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import numpy as np

import matplotlib.pyplot as plt

from matplotlib.animation import FuncAnimation

# 1. Physics Parameters

h0 = 10           # Initial height (m)

vx_red = 2        # Horizontal velocity of red ball (m/s)

g = 9.81          # Gravity (m/s^2)

# 2. Time and Position Calculations

t_flight = np.sqrt(2 * h0 / g)

t = np.linspace(0, t_flight, num=60)

# Red Ball data (Projectile)

x_red = vx_red * t

y_red = h0 - 0.5 * g * t**2

# Velocity components for speed: v = sqrt(vx^2 + vy^2)

vy_red = -g * t  # Vertical velocity changes with time

speed_red = np.sqrt(vx_red**2 + vy_red**2)

# Black Ball data (Free Fall)

y_black = h0 - 0.5 * g * t**2

speed_black = g * t  # vx is 0, so speed is just |vy|

# 3. Setup Plot

fig, ax = plt.subplots(figsize=(10, 6))

ax.set_xlim(-1, max(x_red) + 2)

ax.set_ylim(-1, h0 + 2)

ax.set_title("Projectile Physics: Speed & Range Tracking")

# Visual elements

ball_black, = ax.plot([], [], 'ko', markersize=20)

ball_red, = ax.plot([], [], 'ro', markersize=20)

trail_red, = ax.plot([], [], 'r--', alpha=0.993)

# Text labels for data

stats_text = ax.text(0.05, 0.95, '', transform=ax.transAxes, 

                     bbox=dict(facecolor='white', alpha=0.5), verticalalignment='top')

# 4. Animation Logic

def update(frame):

    # Update positions

    ball_black.set_data([0], [y_black[frame]])

    ball_red.set_data([x_red[frame]], [y_red[frame]])

    trail_red.set_data(x_red[:frame], y_red[:frame])

    # Update text display

    current_range = x_red[frame]

    s_red = speed_red[frame]

    s_black = speed_black[frame]

    stats_text.set_text(

        f"Time: {t[frame]:.2f}s\n"

        f"--- Red Ball (Projectile) ---\n"

        f"Range: {current_range:.2f} m\n"

        f"Speed: {s_red:.2f} m/s\n"

        f"--- Black Ball (Free Fall) ---\n"

        f"Speed: {s_black:.2f} m/s"

    )

    return ball_black, ball_red, trail_red, stats_text

ani = FuncAnimation(fig, update, frames=len(t), blit=True, interval=50)

plt.grid(True, linestyle=':', alpha=0.6)

plt.show()

L = 6;            // number of spins

J = -1.0;            // Ising coupling

h = 1.0;          // transverse field

g = 1.0;         // longitudinal field

dim = 2^L;

// range of h

theta_min = 0.0;

theta_max = %pi/2.0;

dt = 0.01;

// open file

filename = "theta-vs-eg.dat";

fd = mopen(filename, "w");

// loop over h

for theta = theta_min:dt:theta_max

H = zeros(dim,dim);

// loop over basis states

for state = 0:dim-1

    row = state + 1;

    // -------- diagonal part (J * sigma_z sigma_z + g* sigma_z)  --------

    energy = 0;

    for i = 0:L-2

        if bitget(state,i+1) then

            si = 1;

        else

            si = -1;

        end

        if bitget(state,i+2) then

            sj = 1;

        else

            sj = -1;

        end

        energy = energy + J*si*sj;

    end

    // longitudinal field term

    for i = 0:L-1

        si = 2*bitget(state,i+1) - 1;

        energy = energy + g*cos(theta)*si;

    end

    H(row,row) = energy;

    // -------- transverse field (sigma_x) --------

    for i = 0:L-1

        flipped = bitxor(state, 2^i);   // flip spin i

        col = flipped + 1;

        H(row,col) = H(row,col) + h*sin(theta);

    end

end

// eigenvalues

    [V,D] = spec(H);

    eigvals = real(diag(D));

// write one line: h + all eigenvalues

    mfprintf(fd, "%f ", theta);

    for k = 1:dim

        mfprintf(fd, "%f ", eigvals(k));

    end

    mfprintf(fd, "\n");

    // write to file

//    for k = 1:length(eigvals)

//        mfprintf(fd, "%f %f\n", h, eigvals(k));

//    end

end

mclose(fd);

//disp("Data saved to filet");

data = read("theta-vs-eg.dat", -1, dim+1);  // 5 = 1 + number of eigenvalues

h = data(:,1);

// plot ALL eigenvalues together

plot(h, data(:,2:$));

// eigenvalues and eigenvectors

//[V,D] = spec(H);

//disp("Eigenvalues:");

//disp(diag(D));

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