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from __future__ import division, print_function, absolute_import
import numpy as np
from numpy.testing import assert_array_equal, assert_almost_equal, \
assert_array_almost_equal, assert_equal
from scipy.misc import pade, logsumexp, face, ascent
def test_pade_trivial():
nump, denomp = pade([1.0], 0)
assert_array_equal(nump.c, [1.0])
assert_array_equal(denomp.c, [1.0])
def test_pade_4term_exp():
# First four Taylor coefficients of exp(x).
# Unlike poly1d, the first array element is the zero-order term.
an = [1.0, 1.0, 0.5, 1.0/6]
nump, denomp = pade(an, 0)
assert_array_almost_equal(nump.c, [1.0/6, 0.5, 1.0, 1.0])
assert_array_almost_equal(denomp.c, [1.0])
nump, denomp = pade(an, 1)
assert_array_almost_equal(nump.c, [1.0/6, 2.0/3, 1.0])
assert_array_almost_equal(denomp.c, [-1.0/3, 1.0])
nump, denomp = pade(an, 2)
assert_array_almost_equal(nump.c, [1.0/3, 1.0])
assert_array_almost_equal(denomp.c, [1.0/6, -2.0/3, 1.0])
nump, denomp = pade(an, 3)
assert_array_almost_equal(nump.c, [1.0])
assert_array_almost_equal(denomp.c, [-1.0/6, 0.5, -1.0, 1.0])
def test_logsumexp():
"""Test whether logsumexp() function correctly handles large inputs."""
a = np.arange(200)
desired = np.log(np.sum(np.exp(a)))
assert_almost_equal(logsumexp(a), desired)
# Now test with large numbers
b = [1000, 1000]
desired = 1000.0 + np.log(2.0)
assert_almost_equal(logsumexp(b), desired)
n = 1000
b = np.ones(n) * 10000
desired = 10000.0 + np.log(n)
assert_almost_equal(logsumexp(b), desired)
x = np.array([1e-40] * 1000000)
logx = np.log(x)
X = np.vstack([x, x])
logX = np.vstack([logx, logx])
assert_array_almost_equal(np.exp(logsumexp(logX)), X.sum())
assert_array_almost_equal(np.exp(logsumexp(logX, axis=0)), X.sum(axis=0))
assert_array_almost_equal(np.exp(logsumexp(logX, axis=1)), X.sum(axis=1))
def test_logsumexp_b():
a = np.arange(200)
b = np.arange(200, 0, -1)
desired = np.log(np.sum(b*np.exp(a)))
assert_almost_equal(logsumexp(a, b=b), desired)
a = [1000, 1000]
b = [1.2, 1.2]
desired = 1000 + np.log(2 * 1.2)
assert_almost_equal(logsumexp(a, b=b), desired)
x = np.array([1e-40] * 100000)
b = np.linspace(1, 1000, 1e5)
logx = np.log(x)
X = np.vstack((x, x))
logX = np.vstack((logx, logx))
B = np.vstack((b, b))
assert_array_almost_equal(np.exp(logsumexp(logX, b=B)), (B * X).sum())
assert_array_almost_equal(np.exp(logsumexp(logX, b=B, axis=0)),
(B * X).sum(axis=0))
assert_array_almost_equal(np.exp(logsumexp(logX, b=B, axis=1)),
(B * X).sum(axis=1))
def test_face():
assert_equal(face().shape, (768, 1024, 3))
def test_ascent():
assert_equal(ascent().shape, (512, 512))
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