import numpy as np
import plotly.graph_objects as go
import ipywidgets as widgets
from IPython.display import display, clear_output
class LinearSystemSolverPlotly:
def __init__(self):
# Default equations: [a, c, b]
self.default_eqs = [
[20, 50, 700],
[ 1, 1, 20],
[50, 20, 700]
]
self.equation_widgets = []
# Output area & toggle button (start with 3 equations)
self.output_area = widgets.Output()
self.toggle_button = widgets.ToggleButton(
value=True,
description='[-]',
tooltip='Toggle third equation',
layout=widgets.Layout(width='50px')
)
self.toggle_button.observe(self._on_toggle, names='value')
# Plotly figure widget
self.fig = go.FigureWidget()
self.fig.update_layout(
width=600, height=600,
margin=dict(l=40, r=40, b=40, t=40),
xaxis=dict(title='c'),
yaxis=dict(title='t'),
showlegend=True
)
# Build 3 equation rows and track the third
for idx in range(3):
row = self._add_eq_row(idx)
if idx == 2:
self.third_row = row
# Start with third row visible
self.third_row.layout.display = None
# Layout & display
self.container = widgets.VBox(
self.equation_widgets +
[self.toggle_button, self.output_area, self.fig]
)
display(self.container)
# Initial plot
self.update_plot()
def _add_eq_row(self, idx):
a = widgets.FloatText(value=self.default_eqs[idx][0], layout=widgets.Layout(width='60px'))
c = widgets.FloatText(value=self.default_eqs[idx][1], layout=widgets.Layout(width='60px'))
b = widgets.FloatText(value=self.default_eqs[idx][2], layout=widgets.Layout(width='60px'))
for w in (a, c, b):
w.observe(lambda change: self.update_plot(), names='value')
row = widgets.HBox([a, widgets.Label("c +"), c, widgets.Label("t ="), b])
row._entries = (a, c, b)
self.equation_widgets.append(row)
return row
def _on_toggle(self, change):
if change['new']:
# Show third row
self.third_row.layout.display = None
self.toggle_button.description = '[-]'
else:
# Hide third row
self.third_row.layout.display = 'none'
self.toggle_button.description = '[+]'
self.update_plot()
def parse_equations(self):
A, b = [], []
for row in self.equation_widgets:
# Skip hidden third row
if getattr(row.layout, 'display', None) == 'none':
continue
a, c, b_ = row._entries
A.append([a.value, c.value])
b.append(b_.value)
return np.array(A), np.array(b)
def update_plot(self):
A, b = self.parse_equations()
# Clear previous traces and title
self.fig.data = []
self.fig.layout.title = ""
self.fig.layout.showlegend = True
with self.output_area:
clear_output()
if A.shape[0] < 2:
print("Enter at least 2 valid equations.")
return
# Print matrix form
print(" A x = b")
for i in range(A.shape[0]):
a_str = f"[{A[i,0]:>4.0f} {A[i,1]:>4.0f}]"
x_str = "[c]" if i==0 else "[t]" if i==1 else " "
b_str = f"[{b[i]:>5.0f}]"
print(f"{a_str} {x_str} {b_str}")
rank_A = np.linalg.matrix_rank(A)
rank_Ab = np.linalg.matrix_rank(np.hstack([A, b.reshape(-1,1)]))
sol = None
show_dot = False
if A.shape[0] == 3:
# Always least-squares for 3 eqns
sol, residuals, *_ = np.linalg.lstsq(A, b, rcond=None)
rss = residuals[0] if residuals.size else 0.0
if rank_Ab > rank_A:
msg, color = f"Inconsistent: LS fit (RSS={rss:.1f})", 'red'
elif rank_A < A.shape[1]:
msg, color = f"Dependent: LS fit (RSS={rss:.1f})", 'blue'
elif np.isclose(rss, 0):
msg, color = f"Exact intersection: c={sol[0]:.2f}, t={sol[1]:.2f}", 'green'
else:
msg, color = f"Least-squares: c={sol[0]:.2f}, t={sol[1]:.2f} (RSS={rss:.1f})", 'gray'
show_dot = True
else:
# Two eqns: decide exact or no/infinite solutions
if rank_Ab > rank_A:
msg, color, show_dot = "Inconsistent: no solution.", 'red', False
elif rank_A < A.shape[1]:
msg, color, show_dot = "Dependent: infinite solutions.", 'blue', False
else:
sol = np.linalg.solve(A, b)
msg, color, show_dot = (f"Solution: c={sol[0]:.2f}, t={sol[1]:.2f}", 'green', True)
print("\n" + msg)
try:
cond = np.linalg.cond(A)
print(f"Condition number: {cond:.2e}")
except:
print("Condition number: N/A")
# Determine plot range
if sol is not None:
cx, cy = sol
x_min, x_max = cx-20, cx+20
y_min, y_max = cy-20, cy+20
else:
x_min, x_max, y_min, y_max = -40, 40, -40, 40
x_vals = np.linspace(x_min, x_max, 500)
# Plot each visible line
for i in range(A.shape[0]):
a, c = A[i]
rhs = b[i]
label = f"{a}c + {c}t = {rhs}"
if c != 0:
yv = (rhs - a*x_vals)/c
self.fig.add_trace(go.Scatter(x=x_vals, y=yv, mode='lines', name=label))
elif a != 0:
xc = np.full_like(x_vals, rhs/a)
self.fig.add_trace(go.Scatter(x=xc, y=x_vals, mode='lines', name=label))
else:
yc = np.full_like(x_vals, rhs)
self.fig.add_trace(go.Scatter(x=x_vals, y=yc, mode='lines', name=label))
# Plot solution/fit dot
if show_dot:
self.fig.add_trace(go.Scatter(
x=[sol[0]], y=[sol[1]],
mode='markers', name='Solution',
marker=dict(color='red', size=10)
))
# Final layout
self.fig.update_layout(
title=dict(text=msg, font=dict(color=color)),
xaxis=dict(range=[x_min, x_max]),
yaxis=dict(range=[y_min, y_max])
)
LinearSystemSolverPlotly()
