3D_Matrix_Evolution.py

import numpy as np
import pandas as pd
import plotly.graph_objects as go
import plotly.express as px
from plotly.subplots import make_subplots
import time

# Generate a skew-symmetric matrix
def generate_skew_symmetric_matrix(size):
    mat = np.random.rand(size, size)
    skew_symmetric = (mat - mat.T) / 2
    return skew_symmetric

# Create an animated scatter plot using Plotly
def animate_scatter_plot(matrix):
    fig = make_subplots(rows=1, cols=2, specs=[[{'type': 'scatter3d'}, {'type': 'scatter'}]],
                        subplot_titles=("Matrix Evolution", "Heatmap"))
    frames = []

    size = matrix.shape[0]

    for i in range(size):
        frame_data = matrix[:i+1, :i+1]
        x, y = np.meshgrid(np.arange(i+1), np.arange(i+1))
        x = x.flatten()
        y = y.flatten()
        z = frame_data.flatten()

        scatter_trace = go.Scatter3d(x=x, y=y, z=z, mode='markers',
                                     marker=dict(size=10, color=z, colorscale='Viridis'))
        fig.add_trace(scatter_trace, row=1, col=1)

        heatmap_fig = plot_heatmap(frame_data, f"Frame {i + 1}")
        frames.append(go.Frame(data=heatmap_fig.data, layout=heatmap_fig.layout))

    animation_fig = go.Figure(fig, frames=frames)
    animation_fig.update_layout(updatemenus=[{
        "buttons": [
            {
                "args": [None, {"frame": {"duration": 500, "redraw": True}, "fromcurrent": True}],
                "label": "Play",
                "method": "animate",
            },
            {
                "args": [[None], {"frame": {"duration": 0, "redraw": True}, "mode": "immediate", "transition": {"duration": 0}}],
                "label": "Pause",
                "method": "animate",
            },
        ],
        "direction": "left",
        "pad": {"r": 10, "t": 87},
        "showactive": False,
        "type": "buttons",
        "x": 0.1,
        "xanchor": "right",
        "y": 0,
        "yanchor": "top",
    }])

    animation_fig.update_layout(sliders=[{
        "active": 0,
        "steps": [{
            "args": [[f.name], {"frame": {"duration": 300, "redraw": True}, "transition": {"duration": 0}}],
            "label": f"Frame {i + 1}",
            "method": "animate",
        } for i, f in enumerate(animation_fig.frames)],
        "x": 0.1,
        "xanchor": "left",
        "y": 0,
        "yanchor": "top",
        "currentvalue": {
            "font": {"size": 20},
            "prefix": "Frame:",
            "visible": True,
            "xanchor": "right",
        },
    }])

    animation_fig.update_yaxes(showticklabels=False, showgrid=False)
    animation_fig.update_xaxes(showticklabels=False, showgrid=False)

    return animation_fig

# Example usage
size = 7
matrix = generate_skew_symmetric_matrix(size)
animation_fig = animate_scatter_plot(matrix)
animation_fig.show()