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from __future__ import division, print_function, absolute_import
import numpy as np
from numpy.testing import run_module_suite, assert_equal, assert_almost_equal, assert_allclose
from scipy.special import boxcox, boxcox1p, inv_boxcox, inv_boxcox1p
# There are more tests of boxcox and boxcox1p in test_mpmath.py.
def test_boxcox_basic():
x = np.array([0.5, 1, 2, 4])
# lambda = 0 => y = log(x)
y = boxcox(x, 0)
yield assert_almost_equal, y, np.log(x)
# lambda = 1 => y = x - 1
y = boxcox(x, 1)
yield assert_almost_equal, y, x - 1
# lambda = 2 => y = 0.5*(x**2 - 1)
y = boxcox(x, 2)
yield assert_almost_equal, y, 0.5*(x**2 - 1)
# x = 0 and lambda > 0 => y = -1 / lambda
lam = np.array([0.5, 1, 2])
y = boxcox(0, lam)
yield assert_almost_equal, y, -1.0 / lam
def test_boxcox_underflow():
x = 1 + 1e-15
lmbda = 1e-306
y = boxcox(x, lmbda)
assert_allclose(y, np.log(x), rtol=1e-14)
def test_boxcox_nonfinite():
# x < 0 => y = nan
x = np.array([-1, -1, -0.5])
y = boxcox(x, [0.5, 2.0, -1.5])
yield assert_equal, y, np.array([np.nan, np.nan, np.nan])
# x = 0 and lambda <= 0 => y = -inf
x = 0
y = boxcox(x, [-2.5, 0])
yield assert_equal, y, np.array([-np.inf, -np.inf])
def test_boxcox1p_basic():
x = np.array([-0.25, -1e-20, 0, 1e-20, 0.25, 1, 3])
# lambda = 0 => y = log(1+x)
y = boxcox1p(x, 0)
yield assert_almost_equal, y, np.log1p(x)
# lambda = 1 => y = x
y = boxcox1p(x, 1)
yield assert_almost_equal, y, x
# lambda = 2 => y = 0.5*((1+x)**2 - 1) = 0.5*x*(2 + x)
y = boxcox1p(x, 2)
yield assert_almost_equal, y, 0.5*x*(2 + x)
# x = -1 and lambda > 0 => y = -1 / lambda
lam = np.array([0.5, 1, 2])
y = boxcox1p(-1, lam)
yield assert_almost_equal, y, -1.0 / lam
def test_boxcox1p_underflow():
x = np.array([1e-15, 1e-306])
lmbda = np.array([1e-306, 1e-18])
y = boxcox1p(x, lmbda)
assert_allclose(y, np.log1p(x), rtol=1e-14)
def test_boxcox1p_nonfinite():
# x < -1 => y = nan
x = np.array([-2, -2, -1.5])
y = boxcox1p(x, [0.5, 2.0, -1.5])
yield assert_equal, y, np.array([np.nan, np.nan, np.nan])
# x = -1 and lambda <= 0 => y = -inf
x = -1
y = boxcox1p(x, [-2.5, 0])
yield assert_equal, y, np.array([-np.inf, -np.inf])
def test_inv_boxcox():
x = np.array([0., 1., 2.])
lam = np.array([0., 1., 2.])
y = boxcox(x, lam)
x2 = inv_boxcox(y, lam)
assert_almost_equal(x, x2)
x = np.array([0., 1., 2.])
lam = np.array([0., 1., 2.])
y = boxcox1p(x, lam)
x2 = inv_boxcox1p(y, lam)
assert_almost_equal(x, x2)
def test_inv_boxcox1p_underflow():
x = 1e-15
lam = 1e-306
y = inv_boxcox1p(x, lam)
assert_allclose(y, x, rtol=1e-14)
if __name__ == '__main__':
run_module_suite()
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