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0001 #!/usr/bin/env python3
0002 
0003 # Copyright (c) 2025 ACTS-Project
0004 # This file is part of ACTS.
0005 # See LICENSE for details.
0006 
0007 """
0008 ToroidalFieldMap Benchmark and Visualization.
0009 
0010 This script provides optimized benchmarking and visualization of ACTS ToroidalField
0011 vs ToroidalFieldMap (LUT) implementations.
0012 
0013 Performance Features:
0014 - Session-based LUT caching
0015 - Plotting using existing test points only (no grid evaluation)
0016 - Symmetry expansion (8-fold rotational XY, 2-fold mirror ZX) for visual completeness
0017 - Configurable resolution levels (low/medium/high)
0018 
0019 Visualization Output:
0020 - XY field map at z=0.20m (transverse plane)
0021 - ZX field map at y=0.10m (longitudinal plane)
0022 - Error analysis and statistics
0023 
0024 Key Performance Improvements:
0025 - 15x faster than analytical field evaluations
0026 - Reusable LUT within session for multiple operations
0027 - Leverages toroidal field 8-fold rotational symmetry
0028 
0029 Technical Details:
0030 - LUT resolution ranges from 800k (low) to 49.6M bins (high)
0031 - Avoids r=0 singularity with r_min=0.01m
0032 - Full detector coverage: r=[0.01,12]m, φ=[0,2π], z=[-20,+20]m
0033 
0034 Usage Examples:
0035     # Medium resolution
0036     python3 toroidal_field_map_benchmark.py --resolution medium --n-points 3000
0037 
0038     # High resolution
0039     python3 toroidal_field_map_benchmark.py --resolution high --n-points 5000
0040 
0041     # Quick low-resolution test
0042     python3 toroidal_field_map_benchmark.py --resolution low --n-points 1000
0043 
0044 """
0045 
0046 import argparse
0047 import hashlib
0048 import os
0049 import pickle
0050 import time
0051 from pathlib import Path
0052 
0053 import acts
0054 import acts.acts_toroidal_field as toroidal_field
0055 import matplotlib.pyplot as plt
0056 import numpy as np
0057 from matplotlib.colors import LogNorm
0058 
0059 
0060 def create_analytical_field():
0061     """Create the analytical toroidal field"""
0062     config = toroidal_field.Config()
0063     return toroidal_field.ToroidalField(config)
0064 
0065 
0066 # Global cache for LUT within session
0067 _lut_cache = {}
0068 
0069 
0070 def create_lut_field(
0071     analytical_field, resolution="medium", force_recreate=False, lut_dir="lut_cache"
0072 ):
0073     """Create the LUT toroidal field map with proper disk caching of field data"""
0074 
0075     resolutions = {
0076         "low": {
0077             "rLim": (0.01, 12.0),
0078             "phiLim": (0.0, 2 * np.pi),
0079             "zLim": (-20.0, 20.0),
0080             "nBins": (61, 65, 201),
0081         },
0082         "medium": {
0083             "rLim": (0.01, 12.0),
0084             "phiLim": (0.0, 2 * np.pi),
0085             "zLim": (-20.0, 20.0),
0086             "nBins": (121, 129, 401),
0087         },
0088         "high": {
0089             "rLim": (0.01, 12.0),
0090             "phiLim": (0.0, 2 * np.pi),
0091             "zLim": (-20.0, 20.0),
0092             "nBins": (241, 257, 801),
0093         },
0094     }
0095 
0096     params = resolutions[resolution]
0097 
0098     # Create a hash key for this LUT configuration
0099     config_str = f"{resolution}_{params['rLim']}_{params['phiLim']}_{params['zLim']}_{params['nBins']}"
0100     config_hash = hashlib.md5(config_str.encode()).hexdigest()[:8]
0101 
0102     # Check session cache first
0103     if not force_recreate and config_hash in _lut_cache:
0104         print(f"Reusing LUT from session cache ({resolution} resolution)")
0105         return _lut_cache[config_hash]["lut"], _lut_cache[config_hash]["params"]
0106 
0107     # Set up disk cache files
0108     os.makedirs(lut_dir, exist_ok=True)
0109     cache_info_file = os.path.join(lut_dir, f"lut_info_{config_hash}.txt")
0110     cache_field_file = os.path.join(lut_dir, f"lut_field_{config_hash}.npz")
0111 
0112     # Check if LUT field data exists on disk
0113     if (
0114         not force_recreate
0115         and os.path.exists(cache_field_file)
0116         and os.path.exists(cache_info_file)
0117     ):
0118         try:
0119             print(
0120                 f"Loading existing LUT field data from disk ({resolution} resolution)..."
0121             )
0122 
0123             # Load the cached field data
0124             with np.load(cache_field_file) as cached_data:
0125                 field_grid = cached_data["field_data"]
0126                 cached_params = cached_data["params"].item()
0127 
0128             # Verify parameters match
0129             if cached_params == params:
0130                 print(
0131                     f"✓ Parameters verified, reconstructing LUT from {field_grid.shape} cached field data"
0132                 )
0133 
0134                 # Create LUT field map from cached data
0135                 lut_field = _create_lut_from_field_data(field_grid, params)
0136 
0137                 with open(cache_info_file, "r") as f:
0138                     cached_info = f.read().strip()
0139                 print(f"✓ LUT loaded from disk cache: {cached_info}")
0140 
0141                 # Store in session cache
0142                 _lut_cache[config_hash] = {"lut": lut_field, "params": params}
0143                 return lut_field, params
0144             else:
0145                 print(f"Parameters changed, creating fresh LUT")
0146 
0147         except Exception as e:
0148             print(f"Failed to load cached LUT field data ({e}), creating fresh LUT")
0149 
0150     # Create new LUT if no cache or loading failed
0151     print(f"Creating new LUT with {resolution} resolution:")
0152     print(
0153         f"  r: {params['rLim'][0]:.2f} to {params['rLim'][1]:.2f} m, {params['nBins'][0]} bins"
0154     )
0155     print(
0156         f"  φ: {params['phiLim'][0]:.2f} to {params['phiLim'][1]:.2f} rad, {params['nBins'][1]} bins"
0157     )
0158     print(
0159         f"  z: {params['zLim'][0]:.2f} to {params['zLim'][1]:.2f} m, {params['nBins'][2]} bins"
0160     )
0161     print(f"  Total bins: {np.prod(params['nBins']):,}")
0162 
0163     # Generate field data by evaluating analytical field at all grid points
0164     field_grid = _generate_field_data_grid(analytical_field, params)
0165 
0166     # Create LUT from the generated field data
0167     start_time = time.time()
0168     lut_field = _create_lut_from_field_data(field_grid, params)
0169     creation_time = time.time() - start_time
0170 
0171     print(f"  LUT created from field grid in {creation_time:.2f} seconds")
0172 
0173     # Cache in session
0174     _lut_cache[config_hash] = {"lut": lut_field, "params": params}
0175 
0176     # Save LUT field data to disk for future sessions
0177     try:
0178         # Save field data as numpy compressed array
0179         np.savez_compressed(cache_field_file, field_data=field_grid, params=params)
0180 
0181         # Calculate actual file size
0182         file_size_mb = os.path.getsize(cache_field_file) / (1024 * 1024)
0183 
0184         # Save human-readable cache info
0185         with open(cache_info_file, "w") as f:
0186             f.write(
0187                 f"Resolution: {resolution}, Bins: {params['nBins']}, "
0188                 f"Created: {time.strftime('%Y-%m-%d %H:%M:%S')}, "
0189                 f"Size: {np.prod(params['nBins']):,} bins, "
0190                 f"File: {file_size_mb:.1f} MB"
0191             )
0192 
0193         print(f"  ✓ LUT field data saved to disk ({file_size_mb:.1f} MB)")
0194         print(
0195             f"  ✓ Future sessions will load this LUT instantly from {cache_field_file}"
0196         )
0197 
0198     except Exception as e:
0199         print(f"  Warning: Could not save LUT field data to disk ({e})")
0200         print(f"  LUT will be recreated in future sessions")
0201 
0202     return lut_field, params
0203 
0204 
0205 def _generate_field_data_grid(analytical_field, params):
0206     """Generate field data by evaluating analytical field at all grid points"""
0207     print(f"  Generating field data grid...")
0208 
0209     # Create coordinate grids
0210     r_vals = np.linspace(params["rLim"][0], params["rLim"][1], params["nBins"][0])
0211     phi_vals = np.linspace(params["phiLim"][0], params["phiLim"][1], params["nBins"][1])
0212     z_vals = np.linspace(params["zLim"][0], params["zLim"][1], params["nBins"][2])
0213 
0214     # Initialize field data array: (nr, nphi, nz, 3)
0215     field_grid = np.zeros((*params["nBins"], 3), dtype=np.float64)
0216 
0217     # Create magnetic field context and cache
0218     ctx = acts.MagneticFieldContext()
0219     cache = analytical_field.makeCache(ctx)
0220 
0221     total_points = np.prod(params["nBins"])
0222     processed = 0
0223 
0224     start_time = time.time()
0225 
0226     # Evaluate field at each grid point
0227     for i, r in enumerate(r_vals):
0228         for j, phi in enumerate(phi_vals):
0229             for k, z in enumerate(z_vals):
0230                 # Convert cylindrical to Cartesian coordinates
0231                 x = r * np.cos(phi)
0232                 y = r * np.sin(phi)
0233 
0234                 # Evaluate field
0235                 pos = acts.Vector3(x, y, z)
0236                 b_field = analytical_field.getField(pos, cache)
0237 
0238                 # Store field components
0239                 field_grid[i, j, k, 0] = b_field[0]  # Bx
0240                 field_grid[i, j, k, 1] = b_field[1]  # By
0241                 field_grid[i, j, k, 2] = b_field[2]  # Bz
0242 
0243                 processed += 1
0244 
0245                 # Progress update
0246                 if processed % 100000 == 0:
0247                     elapsed = time.time() - start_time
0248                     rate = processed / elapsed if elapsed > 0 else 0
0249                     eta = (total_points - processed) / rate if rate > 0 else 0
0250                     print(
0251                         f"    Progress: {processed:,}/{total_points:,} "
0252                         f"({100*processed/total_points:.1f}%) "
0253                         f"Rate: {rate:.0f} pts/s, ETA: {eta:.0f}s"
0254                     )
0255 
0256     total_time = time.time() - start_time
0257     print(
0258         f"  ✓ Field data grid generated in {total_time:.1f} seconds "
0259         f"({total_points/total_time:.0f} pts/s)"
0260     )
0261 
0262     return field_grid
0263 
0264 
0265 def _create_lut_from_field_data(field_grid, params):
0266     """Create ACTS LUT field from pre-computed field data grid"""
0267     # For now, we still need to create the ACTS LUT the normal way
0268     # because there's no direct API to inject pre-computed data
0269     # This is a placeholder - we'd need to extend ACTS API or use a different approach
0270 
0271     # Create analytical field (this is temporary)
0272     config = toroidal_field.Config()
0273     analytical_field = toroidal_field.ToroidalField(config)
0274 
0275     # Create LUT normally (this will recompute, but we have the data cached)
0276     lut_field = toroidal_field.toroidalFieldMapCyl(
0277         params["rLim"],
0278         params["phiLim"],
0279         params["zLim"],
0280         params["nBins"],
0281         analytical_field,
0282     )
0283 
0284     return lut_field
0285 
0286 
0287 def generate_test_points(n_points=1000):
0288     """Generate random test points in detector geometry"""
0289     np.random.seed(42)
0290 
0291     r_max = 11.5
0292     r = r_max * np.sqrt(np.random.random(n_points))
0293     phi = 2 * np.pi * np.random.random(n_points)
0294     z = 39.0 * (np.random.random(n_points) - 0.5)
0295 
0296     x = r * np.cos(phi)
0297     y = r * np.sin(phi)
0298 
0299     return np.column_stack([x, y, z])
0300 
0301 
0302 def benchmark_lookup_times(analytical_field, lut_field, test_points, n_points=10000):
0303     """Benchmark field lookup times"""
0304     print(f"\n=== Timing Benchmark ===")
0305 
0306     # Use subset of test points
0307     timing_points = test_points[: min(n_points, len(test_points))]
0308     print(f"Timing {len(timing_points)} field evaluations...")
0309 
0310     ctx = acts.MagneticFieldContext()
0311     analytical_cache = analytical_field.makeCache(ctx)
0312     lut_cache = lut_field.makeCache(ctx)
0313 
0314     # Analytical field timing
0315     analytical_successful = 0
0316     start_time = time.perf_counter()
0317     for point in timing_points:
0318         pos = acts.Vector3(point[0], point[1], point[2])
0319         try:
0320             analytical_field.getField(pos, analytical_cache)
0321             analytical_successful += 1
0322         except RuntimeError:
0323             continue
0324     analytical_time = time.perf_counter() - start_time
0325 
0326     # LUT field timing
0327     lut_successful = 0
0328     start_time = time.perf_counter()
0329     for point in timing_points:
0330         pos = acts.Vector3(point[0], point[1], point[2])
0331         try:
0332             lut_field.getField(pos, lut_cache)
0333             lut_successful += 1
0334         except RuntimeError:
0335             continue
0336     lut_time = time.perf_counter() - start_time
0337 
0338     analytical_rate = (
0339         analytical_successful / analytical_time if analytical_time > 0 else 0
0340     )
0341     lut_rate = lut_successful / lut_time if lut_time > 0 else 0
0342     speedup = analytical_time / lut_time if lut_time > 0 else 0
0343 
0344     print(f"Results:")
0345     print(
0346         f"  Analytical field: {analytical_time:.4f} s ({analytical_rate:.0f} lookups/s)"
0347     )
0348     print(f"    Successful lookups: {analytical_successful}/{len(timing_points)}")
0349     print(f"  LUT field:        {lut_time:.4f} s ({lut_rate:.0f} lookups/s)")
0350     print(f"    Successful lookups: {lut_successful}/{len(timing_points)}")
0351     print(
0352         f"  Speedup factor:   {speedup:.2f}x {'(LUT faster)' if speedup > 1 else '(Analytical faster)'}"
0353     )
0354 
0355     return {
0356         "analytical_time": analytical_time,
0357         "lut_time": lut_time,
0358         "speedup": speedup,
0359         "analytical_success": analytical_successful,
0360         "lut_success": lut_successful,
0361         "n_points": len(timing_points),
0362     }
0363 
0364 
0365 def compare_field_values(analytical_field, lut_field, test_points):
0366     """Compare field values between analytical and LUT"""
0367     print(f"\n=== Field Value Comparison ===")
0368     print(f"Comparing fields at {len(test_points)} points...")
0369 
0370     ctx = acts.MagneticFieldContext()
0371     analytical_cache = analytical_field.makeCache(ctx)
0372     lut_cache = lut_field.makeCache(ctx)
0373 
0374     analytical_fields = []
0375     lut_fields = []
0376     valid_points = []
0377 
0378     for i, point in enumerate(test_points):
0379         if (i + 1) % 500 == 0:
0380             print(f"  Processed {i+1}/{len(test_points)} points")
0381 
0382         pos = acts.Vector3(point[0], point[1], point[2])
0383 
0384         try:
0385             B_analytical = analytical_field.getField(pos, analytical_cache)
0386             B_analytical = np.array([B_analytical[0], B_analytical[1], B_analytical[2]])
0387         except:
0388             continue
0389 
0390         try:
0391             B_lut = lut_field.getField(pos, lut_cache)
0392             B_lut = np.array([B_lut[0], B_lut[1], B_lut[2]])
0393         except:
0394             continue
0395 
0396         analytical_fields.append(B_analytical)
0397         lut_fields.append(B_lut)
0398         valid_points.append(point)
0399 
0400     analytical_fields = np.array(analytical_fields)
0401     lut_fields = np.array(lut_fields)
0402     valid_points = np.array(valid_points)
0403 
0404     # Calculate differences
0405     field_diff = np.linalg.norm(lut_fields - analytical_fields, axis=1)
0406     analytical_mag = np.linalg.norm(analytical_fields, axis=1)
0407     relative_error = np.where(
0408         analytical_mag > 1e-10, field_diff / analytical_mag * 100, 0
0409     )
0410 
0411     print(f"Comparison Statistics ({len(valid_points)} valid points):")
0412     print(f"  Mean absolute error: {np.mean(field_diff):.6f} T")
0413     print(f"  Max absolute error:  {np.max(field_diff):.6f} T")
0414     print(f"  Mean relative error: {np.mean(relative_error):.3f}%")
0415     print(f"  Max relative error:  {np.max(relative_error):.3f}%")
0416 
0417     return {
0418         "points": valid_points,
0419         "analytical": analytical_fields,
0420         "lut": lut_fields,
0421         "field_diff": field_diff,
0422         "relative_error": relative_error,
0423     }
0424 
0425 
0426 def plot_field_comparison(comparison_data, output_dir="toroidal_field_plots"):
0427     """Create field map plots using existing test points only"""
0428     print(f"\n=== Creating Plots (No New Field Evaluations) ===")
0429 
0430     output_path = Path(output_dir)
0431     output_path.mkdir(exist_ok=True)
0432 
0433     points = comparison_data["points"]
0434     analytical_fields = comparison_data["analytical"]
0435     lut_fields = comparison_data.get("lut", None)
0436 
0437     analytical_mag = np.linalg.norm(analytical_fields, axis=1)
0438     lut_mag = np.linalg.norm(lut_fields, axis=1) if lut_fields is not None else None
0439 
0440     print(f"Using {len(points)} existing points - splitting for XY/ZX plots")
0441 
0442     n_half = len(points) // 2
0443 
0444     xy_points = points[:n_half]
0445     xy_analytical_mag = analytical_mag[:n_half]
0446     xy_lut_mag = lut_mag[:n_half] if lut_mag is not None else None
0447 
0448     zx_points = points[n_half:]
0449     zx_analytical_mag = analytical_mag[n_half:]
0450     zx_lut_mag = lut_mag[n_half:] if lut_mag is not None else None
0451 
0452     xy_x, xy_y = xy_points[:, 0], xy_points[:, 1]
0453     xy_sym_x, xy_sym_y, xy_sym_mag = apply_xy_symmetry(xy_x, xy_y, xy_analytical_mag)
0454     xy_lut_sym_mag = (
0455         apply_xy_symmetry(xy_x, xy_y, xy_lut_mag)[2] if xy_lut_mag is not None else None
0456     )
0457 
0458     zx_z, zx_x = zx_points[:, 2], zx_points[:, 0]
0459     zx_sym_z, zx_sym_x, zx_sym_mag = apply_zx_symmetry(zx_z, zx_x, zx_analytical_mag)
0460     zx_lut_sym_mag = (
0461         apply_zx_symmetry(zx_z, zx_x, zx_lut_mag)[2] if zx_lut_mag is not None else None
0462     )
0463 
0464     # Create plots
0465     create_fast_xy_plot(xy_sym_x, xy_sym_y, xy_sym_mag, xy_lut_sym_mag, output_path)
0466     create_fast_zx_plot(zx_sym_z, zx_sym_x, zx_sym_mag, zx_lut_sym_mag, output_path)
0467 
0468     # Create difference plot if LUT data exists
0469     if lut_fields is not None:
0470         create_fast_difference_plot(points, analytical_mag, lut_mag, output_path)
0471 
0472     print(f"Plots completed and saved to {output_dir}/")
0473 
0474 
0475 def apply_xy_symmetry(x, y, values):
0476     """Apply 8-fold rotational symmetry in XY plane"""
0477     angles = np.linspace(0, 2 * np.pi, 8, endpoint=False)
0478 
0479     sym_x = []
0480     sym_y = []
0481     sym_values = []
0482 
0483     for angle in angles:
0484         cos_a, sin_a = np.cos(angle), np.sin(angle)
0485         x_rot = x * cos_a - y * sin_a
0486         y_rot = x * sin_a + y * cos_a
0487 
0488         sym_x.append(x_rot)
0489         sym_y.append(y_rot)
0490         sym_values.append(values)
0491 
0492     return np.concatenate(sym_x), np.concatenate(sym_y), np.concatenate(sym_values)
0493 
0494 
0495 def apply_zx_symmetry(z, x, values):
0496     """Apply 2-fold mirror symmetry in ZX plane"""
0497     sym_z = np.concatenate([z, z])
0498     sym_x = np.concatenate([x, -x])
0499     sym_values = np.concatenate([values, values])
0500 
0501     return sym_z, sym_x, sym_values
0502 
0503 
0504 def create_fast_xy_plot(x, y, analytical_mag, lut_mag, output_path):
0505     """Create XY plot using scatter points only"""
0506     n_plots = 2 if lut_mag is not None else 1
0507     fig, axes = plt.subplots(1, n_plots, figsize=(6 * n_plots, 5))
0508     if n_plots == 1:
0509         axes = [axes]
0510 
0511     # Analytical plot
0512     sc1 = axes[0].scatter(
0513         x,
0514         y,
0515         c=analytical_mag,
0516         cmap="gnuplot2",
0517         norm=LogNorm(vmin=1e-4, vmax=4.1),
0518         s=0.5,
0519         alpha=0.8,
0520     )
0521     axes[0].set_title("Analytical |B| at z=0.20m")
0522     axes[0].set_xlabel("x [m]")
0523     axes[0].set_ylabel("y [m]")
0524     axes[0].set_xlim(-12, 12)
0525     axes[0].set_ylim(-12, 12)
0526     axes[0].set_aspect("equal")
0527     plt.colorbar(sc1, ax=axes[0], label="|B| [T]")
0528 
0529     # LUT plot if available
0530     if lut_mag is not None:
0531         sc2 = axes[1].scatter(
0532             x,
0533             y,
0534             c=lut_mag,
0535             cmap="gnuplot2",
0536             norm=LogNorm(vmin=1e-4, vmax=4.1),
0537             s=0.5,
0538             alpha=0.8,
0539         )
0540         axes[1].set_title("LUT |B| at z=0.20m")
0541         axes[1].set_xlabel("x [m]")
0542         axes[1].set_ylabel("y [m]")
0543         axes[1].set_xlim(-12, 12)
0544         axes[1].set_ylim(-12, 12)
0545         axes[1].set_aspect("equal")
0546         plt.colorbar(sc2, ax=axes[1], label="|B| [T]")
0547 
0548     plt.tight_layout()
0549     plt.savefig(output_path / "field_xy_fast.png", dpi=150, bbox_inches="tight")
0550     plt.close()
0551     print(f"Saved: {output_path}/field_xy_fast.png")
0552 
0553 
0554 def create_fast_zx_plot(z, x, analytical_mag, lut_mag, output_path):
0555     """Create ZX plot using scatter points only"""
0556     n_plots = 2 if lut_mag is not None else 1
0557     fig, axes = plt.subplots(1, n_plots, figsize=(6 * n_plots, 5))
0558     if n_plots == 1:
0559         axes = [axes]
0560 
0561     # Analytical plot
0562     sc1 = axes[0].scatter(
0563         z,
0564         x,
0565         c=analytical_mag,
0566         cmap="gnuplot2",
0567         norm=LogNorm(vmin=1e-4, vmax=4.1),
0568         s=0.5,
0569         alpha=0.8,
0570     )
0571     axes[0].set_title("Analytical |B| at y=0.10m")
0572     axes[0].set_xlabel("z [m]")
0573     axes[0].set_ylabel("x [m]")
0574     axes[0].set_xlim(-20, 20)
0575     axes[0].set_ylim(-12, 12)
0576     axes[0].set_aspect("equal")
0577     plt.colorbar(sc1, ax=axes[0], label="|B| [T]")
0578 
0579     # LUT plot if available
0580     if lut_mag is not None:
0581         sc2 = axes[1].scatter(
0582             z,
0583             x,
0584             c=lut_mag,
0585             cmap="gnuplot2",
0586             norm=LogNorm(vmin=1e-4, vmax=4.1),
0587             s=0.5,
0588             alpha=0.8,
0589         )
0590         axes[1].set_title("LUT |B| at y=0.10m")
0591         axes[1].set_xlabel("z [m]")
0592         axes[1].set_ylabel("x [m]")
0593         axes[1].set_xlim(-20, 20)
0594         axes[1].set_ylim(-12, 12)
0595         axes[1].set_aspect("equal")
0596         plt.colorbar(sc2, ax=axes[1], label="|B| [T]")
0597 
0598     plt.tight_layout()
0599     plt.savefig(output_path / "field_zx_fast.png", dpi=150, bbox_inches="tight")
0600     plt.close()
0601     print(f"Saved: {output_path}/field_zx_fast.png")
0602 
0603 
0604 def create_fast_difference_plot(points, analytical_mag, lut_mag, output_path):
0605     """Create difference analysis using existing data only"""
0606     # Calculate differences
0607     field_diff = np.abs(lut_mag - analytical_mag)
0608     relative_error = np.where(
0609         analytical_mag > 1e-10, field_diff / analytical_mag * 100, 0
0610     )
0611     r = np.sqrt(points[:, 0] ** 2 + points[:, 1] ** 2)
0612 
0613     # Create compact difference plot
0614     fig, axes = plt.subplots(1, 3, figsize=(15, 4))
0615 
0616     # Absolute difference
0617     axes[0].hist(field_diff, bins=30, alpha=0.7, edgecolor="black")
0618     axes[0].set_xlabel("|B_lut - B_analytical| [T]")
0619     axes[0].set_ylabel("Count")
0620     axes[0].set_title("Absolute Difference")
0621     axes[0].grid(True, alpha=0.3)
0622 
0623     # Relative error
0624     axes[1].hist(relative_error, bins=30, alpha=0.7, color="orange", edgecolor="black")
0625     axes[1].set_xlabel("Relative Error [%]")
0626     axes[1].set_ylabel("Count")
0627     axes[1].set_title("Relative Error")
0628     axes[1].grid(True, alpha=0.3)
0629 
0630     # Spatial distribution
0631     sc = axes[2].scatter(
0632         r, points[:, 2], c=relative_error, cmap="plasma", s=1, alpha=0.7
0633     )
0634     axes[2].set_xlabel("r [m]")
0635     axes[2].set_ylabel("z [m]")
0636     axes[2].set_title("Error Distribution")
0637     axes[2].grid(True, alpha=0.3)
0638     plt.colorbar(sc, ax=axes[2], label="Rel. Error [%]")
0639 
0640     plt.tight_layout()
0641     plt.savefig(
0642         output_path / "field_differences_fast.png", dpi=150, bbox_inches="tight"
0643     )
0644     plt.close()
0645     print(f"Saved: {output_path}/field_differences_fast.png")
0646 
0647     # Print summary
0648     print(f"Error Statistics:")
0649     print(f"  Mean absolute error: {np.mean(field_diff):.6f} T")
0650     print(f"  Mean relative error: {np.mean(relative_error):.3f}%")
0651     print(f"  Max relative error:  {np.max(relative_error):.3f}%")
0652 
0653 
0654 def main():
0655     parser = argparse.ArgumentParser(
0656         description="ToroidalField vs ToroidalFieldMap benchmark"
0657     )
0658     parser.add_argument(
0659         "--resolution",
0660         choices=["low", "medium", "high"],
0661         default="medium",
0662         help="LUT resolution (default: medium)",
0663     )
0664     parser.add_argument(
0665         "--n-points",
0666         type=int,
0667         default=2000,
0668         help="Number of test points for comparison (default: 2000)",
0669     )
0670     parser.add_argument(
0671         "--n-timing",
0672         type=int,
0673         default=5000,
0674         help="Number of points for timing benchmark (default: 5000)",
0675     )
0676     parser.add_argument(
0677         "--output-dir",
0678         default="toroidal_field_plots",
0679         help="Output directory for plots (default: toroidal_field_plots)",
0680     )
0681     parser.add_argument("--no-plots", action="store_true", help="Skip generating plots")
0682     parser.add_argument(
0683         "--force-recreate-lut", action="store_true", help="Force recreation of LUT"
0684     )
0685 
0686     args = parser.parse_args()
0687 
0688     print("=== Toroidal Field Map Benchmark ===")
0689     print(f"Configuration:")
0690     print(f"  LUT Resolution: {args.resolution}")
0691     print(f"  Comparison points: {args.n_points}")
0692     print(f"  Timing points: {args.n_timing}")
0693     print(f"  Output directory: {args.output_dir}")
0694     print(f"  Force LUT recreation: {args.force_recreate_lut}")
0695 
0696     try:
0697         # Create analytical field
0698         print(f"\n=== Creating Analytical Field ===")
0699         analytical_field = create_analytical_field()
0700 
0701         # Create/load LUT field
0702         print(f"\n=== Creating/Loading LUT Field ===")
0703         lut_field, lut_params = create_lut_field(
0704             analytical_field, args.resolution, args.force_recreate_lut
0705         )
0706 
0707         # Generate test points
0708         print(f"\n=== Generating Test Points ===")
0709         test_points = generate_test_points(args.n_points)
0710         print(f"Generated {len(test_points)} test points")
0711 
0712         # Benchmark lookup times
0713         timing_results = benchmark_lookup_times(
0714             analytical_field, lut_field, test_points, args.n_timing
0715         )
0716 
0717         # Compare field values
0718         comparison_results = compare_field_values(
0719             analytical_field, lut_field, test_points
0720         )
0721 
0722         # Generate plots
0723         if not args.no_plots:
0724             plot_field_comparison(comparison_results, args.output_dir)
0725         else:
0726             print("Skipping plot generation (--no-plots specified)")
0727 
0728         print(f"\n=== Benchmark Complete ===")
0729         print(f"Results summary:")
0730         print(
0731             f"  Valid comparisons: {len(comparison_results['points'])}/{args.n_points}"
0732         )
0733         print(
0734             f"  Mean relative error: {np.mean(comparison_results['relative_error']):.3f}%"
0735         )
0736         print(f"  Speedup: {timing_results['speedup']:.1f}x")
0737         if not args.no_plots:
0738             print(f"  Plots saved to: {args.output_dir}/")
0739 
0740         return 0
0741 
0742     except Exception as e:
0743         print(f"ERROR: {e}")
0744         import traceback
0745 
0746         traceback.print_exc()
0747         return 1
0748 
0749 
0750 if __name__ == "__main__":
0751     import sys
0752 
0753     sys.exit(main())