void sipg_sem_1d<FLOAT_TYPE>::compute_rhs_vector()
{
compute_nodes_and_weights();
const int nop = sem_function<FLOAT_TYPE>::_qt.nop();
const int M = nop-1; //< index of the right node
//< 0 is the index of the left node
_rhs.resize(_vec_size);
for (int i = 0; i < _vec_size; ++i)
_rhs[i] = _w[i] * _f(_x[i]);
// this loop add the nitsche border integral term to the first
// and the last elements
// -1 +-----+- ... -+-----+ +1
for (int i=0; i < nop; ++i)
{
_rhs[i] += _noe*SEM_FUNC::d_phi(i,0)*_u_ex(-1.);
_rhs[_vec_size - nop + i] += -1*_noe*SEM_FUNC::d_phi(i,M)*_u_ex( 1.);
}
_rhs[0] += _pen*_u_ex(-1.);
_rhs[_vec_size-1] += _pen*_u_ex( 1.);
}
int main(int argc, char* argv[]) {
int i, j, k;
int levels[argc-1];
fmpq_poly_t Pn, Ep;
long deg;
char *strf;
acb_ptr nodes;
acb_ptr weights;
int solvable;
int validate_extension, validate_weights;
int valid;
int comp_nodes, comp_weights;
int target_prec;
int nrprintdigits;
int loglevel;
if(argc <= 1) {
printf("Compute a nested generalized Kronrod extension of a Gauss rule\n");
printf("Syntax: kes [-ve] [-vw] [-cn] [-cw] [-dc D] [-dp D] [-l L] n p1 p2 ... pk\n");
printf("Options:\n");
printf(" -ve Validate the polynomial extension by nodes\n");
printf(" -vw Validate the polynomial extension by weights\n");
printf(" -cn Compute the nodes\n");
printf(" -cw Compute the weights\n");
printf(" -dc Compute nodes and weights up to this number of decimal digits\n");
printf(" -dp Print this number of decimal digits\n");
printf(" -l Set the log level\n");
return EXIT_FAILURE;
}
target_prec = 53;
nrprintdigits = 20;
loglevel = 8;
comp_nodes = 0;
comp_weights = 0;
validate_extension = 0;
validate_weights = 0;
k = 0;
for(i = 1; i < argc; i++) {
if (!strcmp(argv[i], "-ve")) {
validate_extension = 1;
} else if (!strcmp(argv[i], "-vw")) {
validate_weights = 1;
} else if (!strcmp(argv[i], "-cn")) {
comp_nodes = 1;
} else if (!strcmp(argv[i], "-cw")) {
comp_weights = 1;
} else if (!strcmp(argv[i], "-dc")) {
/* 'digits' is in base 10 and log(10)/log(2) = 3.32193 */
target_prec = 3.32193 * atoi(argv[i+1]);
i++;
} else if (!strcmp(argv[i], "-dp")) {
nrprintdigits = atoi(argv[i+1]);
i++;
} else if (!strcmp(argv[i], "-l")) {
loglevel = atoi(argv[i+1]);
i++;
} else {
levels[k] = atoi(argv[i]);
k++;
}
}
/* Compute extension */
fmpq_poly_init(Pn);
polynomial(Pn, levels[0]);
printf("Starting with polynomial:\n");
strf = fmpq_poly_get_str_pretty(Pn, "t");
flint_printf("P : %s\n", strf);
printf("Extension levels are:");
for(i = 0; i < k; i++) {
printf(" %i", levels[i]);
}
printf("\n");
fmpq_poly_init(Ep);
solvable = find_multi_extension(Ep, Pn, k, levels, validate_extension, loglevel);
fmpq_poly_mul(Pn, Pn, Ep);
fmpq_poly_canonicalise(Pn);
if(solvable) {
if(! fmpq_poly_is_squarefree(Pn)) {
printf("=====> FINAL POLYNOMIAL NOT SQF <=====");
}
if(loglevel >= 2) {
printf("-------------------------------------------------\n");
printf("Ending with final polynomial:\n");
strf = fmpq_poly_get_str_pretty(Pn, "t");
flint_printf("P : %s\n", strf);
}
deg = fmpq_poly_degree(Pn);
nodes = _acb_vec_init(deg);
weights = _acb_vec_init(deg);
if(comp_weights || validate_weights) {
compute_nodes_and_weights(nodes, weights, Pn, target_prec, loglevel);
} else if(comp_nodes) {
compute_nodes(nodes, Pn, target_prec, loglevel);
}
valid = 1;
if(validate_weights) {
valid = validate_extension_by_weights(weights, deg, target_prec, loglevel);
}
if(! valid) {
printf("**************************************\n");
printf("*** EXTENSION WITH INVALID WEIGHTS ***\n");
printf("**************************************\n");
}
/* Print roots and weights */
if((validate_weights && valid) || ! validate_weights) {
if(comp_nodes) {
printf("-------------------------------------------------\n");
printf("The nodes are:\n");
for(j = 0; j < deg; j++) {
printf("| ");
acb_printd(nodes + j, nrprintdigits);
printf("\n");
}
}
if(comp_weights) {
printf("-------------------------------------------------\n");
printf("The weights are:\n");
for(j = 0; j < deg; j++) {
printf("| ");
acb_printd(weights + j, nrprintdigits);
printf("\n");
}
}
}
_acb_vec_clear(nodes, deg);
_acb_vec_clear(weights, deg);
}
flint_free(strf);
fmpq_poly_clear(Pn);
fmpq_poly_clear(Ep);
return EXIT_SUCCESS;
}
