"""Test inter-conversion of different polynomial classes.

This tests the convert and cast methods of all the polynomial classes.

"""
from __future__ import division, absolute_import, print_function

import operator as op
from numbers import Number

import pytest
import numpy as np
from numpy.polynomial import (
    Polynomial, Legendre, Chebyshev, Laguerre, Hermite, HermiteE)
from numpy.testing import (
    assert_almost_equal, assert_raises, assert_equal, assert_,
    )
from numpy.compat import long


#
# fixtures
#

classes = (
    Polynomial, Legendre, Chebyshev, Laguerre,
    Hermite, HermiteE
    )
classids = tuple(cls.__name__ for cls in classes)

@pytest.fixture(params=classes, ids=classids)
def Poly(request):
    return request.param

#
# helper functions
#
random = np.random.random


def assert_poly_almost_equal(p1, p2, msg=""):
    try:
        assert_(np.all(p1.domain == p2.domain))
        assert_(np.all(p1.window == p2.window))
        assert_almost_equal(p1.coef, p2.coef)
    except AssertionError:
        msg = "Result: %s\nTarget: %s", (p1, p2)
        raise AssertionError(msg)


#
# Test conversion methods that depend on combinations of two classes.
#

Poly1 = Poly
Poly2 = Poly


def test_conversion(Poly1, Poly2):
    x = np.linspace(0, 1, 10)
    coef = random((3,))

    d1 = Poly1.domain + random((2,))*.25
    w1 = Poly1.window + random((2,))*.25
    p1 = Poly1(coef, domain=d1, window=w1)

    d2 = Poly2.domain + random((2,))*.25
    w2 = Poly2.window + random((2,))*.25
    p2 = p1.convert(kind=Poly2, domain=d2, window=w2)

    assert_almost_equal(p2.domain, d2)
    assert_almost_equal(p2.window, w2)
    assert_almost_equal(p2(x), p1(x))


def test_cast(Poly1, Poly2):
    x = np.linspace(0, 1, 10)
    coef = random((3,))

    d1 = Poly1.domain + random((2,))*.25
    w1 = Poly1.window + random((2,))*.25
    p1 = Poly1(coef, domain=d1, window=w1)

    d2 = Poly2.domain + random((2,))*.25
    w2 = Poly2.window + random((2,))*.25
    p2 = Poly2.cast(p1, domain=d2, window=w2)

    assert_almost_equal(p2.domain, d2)
    assert_almost_equal(p2.window, w2)
    assert_almost_equal(p2(x), p1(x))


#
# test methods that depend on one class
#


def test_identity(Poly):
    d = Poly.domain + random((2,))*.25
    w = Poly.window + random((2,))*.25
    x = np.linspace(d[0], d[1], 11)
    p = Poly.identity(domain=d, window=w)
    assert_equal(p.domain, d)
    assert_equal(p.window, w)
    assert_almost_equal(p(x), x)


def test_basis(Poly):
    d = Poly.domain + random((2,))*.25
    w = Poly.window + random((2,))*.25
    p = Poly.basis(5, domain=d, window=w)
    assert_equal(p.domain, d)
    assert_equal(p.window, w)
    assert_equal(p.coef, [0]*5 + [1])


def test_fromroots(Poly):
    # check that requested roots are zeros of a polynomial
    # of correct degree, domain, and window.
    d = Poly.domain + random((2,))*.25
    w = Poly.window + random((2,))*.25
    r = random((5,))
    p1 = Poly.fromroots(r, domain=d, window=w)
    assert_equal(p1.degree(), len(r))
    assert_equal(p1.domain, d)
    assert_equal(p1.window, w)
    assert_almost_equal(p1(r), 0)

    # check that polynomial is monic
    pdom = Polynomial.domain
    pwin = Polynomial.window
    p2 = Polynomial.cast(p1, domain=pdom, window=pwin)
    assert_almost_equal(p2.coef[-1], 1)


def test_fit(Poly):

    def f(x):
        return x*(x - 1)*(x - 2)
    x = np.linspace(0, 3)
    y = f(x)

    # check default value of domain and window
    p = Poly.fit(x, y, 3)
    assert_almost_equal(p.domain, [0, 3])
    assert_almost_equal(p(x), y)
    assert_equal(p.degree(), 3)

    # check with given domains and window
    d = Poly.domain + random((2,))*.25
    w = Poly.window + random((2,))*.25
    p = Poly.fit(x, y, 3, domain=d, window=w)
    assert_almost_equal(p(x), y)
    assert_almost_equal(p.domain, d)
    assert_almost_equal(p.window, w)
    p = Poly.fit(x, y, [0, 1, 2, 3], domain=d, window=w)
    assert_almost_equal(p(x), y)
    assert_almost_equal(p.domain, d)
    assert_almost_equal(p.window, w)

    # check with class domain default
    p = Poly.fit(x, y, 3, [])
    assert_equal(p.domain, Poly.domain)
    assert_equal(p.window, Poly.window)
    p = Poly.fit(x, y, [0, 1, 2, 3], [])
    assert_equal(p.domain, Poly.domain)
    assert_equal(p.window, Poly.window)

    # check that fit accepts weights.
    w = np.zeros_like(x)
    z = y + random(y.shape)*.25
    w[::2] = 1
    p1 = Poly.fit(x[::2], z[::2], 3)
    p2 = Poly.fit(x, z, 3, w=w)
    p3 = Poly.fit(x, z, [0, 1, 2, 3], w=w)
    assert_almost_equal(p1(x), p2(x))
    assert_almost_equal(p2(x), p3(x))


def test_equal(Poly):
    p1 = Poly([1, 2, 3], domain=[0, 1], window=[2, 3])
    p2 = Poly([1, 1, 1], domain=[0, 1], window=[2, 3])
    p3 = Poly([1, 2, 3], domain=[1, 2], window=[2, 3])
    p4 = Poly([1, 2, 3], domain=[0, 1], window=[1, 2])
    assert_(p1 == p1)
    assert_(not p1 == p2)
    assert_(not p1 == p3)
    assert_(not p1 == p4)


def test_not_equal(Poly):
    p1 = Poly([1, 2, 3], domain=[0, 1], window=[2, 3])
    p2 = Poly([1, 1, 1], domain=[0, 1], window=[2, 3])
    p3 = Poly([1, 2, 3], domain=[1, 2], window=[2, 3])
    p4 = Poly([1, 2, 3], domain=[0, 1], window=[1, 2])
    assert_(not p1 != p1)
    assert_(p1 != p2)
    assert_(p1 != p3)
    assert_(p1 != p4)


def test_add(Poly):
    # This checks commutation, not numerical correctness
    c1 = list(random((4,)) + .5)
    c2 = list(random((3,)) + .5)
    p1 = Poly(c1)
    p2 = Poly(c2)
    p3 = p1 + p2
    assert_poly_almost_equal(p2 + p1, p3)
    assert_poly_almost_equal(p1 + c2, p3)
    assert_poly_almost_equal(c2 + p1, p3)
    assert_poly_almost_equal(p1 + tuple(c2), p3)
    assert_poly_almost_equal(tuple(c2) + p1, p3)
    assert_poly_almost_equal(p1 + np.array(c2), p3)
    assert_poly_almost_equal(np.array(c2) + p1, p3)
    assert_raises(TypeError, op.add, p1, Poly([0], domain=Poly.domain + 1))
    assert_raises(TypeError, op.add, p1, Poly([0], window=Poly.window + 1))
    if Poly is Polynomial:
        assert_raises(TypeError, op.add, p1, Chebyshev([0]))
    else:
        assert_raises(TypeError, op.add, p1, Polynomial([0]))


def test_sub(Poly):
    # This checks commutation, not numerical correctness
    c1 = list(random((4,)) + .5)
    c2 = list(random((3,)) + .5)
    p1 = Poly(c1)
    p2 = Poly(c2)
    p3 = p1 - p2
    assert_poly_almost_equal(p2 - p1, -p3)
    assert_poly_almost_equal(p1 - c2, p3)
    assert_poly_almost_equal(c2 - p1, -p3)
    assert_poly_almost_equal(p1 - tuple(c2), p3)
    assert_poly_almost_equal(tuple(c2) - p1, -p3)
    assert_poly_almost_equal(p1 - np.array(c2), p3)
    assert_poly_almost_equal(np.array(c2) - p1, -p3)
    assert_raises(TypeError, op.sub, p1, Poly([0], domain=Poly.domain + 1))
    assert_raises(TypeError, op.sub, p1, Poly([0], window=Poly.window + 1))
    if Poly is Polynomial:
        assert_raises(TypeError, op.sub, p1, Chebyshev([0]))
    else:
        assert_raises(TypeError, op.sub, p1, Polynomial([0]))


def test_mul(Poly):
    c1 = list(random((4,)) + .5)
    c2 = list(random((3,)) + .5)
    p1 = Poly(c1)
    p2 = Poly(c2)
    p3 = p1 * p2
    assert_poly_almost_equal(p2 * p1, p3)
    assert_poly_almost_equal(p1 * c2, p3)
    assert_poly_almost_equal(c2 * p1, p3)
    assert_poly_almost_equal(p1 * tuple(c2), p3)
    assert_poly_almost_equal(tuple(c2) * p1, p3)
    assert_poly_almost_equal(p1 * np.array(c2), p3)
    assert_poly_almost_equal(np.array(c2) * p1, p3)
    assert_poly_almost_equal(p1 * 2, p1 * Poly([2]))
    assert_poly_almost_equal(2 * p1, p1 * Poly([2]))
    assert_raises(TypeError, op.mul, p1, Poly([0], domain=Poly.domain + 1))
    assert_raises(TypeError, op.mul, p1, Poly([0], window=Poly.window + 1))
    if Poly is Polynomial:
        assert_raises(TypeError, op.mul, p1, Chebyshev([0]))
    else:
        assert_raises(TypeError, op.mul, p1, Polynomial([0]))


def test_floordiv(Poly):
    c1 = list(random((4,)) + .5)
    c2 = list(random((3,)) + .5)
    c3 = list(random((2,)) + .5)
    p1 = Poly(c1)
    p2 = Poly(c2)
    p3 = Poly(c3)
    p4 = p1 * p2 + p3
    c4 = list(p4.coef)
    assert_poly_almost_equal(p4 // p2, p1)
    assert_poly_almost_equal(p4 // c2, p1)
    assert_poly_almost_equal(c4 // p2, p1)
    assert_poly_almost_equal(p4 // tuple(c2), p1)
    assert_poly_almost_equal(tuple(c4) // p2, p1)
    assert_poly_almost_equal(p4 // np.array(c2), p1)
    assert_poly_almost_equal(np.array(c4) // p2, p1)
    assert_poly_almost_equal(2 // p2, Poly([0]))
    assert_poly_almost_equal(p2 // 2, 0.5*p2)
    assert_raises(
        TypeError, op.floordiv, p1, Poly([0], domain=Poly.domain + 1))
    assert_raises(
        TypeError, op.floordiv, p1, Poly([0], window=Poly.window + 1))
    if Poly is Polynomial:
        assert_raises(TypeError, op.floordiv, p1, Chebyshev([0]))
    else:
        assert_raises(TypeError, op.floordiv, p1, Polynomial([0]))


def test_truediv(Poly):
    # true division is valid only if the denominator is a Number and
    # not a python bool.
    p1 = Poly([1,2,3])
    p2 = p1 * 5

    for stype in np.ScalarType:
        if not issubclass(stype, Number) or issubclass(stype, bool):
            continue
        s = stype(5)
        assert_poly_almost_equal(op.truediv(p2, s), p1)
        assert_raises(TypeError, op.truediv, s, p2)
    for stype in (int, long, float):
        s = stype(5)
        assert_poly_almost_equal(op.truediv(p2, s), p1)
        assert_raises(TypeError, op.truediv, s, p2)
    for stype in [complex]:
        s = stype(5, 0)
        assert_poly_almost_equal(op.truediv(p2, s), p1)
        assert_raises(TypeError, op.truediv, s, p2)
    for s in [tuple(), list(), dict(), bool(), np.array([1])]:
        assert_raises(TypeError, op.truediv, p2, s)
        assert_raises(TypeError, op.truediv, s, p2)
    for ptype in classes:
        assert_raises(TypeError, op.truediv, p2, ptype(1))


def test_mod(Poly):
    # This checks commutation, not numerical correctness
    c1 = list(random((4,)) + .5)
    c2 = list(random((3,)) + .5)
    c3 = list(random((2,)) + .5)
    p1 = Poly(c1)
    p2 = Poly(c2)
    p3 = Poly(c3)
    p4 = p1 * p2 + p3
    c4 = list(p4.coef)
    assert_poly_almost_equal(p4 % p2, p3)
    assert_poly_almost_equal(p4 % c2, p3)
    assert_poly_almost_equal(c4 % p2, p3)
    assert_poly_almost_equal(p4 % tuple(c2), p3)
    assert_poly_almost_equal(tuple(c4) % p2, p3)
    assert_poly_almost_equal(p4 % np.array(c2), p3)
    assert_poly_almost_equal(np.array(c4) % p2, p3)
    assert_poly_almost_equal(2 % p2, Poly([2]))
    assert_poly_almost_equal(p2 % 2, Poly([0]))
    assert_raises(TypeError, op.mod, p1, Poly([0], domain=Poly.domain + 1))
    assert_raises(TypeError, op.mod, p1, Poly([0], window=Poly.window + 1))
    if Poly is Polynomial: