"""Tests for polynomial module.

"""
from __future__ import division, absolute_import, print_function

from functools import reduce

import numpy as np
import numpy.polynomial.polynomial as poly
from numpy.testing import (
    assert_almost_equal, assert_raises, assert_equal, assert_,
    )


def trim(x):
    return poly.polytrim(x, tol=1e-6)

T0 = [1]
T1 = [0, 1]
T2 = [-1, 0, 2]
T3 = [0, -3, 0, 4]
T4 = [1, 0, -8, 0, 8]
T5 = [0, 5, 0, -20, 0, 16]
T6 = [-1, 0, 18, 0, -48, 0, 32]
T7 = [0, -7, 0, 56, 0, -112, 0, 64]
T8 = [1, 0, -32, 0, 160, 0, -256, 0, 128]
T9 = [0, 9, 0, -120, 0, 432, 0, -576, 0, 256]

Tlist = [T0, T1, T2, T3, T4, T5, T6, T7, T8, T9]


class TestConstants(object):

    def test_polydomain(self):
        assert_equal(poly.polydomain, [-1, 1])

    def test_polyzero(self):
        assert_equal(poly.polyzero, [0])

    def test_polyone(self):
        assert_equal(poly.polyone, [1])

    def test_polyx(self):
        assert_equal(poly.polyx, [0, 1])


class TestArithmetic(object):

    def test_polyadd(self):
        for i in range(5):
            for j in range(5):
                msg = "At i=%d, j=%d" % (i, j)
                tgt = np.zeros(max(i, j) + 1)
                tgt[i] += 1
                tgt[j] += 1
                res = poly.polyadd([0]*i + [1], [0]*j + [1])
                assert_equal(trim(res), trim(tgt), err_msg=msg)

    def test_polysub(self):
        for i in range(5):
            for j in range(5):
                msg = "At i=%d, j=%d" % (i, j)
                tgt = np.zeros(max(i, j) + 1)
                tgt[i] += 1
                tgt[j] -= 1
                res = poly.polysub([0]*i + [1], [0]*j + [1])
                assert_equal(trim(res), trim(tgt), err_msg=msg)

    def test_polymulx(self):
        assert_equal(poly.polymulx([0]), [0])
        assert_equal(poly.polymulx([1]), [0, 1])
        for i in range(1, 5):
            ser = [0]*i + [1]
            tgt = [0]*(i + 1) + [1]
            assert_equal(poly.polymulx(ser), tgt)

    def test_polymul(self):
        for i in range(5):
            for j in range(5):
                msg = "At i=%d, j=%d" % (i, j)
                tgt = np.zeros(i + j + 1)
                tgt[i + j] += 1
                res = poly.polymul([0]*i + [1], [0]*j + [1])
                assert_equal(trim(res), trim(tgt), err_msg=msg)

    def test_polydiv(self):
        # check zero division
        assert_raises(ZeroDivisionError, poly.polydiv, [1], [0])

        # check scalar division
        quo, rem = poly.polydiv([2], [2])
        assert_equal((quo, rem), (1, 0))
        quo, rem = poly.polydiv([2, 2], [2])
        assert_equal((quo, rem), ((1, 1), 0))

        # check rest.
        for i in range(5):
            for j in range(5):
                msg = "At i=%d, j=%d" % (i, j)
                ci = [0]*i + [1, 2]
                cj = [0]*j + [1, 2]
                tgt = poly.polyadd(ci, cj)
                quo, rem = poly.polydiv(tgt, ci)
                res = poly.polyadd(poly.polymul(quo, ci), rem)
                assert_equal(res, tgt, err_msg=msg)

    def test_polypow(self):
        for i in range(5):
            for j in range(5):
                msg = "At i=%d, j=%d" % (i, j)
                c = np.arange(i + 1)
                tgt = reduce(poly.polymul, [c]*j, np.array([1]))
                res = poly.polypow(c, j) 
                assert_equal(trim(res), trim(tgt), err_msg=msg)


class TestEvaluation(object):
    # coefficients of 1 + 2*x + 3*x**2
    c1d = np.array([1., 2., 3.])
    c2d = np.einsum('i,j->ij', c1d, c1d)
    c3d = np.einsum('i,j,k->ijk', c1d, c1d, c1d)

    # some random values in [-1, 1)
    x = np.random.random((3, 5))*2 - 1
    y = poly.polyval(x, [1., 2., 3.])

    def test_polyval(self):
        #check empty input
        assert_equal(poly.polyval([], [1]).size, 0)

        #check normal input)
        x = np.linspace(-1, 1)
        y = [x**i for i in range(5)]
        for i in range(5):
            tgt = y[i]
            res = poly.polyval(x, [0]*i + [1])
            assert_almost_equal(res, tgt)
        tgt = x*(x**2 - 1)
        res = poly.polyval(x, [0, -1, 0, 1])
        assert_almost_equal(res, tgt)

        #check that shape is preserved
        for i in range(3):
            dims = [2]*i
            x = np.zeros(dims)
            assert_equal(poly.polyval(x, [1]).shape, dims)
            assert_equal(poly.polyval(x, [1, 0]).shape, dims)
            assert_equal(poly.polyval(x, [1, 0, 0]).shape, dims)

    def test_polyvalfromroots(self):
        # check exception for broadcasting x values over root array with
        # too few dimensions
        assert_raises(ValueError, poly.polyvalfromroots,
                      [1], [1], tensor=False)

        # check empty input
        assert_equal(poly.polyvalfromroots([], [1]).size, 0)
        assert_(poly.polyvalfromroots([], [1]).shape == (0,))

        # check empty input + multidimensional roots
        assert_equal(poly.polyvalfromroots([], [[1] * 5]).size, 0)
        assert_(poly.polyvalfromroots([], [[1] * 5]).shape == (5, 0))

        # check scalar input
        assert_equal(poly.polyvalfromroots(1, 1), 0)
        assert_(poly.polyvalfromroots(1, np.ones((3, 3))).shape == (3,))

        # check normal input)
        x = np.linspace(-1, 1)
        y = [x**i for i in range(5)]
        for i in range(1, 5):
            tgt = y[i]
            res = poly.polyvalfromroots(x, [0]*i)
            assert_almost_equal(res, tgt)
        tgt = x*(x - 1)*(x + 1)
        res = poly.polyvalfromroots(x, [-1, 0, 1])
        assert_almost_equal(res, tgt)

        # check that shape is preserved
        for i in range(3):
            dims = [2]*i
            x = np.zeros(dims)
            assert_equal(poly.polyvalfromroots(x, [1]).shape, dims)
            assert_equal(poly.polyvalfromroots(x, [1, 0]).shape, dims)
            assert_equal(poly.polyvalfromroots(x, [1, 0, 0]).shape, dims)

        # check compatibility with factorization
        ptest = [15, 2, -16, -2, 1]
        r = poly.polyroots(ptest)
        x = np.linspace(-1, 1)
        assert_almost_equal(poly.polyval(x, ptest),
                            poly.polyvalfromroots(x, r))

        # check multidimensional arrays of roots and values
        # check tensor=False
        rshape = (3, 5)
        x = np.arange(-3, 2)
        r = np.random.randint(-5, 5, size=rshape)
        res = poly.polyvalfromroots(x, r, tensor=False)
        tgt = np.empty(r.shape[1:])
        for ii in range(tgt.size):
            tgt[ii] = poly.polyvalfromroots(x[ii], r[:, ii])
        assert_equal(res, tgt)

        # check tensor=True
        x = np.vstack([x, 2*x])
        res = poly.polyvalfromroots(x, r, tensor=True)
        tgt = np.empty(r.shape[1:] + x.shape)
        for ii in range(r.shape[1]):
            for jj in range(x.shape[0]):
                tgt[ii, jj, :] = poly.polyvalfromroots(x[jj], r[:, ii])
        assert_equal(res, tgt)

    def test_polyval2d(self):
        x1, x2, x3 = self.x
        y1, y2, y3 = self.y

        #test exceptions
        assert_raises(ValueError, poly.polyval2d, x1, x2[:2], self.c2d)

        #test values
        tgt = y1*y2
        res = poly.polyval2d(x1, x2, self.c2d)
        assert_almost_equal(res, tgt)

        #test shape
        z = np.ones((2, 3))
        res = poly.polyval2d(z, z, self.c2d)
        assert_(res.shape == (2, 3))

    def test_polyval3d(self):
        x1, x2, x3 = self.x
        y1, y2, y3 = self.y

        #test exceptions
        assert_raises(ValueError, poly.polyval3d, x1, x2, x3[:2], self.c3d)

        #test values
        tgt = y1*y2*y3
        res = poly.polyval3d(x1, x2, x3, self.c3d)
        assert_almost_equal(res, tgt)

        #test shape
        z = np.ones((2, 3))
        res = poly.polyval3d(z, z, z, self.c3d)
        assert_(res.shape == (2, 3))

    def test_polygrid2d(self):
        x1, x2, x3 = self.x
        y1, y2, y3 = self.y

        #test values
        tgt = np.einsum('i,j->ij', y1, y2)
        res = poly.polygrid2d(x1, x2, self.c2d)
        assert_almost_equal(res, tgt)

        #test shape
        z = np.ones((2, 3))
        res = poly.polygrid2d(z, z, self.c2d)
        assert_(res.shape == (2, 3)*2)

    def test_polygrid3d(self):
        x1, x2, x3 = self.x
        y1, y2, y3 = self.y

        #test values
        tgt = np.einsum('i,j,k->ijk', y1, y2, y3)
        res = poly.polygrid3d(x1, x2, x3, self.c3d)
        assert_almost_equal(res, tgt)

        #test shape
        z = np.ones((2, 3))
        res = poly.polygrid3d(z, z, z, self.c3d)
        assert_(res.shape == (2, 3)*3)


class TestIntegral(object):

    def test_polyint(self):
        # check exceptions
        assert_raises(ValueError, poly.polyint, [0], .5)
        assert_raises(ValueError, poly.polyint, [0], -1)
        assert_raises(ValueError, poly.polyint, [0], 1, [0, 0])
        assert_raises(ValueError, poly.polyint, [0], lbnd=[0])
        assert_raises(ValueError, poly.polyint, [0], scl=[0])
        assert_raises(ValueError, poly.polyint, [0], axis=.5)

        # test integration of zero polynomial
        for i in range(2, 5):
            k = [0]*(i - 2) + [1]
            res = poly.polyint([0], m=i, k=k)
            assert_almost_equal(res, [0, 1])

        # check single integration with integration constant
        for i in range(5):
            scl = i + 1
            pol = [0]*i + [1]
            tgt = [i] + [0]*i + [1/scl]
            res = poly.polyint(pol, m=1, k=[i])
            assert_almost_equal(trim(res), trim(tgt))

        # check single integration with integration constant and lbnd
        for i in range(5):
            scl = i + 1
            pol = [0]*i + [1]
            res = poly.polyint(pol, m=1, k=[i], lbnd=-1)
            assert_almost_equal(poly.polyval(-1, res), i)

        # check single integration with integration constant and scaling
        for i in range(5):
            scl = i + 1
            pol = [0]*i + [1]
            tgt = [i] + [0]*i + [2/scl]
            res = poly.polyint(pol, m=1, k=[i], scl=2)
            assert_almost_equal(trim(res), trim(tgt))

        # check multiple integrations with default k
        for i in range(5):
            for j in range(2, 5):
                pol = [0]*i + [1]
                tgt = pol[:]
                for k in range(j):
                    tgt = poly.polyint(tgt, m=1)
                res = poly.polyint(pol, m=j)
                assert_almost_equal(trim(res), trim(tgt))

        # check multiple integrations with defined k
        for i in range(5):
            for j in range(2, 5):
                pol = [0]*i + [1]
                tgt = pol[:]
                for k in range(j):
                    tgt = poly.polyint(tgt, m=1, k=[k])
                res = poly.polyint(pol, m=j, k=list(range(j)))
                assert_almost_equal(trim(res), trim(tgt))

        # check multiple integrations with lbnd
        for i in range(5):
            for j in range(2, 5):
                pol = [0]*i + [1]
                tgt = pol[:]
                for k in range(j):
                    tgt = poly.polyint(tgt, m=1, k=[k], lbnd=-1)
                res = poly.polyint(pol, m=j, k=list(range(j)), lbnd=-1)
                assert_almost_equal(trim(res), trim(tgt))