839 lines
33 KiB
Python
839 lines
33 KiB
Python
import numpy as np
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from numpy.lib.histograms import histogram, histogramdd, histogram_bin_edges
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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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assert_array_max_ulp, assert_raises_regex, suppress_warnings,
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)
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import pytest
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class TestHistogram:
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def setup(self):
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pass
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def teardown(self):
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pass
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def test_simple(self):
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n = 100
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v = np.random.rand(n)
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(a, b) = histogram(v)
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# check if the sum of the bins equals the number of samples
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assert_equal(np.sum(a, axis=0), n)
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# check that the bin counts are evenly spaced when the data is from
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# a linear function
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(a, b) = histogram(np.linspace(0, 10, 100))
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assert_array_equal(a, 10)
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def test_one_bin(self):
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# Ticket 632
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hist, edges = histogram([1, 2, 3, 4], [1, 2])
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assert_array_equal(hist, [2, ])
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assert_array_equal(edges, [1, 2])
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assert_raises(ValueError, histogram, [1, 2], bins=0)
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h, e = histogram([1, 2], bins=1)
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assert_equal(h, np.array([2]))
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assert_allclose(e, np.array([1., 2.]))
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def test_normed(self):
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sup = suppress_warnings()
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with sup:
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rec = sup.record(np.VisibleDeprecationWarning, '.*normed.*')
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# Check that the integral of the density equals 1.
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n = 100
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v = np.random.rand(n)
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a, b = histogram(v, normed=True)
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area = np.sum(a * np.diff(b))
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assert_almost_equal(area, 1)
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assert_equal(len(rec), 1)
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sup = suppress_warnings()
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with sup:
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rec = sup.record(np.VisibleDeprecationWarning, '.*normed.*')
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# Check with non-constant bin widths (buggy but backwards
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# compatible)
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v = np.arange(10)
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bins = [0, 1, 5, 9, 10]
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a, b = histogram(v, bins, normed=True)
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area = np.sum(a * np.diff(b))
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assert_almost_equal(area, 1)
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assert_equal(len(rec), 1)
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def test_density(self):
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# Check that the integral of the density equals 1.
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n = 100
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v = np.random.rand(n)
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a, b = histogram(v, density=True)
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area = np.sum(a * np.diff(b))
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assert_almost_equal(area, 1)
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# Check with non-constant bin widths
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v = np.arange(10)
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bins = [0, 1, 3, 6, 10]
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a, b = histogram(v, bins, density=True)
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assert_array_equal(a, .1)
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assert_equal(np.sum(a * np.diff(b)), 1)
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# Test that passing False works too
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a, b = histogram(v, bins, density=False)
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assert_array_equal(a, [1, 2, 3, 4])
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# Variable bin widths are especially useful to deal with
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# infinities.
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v = np.arange(10)
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bins = [0, 1, 3, 6, np.inf]
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a, b = histogram(v, bins, density=True)
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assert_array_equal(a, [.1, .1, .1, 0.])
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# Taken from a bug report from N. Becker on the numpy-discussion
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# mailing list Aug. 6, 2010.
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counts, dmy = np.histogram(
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[1, 2, 3, 4], [0.5, 1.5, np.inf], density=True)
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assert_equal(counts, [.25, 0])
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def test_outliers(self):
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# Check that outliers are not tallied
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a = np.arange(10) + .5
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# Lower outliers
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h, b = histogram(a, range=[0, 9])
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assert_equal(h.sum(), 9)
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# Upper outliers
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h, b = histogram(a, range=[1, 10])
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assert_equal(h.sum(), 9)
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# Normalization
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h, b = histogram(a, range=[1, 9], density=True)
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assert_almost_equal((h * np.diff(b)).sum(), 1, decimal=15)
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# Weights
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w = np.arange(10) + .5
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h, b = histogram(a, range=[1, 9], weights=w, density=True)
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assert_equal((h * np.diff(b)).sum(), 1)
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h, b = histogram(a, bins=8, range=[1, 9], weights=w)
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assert_equal(h, w[1:-1])
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def test_arr_weights_mismatch(self):
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a = np.arange(10) + .5
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w = np.arange(11) + .5
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with assert_raises_regex(ValueError, "same shape as"):
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h, b = histogram(a, range=[1, 9], weights=w, density=True)
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def test_type(self):
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# Check the type of the returned histogram
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a = np.arange(10) + .5
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h, b = histogram(a)
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assert_(np.issubdtype(h.dtype, np.integer))
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h, b = histogram(a, density=True)
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assert_(np.issubdtype(h.dtype, np.floating))
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h, b = histogram(a, weights=np.ones(10, int))
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assert_(np.issubdtype(h.dtype, np.integer))
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h, b = histogram(a, weights=np.ones(10, float))
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assert_(np.issubdtype(h.dtype, np.floating))
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def test_f32_rounding(self):
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# gh-4799, check that the rounding of the edges works with float32
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x = np.array([276.318359, -69.593948, 21.329449], dtype=np.float32)
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y = np.array([5005.689453, 4481.327637, 6010.369629], dtype=np.float32)
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counts_hist, xedges, yedges = np.histogram2d(x, y, bins=100)
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assert_equal(counts_hist.sum(), 3.)
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def test_bool_conversion(self):
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# gh-12107
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# Reference integer histogram
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a = np.array([1, 1, 0], dtype=np.uint8)
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int_hist, int_edges = np.histogram(a)
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# Should raise an warning on booleans
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# Ensure that the histograms are equivalent, need to suppress
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# the warnings to get the actual outputs
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with suppress_warnings() as sup:
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rec = sup.record(RuntimeWarning, 'Converting input from .*')
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hist, edges = np.histogram([True, True, False])
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# A warning should be issued
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assert_equal(len(rec), 1)
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assert_array_equal(hist, int_hist)
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assert_array_equal(edges, int_edges)
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def test_weights(self):
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v = np.random.rand(100)
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w = np.ones(100) * 5
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a, b = histogram(v)
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na, nb = histogram(v, density=True)
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wa, wb = histogram(v, weights=w)
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nwa, nwb = histogram(v, weights=w, density=True)
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assert_array_almost_equal(a * 5, wa)
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assert_array_almost_equal(na, nwa)
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# Check weights are properly applied.
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v = np.linspace(0, 10, 10)
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w = np.concatenate((np.zeros(5), np.ones(5)))
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wa, wb = histogram(v, bins=np.arange(11), weights=w)
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assert_array_almost_equal(wa, w)
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# Check with integer weights
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wa, wb = histogram([1, 2, 2, 4], bins=4, weights=[4, 3, 2, 1])
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assert_array_equal(wa, [4, 5, 0, 1])
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wa, wb = histogram(
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[1, 2, 2, 4], bins=4, weights=[4, 3, 2, 1], density=True)
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assert_array_almost_equal(wa, np.array([4, 5, 0, 1]) / 10. / 3. * 4)
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# Check weights with non-uniform bin widths
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a, b = histogram(
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np.arange(9), [0, 1, 3, 6, 10],
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weights=[2, 1, 1, 1, 1, 1, 1, 1, 1], density=True)
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assert_almost_equal(a, [.2, .1, .1, .075])
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def test_exotic_weights(self):
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# Test the use of weights that are not integer or floats, but e.g.
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# complex numbers or object types.
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# Complex weights
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values = np.array([1.3, 2.5, 2.3])
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weights = np.array([1, -1, 2]) + 1j * np.array([2, 1, 2])
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# Check with custom bins
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wa, wb = histogram(values, bins=[0, 2, 3], weights=weights)
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assert_array_almost_equal(wa, np.array([1, 1]) + 1j * np.array([2, 3]))
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# Check with even bins
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wa, wb = histogram(values, bins=2, range=[1, 3], weights=weights)
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assert_array_almost_equal(wa, np.array([1, 1]) + 1j * np.array([2, 3]))
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# Decimal weights
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from decimal import Decimal
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values = np.array([1.3, 2.5, 2.3])
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weights = np.array([Decimal(1), Decimal(2), Decimal(3)])
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# Check with custom bins
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wa, wb = histogram(values, bins=[0, 2, 3], weights=weights)
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assert_array_almost_equal(wa, [Decimal(1), Decimal(5)])
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# Check with even bins
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wa, wb = histogram(values, bins=2, range=[1, 3], weights=weights)
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assert_array_almost_equal(wa, [Decimal(1), Decimal(5)])
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def test_no_side_effects(self):
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# This is a regression test that ensures that values passed to
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# ``histogram`` are unchanged.
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values = np.array([1.3, 2.5, 2.3])
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np.histogram(values, range=[-10, 10], bins=100)
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assert_array_almost_equal(values, [1.3, 2.5, 2.3])
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def test_empty(self):
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a, b = histogram([], bins=([0, 1]))
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assert_array_equal(a, np.array([0]))
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assert_array_equal(b, np.array([0, 1]))
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def test_error_binnum_type (self):
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# Tests if right Error is raised if bins argument is float
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vals = np.linspace(0.0, 1.0, num=100)
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histogram(vals, 5)
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assert_raises(TypeError, histogram, vals, 2.4)
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def test_finite_range(self):
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# Normal ranges should be fine
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vals = np.linspace(0.0, 1.0, num=100)
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histogram(vals, range=[0.25,0.75])
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assert_raises(ValueError, histogram, vals, range=[np.nan,0.75])
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assert_raises(ValueError, histogram, vals, range=[0.25,np.inf])
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def test_invalid_range(self):
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# start of range must be < end of range
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vals = np.linspace(0.0, 1.0, num=100)
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with assert_raises_regex(ValueError, "max must be larger than"):
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np.histogram(vals, range=[0.1, 0.01])
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def test_bin_edge_cases(self):
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# Ensure that floating-point computations correctly place edge cases.
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arr = np.array([337, 404, 739, 806, 1007, 1811, 2012])
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hist, edges = np.histogram(arr, bins=8296, range=(2, 2280))
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mask = hist > 0
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left_edges = edges[:-1][mask]
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right_edges = edges[1:][mask]
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for x, left, right in zip(arr, left_edges, right_edges):
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assert_(x >= left)
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assert_(x < right)
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def test_last_bin_inclusive_range(self):
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arr = np.array([0., 0., 0., 1., 2., 3., 3., 4., 5.])
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hist, edges = np.histogram(arr, bins=30, range=(-0.5, 5))
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assert_equal(hist[-1], 1)
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def test_bin_array_dims(self):
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# gracefully handle bins object > 1 dimension
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vals = np.linspace(0.0, 1.0, num=100)
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bins = np.array([[0, 0.5], [0.6, 1.0]])
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with assert_raises_regex(ValueError, "must be 1d"):
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np.histogram(vals, bins=bins)
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def test_unsigned_monotonicity_check(self):
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# Ensures ValueError is raised if bins not increasing monotonically
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# when bins contain unsigned values (see #9222)
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arr = np.array([2])
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bins = np.array([1, 3, 1], dtype='uint64')
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with assert_raises(ValueError):
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hist, edges = np.histogram(arr, bins=bins)
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def test_object_array_of_0d(self):
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# gh-7864
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assert_raises(ValueError,
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histogram, [np.array(0.4) for i in range(10)] + [-np.inf])
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assert_raises(ValueError,
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histogram, [np.array(0.4) for i in range(10)] + [np.inf])
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# these should not crash
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np.histogram([np.array(0.5) for i in range(10)] + [.500000000000001])
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np.histogram([np.array(0.5) for i in range(10)] + [.5])
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def test_some_nan_values(self):
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# gh-7503
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one_nan = np.array([0, 1, np.nan])
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all_nan = np.array([np.nan, np.nan])
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# the internal comparisons with NaN give warnings
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sup = suppress_warnings()
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sup.filter(RuntimeWarning)
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with sup:
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# can't infer range with nan
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assert_raises(ValueError, histogram, one_nan, bins='auto')
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assert_raises(ValueError, histogram, all_nan, bins='auto')
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# explicit range solves the problem
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h, b = histogram(one_nan, bins='auto', range=(0, 1))
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assert_equal(h.sum(), 2) # nan is not counted
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h, b = histogram(all_nan, bins='auto', range=(0, 1))
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assert_equal(h.sum(), 0) # nan is not counted
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# as does an explicit set of bins
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h, b = histogram(one_nan, bins=[0, 1])
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assert_equal(h.sum(), 2) # nan is not counted
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h, b = histogram(all_nan, bins=[0, 1])
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assert_equal(h.sum(), 0) # nan is not counted
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def test_datetime(self):
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begin = np.datetime64('2000-01-01', 'D')
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offsets = np.array([0, 0, 1, 1, 2, 3, 5, 10, 20])
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bins = np.array([0, 2, 7, 20])
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dates = begin + offsets
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date_bins = begin + bins
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td = np.dtype('timedelta64[D]')
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# Results should be the same for integer offsets or datetime values.
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# For now, only explicit bins are supported, since linspace does not
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# work on datetimes or timedeltas
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d_count, d_edge = histogram(dates, bins=date_bins)
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t_count, t_edge = histogram(offsets.astype(td), bins=bins.astype(td))
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i_count, i_edge = histogram(offsets, bins=bins)
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assert_equal(d_count, i_count)
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assert_equal(t_count, i_count)
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assert_equal((d_edge - begin).astype(int), i_edge)
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assert_equal(t_edge.astype(int), i_edge)
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assert_equal(d_edge.dtype, dates.dtype)
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assert_equal(t_edge.dtype, td)
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def do_signed_overflow_bounds(self, dtype):
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exponent = 8 * np.dtype(dtype).itemsize - 1
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arr = np.array([-2**exponent + 4, 2**exponent - 4], dtype=dtype)
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hist, e = histogram(arr, bins=2)
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assert_equal(e, [-2**exponent + 4, 0, 2**exponent - 4])
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assert_equal(hist, [1, 1])
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def test_signed_overflow_bounds(self):
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self.do_signed_overflow_bounds(np.byte)
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self.do_signed_overflow_bounds(np.short)
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self.do_signed_overflow_bounds(np.intc)
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self.do_signed_overflow_bounds(np.int_)
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self.do_signed_overflow_bounds(np.longlong)
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def do_precision_lower_bound(self, float_small, float_large):
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eps = np.finfo(float_large).eps
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arr = np.array([1.0], float_small)
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range = np.array([1.0 + eps, 2.0], float_large)
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# test is looking for behavior when the bounds change between dtypes
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if range.astype(float_small)[0] != 1:
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return
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# previously crashed
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count, x_loc = np.histogram(arr, bins=1, range=range)
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assert_equal(count, [1])
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# gh-10322 means that the type comes from arr - this may change
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assert_equal(x_loc.dtype, float_small)
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def do_precision_upper_bound(self, float_small, float_large):
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eps = np.finfo(float_large).eps
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arr = np.array([1.0], float_small)
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range = np.array([0.0, 1.0 - eps], float_large)
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# test is looking for behavior when the bounds change between dtypes
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if range.astype(float_small)[-1] != 1:
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return
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# previously crashed
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count, x_loc = np.histogram(arr, bins=1, range=range)
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assert_equal(count, [1])
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# gh-10322 means that the type comes from arr - this may change
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assert_equal(x_loc.dtype, float_small)
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def do_precision(self, float_small, float_large):
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self.do_precision_lower_bound(float_small, float_large)
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self.do_precision_upper_bound(float_small, float_large)
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def test_precision(self):
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# not looping results in a useful stack trace upon failure
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self.do_precision(np.half, np.single)
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self.do_precision(np.half, np.double)
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self.do_precision(np.half, np.longdouble)
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self.do_precision(np.single, np.double)
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self.do_precision(np.single, np.longdouble)
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self.do_precision(np.double, np.longdouble)
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def test_histogram_bin_edges(self):
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hist, e = histogram([1, 2, 3, 4], [1, 2])
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edges = histogram_bin_edges([1, 2, 3, 4], [1, 2])
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assert_array_equal(edges, e)
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arr = np.array([0., 0., 0., 1., 2., 3., 3., 4., 5.])
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hist, e = histogram(arr, bins=30, range=(-0.5, 5))
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edges = histogram_bin_edges(arr, bins=30, range=(-0.5, 5))
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assert_array_equal(edges, e)
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hist, e = histogram(arr, bins='auto', range=(0, 1))
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edges = histogram_bin_edges(arr, bins='auto', range=(0, 1))
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assert_array_equal(edges, e)
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class TestHistogramOptimBinNums:
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"""
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Provide test coverage when using provided estimators for optimal number of
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bins
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"""
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def test_empty(self):
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estimator_list = ['fd', 'scott', 'rice', 'sturges',
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'doane', 'sqrt', 'auto', 'stone']
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# check it can deal with empty data
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for estimator in estimator_list:
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a, b = histogram([], bins=estimator)
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assert_array_equal(a, np.array([0]))
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assert_array_equal(b, np.array([0, 1]))
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def test_simple(self):
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"""
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Straightforward testing with a mixture of linspace data (for
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consistency). All test values have been precomputed and the values
|
|
shouldn't change
|
|
"""
|
|
# Some basic sanity checking, with some fixed data.
|
|
# Checking for the correct number of bins
|
|
basic_test = {50: {'fd': 4, 'scott': 4, 'rice': 8, 'sturges': 7,
|
|
'doane': 8, 'sqrt': 8, 'auto': 7, 'stone': 2},
|
|
500: {'fd': 8, 'scott': 8, 'rice': 16, 'sturges': 10,
|
|
'doane': 12, 'sqrt': 23, 'auto': 10, 'stone': 9},
|
|
5000: {'fd': 17, 'scott': 17, 'rice': 35, 'sturges': 14,
|
|
'doane': 17, 'sqrt': 71, 'auto': 17, 'stone': 20}}
|
|
|
|
for testlen, expectedResults in basic_test.items():
|
|
# Create some sort of non uniform data to test with
|
|
# (2 peak uniform mixture)
|
|
x1 = np.linspace(-10, -1, testlen // 5 * 2)
|
|
x2 = np.linspace(1, 10, testlen // 5 * 3)
|
|
x = np.concatenate((x1, x2))
|
|
for estimator, numbins in expectedResults.items():
|
|
a, b = np.histogram(x, estimator)
|
|
assert_equal(len(a), numbins, err_msg="For the {0} estimator "
|
|
"with datasize of {1}".format(estimator, testlen))
|
|
|
|
def test_small(self):
|
|
"""
|
|
Smaller datasets have the potential to cause issues with the data
|
|
adaptive methods, especially the FD method. All bin numbers have been
|
|
precalculated.
|
|
"""
|
|
small_dat = {1: {'fd': 1, 'scott': 1, 'rice': 1, 'sturges': 1,
|
|
'doane': 1, 'sqrt': 1, 'stone': 1},
|
|
2: {'fd': 2, 'scott': 1, 'rice': 3, 'sturges': 2,
|
|
'doane': 1, 'sqrt': 2, 'stone': 1},
|
|
3: {'fd': 2, 'scott': 2, 'rice': 3, 'sturges': 3,
|
|
'doane': 3, 'sqrt': 2, 'stone': 1}}
|
|
|
|
for testlen, expectedResults in small_dat.items():
|
|
testdat = np.arange(testlen)
|
|
for estimator, expbins in expectedResults.items():
|
|
a, b = np.histogram(testdat, estimator)
|
|
assert_equal(len(a), expbins, err_msg="For the {0} estimator "
|
|
"with datasize of {1}".format(estimator, testlen))
|
|
|
|
def test_incorrect_methods(self):
|
|
"""
|
|
Check a Value Error is thrown when an unknown string is passed in
|
|
"""
|
|
check_list = ['mad', 'freeman', 'histograms', 'IQR']
|
|
for estimator in check_list:
|
|
assert_raises(ValueError, histogram, [1, 2, 3], estimator)
|
|
|
|
def test_novariance(self):
|
|
"""
|
|
Check that methods handle no variance in data
|
|
Primarily for Scott and FD as the SD and IQR are both 0 in this case
|
|
"""
|
|
novar_dataset = np.ones(100)
|
|
novar_resultdict = {'fd': 1, 'scott': 1, 'rice': 1, 'sturges': 1,
|
|
'doane': 1, 'sqrt': 1, 'auto': 1, 'stone': 1}
|
|
|
|
for estimator, numbins in novar_resultdict.items():
|
|
a, b = np.histogram(novar_dataset, estimator)
|
|
assert_equal(len(a), numbins, err_msg="{0} estimator, "
|
|
"No Variance test".format(estimator))
|
|
|
|
def test_limited_variance(self):
|
|
"""
|
|
Check when IQR is 0, but variance exists, we return the sturges value
|
|
and not the fd value.
|
|
"""
|
|
lim_var_data = np.ones(1000)
|
|
lim_var_data[:3] = 0
|
|
lim_var_data[-4:] = 100
|
|
|
|
edges_auto = histogram_bin_edges(lim_var_data, 'auto')
|
|
assert_equal(edges_auto, np.linspace(0, 100, 12))
|
|
|
|
edges_fd = histogram_bin_edges(lim_var_data, 'fd')
|
|
assert_equal(edges_fd, np.array([0, 100]))
|
|
|
|
edges_sturges = histogram_bin_edges(lim_var_data, 'sturges')
|
|
assert_equal(edges_sturges, np.linspace(0, 100, 12))
|
|
|
|
def test_outlier(self):
|
|
"""
|
|
Check the FD, Scott and Doane with outliers.
|
|
|
|
The FD estimates a smaller binwidth since it's less affected by
|
|
outliers. Since the range is so (artificially) large, this means more
|
|
bins, most of which will be empty, but the data of interest usually is
|
|
unaffected. The Scott estimator is more affected and returns fewer bins,
|
|
despite most of the variance being in one area of the data. The Doane
|
|
estimator lies somewhere between the other two.
|
|
"""
|
|
xcenter = np.linspace(-10, 10, 50)
|
|
outlier_dataset = np.hstack((np.linspace(-110, -100, 5), xcenter))
|
|
|
|
outlier_resultdict = {'fd': 21, 'scott': 5, 'doane': 11, 'stone': 6}
|
|
|
|
for estimator, numbins in outlier_resultdict.items():
|
|
a, b = np.histogram(outlier_dataset, estimator)
|
|
assert_equal(len(a), numbins)
|
|
|
|
def test_scott_vs_stone(self):
|
|
"""Verify that Scott's rule and Stone's rule converges for normally distributed data"""
|
|
|
|
def nbins_ratio(seed, size):
|
|
rng = np.random.RandomState(seed)
|
|
x = rng.normal(loc=0, scale=2, size=size)
|
|
a, b = len(np.histogram(x, 'stone')[0]), len(np.histogram(x, 'scott')[0])
|
|
return a / (a + b)
|
|
|
|
ll = [[nbins_ratio(seed, size) for size in np.geomspace(start=10, stop=100, num=4).round().astype(int)]
|
|
for seed in range(10)]
|
|
|
|
# the average difference between the two methods decreases as the dataset size increases.
|
|
avg = abs(np.mean(ll, axis=0) - 0.5)
|
|
assert_almost_equal(avg, [0.15, 0.09, 0.08, 0.03], decimal=2)
|
|
|
|
def test_simple_range(self):
|
|
"""
|
|
Straightforward testing with a mixture of linspace data (for
|
|
consistency). Adding in a 3rd mixture that will then be
|
|
completely ignored. All test values have been precomputed and
|
|
the shouldn't change.
|
|
"""
|
|
# some basic sanity checking, with some fixed data.
|
|
# Checking for the correct number of bins
|
|
basic_test = {
|
|
50: {'fd': 8, 'scott': 8, 'rice': 15,
|
|
'sturges': 14, 'auto': 14, 'stone': 8},
|
|
500: {'fd': 15, 'scott': 16, 'rice': 32,
|
|
'sturges': 20, 'auto': 20, 'stone': 80},
|
|
5000: {'fd': 33, 'scott': 33, 'rice': 69,
|
|
'sturges': 27, 'auto': 33, 'stone': 80}
|
|
}
|
|
|
|
for testlen, expectedResults in basic_test.items():
|
|
# create some sort of non uniform data to test with
|
|
# (3 peak uniform mixture)
|
|
x1 = np.linspace(-10, -1, testlen // 5 * 2)
|
|
x2 = np.linspace(1, 10, testlen // 5 * 3)
|
|
x3 = np.linspace(-100, -50, testlen)
|
|
x = np.hstack((x1, x2, x3))
|
|
for estimator, numbins in expectedResults.items():
|
|
a, b = np.histogram(x, estimator, range = (-20, 20))
|
|
msg = "For the {0} estimator".format(estimator)
|
|
msg += " with datasize of {0}".format(testlen)
|
|
assert_equal(len(a), numbins, err_msg=msg)
|
|
|
|
@pytest.mark.parametrize("bins", ['auto', 'fd', 'doane', 'scott',
|
|
'stone', 'rice', 'sturges'])
|
|
def test_signed_integer_data(self, bins):
|
|
# Regression test for gh-14379.
|
|
a = np.array([-2, 0, 127], dtype=np.int8)
|
|
hist, edges = np.histogram(a, bins=bins)
|
|
hist32, edges32 = np.histogram(a.astype(np.int32), bins=bins)
|
|
assert_array_equal(hist, hist32)
|
|
assert_array_equal(edges, edges32)
|
|
|
|
def test_simple_weighted(self):
|
|
"""
|
|
Check that weighted data raises a TypeError
|
|
"""
|
|
estimator_list = ['fd', 'scott', 'rice', 'sturges', 'auto']
|
|
for estimator in estimator_list:
|
|
assert_raises(TypeError, histogram, [1, 2, 3],
|
|
estimator, weights=[1, 2, 3])
|
|
|
|
|
|
class TestHistogramdd:
|
|
|
|
def test_simple(self):
|
|
x = np.array([[-.5, .5, 1.5], [-.5, 1.5, 2.5], [-.5, 2.5, .5],
|
|
[.5, .5, 1.5], [.5, 1.5, 2.5], [.5, 2.5, 2.5]])
|
|
H, edges = histogramdd(x, (2, 3, 3),
|
|
range=[[-1, 1], [0, 3], [0, 3]])
|
|
answer = np.array([[[0, 1, 0], [0, 0, 1], [1, 0, 0]],
|
|
[[0, 1, 0], [0, 0, 1], [0, 0, 1]]])
|
|
assert_array_equal(H, answer)
|
|
|
|
# Check normalization
|
|
ed = [[-2, 0, 2], [0, 1, 2, 3], [0, 1, 2, 3]]
|
|
H, edges = histogramdd(x, bins=ed, density=True)
|
|
assert_(np.all(H == answer / 12.))
|
|
|
|
# Check that H has the correct shape.
|
|
H, edges = histogramdd(x, (2, 3, 4),
|
|
range=[[-1, 1], [0, 3], [0, 4]],
|
|
density=True)
|
|
answer = np.array([[[0, 1, 0, 0], [0, 0, 1, 0], [1, 0, 0, 0]],
|
|
[[0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 1, 0]]])
|
|
assert_array_almost_equal(H, answer / 6., 4)
|
|
# Check that a sequence of arrays is accepted and H has the correct
|
|
# shape.
|
|
z = [np.squeeze(y) for y in np.split(x, 3, axis=1)]
|
|
H, edges = histogramdd(
|
|
z, bins=(4, 3, 2), range=[[-2, 2], [0, 3], [0, 2]])
|
|
answer = np.array([[[0, 0], [0, 0], [0, 0]],
|
|
[[0, 1], [0, 0], [1, 0]],
|
|
[[0, 1], [0, 0], [0, 0]],
|
|
[[0, 0], [0, 0], [0, 0]]])
|
|
assert_array_equal(H, answer)
|
|
|
|
Z = np.zeros((5, 5, 5))
|
|
Z[list(range(5)), list(range(5)), list(range(5))] = 1.
|
|
H, edges = histogramdd([np.arange(5), np.arange(5), np.arange(5)], 5)
|
|
assert_array_equal(H, Z)
|
|
|
|
def test_shape_3d(self):
|
|
# All possible permutations for bins of different lengths in 3D.
|
|
bins = ((5, 4, 6), (6, 4, 5), (5, 6, 4), (4, 6, 5), (6, 5, 4),
|
|
(4, 5, 6))
|
|
r = np.random.rand(10, 3)
|
|
for b in bins:
|
|
H, edges = histogramdd(r, b)
|
|
assert_(H.shape == b)
|
|
|
|
def test_shape_4d(self):
|
|
# All possible permutations for bins of different lengths in 4D.
|
|
bins = ((7, 4, 5, 6), (4, 5, 7, 6), (5, 6, 4, 7), (7, 6, 5, 4),
|
|
(5, 7, 6, 4), (4, 6, 7, 5), (6, 5, 7, 4), (7, 5, 4, 6),
|
|
(7, 4, 6, 5), (6, 4, 7, 5), (6, 7, 5, 4), (4, 6, 5, 7),
|
|
(4, 7, 5, 6), (5, 4, 6, 7), (5, 7, 4, 6), (6, 7, 4, 5),
|
|
(6, 5, 4, 7), (4, 7, 6, 5), (4, 5, 6, 7), (7, 6, 4, 5),
|
|
(5, 4, 7, 6), (5, 6, 7, 4), (6, 4, 5, 7), (7, 5, 6, 4))
|
|
|
|
r = np.random.rand(10, 4)
|
|
for b in bins:
|
|
H, edges = histogramdd(r, b)
|
|
assert_(H.shape == b)
|
|
|
|
def test_weights(self):
|
|
v = np.random.rand(100, 2)
|
|
hist, edges = histogramdd(v)
|
|
n_hist, edges = histogramdd(v, density=True)
|
|
w_hist, edges = histogramdd(v, weights=np.ones(100))
|
|
assert_array_equal(w_hist, hist)
|
|
w_hist, edges = histogramdd(v, weights=np.ones(100) * 2, density=True)
|
|
assert_array_equal(w_hist, n_hist)
|
|
w_hist, edges = histogramdd(v, weights=np.ones(100, int) * 2)
|
|
assert_array_equal(w_hist, 2 * hist)
|
|
|
|
def test_identical_samples(self):
|
|
x = np.zeros((10, 2), int)
|
|
hist, edges = histogramdd(x, bins=2)
|
|
assert_array_equal(edges[0], np.array([-0.5, 0., 0.5]))
|
|
|
|
def test_empty(self):
|
|
a, b = histogramdd([[], []], bins=([0, 1], [0, 1]))
|
|
assert_array_max_ulp(a, np.array([[0.]]))
|
|
a, b = np.histogramdd([[], [], []], bins=2)
|
|
assert_array_max_ulp(a, np.zeros((2, 2, 2)))
|
|
|
|
def test_bins_errors(self):
|
|
# There are two ways to specify bins. Check for the right errors
|
|
# when mixing those.
|
|
x = np.arange(8).reshape(2, 4)
|
|
assert_raises(ValueError, np.histogramdd, x, bins=[-1, 2, 4, 5])
|
|
assert_raises(ValueError, np.histogramdd, x, bins=[1, 0.99, 1, 1])
|
|
assert_raises(
|
|
ValueError, np.histogramdd, x, bins=[1, 1, 1, [1, 2, 3, -3]])
|
|
assert_(np.histogramdd(x, bins=[1, 1, 1, [1, 2, 3, 4]]))
|
|
|
|
def test_inf_edges(self):
|
|
# Test using +/-inf bin edges works. See #1788.
|
|
with np.errstate(invalid='ignore'):
|
|
x = np.arange(6).reshape(3, 2)
|
|
expected = np.array([[1, 0], [0, 1], [0, 1]])
|
|
h, e = np.histogramdd(x, bins=[3, [-np.inf, 2, 10]])
|
|
assert_allclose(h, expected)
|
|
h, e = np.histogramdd(x, bins=[3, np.array([-1, 2, np.inf])])
|
|
assert_allclose(h, expected)
|
|
h, e = np.histogramdd(x, bins=[3, [-np.inf, 3, np.inf]])
|
|
assert_allclose(h, expected)
|
|
|
|
def test_rightmost_binedge(self):
|
|
# Test event very close to rightmost binedge. See Github issue #4266
|
|
x = [0.9999999995]
|
|
bins = [[0., 0.5, 1.0]]
|
|
hist, _ = histogramdd(x, bins=bins)
|
|
assert_(hist[0] == 0.0)
|
|
assert_(hist[1] == 1.)
|
|
x = [1.0]
|
|
bins = [[0., 0.5, 1.0]]
|
|
hist, _ = histogramdd(x, bins=bins)
|
|
assert_(hist[0] == 0.0)
|
|
assert_(hist[1] == 1.)
|
|
x = [1.0000000001]
|
|
bins = [[0., 0.5, 1.0]]
|
|
hist, _ = histogramdd(x, bins=bins)
|
|
assert_(hist[0] == 0.0)
|
|
assert_(hist[1] == 0.0)
|
|
x = [1.0001]
|
|
bins = [[0., 0.5, 1.0]]
|
|
hist, _ = histogramdd(x, bins=bins)
|
|
assert_(hist[0] == 0.0)
|
|
assert_(hist[1] == 0.0)
|
|
|
|
def test_finite_range(self):
|
|
vals = np.random.random((100, 3))
|
|
histogramdd(vals, range=[[0.0, 1.0], [0.25, 0.75], [0.25, 0.5]])
|
|
assert_raises(ValueError, histogramdd, vals,
|
|
range=[[0.0, 1.0], [0.25, 0.75], [0.25, np.inf]])
|
|
assert_raises(ValueError, histogramdd, vals,
|
|
range=[[0.0, 1.0], [np.nan, 0.75], [0.25, 0.5]])
|
|
|
|
def test_equal_edges(self):
|
|
""" Test that adjacent entries in an edge array can be equal """
|
|
x = np.array([0, 1, 2])
|
|
y = np.array([0, 1, 2])
|
|
x_edges = np.array([0, 2, 2])
|
|
y_edges = 1
|
|
hist, edges = histogramdd((x, y), bins=(x_edges, y_edges))
|
|
|
|
hist_expected = np.array([
|
|
[2.],
|
|
[1.], # x == 2 falls in the final bin
|
|
])
|
|
assert_equal(hist, hist_expected)
|
|
|
|
def test_edge_dtype(self):
|
|
""" Test that if an edge array is input, its type is preserved """
|
|
x = np.array([0, 10, 20])
|
|
y = x / 10
|
|
x_edges = np.array([0, 5, 15, 20])
|
|
y_edges = x_edges / 10
|
|
hist, edges = histogramdd((x, y), bins=(x_edges, y_edges))
|
|
|
|
assert_equal(edges[0].dtype, x_edges.dtype)
|
|
assert_equal(edges[1].dtype, y_edges.dtype)
|
|
|
|
def test_large_integers(self):
|
|
big = 2**60 # Too large to represent with a full precision float
|
|
|
|
x = np.array([0], np.int64)
|
|
x_edges = np.array([-1, +1], np.int64)
|
|
y = big + x
|
|
y_edges = big + x_edges
|
|
|
|
hist, edges = histogramdd((x, y), bins=(x_edges, y_edges))
|
|
|
|
assert_equal(hist[0, 0], 1)
|
|
|
|
def test_density_non_uniform_2d(self):
|
|
# Defines the following grid:
|
|
#
|
|
# 0 2 8
|
|
# 0+-+-----+
|
|
# + | +
|
|
# + | +
|
|
# 6+-+-----+
|
|
# 8+-+-----+
|
|
x_edges = np.array([0, 2, 8])
|
|
y_edges = np.array([0, 6, 8])
|
|
relative_areas = np.array([
|
|
[3, 9],
|
|
[1, 3]])
|
|
|
|
# ensure the number of points in each region is proportional to its area
|
|
x = np.array([1] + [1]*3 + [7]*3 + [7]*9)
|
|
y = np.array([7] + [1]*3 + [7]*3 + [1]*9)
|
|
|
|
# sanity check that the above worked as intended
|
|
hist, edges = histogramdd((y, x), bins=(y_edges, x_edges))
|
|
assert_equal(hist, relative_areas)
|
|
|
|
# resulting histogram should be uniform, since counts and areas are proportional
|
|
hist, edges = histogramdd((y, x), bins=(y_edges, x_edges), density=True)
|
|
assert_equal(hist, 1 / (8*8))
|
|
|
|
def test_density_non_uniform_1d(self):
|
|
# compare to histogram to show the results are the same
|
|
v = np.arange(10)
|
|
bins = np.array([0, 1, 3, 6, 10])
|
|
hist, edges = histogram(v, bins, density=True)
|
|
hist_dd, edges_dd = histogramdd((v,), (bins,), density=True)
|
|
assert_equal(hist, hist_dd)
|
|
assert_equal(edges, edges_dd[0])
|
|
|
|
def test_density_via_normed(self):
|
|
# normed should simply alias to density argument
|
|
v = np.arange(10)
|
|
bins = np.array([0, 1, 3, 6, 10])
|
|
hist, edges = histogram(v, bins, density=True)
|
|
hist_dd, edges_dd = histogramdd((v,), (bins,), normed=True)
|
|
assert_equal(hist, hist_dd)
|
|
assert_equal(edges, edges_dd[0])
|
|
|
|
def test_density_normed_redundancy(self):
|
|
v = np.arange(10)
|
|
bins = np.array([0, 1, 3, 6, 10])
|
|
with assert_raises_regex(TypeError, "Cannot specify both"):
|
|
hist_dd, edges_dd = histogramdd((v,), (bins,),
|
|
density=True,
|
|
normed=True)
|