Commit e16a786351dad4a157db455ed25590ae945dcf69
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72358246
Add IRF display script
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examples/show_irf.py
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| 1 | +#! /usr/bin/env python | |
| 2 | +# ========================================================================== | |
| 3 | +# Display Instrument Response Function | |
| 4 | +# | |
| 5 | +# Copyright (C) 2017 Juergen Knoedlseder | |
| 6 | +# | |
| 7 | +# This program is free software: you can redistribute it and/or modify | |
| 8 | +# it under the terms of the GNU General Public License as published by | |
| 9 | +# the Free Software Foundation, either version 3 of the License, or | |
| 10 | +# (at your option) any later version. | |
| 11 | +# | |
| 12 | +# This program is distributed in the hope that it will be useful, | |
| 13 | +# but WITHOUT ANY WARRANTY; without even the implied warranty of | |
| 14 | +# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | |
| 15 | +# GNU General Public License for more details. | |
| 16 | +# | |
| 17 | +# You should have received a copy of the GNU General Public License | |
| 18 | +# along with this program. If not, see <http://www.gnu.org/licenses/>. | |
| 19 | +# | |
| 20 | +# ========================================================================== | |
| 21 | +import sys | |
| 22 | +import math | |
| 23 | +import gammalib | |
| 24 | +import cscripts | |
| 25 | +try: | |
| 26 | + import matplotlib.pyplot as plt | |
| 27 | + plt.figure() | |
| 28 | + plt.close() | |
| 29 | +except (ImportError, RuntimeError): | |
| 30 | + print('This script needs the "matplotlib" module') | |
| 31 | + sys.exit() | |
| 32 | + | |
| 33 | + | |
| 34 | +# ========= # | |
| 35 | +# Plot Aeff # | |
| 36 | +# ========= # | |
| 37 | +def plot_aeff(sub, aeff, emin=None, emax=None, tmin=None, tmax=None, | |
| 38 | + nengs=100, nthetas=100): | |
| 39 | + """ | |
| 40 | + Plot effective area | |
| 41 | + | |
| 42 | + Parameters | |
| 43 | + ---------- | |
| 44 | + sub : figure | |
| 45 | + Subplot | |
| 46 | + aeff : `~gammalib.GCTAAeff2d` | |
| 47 | + Instrument Response Function | |
| 48 | + emin : float, optional | |
| 49 | + Minimum energy (TeV) | |
| 50 | + emax : float, optional | |
| 51 | + Maximum energy (TeV) | |
| 52 | + tmin : float, optional | |
| 53 | + Minimum offset angle (deg) | |
| 54 | + tmax : float, optional | |
| 55 | + Maximum offset angle (deg) | |
| 56 | + nengs : int, optional | |
| 57 | + Number of energies | |
| 58 | + nthetas : int, optional | |
| 59 | + Number of offset angles | |
| 60 | + """ | |
| 61 | + # Determine energy range | |
| 62 | + ieng = aeff.table().axis('ENERG') | |
| 63 | + neng = aeff.table().axis_bins(ieng) | |
| 64 | + if emin == None: | |
| 65 | + emin = aeff.table().axis_lo(ieng, 0) | |
| 66 | + if emax == None: | |
| 67 | + emax = aeff.table().axis_hi(ieng, neng-1) | |
| 68 | + | |
| 69 | + # Determine offset angle range | |
| 70 | + itheta = aeff.table().axis('THETA') | |
| 71 | + ntheta = aeff.table().axis_bins(itheta) | |
| 72 | + if tmin == None: | |
| 73 | + tmin = aeff.table().axis_lo(itheta, 0) | |
| 74 | + if tmax == None: | |
| 75 | + tmax = aeff.table().axis_hi(itheta, ntheta-1) | |
| 76 | + | |
| 77 | + # Use log energies | |
| 78 | + emin = math.log10(emin) | |
| 79 | + emax = math.log10(emax) | |
| 80 | + | |
| 81 | + # Set axes | |
| 82 | + denergy = (emax - emin)/(nengs-1) | |
| 83 | + dtheta = (tmax - tmin)/(nthetas-1) | |
| 84 | + logenergies = [emin+i*denergy for i in range(nengs)] | |
| 85 | + thetas = [tmax-i*dtheta for i in range(nthetas)] | |
| 86 | + | |
| 87 | + # Initialise image | |
| 88 | + image = [] | |
| 89 | + | |
| 90 | + # Loop over offset angles | |
| 91 | + for theta in thetas: | |
| 92 | + | |
| 93 | + # Initialise row | |
| 94 | + row = [] | |
| 95 | + | |
| 96 | + # Loop over energies | |
| 97 | + for logenergy in logenergies: | |
| 98 | + | |
| 99 | + # Get effective area value | |
| 100 | + value = aeff(logenergy, theta*gammalib.deg2rad) | |
| 101 | + | |
| 102 | + # Append value | |
| 103 | + row.append(value) | |
| 104 | + | |
| 105 | + # Append row | |
| 106 | + image.append(row) | |
| 107 | + | |
| 108 | + # Plot image | |
| 109 | + sub.imshow(image, extent=[emin,emax,tmin,tmax], aspect=0.5) | |
| 110 | + | |
| 111 | + # Show boundary contours | |
| 112 | + contours = sub.contour(logenergies, thetas, image, [0.0], colors=('white')) | |
| 113 | + sub.clabel(contours, inline=1, fontsize=8) | |
| 114 | + | |
| 115 | + # Plot title and axis | |
| 116 | + sub.set_title('Effective area') | |
| 117 | + sub.set_xlabel('log10(E/TeV)') | |
| 118 | + sub.set_ylabel('Offset angle (deg)') | |
| 119 | + | |
| 120 | + # Return | |
| 121 | + return | |
| 122 | + | |
| 123 | + | |
| 124 | +# ======== # | |
| 125 | +# Plot PSF # | |
| 126 | +# ======== # | |
| 127 | +def plot_psf(sub, psf, emin=None, emax=None, tmin=None, tmax=None, | |
| 128 | + nengs=100, nthetas=100): | |
| 129 | + """ | |
| 130 | + Plot Point Spread Function | |
| 131 | + | |
| 132 | + Parameters | |
| 133 | + ---------- | |
| 134 | + sub : figure | |
| 135 | + Subplot | |
| 136 | + psf : `~gammalib.GCTAPsf2D` | |
| 137 | + Instrument Response Function | |
| 138 | + emin : float, optional | |
| 139 | + Minimum energy (TeV) | |
| 140 | + emax : float, optional | |
| 141 | + Maximum energy (TeV) | |
| 142 | + tmin : float, optional | |
| 143 | + Minimum offset angle (deg) | |
| 144 | + tmax : float, optional | |
| 145 | + Maximum offset angle (deg) | |
| 146 | + nengs : int, optional | |
| 147 | + Number of energies | |
| 148 | + nthetas : int, optional | |
| 149 | + Number of offset angles | |
| 150 | + """ | |
| 151 | + # Determine energy range | |
| 152 | + ieng = psf.table().axis('ENERG') | |
| 153 | + neng = psf.table().axis_bins(ieng) | |
| 154 | + if emin == None: | |
| 155 | + emin = psf.table().axis_lo(ieng, 0) | |
| 156 | + if emax == None: | |
| 157 | + emax = psf.table().axis_hi(ieng, neng-1) | |
| 158 | + | |
| 159 | + # Determine offset angle range | |
| 160 | + itheta = psf.table().axis('THETA') | |
| 161 | + ntheta = psf.table().axis_bins(itheta) | |
| 162 | + if tmin == None: | |
| 163 | + tmin = psf.table().axis_lo(itheta, 0) | |
| 164 | + if tmax == None: | |
| 165 | + tmax = psf.table().axis_hi(itheta, ntheta-1) | |
| 166 | + | |
| 167 | + # Use log energies | |
| 168 | + emin = math.log10(emin) | |
| 169 | + emax = math.log10(emax) | |
| 170 | + | |
| 171 | + # Set axes | |
| 172 | + denergy = (emax - emin)/(nengs-1) | |
| 173 | + dtheta = (tmax - tmin)/(nthetas-1) | |
| 174 | + logenergies = [emin+i*denergy for i in range(nengs)] | |
| 175 | + thetas = [tmax-i*dtheta for i in range(nthetas)] | |
| 176 | + | |
| 177 | + # Initialise image | |
| 178 | + image = [] | |
| 179 | + | |
| 180 | + # Loop over offset angles | |
| 181 | + for theta in thetas: | |
| 182 | + | |
| 183 | + # Initialise row | |
| 184 | + row = [] | |
| 185 | + | |
| 186 | + # Loop over energies | |
| 187 | + for logenergy in logenergies: | |
| 188 | + | |
| 189 | + # Get containment radius value | |
| 190 | + value = psf.containment_radius(0.68, logenergy, theta*gammalib.deg2rad) * \ | |
| 191 | + gammalib.rad2deg | |
| 192 | + | |
| 193 | + # Limit containment radius values to [0.0,0.5] | |
| 194 | + if value < 0.0: | |
| 195 | + value = 0.0 | |
| 196 | + if value > 0.5: | |
| 197 | + value = 0.5 | |
| 198 | + | |
| 199 | + # Append value | |
| 200 | + row.append(value) | |
| 201 | + | |
| 202 | + # Append row | |
| 203 | + image.append(row) | |
| 204 | + | |
| 205 | + # Plot image | |
| 206 | + sub.imshow(image, extent=[emin,emax,tmin,tmax], aspect=0.5) | |
| 207 | + | |
| 208 | + # Show boundary contours | |
| 209 | + contours = sub.contour(logenergies, thetas, image, [0.0], colors=('white')) | |
| 210 | + sub.clabel(contours, inline=1, fontsize=8) | |
| 211 | + | |
| 212 | + # Plot title and axis | |
| 213 | + if psf.classname() == 'GCTAPsfKing': | |
| 214 | + sub.set_title('King function PSF 68% containment radius') | |
| 215 | + else: | |
| 216 | + sub.set_title('Gaussian PSF 68% containment radius') | |
| 217 | + sub.set_xlabel('log10(E/TeV)') | |
| 218 | + sub.set_ylabel('Offset angle (deg)') | |
| 219 | + | |
| 220 | + # Return | |
| 221 | + return | |
| 222 | + | |
| 223 | + | |
| 224 | +# ====================== # | |
| 225 | +# Plot energy dispersion # | |
| 226 | +# ====================== # | |
| 227 | +def plot_edisp(sub, edisp, emin=None, emax=None, tmin=None, tmax=None, | |
| 228 | + nengs=100, nthetas=100): | |
| 229 | + """ | |
| 230 | + Plot Background template | |
| 231 | + | |
| 232 | + Parameters | |
| 233 | + ---------- | |
| 234 | + sub : figure | |
| 235 | + Subplot | |
| 236 | + edisp : `~gammalib.GCTAEdisp2D` | |
| 237 | + Instrument Response Function | |
| 238 | + emin : float, optional | |
| 239 | + Minimum energy (TeV) | |
| 240 | + emax : float, optional | |
| 241 | + Maximum energy (TeV) | |
| 242 | + tmin : float, optional | |
| 243 | + Minimum offset angle (deg) | |
| 244 | + tmax : float, optional | |
| 245 | + Maximum offset angle (deg) | |
| 246 | + nengs : int, optional | |
| 247 | + Number of energies | |
| 248 | + nthetas : int, optional | |
| 249 | + Number of offset angles | |
| 250 | + """ | |
| 251 | + # Determine energy range | |
| 252 | + ieng = edisp.table().axis('ETRUE') | |
| 253 | + neng = edisp.table().axis_bins(ieng) | |
| 254 | + if emin == None: | |
| 255 | + emin = edisp.table().axis_lo(ieng, 0) | |
| 256 | + if emax == None: | |
| 257 | + emax = edisp.table().axis_hi(ieng, neng-1) | |
| 258 | + | |
| 259 | + # Determine offset angle range | |
| 260 | + itheta = edisp.table().axis('THETA') | |
| 261 | + ntheta = edisp.table().axis_bins(itheta) | |
| 262 | + if tmin == None: | |
| 263 | + tmin = edisp.table().axis_lo(itheta, 0) | |
| 264 | + if tmax == None: | |
| 265 | + tmax = edisp.table().axis_hi(itheta, ntheta-1) | |
| 266 | + | |
| 267 | + # Use log energies | |
| 268 | + emin = math.log10(emin) | |
| 269 | + emax = math.log10(emax) | |
| 270 | + | |
| 271 | + # Set axes | |
| 272 | + denergy = (emax - emin)/(nengs-1) | |
| 273 | + dtheta = (tmax - tmin)/(nthetas-1) | |
| 274 | + logenergies = [emin+i*denergy for i in range(nengs)] | |
| 275 | + thetas = [tmax-i*dtheta for i in range(nthetas)] | |
| 276 | + | |
| 277 | + # Initialise image | |
| 278 | + image = [] | |
| 279 | + | |
| 280 | + # Loop over offset angles | |
| 281 | + for theta in thetas: | |
| 282 | + | |
| 283 | + # Initialise row | |
| 284 | + row = [] | |
| 285 | + | |
| 286 | + # Compute detx and dety | |
| 287 | + detx = theta*gammalib.deg2rad | |
| 288 | + dety = 0.0 | |
| 289 | + | |
| 290 | + # Loop over energies | |
| 291 | + for logenergy in logenergies: | |
| 292 | + | |
| 293 | + # Get no migration energy dispersion value | |
| 294 | + value = edisp(logenergy, logenergy, theta*gammalib.deg2rad) | |
| 295 | + | |
| 296 | + # Append value | |
| 297 | + row.append(value) | |
| 298 | + | |
| 299 | + # Append row | |
| 300 | + image.append(row) | |
| 301 | + | |
| 302 | + # Plot image | |
| 303 | + sub.imshow(image, extent=[emin,emax,tmin,tmax], aspect=0.5) | |
| 304 | + | |
| 305 | + # Show boundary contours | |
| 306 | + contours = sub.contour(logenergies, thetas, image, [0.0], colors=('white')) | |
| 307 | + sub.clabel(contours, inline=1, fontsize=8) | |
| 308 | + | |
| 309 | + # Plot title and axis | |
| 310 | + sub.set_title('No migration energy dispersion') | |
| 311 | + sub.set_xlabel('log10(E/TeV)') | |
| 312 | + sub.set_ylabel('Offset angle (deg)') | |
| 313 | + | |
| 314 | + # Return | |
| 315 | + return | |
| 316 | + | |
| 317 | + | |
| 318 | +# =============== # | |
| 319 | +# Plot Background # | |
| 320 | +# =============== # | |
| 321 | +def plot_bkg(sub, bkg, emin=None, emax=None, tmin=None, tmax=None, | |
| 322 | + nengs=100, nthetas=100): | |
| 323 | + """ | |
| 324 | + Plot Background template | |
| 325 | + | |
| 326 | + Parameters | |
| 327 | + ---------- | |
| 328 | + sub : figure | |
| 329 | + Subplot | |
| 330 | + bkg : `~gammalib.GCTABackground3D` | |
| 331 | + Instrument Response Function | |
| 332 | + emin : float, optional | |
| 333 | + Minimum energy (TeV) | |
| 334 | + emax : float, optional | |
| 335 | + Maximum energy (TeV) | |
| 336 | + tmin : float, optional | |
| 337 | + Minimum offset angle (deg) | |
| 338 | + tmax : float, optional | |
| 339 | + Maximum offset angle (deg) | |
| 340 | + nengs : int, optional | |
| 341 | + Number of energies | |
| 342 | + nthetas : int, optional | |
| 343 | + Number of offset angles | |
| 344 | + """ | |
| 345 | + # Determine energy range | |
| 346 | + ieng = bkg.table().axis('ENERG') | |
| 347 | + neng = bkg.table().axis_bins(ieng) | |
| 348 | + if emin == None: | |
| 349 | + emin = bkg.table().axis_lo(ieng, 0) | |
| 350 | + if emax == None: | |
| 351 | + emax = bkg.table().axis_hi(ieng, neng-1) | |
| 352 | + | |
| 353 | + # Determine offset angle range | |
| 354 | + if tmin == None: | |
| 355 | + tmin = 0.0 | |
| 356 | + if tmax == None: | |
| 357 | + tmax = 6.0 | |
| 358 | + | |
| 359 | + # Use log energies | |
| 360 | + emin = math.log10(emin) | |
| 361 | + emax = math.log10(emax) | |
| 362 | + | |
| 363 | + # Set axes | |
| 364 | + denergy = (emax - emin)/(nengs-1) | |
| 365 | + dtheta = (tmax - tmin)/(nthetas-1) | |
| 366 | + logenergies = [emin+i*denergy for i in range(nengs)] | |
| 367 | + thetas = [tmax-i*dtheta for i in range(nthetas)] | |
| 368 | + | |
| 369 | + # Initialise image | |
| 370 | + image = [] | |
| 371 | + | |
| 372 | + # Loop over offset angles | |
| 373 | + for theta in thetas: | |
| 374 | + | |
| 375 | + # Initialise row | |
| 376 | + row = [] | |
| 377 | + | |
| 378 | + # Compute detx and dety | |
| 379 | + detx = theta*gammalib.deg2rad | |
| 380 | + dety = 0.0 | |
| 381 | + | |
| 382 | + # Loop over energies | |
| 383 | + for logenergy in logenergies: | |
| 384 | + | |
| 385 | + # Get containment radius value | |
| 386 | + value = bkg(logenergy, detx, dety) | |
| 387 | + | |
| 388 | + # Append value | |
| 389 | + row.append(value) | |
| 390 | + | |
| 391 | + # Append row | |
| 392 | + image.append(row) | |
| 393 | + | |
| 394 | + # Plot image | |
| 395 | + sub.imshow(image, extent=[emin,emax,tmin,tmax], aspect=0.5) | |
| 396 | + | |
| 397 | + # Show boundary contours | |
| 398 | + contours = sub.contour(logenergies, thetas, image, [0.0], colors=('white')) | |
| 399 | + sub.clabel(contours, inline=1, fontsize=8) | |
| 400 | + | |
| 401 | + # Plot title and axis | |
| 402 | + sub.set_title('Background acceptance') | |
| 403 | + sub.set_xlabel('log10(E/TeV)') | |
| 404 | + sub.set_ylabel('Offset angle (deg)') | |
| 405 | + | |
| 406 | + # Return | |
| 407 | + return | |
| 408 | + | |
| 409 | + | |
| 410 | +# ======== # | |
| 411 | +# Plot IRF # | |
| 412 | +# ======== # | |
| 413 | +def plot_irf(irf, emin, emax, tmin, tmax, plotfile): | |
| 414 | + """ | |
| 415 | + Plot Instrument Response Function | |
| 416 | + | |
| 417 | + Parameters | |
| 418 | + ---------- | |
| 419 | + irf : `~gammalib.GCTAResponseIrf` | |
| 420 | + Instrument Response Function | |
| 421 | + emin : float | |
| 422 | + Minimum energy (TeV) | |
| 423 | + emax : float | |
| 424 | + Maximum energy (TeV) | |
| 425 | + tmin : float | |
| 426 | + Minimum offset angle (deg) | |
| 427 | + tmax : float | |
| 428 | + Maximum offset angle (deg) | |
| 429 | + plotfile : str | |
| 430 | + Plot filename | |
| 431 | + """ | |
| 432 | + # Build selection string | |
| 433 | + selection = '' | |
| 434 | + eselection = '' | |
| 435 | + tselection = '' | |
| 436 | + if emin != None and emax != None: | |
| 437 | + eselection += '%.3f-%.1f TeV' % (emin, emax) | |
| 438 | + elif emin != None: | |
| 439 | + eselection += ' >%.3f TeV' % (emin) | |
| 440 | + elif emax != None: | |
| 441 | + eselection += ' <%.1f TeV' % (emax) | |
| 442 | + if tmin != None and tmax != None: | |
| 443 | + tselection += '%.1f-%.1f deg' % (tmin, tmax) | |
| 444 | + elif tmin != None: | |
| 445 | + tselection += ' >%.1f deg' % (tmin) | |
| 446 | + elif tmax != None: | |
| 447 | + tselection += ' <%.1f deg' % (tmax) | |
| 448 | + if len(eselection) > 0 and len(tselection) > 0: | |
| 449 | + selection = ' (%s, %s)' % (eselection, tselection) | |
| 450 | + elif len(eselection) > 0: | |
| 451 | + selection = ' (%s)' % (eselection) | |
| 452 | + elif len(tselection) > 0: | |
| 453 | + selection = ' (%s)' % (tselection) | |
| 454 | + | |
| 455 | + # Build title | |
| 456 | + mission = irf.caldb().mission() | |
| 457 | + instrument = irf.caldb().instrument() | |
| 458 | + response = irf.rspname() | |
| 459 | + title = '%s "%s" Instrument Response Function "%s"%s' % \ | |
| 460 | + (gammalib.toupper(mission), instrument, response, selection) | |
| 461 | + | |
| 462 | + # Create figure | |
| 463 | + fig = plt.figure(figsize=(12,8)) | |
| 464 | + | |
| 465 | + # Add title | |
| 466 | + fig.suptitle(title, fontsize=16) | |
| 467 | + | |
| 468 | + # Plot Aeff | |
| 469 | + ax1 = fig.add_subplot(221) | |
| 470 | + plot_aeff(ax1, irf.aeff(), emin=emin, emax=emax, tmin=tmin, tmax=tmax) | |
| 471 | + | |
| 472 | + # Plot Psf | |
| 473 | + ax2 = fig.add_subplot(222) | |
| 474 | + plot_psf(ax2, irf.psf(), emin=emin, emax=emax, tmin=tmin, tmax=tmax) | |
| 475 | + | |
| 476 | + # Plot Edisp | |
| 477 | + ax3 = fig.add_subplot(223) | |
| 478 | + plot_edisp(ax3, irf.edisp(), emin=emin, emax=emax, tmin=tmin, tmax=tmax) | |
| 479 | + | |
| 480 | + # Plot Background | |
| 481 | + ax4 = fig.add_subplot(224) | |
| 482 | + plot_bkg(ax4, irf.background(), emin=emin, emax=emax, tmin=tmin, tmax=tmax) | |
| 483 | + | |
| 484 | + # Show plots or save it into file | |
| 485 | + if len(plotfile) > 0: | |
| 486 | + plt.savefig(plotfile) | |
| 487 | + else: | |
| 488 | + plt.show() | |
| 489 | + | |
| 490 | + # Return | |
| 491 | + return | |
| 492 | + | |
| 493 | + | |
| 494 | +# ======== # | |
| 495 | +# Show IRF # | |
| 496 | +# ======== # | |
| 497 | +def show_irf(): | |
| 498 | + """ | |
| 499 | + Show Instrument Response Function | |
| 500 | + """ | |
| 501 | + # Set usage string | |
| 502 | + usage = 'show_irf.py [-p plotfile] caldb irf' | |
| 503 | + | |
| 504 | + # Set default options | |
| 505 | + options = [{'option': '-p', 'value': ''}, | |
| 506 | + {'option': '-emin', 'value': None}, | |
| 507 | + {'option': '-emax', 'value': None}, | |
| 508 | + {'option': '-tmin', 'value': None}, | |
| 509 | + {'option': '-tmax', 'value': None}] | |
| 510 | + | |
| 511 | + # Get arguments and options from command line arguments | |
| 512 | + args, options = cscripts.ioutils.get_args_options(options, usage) | |
| 513 | + | |
| 514 | + # Extract script parameters from options | |
| 515 | + plotfile = options[0]['value'] | |
| 516 | + emin = options[1]['value'] | |
| 517 | + emax = options[2]['value'] | |
| 518 | + tmin = options[3]['value'] | |
| 519 | + tmax = options[4]['value'] | |
| 520 | + | |
| 521 | + # Convert limits to float | |
| 522 | + if emin != None: | |
| 523 | + emin = float(emin) | |
| 524 | + if emax != None: | |
| 525 | + emax = float(emax) | |
| 526 | + if tmin != None: | |
| 527 | + tmin = float(tmin) | |
| 528 | + if tmax != None: | |
| 529 | + tmax = float(tmax) | |
| 530 | + | |
| 531 | + # Get IRF | |
| 532 | + caldb = gammalib.GCaldb('cta', args[0]) | |
| 533 | + irf = gammalib.GCTAResponseIrf(args[1], caldb) | |
| 534 | + | |
| 535 | + # Plot IRF | |
| 536 | + plot_irf(irf, emin, emax, tmin, tmax, plotfile) | |
| 537 | + | |
| 538 | + # Return | |
| 539 | + return | |
| 540 | + | |
| 541 | + | |
| 542 | +# ======================== # | |
| 543 | +# Main routine entry point # | |
| 544 | +# ======================== # | |
| 545 | +if __name__ == '__main__': | |
| 546 | + | |
| 547 | + # Show IRF | |
| 548 | + show_irf() | ... | ... |