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
)
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.])))
def test_poly1d_misc(self):
p = np.poly1d([1., 2, 3])
assert_equal(np.asarray(p), np.array([1., 2., 3.]))
assert_equal(len(p), 2)
assert_equal((p[0], p[1], p[2], p[3]), (3.0, 2.0, 1.0, 0))
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_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)
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))