fingerprint.pyx 31.2 KB
 Malthe Kjær Bisbo committed Dec 17, 2019 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 ``````import os import sys from math import erf from itertools import product from scipy.spatial.distance import cdist import time import numpy as np cimport numpy as np from libc.math cimport * from cymem.cymem cimport Pool cimport cython try: cwd = sys.argv[1] except: cwd = os.getcwd() # Custom functions ctypedef struct Point: double coord[3] cdef Point subtract(Point p1, Point p2): cdef Point p p.coord[0] = p1.coord[0] - p2.coord[0] p.coord[1] = p1.coord[1] - p2.coord[1] p.coord[2] = p1.coord[2] - p2.coord[2] return p cdef Point add(Point p1, Point p2): cdef Point p p.coord[0] = p1.coord[0] + p2.coord[0] p.coord[1] = p1.coord[1] + p2.coord[1] p.coord[2] = p1.coord[2] + p2.coord[2] return p cdef double norm(Point p): return sqrt(p.coord[0]*p.coord[0] + p.coord[1]*p.coord[1] + p.coord[2]*p.coord[2]) cdef double euclidean(Point p1, Point p2): return norm(subtract(p1,p2)) cdef double dot(Point v1, Point v2): return v1.coord[0]*v2.coord[0] + v1.coord[1]*v2.coord[1] + v1.coord[2]*v2.coord[2] cdef double get_angle(Point v1, Point v2): """ Returns angle with convention [0,pi] """ norm1 = norm(v1) norm2 = norm(v2) arg = dot(v1,v2)/(norm1*norm2) # This is added to correct for numerical errors if arg < -1: arg = -1. elif arg > 1: arg = 1. return acos(arg) @cython.cdivision(True) cdef double f_cutoff(double r, double gamma, double Rcut): """ Polinomial cutoff function in the, with the steepness determined by "gamma" gamma = 2 resembels the cosine cutoff function. For large gamma, the function goes towards a step function at Rc. """ if not gamma == 0: return 1 + gamma*pow(r/Rcut, gamma+1) - (gamma+1)*pow(r/Rcut, gamma) else: return 1 @cython.cdivision(True) cdef double f_cutoff_grad(double r, double gamma, double Rcut): if not gamma == 0: return gamma*(gamma+1)/Rcut * (pow(r/Rcut, gamma) - pow(r/Rcut, gamma-1)) else: return 0 def convert_atom_types(num): cdef int Natoms = len(num) cdef list atomic_types = sorted(list(set(num))) cdef int Ntypes = len(atomic_types) cdef list num_converted = [0]*Natoms cdef int i, j for i in range(Natoms): for j in range(Ntypes): if num[i] == atomic_types[j]: num_converted[i] = j return num_converted `````` Malthe Kjær Bisbo committed Dec 18, 2019 94 ``````class Fingerprint(object): `````` Malthe Kjær Bisbo committed Dec 17, 2019 95 96 `````` """ comparator for construction of angular fingerprints """ `````` Malthe Kjær Bisbo committed Dec 18, 2019 97 `````` def __init__(self, Rc1=6.0, Rc2=4.0, binwidth1=0.2, Nbins2=30, sigma1=0.2, sigma2=0.2, eta=20, gamma=2, use_angular=True): `````` Malthe Kjær Bisbo committed Dec 17, 2019 98 99 100 101 102 103 104 105 106 107 108 109 110 111 `````` """ Set a common cut of radius """ self.Rc1 = Rc1 self.Rc2 = Rc2 self.binwidth1 = binwidth1 self.Nbins2 = Nbins2 self.binwidth2 = np.pi / Nbins2 self.sigma1 = sigma1 self.sigma2 = sigma2 self.eta = eta self.gamma = gamma self.use_angular = use_angular `````` Malthe Kjær Bisbo committed Dec 18, 2019 112 113 114 115 `````` self.initialized = False def initialize_from_atoms(self, atoms): self.nsigma = 4 `````` Malthe Kjær Bisbo committed Dec 17, 2019 116 117 118 119 120 121 122 123 124 125 126 127 128 `````` self.volume = atoms.get_volume() self.pbc = atoms.get_pbc() self.Natoms = atoms.get_number_of_atoms() self.dim = 3 # parameters for the binning: self.m1 = self.nsigma*self.sigma1/self.binwidth1 # number of neighbour bins included. self.smearing_norm1 = erf(1/np.sqrt(2) * self.m1 * self.binwidth1/self.sigma1) # Integral of the included part of the gauss self.Nbins1 = int(np.ceil(self.Rc1/self.binwidth1)) self.m2 = self.nsigma*self.sigma2/self.binwidth2 # number of neighbour bins included. self.smearing_norm2 = erf(1/np.sqrt(2) * self.m2 * self.binwidth2/self.sigma2) # Integral of the included part of the gauss `````` Malthe Kjær Bisbo committed Dec 18, 2019 129 `````` self.binwidth2 = np.pi/self.Nbins2 `````` Malthe Kjær Bisbo committed Dec 17, 2019 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 `````` # Prepare stuff to handle multiple species self.num = atoms.get_atomic_numbers() self.atomic_types = sorted(list(set(self.num))) self.atomic_count = {type:list(self.num).count(type) for type in self.atomic_types} self.Ntypes = len(self.atomic_types) type_converter = {} for i, type in enumerate(self.atomic_types): type_converter[type] = i # Bondtypes - 2body self.Nbondtypes_2body = 0 self.bondtypes_2body = -np.ones((self.Ntypes, self.Ntypes)).astype(int) count = 0 for tt1 in self.atomic_types: for tt2 in self.atomic_types: type1, type2 = tuple(sorted([tt1, tt2])) t1 = type_converter[type1] t2 = type_converter[type2] if type1 < type2: if self.bondtypes_2body[t1,t2] == -1: self.bondtypes_2body[t1,t2] = count self.Nbondtypes_2body += 1 count += 1 elif type1 == type2 and (self.atomic_count[type1] > 1 or sum(self.pbc) > 0): if self.bondtypes_2body[t1,t2] == -1: self.bondtypes_2body[t1,t2] = count self.Nbondtypes_2body += 1 count += 1 self.bondtypes_2body = self.bondtypes_2body.reshape(-1).tolist() # Bondtypes - 3body self.bondtypes_3body = -np.ones((self.Ntypes, self.Ntypes, self.Ntypes)).astype(int) bondtypes_3body_keys = [] for type1 in self.atomic_types: for type2 in self.atomic_types: if type1 == type2 and not (self.atomic_count[type1] > 1 or sum(self.pbc) > 0): continue for type3 in self.atomic_types: if type1 == type3 and not (self.atomic_count[type1] > 1 or sum(self.pbc) > 0): continue key = tuple([type1] + sorted([type2, type3])) if type2 < type3: bondtypes_3body_keys.append(key) elif type2 == type3: if type2 == type1 and (self.atomic_count[type1] > 2 or sum(self.pbc) > 0): bondtypes_3body_keys.append(key) elif type2 != type1 and (self.atomic_count[type2] > 1 or sum(self.pbc) > 0): bondtypes_3body_keys.append(key) self.Nbondtypes_3body = len(bondtypes_3body_keys) for i, key in enumerate(bondtypes_3body_keys): k1, k2, k3 = key self.bondtypes_3body[type_converter[k1],type_converter[k2],type_converter[k3]] = i self.bondtypes_3body = self.bondtypes_3body.reshape(-1).tolist() self.Nelements_2body = self.Nbondtypes_2body * self.Nbins1 self.Nelements_3body = self.Nbondtypes_3body * self.Nbins2 `````` Malthe Kjær Bisbo committed Dec 18, 2019 190 `````` if self.use_angular: `````` Malthe Kjær Bisbo committed Dec 17, 2019 191 192 193 194 195 196 197 198 199 `````` self.Nelements = self.Nelements_2body + self.Nelements_3body else: self.Nelements = self.Nelements_2body # Get relevant neighbour unit-cells self.pbc = atoms.get_pbc() self.cell = atoms.get_cell() self.neighbourcells_disp = self.__get_neighbour_cells_displacement(self.pbc, self.cell) `````` Malthe Kjær Bisbo committed Dec 18, 2019 200 201 `````` self.initialized = True `````` Malthe Kjær Bisbo committed Dec 17, 2019 202 203 204 `````` def get_feature(self, atoms): """ """ `````` Malthe Kjær Bisbo committed Dec 18, 2019 205 206 207 208 `````` if not self.initialized: self.initialize_from_atoms(atoms) `````` Malthe Kjær Bisbo committed Dec 17, 2019 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 `````` cdef double Rc1 = self.Rc1 cdef double Rc2 = self.Rc2 cdef double binwidth1 = self.binwidth1 cdef double binwidth2 = self.binwidth2 cdef int Nbins1 = self.Nbins1 cdef int Nbins2 = self.Nbins2 cdef double sigma1 = self.sigma1 cdef double sigma2 = self.sigma2 cdef int nsigma = self.nsigma cdef double eta = self.eta cdef double gamma = self.gamma cdef use_angular = self.use_angular cdef double volume = self.volume cdef int dim = self.dim cdef double m1 = self.m1 cdef double m2 = self.m2 cdef double smearing_norm1 = self.smearing_norm1 cdef double smearing_norm2 = self.smearing_norm2 cdef int Nelements_2body = self.Nelements_2body cdef int Nelements_3body = self.Nelements_3body cdef int Nelements = self.Nelements # Memory allocation pool cdef Pool mem mem = Pool() cell = atoms.get_cell() cdef int Natoms = self.Natoms # Get positions and convert to Point-struct cdef list pos_np = atoms.get_positions().tolist() cdef Point *pos pos = mem.alloc(Natoms, sizeof(Point)) cdef int m for m in range(Natoms): pos[m].coord[0] = pos_np[m][0] pos[m].coord[1] = pos_np[m][1] pos[m].coord[2] = pos_np[m][2] # Get neighbourcells and convert to Point-struct cdef int Ncells = len(self.neighbourcells_disp) cdef list cell_displacements_old = self.neighbourcells_disp cdef Point *cell_displacements cell_displacements = mem.alloc(Ncells, sizeof(Point)) for m in range(Ncells): cell_displacements[m].coord[0] = cell_displacements_old[m][0] cell_displacements[m].coord[1] = cell_displacements_old[m][1] cell_displacements[m].coord[2] = cell_displacements_old[m][2] # Convert 2body bondtype list into c-array cdef int Ntypes = self.Ntypes cdef int Nbondtypes_2body = self.Nbondtypes_2body cdef list bondtypes_2body_old = self.bondtypes_2body cdef int *bondtypes_2body bondtypes_2body = mem.alloc(Ntypes*Ntypes, sizeof(int)) for m in range(Ntypes*Ntypes): bondtypes_2body[m] = bondtypes_2body_old[m] # Get converted atom Ntypes cdef list num_converted_old = convert_atom_types(atoms.get_atomic_numbers()) cdef int *num_converted num_converted = mem.alloc(Natoms, sizeof(int)) for m in range(Natoms): num_converted[m] = num_converted_old[m] # RADIAL FEATURE # Initialize radial feature cdef double *feature1 feature1 = mem.alloc(Nelements_2body, sizeof(double)) cdef int num_pairs, center_bin, minbin_lim, maxbin_lim, newbin, bondtype_index, type1, type2 cdef double Rij, normalization, binpos, c, erfarg_low, erfarg_up, value cdef int i, j, n for i in range(Natoms): for cell_index in range(Ncells): displacement = cell_displacements[cell_index] for j in range(Natoms): Rij = euclidean(pos[i], add(pos[j], displacement)) # Stop if distance too long or atoms are the same one. if Rij > Rc1+nsigma*sigma1 or Rij < 1e-6: continue # determine bondtype if num_converted[i] <= num_converted[j]: type1 = num_converted[i] type2 = num_converted[j] else: type1 = num_converted[j] type2 = num_converted[i] bondtype_index = Nbins1*bondtypes_2body[Ntypes*type1+type2] # Calculate normalization num_pairs = Natoms*Natoms normalization = 1./smearing_norm1 normalization /= 4*M_PI*Rij*Rij * binwidth1 * num_pairs/volume # Identify what bin 'Rij' belongs to + it's position in this bin center_bin = floor(Rij/binwidth1) binpos = Rij/binwidth1 - center_bin # Lower and upper range of bins affected by the current atomic distance deltaR. minbin_lim = -ceil(m1 - binpos) maxbin_lim = ceil(m1 - (1-binpos)) for n in range(minbin_lim, maxbin_lim + 1): newbin = center_bin + n if newbin < 0 or newbin >= Nbins1: continue # Calculate gauss contribution to current bin c = 1./sqrt(2)*binwidth1/sigma1 erfarg_low = max(-m1, n-binpos) erfarg_up = min(m1, n+(1-binpos)) value = 0.5*erf(c*erfarg_up)-0.5*erf(c*erfarg_low) # Apply normalization value *= normalization feature1[bondtype_index + newbin] += value #feature1[newbin] += value # Convert radial feature to numpy array feature1_np = np.zeros(Nelements_2body) for m in range(Nelements_2body): feature1_np[m] = feature1[m] # Return feature if only radial part is desired if not use_angular: return feature1_np # ANGULAR FEATURE # Convert 3body bondtype list into c-array cdef int Nbondtypes_3body = self.Nbondtypes_3body cdef list bondtypes_3body_old = self.bondtypes_3body cdef int *bondtypes_3body bondtypes_3body = mem.alloc(Ntypes*Ntypes*Ntypes, sizeof(int)) for m in range(Ntypes*Ntypes*Ntypes): bondtypes_3body[m] = bondtypes_3body_old[m] # Initialize angular feature cdef double *feature2 feature2 = mem.alloc(Nelements_3body, sizeof(double)) cdef Point RijVec, RikVec cdef double angle cdef int k, cond_ij, cond_ik, type3 for i in range(Natoms): pos_i = pos[i] for cell_index1 in range(Ncells): displacement1 = cell_displacements[cell_index1] for j in range(Natoms): pos_j = add(pos[j], displacement1) Rij = euclidean(pos[i], pos_j) if Rij > Rc2 or Rij < 1e-6: continue for cell_index2 in range(cell_index1, Ncells): displacement2 = cell_displacements[cell_index2] if cell_index1 == cell_index2: k_start = j+1 else: k_start = 0 for k in range(k_start, Natoms): pos_k = add(pos[k], displacement2) Rik = euclidean(pos_i, pos_k) if Rik > Rc2 or Rik < 1e-6: continue # determine bondtype type1 = num_converted[i] if num_converted[j] <= num_converted[k]: type2 = num_converted[j] type3 = num_converted[k] else: type2 = num_converted[k] type3 = num_converted[j] bondtype_index = Nbins2*bondtypes_3body[Ntypes*Ntypes*type1 + Ntypes*type2 + type3] # Calculate angle RijVec = subtract(pos_j,pos_i) RikVec = subtract(pos_k, pos_i) angle = get_angle(RijVec, RikVec) # Calculate normalization num_pairs = Natoms*Natoms*Natoms normalization = 1./smearing_norm2 normalization /= num_pairs/volume # Identify what bin 'Rij' belongs to + it's position in this bin center_bin = floor(angle/binwidth1) binpos = angle/binwidth2 - center_bin # Lower and upper range of bins affected by the current atomic distance deltaR. minbin_lim = -ceil(m2 - binpos) maxbin_lim = ceil(m2 - (1-binpos)) for n in range(minbin_lim, maxbin_lim + 1): newbin = center_bin + n # Wrap current bin into correct bin-range if newbin < 0: newbin = abs(newbin) if newbin > Nbins2-1: newbin = 2*Nbins2 - newbin - 1 # Calculate gauss contribution to current bin c = 1./sqrt(2)*binwidth2/sigma2 erfarg_low = max(-m2, n-binpos) erfarg_up = min(m2, n+(1-binpos)) value = 0.5*erf(c*erfarg_up)-0.5*erf(c*erfarg_low) value *= f_cutoff(Rij, gamma, Rc2) * f_cutoff(Rik, gamma, Rc2) # Apply normalization value *= normalization feature2[bondtype_index + newbin] += value #feature2[newbin] += value # Convert angular feature to numpy array feature2_np = np.zeros(Nelements_3body) for m in range(Nelements_3body): feature2_np[m] = eta * feature2[m] feature_np = np.zeros(Nelements) feature_np[:Nelements_2body] = feature1_np feature_np[Nelements_2body:] = feature2_np return feature_np def get_featureMat(self, atoms_list): featureMat = np.array([self.get_feature(atoms) for atoms in atoms_list]) featureMat = np.array(featureMat) return featureMat def get_featureGradient(self, atoms): `````` Malthe Kjær Bisbo committed Dec 18, 2019 449 450 451 `````` if not self.initialized: self.initialize_from_atoms(atoms) `````` Malthe Kjær Bisbo committed Dec 17, 2019 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 `````` cdef double Rc1 = self.Rc1 cdef double Rc2 = self.Rc2 cdef double binwidth1 = self.binwidth1 cdef double binwidth2 = self.binwidth2 cdef int Nbins1 = self.Nbins1 cdef int Nbins2 = self.Nbins2 cdef double sigma1 = self.sigma1 cdef double sigma2 = self.sigma2 cdef int nsigma = self.nsigma cdef double eta = self.eta cdef double gamma = self.gamma cdef use_angular = self.use_angular cdef double volume = self.volume cdef int dim = self.dim cdef double m1 = self.m1 cdef double m2 = self.m2 cdef double smearing_norm1 = self.smearing_norm1 cdef double smearing_norm2 = self.smearing_norm2 cdef int Nelements_2body = self.Nelements_2body cdef int Nelements_3body = self.Nelements_3body cdef int Nelements = self.Nelements # Memory allocation pool cdef Pool mem mem = Pool() cell = atoms.get_cell() cdef int Natoms = self.Natoms # Get positions and convert to Point-struct cdef list pos_np = atoms.get_positions().tolist() cdef Point *pos pos = mem.alloc(Natoms, sizeof(Point)) cdef int m for m in range(Natoms): pos[m].coord[0] = pos_np[m][0] pos[m].coord[1] = pos_np[m][1] pos[m].coord[2] = pos_np[m][2] # Get neighbourcells and convert to Point-struct cdef int Ncells = len(self.neighbourcells_disp) cdef list cell_displacements_old = self.neighbourcells_disp cdef Point *cell_displacements cell_displacements = mem.alloc(Ncells, sizeof(Point)) for m in range(Ncells): cell_displacements[m].coord[0] = cell_displacements_old[m][0] cell_displacements[m].coord[1] = cell_displacements_old[m][1] cell_displacements[m].coord[2] = cell_displacements_old[m][2] # Convert bondtype list into c-array cdef int Ntypes = self.Ntypes cdef int Nbondtypes_2body = self.Nbondtypes_2body cdef list bondtypes_2body_old = self.bondtypes_2body cdef int *bondtypes_2body bondtypes_2body = mem.alloc(Ntypes*Ntypes, sizeof(int)) for m in range(Ntypes*Ntypes): bondtypes_2body[m] = bondtypes_2body_old[m] # Get converted atom Ntypes cdef list num_converted_old = convert_atom_types(atoms.get_atomic_numbers()) cdef int *num_converted num_converted = mem.alloc(Natoms, sizeof(int)) for m in range(Natoms): num_converted[m] = num_converted_old[m] # RADIAL FEATURE GRADIENT # Initialize radial feature-gradient cdef double *feature_grad1 feature_grad1 = mem.alloc(Nelements_2body * Natoms * dim, sizeof(double)) cdef Point RijVec cdef int num_pairs, center_bin, minbin_lim, maxbin_lim, newbin, bondtype_index, type1, type2 cdef double Rij, normalization, binpos, c, arg_low, arg_up, value1, value2, value cdef int i, j, n for i in range(Natoms): pos_i = pos[i] for cell_index in range(Ncells): displacement = cell_displacements[cell_index] for j in range(Natoms): pos_j = add(pos[j], displacement) Rij = euclidean(pos_i, pos_j) # Stop if distance too long or atoms are the same one. if Rij > Rc1+nsigma*sigma1 or Rij < 1e-6: continue RijVec = subtract(pos_j,pos_i) # determine bondtype if num_converted[i] <= num_converted[j]: type1 = num_converted[i] type2 = num_converted[j] else: type1 = num_converted[j] type2 = num_converted[i] bondtype_index = Nbins1*bondtypes_2body[Ntypes*type1+type2] # Calculate normalization num_pairs = Natoms*Natoms normalization = 1./smearing_norm1 normalization /= 4*M_PI*Rij*Rij * binwidth1 * num_pairs/volume # Identify what bin 'Rij' belongs to + it's position in this bin center_bin = floor(Rij/binwidth1) binpos = Rij/binwidth1 - center_bin # Lower and upper range of bins affected by the current atomic distance deltaR. minbin_lim = -ceil(m1 - binpos) maxbin_lim = ceil(m1 - (1-binpos)) for n in range(minbin_lim, maxbin_lim + 1): newbin = center_bin + n if newbin < 0 or newbin >= Nbins1: continue # Calculate gauss contribution to current bin c = 1./sqrt(2)*binwidth1/sigma1 arg_low = max(-m1, n-binpos) arg_up = min(m1, n+(1-binpos)) value1 = -1./Rij * (erf(c*arg_up) - erf(c*arg_low)) value2 = -1./(sigma1*sqrt(2*M_PI)) * (exp(-pow(c*arg_up,2)) - exp(-pow(c*arg_low,2))) value = value1 + value2 # Apply normalization value *= normalization # Add to the the gradient matrix for m in range(3): feature_grad1[(bondtype_index + newbin) * Natoms*dim + dim*i+m] += -value/Rij * RijVec.coord[m] feature_grad1[(bondtype_index + newbin) * Natoms*dim + dim*j+m] += value/Rij * RijVec.coord[m] # Convert radial feature to numpy array cdef int grad_index feature_grad1_np = np.zeros((Natoms*dim, Nelements_2body)) for m in range(Nelements_2body): for grad_index in range(Natoms*dim): feature_grad1_np[grad_index][m] = feature_grad1[m * Natoms*dim + grad_index] # Return feature if only radial part is desired if not use_angular: return feature_grad1_np # ANGULAR FEATURE-GRADIENT # Convert 3body bondtype list into c-array cdef int Nbondtypes_3body = self.Nbondtypes_3body cdef list bondtypes_3body_old = self.bondtypes_3body cdef int *bondtypes_3body bondtypes_3body = mem.alloc(Ntypes*Ntypes*Ntypes, sizeof(int)) for m in range(Ntypes*Ntypes*Ntypes): bondtypes_3body[m] = bondtypes_3body_old[m] # Initialize angular feature-gradient cdef double *feature_grad2 feature_grad2 = mem.alloc(Nelements_3body * Natoms * dim, sizeof(double)) cdef Point RikVec, angle_grad_i, angle_grad_j, angle_grad_k cdef double angle, cos_angle, a cdef int k, cond_ij, cond_ik, bin_index, type3 for i in range(Natoms): pos_i = pos[i] for cell_index1 in range(Ncells): displacement1 = cell_displacements[cell_index1] for j in range(Natoms): pos_j = add(pos[j], displacement1) Rij = euclidean(pos[i], pos_j) if Rij > Rc2 or Rij < 1e-6: continue for cell_index2 in range(cell_index1, Ncells): displacement2 = cell_displacements[cell_index2] if cell_index1 == cell_index2: k_start = j+1 else: k_start = 0 for k in range(k_start, Natoms): pos_k = add(pos[k], displacement2) Rik = euclidean(pos_i, pos_k) if Rik > Rc2 or Rik < 1e-6: continue # determine bondtype type1 = num_converted[i] if num_converted[j] <= num_converted[k]: type2 = num_converted[j] type3 = num_converted[k] else: type2 = num_converted[k] type3 = num_converted[j] bondtype_index = Nbins2*bondtypes_3body[Ntypes*Ntypes*type1 + Ntypes*type2 + type3] # Calculate angle RijVec = subtract(pos_j,pos_i) RikVec = subtract(pos_k, pos_i) angle = get_angle(RijVec, RikVec) cos_angle = cos(angle) for m in range(3): if not (angle == 0 or angle == M_PI): a = -1/sqrt(1 - cos_angle*cos_angle) angle_grad_j.coord[m] = a * (RikVec.coord[m]/(Rij*Rik) - cos_angle*RijVec.coord[m]/(Rij*Rij)) angle_grad_k.coord[m] = a * (RijVec.coord[m]/(Rij*Rik) - cos_angle*RikVec.coord[m]/(Rik*Rik)) angle_grad_i.coord[m] = -(angle_grad_j.coord[m] + angle_grad_k.coord[m]) else: angle_grad_j.coord[m] = 0 angle_grad_k.coord[m] = 0 angle_grad_i.coord[m] = 0 fc_ij = f_cutoff(Rij, gamma, Rc2) fc_ik = f_cutoff(Rik, gamma, Rc2) fc_grad_ij = f_cutoff_grad(Rij, gamma, Rc2) fc_grad_ik = f_cutoff_grad(Rik, gamma, Rc2) # Calculate normalization num_pairs = Natoms*Natoms*Natoms normalization = 1./smearing_norm2 normalization /= num_pairs/volume # Identify what bin 'Rij' belongs to + it's position in this bin center_bin = floor(angle/binwidth1) binpos = angle/binwidth2 - center_bin # Lower and upper range of bins affected by the current atomic distance deltaR. minbin_lim = -ceil(m2 - binpos) maxbin_lim = ceil(m2 - (1-binpos)) for n in range(minbin_lim, maxbin_lim + 1): newbin = center_bin + n # Wrap current bin into correct bin-range if newbin < 0: newbin = abs(newbin) if newbin > Nbins2-1: newbin = 2*Nbins2 - newbin - 1 # Calculate gauss contribution to current bin c = 1./sqrt(2)*binwidth2/sigma2 arg_low = max(-m2, n-binpos) arg_up = min(m2, n+(1-binpos)) value1 = 0.5*erf(c*arg_up)-0.5*erf(c*arg_low) value2 = -1./(sigma2*sqrt(2*M_PI)) * (exp(-pow(c*arg_up, 2)) - exp(-pow(c*arg_low, 2))) # Apply normalization value1 *= normalization value2 *= normalization bin_index = (bondtype_index + newbin) * Natoms*dim for m in range(3): feature_grad2[bin_index + dim*i+m] += -value1 * fc_ik*fc_grad_ij * RijVec.coord[m]/Rij feature_grad2[bin_index + dim*j+m] += value1 * fc_ik*fc_grad_ij * RijVec.coord[m]/Rij feature_grad2[bin_index + dim*i+m] += -value1 * fc_ij*fc_grad_ik * RikVec.coord[m]/Rik feature_grad2[bin_index + dim*k+m] += value1 * fc_ij*fc_grad_ik * RikVec.coord[m]/Rik feature_grad2[bin_index + dim*i+m] += value2 * fc_ij * fc_ik * angle_grad_i.coord[m] feature_grad2[bin_index + dim*j+m] += value2 * fc_ij * fc_ik * angle_grad_j.coord[m] feature_grad2[bin_index + dim*k+m] += value2 * fc_ij * fc_ik * angle_grad_k.coord[m] feature_grad2_np = np.zeros((Natoms*dim, Nelements_3body)) for m in range(Nelements_3body): for grad_index in range(Natoms*dim): feature_grad2_np[grad_index][m] = eta * feature_grad2[m * Natoms*dim + grad_index] feature_grad_np = np.zeros((Natoms*dim, Nelements)) feature_grad_np[:, :Nelements_2body] = feature_grad1_np feature_grad_np[:, Nelements_2body:] = feature_grad2_np return feature_grad_np def get_all_featureGradients(self, atoms_list): feature_grads = np.array([self.get_featureGradient(atoms) for atoms in atoms_list]) feature_grads = np.array(feature_grads) return feature_grads def __get_neighbour_cells_displacement(self, pbc, cell): # Calculate neighbour cells Rc_max = max(self.Rc1+self.sigma1*self.nsigma, self.Rc2) # relevant cutoff cell_vec_norms = np.linalg.norm(cell, axis=0) neighbours = [] for i in range(3): if pbc[i]: ncellmax = int(np.ceil(abs(Rc_max/cell_vec_norms[i]))) + 1 # +1 because atoms can be outside unitcell. neighbours.append(range(-ncellmax,ncellmax+1)) else: neighbours.append([0]) neighbourcells_disp = [] for x,y,z in product(*neighbours): xyz = (x,y,z) displacement = np.dot(xyz, cell) neighbourcells_disp.append(list(displacement)) return neighbourcells_disp``````