from itertools import product
import numpy as np
import math
import pytest

from sklearn import datasets, clone
from sklearn import manifold
from sklearn import neighbors
from sklearn import pipeline
from sklearn import preprocessing
from sklearn.datasets import make_blobs
from sklearn.metrics.pairwise import pairwise_distances
from sklearn.utils._testing import (
    assert_allclose,
    assert_allclose_dense_sparse,
    assert_array_equal,
)
from scipy.sparse import rand as sparse_rand

eigen_solvers = ["auto", "dense", "arpack"]
path_methods = ["auto", "FW", "D"]


def create_sample_data(dtype, n_pts=25, add_noise=False):
    # grid of equidistant points in 2D, n_components = n_dim
    n_per_side = int(math.sqrt(n_pts))
    X = np.array(list(product(range(n_per_side), repeat=2))).astype(dtype, copy=False)
    if add_noise:
        # add noise in a third dimension
        rng = np.random.RandomState(0)
        noise = 0.1 * rng.randn(n_pts, 1).astype(dtype, copy=False)
        X = np.concatenate((X, noise), 1)
    return X


@pytest.mark.parametrize("n_neighbors, radius", [(24, None), (None, np.inf)])
@pytest.mark.parametrize("eigen_solver", eigen_solvers)
@pytest.mark.parametrize("path_method", path_methods)
def test_isomap_simple_grid(
    global_dtype, n_neighbors, radius, eigen_solver, path_method
):
    # Isomap should preserve distances when all neighbors are used
    n_pts = 25
    X = create_sample_data(global_dtype, n_pts=n_pts, add_noise=False)

    # distances from each point to all others
    if n_neighbors is not None:
        G = neighbors.kneighbors_graph(X, n_neighbors, mode="distance")
    else:
        G = neighbors.radius_neighbors_graph(X, radius, mode="distance")

    clf = manifold.Isomap(
        n_neighbors=n_neighbors,
        radius=radius,
        n_components=2,
        eigen_solver=eigen_solver,
        path_method=path_method,
    )
    clf.fit(X)

    if n_neighbors is not None:
        G_iso = neighbors.kneighbors_graph(clf.embedding_, n_neighbors, mode="distance")
    else:
        G_iso = neighbors.radius_neighbors_graph(
            clf.embedding_, radius, mode="distance"
        )
    atol = 1e-5 if global_dtype == np.float32 else 0
    assert_allclose_dense_sparse(G, G_iso, atol=atol)


@pytest.mark.parametrize("n_neighbors, radius", [(24, None), (None, np.inf)])
@pytest.mark.parametrize("eigen_solver", eigen_solvers)
@pytest.mark.parametrize("path_method", path_methods)
def test_isomap_reconstruction_error(
    global_dtype, n_neighbors, radius, eigen_solver, path_method
):
    if global_dtype is np.float32:
        pytest.skip(
            "Skipping test due to numerical instabilities on float32 data"
            "from KernelCenterer used in the reconstruction_error method"
        )

    # Same setup as in test_isomap_simple_grid, with an added dimension
    n_pts = 25
    X = create_sample_data(global_dtype, n_pts=n_pts, add_noise=True)

    # compute input kernel
    if n_neighbors is not None:
        G = neighbors.kneighbors_graph(X, n_neighbors, mode="distance").toarray()
    else:
        G = neighbors.radius_neighbors_graph(X, radius, mode="distance").toarray()
    centerer = preprocessing.KernelCenterer()
    K = centerer.fit_transform(-0.5 * G**2)

    clf = manifold.Isomap(
        n_neighbors=n_neighbors,
        radius=radius,
        n_components=2,
        eigen_solver=eigen_solver,
        path_method=path_method,
    )
    clf.fit(X)

    # compute output kernel
    if n_neighbors is not None:
        G_iso = neighbors.kneighbors_graph(clf.embedding_, n_neighbors, mode="distance")
    else:
        G_iso = neighbors.radius_neighbors_graph(
            clf.embedding_, radius, mode="distance"
        )
    G_iso = G_iso.toarray()
    K_iso = centerer.fit_transform(-0.5 * G_iso**2)

    # make sure error agrees
    reconstruction_error = np.linalg.norm(K - K_iso) / n_pts
    atol = 1e-5 if global_dtype == np.float32 else 0
    assert_allclose(reconstruction_error, clf.reconstruction_error(), atol=atol)


@pytest.mark.parametrize("n_neighbors, radius", [(2, None), (None, 0.5)])
def test_transform(global_dtype, n_neighbors, radius):
    n_samples = 200
    n_components = 10
    noise_scale = 0.01

    # Create S-curve dataset
    X, y = datasets.make_s_curve(n_samples, random_state=0)

    X = X.astype(global_dtype, copy=False)

    # Compute isomap embedding
    iso = manifold.Isomap(
        n_components=n_components, n_neighbors=n_neighbors, radius=radius
    )
    X_iso = iso.fit_transform(X)

    # Re-embed a noisy version of the points
    rng = np.random.RandomState(0)
    noise = noise_scale * rng.randn(*X.shape)
    X_iso2 = iso.transform(X + noise)

    # Make sure the rms error on re-embedding is comparable to noise_scale
    assert np.sqrt(np.mean((X_iso - X_iso2) ** 2)) < 2 * noise_scale


@pytest.mark.parametrize("n_neighbors, radius", [(2, None), (None, 10.0)])
def test_pipeline(n_neighbors, radius, global_dtype):
    # check that Isomap works fine as a transformer in a Pipeline
    # only checks that no error is raised.
    # TODO check that it actually does something useful
    X, y = datasets.make_blobs(random_state=0)
    X = X.astype(global_dtype, copy=False)
    clf = pipeline.Pipeline(
        [
            ("isomap", manifold.Isomap(n_neighbors=n_neighbors, radius=radius)),
            ("clf", neighbors.KNeighborsClassifier()),
        ]
    )
    clf.fit(X, y)
    assert 0.9 < clf.score(X, y)


def test_pipeline_with_nearest_neighbors_transformer(global_dtype):
    # Test chaining NearestNeighborsTransformer and Isomap with
    # neighbors_algorithm='precomputed'
    algorithm = "auto"
    n_neighbors = 10

    X, _ = datasets.make_blobs(random_state=0)
    X2, _ = datasets.make_blobs(random_state=1)

    X = X.astype(global_dtype, copy=False)
    X2 = X2.astype(global_dtype, copy=False)

    # compare the chained version and the compact version
    est_chain = pipeline.make_pipeline(
        neighbors.KNeighborsTransformer(
            n_neighbors=n_neighbors, algorithm=algorithm, mode="distance"
        ),
        manifold.Isomap(n_neighbors=n_neighbors, metric="precomputed"),
    )
    est_compact = manifold.Isomap(
        n_neighbors=n_neighbors, neighbors_algorithm=algorithm
    )

    Xt_chain = est_chain.fit_transform(X)
    Xt_compact = est_compact.fit_transform(X)
    assert_allclose(Xt_chain, Xt_compact)

    Xt_chain = est_chain.transform(X2)
    Xt_compact = est_compact.transform(X2)
    assert_allclose(Xt_chain, Xt_compact)


@pytest.mark.parametrize(
    "metric, p, is_euclidean",
    [
        ("euclidean", 2, True),
        ("manhattan", 1, False),
        ("minkowski", 1, False),
        ("minkowski", 2, True),
        (lambda x1, x2: np.sqrt(np.sum(x1**2 + x2**2)), 2, False),
    ],
)
def test_different_metric(global_dtype, metric, p, is_euclidean):
    # Isomap must work on various metric parameters work correctly
    # and must default to euclidean.
    X, _ = datasets.make_blobs(random_state=0)
    X = X.astype(global_dtype, copy=False)

    reference = manifold.Isomap().fit_transform(X)
    embedding = manifold.Isomap(metric=metric, p=p).fit_transform(X)

    if is_euclidean:
        assert_allclose(embedding, reference)
    else:
        with pytest.raises(AssertionError, match="Not equal to tolerance"):
            assert_allclose(embedding, reference)


def test_isomap_clone_bug():
    # regression test for bug reported in #6062
    model = manifold.Isomap()
    for n_neighbors in [10, 15, 20]:
        model.set_params(n_neighbors=n_neighbors)
        model.fit(np.random.rand(50, 2))
        assert model.nbrs_.n_neighbors == n_neighbors


@pytest.mark.parametrize("eigen_solver", eigen_solvers)
@pytest.mark.parametrize("path_method", path_methods)
def test_sparse_input(global_dtype, eigen_solver, path_method, global_random_seed):
    # TODO: compare results on dense and sparse data as proposed in:
    # https://github.com/scikit-learn/scikit-learn/pull/23585#discussion_r968388186
    X = sparse_rand(
        100,
        3,
        density=0.1,
        format="csr",
        dtype=global_dtype,
        random_state=global_random_seed,
    )

    iso_dense = manifold.Isomap(
        n_components=2,
        eigen_solver=eigen_solver,
        path_method=path_method,
        n_neighbors=8,
    )
    iso_sparse = clone(iso_dense)

    X_trans_dense = iso_dense.fit_transform(X.toarray())
    X_trans_sparse = iso_sparse.fit_transform(X)

    assert_allclose(X_trans_sparse, X_trans_dense, rtol=1e-4, atol=1e-4)


def test_isomap_fit_precomputed_radius_graph(global_dtype):
    # Isomap.fit_transform must yield similar result when using
    # a precomputed distance matrix.

    X, y = datasets.make_s_curve(200, random_state=0)
    X = X.astype(global_dtype, copy=False)
    radius = 10

    g = neighbors.radius_neighbors_graph(X, radius=radius, mode="distance")
    isomap = manifold.Isomap(n_neighbors=None, radius=radius, metric="precomputed")
    isomap.fit(g)
    precomputed_result = isomap.embedding_

    isomap = manifold.Isomap(n_neighbors=None, radius=radius, metric="minkowski")
    result = isomap.fit_transform(X)
    atol = 1e-5 if global_dtype == np.float32 else 0
    assert_allclose(precomputed_result, result, atol=atol)


def test_isomap_fitted_attributes_dtype(global_dtype):
    """Check that the fitted attributes are stored accordingly to the
    data type of X."""
    iso = manifold.Isomap(n_neighbors=2)

    X = np.array([[1, 2], [3, 4], [5, 6]], dtype=global_dtype)

    iso.fit(X)

    assert iso.dist_matrix_.dtype == global_dtype
    assert iso.embedding_.dtype == global_dtype


def test_isomap_dtype_equivalence():
    """Check the equivalence of the results with 32 and 64 bits input."""
    iso_32 = manifold.Isomap(n_neighbors=2)
    X_32 = np.array([[1, 2], [3, 4], [5, 6]], dtype=np.float32)
    iso_32.fit(X_32)

    iso_64 = manifold.Isomap(n_neighbors=2)
    X_64 = np.array([[1, 2], [3, 4], [5, 6]], dtype=np.float64)
    iso_64.fit(X_64)

    assert_allclose(iso_32.dist_matrix_, iso_64.dist_matrix_)


def test_isomap_raise_error_when_neighbor_and_radius_both_set():
    # Isomap.fit_transform must raise a ValueError if
    # radius and n_neighbors are provided.

    X, _ = datasets.load_digits(return_X_y=True)
    isomap = manifold.Isomap(n_neighbors=3, radius=5.5)
    msg = "Both n_neighbors and radius are provided"
    with pytest.raises(ValueError, match=msg):
        isomap.fit_transform(X)


def test_multiple_connected_components():
    # Test that a warning is raised when the graph has multiple components
    X = np.array([0, 1, 2, 5, 6, 7])[:, None]
    with pytest.warns(UserWarning, match="number of connected components"):
        manifold.Isomap(n_neighbors=2).fit(X)


def test_multiple_connected_components_metric_precomputed(global_dtype):
    # Test that an error is raised when the graph has multiple components
    # and when X is a precomputed neighbors graph.
    X = np.array([0, 1, 2, 5, 6, 7])[:, None].astype(global_dtype, copy=False)

    # works with a precomputed distance matrix (dense)
    X_distances = pairwise_distances(X)
    with pytest.warns(UserWarning, match="number of connected components"):
        manifold.Isomap(n_neighbors=1, metric="precomputed").fit(X_distances)

    # does not work with a precomputed neighbors graph (sparse)
    X_graph = neighbors.kneighbors_graph(X, n_neighbors=2, mode="distance")
    with pytest.raises(RuntimeError, match="number of connected components"):
        manifold.Isomap(n_neighbors=1, metric="precomputed").fit(X_graph)


def test_get_feature_names_out():
    """Check get_feature_names_out for Isomap."""
    X, y = make_blobs(random_state=0, n_features=4)
    n_components = 2

    iso = manifold.Isomap(n_components=n_components)
    iso.fit_transform(X)
    names = iso.get_feature_names_out()
    assert_array_equal([f"isomap{i}" for i in range(n_components)], names)