VMLS: Least squares

The data for this plot comes from Introduction to Applied Linear Algebra – Vectors, Matrices, and Least Squares (Boyd and Vandenberghe, 2018).

#| '!! shinylive warning !!': |
#|   shinylive does not work in self-contained HTML documents.
#|   Please set `embed-resources: false` in your metadata.
#| standalone: true
#| viewerHeight: 600

from shiny import App, render, ui, reactive
import numpy as np
import matplotlib.pyplot as plt
import plotly.graph_objects as go
from shinywidgets import render_widget, output_widget

def Z_func(x, y):
    return (2*x - 1)**2 + (-x + y)**2 + (2*y + 1)**2

app_ui = ui.page_fluid(
    ui.layout_columns(
        output_widget('curve'),
        output_widget('contourplot')
    ),
)


def server(input, output, session):

    @render_widget
    def curve():

        X_lin  = np.arange(-1, 1.5, 0.05)
        Y_lin = np.arange(-1.5, 1, 0.05)
        X, Y = np.meshgrid(X_lin, Y_lin)
        Z = Z_func(X, Y)

        fig = go.Figure(data=[go.Surface(x=X, y=Y, z=Z, name='Curve', colorscale='Turbo')])
        
        fig = fig.update_layout(
            autosize=True,
            height=600,
            margin=dict(l=65, r=50, b=65, t=90),
            scene = dict(xaxis = dict(range=[-1, 1.5], title=dict(text='x_1')),
                        yaxis = dict(range=[-1.5, 1], title=dict(text='x_2')),
                        zaxis = dict(range=[np.min(Z) - (np.max(Z) - np.min(Z)) * 0.05, np.max(Z) + (np.max(Z) - np.min(Z)) * 0.05], title=dict(text=''))
                        )
            )
        return fig

    # ========================================================================

    @render_widget
    def contourplot():
        X_lin  = np.arange(-1, 1.5, 0.05)
        Y_lin = np.arange(-1.5, 1, 0.05)
        X, Y = np.meshgrid(X_lin, Y_lin)
        Z = Z_func(X, Y)

        fig = go.Figure(data =
            [go.Contour(
                z=Z,
                x=X_lin,
                y=Y_lin, 
                colorscale='Turbo',
                contours=dict(
                start=0.666666,
                end=22.666666,
                size=1,
            ),
            )])

        fig = fig.update_layout(
            autosize=True,
            height=600,
            margin=dict(l=65, r=50, b=65, t=90),
            scene = dict(xaxis = dict(range=[-1, 1.5], title=dict(text='x_1')),
                        yaxis = dict(range=[-1.5, 1], title=dict(text='x_2')),
                        zaxis = dict(range=[np.min(Z) - (np.max(Z) - np.min(Z)) * 0.05, np.max(Z) + (np.max(Z) - np.min(Z)) * 0.05], title=dict(text=''))
                        )
            )
        return fig

    # ========================================================================


app = App(app_ui, server)

References

Boyd, S. P., & Vandenberghe, L. (2018). Introduction to Applied Linear Algebra : Vectors, Matrices, and Least Squares (First edition.). Cambridge University Press.