/***********************************************************//**
* Compute the points and weights of Gauss-Hermite quadrature
*
* \param[in] N - number of elements
* \param[in,out] pts - quadrature nodes (space already alloc)
* \param[in,out] weights - weights (space alread alloc)
*
* \return 0 if successful
* \note
* weight function is \f$ w(x) = \frac{1}{\sqrt{2\pi}}e^{-x^2/2}\f$
*************************************************************/
int gauss_hermite(size_t N, double * pts, double * weights){
size_t ii;
double * offdiag = calloc_double(N);
double * evec = calloc_double(N*N);
double * work = calloc_double(2*N-2);
int info;
for (ii = 0; ii < N; ii++){
pts[ii] = 0.0;
offdiag[ii] = sqrt((double)(ii+1));
}
int M = N;
int M2 = N;
dstev_("V", &M, pts, offdiag, evec, &M2, work, &info);
if ( info > 0) {
fprintf(stderr, "Gauss-Hermite quadrature failed because eigenvalues did not converge \n");
exit(1);
}
else if ( info < 0) {
fprintf(stderr, "The %d-th argument of dstev_ has an illegal value",info);
exit(1);
}
for (ii = 0; ii < N; ii++){
weights[ii] = evec[ii*N] * evec[ii*N];// * sqrt(2*M_PI);
}
free(offdiag); offdiag = NULL;
free(evec); evec = NULL;
free(work); work = NULL;
return info;
}
/***********************************************************//**
* Compute the points and weights of Gauss-Legendre quadrature
*
* \param[in] N - number of elements
* \param[in,out] pts - quadrature nodes (space already alloc)
* \param[in,out] weights - weights (space alread alloc)
*
* \note
* Here the quadrature and the points are computed
* assuming a weight function of .5. Thus it will differ
* from some results online because the weights computed
* here will be half of the weights computed with a weight
* function of 1
*************************************************************/
void gauss_legendre(size_t N, double * pts, double * weights){
//*
if (N == 1){
pts[0] = 0.0;
weights[0] = 1.0;
}
else if (N < 200){
getLegPtsWts(N,pts,weights);
//size_t ii;
//for (ii = 0; ii < N; ii++){
// weights[ii] /= 2.0;
//}
}
else{
size_t ii;
double temp;
double * offdiag = calloc_double(N);
double * evec = calloc_double(N*N);
double * work = calloc_double(2*N-2);
int info;
for (ii = 0; ii < N; ii++){
pts[ii] = 0.0;
temp = (double)ii + 1.0;
//temp = (double)ii;
offdiag[ii] = temp / sqrt( (2.0 * temp + 1.0) * (2.0 * temp -1.0) );
//offdiag[ii] = 0.5 / sqrt( 1.0 - pow(2.0 * temp, -2.0));
//offdiag[ii] = temp / sqrt((2.0 * temp +1.0));
}
int M = N;
int M2 = N;
dstev_("V", &M, pts, offdiag, evec, &M2, work, &info);
if ( info > 0) {
fprintf(stderr, "Gauss-Hermite quadrature failed because eigenvalues did not converge \n");
exit(1);
}
else if ( info < 0) {
fprintf(stderr, "The %d-th argument of dstev_ has an illegal value",info);
exit(1);
}
for (ii = 0; ii < N; ii++){
//weights[ii] = evec[N*N-2 + ii] * evec[N*N-2 + ii];
//weights[ii] = evec[N*N-2 + ii] * evec[N*N-2 + ii];
//weights[ii] = 2.0* evec[ii] * evec[ii];
weights[ii] = evec[ii*N] * evec[ii*N];
}
free(offdiag); offdiag = NULL;
free(evec); evec = NULL;
free(work); work = NULL;
}
}
void calc_eigenvalues(struct ed_s *ed, unsigned iter)
{
int n, ldz, info;
char* job = "N";
n = iter + 1;
ldz = 1;
memcpy(ed->d, ed->alpha, sizeof(double) * (iter + 1));
memcpy(ed->e, ed->beta + 1, sizeof(double) * iter);
dstev_("N", &n, ed->d, ed->e, NULL, &ldz, NULL, &info);
// assert(info == 0);
}
