"""Testing for Gaussian process classification """

# Author: Jan Hendrik Metzen <jhm@informatik.uni-bremen.de>
# License: BSD 3 clause

import numpy as np

from scipy.optimize import approx_fprime

from sklearn.gaussian_process import GaussianProcessClassifier
from sklearn.gaussian_process.kernels import RBF, ConstantKernel as C

from sklearn.utils.testing import (assert_true, assert_greater,
                                   assert_almost_equal, assert_array_equal)


def f(x):
    return np.sin(x)
X = np.atleast_2d(np.linspace(0, 10, 30)).T
X2 = np.atleast_2d([2., 4., 5.5, 6.5, 7.5]).T
y = np.array(f(X).ravel() > 0, dtype=int)
fX = f(X).ravel()
y_mc = np.empty(y.shape, dtype=int)  # multi-class
y_mc[fX < -0.35] = 0
y_mc[(fX >= -0.35) & (fX < 0.35)] = 1
y_mc[fX > 0.35] = 2


fixed_kernel = RBF(length_scale=1.0, length_scale_bounds="fixed")
kernels = [RBF(length_scale=0.1), fixed_kernel,
           RBF(length_scale=1.0, length_scale_bounds=(1e-3, 1e3)),
           C(1.0, (1e-2, 1e2)) *
           RBF(length_scale=1.0, length_scale_bounds=(1e-3, 1e3))]


def test_predict_consistent():
    # Check binary predict decision has also predicted probability above 0.5.
    for kernel in kernels:
        gpc = GaussianProcessClassifier(kernel=kernel).fit(X, y)
        assert_array_equal(gpc.predict(X),
                           gpc.predict_proba(X)[:, 1] >= 0.5)


def test_lml_improving():
    # Test that hyperparameter-tuning improves log-marginal likelihood.
    for kernel in kernels:
        if kernel == fixed_kernel:
            continue
        gpc = GaussianProcessClassifier(kernel=kernel).fit(X, y)
        assert_greater(gpc.log_marginal_likelihood(gpc.kernel_.theta),
                       gpc.log_marginal_likelihood(kernel.theta))


def test_lml_precomputed():
    # Test that lml of optimized kernel is stored correctly.
    for kernel in kernels:
        gpc = GaussianProcessClassifier(kernel=kernel).fit(X, y)
        assert_almost_equal(gpc.log_marginal_likelihood(gpc.kernel_.theta),
                            gpc.log_marginal_likelihood(), 7)


def test_converged_to_local_maximum():
    # Test that we are in local maximum after hyperparameter-optimization.
    for kernel in kernels:
        if kernel == fixed_kernel:
            continue
        gpc = GaussianProcessClassifier(kernel=kernel).fit(X, y)

        lml, lml_gradient = \
            gpc.log_marginal_likelihood(gpc.kernel_.theta, True)

        assert_true(np.all((np.abs(lml_gradient) < 1e-4) |
                           (gpc.kernel_.theta == gpc.kernel_.bounds[:, 0]) |
                           (gpc.kernel_.theta == gpc.kernel_.bounds[:, 1])))


def test_lml_gradient():
    # Compare analytic and numeric gradient of log marginal likelihood.
    for kernel in kernels:
        gpc = GaussianProcessClassifier(kernel=kernel).fit(X, y)

        lml, lml_gradient = gpc.log_marginal_likelihood(kernel.theta, True)
        lml_gradient_approx = \
            approx_fprime(kernel.theta,
                          lambda theta: gpc.log_marginal_likelihood(theta,
                                                                    False),
                          1e-10)

        assert_almost_equal(lml_gradient, lml_gradient_approx, 3)


def test_random_starts():
    # Test that an increasing number of random-starts of GP fitting only
    # increases the log marginal likelihood of the chosen theta.
    n_samples, n_features = 25, 2
    rng = np.random.RandomState(0)
    X = rng.randn(n_samples, n_features) * 2 - 1
    y = (np.sin(X).sum(axis=1) + np.sin(3 * X).sum(axis=1)) > 0

    kernel = C(1.0, (1e-2, 1e2)) \
        * RBF(length_scale=[1e-3] * n_features,
              length_scale_bounds=[(1e-4, 1e+2)] * n_features)
    last_lml = -np.inf
    for n_restarts_optimizer in range(5):
        gp = GaussianProcessClassifier(
            kernel=kernel, n_restarts_optimizer=n_restarts_optimizer,
            random_state=0).fit(X, y)
        lml = gp.log_marginal_likelihood(gp.kernel_.theta)
        assert_greater(lml, last_lml - np.finfo(np.float32).eps)
        last_lml = lml


def test_custom_optimizer():
    # Test that GPC can use externally defined optimizers.
    # Define a dummy optimizer that simply tests 50 random hyperparameters
    def optimizer(obj_func, initial_theta, bounds):
        rng = np.random.RandomState(0)
        theta_opt, func_min = \
            initial_theta, obj_func(initial_theta, eval_gradient=False)
        for _ in range(50):
            theta = np.atleast_1d(rng.uniform(np.maximum(-2, bounds[:, 0]),
                                              np.minimum(1, bounds[:, 1])))
            f = obj_func(theta, eval_gradient=False)
            if f < func_min:
                theta_opt, func_min = theta, f
        return theta_opt, func_min

    for kernel in kernels:
        if kernel == fixed_kernel:
            continue
        gpc = GaussianProcessClassifier(kernel=kernel, optimizer=optimizer)
        gpc.fit(X, y_mc)
        # Checks that optimizer improved marginal likelihood
        assert_greater(gpc.log_marginal_likelihood(gpc.kernel_.theta),
                       gpc.log_marginal_likelihood(kernel.theta))


def test_multi_class():
    # Test GPC for multi-class classification problems.
    for kernel in kernels:
        gpc = GaussianProcessClassifier(kernel=kernel)
        gpc.fit(X, y_mc)

        y_prob = gpc.predict_proba(X2)
        assert_almost_equal(y_prob.sum(1), 1)

        y_pred = gpc.predict(X2)
        assert_array_equal(np.argmax(y_prob, 1), y_pred)


def test_multi_class_n_jobs():
    # Test that multi-class GPC produces identical results with n_jobs>1.
    for kernel in kernels:
        gpc = GaussianProcessClassifier(kernel=kernel)
        gpc.fit(X, y_mc)

        gpc_2 = GaussianProcessClassifier(kernel=kernel, n_jobs=2)
        gpc_2.fit(X, y_mc)

        y_prob = gpc.predict_proba(X2)
        y_prob_2 = gpc_2.predict_proba(X2)
        assert_almost_equal(y_prob, y_prob_2)
