"""Tests for chebyshev module.

"""
from functools import reduce

import numpy as np
import numpy.polynomial.chebyshev as cheb
from numpy.polynomial.polynomial import polyval
from numpy.testing import (
    assert_almost_equal, assert_raises, assert_equal, assert_,
    )


def trim(x):
    return cheb.chebtrim(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 TestPrivate:

    def test__cseries_to_zseries(self):
        for i in range(5):
            inp = np.array([2] + [1]*i, np.double)
            tgt = np.array([.5]*i + [2] + [.5]*i, np.double)
            res = cheb._cseries_to_zseries(inp)
            assert_equal(res, tgt)

    def test__zseries_to_cseries(self):
        for i in range(5):
            inp = np.array([.5]*i + [2] + [.5]*i, np.double)
            tgt = np.array([2] + [1]*i, np.double)
            res = cheb._zseries_to_cseries(inp)
            assert_equal(res, tgt)


class TestConstants:

    def test_chebdomain(self):
        assert_equal(cheb.chebdomain, [-1, 1])

    def test_chebzero(self):
        assert_equal(cheb.chebzero, [0])

    def test_chebone(self):
        assert_equal(cheb.chebone, [1])

    def test_chebx(self):
        assert_equal(cheb.chebx, [0, 1])


class TestArithmetic:

    def test_chebadd(self):
        for i in range(5):
            for j in range(5):
                msg = f"At i={i}, j={j}"
                tgt = np.zeros(max(i, j) + 1)
                tgt[i] += 1
                tgt[j] += 1
                res = cheb.chebadd([0]*i + [1], [0]*j + [1])
                assert_equal(trim(res), trim(tgt), err_msg=msg)

    def test_chebsub(self):
        for i in range(5):
            for j in range(5):
                msg = f"At i={i}, j={j}"
                tgt = np.zeros(max(i, j) + 1)
                tgt[i] += 1
                tgt[j] -= 1
                res = cheb.chebsub([0]*i + [1], [0]*j + [1])
                assert_equal(trim(res), trim(tgt), err_msg=msg)

    def test_chebmulx(self):
        assert_equal(cheb.chebmulx([0]), [0])
        assert_equal(cheb.chebmulx([1]), [0, 1])
        for i in range(1, 5):
            ser = [0]*i + [1]
            tgt = [0]*(i - 1) + [.5, 0, .5]
            assert_equal(cheb.chebmulx(ser), tgt)

    def test_chebmul(self):
        for i in range(5):
            for j in range(5):
                msg = f"At i={i}, j={j}"
                tgt = np.zeros(i + j + 1)
                tgt[i + j] += .5
                tgt[abs(i - j)] += .5
                res = cheb.chebmul([0]*i + [1], [0]*j + [1])
                assert_equal(trim(res), trim(tgt), err_msg=msg)

    def test_chebdiv(self):
        for i in range(5):
            for j in range(5):
                msg = f"At i={i}, j={j}"
                ci = [0]*i + [1]
                cj = [0]*j + [1]
                tgt = cheb.chebadd(ci, cj)
                quo, rem = cheb.chebdiv(tgt, ci)
                res = cheb.chebadd(cheb.chebmul(quo, ci), rem)
                assert_equal(trim(res), trim(tgt), err_msg=msg)

    def test_chebpow(self):
        for i in range(5):
            for j in range(5):
                msg = f"At i={i}, j={j}"
                c = np.arange(i + 1)
                tgt = reduce(cheb.chebmul, [c]*j, np.array([1]))
                res = cheb.chebpow(c, j)
                assert_equal(trim(res), trim(tgt), err_msg=msg)


class TestEvaluation:
    # coefficients of 1 + 2*x + 3*x**2
    c1d = np.array([2.5, 2., 1.5])
    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 = polyval(x, [1., 2., 3.])

    def test_chebval(self):
        #check empty input
        assert_equal(cheb.chebval([], [1]).size, 0)

        #check normal input)
        x = np.linspace(-1, 1)
        y = [polyval(x, c) for c in Tlist]
        for i in range(10):
            msg = f"At i={i}"
            tgt = y[i]
            res = cheb.chebval(x, [0]*i + [1])
            assert_almost_equal(res, tgt, err_msg=msg)

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

    def test_chebval2d(self):
        x1, x2, x3 = self.x
        y1, y2, y3 = self.y

        #test exceptions
        assert_raises(ValueError, cheb.chebval2d, x1, x2[:2], self.c2d)

        #test values
        tgt = y1*y2
        res = cheb.chebval2d(x1, x2, self.c2d)
        assert_almost_equal(res, tgt)

        #test shape
        z = np.ones((2, 3))
        res = cheb.chebval2d(z, z, self.c2d)
        assert_(res.shape == (2, 3))

    def test_chebval3d(self):
        x1, x2, x3 = self.x
        y1, y2, y3 = self.y

        #test exceptions
        assert_raises(ValueError, cheb.chebval3d, x1, x2, x3[:2], self.c3d)

        #test values
        tgt = y1*y2*y3
        res = cheb.chebval3d(x1, x2, x3, self.c3d)
        assert_almost_equal(res, tgt)

        #test shape
        z = np.ones((2, 3))
        res = cheb.chebval3d(z, z, z, self.c3d)
        assert_(res.shape == (2, 3))

    def test_chebgrid2d(self):
        x1, x2, x3 = self.x
        y1, y2, y3 = self.y

        #test values
        tgt = np.einsum('i,j->ij', y1, y2)
        res = cheb.chebgrid2d(x1, x2, self.c2d)
        assert_almost_equal(res, tgt)

        #test shape
        z = np.ones((2, 3))
        res = cheb.chebgrid2d(z, z, self.c2d)
        assert_(res.shape == (2, 3)*2)

    def test_chebgrid3d(self):
        x1, x2, x3 = self.x
        y1, y2, y3 = self.y

        #test values
        tgt = np.einsum('i,j,k->ijk', y1, y2, y3)
        res = cheb.chebgrid3d(x1, x2, x3, self.c3d)
        assert_almost_equal(res, tgt)

        #test shape
        z = np.ones((2, 3))
        res = cheb.chebgrid3d(z, z, z, self.c3d)
        assert_(res.shape == (2, 3)*3)


class TestIntegral:

    def test_chebint(self):
        # check exceptions
        assert_raises(TypeError, cheb.chebint, [0], .5)
        assert_raises(ValueError, cheb.chebint, [0], -1)
        assert_raises(ValueError, cheb.chebint, [0], 1, [0, 0])
        assert_raises(ValueError, cheb.chebint, [0], lbnd=[0])
        assert_raises(ValueError, cheb.chebint, [0], scl=[0])
        assert_raises(TypeError, cheb.chebint, [0], axis=.5)

        # test integration of zero polynomial
        for i in range(2, 5):
            k = [0]*(i - 2) + [1]
            res = cheb.chebint([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]
            chebpol = cheb.poly2cheb(pol)
            chebint = cheb.chebint(chebpol, m=1, k=[i])
            res = cheb.cheb2poly(chebint)
            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]
            chebpol = cheb.poly2cheb(pol)
            chebint = cheb.chebint(chebpol, m=1, k=[i], lbnd=-1)
            assert_almost_equal(cheb.chebval(-1, chebint), 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]
            chebpol = cheb.poly2cheb(pol)
            chebint = cheb.chebint(chebpol, m=1, k=[i], scl=2)
            res = cheb.cheb2poly(chebint)
            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 = cheb.chebint(tgt, m=1)
                res = cheb.chebint(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 = cheb.chebint(tgt, m=1, k=[k])
                res = cheb.chebint(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 = cheb.chebint(tgt, m=1, k=[k], lbnd=-1)
                res = cheb.chebint(pol, m=j, k=list(range(j)), lbnd=-1)
                assert_almost_equal(trim(res), trim(tgt))

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

    def test_chebint_axis(self):
        # check that axis keyword works
        c2d = np.random.random((3, 4))

        tgt = np.vstack([cheb.chebint(c) for c in c2d.T]).T
        res = cheb.chebint(c2d, axis=0)
        assert_almost_equal(res, tgt)

        tgt = np.vstack([cheb.chebint(c) for c in c2d])
        res = cheb.chebint(c2d, axis=1)
        assert_almost_equal(res, tgt)

        tgt = np.vstack([cheb.chebint(c, k=3) for c in c2d])
        res = cheb.chebint(c2d, k=3, axis=1)
        assert_almost_equal(res, tgt)


class TestDerivative:

    def test_chebder(self):
        # check exceptions
        assert_raises(TypeError, cheb.chebder, [0], .5)
        assert_raises(ValueError, cheb.chebder, [0], -1)

        # check that zeroth derivative does nothing
        for i in range(5):
            tgt = [0]*i + [1]
            res = cheb.chebder(tgt, m=0)
            assert_equal(trim(res), trim(tgt))

        # check that derivation is the inverse of integration
        for i in range(5):
            for j in range(2, 5):
                tgt = [0]*i + [1]
                res = cheb.chebder(cheb.chebint(tgt, m=j), m=j)
                assert_almost_equal(trim(res), trim(tgt))

        # check derivation with scaling
        for i in range(5):
            for j in range(2, 5):
                tgt = [0]*i + [1]
                res = cheb.chebder(cheb.chebint(tgt, m=j, scl=2), m=j, scl=.5)
                assert_almost_equal(trim(res), trim(tgt))