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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, assert_)
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))
# Handling special values properly
assert_equal(logsumexp(np.inf), np.inf)
assert_equal(logsumexp(-np.inf), -np.inf)
assert_equal(logsumexp(np.nan), np.nan)
assert_equal(logsumexp([-np.inf, -np.inf]), -np.inf)
# Handling an array with different magnitudes on the axes
assert_array_almost_equal(logsumexp([[1e10, 1e-10],
[-1e10, -np.inf]], axis=-1),
[1e10, -1e10])
# Test keeping dimensions
assert_array_almost_equal(logsumexp([[1e10, 1e-10],
[-1e10, -np.inf]],
axis=-1,
keepdims=True),
[[1e10], [-1e10]])
# Test multiple axes
assert_array_almost_equal(logsumexp([[1e10, 1e-10],
[-1e10, -np.inf]],
axis=(-1,-2)),
1e10)
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, 100000)
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_logsumexp_sign():
a = [1,1,1]
b = [1,-1,-1]
r, s = logsumexp(a, b=b, return_sign=True)
assert_almost_equal(r,1)
assert_equal(s,-1)
def test_logsumexp_sign_zero():
a = [1,1]
b = [1,-1]
r, s = logsumexp(a, b=b, return_sign=True)
assert_(not np.isfinite(r))
assert_(not np.isnan(r))
assert_(r < 0)
assert_equal(s,0)
def test_logsumexp_sign_shape():
a = np.ones((1,2,3,4))
b = np.ones_like(a)
r, s = logsumexp(a, axis=2, b=b, return_sign=True)
assert_equal(r.shape, s.shape)
assert_equal(r.shape, (1,2,4))
r, s = logsumexp(a, axis=(1,3), b=b, return_sign=True)
assert_equal(r.shape, s.shape)
assert_equal(r.shape, (1,3))
def test_logsumexp_shape():
a = np.ones((1, 2, 3, 4))
b = np.ones_like(a)
r = logsumexp(a, axis=2, b=b)
assert_equal(r.shape, (1, 2, 4))
r = logsumexp(a, axis=(1, 3), b=b)
assert_equal(r.shape, (1, 3))
def test_logsumexp_b_zero():
a = [1,10000]
b = [1,0]
assert_almost_equal(logsumexp(a, b=b), 1)
def test_logsumexp_b_shape():
a = np.zeros((4,1,2,1))
b = np.ones((3,1,5))
logsumexp(a, b=b)
def test_face():
assert_equal(face().shape, (768, 1024, 3))
def test_ascent():
assert_equal(ascent().shape, (512, 512))
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