import numpy as np
import matplotlib.pyplot as plt
import ipywidgets as widgets
from IPython.display import display, clear_output
class LinearSystemSolverNotebook:
def __init__(self):
self.default_eqs = [
[20, 50, 700],
[1, 1, 20],
[50, 20, 700]
]
self.equation_widgets = []
self.third_eq_shown = False
# UI elements
self.output_area = widgets.Output()
self.plot_area = widgets.Output()
self.toggle_button = widgets.ToggleButton(
value=False,
description='[+]',
tooltip='Toggle third equation',
layout=widgets.Layout(width='50px')
)
self.toggle_button.observe(self.toggle_third_equation, names='value')
self.create_equation_rows(2)
# Display layout
self.input_area = widgets.VBox(
self.equation_widgets + [self.toggle_button, self.output_area]
)
self.container = widgets.HBox([self.input_area, self.plot_area])
display(self.container)
self.update_plot()
def create_equation_rows(self, count):
for i in range(count):
self.add_equation_row(i)
def add_equation_row(self, idx):
default = self.default_eqs[idx]
a = widgets.Text(value=str(default[0]), layout=widgets.Layout(width='60px'))
c = widgets.Text(value=str(default[1]), layout=widgets.Layout(width='60px'))
b = widgets.Text(value=str(default[2]), layout=widgets.Layout(width='60px'))
for box in (a, c, b):
box.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)
def toggle_third_equation(self, change):
if change['new']:
self.add_equation_row(2)
self.input_area.children = self.equation_widgets + [self.toggle_button, self.output_area]
self.toggle_button.description = '[-]'
self.third_eq_shown = True
else:
self.equation_widgets.pop()
self.input_area.children = self.equation_widgets + [self.toggle_button, self.output_area]
self.toggle_button.description = '[+]'
self.third_eq_shown = False
self.update_plot()
def parse_equations(self):
A, b = [], []
for row in self.equation_widgets:
a, c, b_ = row._entries
try:
a_val = float(a.value) if a.value.strip() else 1.0
c_val = float(c.value) if c.value.strip() else 1.0
b_val = float(b_.value) if b_.value.strip() else 1.0
A.append([a_val, c_val])
b.append(b_val)
except ValueError:
continue
return np.array(A), np.array(b)
def update_plot(self):
A, b = self.parse_equations()
with self.output_area:
clear_output()
if len(A) < 2:
print("Enter at least 2 valid equations.")
return
print(" A x = b")
for i in range(len(A)):
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}")
# Initialize flags
sol = None
show_dot = False
msg = ""
title_color = 'black'
try:
rank_A = np.linalg.matrix_rank(A)
Ab = np.hstack([A, b.reshape(-1, 1)])
rank_Ab = np.linalg.matrix_rank(Ab)
if rank_Ab != rank_A:
msg = "System is inconsistent: No solution."
title_color = 'red'
elif rank_A < A.shape[1]:
msg = "System is dependent: Infinite solutions."
title_color = 'blue'
else:
if A.shape[0] == A.shape[1]:
sol = np.linalg.solve(A, b)
msg = f"Unique solution: c = {sol[0]:.2f}, t = {sol[1]:.2f}" # Include t in the output
show_dot = True
title_color = 'green'
else:
sol, residuals, rank, s = np.linalg.lstsq(A, b, rcond=None)
msg = f"Least squares solution: c = {sol[0]:.2f}, t = {sol[1]:.2f}" # Include t in the output
show_dot = True
title_color = 'gray'
except Exception as e:
msg = f"Error solving system: {e}"
print("\n" + msg)
try:
cond = np.linalg.cond(A)
print(f"Condition number: {cond:.2e}")
except:
print("Condition number: N/A")
# Plotting
with self.plot_area:
clear_output(wait=True)
fig, ax = plt.subplots(figsize=(6, 6))
# Center on solution if available
if sol is not None:
x_center, y_center = sol
x_min, x_max = x_center - 20, x_center + 20
y_min, y_max = y_center - 20, y_center + 20
else:
x_min, x_max = -40, 40
y_min, y_max = -40, 40
x_vals = np.linspace(x_min, x_max, 1000)
for i in range(len(A)):
a, c = A[i]
rhs = b[i]
label = f"{a:.0f}c + {c:.0f}t = {rhs:.0f}"
if c != 0:
y_vals = (rhs - a * x_vals) / c
ax.plot(x_vals, y_vals, label=label)
elif a != 0:
ax.axvline(x=rhs / a, label=label)
else:
ax.axhline(y=rhs, label=label)
if sol is not None and show_dot:
ax.plot(*sol, 'ro', label="Solution")
ax.set_title(msg, color=title_color)
ax.set_xlim(x_min, x_max)
ax.set_ylim(y_min, y_max)
ax.axhline(0, color='black', lw=0.5)
ax.axvline(0, color='black', lw=0.5)
ax.set_xlabel("c")
ax.set_ylabel("t")
ax.legend()
plt.grid(True)
plt.tight_layout()
plt.show()
LinearSystemSolverNotebook()
