Spaces:
Paused
Paused
File size: 10,995 Bytes
dc2106c |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 |
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_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))
|