PetscErrorCode cHamiltonianMatrix::assemblance(){
/*
Assemble matrix.
*/
int nonzeros; // TODO: check if nonzeros < __MAXNOZEROS__ is true.
int spin_flag;
// PetscReal _val_;
for (ROW=rstart; ROW<rend; ROW++) {
nonzeros = 0;
// cout << "row is " << ROW << endl;
block(ROW,_jdim1,_jdim2);
// cout << _jdim1 << '\t' << _jdim2 << endl;
// random potential and interaction terms are diagonal.
col[nonzeros] = ROW;value[nonzeros] = compute_diag();nonzeros++;
// hopping terms are off-diagonal.
// --------- hopping of spin down -------------
spin_flag = 2; // to be consistent with convention in construct_basis member function.
compute_hopping(nonzeros,spin_flag);
// ----------- hopping of spin up ---------------
spin_flag = 1;
compute_hopping(nonzeros,spin_flag);
if (nonzeros > __MAXNOZEROS__){
cerr << "nonzeros on a row " << nonzeros << " is larger than the pre-allocated range of"
<< __MAXNOZEROS__ <<" const arrays. Try increasing the max number in polaron.h" << endl;
exit(1);
} else {
ierr = MatSetValues(Hpolaron,1,&ROW,nonzeros,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
}
return ierr;
}
static int
set (void *vstate, gsl_multiroot_function * func, gsl_vector * x, gsl_vector * f, gsl_vector * dx, int scale)
{
hybrid_state_t *state = (hybrid_state_t *) vstate;
gsl_matrix *J = state->J;
gsl_matrix *q = state->q;
gsl_matrix *r = state->r;
gsl_vector *tau = state->tau;
gsl_vector *diag = state->diag;
GSL_MULTIROOT_FN_EVAL (func, x, f);
gsl_multiroot_fdjacobian (func, x, f, GSL_SQRT_DBL_EPSILON, J) ;
state->iter = 1;
state->fnorm = enorm (f);
state->ncfail = 0;
state->ncsuc = 0;
state->nslow1 = 0;
state->nslow2 = 0;
gsl_vector_set_all (dx, 0.0);
/* Store column norms in diag */
if (scale)
compute_diag (J, diag);
else
gsl_vector_set_all (diag, 1.0);
/* Set delta to factor |D x| or to factor if |D x| is zero */
state->delta = compute_delta (diag, x);
/* Factorize J into QR decomposition */
gsl_linalg_QR_decomp (J, tau);
gsl_linalg_QR_unpack (J, tau, q, r);
return GSL_SUCCESS;
}
static int
iterate (void *vstate, gsl_multiroot_function * func, gsl_vector * x, gsl_vector * f, gsl_vector * dx, int scale)
{
hybrid_state_t *state = (hybrid_state_t *) vstate;
const double fnorm = state->fnorm;
gsl_matrix *J = state->J;
gsl_matrix *q = state->q;
gsl_matrix *r = state->r;
gsl_vector *tau = state->tau;
gsl_vector *diag = state->diag;
gsl_vector *qtf = state->qtf;
gsl_vector *x_trial = state->x_trial;
gsl_vector *f_trial = state->f_trial;
gsl_vector *df = state->df;
gsl_vector *qtdf = state->qtdf;
gsl_vector *rdx = state->rdx;
gsl_vector *w = state->w;
gsl_vector *v = state->v;
double prered, actred;
double pnorm, fnorm1, fnorm1p;
double ratio;
double p1 = 0.1, p5 = 0.5, p001 = 0.001, p0001 = 0.0001;
/* Compute qtf = Q^T f */
compute_qtf (q, f, qtf);
/* Compute dogleg step */
dogleg (r, qtf, diag, state->delta, state->newton, state->gradient, dx);
/* Take a trial step */
compute_trial_step (x, dx, state->x_trial);
pnorm = scaled_enorm (diag, dx);
if (state->iter == 1)
{
if (pnorm < state->delta)
{
state->delta = pnorm;
}
}
/* Evaluate function at x + p */
{
int status = GSL_MULTIROOT_FN_EVAL (func, x_trial, f_trial);
if (status != GSL_SUCCESS)
{
return GSL_EBADFUNC;
}
}
/* Set df = f_trial - f */
compute_df (f_trial, f, df);
/* Compute the scaled actual reduction */
fnorm1 = enorm (f_trial);
actred = compute_actual_reduction (fnorm, fnorm1);
/* Compute rdx = R dx */
compute_rdx (r, dx, rdx);
/* Compute the scaled predicted reduction phi1p = |Q^T f + R dx| */
fnorm1p = enorm_sum (qtf, rdx);
prered = compute_predicted_reduction (fnorm, fnorm1p);
/* Compute the ratio of the actual to predicted reduction */
if (prered > 0)
{
ratio = actred / prered;
}
else
{
ratio = 0;
}
/* Update the step bound */
if (ratio < p1)
{
state->ncsuc = 0;
state->ncfail++;
state->delta *= p5;
}
else
{
state->ncfail = 0;
state->ncsuc++;
if (ratio >= p5 || state->ncsuc > 1)
state->delta = GSL_MAX (state->delta, pnorm / p5);
if (fabs (ratio - 1) <= p1)
state->delta = pnorm / p5;
}
/* Test for successful iteration */
if (ratio >= p0001)
{
gsl_vector_memcpy (x, x_trial);
gsl_vector_memcpy (f, f_trial);
state->fnorm = fnorm1;
state->iter++;
}
/* Determine the progress of the iteration */
state->nslow1++;
if (actred >= p001)
state->nslow1 = 0;
if (actred >= p1)
state->nslow2 = 0;
if (state->ncfail == 2)
{
gsl_multiroot_fdjacobian (func, x, f, GSL_SQRT_DBL_EPSILON, J) ;
state->nslow2++;
if (state->iter == 1)
{
if (scale)
compute_diag (J, diag);
state->delta = compute_delta (diag, x);
}
else
{
if (scale)
update_diag (J, diag);
}
/* Factorize J into QR decomposition */
gsl_linalg_QR_decomp (J, tau);
gsl_linalg_QR_unpack (J, tau, q, r);
return GSL_SUCCESS;
}
/* Compute qtdf = Q^T df, w = (Q^T df - R dx)/|dx|, v = D^2 dx/|dx| */
compute_qtf (q, df, qtdf);
compute_wv (qtdf, rdx, dx, diag, pnorm, w, v);
/* Rank-1 update of the jacobian Q'R' = Q(R + w v^T) */
gsl_linalg_QR_update (q, r, w, v);
/* No progress as measured by jacobian evaluations */
if (state->nslow2 == 5)
{
return GSL_ENOPROGJ;
}
/* No progress as measured by function evaluations */
if (state->nslow1 == 10)
{
return GSL_ENOPROG;
}
return GSL_SUCCESS;
}
static int
set (void *vstate, gsl_multifit_function_fdf * fdf, gsl_vector * x, gsl_vector * f, gsl_matrix * J, gsl_vector * dx, int scale)
{
lmder_state_t *state = (lmder_state_t *) vstate;
gsl_matrix *r = state->r;
gsl_vector *tau = state->tau;
gsl_vector *diag = state->diag;
gsl_vector *work1 = state->work1;
gsl_permutation *perm = state->perm;
int signum;
/* Evaluate function at x */
/* return immediately if evaluation raised error */
{
int status = GSL_MULTIFIT_FN_EVAL_F_DF (fdf, x, f, J);
if (status)
return status;
}
state->par = 0;
state->iter = 1;
state->fnorm = enorm (f);
gsl_vector_set_all (dx, 0.0);
/* store column norms in diag */
if (scale)
{
compute_diag (J, diag);
}
else
{
gsl_vector_set_all (diag, 1.0);
}
/* set delta to 100 |D x| or to 100 if |D x| is zero */
state->xnorm = scaled_enorm (diag, x);
state->delta = compute_delta (diag, x);
/* Factorize J into QR decomposition */
gsl_matrix_memcpy (r, J);
gsl_linalg_QRPT_decomp (r, tau, perm, &signum, work1);
gsl_vector_set_zero (state->rptdx);
gsl_vector_set_zero (state->w);
/* Zero the trial vector, as in the alloc function */
gsl_vector_set_zero (state->f_trial);
#ifdef DEBUG
printf("r = "); gsl_matrix_fprintf(stdout, r, "%g");
printf("perm = "); gsl_permutation_fprintf(stdout, perm, "%d");
printf("tau = "); gsl_vector_fprintf(stdout, tau, "%g");
#endif
return GSL_SUCCESS;
}
