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_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 propotional
hist, edges = histogramdd((y, x),
bins=(y_edges, x_edges),
density=True)
assert_equal(hist, 1 / (8 * 8))
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_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_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_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_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_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_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_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_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]))