"""
Test cdflib functions versus mpmath, if available.

The following functions still need tests:

- ncfdtr
- ncfdtri
- ncfdtridfn
- ncfdtridfd
- ncfdtrinc
- nbdtrik
- nbdtrin
- nrdtrimn
- nrdtrisd
- pdtrik
- nctdtr
- nctdtrit
- nctdtridf
- nctdtrinc

"""
from __future__ import division, print_function, absolute_import

import itertools

import numpy as np
from numpy.testing import assert_equal
import pytest

import scipy.special as sp
from scipy._lib.six import with_metaclass
from scipy.special._testutils import (
    MissingModule, check_version, FuncData)
from scipy.special._mptestutils import (
    Arg, IntArg, get_args, mpf2float, assert_mpmath_equal)

try:
    import mpmath
except ImportError:
    mpmath = MissingModule('mpmath')


class ProbArg(object):
    """Generate a set of probabilities on [0, 1]."""
    def __init__(self):
        # Include the endpoints for compatibility with Arg et. al.
        self.a = 0
        self.b = 1

    def values(self, n):
        """Return an array containing approximatively n numbers."""
        m = max(1, n//3)
        v1 = np.logspace(-30, np.log10(0.3), m)
        v2 = np.linspace(0.3, 0.7, m + 1, endpoint=False)[1:]
        v3 = 1 - np.logspace(np.log10(0.3), -15, m)
        v = np.r_[v1, v2, v3]
        return np.unique(v)


class EndpointFilter(object):
    def __init__(self, a, b, rtol, atol):
        self.a = a
        self.b = b
        self.rtol = rtol
        self.atol = atol

    def __call__(self, x):
        mask1 = np.abs(x - self.a) < self.rtol*np.abs(self.a) + self.atol
        mask2 = np.abs(x - self.b) < self.rtol*np.abs(self.b) + self.atol
        return np.where(mask1 | mask2, False, True)


class _CDFData(object):
    def __init__(self, spfunc, mpfunc, index, argspec, spfunc_first=True,
                 dps=20, n=5000, rtol=None, atol=None,
                 endpt_rtol=None, endpt_atol=None):
        self.spfunc = spfunc
        self.mpfunc = mpfunc
        self.index = index
        self.argspec = argspec
        self.spfunc_first = spfunc_first
        self.dps = dps
        self.n = n
        self.rtol = rtol
        self.atol = atol

        if not isinstance(argspec, list):
            self.endpt_rtol = None
            self.endpt_atol = None
        elif endpt_rtol is not None or endpt_atol is not None:
            if isinstance(endpt_rtol, list):
                self.endpt_rtol = endpt_rtol
            else:
                self.endpt_rtol = [endpt_rtol]*len(self.argspec)
            if isinstance(endpt_atol, list):
                self.endpt_atol = endpt_atol
            else:
                self.endpt_atol = [endpt_atol]*len(self.argspec)
        else:
            self.endpt_rtol = None
            self.endpt_atol = None

    def idmap(self, *args):
        if self.spfunc_first:
            res = self.spfunc(*args)
            if np.isnan(res):
                return np.nan
            args = list(args)
            args[self.index] = res
            with mpmath.workdps(self.dps):
                res = self.mpfunc(*tuple(args))
                # Imaginary parts are spurious
                res = mpf2float(res.real)
        else:
            with mpmath.workdps(self.dps):
                res = self.mpfunc(*args)
                res = mpf2float(res.real)
            args = list(args)
            args[self.index] = res
            res = self.spfunc(*tuple(args))
        return res

    def get_param_filter(self):
        if self.endpt_rtol is None and self.endpt_atol is None:
            return None

        filters = []
        for rtol, atol, spec in zip(self.endpt_rtol, self.endpt_atol, self.argspec):
            if rtol is None and atol is None:
                filters.append(None)
                continue
            elif rtol is None:
                rtol = 0.0
            elif atol is None:
                atol = 0.0

            filters.append(EndpointFilter(spec.a, spec.b, rtol, atol))
        return filters

    def check(self):
        # Generate values for the arguments
        args = get_args(self.argspec, self.n)
        param_filter = self.get_param_filter()
        param_columns = tuple(range(args.shape[1]))
        result_columns = args.shape[1]
        args = np.hstack((args, args[:,self.index].reshape(args.shape[0], 1)))
        FuncData(self.idmap, args,
                 param_columns=param_columns, result_columns=result_columns,
                 rtol=self.rtol, atol=self.atol, vectorized=False,
                 param_filter=param_filter).check()


def _assert_inverts(*a, **kw):
    d = _CDFData(*a, **kw)
    d.check()


def _binomial_cdf(k, n, p):
    k, n, p = mpmath.mpf(k), mpmath.mpf(n), mpmath.mpf(p)
    if k <= 0:
        return mpmath.mpf(0)
    elif k >= n:
        return mpmath.mpf(1)

    onemp = mpmath.fsub(1, p, exact=True)
    return mpmath.betainc(n - k, k + 1, x2=onemp, regularized=True)


def _f_cdf(dfn, dfd, x):
    if x < 0:
        return mpmath.mpf(0)
    dfn, dfd, x = mpmath.mpf(dfn), mpmath.mpf(dfd), mpmath.mpf(x)
    ub = dfn*x/(dfn*x + dfd)
    res = mpmath.betainc(dfn/2, dfd/2, x2=ub, regularized=True)
    return res


def _student_t_cdf(df, t, dps=None):
    if dps is None:
        dps = mpmath.mp.dps
    with mpmath.workdps(dps):
        df, t = mpmath.mpf(df), mpmath.mpf(t)
        fac = mpmath.hyp2f1(0.5, 0.5*(df + 1), 1.5, -t**2/df)
        fac *= t*mpmath.gamma(0.5*(df + 1))
        fac /= mpmath.sqrt(mpmath.pi*df)*mpmath.gamma(0.5*df)
        return 0.5 + fac


def _noncentral_chi_pdf(t, df, nc):
    res = mpmath.besseli(df/2 - 1, mpmath.sqrt(nc*t))
    res *= mpmath.exp(-(t + nc)/2)*(t/nc)**(df/4 - 1/2)/2
    return res


def _noncentral_chi_cdf(x, df, nc, dps=None):
    if dps is None:
        dps = mpmath.mp.dps
    x, df, nc = mpmath.mpf(x), mpmath.mpf(df), mpmath.mpf(nc)
    with mpmath.workdps(dps):
        res = mpmath.quad(lambda t: _noncentral_chi_pdf(t, df, nc), [0, x])
        return res


def _tukey_lmbda_quantile(p, lmbda):
    # For lmbda != 0
    return (p**lmbda - (1 - p)**lmbda)/lmbda


@pytest.mark.slow
@check_version(mpmath, '0.19')
class TestCDFlib(object):

    @pytest.mark.xfail(run=False)
    def test_bdtrik(self):
        _assert_inverts(
            sp.bdtrik,
            _binomial_cdf,
            0, [ProbArg(), IntArg(1, 1000), ProbArg()],
            rtol=1e-4)

    def test_bdtrin(self):
        _assert_inverts(
            sp.bdtrin,
            _binomial_cdf,
            1, [IntArg(1, 1000), ProbArg(), ProbArg()],
            rtol=1e-4, endpt_atol=[None, None, 1e-6])

    def test_btdtria(self):
        _assert_inverts(
            sp.btdtria,
            lambda a, b, x: mpmath.betainc(a, b, x2=x, regularized=True),
            0, [ProbArg(), Arg(0, 1e2, inclusive_a=False),
                Arg(0, 1, inclusive_a=False, inclusive_b=False)],
            rtol=1e-6)

    def test_btdtrib(self):
        # Use small values of a or mpmath doesn't converge
        _assert_inverts(
            sp.btdtrib,
            lambda a, b, x: mpmath.betainc(a, b, x2=x, regularized=True),
            1, [Arg(0, 1e2, inclusive_a=False), ProbArg(),
             Arg(0, 1, inclusive_a=False, inclusive_b=False)],
            rtol=1e-7, endpt_atol=[None, 1e-18, 1e-15])

    @pytest.mark.xfail(run=False)
    def test_fdtridfd(self):
        _assert_inverts(
            sp.fdtridfd,
            _f_cdf,
            1, [IntArg(1, 100), ProbArg(), Arg(0, 100, inclusive_a=False)],
            rtol=1e-7)

    def test_gdtria(self):
        _assert_inverts(
            sp.gdtria,
            lambda a, b, x: mpmath.gammainc(b, b=a*x, regularized=True),
            0, [ProbArg(), Arg(0, 1e3, inclusive_a=False),
                Arg(0, 1e4, inclusive_a=False)], rtol=1e-7,
            endpt_atol=[None, 1e-7, 1e-10])

    def test_gdtrib(self):
        # Use small values of a and x or mpmath doesn't converge
        _assert_inverts(
            sp.gdtrib,
            lambda a, b, x: mpmath.gammainc(b, b=a*x, regularized=True),
            1, [Arg(0, 1e2, inclusive_a=False), ProbArg(),
                Arg(0, 1e3, inclusive_a=False)], rtol=1e-5)

    def test_gdtrix(self):
        _assert_inverts(
            sp.gdtrix,
            lambda a, b, x: mpmath.gammainc(b, b=a*x, regularized=True),
            2, [Arg(0, 1e3, inclusive_a=False), Arg(0, 1e3, inclusive_a=False),
                ProbArg()], rtol=1e-7,
            endpt_atol=[None, 1e-7, 1e-10])

    def test_stdtr(self):
        # Ideally the left endpoint for Arg() should be 0.
        assert_mpmath_equal(
            sp.stdtr,
            _student_t_cdf,
            [IntArg(1, 100), Arg(1e-10, np.inf)], rtol=1e-7)

    @pytest.mark.xfail(run=False)
    def test_stdtridf(self):
        _assert_inverts(
            sp.stdtridf,
            _student_t_cdf,
            0, [ProbArg(), Arg()], rtol=1e-7)

    def test_stdtrit(self):
        _assert_inverts(
            sp.stdtrit,
            _student_t_cdf,
            1, [IntArg(1, 100), ProbArg()], rtol=1e-7,
            endpt_atol=[None, 1e-10])

    def test_chdtriv(self):
        _assert_inverts(
            sp.chdtriv,
            lambda v, x: mpmath.gammainc(v/2, b=x/2, regularized=True),
            0, [ProbArg(), IntArg(1, 100)], rtol=1e-4)

    @pytest.mark.xfail(run=False)
    def test_chndtridf(self):
        # Use a larger atol since mpmath is doing numerical integration
        _assert_inverts(
            sp.chndtridf,
            _noncentral_chi_cdf,
            1, [Arg(0, 100, inclusive_a=False), ProbArg(),
                Arg(0, 100, inclusive_a=False)],
            n=1000, rtol=1e-4, atol=1e-15)

    @pytest.mark.xfail(run=False)
    def test_chndtrinc(self):
        # Use a larger atol since mpmath is doing numerical integration
        _assert_inverts(
            sp.chndtrinc,
            _noncentral_chi_cdf,
            2, [Arg(0, 100, inclusive_a=False), IntArg(1, 100), ProbArg()],
            n=1000, rtol=1e-4, atol=1e-15)

    def test_chndtrix(self):
        # Use a larger atol since mpmath is doing numerical integration
        _assert_inverts(
            sp.chndtrix,
            _noncentral_chi_cdf,
            0, [ProbArg(), IntArg(1, 100), Arg(0, 100, inclusive_a=False)],
            n=1000, rtol=1e-4, atol=1e-15,
            endpt_atol=[1e-6, None, None])

    def test_tklmbda_zero_shape(self):
        # When lmbda = 0 the CDF has a simple closed form
        one = mpmath.mpf(1)
        assert_mpmath_equal(
            lambda x: sp.tklmbda(x, 0),
            lambda x: one/(mpmath.exp(-x) + one),
            [Arg()], rtol=1e-7)

    def test_tklmbda_neg_shape(self):
        _assert_inverts(
            sp.tklmbda,
            _tukey_lmbda_quantile,
            0, [ProbArg(), Arg(-25, 0, inclusive_b=False)],
            spfunc_first=False, rtol=1e-5,
            endpt_atol=[1e-9, 1e-5])

    @pytest.mark.xfail(run=False)
    def test_tklmbda_pos_shape(self):
        _assert_inverts(
            sp.tklmbda,
            _tukey_lmbda_quantile,
            0, [ProbArg(), Arg(0, 100, inclusive_a=False)],
            spfunc_first=False, rtol=1e-5)


def test_nonfinite():
    funcs = [
        ("btdtria", 3),
        ("btdtrib", 3),
        ("bdtrik", 3),
        ("bdtrin", 3),
        ("chdtriv", 2),
        ("chndtr", 3),
        ("chndtrix", 3),
        ("chndtridf", 3),
        ("chndtrinc", 3),
        ("fdtridfd", 3),
        ("ncfdtr", 4),
        ("ncfdtri", 4),
        ("ncfdtridfn", 4),
        ("ncfdtridfd", 4),
        ("ncfdtrinc", 4),
        ("gdtrix", 3),
        ("gdtrib", 3),
        ("gdtria", 3),
        ("nbdtrik", 3),
        ("nbdtrin", 3),
        ("nrdtrimn", 3),
        ("nrdtrisd", 3),
        ("pdtrik", 2),
        ("stdtr", 2),
        ("stdtrit", 2),
        ("stdtridf", 2),
        ("nctdtr", 3),
        ("nctdtrit", 3),
        ("nctdtridf", 3),
        ("nctdtrinc", 3),
        ("tklmbda", 2),
    ]

    np.random.seed(1)

    for func, numargs in funcs:
        func = getattr(sp, func)

        args_choices = [(float(x), np.nan, np.inf, -np.inf) for x in
                        np.random.rand(numargs)]

        for args in itertools.product(*args_choices):
            res = func(*args)

            if any(np.isnan(x) for x in args):
                # Nan inputs should result to nan output
                assert_equal(res, np.nan)
            else:
                # All other inputs should return something (but not
                # raise exceptions or cause hangs)
                pass