File size: 13,953 Bytes
7885a28 |
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 |
import math
import pytest
from pytest import raises as assert_raises
import numpy as np
from scipy import stats
from scipy.stats import norm, expon # type: ignore[attr-defined]
from scipy.conftest import array_api_compatible
from scipy._lib._array_api import array_namespace, is_array_api_strict, is_jax
from scipy._lib._array_api_no_0d import (xp_assert_close, xp_assert_equal,
xp_assert_less)
class TestEntropy:
@array_api_compatible
def test_entropy_positive(self, xp):
# See ticket #497
pk = xp.asarray([0.5, 0.2, 0.3])
qk = xp.asarray([0.1, 0.25, 0.65])
eself = stats.entropy(pk, pk)
edouble = stats.entropy(pk, qk)
xp_assert_equal(eself, xp.asarray(0.))
xp_assert_less(-edouble, xp.asarray(0.))
@array_api_compatible
def test_entropy_base(self, xp):
pk = xp.ones(16)
S = stats.entropy(pk, base=2.)
xp_assert_less(xp.abs(S - 4.), xp.asarray(1.e-5))
qk = xp.ones(16)
qk = xp.where(xp.arange(16) < 8, xp.asarray(2.), qk)
S = stats.entropy(pk, qk)
S2 = stats.entropy(pk, qk, base=2.)
xp_assert_less(xp.abs(S/S2 - math.log(2.)), xp.asarray(1.e-5))
@array_api_compatible
def test_entropy_zero(self, xp):
# Test for PR-479
x = xp.asarray([0., 1., 2.])
xp_assert_close(stats.entropy(x),
xp.asarray(0.63651416829481278))
@array_api_compatible
def test_entropy_2d(self, xp):
pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
qk = xp.asarray([[0.2, 0.1], [0.3, 0.6], [0.5, 0.3]])
xp_assert_close(stats.entropy(pk, qk),
xp.asarray([0.1933259, 0.18609809]))
@array_api_compatible
def test_entropy_2d_zero(self, xp):
pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
qk = xp.asarray([[0.0, 0.1], [0.3, 0.6], [0.5, 0.3]])
xp_assert_close(stats.entropy(pk, qk),
xp.asarray([xp.inf, 0.18609809]))
pk = xp.asarray([[0.0, 0.2], [0.6, 0.3], [0.3, 0.5]])
xp_assert_close(stats.entropy(pk, qk),
xp.asarray([0.17403988, 0.18609809]))
@array_api_compatible
def test_entropy_base_2d_nondefault_axis(self, xp):
pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
xp_assert_close(stats.entropy(pk, axis=1),
xp.asarray([0.63651417, 0.63651417, 0.66156324]))
@array_api_compatible
def test_entropy_2d_nondefault_axis(self, xp):
pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
qk = xp.asarray([[0.2, 0.1], [0.3, 0.6], [0.5, 0.3]])
xp_assert_close(stats.entropy(pk, qk, axis=1),
xp.asarray([0.23104906, 0.23104906, 0.12770641]))
@array_api_compatible
def test_entropy_raises_value_error(self, xp):
pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
qk = xp.asarray([[0.1, 0.2], [0.6, 0.3]])
message = "Array shapes are incompatible for broadcasting."
with pytest.raises(ValueError, match=message):
stats.entropy(pk, qk)
@array_api_compatible
def test_base_entropy_with_axis_0_is_equal_to_default(self, xp):
pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
xp_assert_close(stats.entropy(pk, axis=0),
stats.entropy(pk))
@array_api_compatible
def test_entropy_with_axis_0_is_equal_to_default(self, xp):
pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
qk = xp.asarray([[0.2, 0.1], [0.3, 0.6], [0.5, 0.3]])
xp_assert_close(stats.entropy(pk, qk, axis=0),
stats.entropy(pk, qk))
@array_api_compatible
def test_base_entropy_transposed(self, xp):
pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
xp_assert_close(stats.entropy(pk.T),
stats.entropy(pk, axis=1))
@array_api_compatible
def test_entropy_transposed(self, xp):
pk = xp.asarray([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
qk = xp.asarray([[0.2, 0.1], [0.3, 0.6], [0.5, 0.3]])
xp_assert_close(stats.entropy(pk.T, qk.T),
stats.entropy(pk, qk, axis=1))
@array_api_compatible
def test_entropy_broadcasting(self, xp):
rng = np.random.default_rng(74187315492831452)
x = xp.asarray(rng.random(3))
y = xp.asarray(rng.random((2, 1)))
res = stats.entropy(x, y, axis=-1)
xp_assert_equal(res[0], stats.entropy(x, y[0, ...]))
xp_assert_equal(res[1], stats.entropy(x, y[1, ...]))
@array_api_compatible
def test_entropy_shape_mismatch(self, xp):
x = xp.ones((10, 1, 12))
y = xp.ones((11, 2))
message = "Array shapes are incompatible for broadcasting."
with pytest.raises(ValueError, match=message):
stats.entropy(x, y)
@array_api_compatible
def test_input_validation(self, xp):
x = xp.ones(10)
message = "`base` must be a positive number."
with pytest.raises(ValueError, match=message):
stats.entropy(x, base=-2)
@array_api_compatible
@pytest.mark.usefixtures("skip_xp_backends")
class TestDifferentialEntropy:
"""
Vasicek results are compared with the R package vsgoftest.
# library(vsgoftest)
#
# samp <- c(<values>)
# entropy.estimate(x = samp, window = <window_length>)
"""
def test_differential_entropy_vasicek(self, xp):
random_state = np.random.RandomState(0)
values = random_state.standard_normal(100)
values = xp.asarray(values.tolist())
entropy = stats.differential_entropy(values, method='vasicek')
xp_assert_close(entropy, xp.asarray(1.342551187000946))
entropy = stats.differential_entropy(values, window_length=1,
method='vasicek')
xp_assert_close(entropy, xp.asarray(1.122044177725947))
entropy = stats.differential_entropy(values, window_length=8,
method='vasicek')
xp_assert_close(entropy, xp.asarray(1.349401487550325))
def test_differential_entropy_vasicek_2d_nondefault_axis(self, xp):
random_state = np.random.RandomState(0)
values = random_state.standard_normal((3, 100))
values = xp.asarray(values.tolist())
entropy = stats.differential_entropy(values, axis=1, method='vasicek')
ref = xp.asarray([1.342551187000946, 1.341825903922332, 1.293774601883585])
xp_assert_close(entropy, ref)
entropy = stats.differential_entropy(values, axis=1, window_length=1,
method='vasicek')
ref = xp.asarray([1.122044177725947, 1.10294413850758, 1.129615790292772])
xp_assert_close(entropy, ref)
entropy = stats.differential_entropy(values, axis=1, window_length=8,
method='vasicek')
ref = xp.asarray([1.349401487550325, 1.338514126301301, 1.292331889365405])
xp_assert_close(entropy, ref)
def test_differential_entropy_raises_value_error(self, xp):
random_state = np.random.RandomState(0)
values = random_state.standard_normal((3, 100))
values = xp.asarray(values.tolist())
error_str = (
r"Window length \({window_length}\) must be positive and less "
r"than half the sample size \({sample_size}\)."
)
sample_size = values.shape[1]
for window_length in {-1, 0, sample_size//2, sample_size}:
formatted_error_str = error_str.format(
window_length=window_length,
sample_size=sample_size,
)
with assert_raises(ValueError, match=formatted_error_str):
stats.differential_entropy(
values,
window_length=window_length,
axis=1,
)
@pytest.mark.skip_xp_backends('jax.numpy',
reason="JAX doesn't support item assignment")
def test_base_differential_entropy_with_axis_0_is_equal_to_default(self, xp):
random_state = np.random.RandomState(0)
values = random_state.standard_normal((100, 3))
values = xp.asarray(values.tolist())
entropy = stats.differential_entropy(values, axis=0)
default_entropy = stats.differential_entropy(values)
xp_assert_close(entropy, default_entropy)
@pytest.mark.skip_xp_backends('jax.numpy',
reason="JAX doesn't support item assignment")
def test_base_differential_entropy_transposed(self, xp):
random_state = np.random.RandomState(0)
values = random_state.standard_normal((3, 100))
values = xp.asarray(values.tolist())
xp_assert_close(
stats.differential_entropy(values.T),
stats.differential_entropy(values, axis=1),
)
def test_input_validation(self, xp):
x = np.random.rand(10)
x = xp.asarray(x.tolist())
message = "`base` must be a positive number or `None`."
with pytest.raises(ValueError, match=message):
stats.differential_entropy(x, base=-2)
message = "`method` must be one of..."
with pytest.raises(ValueError, match=message):
stats.differential_entropy(x, method='ekki-ekki')
@pytest.mark.parametrize('method', ['vasicek', 'van es',
'ebrahimi', 'correa'])
def test_consistency(self, method, xp):
if is_jax(xp) and method == 'ebrahimi':
pytest.xfail("Needs array assignment.")
elif is_array_api_strict(xp) and method == 'correa':
pytest.xfail("Needs fancy indexing.")
# test that method is a consistent estimator
n = 10000 if method == 'correa' else 1000000
rvs = stats.norm.rvs(size=n, random_state=0)
rvs = xp.asarray(rvs.tolist())
expected = xp.asarray(float(stats.norm.entropy()))
res = stats.differential_entropy(rvs, method=method)
xp_assert_close(res, expected, rtol=0.005)
# values from differential_entropy reference [6], table 1, n=50, m=7
norm_rmse_std_cases = { # method: (RMSE, STD)
'vasicek': (0.198, 0.109),
'van es': (0.212, 0.110),
'correa': (0.135, 0.112),
'ebrahimi': (0.128, 0.109)
}
# values from differential_entropy reference [6], table 2, n=50, m=7
expon_rmse_std_cases = { # method: (RMSE, STD)
'vasicek': (0.194, 0.148),
'van es': (0.179, 0.149),
'correa': (0.155, 0.152),
'ebrahimi': (0.151, 0.148)
}
rmse_std_cases = {norm: norm_rmse_std_cases,
expon: expon_rmse_std_cases}
@pytest.mark.parametrize('method', ['vasicek', 'van es', 'ebrahimi', 'correa'])
@pytest.mark.parametrize('dist', [norm, expon])
def test_rmse_std(self, method, dist, xp):
# test that RMSE and standard deviation of estimators matches values
# given in differential_entropy reference [6]. Incidentally, also
# tests vectorization.
if is_jax(xp) and method == 'ebrahimi':
pytest.xfail("Needs array assignment.")
elif is_array_api_strict(xp) and method == 'correa':
pytest.xfail("Needs fancy indexing.")
reps, n, m = 10000, 50, 7
expected = self.rmse_std_cases[dist][method]
rmse_expected, std_expected = xp.asarray(expected[0]), xp.asarray(expected[1])
rvs = dist.rvs(size=(reps, n), random_state=0)
rvs = xp.asarray(rvs.tolist())
true_entropy = xp.asarray(float(dist.entropy()))
res = stats.differential_entropy(rvs, window_length=m,
method=method, axis=-1)
xp_assert_close(xp.sqrt(xp.mean((res - true_entropy)**2)),
rmse_expected, atol=0.005)
xp_test = array_namespace(res)
xp_assert_close(xp_test.std(res, correction=0), std_expected, atol=0.002)
@pytest.mark.parametrize('n, method', [(8, 'van es'),
(12, 'ebrahimi'),
(1001, 'vasicek')])
def test_method_auto(self, n, method, xp):
if is_jax(xp) and method == 'ebrahimi':
pytest.xfail("Needs array assignment.")
rvs = stats.norm.rvs(size=(n,), random_state=0)
rvs = xp.asarray(rvs.tolist())
res1 = stats.differential_entropy(rvs)
res2 = stats.differential_entropy(rvs, method=method)
xp_assert_equal(res1, res2)
@pytest.mark.skip_xp_backends('jax.numpy',
reason="JAX doesn't support item assignment")
@pytest.mark.parametrize('method', ["vasicek", "van es", "correa", "ebrahimi"])
@pytest.mark.parametrize('dtype', [None, 'float32', 'float64'])
def test_dtypes_gh21192(self, xp, method, dtype):
# gh-21192 noted a change in the output of method='ebrahimi'
# with integer input. Check that the output is consistent regardless
# of input dtype.
if is_array_api_strict(xp) and method == 'correa':
pytest.xfail("Needs fancy indexing.")
x = [1, 1, 2, 3, 3, 4, 5, 5, 6, 7, 8, 9, 10, 11]
dtype_in = getattr(xp, str(dtype), None)
dtype_out = getattr(xp, str(dtype), xp.asarray(1.).dtype)
res = stats.differential_entropy(xp.asarray(x, dtype=dtype_in), method=method)
ref = stats.differential_entropy(xp.asarray(x, dtype=xp.float64), method=method)
xp_assert_close(res, xp.asarray(ref, dtype=dtype_out)[()])
|