lib.structure.cones

1 ############################################################################### 2 # # 3 # Copyright (C) 2010 Edward d'Auvergne # 4 # # 5 # This file is part of the program relax (http://www.nmr-relax.com). # 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 22 # Module docstring. 23 """Module containing all the different cone type classes.""" 24 25 # Python module imports. 26 from math import acos, asin, cos, pi, sqrt, sin 27 28

29 -class Base:

30 """A base class for all the cone objects.""" 31

32 - def __init__(self, phi_x, phi_y):

33 """Set up the cone object. 34 35 @param phi_x: The maximum cone angle along the x-eigenvector. 36 @type phi_x: float 37 @param phi_y: The maximum cone angle along the y-eigenvector. 38 @type phi_y: float 39 """ 40 41 # Store the cone limits. 42 self._phi_x = phi_x 43 self._phi_y = phi_y

44 45

46 - def limit_check(self, phi, theta):

47 """Determine if the point is within the cone. 48 49 @param phi: The polar angle. 50 @type phi: float 51 @param theta: The azimuthal angle. 52 @type theta: float 53 @return: True if the point is within the cone, False otherwise. 54 @rtype: bool 55 """ 56 57 # Outside. 58 if phi > self.phi_max(theta): 59 return False 60 61 # Else inside. 62 return True

63 64 65

66 -class Cosine(Base):

67 """The class for the cosine cone. 68 69 The ellipse is defined by:: 70 71 phi_max = cos(theta) * phi_x + sin(theta) * phi_y, 72 73 where phi_max is the maximum polar angle for the given azimuthal angle theta, phi_x is the maximum cone angle along the x-eigenvector, and phi_y is that of the y-eigenvector. The cone axis is assumed to be the z-axis. The maximum cone opening angle allowed is pi/2. 74 """ 75

76 - def __init__(self, phi_x, phi_y):

77 """Set up the cone object. 78 79 @param phi_x: The maximum cone angle along the x-eigenvector. 80 @type phi_x: float 81 @param phi_y: The maximum cone angle along the y-eigenvector. 82 @type phi_y: float 83 """ 84 85 # Store the cone limits. 86 self._phi_x = phi_x 87 self._phi_y = phi_y 88 89 # The scaling factor. 90 self._scale = (phi_x - phi_y)/2 91 92 # The shift. 93 self._shift = (phi_x + phi_y)/2

94 95

96 - def phi_max(self, theta):

97 """Return the maximum polar angle phi for the given azimuthal angle theta. 98 99 @param theta: The azimuthal angle. 100 @type theta: float 101 @return: The maximum polar angle phi for the value of theta. 102 @rtype: float 103 """ 104 105 # Determine phi_max. 106 phi_max = self._scale * cos(theta*2) + self._shift 107 108 # Return the limit. 109 return phi_max

110 111

112 - def theta_max(self, phi, theta_min=0.0, theta_max=2*pi):

113 """Return the maximum azimuthal angle theta for the given polar angle phi. 114 115 @param phi: The polar angle. 116 @type phi: float 117 @keyword theta_min: The lower limit of the azimuthal angle range for complex distributions. 118 @type theta_min: float 119 @keyword theta_max: The upper limit of the azimuthal angle range for complex distributions. 120 @type theta_max: float 121 @return: The maximum azimuthal angle theta for the value of phi. 122 @rtype: float 123 """ 124 125 # The factor. 126 b = (phi - self._shift)/self._scale 127 128 # The 4 quadrants. 129 if theta_max < pi/2: 130 theta = 0.5*acos(b) 131 elif theta_max < pi: 132 theta = 0.5*acos(-b) + pi/2 133 elif theta_max < 3*pi/2: 134 theta = 0.5*acos(b) + pi 135 elif theta_max < 2*pi: 136 theta = 0.5*acos(-b) + 3*pi/2 137 138 # Return the azimuthal angle. 139 return theta

140 141 142

143 -class Elliptic(Base):

144 """The class for the elliptic cone. 145 146 The ellipse is defined by:: 147 148 1 / sin(phi_max)^2 = cos(theta)^2 / sin(phi_x)^2 + sin(theta)^2 / sin(phi_y)^2, 149 150 where phi_max is the maximum polar angle for the given azimuthal angle theta, phi_x is the maximum cone angle along the x-eigenvector, and phi_y is that of the y-eigenvector. The cone axis is assumed to be the z-axis. The maximum cone opening angle allowed is pi/2. 151 """ 152

153 - def phi_max(self, theta):

154 """Return the maximum polar angle phi for the given azimuthal angle theta. 155 156 @param theta: The azimuthal angle. 157 @type theta: float 158 @return: The maximum polar angle phi for the value of theta. 159 @rtype: float 160 """ 161 162 # Determine phi_max. 163 phi_max = asin(1.0/sqrt((cos(theta) / sin(self._phi_x))**2 + (sin(theta) / sin(self._phi_y))**2)) 164 165 # Return the limit. 166 return phi_max

167 168

169 - def theta_max(self, phi, theta_min=0.0, theta_max=2*pi):

170 """Return the maximum azimuthal angle theta for the given polar angle phi. 171 172 @param phi: The polar angle. 173 @type phi: float 174 @keyword theta_min: The lower limit of the azimuthal angle range for complex distributions. 175 @type theta_min: float 176 @keyword theta_max: The upper limit of the azimuthal angle range for complex distributions. 177 @type theta_max: float 178 @return: The maximum azimuthal angle theta for the value of phi. 179 @rtype: float 180 """ 181 182 # The factor. 183 b = sqrt((1.0/sin(phi)**2 - 1.0/sin(self._phi_y)**2)/(1.0/sin(self._phi_x)**2 - 1.0/sin(self._phi_y)**2)) 184 185 # The 4 quadrants. 186 if theta_max < pi/2: 187 theta = acos(b) 188 elif theta_max < pi: 189 theta = acos(-b) 190 elif theta_max < 3*pi/2: 191 theta = -acos(-b) 192 elif theta_max < 2*pi: 193 theta = -acos(b) 194 195 # Return the azimuthal angle. 196 return theta

197 198 199

200 -class Iso_cone(Base):

201 """The class for the isotropic cone.""" 202

203 - def __init__(self, angle):

204 """Set up the cone object. 205 206 @param angle: The cone angle. 207 @type angle: float 208 """ 209 210 # Store the cone angle. 211 self._angle = angle

212 213

214 - def phi_max(self, theta):

215 """Return the maximum polar angle phi for the given azimuthal angle theta. 216 217 @param theta: The azimuthal angle. 218 @type theta: float 219 @return: The maximum polar angle phi for the value of theta. 220 @rtype: float 221 """ 222 223 # The polar angle is fixed! 224 return self._angle

225 226

227 - def theta_max(self, phi):

228 """Return the maximum azimuthal angle theta for the given polar angle phi. 229 230 @param phi: The polar angle. 231 @type phi: float 232 @return: The maximum azimuthal angle theta for the value of phi. 233 @rtype: float 234 """ 235 236 # The polar angle is fixed, so return zero. 237 return 0.0

238 239 240

241 -class Pseudo_elliptic(Base):

242 """The class for another pseudo-elliptic cone. 243 244 The pseudo-ellipse is defined by:: 245 246 1/phi_max^2 = 1/phi_x^2 * cos(theta)^2 + 1/phi_y^2 * sin(theta)^2, 247 248 where phi_max is the maximum polar angle for the given azimuthal angle theta, phi_x is the maximum cone angle along the x-eigenvector, and phi_y is that of the y-eigenvector. The cone axis is assumed to be the z-axis. 249 """ 250

251 - def phi_max(self, theta):

252 """Return the maximum polar angle phi for the given azimuthal angle theta. 253 254 @param theta: The azimuthal angle. 255 @type theta: float 256 @return: The maximum polar angle phi for the value of theta. 257 @rtype: float 258 """ 259 260 # Zero value handling. 261 if self._phi_x == 0.0 or self._phi_y == 0.0: 262 return 0.0 263 264 # Determine phi_max. 265 phi_max = 1.0/sqrt(((1.0/self._phi_x) * cos(theta))**2 + ((1.0/self._phi_y) * sin(theta))**2) 266 267 # Return the limit. 268 return phi_max

269 270

271 - def theta_max(self, phi, theta_min=0.0, theta_max=2*pi):

272 """Return the maximum azimuthal angle theta for the given polar angle phi. 273 274 @param phi: The polar angle. 275 @type phi: float 276 @keyword theta_min: The lower limit of the azimuthal angle range for complex distributions. 277 @type theta_min: float 278 @keyword theta_max: The upper limit of the azimuthal angle range for complex distributions. 279 @type theta_max: float 280 @return: The maximum azimuthal angle theta for the value of phi. 281 @rtype: float 282 """ 283 284 # The factor. 285 b = sqrt(((1.0/phi)**2 - (1.0/self._phi_y)**2) / ((1.0/self._phi_x)**2 - (1.0/self._phi_y)**2)) 286 287 # The 4 quadrants. 288 if theta_max < pi/2: 289 phi = acos(b) 290 elif theta_max < pi: 291 phi = acos(-b) 292 elif theta_max < 3*pi/2: 293 phi = -acos(-b) 294 elif theta_max < 2*pi: 295 phi = -acos(b) 296 297 # Return the polar angle. 298 return phi

299 300 301

302 -class Pseudo_elliptic2(Base):

303 """The class for the pseudo-elliptic cone. 304 305 This is not an elliptic cone! The pseudo-ellipse is defined by:: 306 307 phi_max^2 = phi_x^2 * cos(theta)^2 + phi_y^2 * sin(theta)^2, 308 309 where phi_max is the maximum polar angle for the given azimuthal angle theta, phi_x is the maximum cone angle along the x-eigenvector, and phi_y is that of the y-eigenvector. The cone axis is assumed to be the z-axis. 310 """ 311

312 - def phi_max(self, theta):

313 """Return the maximum polar angle phi for the given azimuthal angle theta. 314 315 @param theta: The azimuthal angle. 316 @type theta: float 317 @return: The maximum polar angle phi for the value of theta. 318 @rtype: float 319 """ 320 321 # Determine phi_max. 322 phi_max = sqrt((self._phi_x * cos(theta))**2 + (self._phi_y * sin(theta))**2) 323 324 # Return the limit. 325 return phi_max

326 327

328 - def theta_max(self, phi, theta_min=0.0, theta_max=2*pi):

329 """Return the maximum azimuthal angle theta for the given polar angle phi. 330 331 @param phi: The polar angle. 332 @type phi: float 333 @keyword theta_min: The lower limit of the azimuthal angle range for complex distributions. 334 @type theta_min: float 335 @keyword theta_max: The upper limit of the azimuthal angle range for complex distributions. 336 @type theta_max: float 337 @return: The maximum azimuthal angle theta for the value of phi. 338 @rtype: float 339 """ 340 341 # The factor. 342 b = sqrt((phi**2 - self._phi_y**2)/(self._phi_x**2 - self._phi_y**2)) 343 344 # The 4 quadrants. 345 if theta_max < pi/2: 346 phi = acos(b) 347 elif theta_max < pi: 348 phi = acos(-b) 349 elif theta_max < 3*pi/2: 350 phi = -acos(-b) 351 elif theta_max < 2*pi: 352 phi = -acos(b) 353 354 # Return the polar angle. 355 return phi

356 357 358

359 -class Square(Base):

360 """The class for the square cone. 361 362 The cone is defined by:: 363 364 / phi_y, if 0 <= theta < pi/2, 365 | 366 phi_max = < phi_x, if pi/2 <= theta < 3*pi/3, 367 | 368 \ phi_y, if 3*pi/2 <= theta < 2*pi, 369 370 where phi_max is the maximum polar angle for the given azimuthal angle theta, phi_x is the maximum cone angle along the x-eigenvector, and phi_y is that of the y-eigenvector. The cone axis is assumed to be the z-axis. The maximum cone opening angle allowed is pi/2. 371 """ 372

373 - def phi_max(self, theta):

374 """Return the maximum polar angle phi for the given azimuthal angle theta. 375 376 @param theta: The azimuthal angle. 377 @type theta: float 378 @return: The maximum polar angle phi for the value of theta. 379 @rtype: float 380 """ 381 382 # The 4 quadrants. 383 if theta < pi/2: 384 phi_max = self._phi_y 385 elif theta < 3*pi/2: 386 phi_max = self._phi_x 387 elif theta < 2*pi: 388 phi_max = self._phi_y 389 390 # Return the limit. 391 return phi_max

392 393

394 - def theta_max(self, phi, theta_min=0.0, theta_max=2*pi):

395 """Return the maximum azimuthal angle theta for the given polar angle phi. 396 397 @param phi: The polar angle. 398 @type phi: float 399 @keyword theta_min: The lower limit of the azimuthal angle range for complex distributions. 400 @type theta_min: float 401 @keyword theta_max: The upper limit of the azimuthal angle range for complex distributions. 402 @type theta_max: float 403 @return: The maximum azimuthal angle theta for the value of phi. 404 @rtype: float 405 """ 406 407 # The factor. 408 return 0 409 b = (phi - self._shift)/self._scale 410 411 # The 4 quadrants. 412 if theta_max < pi/2: 413 theta = pi/4 *(1 - b) 414 elif theta_max < pi: 415 theta = pi/4 *(3 + b) 416 elif theta_max < 3*pi/2: 417 theta = pi/4 *(5 - b) 418 elif theta_max < 2*pi: 419 theta = pi/4 *(7 + b) 420 421 # Return the azimuthal angle. 422 return theta

423 424 425

426 -class Zig_zag(Base):

427 """The class for the zig-zag cone. 428 429 The cone is defined by:: 430 431 phi_max = c * asin(cos(theta*2)) + a, 432 433 where:: 434 435 c = (phi_x - phi_y)/2, 436 437 a = (phi_x + phi_y)/2, 438 439 and where phi_max is the maximum polar angle for the given azimuthal angle theta, phi_x is the maximum cone angle along the x-eigenvector, and phi_y is that of the y-eigenvector. The cone axis is assumed to be the z-axis. The maximum cone opening angle allowed is pi/2. 440 """ 441

442 - def __init__(self, phi_x, phi_y):

443 """Set up the cone object. 444 445 @param phi_x: The maximum cone angle along the x-eigenvector. 446 @type phi_x: float 447 @param phi_y: The maximum cone angle along the y-eigenvector. 448 @type phi_y: float 449 """ 450 451 # Store the cone limits. 452 self._phi_x = phi_x 453 self._phi_y = phi_y 454 455 # The scaling factor. 456 self._scale = (phi_x - phi_y)/2 457 458 # The shift. 459 self._shift = (phi_x + phi_y)/2

460 461

462 - def phi_max(self, theta):

463 """Return the maximum polar angle phi for the given azimuthal angle theta. 464 465 @param theta: The azimuthal angle. 466 @type theta: float 467 @return: The maximum polar angle phi for the value of theta. 468 @rtype: float 469 """ 470 471 # The factor. 472 b = 4.0 * theta / pi 473 474 # The 4 quadrants. 475 if theta < pi/2: 476 phi_max = 1 - b 477 elif theta < pi: 478 phi_max = b - 3 479 elif theta < 3*pi/2: 480 phi_max = 5 - b 481 elif theta < 2*pi: 482 phi_max = b - 7 483 484 # Determine phi_max. 485 phi_max = self._scale * phi_max + self._shift 486 487 # Return the limit. 488 return phi_max

489 490

491 - def theta_max(self, phi, theta_min=0.0, theta_max=2*pi):

492 """Return the maximum azimuthal angle theta for the given polar angle phi. 493 494 @param phi: The polar angle. 495 @type phi: float 496 @keyword theta_min: The lower limit of the azimuthal angle range for complex distributions. 497 @type theta_min: float 498 @keyword theta_max: The upper limit of the azimuthal angle range for complex distributions. 499 @type theta_max: float 500 @return: The maximum azimuthal angle theta for the value of phi. 501 @rtype: float 502 """ 503 504 # The factor. 505 b = (phi - self._shift)/self._scale 506 507 # The 4 quadrants. 508 if theta_max < pi/2: 509 theta = pi/4 *(1 - b) 510 elif theta_max < pi: 511 theta = pi/4 *(3 + b) 512 elif theta_max < 3*pi/2: 513 theta = pi/4 *(5 - b) 514 elif theta_max < 2*pi: 515 theta = pi/4 *(7 + b) 516 517 # Return the azimuthal angle. 518 return theta

519

Source Code for Module lib.structure.cones