from __future__ import division, print_function, absolute_import

from numpy.testing import (assert_array_equal, assert_array_almost_equal)
from scipy.interpolate import pade

def test_pade_trivial():
    nump, denomp = pade([1.0], 0)
    assert_array_equal(nump.c, [1.0])
    assert_array_equal(denomp.c, [1.0])
    
    nump, denomp = pade([1.0], 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])
   
    # Testing inclusion of optional parameter
    nump, denomp = pade(an, 0, 3)
    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, 2)
    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, 1)
    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, 0)
    assert_array_almost_equal(nump.c, [1.0])
    assert_array_almost_equal(denomp.c, [-1.0/6, 0.5, -1.0, 1.0])
   
    # Testing reducing array
    nump, denomp = pade(an, 0, 2)
    assert_array_almost_equal(nump.c, [0.5, 1.0, 1.0])
    assert_array_almost_equal(denomp.c, [1.0])

    nump, denomp = pade(an, 1, 1)
    assert_array_almost_equal(nump.c, [1.0/2, 1.0])
    assert_array_almost_equal(denomp.c, [-1.0/2, 1.0])

    nump, denomp = pade(an, 2, 0)
    assert_array_almost_equal(nump.c, [1.0])
    assert_array_almost_equal(denomp.c, [1.0/2, -1.0, 1.0])