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"""Tests for polynomial module. |
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""" |
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import pickle |
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from copy import deepcopy |
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from fractions import Fraction |
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from functools import reduce |
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import numpy as np |
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import numpy.polynomial.polynomial as poly |
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import numpy.polynomial.polyutils as pu |
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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_array_equal, |
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assert_equal, |
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assert_raises, |
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assert_raises_regex, |
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assert_warns, |
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) |
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def trim(x): |
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return poly.polytrim(x, tol=1e-6) |
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T0 = [1] |
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T1 = [0, 1] |
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T2 = [-1, 0, 2] |
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T3 = [0, -3, 0, 4] |
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T4 = [1, 0, -8, 0, 8] |
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T5 = [0, 5, 0, -20, 0, 16] |
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T6 = [-1, 0, 18, 0, -48, 0, 32] |
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T7 = [0, -7, 0, 56, 0, -112, 0, 64] |
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T8 = [1, 0, -32, 0, 160, 0, -256, 0, 128] |
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T9 = [0, 9, 0, -120, 0, 432, 0, -576, 0, 256] |
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Tlist = [T0, T1, T2, T3, T4, T5, T6, T7, T8, T9] |
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class TestConstants: |
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def test_polydomain(self): |
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assert_equal(poly.polydomain, [-1, 1]) |
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def test_polyzero(self): |
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assert_equal(poly.polyzero, [0]) |
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def test_polyone(self): |
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assert_equal(poly.polyone, [1]) |
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def test_polyx(self): |
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assert_equal(poly.polyx, [0, 1]) |
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def test_copy(self): |
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x = poly.Polynomial([1, 2, 3]) |
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y = deepcopy(x) |
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assert_equal(x, y) |
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def test_pickle(self): |
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x = poly.Polynomial([1, 2, 3]) |
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y = pickle.loads(pickle.dumps(x)) |
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assert_equal(x, y) |
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class TestArithmetic: |
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def test_polyadd(self): |
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for i in range(5): |
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for j in range(5): |
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msg = f"At i={i}, j={j}" |
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tgt = np.zeros(max(i, j) + 1) |
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tgt[i] += 1 |
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tgt[j] += 1 |
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res = poly.polyadd([0] * i + [1], [0] * j + [1]) |
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assert_equal(trim(res), trim(tgt), err_msg=msg) |
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def test_polysub(self): |
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for i in range(5): |
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for j in range(5): |
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msg = f"At i={i}, j={j}" |
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tgt = np.zeros(max(i, j) + 1) |
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tgt[i] += 1 |
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tgt[j] -= 1 |
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res = poly.polysub([0] * i + [1], [0] * j + [1]) |
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assert_equal(trim(res), trim(tgt), err_msg=msg) |
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def test_polymulx(self): |
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assert_equal(poly.polymulx([0]), [0]) |
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assert_equal(poly.polymulx([1]), [0, 1]) |
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for i in range(1, 5): |
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ser = [0] * i + [1] |
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tgt = [0] * (i + 1) + [1] |
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assert_equal(poly.polymulx(ser), tgt) |
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def test_polymul(self): |
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for i in range(5): |
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for j in range(5): |
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msg = f"At i={i}, j={j}" |
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tgt = np.zeros(i + j + 1) |
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tgt[i + j] += 1 |
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res = poly.polymul([0] * i + [1], [0] * j + [1]) |
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assert_equal(trim(res), trim(tgt), err_msg=msg) |
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def test_polydiv(self): |
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assert_raises(ZeroDivisionError, poly.polydiv, [1], [0]) |
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quo, rem = poly.polydiv([2], [2]) |
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assert_equal((quo, rem), (1, 0)) |
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quo, rem = poly.polydiv([2, 2], [2]) |
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assert_equal((quo, rem), ((1, 1), 0)) |
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for i in range(5): |
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for j in range(5): |
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msg = f"At i={i}, j={j}" |
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ci = [0] * i + [1, 2] |
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cj = [0] * j + [1, 2] |
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tgt = poly.polyadd(ci, cj) |
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quo, rem = poly.polydiv(tgt, ci) |
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res = poly.polyadd(poly.polymul(quo, ci), rem) |
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assert_equal(res, tgt, err_msg=msg) |
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def test_polypow(self): |
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for i in range(5): |
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for j in range(5): |
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msg = f"At i={i}, j={j}" |
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c = np.arange(i + 1) |
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tgt = reduce(poly.polymul, [c] * j, np.array([1])) |
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res = poly.polypow(c, j) |
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assert_equal(trim(res), trim(tgt), err_msg=msg) |
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class TestFraction: |
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def test_Fraction(self): |
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f = Fraction(2, 3) |
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one = Fraction(1, 1) |
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zero = Fraction(0, 1) |
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p = poly.Polynomial([f, f], domain=[zero, one], window=[zero, one]) |
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x = 2 * p + p ** 2 |
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assert_equal(x.coef, np.array([Fraction(16, 9), Fraction(20, 9), |
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Fraction(4, 9)], dtype=object)) |
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assert_equal(p.domain, [zero, one]) |
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assert_equal(p.coef.dtype, np.dtypes.ObjectDType()) |
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assert_(isinstance(p(f), Fraction)) |
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assert_equal(p(f), Fraction(10, 9)) |
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p_deriv = poly.Polynomial([Fraction(2, 3)], domain=[zero, one], |
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window=[zero, one]) |
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assert_equal(p.deriv(), p_deriv) |
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class TestEvaluation: |
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c1d = np.array([1., 2., 3.]) |
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c2d = np.einsum('i,j->ij', c1d, c1d) |
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c3d = np.einsum('i,j,k->ijk', c1d, c1d, c1d) |
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x = np.random.random((3, 5)) * 2 - 1 |
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y = poly.polyval(x, [1., 2., 3.]) |
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def test_polyval(self): |
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assert_equal(poly.polyval([], [1]).size, 0) |
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x = np.linspace(-1, 1) |
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y = [x**i for i in range(5)] |
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for i in range(5): |
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tgt = y[i] |
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res = poly.polyval(x, [0] * i + [1]) |
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assert_almost_equal(res, tgt) |
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tgt = x * (x**2 - 1) |
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res = poly.polyval(x, [0, -1, 0, 1]) |
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assert_almost_equal(res, tgt) |
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for i in range(3): |
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dims = [2] * i |
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x = np.zeros(dims) |
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assert_equal(poly.polyval(x, [1]).shape, dims) |
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assert_equal(poly.polyval(x, [1, 0]).shape, dims) |
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assert_equal(poly.polyval(x, [1, 0, 0]).shape, dims) |
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mask = [False, True, False] |
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mx = np.ma.array([1, 2, 3], mask=mask) |
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res = np.polyval([7, 5, 3], mx) |
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assert_array_equal(res.mask, mask) |
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class C(np.ndarray): |
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pass |
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cx = np.array([1, 2, 3]).view(C) |
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assert_equal(type(np.polyval([2, 3, 4], cx)), C) |
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def test_polyvalfromroots(self): |
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assert_raises(ValueError, poly.polyvalfromroots, |
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[1], [1], tensor=False) |
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assert_equal(poly.polyvalfromroots([], [1]).size, 0) |
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assert_(poly.polyvalfromroots([], [1]).shape == (0,)) |
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assert_equal(poly.polyvalfromroots([], [[1] * 5]).size, 0) |
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assert_(poly.polyvalfromroots([], [[1] * 5]).shape == (5, 0)) |
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assert_equal(poly.polyvalfromroots(1, 1), 0) |
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assert_(poly.polyvalfromroots(1, np.ones((3, 3))).shape == (3,)) |
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x = np.linspace(-1, 1) |
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y = [x**i for i in range(5)] |
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for i in range(1, 5): |
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tgt = y[i] |
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res = poly.polyvalfromroots(x, [0] * i) |
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assert_almost_equal(res, tgt) |
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tgt = x * (x - 1) * (x + 1) |
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res = poly.polyvalfromroots(x, [-1, 0, 1]) |
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assert_almost_equal(res, tgt) |
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for i in range(3): |
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dims = [2] * i |
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x = np.zeros(dims) |
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assert_equal(poly.polyvalfromroots(x, [1]).shape, dims) |
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assert_equal(poly.polyvalfromroots(x, [1, 0]).shape, dims) |
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assert_equal(poly.polyvalfromroots(x, [1, 0, 0]).shape, dims) |
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ptest = [15, 2, -16, -2, 1] |
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r = poly.polyroots(ptest) |
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x = np.linspace(-1, 1) |
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assert_almost_equal(poly.polyval(x, ptest), |
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poly.polyvalfromroots(x, r)) |
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rshape = (3, 5) |
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x = np.arange(-3, 2) |
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r = np.random.randint(-5, 5, size=rshape) |
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res = poly.polyvalfromroots(x, r, tensor=False) |
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tgt = np.empty(r.shape[1:]) |
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for ii in range(tgt.size): |
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tgt[ii] = poly.polyvalfromroots(x[ii], r[:, ii]) |
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assert_equal(res, tgt) |
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x = np.vstack([x, 2 * x]) |
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res = poly.polyvalfromroots(x, r, tensor=True) |
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tgt = np.empty(r.shape[1:] + x.shape) |
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for ii in range(r.shape[1]): |
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for jj in range(x.shape[0]): |
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tgt[ii, jj, :] = poly.polyvalfromroots(x[jj], r[:, ii]) |
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assert_equal(res, tgt) |
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def test_polyval2d(self): |
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x1, x2, x3 = self.x |
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y1, y2, y3 = self.y |
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assert_raises_regex(ValueError, 'incompatible', |
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poly.polyval2d, x1, x2[:2], self.c2d) |
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tgt = y1 * y2 |
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res = poly.polyval2d(x1, x2, self.c2d) |
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assert_almost_equal(res, tgt) |
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z = np.ones((2, 3)) |
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res = poly.polyval2d(z, z, self.c2d) |
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assert_(res.shape == (2, 3)) |
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def test_polyval3d(self): |
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x1, x2, x3 = self.x |
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y1, y2, y3 = self.y |
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assert_raises_regex(ValueError, 'incompatible', |
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poly.polyval3d, x1, x2, x3[:2], self.c3d) |
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tgt = y1 * y2 * y3 |
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res = poly.polyval3d(x1, x2, x3, self.c3d) |
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assert_almost_equal(res, tgt) |
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z = np.ones((2, 3)) |
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res = poly.polyval3d(z, z, z, self.c3d) |
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assert_(res.shape == (2, 3)) |
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def test_polygrid2d(self): |
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x1, x2, x3 = self.x |
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y1, y2, y3 = self.y |
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tgt = np.einsum('i,j->ij', y1, y2) |
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res = poly.polygrid2d(x1, x2, self.c2d) |
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assert_almost_equal(res, tgt) |
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z = np.ones((2, 3)) |
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res = poly.polygrid2d(z, z, self.c2d) |
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assert_(res.shape == (2, 3) * 2) |
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def test_polygrid3d(self): |
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x1, x2, x3 = self.x |
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y1, y2, y3 = self.y |
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tgt = np.einsum('i,j,k->ijk', y1, y2, y3) |
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res = poly.polygrid3d(x1, x2, x3, self.c3d) |
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assert_almost_equal(res, tgt) |
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z = np.ones((2, 3)) |
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res = poly.polygrid3d(z, z, z, self.c3d) |
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assert_(res.shape == (2, 3) * 3) |
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class TestIntegral: |
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def test_polyint(self): |
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assert_raises(TypeError, poly.polyint, [0], .5) |
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assert_raises(ValueError, poly.polyint, [0], -1) |
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assert_raises(ValueError, poly.polyint, [0], 1, [0, 0]) |
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assert_raises(ValueError, poly.polyint, [0], lbnd=[0]) |
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assert_raises(ValueError, poly.polyint, [0], scl=[0]) |
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assert_raises(TypeError, poly.polyint, [0], axis=.5) |
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assert_raises(TypeError, poly.polyint, [1, 1], 1.) |
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for i in range(2, 5): |
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k = [0] * (i - 2) + [1] |
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res = poly.polyint([0], m=i, k=k) |
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assert_almost_equal(res, [0, 1]) |
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for i in range(5): |
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scl = i + 1 |
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pol = [0] * i + [1] |
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tgt = [i] + [0] * i + [1 / scl] |
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res = poly.polyint(pol, m=1, k=[i]) |
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assert_almost_equal(trim(res), trim(tgt)) |
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for i in range(5): |
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scl = i + 1 |
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pol = [0] * i + [1] |
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res = poly.polyint(pol, m=1, k=[i], lbnd=-1) |
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assert_almost_equal(poly.polyval(-1, res), i) |
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for i in range(5): |
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scl = i + 1 |
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pol = [0] * i + [1] |
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tgt = [i] + [0] * i + [2 / scl] |
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res = poly.polyint(pol, m=1, k=[i], scl=2) |
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assert_almost_equal(trim(res), trim(tgt)) |
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for i in range(5): |
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for j in range(2, 5): |
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pol = [0] * i + [1] |
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tgt = pol[:] |
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for k in range(j): |
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tgt = poly.polyint(tgt, m=1) |
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res = poly.polyint(pol, m=j) |
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assert_almost_equal(trim(res), trim(tgt)) |
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for i in range(5): |
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for j in range(2, 5): |
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pol = [0] * i + [1] |
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tgt = pol[:] |
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for k in range(j): |
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tgt = poly.polyint(tgt, m=1, k=[k]) |
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res = poly.polyint(pol, m=j, k=list(range(j))) |
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assert_almost_equal(trim(res), trim(tgt)) |
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for i in range(5): |
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for j in range(2, 5): |
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pol = [0] * i + [1] |
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tgt = pol[:] |
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for k in range(j): |
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tgt = poly.polyint(tgt, m=1, k=[k], lbnd=-1) |
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res = poly.polyint(pol, m=j, k=list(range(j)), lbnd=-1) |
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assert_almost_equal(trim(res), trim(tgt)) |
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for i in range(5): |
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for j in range(2, 5): |
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pol = [0] * i + [1] |
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tgt = pol[:] |
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for k in range(j): |
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tgt = poly.polyint(tgt, m=1, k=[k], scl=2) |
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res = poly.polyint(pol, m=j, k=list(range(j)), scl=2) |
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assert_almost_equal(trim(res), trim(tgt)) |
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def test_polyint_axis(self): |
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c2d = np.random.random((3, 4)) |
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tgt = np.vstack([poly.polyint(c) for c in c2d.T]).T |
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res = poly.polyint(c2d, axis=0) |
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assert_almost_equal(res, tgt) |
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tgt = np.vstack([poly.polyint(c) for c in c2d]) |
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res = poly.polyint(c2d, axis=1) |
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assert_almost_equal(res, tgt) |
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tgt = np.vstack([poly.polyint(c, k=3) for c in c2d]) |
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res = poly.polyint(c2d, k=3, axis=1) |
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assert_almost_equal(res, tgt) |
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class TestDerivative: |
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def test_polyder(self): |
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assert_raises(TypeError, poly.polyder, [0], .5) |
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assert_raises(ValueError, poly.polyder, [0], -1) |
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for i in range(5): |
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tgt = [0] * i + [1] |
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res = poly.polyder(tgt, m=0) |
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assert_equal(trim(res), trim(tgt)) |
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for i in range(5): |
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for j in range(2, 5): |
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tgt = [0] * i + [1] |
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res = poly.polyder(poly.polyint(tgt, m=j), m=j) |
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assert_almost_equal(trim(res), trim(tgt)) |
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for i in range(5): |
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for j in range(2, 5): |
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tgt = [0] * i + [1] |
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res = poly.polyder(poly.polyint(tgt, m=j, scl=2), m=j, scl=.5) |
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assert_almost_equal(trim(res), trim(tgt)) |
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def test_polyder_axis(self): |
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c2d = np.random.random((3, 4)) |
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tgt = np.vstack([poly.polyder(c) for c in c2d.T]).T |
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res = poly.polyder(c2d, axis=0) |
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assert_almost_equal(res, tgt) |
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tgt = np.vstack([poly.polyder(c) for c in c2d]) |
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res = poly.polyder(c2d, axis=1) |
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assert_almost_equal(res, tgt) |
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class TestVander: |
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x = np.random.random((3, 5)) * 2 - 1 |
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def test_polyvander(self): |
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x = np.arange(3) |
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v = poly.polyvander(x, 3) |
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assert_(v.shape == (3, 4)) |
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for i in range(4): |
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coef = [0] * i + [1] |
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assert_almost_equal(v[..., i], poly.polyval(x, coef)) |
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x = np.array([[1, 2], [3, 4], [5, 6]]) |
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v = poly.polyvander(x, 3) |
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assert_(v.shape == (3, 2, 4)) |
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for i in range(4): |
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coef = [0] * i + [1] |
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assert_almost_equal(v[..., i], poly.polyval(x, coef)) |
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def test_polyvander2d(self): |
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x1, x2, x3 = self.x |
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c = np.random.random((2, 3)) |
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van = poly.polyvander2d(x1, x2, [1, 2]) |
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tgt = poly.polyval2d(x1, x2, c) |
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res = np.dot(van, c.flat) |
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assert_almost_equal(res, tgt) |
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van = poly.polyvander2d([x1], [x2], [1, 2]) |
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assert_(van.shape == (1, 5, 6)) |
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def test_polyvander3d(self): |
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x1, x2, x3 = self.x |
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c = np.random.random((2, 3, 4)) |
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van = poly.polyvander3d(x1, x2, x3, [1, 2, 3]) |
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tgt = poly.polyval3d(x1, x2, x3, c) |
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res = np.dot(van, c.flat) |
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assert_almost_equal(res, tgt) |
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van = poly.polyvander3d([x1], [x2], [x3], [1, 2, 3]) |
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assert_(van.shape == (1, 5, 24)) |
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def test_polyvandernegdeg(self): |
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x = np.arange(3) |
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assert_raises(ValueError, poly.polyvander, x, -1) |
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class TestCompanion: |
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def test_raises(self): |
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assert_raises(ValueError, poly.polycompanion, []) |
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assert_raises(ValueError, poly.polycompanion, [1]) |
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def test_dimensions(self): |
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for i in range(1, 5): |
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coef = [0] * i + [1] |
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assert_(poly.polycompanion(coef).shape == (i, i)) |
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def test_linear_root(self): |
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assert_(poly.polycompanion([1, 2])[0, 0] == -.5) |
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class TestMisc: |
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|
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def test_polyfromroots(self): |
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res = poly.polyfromroots([]) |
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assert_almost_equal(trim(res), [1]) |
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for i in range(1, 5): |
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roots = np.cos(np.linspace(-np.pi, 0, 2 * i + 1)[1::2]) |
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tgt = Tlist[i] |
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res = poly.polyfromroots(roots) * 2**(i - 1) |
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assert_almost_equal(trim(res), trim(tgt)) |
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def test_polyroots(self): |
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assert_almost_equal(poly.polyroots([1]), []) |
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assert_almost_equal(poly.polyroots([1, 2]), [-.5]) |
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for i in range(2, 5): |
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tgt = np.linspace(-1, 1, i) |
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res = poly.polyroots(poly.polyfromroots(tgt)) |
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assert_almost_equal(trim(res), trim(tgt)) |
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for i in np.logspace(10, 25, num=1000, base=10): |
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tgt = np.array([-1, 1, i]) |
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res = poly.polyroots(poly.polyfromroots(tgt)) |
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assert_almost_equal(res, tgt, 15 - int(np.log10(i))) |
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for i in np.logspace(10, 25, num=1000, base=10): |
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tgt = np.array([-1, 1.01, i]) |
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res = poly.polyroots(poly.polyfromroots(tgt)) |
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assert_almost_equal(res, tgt, 14 - int(np.log10(i))) |
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def test_polyfit(self): |
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def f(x): |
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return x * (x - 1) * (x - 2) |
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def f2(x): |
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return x**4 + x**2 + 1 |
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assert_raises(ValueError, poly.polyfit, [1], [1], -1) |
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assert_raises(TypeError, poly.polyfit, [[1]], [1], 0) |
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assert_raises(TypeError, poly.polyfit, [], [1], 0) |
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assert_raises(TypeError, poly.polyfit, [1], [[[1]]], 0) |
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assert_raises(TypeError, poly.polyfit, [1, 2], [1], 0) |
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assert_raises(TypeError, poly.polyfit, [1], [1, 2], 0) |
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assert_raises(TypeError, poly.polyfit, [1], [1], 0, w=[[1]]) |
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assert_raises(TypeError, poly.polyfit, [1], [1], 0, w=[1, 1]) |
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assert_raises(ValueError, poly.polyfit, [1], [1], [-1,]) |
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assert_raises(ValueError, poly.polyfit, [1], [1], [2, -1, 6]) |
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assert_raises(TypeError, poly.polyfit, [1], [1], []) |
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|
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x = np.linspace(0, 2) |
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y = f(x) |
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coef3 = poly.polyfit(x, y, 3) |
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assert_equal(len(coef3), 4) |
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assert_almost_equal(poly.polyval(x, coef3), y) |
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coef3 = poly.polyfit(x, y, [0, 1, 2, 3]) |
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assert_equal(len(coef3), 4) |
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assert_almost_equal(poly.polyval(x, coef3), y) |
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coef4 = poly.polyfit(x, y, 4) |
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assert_equal(len(coef4), 5) |
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assert_almost_equal(poly.polyval(x, coef4), y) |
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coef4 = poly.polyfit(x, y, [0, 1, 2, 3, 4]) |
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assert_equal(len(coef4), 5) |
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assert_almost_equal(poly.polyval(x, coef4), y) |
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|
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coef2d = poly.polyfit(x, np.array([y, y]).T, 3) |
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assert_almost_equal(coef2d, np.array([coef3, coef3]).T) |
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coef2d = poly.polyfit(x, np.array([y, y]).T, [0, 1, 2, 3]) |
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assert_almost_equal(coef2d, np.array([coef3, coef3]).T) |
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|
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w = np.zeros_like(x) |
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yw = y.copy() |
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w[1::2] = 1 |
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yw[0::2] = 0 |
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wcoef3 = poly.polyfit(x, yw, 3, w=w) |
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assert_almost_equal(wcoef3, coef3) |
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wcoef3 = poly.polyfit(x, yw, [0, 1, 2, 3], w=w) |
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assert_almost_equal(wcoef3, coef3) |
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|
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wcoef2d = poly.polyfit(x, np.array([yw, yw]).T, 3, w=w) |
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assert_almost_equal(wcoef2d, np.array([coef3, coef3]).T) |
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wcoef2d = poly.polyfit(x, np.array([yw, yw]).T, [0, 1, 2, 3], w=w) |
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assert_almost_equal(wcoef2d, np.array([coef3, coef3]).T) |
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|
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x = [1, 1j, -1, -1j] |
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assert_almost_equal(poly.polyfit(x, x, 1), [0, 1]) |
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assert_almost_equal(poly.polyfit(x, x, [0, 1]), [0, 1]) |
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|
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x = np.linspace(-1, 1) |
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y = f2(x) |
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coef1 = poly.polyfit(x, y, 4) |
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assert_almost_equal(poly.polyval(x, coef1), y) |
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coef2 = poly.polyfit(x, y, [0, 2, 4]) |
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assert_almost_equal(poly.polyval(x, coef2), y) |
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assert_almost_equal(coef1, coef2) |
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|
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def test_polytrim(self): |
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coef = [2, -1, 1, 0] |
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|
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|
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assert_raises(ValueError, poly.polytrim, coef, -1) |
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|
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assert_equal(poly.polytrim(coef), coef[:-1]) |
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assert_equal(poly.polytrim(coef, 1), coef[:-3]) |
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assert_equal(poly.polytrim(coef, 2), [0]) |
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|
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def test_polyline(self): |
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assert_equal(poly.polyline(3, 4), [3, 4]) |
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|
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def test_polyline_zero(self): |
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assert_equal(poly.polyline(3, 0), [3]) |
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|
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def test_fit_degenerate_domain(self): |
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p = poly.Polynomial.fit([1], [2], deg=0) |
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assert_equal(p.coef, [2.]) |
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p = poly.Polynomial.fit([1, 1], [2, 2.1], deg=0) |
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assert_almost_equal(p.coef, [2.05]) |
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with assert_warns(pu.RankWarning): |
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p = poly.Polynomial.fit([1, 1], [2, 2.1], deg=1) |
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|
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def test_result_type(self): |
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w = np.array([-1, 1], dtype=np.float32) |
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p = np.polynomial.Polynomial(w, domain=w, window=w) |
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v = p(2) |
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assert_equal(v.dtype, np.float32) |
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|
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arr = np.polydiv(1, np.float32(1)) |
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assert_equal(arr[0].dtype, np.float64) |
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