619 lines
18 KiB
Python
619 lines
18 KiB
Python
"""Test inter-conversion of different polynomial classes.
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This tests the convert and cast methods of all the polynomial classes.
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"""
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import operator as op
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from numbers import Number
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import pytest
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import numpy as np
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from numpy.exceptions import RankWarning
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from numpy.polynomial import (
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Chebyshev,
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Hermite,
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HermiteE,
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Laguerre,
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Legendre,
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Polynomial,
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)
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from numpy.testing import (
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assert_,
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assert_almost_equal,
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assert_equal,
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assert_raises,
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)
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#
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# fixtures
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#
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classes = (
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Polynomial, Legendre, Chebyshev, Laguerre,
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Hermite, HermiteE
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)
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classids = tuple(cls.__name__ for cls in classes)
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@pytest.fixture(params=classes, ids=classids)
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def Poly(request):
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return request.param
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#
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# helper functions
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#
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random = np.random.random
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def assert_poly_almost_equal(p1, p2, msg=""):
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try:
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assert_(np.all(p1.domain == p2.domain))
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assert_(np.all(p1.window == p2.window))
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assert_almost_equal(p1.coef, p2.coef)
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except AssertionError:
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msg = f"Result: {p1}\nTarget: {p2}"
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raise AssertionError(msg)
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#
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# Test conversion methods that depend on combinations of two classes.
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#
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Poly1 = Poly
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Poly2 = Poly
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def test_conversion(Poly1, Poly2):
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x = np.linspace(0, 1, 10)
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coef = random((3,))
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d1 = Poly1.domain + random((2,)) * .25
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w1 = Poly1.window + random((2,)) * .25
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p1 = Poly1(coef, domain=d1, window=w1)
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d2 = Poly2.domain + random((2,)) * .25
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w2 = Poly2.window + random((2,)) * .25
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p2 = p1.convert(kind=Poly2, domain=d2, window=w2)
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assert_almost_equal(p2.domain, d2)
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assert_almost_equal(p2.window, w2)
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assert_almost_equal(p2(x), p1(x))
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def test_cast(Poly1, Poly2):
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x = np.linspace(0, 1, 10)
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coef = random((3,))
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d1 = Poly1.domain + random((2,)) * .25
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w1 = Poly1.window + random((2,)) * .25
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p1 = Poly1(coef, domain=d1, window=w1)
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d2 = Poly2.domain + random((2,)) * .25
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w2 = Poly2.window + random((2,)) * .25
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p2 = Poly2.cast(p1, domain=d2, window=w2)
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assert_almost_equal(p2.domain, d2)
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assert_almost_equal(p2.window, w2)
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assert_almost_equal(p2(x), p1(x))
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#
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# test methods that depend on one class
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#
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def test_identity(Poly):
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d = Poly.domain + random((2,)) * .25
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w = Poly.window + random((2,)) * .25
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x = np.linspace(d[0], d[1], 11)
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p = Poly.identity(domain=d, window=w)
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assert_equal(p.domain, d)
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assert_equal(p.window, w)
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assert_almost_equal(p(x), x)
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def test_basis(Poly):
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d = Poly.domain + random((2,)) * .25
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w = Poly.window + random((2,)) * .25
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p = Poly.basis(5, domain=d, window=w)
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assert_equal(p.domain, d)
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assert_equal(p.window, w)
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assert_equal(p.coef, [0] * 5 + [1])
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def test_fromroots(Poly):
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# check that requested roots are zeros of a polynomial
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# of correct degree, domain, and window.
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d = Poly.domain + random((2,)) * .25
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w = Poly.window + random((2,)) * .25
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r = random((5,))
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p1 = Poly.fromroots(r, domain=d, window=w)
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assert_equal(p1.degree(), len(r))
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assert_equal(p1.domain, d)
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assert_equal(p1.window, w)
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assert_almost_equal(p1(r), 0)
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# check that polynomial is monic
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pdom = Polynomial.domain
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pwin = Polynomial.window
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p2 = Polynomial.cast(p1, domain=pdom, window=pwin)
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assert_almost_equal(p2.coef[-1], 1)
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def test_bad_conditioned_fit(Poly):
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x = [0., 0., 1.]
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y = [1., 2., 3.]
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# check RankWarning is raised
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with pytest.warns(RankWarning) as record:
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Poly.fit(x, y, 2)
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assert record[0].message.args[0] == "The fit may be poorly conditioned"
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def test_fit(Poly):
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def f(x):
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return x * (x - 1) * (x - 2)
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x = np.linspace(0, 3)
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y = f(x)
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# check default value of domain and window
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p = Poly.fit(x, y, 3)
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assert_almost_equal(p.domain, [0, 3])
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assert_almost_equal(p(x), y)
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assert_equal(p.degree(), 3)
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# check with given domains and window
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d = Poly.domain + random((2,)) * .25
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w = Poly.window + random((2,)) * .25
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p = Poly.fit(x, y, 3, domain=d, window=w)
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assert_almost_equal(p(x), y)
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assert_almost_equal(p.domain, d)
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assert_almost_equal(p.window, w)
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p = Poly.fit(x, y, [0, 1, 2, 3], domain=d, window=w)
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assert_almost_equal(p(x), y)
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assert_almost_equal(p.domain, d)
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assert_almost_equal(p.window, w)
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# check with class domain default
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p = Poly.fit(x, y, 3, [])
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assert_equal(p.domain, Poly.domain)
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assert_equal(p.window, Poly.window)
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p = Poly.fit(x, y, [0, 1, 2, 3], [])
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assert_equal(p.domain, Poly.domain)
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assert_equal(p.window, Poly.window)
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# check that fit accepts weights.
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w = np.zeros_like(x)
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z = y + random(y.shape) * .25
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w[::2] = 1
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p1 = Poly.fit(x[::2], z[::2], 3)
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p2 = Poly.fit(x, z, 3, w=w)
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p3 = Poly.fit(x, z, [0, 1, 2, 3], w=w)
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assert_almost_equal(p1(x), p2(x))
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assert_almost_equal(p2(x), p3(x))
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def test_equal(Poly):
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p1 = Poly([1, 2, 3], domain=[0, 1], window=[2, 3])
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p2 = Poly([1, 1, 1], domain=[0, 1], window=[2, 3])
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p3 = Poly([1, 2, 3], domain=[1, 2], window=[2, 3])
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p4 = Poly([1, 2, 3], domain=[0, 1], window=[1, 2])
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assert_(p1 == p1)
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assert_(not p1 == p2)
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assert_(not p1 == p3)
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assert_(not p1 == p4)
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def test_not_equal(Poly):
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p1 = Poly([1, 2, 3], domain=[0, 1], window=[2, 3])
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p2 = Poly([1, 1, 1], domain=[0, 1], window=[2, 3])
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p3 = Poly([1, 2, 3], domain=[1, 2], window=[2, 3])
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p4 = Poly([1, 2, 3], domain=[0, 1], window=[1, 2])
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assert_(not p1 != p1)
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assert_(p1 != p2)
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assert_(p1 != p3)
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assert_(p1 != p4)
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def test_add(Poly):
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# This checks commutation, not numerical correctness
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c1 = list(random((4,)) + .5)
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c2 = list(random((3,)) + .5)
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p1 = Poly(c1)
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p2 = Poly(c2)
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p3 = p1 + p2
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assert_poly_almost_equal(p2 + p1, p3)
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assert_poly_almost_equal(p1 + c2, p3)
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assert_poly_almost_equal(c2 + p1, p3)
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assert_poly_almost_equal(p1 + tuple(c2), p3)
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assert_poly_almost_equal(tuple(c2) + p1, p3)
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assert_poly_almost_equal(p1 + np.array(c2), p3)
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assert_poly_almost_equal(np.array(c2) + p1, p3)
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assert_raises(TypeError, op.add, p1, Poly([0], domain=Poly.domain + 1))
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assert_raises(TypeError, op.add, p1, Poly([0], window=Poly.window + 1))
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if Poly is Polynomial:
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assert_raises(TypeError, op.add, p1, Chebyshev([0]))
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else:
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assert_raises(TypeError, op.add, p1, Polynomial([0]))
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def test_sub(Poly):
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# This checks commutation, not numerical correctness
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c1 = list(random((4,)) + .5)
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c2 = list(random((3,)) + .5)
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p1 = Poly(c1)
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p2 = Poly(c2)
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p3 = p1 - p2
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assert_poly_almost_equal(p2 - p1, -p3)
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assert_poly_almost_equal(p1 - c2, p3)
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assert_poly_almost_equal(c2 - p1, -p3)
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assert_poly_almost_equal(p1 - tuple(c2), p3)
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assert_poly_almost_equal(tuple(c2) - p1, -p3)
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assert_poly_almost_equal(p1 - np.array(c2), p3)
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assert_poly_almost_equal(np.array(c2) - p1, -p3)
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assert_raises(TypeError, op.sub, p1, Poly([0], domain=Poly.domain + 1))
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assert_raises(TypeError, op.sub, p1, Poly([0], window=Poly.window + 1))
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if Poly is Polynomial:
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assert_raises(TypeError, op.sub, p1, Chebyshev([0]))
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else:
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assert_raises(TypeError, op.sub, p1, Polynomial([0]))
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def test_mul(Poly):
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c1 = list(random((4,)) + .5)
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c2 = list(random((3,)) + .5)
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p1 = Poly(c1)
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p2 = Poly(c2)
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p3 = p1 * p2
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assert_poly_almost_equal(p2 * p1, p3)
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assert_poly_almost_equal(p1 * c2, p3)
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assert_poly_almost_equal(c2 * p1, p3)
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assert_poly_almost_equal(p1 * tuple(c2), p3)
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assert_poly_almost_equal(tuple(c2) * p1, p3)
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assert_poly_almost_equal(p1 * np.array(c2), p3)
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assert_poly_almost_equal(np.array(c2) * p1, p3)
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assert_poly_almost_equal(p1 * 2, p1 * Poly([2]))
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assert_poly_almost_equal(2 * p1, p1 * Poly([2]))
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assert_raises(TypeError, op.mul, p1, Poly([0], domain=Poly.domain + 1))
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assert_raises(TypeError, op.mul, p1, Poly([0], window=Poly.window + 1))
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if Poly is Polynomial:
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assert_raises(TypeError, op.mul, p1, Chebyshev([0]))
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else:
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assert_raises(TypeError, op.mul, p1, Polynomial([0]))
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def test_floordiv(Poly):
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c1 = list(random((4,)) + .5)
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c2 = list(random((3,)) + .5)
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c3 = list(random((2,)) + .5)
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p1 = Poly(c1)
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p2 = Poly(c2)
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p3 = Poly(c3)
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p4 = p1 * p2 + p3
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c4 = list(p4.coef)
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assert_poly_almost_equal(p4 // p2, p1)
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assert_poly_almost_equal(p4 // c2, p1)
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assert_poly_almost_equal(c4 // p2, p1)
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assert_poly_almost_equal(p4 // tuple(c2), p1)
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assert_poly_almost_equal(tuple(c4) // p2, p1)
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assert_poly_almost_equal(p4 // np.array(c2), p1)
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assert_poly_almost_equal(np.array(c4) // p2, p1)
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assert_poly_almost_equal(2 // p2, Poly([0]))
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assert_poly_almost_equal(p2 // 2, 0.5 * p2)
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assert_raises(
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TypeError, op.floordiv, p1, Poly([0], domain=Poly.domain + 1))
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assert_raises(
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TypeError, op.floordiv, p1, Poly([0], window=Poly.window + 1))
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if Poly is Polynomial:
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assert_raises(TypeError, op.floordiv, p1, Chebyshev([0]))
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else:
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assert_raises(TypeError, op.floordiv, p1, Polynomial([0]))
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def test_truediv(Poly):
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# true division is valid only if the denominator is a Number and
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# not a python bool.
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p1 = Poly([1, 2, 3])
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p2 = p1 * 5
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for stype in np.ScalarType:
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if not issubclass(stype, Number) or issubclass(stype, bool):
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continue
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s = stype(5)
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assert_poly_almost_equal(op.truediv(p2, s), p1)
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assert_raises(TypeError, op.truediv, s, p2)
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for stype in (int, float):
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s = stype(5)
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assert_poly_almost_equal(op.truediv(p2, s), p1)
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assert_raises(TypeError, op.truediv, s, p2)
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for stype in [complex]:
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s = stype(5, 0)
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assert_poly_almost_equal(op.truediv(p2, s), p1)
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assert_raises(TypeError, op.truediv, s, p2)
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for s in [(), [], {}, False, np.array([1])]:
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assert_raises(TypeError, op.truediv, p2, s)
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assert_raises(TypeError, op.truediv, s, p2)
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for ptype in classes:
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assert_raises(TypeError, op.truediv, p2, ptype(1))
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def test_mod(Poly):
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# This checks commutation, not numerical correctness
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c1 = list(random((4,)) + .5)
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c2 = list(random((3,)) + .5)
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c3 = list(random((2,)) + .5)
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p1 = Poly(c1)
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p2 = Poly(c2)
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p3 = Poly(c3)
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p4 = p1 * p2 + p3
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c4 = list(p4.coef)
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assert_poly_almost_equal(p4 % p2, p3)
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assert_poly_almost_equal(p4 % c2, p3)
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assert_poly_almost_equal(c4 % p2, p3)
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assert_poly_almost_equal(p4 % tuple(c2), p3)
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assert_poly_almost_equal(tuple(c4) % p2, p3)
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assert_poly_almost_equal(p4 % np.array(c2), p3)
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assert_poly_almost_equal(np.array(c4) % p2, p3)
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assert_poly_almost_equal(2 % p2, Poly([2]))
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assert_poly_almost_equal(p2 % 2, Poly([0]))
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assert_raises(TypeError, op.mod, p1, Poly([0], domain=Poly.domain + 1))
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assert_raises(TypeError, op.mod, p1, Poly([0], window=Poly.window + 1))
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if Poly is Polynomial:
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assert_raises(TypeError, op.mod, p1, Chebyshev([0]))
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else:
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assert_raises(TypeError, op.mod, p1, Polynomial([0]))
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def test_divmod(Poly):
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# This checks commutation, not numerical correctness
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c1 = list(random((4,)) + .5)
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c2 = list(random((3,)) + .5)
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c3 = list(random((2,)) + .5)
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p1 = Poly(c1)
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p2 = Poly(c2)
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p3 = Poly(c3)
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p4 = p1 * p2 + p3
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c4 = list(p4.coef)
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quo, rem = divmod(p4, p2)
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assert_poly_almost_equal(quo, p1)
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assert_poly_almost_equal(rem, p3)
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quo, rem = divmod(p4, c2)
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assert_poly_almost_equal(quo, p1)
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assert_poly_almost_equal(rem, p3)
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quo, rem = divmod(c4, p2)
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assert_poly_almost_equal(quo, p1)
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assert_poly_almost_equal(rem, p3)
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quo, rem = divmod(p4, tuple(c2))
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assert_poly_almost_equal(quo, p1)
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assert_poly_almost_equal(rem, p3)
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quo, rem = divmod(tuple(c4), p2)
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assert_poly_almost_equal(quo, p1)
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assert_poly_almost_equal(rem, p3)
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quo, rem = divmod(p4, np.array(c2))
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assert_poly_almost_equal(quo, p1)
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assert_poly_almost_equal(rem, p3)
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quo, rem = divmod(np.array(c4), p2)
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assert_poly_almost_equal(quo, p1)
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assert_poly_almost_equal(rem, p3)
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quo, rem = divmod(p2, 2)
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assert_poly_almost_equal(quo, 0.5 * p2)
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assert_poly_almost_equal(rem, Poly([0]))
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quo, rem = divmod(2, p2)
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assert_poly_almost_equal(quo, Poly([0]))
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assert_poly_almost_equal(rem, Poly([2]))
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assert_raises(TypeError, divmod, p1, Poly([0], domain=Poly.domain + 1))
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assert_raises(TypeError, divmod, p1, Poly([0], window=Poly.window + 1))
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if Poly is Polynomial:
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assert_raises(TypeError, divmod, p1, Chebyshev([0]))
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else:
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assert_raises(TypeError, divmod, p1, Polynomial([0]))
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def test_roots(Poly):
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d = Poly.domain * 1.25 + .25
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w = Poly.window
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tgt = np.linspace(d[0], d[1], 5)
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res = np.sort(Poly.fromroots(tgt, domain=d, window=w).roots())
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assert_almost_equal(res, tgt)
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# default domain and window
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res = np.sort(Poly.fromroots(tgt).roots())
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assert_almost_equal(res, tgt)
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def test_degree(Poly):
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p = Poly.basis(5)
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assert_equal(p.degree(), 5)
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def test_copy(Poly):
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p1 = Poly.basis(5)
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p2 = p1.copy()
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assert_(p1 == p2)
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assert_(p1 is not p2)
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assert_(p1.coef is not p2.coef)
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assert_(p1.domain is not p2.domain)
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assert_(p1.window is not p2.window)
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def test_integ(Poly):
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P = Polynomial
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# Check defaults
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p0 = Poly.cast(P([1 * 2, 2 * 3, 3 * 4]))
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p1 = P.cast(p0.integ())
|
|
p2 = P.cast(p0.integ(2))
|
|
assert_poly_almost_equal(p1, P([0, 2, 3, 4]))
|
|
assert_poly_almost_equal(p2, P([0, 0, 1, 1, 1]))
|
|
# Check with k
|
|
p0 = Poly.cast(P([1 * 2, 2 * 3, 3 * 4]))
|
|
p1 = P.cast(p0.integ(k=1))
|
|
p2 = P.cast(p0.integ(2, k=[1, 1]))
|
|
assert_poly_almost_equal(p1, P([1, 2, 3, 4]))
|
|
assert_poly_almost_equal(p2, P([1, 1, 1, 1, 1]))
|
|
# Check with lbnd
|
|
p0 = Poly.cast(P([1 * 2, 2 * 3, 3 * 4]))
|
|
p1 = P.cast(p0.integ(lbnd=1))
|
|
p2 = P.cast(p0.integ(2, lbnd=1))
|
|
assert_poly_almost_equal(p1, P([-9, 2, 3, 4]))
|
|
assert_poly_almost_equal(p2, P([6, -9, 1, 1, 1]))
|
|
# Check scaling
|
|
d = 2 * Poly.domain
|
|
p0 = Poly.cast(P([1 * 2, 2 * 3, 3 * 4]), domain=d)
|
|
p1 = P.cast(p0.integ())
|
|
p2 = P.cast(p0.integ(2))
|
|
assert_poly_almost_equal(p1, P([0, 2, 3, 4]))
|
|
assert_poly_almost_equal(p2, P([0, 0, 1, 1, 1]))
|
|
|
|
|
|
def test_deriv(Poly):
|
|
# Check that the derivative is the inverse of integration. It is
|
|
# assumes that the integration has been checked elsewhere.
|
|
d = Poly.domain + random((2,)) * .25
|
|
w = Poly.window + random((2,)) * .25
|
|
p1 = Poly([1, 2, 3], domain=d, window=w)
|
|
p2 = p1.integ(2, k=[1, 2])
|
|
p3 = p1.integ(1, k=[1])
|
|
assert_almost_equal(p2.deriv(1).coef, p3.coef)
|
|
assert_almost_equal(p2.deriv(2).coef, p1.coef)
|
|
# default domain and window
|
|
p1 = Poly([1, 2, 3])
|
|
p2 = p1.integ(2, k=[1, 2])
|
|
p3 = p1.integ(1, k=[1])
|
|
assert_almost_equal(p2.deriv(1).coef, p3.coef)
|
|
assert_almost_equal(p2.deriv(2).coef, p1.coef)
|
|
|
|
|
|
def test_linspace(Poly):
|
|
d = Poly.domain + random((2,)) * .25
|
|
w = Poly.window + random((2,)) * .25
|
|
p = Poly([1, 2, 3], domain=d, window=w)
|
|
# check default domain
|
|
xtgt = np.linspace(d[0], d[1], 20)
|
|
ytgt = p(xtgt)
|
|
xres, yres = p.linspace(20)
|
|
assert_almost_equal(xres, xtgt)
|
|
assert_almost_equal(yres, ytgt)
|
|
# check specified domain
|
|
xtgt = np.linspace(0, 2, 20)
|
|
ytgt = p(xtgt)
|
|
xres, yres = p.linspace(20, domain=[0, 2])
|
|
assert_almost_equal(xres, xtgt)
|
|
assert_almost_equal(yres, ytgt)
|
|
|
|
|
|
def test_pow(Poly):
|
|
d = Poly.domain + random((2,)) * .25
|
|
w = Poly.window + random((2,)) * .25
|
|
tgt = Poly([1], domain=d, window=w)
|
|
tst = Poly([1, 2, 3], domain=d, window=w)
|
|
for i in range(5):
|
|
assert_poly_almost_equal(tst**i, tgt)
|
|
tgt = tgt * tst
|
|
# default domain and window
|
|
tgt = Poly([1])
|
|
tst = Poly([1, 2, 3])
|
|
for i in range(5):
|
|
assert_poly_almost_equal(tst**i, tgt)
|
|
tgt = tgt * tst
|
|
# check error for invalid powers
|
|
assert_raises(ValueError, op.pow, tgt, 1.5)
|
|
assert_raises(ValueError, op.pow, tgt, -1)
|
|
|
|
|
|
def test_call(Poly):
|
|
P = Polynomial
|
|
d = Poly.domain
|
|
x = np.linspace(d[0], d[1], 11)
|
|
|
|
# Check defaults
|
|
p = Poly.cast(P([1, 2, 3]))
|
|
tgt = 1 + x * (2 + 3 * x)
|
|
res = p(x)
|
|
assert_almost_equal(res, tgt)
|
|
|
|
|
|
def test_call_with_list(Poly):
|
|
p = Poly([1, 2, 3])
|
|
x = [-1, 0, 2]
|
|
res = p(x)
|
|
assert_equal(res, p(np.array(x)))
|
|
|
|
|
|
def test_cutdeg(Poly):
|
|
p = Poly([1, 2, 3])
|
|
assert_raises(ValueError, p.cutdeg, .5)
|
|
assert_raises(ValueError, p.cutdeg, -1)
|
|
assert_equal(len(p.cutdeg(3)), 3)
|
|
assert_equal(len(p.cutdeg(2)), 3)
|
|
assert_equal(len(p.cutdeg(1)), 2)
|
|
assert_equal(len(p.cutdeg(0)), 1)
|
|
|
|
|
|
def test_truncate(Poly):
|
|
p = Poly([1, 2, 3])
|
|
assert_raises(ValueError, p.truncate, .5)
|
|
assert_raises(ValueError, p.truncate, 0)
|
|
assert_equal(len(p.truncate(4)), 3)
|
|
assert_equal(len(p.truncate(3)), 3)
|
|
assert_equal(len(p.truncate(2)), 2)
|
|
assert_equal(len(p.truncate(1)), 1)
|
|
|
|
|
|
def test_trim(Poly):
|
|
c = [1, 1e-6, 1e-12, 0]
|
|
p = Poly(c)
|
|
assert_equal(p.trim().coef, c[:3])
|
|
assert_equal(p.trim(1e-10).coef, c[:2])
|
|
assert_equal(p.trim(1e-5).coef, c[:1])
|
|
|
|
|
|
def test_mapparms(Poly):
|
|
# check with defaults. Should be identity.
|
|
d = Poly.domain
|
|
w = Poly.window
|
|
p = Poly([1], domain=d, window=w)
|
|
assert_almost_equal([0, 1], p.mapparms())
|
|
#
|
|
w = 2 * d + 1
|
|
p = Poly([1], domain=d, window=w)
|
|
assert_almost_equal([1, 2], p.mapparms())
|
|
|
|
|
|
def test_ufunc_override(Poly):
|
|
p = Poly([1, 2, 3])
|
|
x = np.ones(3)
|
|
assert_raises(TypeError, np.add, p, x)
|
|
assert_raises(TypeError, np.add, x, p)
|
|
|
|
|
|
#
|
|
# Test class method that only exists for some classes
|
|
#
|
|
|
|
|
|
class TestInterpolate:
|
|
|
|
def f(self, x):
|
|
return x * (x - 1) * (x - 2)
|
|
|
|
def test_raises(self):
|
|
assert_raises(ValueError, Chebyshev.interpolate, self.f, -1)
|
|
assert_raises(TypeError, Chebyshev.interpolate, self.f, 10.)
|
|
|
|
def test_dimensions(self):
|
|
for deg in range(1, 5):
|
|
assert_(Chebyshev.interpolate(self.f, deg).degree() == deg)
|
|
|
|
def test_approximation(self):
|
|
|
|
def powx(x, p):
|
|
return x**p
|
|
|
|
x = np.linspace(0, 2, 10)
|
|
for deg in range(10):
|
|
for t in range(deg + 1):
|
|
p = Chebyshev.interpolate(powx, deg, domain=[0, 2], args=(t,))
|
|
assert_almost_equal(p(x), powx(x, t), decimal=11)
|