import numpy as np
import pytest
import tensorflow as tf
import tensorflow_probability as tfp
from gpflow.base import PriorOn
from tensorflow_probability.python.distributions import Uniform
from tensorflow_probability.python.bijectors import Exp

import gpflow
from gpflow.config import set_default_float
from gpflow.utilities import to_default_float

np.random.seed(1)


class Datum:
    X = 10 * np.random.randn(5, 1)
    Y = 10 * np.random.randn(5, 1)
    lengthscale = 3.3


def test_gpr_objective_equivalence():
    """
    In Maximum Likelihood Estimation (MLE), i.e. when there are no priors on
    the parameters, the objective should not depend on any transforms on the
    parameters.
    We use GPR as a simple model that has an objective.
    """
    data = (Datum.X, Datum.Y)
    l_value = Datum.lengthscale

    l_variable = tf.Variable(l_value, dtype=gpflow.default_float(), trainable=True)
    m1 = gpflow.models.GPR(data, kernel=gpflow.kernels.SquaredExponential(lengthscale=l_value))
    m2 = gpflow.models.GPR(data, kernel=gpflow.kernels.SquaredExponential())
    m2.kernel.lengthscale = gpflow.Parameter(l_variable, transform=None)
    assert np.allclose(m1.kernel.lengthscale.numpy(), m2.kernel.lengthscale.numpy())  # consistency check

    assert np.allclose(m1.log_marginal_likelihood().numpy(),
                       m2.log_marginal_likelihood().numpy()), \
                       "MLE objective should not depend on Parameter transform"


def test_log_prior_with_no_prior():
    """
    A parameter without any prior should have zero log-prior,
    even if it has a transform to constrain it.
    """
    param = gpflow.Parameter(5.3, transform=gpflow.utilities.positive())
    assert param.log_prior().numpy() == 0.0


def test_log_prior_for_uniform_prior():
    """
    If we assign a Uniform prior to a parameter, we should not expect the value of the prior density
    to change with the parameter value, even if it has a transform associated with it.
    """

    uniform_prior = Uniform(low=np.float64(0), high=np.float64(100))
    param = gpflow.Parameter(1., transform=gpflow.utilities.positive(),
                             prior=uniform_prior)
    low_value = param.log_prior().numpy()
    param.assign(10.)
    high_value = param.log_prior().numpy()

    assert np.isclose(low_value, high_value)


def test_log_prior_on_unconstrained():
    """
    A parameter with an Exp transform, and a uniform prior on its unconstrained, should have a
    prior in the constrained space that scales as 1/value.
    """

    initial_value = 1.
    scale_factor = 10.
    uniform_prior = Uniform(low=np.float64(0), high=np.float64(100))
    param = gpflow.Parameter(initial_value, transform=Exp(),
                             prior=uniform_prior,
                             prior_on=PriorOn.UNCONSTRAINED)
    low_value = param.log_prior().numpy()
    param.assign(scale_factor * initial_value)
    high_value = param.log_prior().numpy()

    assert np.isclose(low_value, high_value + np.log(scale_factor))


class DummyModel(gpflow.models.BayesianModel):
    value = 3.3
    log_scale = 0.4

    def __init__(self, with_transform):
        super().__init__()

        prior = tfp.distributions.Normal(to_default_float(1.0), to_default_float(1.0))

        scale = np.exp(self.log_scale)
        if with_transform:
            transform = tfp.bijectors.AffineScalar(scale=to_default_float(scale))
        else:
            transform = None

        self.theta = gpflow.Parameter(self.value, prior=prior, transform=transform)

    def log_likelihood(self):
        return (self.theta + 5)**2


def test_map_invariance_to_transform():
    m1 = DummyModel(with_transform=True)
    m2 = DummyModel(with_transform=False)
    assert np.allclose(m1.log_marginal_likelihood().numpy(),
                       m2.log_marginal_likelihood().numpy()), \
                       "MAP objective should not be affected by a transform"


def get_gpmc_model_params():
    kernel = gpflow.kernels.Matern32()
    likelihood = gpflow.likelihoods.Gaussian()
    data = [np.arange(5), np.arange(5)]
    return data, kernel, likelihood


@pytest.mark.parametrize(
    'model_class, args',
    [
        (gpflow.models.GPMC, get_gpmc_model_params()),
        #(gpflow.models.SGPMC, get_SGPMC_model_params()) # Fails due to inducing_variable=None bug
    ])
def test_v_prior_dtypes(model_class, args):
    with gpflow.config.as_context():
        set_default_float(np.float32)
        m = model_class(*args)
        assert m.V.prior.dtype == np.float32
        set_default_float(np.float64)
        m = model_class(*args)
        assert m.V.prior.dtype == np.float64