/usr/include/sc/math/symmetry/pointgrp.h is in libsc-dev 2.3.1-16.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 | //
// pointgrp.h
//
// Modifications are
// Copyright (C) 1996 Limit Point Systems, Inc.
//
// Author: Edward Seidl <seidl@janed.com>
// Maintainer: LPS
//
// This file is part of the SC Toolkit.
//
// The SC Toolkit is free software; you can redistribute it and/or modify
// it under the terms of the GNU Library General Public License as published by
// the Free Software Foundation; either version 2, or (at your option)
// any later version.
//
// The SC Toolkit is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU Library General Public License for more details.
//
// You should have received a copy of the GNU Library General Public License
// along with the SC Toolkit; see the file COPYING.LIB. If not, write to
// the Free Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA.
//
// The U.S. Government is granted a limited license as per AL 91-7.
//
/* pointgrp.h -- definition of the point group classes
*
* THIS SOFTWARE FITS THE DESCRIPTION IN THE U.S. COPYRIGHT ACT OF A
* "UNITED STATES GOVERNMENT WORK". IT WAS WRITTEN AS A PART OF THE
* AUTHOR'S OFFICIAL DUTIES AS A GOVERNMENT EMPLOYEE. THIS MEANS IT
* CANNOT BE COPYRIGHTED. THIS SOFTWARE IS FREELY AVAILABLE TO THE
* PUBLIC FOR USE WITHOUT A COPYRIGHT NOTICE, AND THERE ARE NO
* RESTRICTIONS ON ITS USE, NOW OR SUBSEQUENTLY.
*
* Author:
* E. T. Seidl
* Bldg. 12A, Rm. 2033
* Computer Systems Laboratory
* Division of Computer Research and Technology
* National Institutes of Health
* Bethesda, Maryland 20892
* Internet: seidl@alw.nih.gov
* June, 1993
*/
#ifdef __GNUC__
#pragma interface
#endif
#ifndef _math_symmetry_pointgrp_h
#define _math_symmetry_pointgrp_h
#include <iostream>
#include <util/class/class.h>
#include <util/state/state.h>
#include <util/keyval/keyval.h>
#include <math/scmat/vector3.h>
namespace sc {
// //////////////////////////////////////////////////////////////////
/** The SymmetryOperation class provides a 3 by 3 matrix
representation of a symmetry operation, such as a rotation or reflection.
*/
class SymmetryOperation {
private:
double d[3][3];
public:
SymmetryOperation();
SymmetryOperation(const SymmetryOperation &);
~SymmetryOperation();
/// returns the trace of the transformation matrix
double trace() const { return d[0][0]+d[1][1]+d[2][2]; }
/// returns the i'th row of the transformation matrix
double* operator[](int i) { return d[i]; }
/// const version of the above
const double* operator[](int i) const { return d[i]; }
/** returns a reference to the (i,j)th element of the transformation
matrix */
double& operator()(int i, int j) { return d[i][j]; }
/// const version of the above
double operator()(int i, int j) const { return d[i][j]; }
/// zero out the symop
void zero() { memset(d,0,sizeof(double)*9); }
/// This operates on this with r (i.e. return r * this).
SymmetryOperation operate(const SymmetryOperation& r) const;
/// This performs the transform r * this * r~
SymmetryOperation transform(const SymmetryOperation& r) const;
/// Set equal to a unit matrix
void unit() { zero(); d[0][0] = d[1][1] = d[2][2] = 1.0; }
/// Set equal to E
void E() { unit(); }
/// Set equal to an inversion
void i() { zero(); d[0][0] = d[1][1] = d[2][2] = -1.0; }
/// Set equal to reflection in xy plane
void sigma_h() { unit(); d[2][2] = -1.0; }
/// Set equal to reflection in xz plane
void sigma_xz() { unit(); d[1][1] = -1.0; }
/// Set equal to reflection in yz plane
void sigma_yz() { unit(); d[0][0] = -1.0; }
/// Set equal to a clockwise rotation by 2pi/n
void rotation(int n);
void rotation(double theta);
/// Set equal to C2 about the x axis
void c2_x() { i(); d[0][0] = 1.0; }
/// Set equal to C2 about the x axis
void c2_y() { i(); d[1][1] = 1.0; }
void transpose();
/// print the matrix
void print(std::ostream& =ExEnv::out0()) const;
};
// //////////////////////////////////////////////////////////////////
/** The SymRep class provides an n dimensional matrix representation of a
symmetry operation, such as a rotation or reflection. The trace of a
SymRep can be used as the character for that symmetry operation. d is
hardwired to 5x5 since the H irrep in Ih is 5 dimensional.
*/
class SymRep {
private:
int n;
double d[5][5];
public:
SymRep(int =0);
SymRep(const SymmetryOperation&);
~SymRep();
/// Cast to a SymmetryOperation.
operator SymmetryOperation() const;
/// returns the trace of the transformation matrix
inline double trace() const;
/// set the dimension of d
void set_dim(int i) { n=i; }
/// returns the i'th row of the transformation matrix
double* operator[](int i) { return d[i]; }
/// const version of the above
const double* operator[](int i) const { return d[i]; }
/** returns a reference to the (i,j)th element of the transformation
matrix */
double& operator()(int i, int j) { return d[i][j]; }
/// const version of double& operator()(int i, int j)
double operator()(int i, int j) const { return d[i][j]; }
/// zero out the symop
void zero() { memset(d,0,sizeof(double)*25); }
/// This operates on this with r (i.e. return r * this).
SymRep operate(const SymRep& r) const;
/// This performs the transform r * this * r~
SymRep transform(const SymRep& r) const;
/// Set equal to a unit matrix
void unit() {
zero(); d[0][0] = d[1][1] = d[2][2] = d[3][3] = d[4][4] = 1.0;
}
/// Set equal to the identity
void E() { unit(); }
/// Set equal to an inversion
void i() { zero(); d[0][0] = d[1][1] = d[2][2] = d[3][3] = d[4][4] = -1.0;}
/// Set equal to reflection in xy plane
void sigma_h();
/// Set equal to reflection in xz plane
void sigma_xz();
/// Set equal to reflection in yz plane
void sigma_yz();
/// Set equal to a clockwise rotation by 2pi/n
void rotation(int n);
void rotation(double theta);
/// Set equal to C2 about the x axis
void c2_x();
/// Set equal to C2 about the x axis
void c2_y();
/// print the matrix
void print(std::ostream& =ExEnv::out0()) const;
};
inline double
SymRep::trace() const
{
double r=0;
for (int i=0; i < n; i++)
r += d[i][i];
return r;
}
// //////////////////////////////////////////////////////////////////
class CharacterTable;
/** The IrreducibleRepresentation class provides information associated
with a particular irreducible representation of a point group. This
includes the Mulliken symbol for the irrep, the degeneracy of the
irrep, the characters which represent the irrep, and the number of
translations and rotations in the irrep. The order of the point group
is also provided (this is equal to the number of characters in an
irrep). */
class IrreducibleRepresentation {
friend class CharacterTable;
private:
int g; // the order of the group
int degen; // the degeneracy of the irrep
int nrot_; // the number of rotations in this irrep
int ntrans_; // the number of translations in this irrep
int complex_; // true if this irrep has a complex representation
char *symb; // mulliken symbol for this irrep
char *csymb; // mulliken symbol for this irrep w/o special characters
SymRep *rep; // representation matrices for the symops
public:
IrreducibleRepresentation();
IrreducibleRepresentation(const IrreducibleRepresentation&);
/** This constructor takes as arguments the order of the point group,
the degeneracy of the irrep, and the Mulliken symbol of the irrep.
The Mulliken symbol is copied internally. */
IrreducibleRepresentation(int,int,const char*,const char* =0);
~IrreducibleRepresentation();
IrreducibleRepresentation& operator=(const IrreducibleRepresentation&);
/// Initialize the order, degeneracy, and Mulliken symbol of the irrep.
void init(int =0, int =0, const char* =0, const char* =0);
/// Returns the order of the group.
int order() const { return g; }
/// Returns the degeneracy of the irrep.
int degeneracy() const { return degen; }
/// Returns the value of complex_.
int complex() const { return complex_; }
/// Returns the number of projection operators for the irrep.
int nproj() const { return degen*degen; }
/// Returns the number of rotations associated with the irrep.
int nrot() const { return nrot_; }
/// Returns the number of translations associated with the irrep.
int ntrans() const { return ntrans_; }
/// Returns the Mulliken symbol for the irrep.
const char * symbol() const { return symb; }
/** Returns the Mulliken symbol for the irrep without special
characters.
*/
const char * symbol_ns() const { return (csymb?csymb:symb); }
/** Returns the character for the i'th symmetry operation of the point
group. */
double character(int i) const {
return complex_ ? 0.5*rep[i].trace() : rep[i].trace();
}
/// Returns the element (x1,x2) of the i'th representation matrix.
double p(int x1, int x2, int i) const { return rep[i](x1,x2); }
/** Returns the character for the d'th contribution to the i'th
representation matrix. */
double p(int d, int i) const {
int dc=d/degen; int dr=d%degen;
return rep[i](dr,dc);
}
/** This prints the irrep to the given file, or stdout if none is
given. The second argument is an optional string of spaces to offset
by. */
void print(std::ostream& =ExEnv::out0()) const;
};
// ///////////////////////////////////////////////////////////
/** The CharacterTable class provides a workable character table
for all of the non-cubic point groups. While I have tried to match the
ordering in Cotton's book, I don't guarantee that it is always followed.
It shouldn't matter anyway. Also note that I don't lump symmetry
operations of the same class together. For example, in C3v there are two
distinct C3 rotations and 3 distinct reflections, each with a separate
character. Thus symop has 6 elements rather than the 3 you'll find in
most published character tables. */
class CharacterTable {
public:
enum pgroups {C1, CS, CI, CN, CNV, CNH, DN, DND, DNH, SN, T, TH, TD, O,
OH, I, IH};
private:
int g; // the order of the point group
int nt; // order of the princ rot axis
pgroups pg; // the class of the point group
int nirrep_; // the number of irreps in this pg
IrreducibleRepresentation *gamma_; // an array of irreps
SymmetryOperation *symop; // the matrices describing sym ops
int *_inv; // index of the inverse symop
char *symb; // the Schoenflies symbol for the pg
/// this determines what type of point group we're dealing with
int parse_symbol();
/// this fills in the irrep and symop arrays.
int make_table();
// these create the character tables for the cubic groups
void t();
void th();
void td();
void o();
void oh();
void i();
void ih();
public:
CharacterTable();
/** This constructor takes the Schoenflies symbol of a point group as
input. */
CharacterTable(const char*);
/** This is like the above, but it also takes a reference to a
SymmetryOperation which is the frame of reference. All symmetry
operations are transformed to this frame of reference. */
CharacterTable(const char*,const SymmetryOperation&);
CharacterTable(const CharacterTable&);
~CharacterTable();
CharacterTable& operator=(const CharacterTable&);
/// Returns the number of irreps.
int nirrep() const { return nirrep_; }
/// Returns the order of the point group
int order() const { return g; }
/// Returns the Schoenflies symbol for the point group
const char * symbol() const { return symb; }
/// Returns the i'th irrep.
IrreducibleRepresentation& gamma(int i) { return gamma_[i]; }
/// Returns the i'th symmetry operation.
SymmetryOperation& symm_operation(int i) { return symop[i]; }
/** Cn, Cnh, Sn, T, and Th point groups have complex representations.
This function returns 1 if the point group has a complex
representation, 0 otherwise. */
int complex() const {
if (pg==CN || pg==SN || pg==CNH || pg==T || pg==TH)
return 1;
return 0;
}
/// Returns the index of the symop which is the inverse of symop[i].
int inverse(int i) const { return _inv[i]; }
int ncomp() const {
int ret=0;
for (int i=0; i < nirrep_; i++) {
int nc = (gamma_[i].complex()) ? 1 : gamma_[i].degen;
ret += nc;
}
return ret;
}
/// Returns the irrep component i belongs to.
int which_irrep(int i) {
for (int ir=0, cn=0; ir < nirrep_; ir++) {
int nc = (gamma_[ir].complex()) ? 1 : gamma_[ir].degen;
for (int c=0; c < nc; c++,cn++)
if (cn==i)
return ir;
}
return -1;
}
/// Returns which component i is.
int which_comp(int i) {
for (int ir=0, cn=0; ir < nirrep_; ir++) {
int nc = (gamma_[ir].complex()) ? 1 : gamma_[ir].degen;
for (int c=0; c < nc; c++,cn++)
if (cn==i)
return c;
}
return -1;
}
/// This prints the irrep to the given file, or stdout if none is given.
void print(std::ostream& =ExEnv::out0()) const;
};
// ///////////////////////////////////////////////////////////
/** The PointGroup class is really a place holder for a CharacterTable. It
contains a string representation of the Schoenflies symbol of a point
group, a frame of reference for the symmetry operation transformation
matrices, and a point of origin. The origin is not respected by the
symmetry operations, so if you want to use a point group with a nonzero
origin, first translate all your coordinates to the origin and then set
the origin to zero. */
class PointGroup: public SavableState {
private:
char *symb;
SymmetryOperation frame;
SCVector3 origin_;
public:
PointGroup();
/** This constructor takes a string containing the Schoenflies symbol
of the point group as its only argument. */
PointGroup(const char*);
/** Like the above, but this constructor also takes a frame of reference
as an argument. */
PointGroup(const char*,SymmetryOperation&);
/** Like the above, but this constructor also takes a point of origin
as an argument. */
PointGroup(const char*,SymmetryOperation&,const SCVector3&);
/** The PointGroup KeyVal constructor looks for three keywords:
symmetry, symmetry_frame, and origin. symmetry is a string
containing the Schoenflies symbol of the point group. origin is an
array of doubles which gives the x, y, and z coordinates of the
origin of the symmetry frame. symmetry_frame is a 3 by 3 array of
arrays of doubles which specify the principal axes for the
transformation matrices as a unitary rotation.
For example, a simple input which will use the default origin and
symmetry_frame ((0,0,0) and the unit matrix, respectively), might
look like this:
<pre>
pointgrp<PointGroup>: (
symmetry = "c2v"
)
</pre>
By default, the principal rotation axis is taken to be the z axis.
If you already have a set of coordinates which assume that the
rotation axis is the x axis, then you'll have to rotate your frame
of reference with symmetry_frame:
<pre>
pointgrp<PointGroup>: (
symmetry = "c2v"
symmetry_frame = [
[ 0 0 1 ]
[ 0 1 0 ]
[ 1 0 0 ]
]
)
</pre>
*/
PointGroup(const Ref<KeyVal>&);
PointGroup(StateIn&);
PointGroup(const PointGroup&);
PointGroup(const Ref<PointGroup>&);
~PointGroup();
PointGroup& operator=(const PointGroup&);
/// Returns 1 if the point groups are equivalent, 0 otherwise.
int equiv(const Ref<PointGroup> &, double tol = 1.0e-6) const;
/// Returns the CharacterTable for this point group.
CharacterTable char_table() const;
/// Returns the Schoenflies symbol for this point group.
const char * symbol() const { return symb; }
/// Returns the frame of reference for this point group.
SymmetryOperation& symm_frame() { return frame; }
/// A const version of the above
const SymmetryOperation& symm_frame() const { return frame; }
/// Returns the origin of the symmetry frame.
SCVector3& origin() { return origin_; }
const SCVector3& origin() const { return origin_; }
/// Sets (or resets) the Schoenflies symbol.
void set_symbol(const char*);
void save_data_state(StateOut& so);
void print(std::ostream&o=ExEnv::out0()) const;
};
}
#endif
// Local Variables:
// mode: c++
// c-file-style: "ETS"
// End:
|