""" Gradient Descent на разных поверхностях 4 loss landscapes side-by-side: convex, Rosenbrock, Rastrigin, saddle point 1080x1080, 25 seconds, 30fps, dark theme """ import numpy as np import matplotlib matplotlib.use('Agg') import matplotlib.pyplot as plt from matplotlib.animation import FuncAnimation, FFMpegWriter from matplotlib import cm from matplotlib.colors import LinearSegmentedColormap # === Config === FPS = 30 DURATION = 25 N_FRAMES = FPS * DURATION W, H = 1080, 1080 DPI = 120 # Dark theme BG_COLOR = '#1a1a2e' TEXT_COLOR = '#e0e0e0' ACCENT_COLORS = ['#00d2ff', '#ff6b6b', '#ffd93d', '#6bcb77'] # Custom colormap (dark-themed) colors_cmap = ['#1a1a2e', '#16213e', '#0f3460', '#533483', '#e94560'] custom_cmap = LinearSegmentedColormap.from_list('dark_heat', colors_cmap, N=256) # === Loss functions === def convex(x, y): return x**2 + y**2 def rosenbrock(x, y): a, b = 1, 100 return (a - x)**2 + b * (y - x**2)**2 def rastrigin(x, y): A = 10 return A * 2 + (x**2 - A * np.cos(2 * np.pi * x)) + (y**2 - A * np.cos(2 * np.pi * y)) def saddle(x, y): return x**2 - y**2 # === Gradients === def grad_convex(x, y): return 2*x, 2*y def grad_rosenbrock(x, y): a, b = 1, 100 dx = -2*(a - x) + b * 2 * (y - x**2) * (-2*x) dy = b * 2 * (y - x**2) return dx, dy def grad_rastrigin(x, y): A = 10 dx = 2*x + A * 2 * np.pi * np.sin(2 * np.pi * x) dy = 2*y + A * 2 * np.pi * np.sin(2 * np.pi * y) return dx, dy def grad_saddle(x, y): return 2*x, -2*y # === Pre-compute trajectories === def run_gd(grad_fn, x0, y0, lr, n_steps, clip_val=5.0): traj = [(x0, y0)] x, y = x0, y0 for _ in range(n_steps): gx, gy = grad_fn(x, y) # clip gradient norm = np.sqrt(gx**2 + gy**2) if norm > clip_val: gx, gy = gx * clip_val / norm, gy * clip_val / norm x -= lr * gx y -= lr * gy traj.append((x, y)) return np.array(traj) N_STEPS = N_FRAMES configs = [ { 'name': 'Convex (квадрат.)', 'func': convex, 'grad': grad_convex, 'x0': 1.8, 'y0': 1.8, 'lr': 0.02, 'xlim': (-2.5, 2.5), 'ylim': (-2.5, 2.5), 'color': ACCENT_COLORS[0], 'levels': 20, }, { 'name': 'Rosenbrock', 'func': rosenbrock, 'grad': grad_rosenbrock, 'x0': -1.5, 'y0': 2.0, 'lr': 0.0005, 'xlim': (-2.5, 2.5), 'ylim': (-1.5, 3.5), 'color': ACCENT_COLORS[1], 'levels': np.logspace(0, 4, 25), }, { 'name': 'Rastrigin', 'func': rastrigin, 'grad': grad_rastrigin, 'x0': 3.5, 'y0': 3.5, 'lr': 0.002, 'xlim': (-5, 5), 'ylim': (-5, 5), 'color': ACCENT_COLORS[2], 'levels': 25, }, { 'name': 'Седловая точка', 'func': saddle, 'grad': grad_saddle, 'x0': 1.5, 'y0': 0.3, 'lr': 0.01, 'xlim': (-2.5, 2.5), 'ylim': (-2.5, 2.5), 'color': ACCENT_COLORS[3], 'levels': 20, }, ] # Pre-compute trajectories = [] for cfg in configs: traj = run_gd(cfg['grad'], cfg['x0'], cfg['y0'], cfg['lr'], N_STEPS) trajectories.append(traj) # === Create figure === fig, axes = plt.subplots(2, 2, figsize=(W/DPI, H/DPI), dpi=DPI) fig.patch.set_facecolor(BG_COLOR) fig.suptitle('Gradient Descent на разных ландшафтах', fontsize=18, color=TEXT_COLOR, fontweight='bold', y=0.97, fontfamily='sans-serif') contour_sets = [] trail_lines = [] point_markers = [] loss_texts = [] step_text = fig.text(0.5, 0.015, '', ha='center', va='bottom', fontsize=13, color='#888888', fontfamily='monospace') for idx, (ax, cfg) in enumerate(zip(axes.flat, configs)): ax.set_facecolor(BG_COLOR) ax.set_xlim(cfg['xlim']) ax.set_ylim(cfg['ylim']) ax.set_aspect('equal') ax.set_title(cfg['name'], fontsize=13, color=cfg['color'], fontweight='bold', pad=6) ax.tick_params(colors='#555555', labelsize=7) for spine in ax.spines.values(): spine.set_color('#333355') # Contour xx = np.linspace(cfg['xlim'][0], cfg['xlim'][1], 300) yy = np.linspace(cfg['ylim'][0], cfg['ylim'][1], 300) X, Y = np.meshgrid(xx, yy) Z = cfg['func'](X, Y) if isinstance(cfg['levels'], np.ndarray): cs = ax.contourf(X, Y, Z, levels=cfg['levels'], cmap=custom_cmap, alpha=0.85) ax.contour(X, Y, Z, levels=cfg['levels'], colors='#333355', linewidths=0.3, alpha=0.5) else: cs = ax.contourf(X, Y, Z, levels=cfg['levels'], cmap=custom_cmap, alpha=0.85) ax.contour(X, Y, Z, levels=cfg['levels'], colors='#333355', linewidths=0.3, alpha=0.5) contour_sets.append(cs) # Trail line line, = ax.plot([], [], color=cfg['color'], linewidth=1.5, alpha=0.7) trail_lines.append(line) # Current point point, = ax.plot([], [], 'o', color=cfg['color'], markersize=8, markeredgecolor='white', markeredgewidth=1.5, zorder=10) point_markers.append(point) # Loss text txt = ax.text(0.05, 0.92, '', transform=ax.transAxes, fontsize=9, color=cfg['color'], fontfamily='monospace', fontweight='bold', bbox=dict(boxstyle='round,pad=0.3', facecolor=BG_COLOR, edgecolor=cfg['color'], alpha=0.8)) loss_texts.append(txt) plt.tight_layout(rect=[0.01, 0.04, 0.99, 0.94]) def animate(frame): for idx, cfg in enumerate(configs): traj = trajectories[idx] # Show trajectory up to current frame show_len = min(frame + 1, len(traj)) trail_lines[idx].set_data(traj[:show_len, 0], traj[:show_len, 1]) cx, cy = traj[min(frame, len(traj)-1)] point_markers[idx].set_data([cx], [cy]) loss_val = cfg['func'](cx, cy) loss_texts[idx].set_text(f'L = {loss_val:.2f}') step_text.set_text(f'step {frame}/{N_FRAMES}') return trail_lines + point_markers + loss_texts + [step_text] anim = FuncAnimation(fig, animate, frames=N_FRAMES, interval=1000/FPS, blit=True) outpath = '/root/Strategy/content/generated/gradient_surfaces_animation.mp4' writer = FFMpegWriter(fps=FPS, bitrate=3000, extra_args=['-vcodec', 'libx264', '-pix_fmt', 'yuv420p']) anim.save(outpath, writer=writer) plt.close() print(f"Saved: {outpath}")