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#ifdef __GNUC__
00050
#pragma interface
00051
#endif
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00053
#ifndef _math_symmetry_pointgrp_h
00054
#define _math_symmetry_pointgrp_h
00055
00056
#include <iostream>
00057
00058
#include <util/class/class.h>
00059
#include <util/state/state.h>
00060
#include <util/keyval/keyval.h>
00061
#include <math/scmat/vector3.h>
00062
00063
namespace sc {
00064
00065
00066
00070 class SymmetryOperation {
00071
private:
00072
double d[3][3];
00073
00074
public:
00075
SymmetryOperation();
00076
SymmetryOperation(
const SymmetryOperation &);
00077 ~
SymmetryOperation();
00078
00080 double trace()
const {
return d[0][0]+d[1][1]+d[2][2]; }
00081
00083 double*
operator[](
int i) {
return d[i]; }
00084
00086 const double*
operator[](
int i)
const {
return d[i]; }
00087
00090 double&
operator()(
int i,
int j) {
return d[i][j]; }
00091
00093 double operator()(
int i,
int j)
const {
return d[i][j]; }
00094
00096 void zero() { memset(d,0,
sizeof(
double)*9); }
00097
00099
SymmetryOperation operate(
const SymmetryOperation& r)
const;
00100
00102
SymmetryOperation transform(
const SymmetryOperation& r)
const;
00103
00105 void unit() {
zero(); d[0][0] = d[1][1] = d[2][2] = 1.0; }
00106
00108 void E() {
unit(); }
00109
00111 void i() {
zero(); d[0][0] = d[1][1] = d[2][2] = -1.0; }
00112
00114 void sigma_h() {
unit(); d[2][2] = -1.0; }
00115
00117 void sigma_xz() {
unit(); d[1][1] = -1.0; }
00118
00120 void sigma_yz() {
unit(); d[0][0] = -1.0; }
00121
00123
void rotation(
int n);
00124
void rotation(
double theta);
00125
00127 void c2_x() {
i(); d[0][0] = 1.0; }
00128
00130 void c2_y() {
i(); d[1][1] = 1.0; }
00131
00132
void transpose();
00133
00135
void print(std::ostream& =ExEnv::out0())
const;
00136 };
00137
00138
00139
00145 class SymRep {
00146
private:
00147
int n;
00148
double d[5][5];
00149
00150
public:
00151
SymRep(
int =0);
00152
SymRep(
const SymmetryOperation&);
00153 ~
SymRep();
00154
00156
operator SymmetryOperation()
const;
00157
00159
inline double trace()
const;
00160
00162 void set_dim(
int i) { n=i; }
00163
00165 double*
operator[](
int i) {
return d[i]; }
00167 const double*
operator[](
int i)
const {
return d[i]; }
00168
00171 double&
operator()(
int i,
int j) {
return d[i][j]; }
00173 double operator()(
int i,
int j)
const {
return d[i][j]; }
00174
00176 void zero() { memset(d,0,
sizeof(
double)*25); }
00177
00179
SymRep operate(
const SymRep& r)
const;
00180
00182
SymRep transform(
const SymRep& r)
const;
00183
00185 void unit() {
00186
zero(); d[0][0] = d[1][1] = d[2][2] = d[3][3] = d[4][4] = 1.0;
00187 }
00188
00190 void E() {
unit(); }
00191
00193 void i() {
zero(); d[0][0] = d[1][1] = d[2][2] = d[3][3] = d[4][4] = -1.0;}
00194
00196
void sigma_h();
00197
00199
void sigma_xz();
00200
00202
void sigma_yz();
00203
00205
void rotation(
int n);
00206
void rotation(
double theta);
00207
00209
void c2_x();
00210
00212
void c2_y();
00213
00215
void print(std::ostream& =ExEnv::out0())
const;
00216 };
00217
00218
inline double
00219 SymRep::trace()
const
00220
{
00221
double r=0;
00222
for (
int i=0; i < n; i++)
00223 r += d[i][i];
00224
return r;
00225 }
00226
00227
00228
00229
00230
class CharacterTable;
00231
00239 class IrreducibleRepresentation {
00240
friend class CharacterTable;
00241
00242
private:
00243
int g;
00244
int degen;
00245
int nrot_;
00246
int ntrans_;
00247
int complex_;
00248
char *symb;
00249
char *csymb;
00250
00251
SymRep *rep;
00252
00253
public:
00254
IrreducibleRepresentation();
00255
IrreducibleRepresentation(
const IrreducibleRepresentation&);
00259
IrreducibleRepresentation(
int,
int,
const char*,
const char* =0);
00260
00261 ~
IrreducibleRepresentation();
00262
00263
IrreducibleRepresentation& operator=(
const IrreducibleRepresentation&);
00264
00266
void init(
int =0,
int =0,
const char* =0,
const char* =0);
00267
00269 int order()
const {
return g; }
00270
00272 int degeneracy()
const {
return degen; }
00273
00275 int complex()
const {
return complex_; }
00276
00278 int nproj()
const {
return degen*degen; }
00279
00281 int nrot()
const {
return nrot_; }
00282
00284 int ntrans()
const {
return ntrans_; }
00285
00287 const char *
symbol()
const {
return symb; }
00288
00292 const char *
symbol_ns()
const {
return (csymb?csymb:symb); }
00293
00296 double character(
int i)
const {
00297
return complex_ ? 0.5*rep[i].
trace() : rep[i].
trace();
00298 }
00299
00301 double p(
int x1,
int x2,
int i)
const {
return rep[i](x1,x2); }
00302
00305 double p(
int d,
int i)
const {
00306
int dc=d/degen;
int dr=d%degen;
00307
return rep[i](dr,dc);
00308 }
00309
00313
void print(std::ostream& =ExEnv::out0())
const;
00314 };
00315
00316
00325 class CharacterTable {
00326
public:
00327
enum pgroups {C1, CS, CI, CN, CNV, CNH, DN, DND, DNH, SN, T, TH, TD, O,
00328 OH, I, IH};
00329
00330
private:
00331
int g;
00332
int nt;
00333 pgroups pg;
00334
int nirrep_;
00335
IrreducibleRepresentation *gamma_;
00336
SymmetryOperation *symop;
00337
int *_inv;
00338
char *symb;
00339
00341
int parse_symbol();
00343
int make_table();
00344
00345
00346
void t();
00347
void th();
00348
void td();
00349
void o();
00350
void oh();
00351
void i();
00352
void ih();
00353
00354
public:
00355
CharacterTable();
00358
CharacterTable(
const char*);
00362
CharacterTable(
const char*,
const SymmetryOperation&);
00363
00364
CharacterTable(
const CharacterTable&);
00365 ~
CharacterTable();
00366
00367
CharacterTable& operator=(
const CharacterTable&);
00368
00370 int nirrep()
const {
return nirrep_; }
00372 int order()
const {
return g; }
00374 const char *
symbol()
const {
return symb; }
00376 IrreducibleRepresentation&
gamma(
int i) {
return gamma_[i]; }
00378 SymmetryOperation&
symm_operation(
int i) {
return symop[i]; }
00379
00383 int complex()
const {
00384
if (pg==CN || pg==SN || pg==CNH || pg==T || pg==TH)
00385
return 1;
00386
return 0;
00387 }
00388
00390 int inverse(
int i)
const {
return _inv[i]; }
00391
00392
int ncomp()
const {
00393
int ret=0;
00394
for (
int i=0; i < nirrep_; i++) {
00395
int nc = (gamma_[i].
complex()) ? 1 : gamma_[i].degen;
00396 ret += nc;
00397 }
00398
return ret;
00399 }
00400
00402 int which_irrep(
int i) {
00403
for (
int ir=0, cn=0; ir < nirrep_; ir++) {
00404
int nc = (gamma_[ir].
complex()) ? 1 : gamma_[ir].degen;
00405
for (
int c=0; c < nc; c++,cn++)
00406
if (cn==i)
00407
return ir;
00408 }
00409
return -1;
00410 }
00411
00413 int which_comp(
int i) {
00414
for (
int ir=0, cn=0; ir < nirrep_; ir++) {
00415
int nc = (gamma_[ir].
complex()) ? 1 : gamma_[ir].degen;
00416
for (
int c=0; c < nc; c++,cn++)
00417
if (cn==i)
00418
return c;
00419 }
00420
return -1;
00421 }
00422
00424
void print(std::ostream& =ExEnv::out0())
const;
00425 };
00426
00427
00428
00436 class PointGroup:
public SavableState {
00437
private:
00438
char *symb;
00439
SymmetryOperation frame;
00440 SCVector3 origin_;
00441
00442
public:
00443
PointGroup();
00446
PointGroup(
const char*);
00449
PointGroup(
const char*,
SymmetryOperation&);
00452
PointGroup(
const char*,
SymmetryOperation&,
const SCVector3&);
00487
PointGroup(
const Ref<KeyVal>&);
00488
00489
PointGroup(
StateIn&);
00490
PointGroup(
const PointGroup&);
00491
PointGroup(
const Ref<PointGroup>&);
00492 ~
PointGroup();
00493
00494
PointGroup& operator=(
const PointGroup&);
00495
00497
int equiv(
const Ref<PointGroup> &,
double tol = 1.0e-6)
const;
00498
00500
CharacterTable char_table()
const;
00502 const char *
symbol()
const {
return symb; }
00504 SymmetryOperation&
symm_frame() {
return frame; }
00506 const SymmetryOperation&
symm_frame()
const {
return frame; }
00508 SCVector3&
origin() {
return origin_; }
00509
const SCVector3&
origin()
const {
return origin_; }
00510
00512
void set_symbol(
const char*);
00513
00514
void save_data_state(StateOut& so);
00515
00516
void print(std::ostream&o=ExEnv::out0())
const;
00517 };
00518
00519 }
00520
00521
#endif
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00526