"""
Multivariate and time series
============================

Principal components and clustering (via scikit-learn), and a seasonal
decomposition (via statsmodels), all redrawn in the depictr theme.
"""

import numpy as np
import pandas as pd

import depictr as dp

wb = dp.wellbeing_survey()

# %%
# A PCA biplot, coloured by group, with the variable loadings.
p = dp.pca_plot(wb, group="region")
p

# %%
# k-means clusters on the first two principal components.
p = dp.cluster_plot(wb, k=3)
p

# %%
# A monthly series with a trend, a 12-period season and noise.
rng = np.random.default_rng(0)
t = np.arange(120)
series = pd.Series(
    50 + 0.3 * t + 10 * np.sin(2 * np.pi * t / 12) + rng.normal(0, 3, 120),
    index=pd.period_range("2016-01", periods=120, freq="M"),
)

# %%
# Its seasonal decomposition (observed, trend, seasonal, residual).
p = dp.decompose_plot(series, period=12)
p