void gsl_matrix_complex_conjugate(gsl_matrix_complex *cm)
{
gsl_complex z;
size_t i, j;
for (i = 0; i < cm->size1; i++) {
for (j = 0; j < cm->size2; j++) {
z = gsl_matrix_complex_get(cm, i, j);
gsl_matrix_complex_set(cm, i, j, gsl_complex_conjugate(z));
}
}
}
static void
cholesky_complex_conj_vector(gsl_vector_complex *v)
{
size_t i;
for (i = 0; i < v->size; ++i)
{
gsl_complex z = gsl_vector_complex_get(v, i);
gsl_vector_complex_set(v, i, gsl_complex_conjugate(z));
}
} /* cholesky_complex_conj_vector() */
gsl_complex complex_spinor::operator* (const complex_spinor & complex_spinor_param) const{
gsl_complex aux_UP;
gsl_complex aux_DOWN;
gsl_complex aux;
GSL_SET_COMPLEX(&aux_UP, 0, 0);
GSL_SET_COMPLEX(&aux_DOWN, 0, 0);
GSL_SET_COMPLEX(&aux, 0, 0);
int i;
int nSitios = this->_numSites;
for(i=0; i<nSitios ; i++){
aux_UP = gsl_complex_mul(gsl_complex_conjugate(complex_spinor_param.complex_spinor_get(i,UP)) ,this->complex_spinor_get(i,UP));
aux_DOWN = gsl_complex_mul(gsl_complex_conjugate(complex_spinor_param.complex_spinor_get(i,DOWN)),this->complex_spinor_get(i,DOWN));
aux=gsl_complex_add(aux, gsl_complex_add(aux_UP,aux_DOWN));
}
return aux;
}
double intensita(gsl_complex A, gsl_complex B) {
// PROVVISORIO
//~ double intensita = (gsl_complex_abs2(A) + gsl_complex_abs2(B) )/(2*in.Z_st);
double intensita = gsl_complex_abs(gsl_complex_mul(gsl_complex_add(A,B) , gsl_complex_conjugate(gsl_complex_add(A,B))));
printf("I=%e\n",intensita);
#ifdef DEBUG
printf("|A|=%e\n",gsl_complex_abs(A));
printf("|B|=%e\n",gsl_complex_abs(B));
printf("intensita=%e\n",intensita);
#endif
return intensita;
}
//go through all sets of Bethe rapidities and calculate g1 for all identical sets. return value is sum of all these terms.
gsl_complex exact_integrationDE(double orteins, double ortzwei, double** kEp_plusminus, int anzahl_sets, double** coeffoverlap)
{
//variables to make loop easily readable, could delete from final version
double c, Energie, Energieprime, normierung, normierungprime;
double k[N];
double kprime[N];//corresponds to primed Bethe rapidity set in papers
gsl_complex overlap, overlapprime, integral;
GSL_SET_COMPLEX(&integral, 0.0, 0.0);//sum of all values, technically no needed but good for quick check of initial shape of g1
int zaehler_integrale = 0;//counter of total sets of integrals
double Nminusone_fak = 1.0;//(N-1) factorial, see definition of integrals on restricted spatial domain
for(int j=1; j<=(N-1); j++)
Nminusone_fak = Nminusone_fak * ((double) j);
for(int zaehler_eigenstate = 0 ; zaehler_eigenstate < anzahl_sets; zaehler_eigenstate++){//loop over all Bethe rapidity sets
c = kEp_plusminus[zaehler_eigenstate][0];//interaction strength
for(int bb=0; bb<N; bb++)
k[bb]=kEp_plusminus[zaehler_eigenstate][bb+1];//Bethe rapidities
Energie = kEp_plusminus[zaehler_eigenstate][N+1];//energy
normierung=kEp_plusminus[zaehler_eigenstate][N+6];//norm
GSL_SET_COMPLEX(&overlap, coeffoverlap[zaehler_eigenstate][0], coeffoverlap[zaehler_eigenstate][1]);//overlap of set with initial state
//calculate g1_DE for this Bethe set
gsl_complex integralwert = integraleigenfunction(k, k, c, normierung, normierung, orteins, ortzwei);
integralwert = gsl_complex_mul_real(integralwert, (Nminusone_fak*Laenge));//integral evaluated in Rp only -> missing factor of (N-1)!. Laenge (=system length): definition of g1 has prefactor of N!/(n*(N-1)!) = Laenge
integral = gsl_complex_add(integral, gsl_complex_mul(gsl_complex_mul(overlap, gsl_complex_conjugate(overlap)), integralwert));
}//end for loop zaehler_eigenstate
return integral;
};
void
create_random_complex_posdef_matrix(gsl_matrix_complex *m, gsl_rng *r,
gsl_vector_complex *work)
{
const size_t N = m->size1;
size_t i, j;
double x, y;
gsl_complex z;
gsl_complex tau;
GSL_SET_IMAG(&z, 0.0);
/* make a positive diagonal matrix */
gsl_matrix_complex_set_zero(m);
for (i = 0; i < N; ++i)
{
x = gsl_rng_uniform(r);
GSL_SET_REAL(&z, x);
gsl_matrix_complex_set(m, i, i, z);
}
/* now generate random householder reflections and form P D P^H */
for (i = 0; i < N; ++i)
{
/* form complex vector */
for (j = 0; j < N; ++j)
{
x = 2.0 * gsl_rng_uniform(r) - 1.0;
y = 2.0 * gsl_rng_uniform(r) - 1.0;
GSL_SET_COMPLEX(&z, x, y);
gsl_vector_complex_set(work, j, z);
}
tau = gsl_linalg_complex_householder_transform(work);
gsl_linalg_complex_householder_hm(tau, work, m);
gsl_linalg_complex_householder_mh(gsl_complex_conjugate(tau), work, m);
}
} /* create_random_complex_posdef_matrix() */
void
create_random_herm_matrix(gsl_matrix_complex *m, gsl_rng *r, int lower,
int upper)
{
size_t i, j;
for (i = 0; i < m->size1; ++i)
{
for (j = i; j < m->size2; ++j)
{
gsl_complex z;
GSL_REAL(z) = gsl_rng_uniform(r) * (upper - lower) + lower;
if (i == j)
GSL_IMAG(z) = 0.0;
else
GSL_IMAG(z) = gsl_rng_uniform(r) * (upper - lower) + lower;
gsl_matrix_complex_set(m, i, j, z);
gsl_matrix_complex_set(m, j, i, gsl_complex_conjugate(z));
}
}
} /* create_random_herm_matrix() */
double Calculator::getIntensity(double Q)
{
std::complex<double> cppf1, cppf2;
gsl_complex alpha, beta;
gsl_complex gslf1, gslf2;
int s;
double avFactor;
cppf1 = m_sf1->F(0.0, 0.0, Q, m_energy);
cppf2 = m_sf2->F(0.0, 0.0, Q, m_energy);
gslf1 = gsl_complex_rect(cppf1.real(), cppf1.imag());
gslf2 = gsl_complex_rect(cppf2.real(), cppf2.imag());
avFactor = exp(-2.0 / m_N);
alpha = gsl_complex_rect (1.0, 0.0);
beta = gsl_complex_rect (0.0, 0.0);
/*set vector F (scattering factors)*/
gsl_vector_complex_set(F, 0, gslf1);
gsl_vector_complex_set(F, 1, gslf2);
/*set vector conj(F) (scattering factors)*/
gsl_vector_complex_set(Fconj, 0, gsl_complex_conjugate(gslf1));
gsl_vector_complex_set(Fconj, 1, gsl_complex_conjugate(gslf2));
/*set exp matrix*/
setMatrixExp(m_Exp, Q);
/*find W = P * Exp * Ps * conj(F) vector:*/
/* (1) W = alpha * Ps * conj(F) + beta * W */
gsl_blas_zgemv (CblasNoTrans, alpha, m_Ps, Fconj, beta, W);
/*printf("W(1):\n");
gsl_vector_complex_fprintf (stdout, W, "%g");*/
/* (2) W = alpha * Exp * tmp_vec + beta * W */
gsl_blas_zgemv (CblasNoTrans, alpha, m_Exp, W, beta, tmp_vec);
/*printf("W(2):\n");
gsl_vector_complex_fprintf (stdout, tmp_vec, "%g");*/
/* (3) W = alpha * P * tmp_vec + beta * W */
gsl_blas_zgemv (CblasNoTrans, alpha, m_P, tmp_vec, beta, W);
/*Find J0 = F.(Ps * conj(F)) */
gsl_blas_zgemv (CblasNoTrans, alpha, m_Ps, Fconj, beta, tmp_vec);
gsl_blas_zdotu (F, tmp_vec, &J0);
/*alpha = exp(-2 / N)*/
alpha = gsl_complex_rect (avFactor, 0.0);
beta = gsl_complex_rect (0.0, 0.0);
/*find T matrix: T = alpha * P * exp + beta * T*/
gsl_blas_zgemm (CblasNoTrans, CblasNoTrans, alpha, m_P, m_Exp, beta, T);
/*printf("T:\n");
gsl_matrix_complex_fprintf (stdout, T, "%g");*/
/*Find Jns = F. (G * W) */
/*tmp_mat = I */
gsl_matrix_complex_set_identity (tmp_mat);
/*tmp_mat = I - T */
gsl_matrix_complex_sub (tmp_mat, T);
/*LU decomposition*/
gsl_linalg_complex_LU_decomp(tmp_mat, perm, &s);
/*calculate product G * W = (I - T)^(-1) W directly using LU decomposition*/
gsl_linalg_complex_LU_solve (tmp_mat, perm, W, tmp_vec);
/*calculate F.(G * W)*/
gsl_blas_zdotu (F, tmp_vec, &Jns);
/*Find Js = F.(G^2 * (I - T^N) * W) however, this term should be negligible*/
/*result = N *(2 * Jns + J0) - Js */
alpha = gsl_complex_mul_real (Jns, 2.0 * avFactor);
alpha = gsl_complex_add (alpha, J0);
return m_N * m_I0 * GSL_REAL(alpha) * getPLGfactor(getTheta(Q)) + m_Ibg;
}
complex complex::conjugate() const
{
gsl_complex t = gsl_complex_conjugate(_complex);
return complex(t);
}
int
gsl_linalg_complex_cholesky_decomp(gsl_matrix_complex *A)
{
const size_t N = A->size1;
if (N != A->size2)
{
GSL_ERROR("cholesky decomposition requires square matrix", GSL_ENOTSQR);
}
else
{
size_t i, j;
gsl_complex z;
double ajj;
for (j = 0; j < N; ++j)
{
z = gsl_matrix_complex_get(A, j, j);
ajj = GSL_REAL(z);
if (j > 0)
{
gsl_vector_complex_const_view aj =
gsl_matrix_complex_const_subrow(A, j, 0, j);
gsl_blas_zdotc(&aj.vector, &aj.vector, &z);
ajj -= GSL_REAL(z);
}
if (ajj <= 0.0)
{
GSL_ERROR("matrix is not positive definite", GSL_EDOM);
}
ajj = sqrt(ajj);
GSL_SET_COMPLEX(&z, ajj, 0.0);
gsl_matrix_complex_set(A, j, j, z);
if (j < N - 1)
{
gsl_vector_complex_view av =
gsl_matrix_complex_subcolumn(A, j, j + 1, N - j - 1);
if (j > 0)
{
gsl_vector_complex_view aj =
gsl_matrix_complex_subrow(A, j, 0, j);
gsl_matrix_complex_view am =
gsl_matrix_complex_submatrix(A, j + 1, 0, N - j - 1, j);
cholesky_complex_conj_vector(&aj.vector);
gsl_blas_zgemv(CblasNoTrans,
GSL_COMPLEX_NEGONE,
&am.matrix,
&aj.vector,
GSL_COMPLEX_ONE,
&av.vector);
cholesky_complex_conj_vector(&aj.vector);
}
gsl_blas_zdscal(1.0 / ajj, &av.vector);
}
}
/* Now store L^H in upper triangle */
for (i = 1; i < N; ++i)
{
for (j = 0; j < i; ++j)
{
z = gsl_matrix_complex_get(A, i, j);
gsl_matrix_complex_set(A, j, i, gsl_complex_conjugate(z));
}
}
return GSL_SUCCESS;
}
} /* gsl_linalg_complex_cholesky_decomp() */
int
gsl_linalg_complex_cholesky_invert(gsl_matrix_complex * LLT)
{
if (LLT->size1 != LLT->size2)
{
GSL_ERROR ("cholesky matrix must be square", GSL_ENOTSQR);
}
else
{
size_t N = LLT->size1;
size_t i, j;
gsl_vector_complex_view v1;
/* invert the lower triangle of LLT */
for (i = 0; i < N; ++i)
{
double ajj;
gsl_complex z;
j = N - i - 1;
{
gsl_complex z0 = gsl_matrix_complex_get(LLT, j, j);
ajj = 1.0 / GSL_REAL(z0);
}
GSL_SET_COMPLEX(&z, ajj, 0.0);
gsl_matrix_complex_set(LLT, j, j, z);
{
gsl_complex z1 = gsl_matrix_complex_get(LLT, j, j);
ajj = -GSL_REAL(z1);
}
if (j < N - 1)
{
gsl_matrix_complex_view m;
m = gsl_matrix_complex_submatrix(LLT, j + 1, j + 1,
N - j - 1, N - j - 1);
v1 = gsl_matrix_complex_subcolumn(LLT, j, j + 1, N - j - 1);
gsl_blas_ztrmv(CblasLower, CblasNoTrans, CblasNonUnit,
&m.matrix, &v1.vector);
gsl_blas_zdscal(ajj, &v1.vector);
}
} /* for (i = 0; i < N; ++i) */
/*
* The lower triangle of LLT now contains L^{-1}. Now compute
* A^{-1} = L^{-H} L^{-1}
*
* The (ij) element of A^{-1} is column i of conj(L^{-1}) dotted into
* column j of L^{-1}
*/
for (i = 0; i < N; ++i)
{
gsl_complex sum;
for (j = i + 1; j < N; ++j)
{
gsl_vector_complex_view v2;
v1 = gsl_matrix_complex_subcolumn(LLT, i, j, N - j);
v2 = gsl_matrix_complex_subcolumn(LLT, j, j, N - j);
/* compute Ainv[i,j] = sum_k{conj(Linv[k,i]) * Linv[k,j]} */
gsl_blas_zdotc(&v1.vector, &v2.vector, &sum);
/* store in upper triangle */
gsl_matrix_complex_set(LLT, i, j, sum);
}
/* now compute the diagonal element */
v1 = gsl_matrix_complex_subcolumn(LLT, i, i, N - i);
gsl_blas_zdotc(&v1.vector, &v1.vector, &sum);
gsl_matrix_complex_set(LLT, i, i, sum);
}
/* copy the Hermitian upper triangle to the lower triangle */
for (j = 1; j < N; j++)
{
for (i = 0; i < j; i++)
{
gsl_complex z = gsl_matrix_complex_get(LLT, i, j);
gsl_matrix_complex_set(LLT, j, i, gsl_complex_conjugate(z));
}
}
return GSL_SUCCESS;
}
} /* gsl_linalg_complex_cholesky_invert() */
void get2Dnoisematrix(struct data *d,int mode)
{
int dim1,dim2,dim3,nr;
double noisefrac;
int h,i,j,k,l;
int n=0;
gsl_complex cx,cx1,cx2;
#ifdef DEBUG
struct timeval tp;
double t1,t2;
char function[20];
strcpy(function,"get2Dnoisematrix"); /* Set function name */
#endif
/* Get noise if it has not been measured */
if (!d->noise.data) getnoise2D(d,mode);
/* Equalize noise if it has not been done */
if (!d->noise.equal) equalizenoise2D(d,mode);
#ifdef DEBUG
fprintf(stdout,"\n%s: %s()\n",SOURCEFILE,function);
gettimeofday(&tp, NULL);
t1=(double)tp.tv_sec+(1.e-6)*tp.tv_usec;
fflush(stdout);
#endif
/* Data dimensions */
dim1=d->np/2; dim2=d->nv; dim3=d->endpos-d->startpos; nr=d->nr;
noisefrac=0.0;
switch(mode) {
case MK: /* Mask parameters */
switch(d->datamode) {
case FID:
noisefrac=*val("masknoisefrac",&d->p);
if (!noisefrac) noisefrac=Knoisefraction;
break;
default:
noisefrac=*val("masklvlnoisefrac",&d->p);
if (!noisefrac) noisefrac=IMnoisefraction;
} /* end datamode switch */
break;
case SM: /* Sensitivity map parameters */
switch(d->datamode) {
case FID:
noisefrac=*val("smapnoisefrac",&d->p);
if (!noisefrac) noisefrac=Knoisefraction;
break;
default:
noisefrac=*val("masklvlnoisefrac",&d->p);
if (!noisefrac) noisefrac=IMnoisefraction;
} /* end datamode switch */
break;
default: /* Default parameters */
switch(d->datamode) {
case FID:
noisefrac=Knoisefraction;
break;
default:
noisefrac=IMnoisefraction;
} /* end datamode switch */
} /* end mode switch */
/* Allocate memory for noise matrix */ /* Get noise if it has not been measured */
if (!d->noise.data) getnoise2D(d,mode);
if ((d->noise.mat = (gsl_matrix_complex **)malloc(dim3*sizeof(gsl_matrix_complex *))) == NULL) nomem();
for (j=0;j<dim3;j++)
d->noise.mat[j]=(gsl_matrix_complex *)gsl_matrix_complex_calloc(nr,nr);
for (h=0;h<nr;h++) {
for (i=0;i<nr;i++) {
if (((d->datamode == FID) && d->shift) || ((d->datamode == IMAGE) && !d->shift)) {
/* For shifted FID and not-shifted IMAGE the noise is at centre */
for (j=0;j<dim3;j++) {
n=0;
GSL_SET_COMPLEX(&cx,0.0,0.0);
for(k=dim2/2-dim2*noisefrac/2;k<dim2/2+dim2*noisefrac/2;k++) {
for (l=dim1/2-dim1*noisefrac/2;l<dim1/2+dim1*noisefrac/2;l++) {
GSL_SET_REAL(&cx1,d->data[h][j][k*dim1+l][0]);
GSL_SET_IMAG(&cx1,d->data[h][j][k*dim1+l][1]);
GSL_SET_REAL(&cx2,d->data[i][j][k*dim1+l][0]);
GSL_SET_IMAG(&cx2,d->data[i][j][k*dim1+l][1]);
cx=gsl_complex_add(cx,gsl_complex_mul(cx1,gsl_complex_conjugate(cx2)));
n++;
}
}
/* Take the mean and normalize */
GSL_SET_COMPLEX(&cx,GSL_REAL(cx)/(n*d->noise.avM2),GSL_IMAG(cx)/(n*d->noise.avM2));
gsl_matrix_complex_set(d->noise.mat[j],h,i,cx);
}
} else {
/* For not shifted FID and shifted IMAGE the noise is at edges */
for (j=0;j<dim3;j++) {
n=0;
GSL_SET_COMPLEX(&cx,0.0,0.0);
for(k=0;k<dim2*noisefrac/2;k++) {
for (l=0;l<dim1*noisefrac/2;l++) {
GSL_SET_REAL(&cx1,d->data[h][j][k*dim1+l][0]);
GSL_SET_IMAG(&cx1,d->data[h][j][k*dim1+l][1]);
GSL_SET_REAL(&cx2,d->data[i][j][k*dim1+l][0]);
GSL_SET_IMAG(&cx2,d->data[i][j][k*dim1+l][1]);
cx=gsl_complex_add(cx,gsl_complex_mul(cx1,gsl_complex_conjugate(cx2)));
n++;
}
for (l=dim1-dim1*noisefrac/2;l<dim1;l++) {
GSL_SET_REAL(&cx1,d->data[h][j][k*dim1+l][0]);
GSL_SET_IMAG(&cx1,d->data[h][j][k*dim1+l][1]);
GSL_SET_REAL(&cx2,d->data[i][j][k*dim1+l][0]);
GSL_SET_IMAG(&cx2,d->data[i][j][k*dim1+l][1]);
cx=gsl_complex_add(cx,gsl_complex_mul(cx1,gsl_complex_conjugate(cx2)));
n++;
}
}
for(k=dim2-dim2*noisefrac/2;k<dim2;k++) {
for (l=0;l<dim1*noisefrac/2;l++) {
GSL_SET_REAL(&cx1,d->data[h][j][k*dim1+l][0]);
GSL_SET_IMAG(&cx1,d->data[h][j][k*dim1+l][1]);
GSL_SET_REAL(&cx2,d->data[i][j][k*dim1+l][0]);
GSL_SET_IMAG(&cx2,d->data[i][j][k*dim1+l][1]);
cx=gsl_complex_add(cx,gsl_complex_mul(cx1,gsl_complex_conjugate(cx2)));
n++;
}
for (l=dim1-dim1*noisefrac/2;l<dim1;l++) {
GSL_SET_REAL(&cx1,d->data[h][j][k*dim1+l][0]);
GSL_SET_IMAG(&cx1,d->data[h][j][k*dim1+l][1]);
GSL_SET_REAL(&cx2,d->data[i][j][k*dim1+l][0]);
GSL_SET_IMAG(&cx2,d->data[i][j][k*dim1+l][1]);
cx=gsl_complex_add(cx,gsl_complex_mul(cx1,gsl_complex_conjugate(cx2)));
n++;
}
}
/* Take the mean and normalize */
GSL_SET_COMPLEX(&cx,GSL_REAL(cx)/(n*d->noise.avM2),GSL_IMAG(cx)/(n*d->noise.avM2));
gsl_matrix_complex_set(d->noise.mat[j],h,i,cx);
}
}
}
}
/* Set noise matrix flag */
d->noise.matrix=TRUE;
#ifdef DEBUG
gettimeofday(&tp, NULL);
t2=(double)tp.tv_sec+(1.e-6)*tp.tv_usec;
fprintf(stdout," Took %f secs\n",t2-t1);
print2Dnoisematrix(d);
fflush(stdout);
#else
/* Print Noise Matrix, if requested */
if (!(strcmp(*sval("printNM",&d->p),"y"))) print2Dnoisematrix(d);
#endif
}
int main(int argc, char *argv[]){
int i,j,k,
c,
N;
int dflag=0,
eflag=0,
gflag=0,
vflag=0,
hflag=0;
float w; /* frec */
//char *lvalue=NULL;
double **M, // XYZ coordinates
dos,
lambda=0;
while((c = getopt (argc, argv, "degvhl:")) != -1){
switch (c){
case 'd':
dflag = 1;
break;
case 'e':
eflag = 1;
break;
case 'g':
gflag = 1;
break;
case 'v':
vflag = 1;
break;
case 'h':
hflag = 1;
break;
case 'l':
lambda = atof(optarg);
break;
}
}
scanf("%d",&N);
M = (double **) malloc (N*sizeof(double *)); // coordinate matrix
// read coordinates (XYZ format file)
for (int i=0; i<N; i++){
char null[5]; // discard element
double *tmp = (double *) malloc (3 * sizeof(double)); // 3 coordinates
scanf("%s%lf%lf%lf", null, &tmp[0], &tmp[1], &tmp[2]);
M[i] = tmp;
// printf("- %.2f %.2f\n",M[i][0], M[i][1]); // DEBUG
}
/* M: coordinate matrix, N: number of atoms, l: spin-orbit parameter (set to 0 to tight-binding)*/
gsl_matrix_complex * Hso = hamiltonian(M, N, lambda);
/* print hamiltonial */
if (hflag){
printComMat(Hso,N*SPIN*ORB);
return 0;
}
/* eigenvalues */
gsl_matrix_complex * evec = gsl_matrix_complex_alloc(N*SPIN*ORB, N*SPIN*ORB);
gsl_vector * eval = gsl_vector_alloc(N*SPIN*ORB);
gsl_eigen_hermv_workspace * ws = gsl_eigen_hermv_alloc(N*SPIN*ORB);
gsl_matrix_complex * A = Hso; // gsl_eigen_hermv() destroys Hso matrix, use a copy instead
gsl_eigen_hermv (A, eval, evec, ws);
gsl_eigen_hermv_sort (eval, evec, GSL_EIGEN_SORT_VAL_ASC);
gsl_eigen_hermv_free(ws);
if (eflag){
for (int i=0; i<N*SPIN*ORB; i++)
printf("%d %.4g \n", i, gsl_vector_get(eval,i));
return 0;
}
if (vflag){
printComMat(evec, N*SPIN*ORB);
return 0;
}
/* calculate DoS
* __ __
* \ \ Hij Hji
* DOS(E) = -imag /_ /_ ----------------
* i j E - En + i*eta
*
* where H is the hamiltonian, and n is the state.
* NOTE: i and j 0-indexed list. i*eta
*/
double eval_min = gsl_vector_min (eval), /* lower bound */
eval_max = gsl_vector_max (eval); /* upper bound */
if (dflag)
for (w = eval_min; w < eval_max; w += 1e-3){
dos = 0;
#pragma omp parallel num_threads(4)
{
int tid = omp_get_thread_num();
#pragma omp for private(i,k) reduction (+:dos)
for (i=0; i<N*SPIN*ORB; i++)
for (k=0; k<N*SPIN*ORB; k++){
gsl_complex h = gsl_matrix_complex_get (Hso, i, k);
double l = gsl_vector_get (eval ,k);
gsl_complex z = gsl_complex_rect(0,5e-3); /* parte imaginaria */
gsl_complex num = gsl_complex_mul(h,gsl_complex_conjugate(h)); /* numerador */
gsl_complex den = gsl_complex_add_real(z, w-l); /* denominador */
gsl_complex g = gsl_complex_div(num,den);
dos += GSL_IMAG(g);
}
if (dflag && tid==0)
printf("%.3g %g \n", w, -dos/PI);
}
}
/* Green's function
*
* <i|n> <n|j>
* Gij(E) = ----------------
* E - En + i*eta
*
* where i and j are atoms, and n is the state.
* NOTE: i and j 0-indexed list.
*/
int list[]={0,1,2,5,6,7}; /* atoms to get conductance */
int NL = (int) sizeof(list)/sizeof(list[0]);
gsl_matrix_complex * G = gsl_matrix_complex_alloc(NL*SPIN*ORB, NL*SPIN*ORB); // Green
if (gflag)
for (double E = eval_min; E < eval_max; E += 1e-3){ // energy
gsl_matrix_complex_set_all(G, GSL_COMPLEX_ZERO); // init
for (int n=0; n<N*SPIN*ORB; n++) // states
for (i=0; i<NL; i++) // atoms
for (j=0; j<NL; j++) // atoms
for (int k0=0; k0<SPIN*ORB; k0++){ // orbitals
for (int k1=0; k1<SPIN*ORB; k1++){ // orbitals
gsl_complex in = gsl_matrix_complex_get (evec, n, list[i]*SPIN*ORB+k0);
gsl_complex nj = gsl_matrix_complex_get (evec, n, list[j]*SPIN*ORB+k1);
double En = gsl_vector_get (eval ,n);
gsl_complex eta = gsl_complex_rect(0,5e-3); /* delta */
gsl_complex num = gsl_complex_mul(in, gsl_complex_conjugate(nj)); /* num */
gsl_complex den = gsl_complex_add_real(eta, E - En); /* den */
gsl_complex Gij = gsl_complex_div(num,den);
gsl_complex tmp = gsl_matrix_complex_get(G, i*SPIN*ORB+k0, j*SPIN*ORB+k1);
gsl_complex sum = gsl_complex_add(tmp, Gij);
gsl_matrix_complex_set(G, i*SPIN*ORB+k0, j*SPIN*ORB+k1, sum);
}
}
dos = 0 ;
for(int i=0; i<NL*SPIN*ORB; i++)
dos += GSL_IMAG( gsl_matrix_complex_get(G, i, i) );
printf("%.3g %g\n", E, -dos/PI);
// printComMat(G, NL*SPIN*ORB);
}
gsl_matrix_complex_free(G);
gsl_vector_free(eval);
gsl_matrix_complex_free(evec);
return 0;
}
