# normal_gui_fixed_xy.py
import tkinter as tk
from tkinter import ttk
import numpy as np
import matplotlib
import matplotlib.pyplot as plt
from matplotlib.backends.backend_tkagg import FigureCanvasTkAgg

matplotlib.use('TkAgg')


def generate_data(mu, sigma, n=1000):
    """Generate n samples from N(μ,σ²)."""
    return np.random.normal(loc=mu, scale=sigma, size=n)


def draw_plot(ax, mu, sigma):
    """Redraw histogram + theoretical PDF while keeping axis limits fixed."""
    ax.clear()
    data = generate_data(mu, sigma)

    # Histogram (density=True → area = 1)
    ax.hist(data, bins=30, density=True, alpha=0.6, color='steelblue')

    # Theoretical normal PDF evaluated on the fixed x‑range
    x = np.linspace(FIXED_XMIN, FIXED_XMAX, 300)
    pdf = (1 / (sigma * np.sqrt(2 * np.pi))) * np.exp(-0.5 * ((x - mu) / sigma) ** 2)
    ax.plot(x, pdf, color='darkred', lw=2)

    ax.set_title(f'Normal Distribution (μ={mu:.2f}, σ={sigma:.2f})')
    ax.set_xlabel('Value')
    ax.set_ylabel('Density')

    # Keep the pre‑defined limits
    ax.set_xlim(FIXED_XMIN, FIXED_XMAX)
    ax.set_ylim(FIXED_YMIN, FIXED_YMAX)
    ax.figure.canvas.draw_idle()


# -------------------- Fixed axis limits --------------------
# X limits: wide enough for all µ (±10) plus 4 σ (max σ = 5)
FIXED_XMIN = -15
FIXED_XMAX = 15

# Y limits: maximum PDF occurs at the smallest σ (0.1)
#   peak = 1/(σ·√(2π)) ≈ 3.989 for σ=0.1 → give a small margin
FIXED_YMIN = 0
FIXED_YMAX = 4.5


# -------------------- Tkinter UI --------------------
root = tk.Tk()
root.title("Normal Distribution Explorer (fixed X & Y axes)")

fig, ax = plt.subplots(figsize=(5, 3), dpi=100)
canvas = FigureCanvasTkAgg(fig, master=root)
canvas.get_tk_widget().pack(fill=tk.BOTH, expand=True)

slider_frame = ttk.Frame(root, padding=10)
slider_frame.pack(fill=tk.X)

# µ (mean) slider
mu_label = ttk.Label(slider_frame, text="μ (mean):")
mu_label.grid(row=0, column=0, sticky="w")
mu_var = tk.DoubleVar(value=0.0)
mu_slider = ttk.Scale(
    slider_frame,
    from_=-10, to=10, orient="horizontal",
    variable=mu_var,
    command=lambda e: draw_plot(ax, mu_var.get(), sigma_var.get())
)
mu_slider.grid(row=0, column=1, sticky="ew", padx=5)

# σ (std dev) slider
sigma_label = ttk.Label(slider_frame, text="σ (std dev):")
sigma_label.grid(row=1, column=0, sticky="w")
sigma_var = tk.DoubleVar(value=1.0)
sigma_slider = ttk.Scale(
    slider_frame,
    from_=0.1, to=5, orient="horizontal",
    variable=sigma_var,
    command=lambda e: draw_plot(ax, mu_var.get(), sigma_var.get())
)
sigma_slider.grid(row=1, column=1, sticky="ew", padx=5)

slider_frame.columnconfigure(1, weight=1)

# Initial plot with fixed limits
draw_plot(ax, mu_var.get(), sigma_var.get())

root.mainloop()