double gaussian_pdf_log(const gaussian_t* dist,
const gsl_vector* x) {
double r = 0.0;
double logdet = 0.0;
if (gaussian_isdiagonal(dist)) {
size_t i;
double dx, dd;
for (i = 0; i < dist->dim; i++) {
dx = gsl_vector_get(x, i) - gsl_vector_get(dist->mean, i);
dd = gsl_vector_get(dist->diag, i);
r += dx * dx / dd;
logdet += DEBUG_LOG(dd);
}
}
else {
int signum;
gsl_vector* w1 = gsl_vector_alloc(dist->dim);
gsl_vector* w2 = gsl_vector_alloc(dist->dim);
gsl_vector_memcpy(w1, x);
gsl_vector_sub(w1, dist->mean);
gsl_matrix* v = gsl_matrix_alloc(dist->dim, dist->dim);
gsl_matrix_memcpy(v, dist->cov);
gsl_permutation* p = gsl_permutation_alloc(dist->dim);
gsl_linalg_LU_decomp(v, p, &signum);
gsl_linalg_LU_solve(v, p, w1, w2);
gsl_blas_ddot(w1, w2, &r);
logdet = gsl_linalg_LU_lndet(v);
assert(gsl_linalg_LU_sgndet(v, signum) == 1.0);
gsl_vector_free(w1);
gsl_vector_free(w2);
gsl_matrix_free(v);
gsl_permutation_free(p);
}
/* Use log to avoid underflow !
here
r = (x - mean)^T * cov^-1 * (x - mean)
logdet = log(det(cov))
then
logpdf = -.5 * (k * log(2*pi) + logdet + r);
*/
r = r + dist->dim * DEBUG_LOG(2 * M_PI) + logdet;
r = -0.5 * r;
assert(!isnan(r));
return r;
}
/**
* C++ version of gsl_linalg_LU_sgndet().
* @param lu An LU decomposition marix
* @param signum The sign of the permutation
* @return The sign of the determinant of the matrix with LU decomposition @c LU
*/
inline int LU_sgndet( matrix& lu, int signum ){ return gsl_linalg_LU_sgndet( lu.get(), signum ); }
CAMLprim value ml_gsl_linalg_LU_sgndet(value LU, value sig)
{
_DECLARE_MATRIX(LU);
_CONVERT_MATRIX(LU);
return Val_int(gsl_linalg_LU_sgndet(&m_LU, Int_val(sig)));
}
