"""Tests for legendre module.

"""
from __future__ import division, absolute_import, print_function

from functools import reduce

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

L0 = np.array([1])
L1 = np.array([0, 1])
L2 = np.array([-1, 0, 3])/2
L3 = np.array([0, -3, 0, 5])/2
L4 = np.array([3, 0, -30, 0, 35])/8
L5 = np.array([0, 15, 0, -70, 0, 63])/8
L6 = np.array([-5, 0, 105, 0, -315, 0, 231])/16
L7 = np.array([0, -35, 0, 315, 0, -693, 0, 429])/16
L8 = np.array([35, 0, -1260, 0, 6930, 0, -12012, 0, 6435])/128
L9 = np.array([0, 315, 0, -4620, 0, 18018, 0, -25740, 0, 12155])/128

Llist = [L0, L1, L2, L3, L4, L5, L6, L7, L8, L9]


def trim(x):
    return leg.legtrim(x, tol=1e-6)


class TestConstants(object):

    def test_legdomain(self):
        assert_equal(leg.legdomain, [-1, 1])

    def test_legzero(self):
        assert_equal(leg.legzero, [0])

    def test_legone(self):
        assert_equal(leg.legone, [1])

    def test_legx(self):
        assert_equal(leg.legx, [0, 1])


class TestArithmetic(object):
    x = np.linspace(-1, 1, 100)

    def test_legadd(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 = leg.legadd([0]*i + [1], [0]*j + [1])
                assert_equal(trim(res), trim(tgt), err_msg=msg)

    def test_legsub(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 = leg.legsub([0]*i + [1], [0]*j + [1])
                assert_equal(trim(res), trim(tgt), err_msg=msg)

    def test_legmulx(self):
        assert_equal(leg.legmulx([0]), [0])
        assert_equal(leg.legmulx([1]), [0, 1])
        for i in range(1, 5):
            tmp = 2*i + 1
            ser = [0]*i + [1]
            tgt = [0]*(i - 1) + [i/tmp, 0, (i + 1)/tmp]
            assert_equal(leg.legmulx(ser), tgt)

    def test_legmul(self):
        # check values of result
        for i in range(5):
            pol1 = [0]*i + [1]
            val1 = leg.legval(self.x, pol1)
            for j in range(5):
                msg = "At i=%d, j=%d" % (i, j)
                pol2 = [0]*j + [1]
                val2 = leg.legval(self.x, pol2)
                pol3 = leg.legmul(pol1, pol2)
                val3 = leg.legval(self.x, pol3)
                assert_(len(pol3) == i + j + 1, msg)
                assert_almost_equal(val3, val1*val2, err_msg=msg)

    def test_legdiv(self):
        for i in range(5):
            for j in range(5):
                msg = "At i=%d, j=%d" % (i, j)
                ci = [0]*i + [1]
                cj = [0]*j + [1]
                tgt = leg.legadd(ci, cj)
                quo, rem = leg.legdiv(tgt, ci)
                res = leg.legadd(leg.legmul(quo, ci), rem)
                assert_equal(trim(res), trim(tgt), err_msg=msg)

    def test_legpow(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(leg.legmul, [c]*j, np.array([1]))
                res = leg.legpow(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([2., 2., 2.])
    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_legval(self):
        #check empty input
        assert_equal(leg.legval([], [1]).size, 0)

        #check normal input)
        x = np.linspace(-1, 1)
        y = [polyval(x, c) for c in Llist]
        for i in range(10):
            msg = "At i=%d" % i
            tgt = y[i]
            res = leg.legval(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(leg.legval(x, [1]).shape, dims)
            assert_equal(leg.legval(x, [1, 0]).shape, dims)
            assert_equal(leg.legval(x, [1, 0, 0]).shape, dims)

    def test_legval2d(self):
        x1, x2, x3 = self.x
        y1, y2, y3 = self.y

        #test exceptions
        assert_raises(ValueError, leg.legval2d, x1, x2[:2], self.c2d)

        #test values
        tgt = y1*y2
        res = leg.legval2d(x1, x2, self.c2d)
        assert_almost_equal(res, tgt)

        #test shape
        z = np.ones((2, 3))
        res = leg.legval2d(z, z, self.c2d)
        assert_(res.shape == (2, 3))

    def test_legval3d(self):
        x1, x2, x3 = self.x
        y1, y2, y3 = self.y

        #test exceptions
        assert_raises(ValueError, leg.legval3d, x1, x2, x3[:2], self.c3d)

        #test values
        tgt = y1*y2*y3
        res = leg.legval3d(x1, x2, x3, self.c3d)
        assert_almost_equal(res, tgt)

        #test shape
        z = np.ones((2, 3))
        res = leg.legval3d(z, z, z, self.c3d)
        assert_(res.shape == (2, 3))

    def test_leggrid2d(self):
        x1, x2, x3 = self.x
        y1, y2, y3 = self.y

        #test values
        tgt = np.einsum('i,j->ij', y1, y2)
        res = leg.leggrid2d(x1, x2, self.c2d)
        assert_almost_equal(res, tgt)

        #test shape
        z = np.ones((2, 3))
        res = leg.leggrid2d(z, z, self.c2d)
        assert_(res.shape == (2, 3)*2)

    def test_leggrid3d(self):
        x1, x2, x3 = self.x
        y1, y2, y3 = self.y

        #test values
        tgt = np.einsum('i,j,k->ijk', y1, y2, y3)
        res = leg.leggrid3d(x1, x2, x3, self.c3d)
        assert_almost_equal(res, tgt)

        #test shape
        z = np.ones((2, 3))
        res = leg.leggrid3d(z, z, z, self.c3d)
        assert_(res.shape == (2, 3)*3)


class TestIntegral(object):

    def test_legint(self):
        # check exceptions
        assert_raises(ValueError, leg.legint, [0], .5)
        assert_raises(ValueError, leg.legint, [0], -1)
        assert_raises(ValueError, leg.legint, [0], 1, [0, 0])
        assert_raises(ValueError, leg.legint, [0], lbnd=[0])
        assert_raises(ValueError, leg.legint, [0], scl=[0])
        assert_raises(ValueError, leg.legint, [0], axis=.5)

        # test integration of zero polynomial
        for i in range(2, 5):
            k = [0]*(i - 2) + [1]
            res = leg.legint([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]
            legpol = leg.poly2leg(pol)
            legint = leg.legint(legpol, m=1, k=[i])
            res = leg.leg2poly(legint)
            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]
            legpol = leg.poly2leg(pol)
            legint = leg.legint(legpol, m=1, k=[i], lbnd=-1)
            assert_almost_equal(leg.legval(-1, legint), 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]
            legpol = leg.poly2leg(pol)
            legint = leg.legint(legpol, m=1, k=[i], scl=2)
            res = leg.leg2poly(legint)
            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 = leg.legint(tgt, m=1)
                res = leg.legint(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 = leg.legint(tgt, m=1, k=[k])
                res = leg.legint(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 = leg.legint(tgt, m=1, k=[k], lbnd=-1)
                res = leg.legint(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 = leg.legint(tgt, m=1, k=[k], scl=2)
                res = leg.legint(pol, m=j, k=list(range(j)), scl=2)
                assert_almost_equal(trim(res), trim(tgt))

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

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

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

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


class TestDerivative(object):

    def test_legder(self):
        # check exceptions
        assert_raises(ValueError, leg.legder, [0], .5)
        assert_raises(ValueError, leg.legder, [0], -1)

        # check that zeroth derivative does nothing
        for i in range(5):
            tgt = [0]*i + [1]
            res = leg.legder(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 = leg.legder(leg.legint(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 = leg.legder(leg.legint(tgt, m=j, scl=2), m=j, scl=.5)
                assert_almost_equal(trim(res), trim(tgt))

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

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