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test_polynomial.py
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import numpy as np from numpy.testing import ( assert_, assert_equal, assert_array_equal, assert_almost_equal, assert_array_almost_equal, assert_raises, assert_allclose ) import pytest # `poly1d` has some support for `bool_` and `timedelta64`, # but it is limited and they are therefore excluded here TYPE_CODES = np.typecodes["AllInteger"] + np.typecodes["AllFloat"] + "O" class TestPolynomial: def test_poly1d_str_and_repr(self): p = np.poly1d([1., 2, 3]) assert_equal(repr(p), 'poly1d([1., 2., 3.])') assert_equal(str(p), ' 2\n' '1 x + 2 x + 3') q = np.poly1d([3., 2, 1]) assert_equal(repr(q), 'poly1d([3., 2., 1.])') assert_equal(str(q), ' 2\n' '3 x + 2 x + 1') r = np.poly1d([1.89999 + 2j, -3j, -5.12345678, 2 + 1j]) assert_equal(str(r), ' 3 2\n' '(1.9 + 2j) x - 3j x - 5.123 x + (2 + 1j)') assert_equal(str(np.poly1d([-3, -2, -1])), ' 2\n' '-3 x - 2 x - 1') def test_poly1d_resolution(self): p = np.poly1d([1., 2, 3]) q = np.poly1d([3., 2, 1]) assert_equal(p(0), 3.0) assert_equal(p(5), 38.0) assert_equal(q(0), 1.0) assert_equal(q(5), 86.0) def test_poly1d_math(self): # here we use some simple coeffs to make calculations easier p = np.poly1d([1., 2, 4]) q = np.poly1d([4., 2, 1]) assert_equal(p/q, (np.poly1d([0.25]), np.poly1d([1.5, 3.75]))) assert_equal(p.integ(), np.poly1d([1/3, 1., 4., 0.])) assert_equal(p.integ(1), np.poly1d([1/3, 1., 4., 0.])) p = np.poly1d([1., 2, 3]) q = np.poly1d([3., 2, 1]) assert_equal(p * q, np.poly1d([3., 8., 14., 8., 3.])) assert_equal(p + q, np.poly1d([4., 4., 4.])) assert_equal(p - q, np.poly1d([-2., 0., 2.])) assert_equal(p ** 4, np.poly1d([1., 8., 36., 104., 214., 312., 324., 216., 81.])) assert_equal(p(q), np.poly1d([9., 12., 16., 8., 6.])) assert_equal(q(p), np.poly1d([3., 12., 32., 40., 34.])) assert_equal(p.deriv(), np.poly1d([2., 2.])) assert_equal(p.deriv(2), np.poly1d([2.])) assert_equal(np.polydiv(np.poly1d([1, 0, -1]), np.poly1d([1, 1])), (np.poly1d([1., -1.]), np.poly1d([0.]))) @pytest.mark.parametrize("type_code", TYPE_CODES) def test_poly1d_misc(self, type_code: str) -> None: dtype = np.dtype(type_code) ar = np.array([1, 2, 3], dtype=dtype) p = np.poly1d(ar) # `__eq__` assert_equal(np.asarray(p), ar) assert_equal(np.asarray(p).dtype, dtype) assert_equal(len(p), 2) # `__getitem__` comparison_dct = {-1: 0, 0: 3, 1: 2, 2: 1, 3: 0} for index, ref in comparison_dct.items(): scalar = p[index] assert_equal(scalar, ref) if dtype == np.object_: assert isinstance(scalar, int) else: assert_equal(scalar.dtype, dtype) def test_poly1d_variable_arg(self): q = np.poly1d([1., 2, 3], variable='y') assert_equal(str(q), ' 2\n' '1 y + 2 y + 3') q = np.poly1d([1., 2, 3], variable='lambda') assert_equal(str(q), ' 2\n' '1 lambda + 2 lambda + 3') def test_poly(self): assert_array_almost_equal(np.poly([3, -np.sqrt(2), np.sqrt(2)]), [1, -3, -2, 6]) # From matlab docs A = [[1, 2, 3], [4, 5, 6], [7, 8, 0]] assert_array_almost_equal(np.poly(A), [1, -6, -72, -27]) # Should produce real output for perfect conjugates assert_(np.isrealobj(np.poly([+1.082j, +2.613j, -2.613j, -1.082j]))) assert_(np.isrealobj(np.poly([0+1j, -0+-1j, 1+2j, 1-2j, 1.+3.5j, 1-3.5j]))) assert_(np.isrealobj(np.poly([1j, -1j, 1+2j, 1-2j, 1+3j, 1-3.j]))) assert_(np.isrealobj(np.poly([1j, -1j, 1+2j, 1-2j]))) assert_(np.isrealobj(np.poly([1j, -1j, 2j, -2j]))) assert_(np.isrealobj(np.poly([1j, -1j]))) assert_(np.isrealobj(np.poly([1, -1]))) assert_(np.iscomplexobj(np.poly([1j, -1.0000001j]))) np.random.seed(42) a = np.random.randn(100) + 1j*np.random.randn(100) assert_(np.isrealobj(np.poly(np.concatenate((a, np.conjugate(a)))))) def test_roots(self): assert_array_equal(np.roots([1, 0, 0]), [0, 0]) def test_str_leading_zeros(self): p = np.poly1d([4, 3, 2, 1]) p[3] = 0 assert_equal(str(p), " 2\n" "3 x + 2 x + 1") p = np.poly1d([1, 2]) p[0] = 0 p[1] = 0 assert_equal(str(p), " \n0") def test_polyfit(self): c = np.array([3., 2., 1.]) x = np.linspace(0, 2, 7) y = np.polyval(c, x) err = [1, -1, 1, -1, 1, -1, 1] weights = np.arange(8, 1, -1)**2/7.0 # Check exception when too few points for variance estimate. Note that # the estimate requires the number of data points to exceed # degree + 1 assert_raises(ValueError, np.polyfit, [1], [1], deg=0, cov=True) # check 1D case m, cov = np.polyfit(x, y+err, 2, cov=True) est = [3.8571, 0.2857, 1.619] assert_almost_equal(est, m, decimal=4) val0 = [[ 1.4694, -2.9388, 0.8163], [-2.9388, 6.3673, -2.1224], [ 0.8163, -2.1224, 1.161 ]] assert_almost_equal(val0, cov, decimal=4) m2, cov2 = np.polyfit(x, y+err, 2, w=weights, cov=True) assert_almost_equal([4.8927, -1.0177, 1.7768], m2, decimal=4) val = [[ 4.3964, -5.0052, 0.4878], [-5.0052, 6.8067, -0.9089], [ 0.4878, -0.9089, 0.3337]] assert_almost_equal(val, cov2, decimal=4) m3, cov3 = np.polyfit(x, y+err, 2, w=weights, cov="unscaled") assert_almost_equal([4.8927, -1.0177, 1.7768], m3, decimal=4) val = [[ 0.1473, -0.1677, 0.0163], [-0.1677, 0.228 , -0.0304], [ 0.0163, -0.0304, 0.0112]] assert_almost_equal(val, cov3, decimal=4) # check 2D (n,1) case y = y[:, np.newaxis] c = c[:, np.newaxis] assert_almost_equal(c, np.polyfit(x, y, 2)) # check 2D (n,2) case yy = np.concatenate((y, y), axis=1) cc = np.concatenate((c, c), axis=1) assert_almost_equal(cc, np.polyfit(x, yy, 2)) m, cov = np.polyfit(x, yy + np.array(err)[:, np.newaxis], 2, cov=True) assert_almost_equal(est, m[:, 0], decimal=4) assert_almost_equal(est, m[:, 1], decimal=4) assert_almost_equal(val0, cov[:, :, 0], decimal=4) assert_almost_equal(val0, cov[:, :, 1], decimal=4) # check order 1 (deg=0) case, were the analytic results are simple np.random.seed(123) y = np.random.normal(size=(4, 10000)) mean, cov = np.polyfit(np.zeros(y.shape[0]), y, deg=0, cov=True) # Should get sigma_mean = sigma/sqrt(N) = 1./sqrt(4) = 0.5. assert_allclose(mean.std(), 0.5, atol=0.01) assert_allclose(np.sqrt(cov.mean()), 0.5, atol=0.01) # Without scaling, since reduced chi2 is 1, the result should be the same. mean, cov = np.polyfit(np.zeros(y.shape[0]), y, w=np.ones(y.shape[0]), deg=0, cov="unscaled") assert_allclose(mean.std(), 0.5, atol=0.01) assert_almost_equal(np.sqrt(cov.mean()), 0.5) # If we estimate our errors wrong, no change with scaling: w = np.full(y.shape[0], 1./0.5) mean, cov = np.polyfit(np.zeros(y.shape[0]), y, w=w, deg=0, cov=True) assert_allclose(mean.std(), 0.5, atol=0.01) assert_allclose(np.sqrt(cov.mean()), 0.5, atol=0.01) # But if we do not scale, our estimate for the error in the mean will # differ. mean, cov = np.polyfit(np.zeros(y.shape[0]), y, w=w, deg=0, cov="unscaled") assert_allclose(mean.std(), 0.5, atol=0.01) assert_almost_equal(np.sqrt(cov.mean()), 0.25) def test_objects(self): from decimal import Decimal p = np.poly1d([Decimal('4.0'), Decimal('3.0'), Decimal('2.0')]) p2 = p * Decimal('1.333333333333333') assert_(p2[1] == Decimal("3.9999999999999990")) p2 = p.deriv() assert_(p2[1] == Decimal('8.0')) p2 = p.integ() assert_(p2[3] == Decimal("1.333333333333333333333333333")) assert_(p2[2] == Decimal('1.5')) assert_(np.issubdtype(p2.coeffs.dtype, np.object_)) p = np.poly([Decimal(1), Decimal(2)]) assert_equal(np.poly([Decimal(1), Decimal(2)]), [1, Decimal(-3), Decimal(2)]) def test_complex(self): p = np.poly1d([3j, 2j, 1j]) p2 = p.integ() assert_((p2.coeffs == [1j, 1j, 1j, 0]).all()) p2 = p.deriv() assert_((p2.coeffs == [6j, 2j]).all()) def test_integ_coeffs(self): p = np.poly1d([3, 2, 1]) p2 = p.integ(3, k=[9, 7, 6]) assert_( (p2.coeffs == [1/4./5., 1/3./4., 1/2./3., 9/1./2., 7, 6]).all()) def test_zero_dims(self): try: np.poly(np.zeros((0, 0))) except ValueError: pass def test_poly_int_overflow(self): """ Regression test for gh-5096. """ v = np.arange(1, 21) assert_almost_equal(np.poly(v), np.poly(np.diag(v))) def test_zero_poly_dtype(self): """ Regression test for gh-16354. """ z = np.array([0, 0, 0]) p = np.poly1d(z.astype(np.int64)) assert_equal(p.coeffs.dtype, np.int64) p = np.poly1d(z.astype(np.float32)) assert_equal(p.coeffs.dtype, np.float32) p = np.poly1d(z.astype(np.complex64)) assert_equal(p.coeffs.dtype, np.complex64) def test_poly_eq(self): p = np.poly1d([1, 2, 3]) p2 = np.poly1d([1, 2, 4]) assert_equal(p == None, False) assert_equal(p != None, True) assert_equal(p == p, True) assert_equal(p == p2, False) assert_equal(p != p2, True) def test_polydiv(self): b = np.poly1d([2, 6, 6, 1]) a = np.poly1d([-1j, (1+2j), -(2+1j), 1]) q, r = np.polydiv(b, a) assert_equal(q.coeffs.dtype, np.complex128) assert_equal(r.coeffs.dtype, np.complex128) assert_equal(q*a + r, b) c = [1, 2, 3] d = np.poly1d([1, 2, 3]) s, t = np.polydiv(c, d) assert isinstance(s, np.poly1d) assert isinstance(t, np.poly1d) u, v = np.polydiv(d, c) assert isinstance(u, np.poly1d) assert isinstance(v, np.poly1d) def test_poly_coeffs_mutable(self): """ Coefficients should be modifiable """ p = np.poly1d([1, 2, 3]) p.coeffs += 1 assert_equal(p.coeffs, [2, 3, 4]) p.coeffs[2] += 10 assert_equal(p.coeffs, [2, 3, 14]) # this never used to be allowed - let's not add features to deprecated # APIs assert_raises(AttributeError, setattr, p, 'coeffs', np.array(1))