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)[()])