from sklearn.decomposition import PCA
import matplotlib
matplotlib.use("Agg")
import matplotlib.pyplot as plt
import numpy as np
from scipy import stats
import gradio as gr

e = np.exp(1)
np.random.seed(4)


def pdf(x):
    return 0.5 * (stats.norm(scale=0.25 / e).pdf(x) + stats.norm(scale=4 / e).pdf(x))


y = np.random.normal(scale=0.5, size=(30000))
x = np.random.normal(scale=0.5, size=(30000))
z = np.random.normal(scale=0.1, size=len(x))

density = pdf(x) * pdf(y)
pdf_z = pdf(5 * z)

density *= pdf_z

a = x + y
b = 2 * y
c = a - b + z

norm = np.sqrt(a.var() + b.var())
a /= norm
b /= norm

def plot_figs(fig_num, elev, azim):
    fig = plt.figure()
    plt.clf()
    ax = fig.add_subplot(111, projection="3d", elev=elev, azim=azim)
    ax.set_position([0, 0, 0.95, 1])

    ax.scatter(a[::10], b[::10], c[::10], c=density[::10], marker="+", alpha=0.4)
    Y = np.c_[a, b, c]

    # Using SciPy's SVD, this would be:
    # _, pca_score, Vt = scipy.linalg.svd(Y, full_matrices=False)

    pca = PCA(n_components=3)
    pca.fit(Y)
    V = pca.components_.T

    x_pca_axis, y_pca_axis, z_pca_axis = 3 * V
    x_pca_plane = np.r_[x_pca_axis[:2], -x_pca_axis[1::-1]]
    y_pca_plane = np.r_[y_pca_axis[:2], -y_pca_axis[1::-1]]
    z_pca_plane = np.r_[z_pca_axis[:2], -z_pca_axis[1::-1]]
    x_pca_plane.shape = (2, 2)
    y_pca_plane.shape = (2, 2)
    z_pca_plane.shape = (2, 2)
    ax.plot_surface(x_pca_plane, y_pca_plane, z_pca_plane)
    ax.xaxis.set_ticklabels([])
    ax.yaxis.set_ticklabels([])
    ax.zaxis.set_ticklabels([])

    return fig

def make_plot(plot_type):
    if plot_type == "Very flat direction":
        elev = -40
        azim = -80
        fig_num = 1
    else:
        elev = 30
        azim = 20
        fig_num = 2
    return plot_figs(fig_num, elev, azim)

title = "Principal components analysis (PCA)"
with gr.Blocks(title=title) as demo:
    gr.Markdown(f"## {title}")
    gr.Markdown("These figures aid in illustrating how a point cloud can be \
    very flat in one direction–which is where PCA comes in to choose a direction that is not flat.")
    with gr.Row():
        plot1 = gr.Plot(value=make_plot("Very flat direction"), label="Very flat direction")
        plot2 = gr.Plot(value=make_plot("Not flat direction"), label="Not flat direction")

if __name__ == "__main__":
    demo.launch()