import numpy as np from numpy.testing import 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) assert_almost_equal(y, np.log(x)) # lambda = 1 => y = x - 1 y = boxcox(x, 1) assert_almost_equal(y, x - 1) # lambda = 2 => y = 0.5*(x**2 - 1) y = boxcox(x, 2) 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) 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]) 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]) 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) assert_almost_equal(y, np.log1p(x)) # lambda = 1 => y = x y = boxcox1p(x, 1) assert_almost_equal(y, x) # lambda = 2 => y = 0.5*((1+x)**2 - 1) = 0.5*x*(2 + x) y = boxcox1p(x, 2) 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) 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]) 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]) 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)