text: from __future__ import division, print_function, absolute_import
  
  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)
  
  