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