lib.auto_relaxation.ri

Source Code for Module lib.auto_relaxation.ri_prime

1 ############################################################################### 2 # # 3 # Copyright (C) 2001-2004,2008 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 23 # The transformed relaxation equations 24 # ==================================== 25 # 26 # Relaxation equations 27 # ==================== 28 # 29 # R1() = dip_const_func . dip_Jw_R1_func + csa_const_func . csa_Jw_R1_func 30 # 31 # 32 # dip_const_func csa_const_func 33 # R2() = -------------- . dip_Jw_R2_func + -------------- . csa_Jw_R2_func + rex_const_func 34 # 2 6 35 # 36 # 37 # sigma_noe() = dip_const_func . dip_Jw_sigma_noe_func 38 # 39 # 40 # Ri = dip_comps_func . dip_jw_comps_func + csa_comps_func * csa_jw_comps_func + rex_comps_func 41 # 42 # 43 # 44 # The transformed relaxation gradients 45 # ==================================== 46 # 47 # Spectral density parameter 48 # ========================== 49 # 50 # dR1() 51 # ----- = dip_const_func . dip_Jw_R1_grad + csa_const_func . csa_Jw_R1_grad 52 # dJw 53 # 54 # 55 # dR2() dip_const_func csa_const_func 56 # ----- = -------------- . dip_Jw_R2_grad + -------------- . csa_Jw_R2_grad 57 # dJw 2 6 58 # 59 # 60 # dsigma_noe() 61 # ------------ = dip_const_func . dip_Jw_sigma_noe_grad 62 # dJw 63 # 64 # 65 # dRi() 66 # ----- = dip_comps_func . dip_jw_comps_grad + csa_comps_func . csa_jw_comps_grad 67 # dJw 68 # 69 # 70 # Chemical exchange 71 # ================= 72 # 73 # dR1() 74 # ----- = 0 75 # dRex 76 # 77 # 78 # dR2() 79 # ----- = rex_const_grad 80 # dRex 81 # 82 # 83 # dsigma_noe() 84 # ------------ = 0 85 # dRex 86 # 87 # 88 # dRi() 89 # ----- = rex_comps_grad 90 # dRex 91 # 92 # 93 # Bond length 94 # =========== 95 # 96 # dR1() 97 # ----- = dip_const_grad . dip_Jw_R1_func 98 # dr 99 # 100 # 101 # dR2() dip_const_grad 102 # ----- = -------------- . dip_Jw_R2_func 103 # dr 2 104 # 105 # 106 # dsigma_noe() 107 # ------------ = dip_const_grad . dip_Jw_sigma_noe_func 108 # dr 109 # 110 # 111 # dRi() 112 # ----- = dip_comps_grad . dip_jw_comps_func 113 # dr 114 # 115 # 116 # CSA 117 # === 118 # 119 # dR1() 120 # ----- = csa_const_grad . csa_Jw_R1_func 121 # dcsa 122 # 123 # 124 # dR2() csa_const_grad 125 # ----- = -------------- . csa_Jw_R2_func 126 # dcsa 6 127 # 128 # 129 # dsigma_noe() 130 # ------------ = 0 131 # dcsa 132 # 133 # 134 # dRi() 135 # ----- = csa_comps_grad . csa_jw_comps_func 136 # dcsa 137 # 138 # 139 # 140 # The transformed relaxation Hessians 141 # =================================== 142 # 143 # Spectral density parameter - Spectral density parameter 144 # ======================================================= 145 # 146 # d2R1() 147 # --------- = dip_const_func . dip_Jw_R1_hess + csa_const_func . csa_Jw_R1_hess 148 # dJwi.dJwj 149 # 150 # 151 # d2R2() dip_const_func csa_const_func 152 # --------- = -------------- . dip_Jw_R2_hess + -------------- . csa_Jw_R2_hess 153 # dJwi.dJwj 2 6 154 # 155 # 156 # d2sigma_noe() 157 # ------------- = dip_const_func . dip_Jw_sigma_noe_hess 158 # dJwi.dJwj 159 # 160 # 161 # d2Ri() 162 # --------- = dip_comps_func . dip_jw_comps_hess + csa_comps_func . csa_jw_comps_hess 163 # dJwi.dJwj 164 # 165 # 166 # Spectral density parameter - Chemical exchange 167 # ============================================== 168 # 169 # d2R1() d2R2() d2sigma_noe() 170 # -------- = 0 , -------- = 0 , ------------- = 0 171 # dJw.dRex dJw.dRex dJw.dRex 172 # 173 # 174 # Spectral density parameter - CSA 175 # ================================ 176 # 177 # d2R1() 178 # -------- = csa_const_grad . csa_Jw_R1_grad 179 # dJw.dcsa 180 # 181 # 182 # d2R2() csa_const_grad 183 # -------- = -------------- . csa_Jw_R2_grad 184 # dJw.dcsa 6 185 # 186 # 187 # d2sigma_noe() 188 # ------------- = 0 189 # dJw.dcsa 190 # 191 # 192 # d2Ri() 193 # -------- = csa_comps_grad . csa_jw_comps_grad 194 # dJw.dcsa 195 # 196 # 197 # Spectral density parameter - Bond length 198 # ======================================== 199 # 200 # d2R1() 201 # ------ = dip_const_grad . dip_Jw_R1_grad 202 # dJw.dr 203 # 204 # 205 # d2R2() dip_const_grad 206 # ------ = -------------- . dip_Jw_R2_grad 207 # dJw.dr 2 208 # 209 # 210 # d2sigma_noe() 211 # ------------- = dip_const_grad . dip_Jw_sigma_noe_grad 212 # dJw.dr 213 # 214 # 215 # d2Ri() 216 # ------ = dip_comps_grad . dip_jw_comps_grad 217 # dJw.dr 218 # 219 # 220 # Chemical exchange - Chemical exchange 221 # ===================================== 222 # 223 # d2R1() d2R2() d2sigma_noe() 224 # ------- = 0 , ------- = 0 , ------------- = 0 225 # dRex**2 dRex**2 dRex**2 226 # 227 # 228 # Chemical exchange - CSA 229 # ======================= 230 # 231 # d2R1() d2R2() d2sigma_noe() 232 # --------- = 0 , --------- = 0 , ------------- = 0 233 # dRex.dcsa dRex.dcsa dRex.dcsa 234 # 235 # 236 # Chemical exchange - Bond length 237 # =============================== 238 # 239 # d2R1() d2R2() d2sigma_noe() 240 # ------- = 0 , ------- = 0 , ------------- = 0 241 # dRex.dr dRex.dr dRex.dr 242 # 243 # 244 # CSA - CSA 245 # ========= 246 # 247 # d2R1() 248 # ------- = csa_const_hess . csa_Jw_R1_func 249 # dcsa**2 250 # 251 # 252 # d2R2() csa_const_hess 253 # ------- = -------------- . csa_Jw_R2_func 254 # dcsa**2 6 255 # 256 # 257 # d2sigma_noe() 258 # ------------- = 0 259 # dcsa**2 260 # 261 # 262 # d2Ri() 263 # ------- = csa_comps_hess . csa_jw_comps_func 264 # dcsa**2 265 # 266 # 267 # CSA - Bond length 268 # ================= 269 # 270 # d2R1() d2R2() d2sigma_noe() 271 # ------- = 0 , ------- = 0 , ------------- = 0 272 # dcsa.dr dcsa.dr dcsa.dr 273 # 274 # 275 # Bond length - Bond length 276 # ========================= 277 # 278 # d2R1() 279 # ------ = dip_const_hess . dip_Jw_R1_func 280 # dr**2 281 # 282 # 283 # d2R2() dip_const_hess 284 # ------ = -------------- . dip_Jw_R2_func 285 # dr**2 2 286 # 287 # 288 # d2sigma_noe() 289 # ------------- = dip_const_hess . dip_Jw_sigma_noe_func 290 # dr**2 291 # 292 # 293 # d2Ri() 294 # ------ = dip_comps_hess . dip_jw_comps_func 295 # dr**2 296 # 297 # 298 299 300 # Transformed relaxation equatons. 301 ################################## 302

303 -def func_ri_prime(data):

304 """Calculate the transformed relaxation values.""" 305 306 return data.dip_comps_func * data.dip_jw_comps_func + data.csa_comps_func * data.csa_jw_comps_func

307 308

309 -def func_ri_prime_rex(data):

310 """Calculate the transformed relaxation values.""" 311 312 return data.dip_comps_func * data.dip_jw_comps_func + data.csa_comps_func * data.csa_jw_comps_func + data.rex_comps_func

313 314 315 # Transformed relaxation gradients. 316 ################################### 317 318 # dRi/dJ(w)

319 -def func_dri_djw_prime(data):

320 """Spectral density parameter derivatives.""" 321 322 return data.dip_comps_func * data.dip_jw_comps_grad + data.csa_comps_func * data.csa_jw_comps_grad

323 324 325 # dRi/dRex

326 -def func_dri_drex_prime(data):

327 """Chemical exchange derivatives.""" 328 329 return data.rex_comps_grad

330 331 332 # dRi/dr

333 -def func_dri_dr_prime(data):

334 """Bond length derivatives.""" 335 336 return data.dip_comps_grad * data.dip_jw_comps_func

337 338 339 # dRi/dCSA

340 -def func_dri_dcsa_prime(data):

341 """CSA derivatives.""" 342 343 return data.csa_comps_grad * data.csa_jw_comps_func

344 345 346 347 348 # Transformed relaxation Hessians. 349 ################################## 350 351 352 # d2Ri/dJ(w)i.dJ(w)j

353 -def func_d2ri_djwidjwj_prime(data):

354 """Spectral density parameter / spectral density parameter Hessian. 355 356 The equations are:: 357 358 d2R1() 359 --------- = dip_const_func . dip_Jw_R1_hess + csa_const_func . csa_Jw_R1_hess 360 dJwi.dJwj 361 362 d2R2() dip_const_func csa_const_func 363 --------- = -------------- . dip_Jw_R2_hess + -------------- . csa_Jw_R2_hess 364 dJwi.dJwj 2 6 365 366 d2sigma_noe() 367 ------------- = dip_const_func . dip_Jw_sigma_noe_hess 368 dJwi.dJwj 369 370 d2Ri() 371 --------- = dip_comps_func . dip_jw_comps_hess + csa_comps_func . csa_jw_comps_hess 372 dJwi.dJwj 373 """ 374 375 return data.dip_comps_func * data.dip_jw_comps_hess + data.csa_comps_func * data.csa_jw_comps_hess

376 377 378 # d2Ri/dJ(w).dCSA

379 -def func_d2ri_djwdcsa_prime(data):

380 """Spectral density parameter / CSA Hessian. 381 382 The equations are:: 383 384 d2R1() 385 -------- = csa_const_grad . csa_Jw_R1_grad 386 dJw.dcsa 387 388 d2R2() csa_const_grad 389 -------- = -------------- . csa_Jw_R2_grad 390 dJw.dcsa 6 391 392 d2sigma_noe() 393 ------------- = 0 394 dJw.dcsa 395 396 d2Ri() 397 -------- = csa_comps_grad . csa_jw_comps_grad 398 dJw.dcsa 399 """ 400 401 return data.csa_comps_grad * data.csa_jw_comps_grad

402 403 404 # d2Ri/dJ(w).dr

405 -def func_d2ri_djwdr_prime(data):

406 """Spectral density parameter / bond length Hessian. 407 408 The equations are:: 409 410 d2R1() 411 ------ = dip_const_grad . dip_Jw_R1_grad 412 dJw.dr 413 414 d2R2() dip_const_grad 415 ------ = -------------- . dip_Jw_R2_grad 416 dJw.dr 2 417 418 d2sigma_noe() 419 ------------- = dip_const_grad . dip_Jw_sigma_noe_grad 420 dJw.dr 421 422 d2Ri() 423 ------ = dip_comps_grad . dip_jw_comps_grad 424 dJw.dr 425 """ 426 427 return data.dip_comps_grad * data.dip_jw_comps_grad

428 429 430 # d2Ri/dCSA^2

431 -def func_d2ri_dcsa2_prime(data):

432 """CSA / CSA Hessian. 433 434 The equations are:: 435 436 d2R1() 437 ------- = csa_const_hess . csa_Jw_R1_func 438 dcsa**2 439 440 d2R2() csa_const_hess 441 ------- = -------------- . csa_Jw_R2_func 442 dcsa**2 6 443 444 d2sigma_noe() 445 ------------- = 0 446 dcsa**2 447 448 d2Ri() 449 ------- = csa_comps_hess . csa_jw_comps_func 450 dcsa**2 451 """ 452 453 return data.csa_comps_hess * data.csa_jw_comps_func

454 455 456 # d2Ri/dr^2

457 -def func_d2ri_dr2_prime(data):

458 """Bond length / bond length Hessian. 459 460 The equations are:: 461 462 d2R1() 463 ------ = dip_const_hess . dip_Jw_R1_func 464 dr**2 465 466 d2R2() dip_const_hess 467 ------ = -------------- . dip_Jw_R2_func 468 dr**2 2 469 470 d2sigma_noe() 471 ------------- = dip_const_hess . dip_Jw_sigma_noe_func 472 dr**2 473 474 d2Ri() 475 ------ = dip_comps_hess . dip_jw_comps_func 476 dr**2 477 """ 478 479 return data.dip_comps_hess * data.dip_jw_comps_func

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