maths_fns.ri

Source Code for Module maths_fns.ri_prime

1 ############################################################################### 2 # # 3 # Copyright (C) 2003, 2004 Edward d'Auvergne # 4 # # 5 # This file is part of the program relax. # 6 # # 7 # relax 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 2 of the License, or # 10 # (at your option) any later version. # 11 # # 12 # relax 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 relax; if not, write to the Free Software # 19 # Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA # 20 # # 21 ############################################################################### 22 23 24 # The transformed relaxation equations 25 # ==================================== 26 # 27 # Relaxation equations 28 # ==================== 29 # 30 # R1() = dip_const_func . dip_Jw_R1_func + csa_const_func . csa_Jw_R1_func 31 # 32 # 33 # dip_const_func csa_const_func 34 # R2() = -------------- . dip_Jw_R2_func + -------------- . csa_Jw_R2_func + rex_const_func 35 # 2 6 36 # 37 # 38 # sigma_noe() = dip_const_func . dip_Jw_sigma_noe_func 39 # 40 # 41 # Ri = dip_comps_func . dip_jw_comps_func + csa_comps_func * csa_jw_comps_func + rex_comps_func 42 # 43 # 44 # 45 # The transformed relaxation gradients 46 # ==================================== 47 # 48 # Spectral density parameter 49 # ========================== 50 # 51 # dR1() 52 # ----- = dip_const_func . dip_Jw_R1_grad + csa_const_func . csa_Jw_R1_grad 53 # dJw 54 # 55 # 56 # dR2() dip_const_func csa_const_func 57 # ----- = -------------- . dip_Jw_R2_grad + -------------- . csa_Jw_R2_grad 58 # dJw 2 6 59 # 60 # 61 # dsigma_noe() 62 # ------------ = dip_const_func . dip_Jw_sigma_noe_grad 63 # dJw 64 # 65 # 66 # dRi() 67 # ----- = dip_comps_func . dip_jw_comps_grad + csa_comps_func . csa_jw_comps_grad 68 # dJw 69 # 70 # 71 # Chemical exchange 72 # ================= 73 # 74 # dR1() 75 # ----- = 0 76 # dRex 77 # 78 # 79 # dR2() 80 # ----- = rex_const_grad 81 # dRex 82 # 83 # 84 # dsigma_noe() 85 # ------------ = 0 86 # dRex 87 # 88 # 89 # dRi() 90 # ----- = rex_comps_grad 91 # dRex 92 # 93 # 94 # Bond length 95 # =========== 96 # 97 # dR1() 98 # ----- = dip_const_grad . dip_Jw_R1_func 99 # dr 100 # 101 # 102 # dR2() dip_const_grad 103 # ----- = -------------- . dip_Jw_R2_func 104 # dr 2 105 # 106 # 107 # dsigma_noe() 108 # ------------ = dip_const_grad . dip_Jw_sigma_noe_func 109 # dr 110 # 111 # 112 # dRi() 113 # ----- = dip_comps_grad . dip_jw_comps_func 114 # dr 115 # 116 # 117 # CSA 118 # === 119 # 120 # dR1() 121 # ----- = csa_const_grad . csa_Jw_R1_func 122 # dcsa 123 # 124 # 125 # dR2() csa_const_grad 126 # ----- = -------------- . csa_Jw_R2_func 127 # dcsa 6 128 # 129 # 130 # dsigma_noe() 131 # ------------ = 0 132 # dcsa 133 # 134 # 135 # dRi() 136 # ----- = csa_comps_grad . csa_jw_comps_func 137 # dcsa 138 # 139 # 140 # 141 # The transformed relaxation Hessians 142 # =================================== 143 # 144 # Spectral density parameter - Spectral density parameter 145 # ======================================================= 146 # 147 # d2R1() 148 # --------- = dip_const_func . dip_Jw_R1_hess + csa_const_func . csa_Jw_R1_hess 149 # dJwi.dJwj 150 # 151 # 152 # d2R2() dip_const_func csa_const_func 153 # --------- = -------------- . dip_Jw_R2_hess + -------------- . csa_Jw_R2_hess 154 # dJwi.dJwj 2 6 155 # 156 # 157 # d2sigma_noe() 158 # ------------- = dip_const_func . dip_Jw_sigma_noe_hess 159 # dJwi.dJwj 160 # 161 # 162 # d2Ri() 163 # --------- = dip_comps_func . dip_jw_comps_hess + csa_comps_func . csa_jw_comps_hess 164 # dJwi.dJwj 165 # 166 # 167 # Spectral density parameter - Chemical exchange 168 # ============================================== 169 # 170 # d2R1() d2R2() d2sigma_noe() 171 # -------- = 0 , -------- = 0 , ------------- = 0 172 # dJw.dRex dJw.dRex dJw.dRex 173 # 174 # 175 # Spectral density parameter - CSA 176 # ================================ 177 # 178 # d2R1() 179 # -------- = csa_const_grad . csa_Jw_R1_grad 180 # dJw.dcsa 181 # 182 # 183 # d2R2() csa_const_grad 184 # -------- = -------------- . csa_Jw_R2_grad 185 # dJw.dcsa 6 186 # 187 # 188 # d2sigma_noe() 189 # ------------- = 0 190 # dJw.dcsa 191 # 192 # 193 # d2Ri() 194 # -------- = csa_comps_grad . csa_jw_comps_grad 195 # dJw.dcsa 196 # 197 # 198 # Spectral density parameter - Bond length 199 # ======================================== 200 # 201 # d2R1() 202 # ------ = dip_const_grad . dip_Jw_R1_grad 203 # dJw.dr 204 # 205 # 206 # d2R2() dip_const_grad 207 # ------ = -------------- . dip_Jw_R2_grad 208 # dJw.dr 2 209 # 210 # 211 # d2sigma_noe() 212 # ------------- = dip_const_grad . dip_Jw_sigma_noe_grad 213 # dJw.dr 214 # 215 # 216 # d2Ri() 217 # ------ = dip_comps_grad . dip_jw_comps_grad 218 # dJw.dr 219 # 220 # 221 # Chemical exchange - Chemical exchange 222 # ===================================== 223 # 224 # d2R1() d2R2() d2sigma_noe() 225 # ------- = 0 , ------- = 0 , ------------- = 0 226 # dRex**2 dRex**2 dRex**2 227 # 228 # 229 # Chemical exchange - CSA 230 # ======================= 231 # 232 # d2R1() d2R2() d2sigma_noe() 233 # --------- = 0 , --------- = 0 , ------------- = 0 234 # dRex.dcsa dRex.dcsa dRex.dcsa 235 # 236 # 237 # Chemical exchange - Bond length 238 # =============================== 239 # 240 # d2R1() d2R2() d2sigma_noe() 241 # ------- = 0 , ------- = 0 , ------------- = 0 242 # dRex.dr dRex.dr dRex.dr 243 # 244 # 245 # CSA - CSA 246 # ========= 247 # 248 # d2R1() 249 # ------- = csa_const_hess . csa_Jw_R1_func 250 # dcsa**2 251 # 252 # 253 # d2R2() csa_const_hess 254 # ------- = -------------- . csa_Jw_R2_func 255 # dcsa**2 6 256 # 257 # 258 # d2sigma_noe() 259 # ------------- = 0 260 # dcsa**2 261 # 262 # 263 # d2Ri() 264 # ------- = csa_comps_hess . csa_jw_comps_func 265 # dcsa**2 266 # 267 # 268 # CSA - Bond length 269 # ================= 270 # 271 # d2R1() d2R2() d2sigma_noe() 272 # ------- = 0 , ------- = 0 , ------------- = 0 273 # dcsa.dr dcsa.dr dcsa.dr 274 # 275 # 276 # Bond length - Bond length 277 # ========================= 278 # 279 # d2R1() 280 # ------ = dip_const_hess . dip_Jw_R1_func 281 # dr**2 282 # 283 # 284 # d2R2() dip_const_hess 285 # ------ = -------------- . dip_Jw_R2_func 286 # dr**2 2 287 # 288 # 289 # d2sigma_noe() 290 # ------------- = dip_const_hess . dip_Jw_sigma_noe_func 291 # dr**2 292 # 293 # 294 # d2Ri() 295 # ------ = dip_comps_hess . dip_jw_comps_func 296 # dr**2 297 # 298 # 299 300 301 # Transformed relaxation equatons. 302 ################################## 303

304 -def func_ri_prime(data):

305 """Calculate the transformed relaxation values.""" 306 307 return data.dip_comps_func * data.dip_jw_comps_func + data.csa_comps_func * data.csa_jw_comps_func

308 309

310 -def func_ri_prime_rex(data):

311 """Calculate the transformed relaxation values.""" 312 313 return data.dip_comps_func * data.dip_jw_comps_func + data.csa_comps_func * data.csa_jw_comps_func + data.rex_comps_func

314 315 316 # Transformed relaxation gradients. 317 ################################### 318 319 # dRi/dJ(w)

320 -def func_dri_djw_prime(data):

321 """Spectral density parameter derivatives.""" 322 323 return data.dip_comps_func * data.dip_jw_comps_grad + data.csa_comps_func * data.csa_jw_comps_grad

324 325 326 # dRi/dRex

327 -def func_dri_drex_prime(data):

328 """Chemical exchange derivatives.""" 329 330 return data.rex_comps_grad

331 332 333 # dRi/dr

334 -def func_dri_dr_prime(data):

335 """Bond length derivatives.""" 336 337 return data.dip_comps_grad * data.dip_jw_comps_func

338 339 340 # dRi/dCSA

341 -def func_dri_dcsa_prime(data):

342 """CSA derivatives.""" 343 344 return data.csa_comps_grad * data.csa_jw_comps_func

345 346 347 348 349 # Transformed relaxation Hessians. 350 ################################## 351 352 353 # d2Ri/dJ(w)i.dJ(w)j

354 -def func_d2ri_djwidjwj_prime(data):

355 """Spectral density parameter / spectral density parameter Hessian. 356 357 The equations are:: 358 359 d2R1() 360 --------- = dip_const_func . dip_Jw_R1_hess + csa_const_func . csa_Jw_R1_hess 361 dJwi.dJwj 362 363 d2R2() dip_const_func csa_const_func 364 --------- = -------------- . dip_Jw_R2_hess + -------------- . csa_Jw_R2_hess 365 dJwi.dJwj 2 6 366 367 d2sigma_noe() 368 ------------- = dip_const_func . dip_Jw_sigma_noe_hess 369 dJwi.dJwj 370 371 d2Ri() 372 --------- = dip_comps_func . dip_jw_comps_hess + csa_comps_func . csa_jw_comps_hess 373 dJwi.dJwj 374 """ 375 376 return data.dip_comps_func * data.dip_jw_comps_hess + data.csa_comps_func * data.csa_jw_comps_hess

377 378 379 # d2Ri/dJ(w).dCSA

380 -def func_d2ri_djwdcsa_prime(data):

381 """Spectral density parameter / CSA Hessian. 382 383 The equations are:: 384 385 d2R1() 386 -------- = csa_const_grad . csa_Jw_R1_grad 387 dJw.dcsa 388 389 d2R2() csa_const_grad 390 -------- = -------------- . csa_Jw_R2_grad 391 dJw.dcsa 6 392 393 d2sigma_noe() 394 ------------- = 0 395 dJw.dcsa 396 397 d2Ri() 398 -------- = csa_comps_grad . csa_jw_comps_grad 399 dJw.dcsa 400 """ 401 402 return data.csa_comps_grad * data.csa_jw_comps_grad

403 404 405 # d2Ri/dJ(w).dr

406 -def func_d2ri_djwdr_prime(data):

407 """Spectral density parameter / bond length Hessian. 408 409 The equations are:: 410 411 d2R1() 412 ------ = dip_const_grad . dip_Jw_R1_grad 413 dJw.dr 414 415 d2R2() dip_const_grad 416 ------ = -------------- . dip_Jw_R2_grad 417 dJw.dr 2 418 419 d2sigma_noe() 420 ------------- = dip_const_grad . dip_Jw_sigma_noe_grad 421 dJw.dr 422 423 d2Ri() 424 ------ = dip_comps_grad . dip_jw_comps_grad 425 dJw.dr 426 """ 427 428 return data.dip_comps_grad * data.dip_jw_comps_grad

429 430 431 # d2Ri/dCSA^2

432 -def func_d2ri_dcsa2_prime(data):

433 """CSA / CSA Hessian. 434 435 The equations are:: 436 437 d2R1() 438 ------- = csa_const_hess . csa_Jw_R1_func 439 dcsa**2 440 441 d2R2() csa_const_hess 442 ------- = -------------- . csa_Jw_R2_func 443 dcsa**2 6 444 445 d2sigma_noe() 446 ------------- = 0 447 dcsa**2 448 449 d2Ri() 450 ------- = csa_comps_hess . csa_jw_comps_func 451 dcsa**2 452 """ 453 454 return data.csa_comps_hess * data.csa_jw_comps_func

455 456 457 # d2Ri/dr^2

458 -def func_d2ri_dr2_prime(data):

459 """Bond length / bond length Hessian. 460 461 The equations are:: 462 463 d2R1() 464 ------ = dip_const_hess . dip_Jw_R1_func 465 dr**2 466 467 d2R2() dip_const_hess 468 ------ = -------------- . dip_Jw_R2_func 469 dr**2 2 470 471 d2sigma_noe() 472 ------------- = dip_const_hess . dip_Jw_sigma_noe_func 473 dr**2 474 475 d2Ri() 476 ------ = dip_comps_hess . dip_jw_comps_func 477 dr**2 478 """ 479 480 return data.dip_comps_hess * data.dip_jw_comps_func

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