(poly / [[1, 2], [2, 1]] == [[0, 0.5 * Y], [0.5 * X, 1]])
assert numpy.all(
func_interface.divide(poly, [[1, 2], [2, 1]]) == [[0, 0.5 *
Y], [0.5 * X, 1]])
def test_array_str(func_interface):
"""Tests for numpoly.array_str."""
assert str(polynomial([])).startswith("[]")
assert str(4 + 6 * X**2) == "6*q0**2+4"
assert func_interface.array_str(4 + 6 * X**2) == "6*q0**2+4"
assert str(polynomial([1., -5 * X,
3 - X**2])) == "[1.0 -5.0*q0 -q0**2+3.0]"
assert func_interface.array_str(polynomial(
[1., -5 * X, 3 - X**2])) == "[1.0 -5.0*q0 -q0**2+3.0]"
assert str(polynomial([[[1, 2], [5, Y]]])) == """\
[[[1 2]
[5 q1]]]"""
assert func_interface.array_str(polynomial([[[1, 2], [5, Y]]])) == """\
def test_diag(func_interface):
"""Tests for numpoly.diag."""
poly = polynomial([[1, 2, X], [4, Y, 6], [7, 8, X + Y]])
assert_equal(func_interface.diag(poly), [1, Y, X + Y])
assert_equal(func_interface.diag(poly, k=1), [2, 6])
assert_equal(func_interface.diag(poly, k=-1), [4, 8])
poly = polynomial([X, Y])
assert_equal(func_interface.diag(poly), [[X, 0], [0, Y]])
assert_equal(func_interface.diag(poly, k=1),
[[0, X, 0], [0, 0, Y], [0, 0, 0]])
assert_equal(func_interface.diag(poly, k=-1),
[[0, 0, 0], [X, 0, 0], [0, Y, 0]])
def test_numpy_matmul(func_interface):
poly1 = numpoly.polynomial([[0, X], [1, Y]])
poly2 = numpoly.polynomial([X, 2])
assert numpy.all(
func_interface.matmul(poly1, poly2) == [[X**2, 2 *
X], [X + X * Y, 2 + 2 * Y]])
assert func_interface.matmul(numpy.zeros((9, 5, 7, 4)),
numpy.ones(
(9, 5, 4, 3))).shape == (9, 5, 7, 3)
with raises(ValueError):
func_interface.matmul(poly1, 4)
with raises(ValueError):
func_interface.matmul(3, poly2)
def test_matmul(func_interface):
"""Tests for numpoly.matmul."""
poly1 = numpoly.polynomial([[0, X], [1, Y]])
poly2 = numpoly.polynomial([X, 2])
assert_equal(func_interface.matmul(poly1, poly2),
[[X**2, 2 * X], [X + X * Y, 2 + 2 * Y]])
assert_equal(
func_interface.matmul(numpy.ones((2, 5, 6, 4)), numpy.ones(
(2, 5, 4, 3))), 4 * numpy.ones((2, 5, 6, 3)))
with raises(ValueError):
func_interface.matmul(poly1, 4)
with raises(ValueError):
func_interface.matmul(3, poly2)
def test_equal(interface):
"""Tests for numpoly.equal."""
poly = polynomial([[0, 2 + Y], [X, 2]])
assert_equal(interface.equal(X, X), True)
assert_equal(interface.equal(X, [X]), [True])
assert_equal([X] == X, [True])
assert_equal(interface.equal(X, Y), False)
assert_equal(([X, 2 + Y] == poly), [[False, True], [True, False]])
assert_equal(interface.equal(numpoly.polynomial([X, 2 + Y]), poly),
[[False, True], [True, False]])
assert_equal((X == poly), [[False, False], [True, False]])
assert_equal(interface.equal(X, poly), [[False, False], [True, False]])
assert_equal(poly == poly.T, [[True, False], [False, True]])
assert_equal(interface.equal(poly, poly.T), [[True, False], [False, True]])
def ones(
shape: Union[int, Sequence[int]],
dtype: numpy.typing.DTypeLike = float,
order: Order = "C",
) -> ndpoly:
"""
Return a new array of given shape and type, filled with ones.
Args:
shape:
Shape of the new array, e.g., ``(2, 3)`` or ``2``.
dtype:
The desired data-type for the array, e.g., `numpy.int8`.
Default is `numpy.float64`.
order:
Whether to store multi-dimensional data in row-major
(C-style) or column-major (Fortran-style) order in
memory.
Returns:
Array of ones with the given shape, dtype, and order.
Examples:
>>> numpoly.ones(5)
polynomial([1.0, 1.0, 1.0, 1.0, 1.0])
"""
return numpoly.polynomial(numpy.ones(shape, dtype=dtype, order=order))
def test_numpy_sum(interface):
poly = polynomial([[1, 5 * X], [X + 3, -Y]])
assert interface.sum(poly) == -Y + X * 6 + 4
assert numpy.all(interface.sum(poly, axis=0) == [X + 4, -Y + X * 5])
assert numpy.all(
interface.sum(poly, axis=-1, keepdims=True) == [[X * 5 +
1], [X - Y + 3]])
def test_numpy_mean(interface):
poly = numpoly.polynomial([[1, 2 * X], [3 * Y + X, 4]])
assert interface.mean(poly) == 1.25 + 0.75 * Y + 0.75 * X
assert numpy.all(
interface.mean(poly, axis=0) == [0.5 + 1.5 * Y + 0.5 * X, 2.0 + X])
assert numpy.all(
interface.mean(poly, axis=1) == [0.5 + X, 2.0 + 1.5 * Y + 0.5 * X])