"""
Using a distance matrix
---------
"""

# %%
# Generating data
# ===============
#
# For this example we will generate evenly distributed points on a circle then
# compute the distance matrix of those points. In practice it makes little
# sense to go through this song and dance unless your data is given as a
# distance matrix.

import matplotlib.pyplot as plt
import numpy as np
from sklearn.metrics import pairwise_distances

theta = np.linspace(0, 2 * np.pi, 50)
circle = np.c_[np.cos(theta), np.sin(theta)]
data = pairwise_distances(circle)

plt.matshow(data)
plt.show()


# %%
# Projecting our data
# ===================
#
# From here we will pretend that we don't know the underlying data which
# generated the distance matrix. We pick [MDS](https://scikit-learn.org/stable/modules/generated/sklearn.manifold.MDS.html) as our
# lense function as it plays nicely with distance matrices.

from sklearn.manifold import MDS

projection: np.ndarray = MDS(
    n_components=1,
    metric="precomputed",
    n_init=1,  # type: ignore
    init="classical_mds",
).fit_transform(data)

plt.scatter(circle[:, 0], circle[:, 1], label="data")
plt.scatter(projection, np.zeros_like(projection), label="projection")
plt.legend()
plt.show()


# %%
# Defining a clusterer
# ====================
#
# This is the last place where we need to do something different to facilitate
# running mapper on a distance matrix. All we have to do is tell the base
# clusterer that the metric is precomputed. From there the adapter should be
# clever enough to detect this fact.
from sklearn.cluster import AgglomerativeClustering

import zen_mapper as zm

sk = AgglomerativeClustering(
    linkage="single",
    n_clusters=None,  # type: ignore
    distance_threshold=0.2,
    metric="precomputed",
)
clusterer = zm.sk_learn(sk)

# %%
# Computing the mapper graph
# ==========================
cover_scheme = zm.Width_Balanced_Cover(n_elements=3, percent_overlap=0.4)

result = zm.mapper(
    data=data,
    projection=projection,
    cover_scheme=cover_scheme,
    clusterer=clusterer,
    dim=1,
)


# %%
# Visualizing the mapper graph
# ============================
import networkx as nx

graph = zm.to_networkx(result.nerve)
nx.draw(graph)