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kpath.cpp
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kpath.cpp
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#include "kpath.h"
#include "global.h"
#include "dynmat.h"
#include "memory.h"
#include "qnodes.h"
#ifdef UseSPG
extern "C"{
#include "spglib.h"
}
#include <cmath>
#include <cstdio>
#include <string>
#include <vector>
/* ----------------------------------------------------------------------------
* Class kPath will help to find the high symmetry k-path for a given lattice.
* The lattice info is passed via a DynMat object.
* ---------------------------------------------------------------------------- */
kPath::kPath(DynMat *dm, QNodes *qn)
{
// create memory
memory = new Memory();
// pass the class from main
q = qn;
dynmat = dm;
sysdim = dynmat->sysdim;
num_atom = dynmat->nucell;
memory->create(atpos, num_atom, 3, "kpath:atpos");
memory->create(attyp, num_atom, "kpath:attyp");
// set default, in case system dimension under study is not 3.
for (int i = 0; i < num_atom; ++i)
for (int idim = 0; idim < 3; ++idim) atpos[i][idim] = 0.;
for (int i = 0; i < 3; ++i)
for (int j = 0; j < 3; ++j) latvec[i][j] = 0.;
for (int i = 0; i < 3; ++i) latvec[i][i] = 1.;
// get atomic type info
for (int i = 0; i < num_atom; ++i) attyp[i] = dynmat->attyp[i];
// get unit cell vector info
int ndim = 0;
for (int idim = 0; idim < 3; ++idim)
for (int jdim = 0; jdim < 3; ++jdim) latvec[jdim][idim] = dynmat->basevec[ndim++];
// get atom position in unit cell; fractional
for (int i = 0; i < num_atom; ++i)
for (int idim = 0; idim < sysdim; ++idim) atpos[i][idim] = dynmat->basis[i][idim];
// get the space group number
double symprec = 1.0e-3;
double **pos;
memory->create(pos,num_atom,3,"kpath:pos");
if (dynmat->symprec > 0.0) symprec = dynmat->symprec;
for (int i = 0; i < num_atom; ++i)
for (int j = 0; j < 3; ++j) pos[i][j] = atpos[i][j];
spgnum = spg_get_international(symbol, latvec, (double (*)[3])pos, attyp, num_atom, symprec);
memory->destroy(pos);
return;
}
/* ----------------------------------------------------------------------------
* Show the lattice info
* ---------------------------------------------------------------------------- */
void kPath::show_info()
{
// display the unit cell info read
puts("--------------------------------------------------------------------------------");
printf("The basis vectors of the unit cell:\n");
for (int idim = 0; idim < 3; ++idim){
printf(" A%d =", idim+1);
for (int jdim = 0; jdim < 3; ++jdim) printf(" %lg", latvec[jdim][idim]);
printf("\n");
}
printf("Atom(s) in the unit cell:\n");
printf(" No. type sx sy sz\n");
for (int i = 0; i < MIN(num_atom, NUMATOM); ++i)
printf(" %d %d %lg %lg %lg\n", i+1, attyp[i], atpos[i][0], atpos[i][1], atpos[i][2]);
if (num_atom > NUMATOM) printf(" ... (%d atoms omitted.)\n", num_atom-NUMATOM);
printf("The space group number of your unit cell is: %d => %s\n", spgnum, symbol);
puts("--------------------------------------------------------------------------------");
return;
}
/* ----------------------------------------------------------------------------
* Free the memeory used by kPath.
* ---------------------------------------------------------------------------- */
kPath::~kPath( )
{
memory->destroy(attyp);
memory->destroy(atpos);
delete memory;
dynmat = NULL;
q = NULL;
return;
}
/* ----------------------------------------------------------------------------
* Main workhorse
* ---------------------------------------------------------------------------- */
void kPath::kpath( )
{
q->ndstr.clear();
q->qs.clear();
q->qe.clear();
q->nqbin.clear();
// angles
const double la = sqrt(latvec[0][0] * latvec[0][0] + latvec[0][1] * latvec[0][1] + latvec[0][2] * latvec[0][2]);
const double lb = sqrt(latvec[1][0] * latvec[1][0] + latvec[1][1] * latvec[1][1] + latvec[1][2] * latvec[1][2]);
const double lc = sqrt(latvec[2][0] * latvec[2][0] + latvec[2][1] * latvec[2][1] + latvec[2][2] * latvec[2][2]);
const double cosa = sqrt(latvec[1][0] * latvec[2][0] + latvec[1][1] * latvec[2][1] + latvec[1][2] * latvec[2][2])/(lb*lc);
const double cosg = sqrt(latvec[0][0] * latvec[1][0] + latvec[0][1] * latvec[1][1] + latvec[0][2] * latvec[1][2])/(la*lb);
double ivec[3][3];
int ndim = 0;
for (int idim = 0; idim < 3; ++idim)
for (int jdim = 0; jdim < 3; ++jdim) ivec[jdim][idim] = dynmat->ibasevec[ndim++];
const double ka = sqrt(ivec[0][0] * ivec[0][0] + ivec[0][1] * ivec[0][1] + ivec[0][2] * ivec[0][2]);
const double kb = sqrt(ivec[1][0] * ivec[1][0] + ivec[1][1] * ivec[1][1] + ivec[1][2] * ivec[1][2]);
const double coskg = sqrt(ivec[0][0] * ivec[1][0] + ivec[0][1] * ivec[1][1] + ivec[0][2] * ivec[1][2])/(ka*kb);
double *qtmp;
if (spgnum >= 1 && spgnum <= 2){ // Triclinic system
if (fabs(coskg) > ZERO){ // A.14, TRI1a and TRI2a
q->ndstr.push_back("X");
// X-G
qtmp = new double [3];
qtmp[0] = 0.5; qtmp[1] = qtmp[2] = 0.;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = qtmp[2] = 0.;
q->qe.push_back(qtmp);
q->ndstr.push_back("{/Symbol G}");
// G-Y
qtmp = new double [3];
qtmp[0] = qtmp[1] = qtmp[2] = 0.;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[2] = 0.; qtmp[1] = 0.5;
q->qe.push_back(qtmp);
q->ndstr.push_back("Y/L");
// L-G
qtmp = new double [3];
qtmp[0] = qtmp[1] = 0.5; qtmp[2] = 0.;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = qtmp[2] = 0.;
q->qe.push_back(qtmp);
q->ndstr.push_back("{/Symbol G}");
// G-Z
qtmp = new double [3];
qtmp[0] = qtmp[1] = qtmp[2] = 0.;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = 0.; qtmp[2] = 0.5;
q->qe.push_back(qtmp);
q->ndstr.push_back("Z/N");
// N-G
qtmp = new double [3];
qtmp[0] = qtmp[2] = 0.5; qtmp[1] = 0.;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = qtmp[2] = 0.;
q->qe.push_back(qtmp);
q->ndstr.push_back("{/Symbol G}");
// G-M
qtmp = new double [3];
qtmp[0] = qtmp[1] = qtmp[2] = 0.;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = 0.; qtmp[1] = qtmp[2] = 0.5;
q->qe.push_back(qtmp);
q->ndstr.push_back("M/R");
// R-G
qtmp = new double [3];
qtmp[0] = qtmp[2] = qtmp[1] = 0.5;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = qtmp[2] = 0.;
q->qe.push_back(qtmp);
q->ndstr.push_back("{/Symbol G}");
} else { // A.14, TRI1b and TRI2b
q->ndstr.push_back("X");
// X-G
qtmp = new double [3];
qtmp[0] = qtmp[2] = 0.; qtmp[1] = -0.5;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = qtmp[2] = 0.;
q->qe.push_back(qtmp);
q->ndstr.push_back("{/Symbol G}");
// G-Y
qtmp = new double [3];
qtmp[0] = qtmp[1] = qtmp[2] = 0.;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[1] = qtmp[2] = 0.; qtmp[0] = 0.5;
q->qe.push_back(qtmp);
q->ndstr.push_back("Y/L");
// L-G
qtmp = new double [3];
qtmp[0] = 0.5; qtmp[1] = -0.5; qtmp[2] = 0.;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = qtmp[2] = 0.;
q->qe.push_back(qtmp);
q->ndstr.push_back("{/Symbol G}");
// G-Z
qtmp = new double [3];
qtmp[0] = qtmp[1] = qtmp[2] = 0.;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = -0.5; qtmp[1] = 0.; qtmp[2] = 0.5;
q->qe.push_back(qtmp);
q->ndstr.push_back("Z/N");
// N-G
qtmp = new double [3];
qtmp[0] = qtmp[2] = -0.5; qtmp[1] = 0.5;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = qtmp[2] = 0.;
q->qe.push_back(qtmp);
q->ndstr.push_back("{/Symbol G}");
// G-M
qtmp = new double [3];
qtmp[0] = qtmp[1] = qtmp[2] = 0.;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = 0.; qtmp[2] = 0.5;
q->qe.push_back(qtmp);
q->ndstr.push_back("M/R");
// R-G
qtmp = new double [3];
qtmp[0] = 0.; qtmp[1] = -0.5; qtmp[2] = 0.5;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = qtmp[2] = 0.;
q->qe.push_back(qtmp);
q->ndstr.push_back("{/Symbol G}");
}
} else if (spgnum >= 3 && spgnum <= 15){ // Monoclinic
if (symbol[0] == 'P'){ // MCL-P
const double eta = (1.-lb*cosa/lc)/(2.*(1.-cosa*cosa));
const double niu = 0.5 - eta * lc * cosa / lb;
q->ndstr.push_back("{/Symbol G}");
// G-Y
qtmp = new double [3];
qtmp[0] = qtmp[1] = qtmp[2] = 0.;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = 0.; qtmp[2] = 0.5;
q->qe.push_back(qtmp);
q->ndstr.push_back("Y");
// Y-H
qtmp = new double [3];
qtmp[0] = qtmp[1] = 0.; qtmp[2] = 0.5;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = 0.; qtmp[1] = eta; qtmp[2] = 1.-niu;
q->qe.push_back(qtmp);
q->ndstr.push_back("H");
// H-C
qtmp = new double [3];
qtmp[0] = 0.; qtmp[1] = eta; qtmp[2] = 1.-niu;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = 0.; qtmp[1] = qtmp[2] = 0.5;
q->qe.push_back(qtmp);
q->ndstr.push_back("C");
// C-E
qtmp = new double [3];
qtmp[0] = 0.; qtmp[1] = qtmp[2] = 0.5;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = qtmp[2] = 0.5;
q->qe.push_back(qtmp);
q->ndstr.push_back("E");
// E-M1
qtmp = new double [3];
qtmp[0] = qtmp[1] = qtmp[2] = 0.5;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = 0.5; qtmp[1] = 1.-eta; qtmp[2] = niu;
q->qe.push_back(qtmp);
q->ndstr.push_back("M_1");
// M1-A
qtmp = new double [3];
qtmp[0] = 0.5; qtmp[1] = 1.-eta; qtmp[2] = niu;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = 0.5; qtmp[2] = 0.;
q->qe.push_back(qtmp);
q->ndstr.push_back("A");
// A-X
qtmp = new double [3];
qtmp[0] = qtmp[1] = 0.5; qtmp[2] = 0.;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[2] = 0.; qtmp[1] = 0.5;
q->qe.push_back(qtmp);
q->ndstr.push_back("X");
// X-H1
qtmp = new double [3];
qtmp[0] = qtmp[2] = 0.; qtmp[1] = 0.5;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = 0.; qtmp[2] = 1.-eta; qtmp[1] = niu;
q->qe.push_back(qtmp);
q->ndstr.push_back("H_1/M");
// M-D
qtmp = new double [3];
qtmp[0] = 0.5; qtmp[2] = eta; qtmp[1] = 1.-niu;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[2] = 0.5; qtmp[1] = 0.;
q->qe.push_back(qtmp);
q->ndstr.push_back("D");
// D-Z
qtmp = new double [3];
qtmp[0] = qtmp[2] = 0.5; qtmp[1] = 0.;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = 0.5; qtmp[1] = qtmp[2] = 0.;
q->qe.push_back(qtmp);
q->ndstr.push_back("Z/Y");
// Y-D
qtmp = new double [3];
qtmp[0] = qtmp[1] = 0.; qtmp[2] = 0.5;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[2] = 0.5; qtmp[1] = 0.;
q->qe.push_back(qtmp);
q->ndstr.push_back("D");
} else { // MCL-C
if (coskg < 0.){ // MCLC1
const double xi = (2. - lb * cosa / lc) / (4.*(1.-cosa*cosa));
const double eta = 0.5 + 2.*xi*lc/lb*cosa;
const double psi = 0.75 - la * la /(4.*lb*lb*(1.-cosa*cosa));
const double phi = psi + (0.75 - psi) * lb / lc * cosa;
q->ndstr.push_back("{/Symbol G}");
// G-Y
qtmp = new double [3];
qtmp[0] = qtmp[1] = qtmp[2] = 0.;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = 0.5; qtmp[2] = 0.;
q->qe.push_back(qtmp);
q->ndstr.push_back("Y");
// Y-F
qtmp = new double [3];
qtmp[0] = qtmp[1] = 0.5; qtmp[2] = 0.;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = 1.-xi; qtmp[2] = 1.-eta;
q->qe.push_back(qtmp);
q->ndstr.push_back("F");
// F-L
qtmp = new double [3];
qtmp[0] = qtmp[1] = 1.-xi; qtmp[2] = 1.-eta;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = qtmp[2] = 0.5;
q->qe.push_back(qtmp);
q->ndstr.push_back("L");
// L-I
qtmp = new double [3];
qtmp[0] = qtmp[1] = qtmp[2] = 0.5;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = phi; qtmp[1] = 1.-phi; qtmp[2] = 0.5;
q->qe.push_back(qtmp);
q->ndstr.push_back("I/I_1");
// I1-Z
qtmp = new double [3];
qtmp[0] = 1.-phi; qtmp[1] = -qtmp[0]; qtmp[2] = 0.5;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = 0.; qtmp[2] = 0.5;
q->qe.push_back(qtmp);
q->ndstr.push_back("Z");
// Z-F1
qtmp = new double [3];
qtmp[0] = qtmp[1] = 0.; qtmp[2] = 0.5;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = xi; qtmp[2] = eta;
q->qe.push_back(qtmp);
q->ndstr.push_back("F_1/Y");
// Y-X1
qtmp = new double [3];
qtmp[0] = qtmp[1] = 0.5; qtmp[2] = 0.;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = psi; qtmp[1] = 1.-psi; qtmp[2] = 0.;
q->qe.push_back(qtmp);
q->ndstr.push_back("X_1/X");
// X-G
qtmp = new double [3];
qtmp[0] = 1.-psi; qtmp[1] = -qtmp[0]; qtmp[2] = 0.;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = qtmp[2] = 0.;
q->qe.push_back(qtmp);
q->ndstr.push_back("{/Symbol G}");
// G-N
qtmp = new double [3];
qtmp[0] = qtmp[1] = qtmp[2] = 0.;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = 0.5; qtmp[1] = qtmp[2] = 0.;
q->qe.push_back(qtmp);
q->ndstr.push_back("N/M");
// M-G
qtmp = new double [3];
qtmp[0] = qtmp[2] = 0.5; qtmp[2] = 0.;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = qtmp[2] = 0.;
q->qe.push_back(qtmp);
q->ndstr.push_back("{/Symbol G}");
} else if ( fabs(coskg) < ZERO) { // MCLC2
const double xi = (2. - lb * cosa / lc) / (4.*(1.-cosa*cosa));
const double eta = 0.5 + 2.*xi*lc/lb*cosa;
const double psi = 0.75 - la * la /(4.*lb*lb*(1.-cosa*cosa));
const double phi = psi + (0.75 - psi) * lb / lc * cosa;
q->ndstr.push_back("{/Symbol G}");
// G-Y
qtmp = new double [3];
qtmp[0] = qtmp[1] = qtmp[2] = 0.;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = 0.5; qtmp[2] = 0.;
q->qe.push_back(qtmp);
q->ndstr.push_back("Y");
// Y-F
qtmp = new double [3];
qtmp[0] = qtmp[1] = 0.5; qtmp[2] = 0.;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = 1.-xi; qtmp[2] = 1.-eta;
q->qe.push_back(qtmp);
q->ndstr.push_back("F");
// F-L
qtmp = new double [3];
qtmp[0] = qtmp[1] = 1.-xi; qtmp[2] = 1.-eta;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = qtmp[2] = 0.5;
q->qe.push_back(qtmp);
q->ndstr.push_back("L");
// L-I
qtmp = new double [3];
qtmp[0] = qtmp[1] = qtmp[2] = 0.5;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = phi; qtmp[1] = 1.-phi; qtmp[2] = 0.5;
q->qe.push_back(qtmp);
q->ndstr.push_back("I/I_1");
// I1-Z
qtmp = new double [3];
qtmp[0] = 1.-phi; qtmp[1] = -qtmp[0]; qtmp[2] = 0.5;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = 0.; qtmp[2] = 0.5;
q->qe.push_back(qtmp);
q->ndstr.push_back("Z");
// Z-F1
qtmp = new double [3];
qtmp[0] = qtmp[1] = 0.; qtmp[2] = 0.5;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = xi; qtmp[2] = eta;
q->qe.push_back(qtmp);
q->ndstr.push_back("F_1/N");
// N-G
qtmp = new double [3];
qtmp[0] = 0.5; qtmp[1] = qtmp[2] = 0.;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = qtmp[2] = 0.;
q->qe.push_back(qtmp);
q->ndstr.push_back("{/Symbol G}");
// G-M
qtmp = new double [3];
qtmp[0] = qtmp[1] = qtmp[2] = 0.;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[2] = 0.5; qtmp[2] = 0.;
q->qe.push_back(qtmp);
q->ndstr.push_back("M");
} else {
double flag = lb / lc * cosa + lb * lb / (la * la *(1.-cosa*cosa));
if (fabs(flag) < ZERO){ // MCLC4
const double miu = 0.25*(1. + lb * lb / (la *la));
const double del = lb * lc * cosa / (2.*la*la);
const double xi = miu - 0.25 + (1. - lb * cosa / lc)/(4.*(1.-cosa*cosa));
const double eta = 0.5 + 2.*xi*lc/lb*cosa;
const double phi = 1. + xi - 2.*miu;
const double psi = eta - 2.*del;
q->ndstr.push_back("{/Symbol G}");
// G-Y
qtmp = new double [3];
qtmp[0] = qtmp[1] = qtmp[2] = 0.;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = miu; qtmp[2] = del;
q->qe.push_back(qtmp);
q->ndstr.push_back("Y");
// Y-F
qtmp = new double [3];
qtmp[0] = qtmp[1] = miu; qtmp[2] = del;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = 1.-phi; qtmp[2] = 1.-psi;
q->qe.push_back(qtmp);
q->ndstr.push_back("F");
// F-H
qtmp = new double [3];
qtmp[0] = qtmp[1] = 1.-phi; qtmp[2] = 1.-psi;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = xi; qtmp[2] = eta;
q->qe.push_back(qtmp);
q->ndstr.push_back("H");
// H-Z
qtmp = new double [3];
qtmp[0] = qtmp[1] = xi; qtmp[2] = eta;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = 0.; qtmp[2] = 0.5;
q->qe.push_back(qtmp);
q->ndstr.push_back("Z");
// Z-I
qtmp = new double [3];
qtmp[0] = qtmp[1] = 0.; qtmp[2] = 0.5;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[2] = 0.5; qtmp[1] = -0.5;
q->qe.push_back(qtmp);
q->ndstr.push_back("I/H_1");
// H1-Y1
qtmp = new double [3];
qtmp[0] = 1.-xi; qtmp[1] = -xi; qtmp[2] = 1.-eta;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = 1.-miu; qtmp[1] = -miu; qtmp[2] = -del;
q->qe.push_back(qtmp);
q->ndstr.push_back("Y_1");
// Y1-X
qtmp = new double [3];
qtmp[0] = 1.-miu; qtmp[1] = -miu; qtmp[2] = -del;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = 0.5; qtmp[1] = -0.5; qtmp[2] = 0.;
q->qe.push_back(qtmp);
q->ndstr.push_back("X");
// X-G
qtmp = new double [3];
qtmp[0] = 0.5; qtmp[1] = -0.5; qtmp[2] = 0.;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = qtmp[2] = 0.;
q->qe.push_back(qtmp);
q->ndstr.push_back("{/Symbol G}");
// G-N
qtmp = new double [3];
qtmp[0] = qtmp[1] = qtmp[2] = 0.;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = 0.5; qtmp[1] = qtmp[2] = 0.;
q->qe.push_back(qtmp);
q->ndstr.push_back("N/M");
// M-G
qtmp = new double [3];
qtmp[0] = qtmp[2] = 0.5; qtmp[1] = 0.;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = qtmp[2] = 0.;
q->qe.push_back(qtmp);
q->ndstr.push_back("{/Symbol G}");
} else if (flag < 1.){ // MCLC3
const double miu = 0.25*(1. + lb * lb / (la *la));
const double del = lb * lc * cosa / (2.*la*la);
const double xi = miu - 0.25 + (1. - lb * cosa / lc)/(4.*(1.-cosa*cosa));
const double eta = 0.5 + 2.*xi*lc/lb*cosa;
const double phi = 1. + xi - 2.*miu;
const double psi = eta - 2.*del;
q->ndstr.push_back("{/Symbol G}");
// G-Y
qtmp = new double [3];
qtmp[0] = qtmp[1] = qtmp[2] = 0.;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = miu; qtmp[2] = del;
q->qe.push_back(qtmp);
q->ndstr.push_back("Y");
// Y-F
qtmp = new double [3];
qtmp[0] = qtmp[1] = miu; qtmp[2] = del;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = 1.-phi; qtmp[2] = 1.-psi;
q->qe.push_back(qtmp);
q->ndstr.push_back("F");
// F-H
qtmp = new double [3];
qtmp[0] = qtmp[1] = 1.-phi; qtmp[2] = 1.-psi;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = xi; qtmp[2] = eta;
q->qe.push_back(qtmp);
q->ndstr.push_back("H");
// H-Z
qtmp = new double [3];
qtmp[0] = qtmp[1] = xi; qtmp[2] = eta;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = 0.; qtmp[2] = 0.5;
q->qe.push_back(qtmp);
q->ndstr.push_back("Z");
// Z-I
qtmp = new double [3];
qtmp[0] = qtmp[1] = 0.; qtmp[2] = 0.5;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[2] = 0.5; qtmp[1] = -0.5;
q->qe.push_back(qtmp);
q->ndstr.push_back("I/H_1");
// I-F1
qtmp = new double [3];
qtmp[0] = qtmp[1] = 0.; qtmp[2] = 0.5;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = phi; qtmp[2] = phi - 1.; qtmp[1] = psi;
q->qe.push_back(qtmp);
q->ndstr.push_back("F_1/H_1");
// H1-Y1
qtmp = new double [3];
qtmp[0] = 1.-xi; qtmp[1] = -xi; qtmp[2] = 1.-eta;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = 1.-miu; qtmp[1] = -miu; qtmp[2] = -del;
q->qe.push_back(qtmp);
q->ndstr.push_back("Y_1");
// Y1-X
qtmp = new double [3];
qtmp[0] = 1.-miu; qtmp[1] = -miu; qtmp[2] = -del;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = 0.5; qtmp[1] = -0.5; qtmp[2] = 0.;
q->qe.push_back(qtmp);
q->ndstr.push_back("X");
// X-G
qtmp = new double [3];
qtmp[0] = 0.5; qtmp[1] = -0.5; qtmp[2] = 0.;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = qtmp[2] = 0.;
q->qe.push_back(qtmp);
q->ndstr.push_back("{/Symbol G}");
// G-N
qtmp = new double [3];
qtmp[0] = qtmp[1] = qtmp[2] = 0.;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = 0.5; qtmp[1] = qtmp[2] = 0.;
q->qe.push_back(qtmp);
q->ndstr.push_back("N/M");
// M-G
qtmp = new double [3];
qtmp[0] = qtmp[2] = 0.5; qtmp[1] = 0.;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = qtmp[2] = 0.;
q->qe.push_back(qtmp);
q->ndstr.push_back("{/Symbol G}");
} else { // MCLC5
const double xi = (lb*lb/(la*la) + (1.-lb*cosa/lc)/(1.-cosa*cosa))*0.25;
const double eta = 0.5 + 2.*xi*lc*cosa/lb;
const double miu = 0.5*eta + lb * lb /(4.*la*la) - lb*lc/(2.*la*la)*cosa;
const double niu = 2.*miu - xi;
const double omg = (4.*niu - 1. - lb*lb*(1.-cosa*cosa)/(la*la))*lc/(2.*lb*cosa);
const double del = xi*lc*cosa/lb + omg*0.5 - 0.25;
const double rho = 1.-xi*la*la/(lb*lb);
q->ndstr.push_back("{/Symbol G}");
// G-Y
qtmp = new double [3];
qtmp[0] = qtmp[1] = qtmp[2] = 0.;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = miu; qtmp[2] = del;
q->qe.push_back(qtmp);
q->ndstr.push_back("Y");
// Y-F
qtmp = new double [3];
qtmp[0] = qtmp[1] = miu; qtmp[2] = del;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = niu; qtmp[2] = omg;
q->qe.push_back(qtmp);
q->ndstr.push_back("F");
// F-L
qtmp = new double [3];
qtmp[0] = qtmp[1] = niu; qtmp[2] = omg;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = qtmp[2] = 0.5;
q->qe.push_back(qtmp);
q->ndstr.push_back("Y");
// L-I
qtmp = new double [3];
qtmp[0] = qtmp[1] = qtmp[2] = 0.5;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = rho; qtmp[1] = 1.-rho; qtmp[2] = 0.5;
q->qe.push_back(qtmp);
q->ndstr.push_back("I/I_1");
// I1-Z
qtmp = new double [3];
qtmp[0] = 1.-rho; qtmp[1] = -qtmp[0]; qtmp[2] = 0.5;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = 0.; qtmp[2] = 0.5;
q->qe.push_back(qtmp);
q->ndstr.push_back("Z");
// Z-H
qtmp = new double [3];
qtmp[0] = qtmp[1] = 0.; qtmp[2] = 0.5;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = xi; qtmp[2] = eta;
q->qe.push_back(qtmp);
q->ndstr.push_back("H");
// H-F1
qtmp = new double [3];
qtmp[0] = qtmp[1] = xi; qtmp[2] = eta;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = 1.-niu; qtmp[2] = 1.-omg;
q->qe.push_back(qtmp);
q->ndstr.push_back("F_1/H_1");
// H1-Y1
qtmp = new double [3];
qtmp[0] = 1.-xi; qtmp[1] = -xi; qtmp[2] = 1.-eta;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = 1.-miu; qtmp[1] = -miu; qtmp[2] = -del;
q->qe.push_back(qtmp);
q->ndstr.push_back("Y_1");
// Y1-X
qtmp = new double [3];
qtmp[0] = 1.-miu; qtmp[1] = -miu; qtmp[2] = -del;
q->qs.push_back(qtmp);
qtmp = new double [3];
qtmp[0] = qtmp[1] = 0.5; qtmp[2] = 0.;
q->qe.push_back(qtmp);
q->ndstr.push_back("Y_1");
// X-G
qtmp = new double [3];