//' Construct a copula using uniform sampling from the unit simplex
//'
//' Given two families of parallel hyperplanes intersecting the canonical simplex, this function uniformly samples from the canonical simplex and construct an approximation of the bivariate probability distribution, called copula.
//'
//' @param h1 A \eqn{d}-dimensional vector that describes the direction of the first family of parallel hyperplanes.
//' @param h2 A \eqn{d}-dimensional vector that describes the direction of the second family of parallel hyperplanes.
//' @param numSlices The number of the slices for the copula. Default value is 100.
//' @param N The number of points to sample. Default value is \eqn{4\cdot 10^6}.
//'
//' @references \cite{L. Cales, A. Chalkis, I.Z. Emiris, V. Fisikopoulos,
//' \dQuote{Practical volume computation of structured convex bodies, and an application to modeling portfolio dependencies and financial crises,} \emph{Proc. of Symposium on Computational Geometry, Budapest, Hungary,} 2018.}
//'
//' @return A \eqn{numSlices\times numSlices} numerical matrix that corresponds to a copula.
//' @examples
//' # compute a copula for two random families of parallel hyperplanes
//' h1 = runif(n = 10, min = 1, max = 1000)
//' h1 = h1 / 1000
//' h2=runif(n = 10, min = 1, max = 1000)
//' h2 = h2 / 1000
//' cop = copula1(h1=h1, h2=h2, numSlices = 10, N = 100000)
//' @export
// [[Rcpp::export]]
Rcpp::NumericMatrix copula1 (Rcpp::NumericVector h1, Rcpp::NumericVector h2,
Rcpp::Nullable<unsigned int> numSlices, Rcpp::Nullable<unsigned int> N){
typedef double NT;
typedef Cartesian<NT> Kernel;
typedef typename Kernel::Point Point;
typedef boost::mt19937 RNGType;
unsigned int num_slices = 100, numpoints = 4000000;
if (numSlices.isNotNull()) {
num_slices = Rcpp::as<unsigned int>(numSlices);
}
if (N.isNotNull()) {
numpoints = Rcpp::as<unsigned int>(N);
}
Rcpp::NumericMatrix copula(num_slices, num_slices);
std::vector<std::vector<NT> > StdCopula;
unsigned int dim = h1.size(), i, j;
std::vector<NT> hyp1 = Rcpp::as<std::vector<NT> >(h1);
std::vector<NT> hyp2 = Rcpp::as<std::vector<NT> >(h2);
StdCopula = twoParHypFam<Point, RNGType >(dim, numpoints, num_slices, hyp1, hyp2);
for(i=0; i<num_slices; i++) {
for(j=0; j<num_slices; j++){
copula(i,j) = StdCopula[i][j];
}
}
return copula;
}
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
// Calculating Ds = D + S for the BDMCMC sampling algorithm
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
void get_Ds( double K[], double Z[], int R[], int not_continuous[], double D[], double Ds[], double S[], int *gcgm, int *n, int *p )
{
int dim = *p;
( *gcgm == 0 ) ? copula( Z, K, R, not_continuous, n, &dim ) : copula_NA( Z, K, R, not_continuous, n, &dim );
// S <- t(Z) %*% Z; NOTE, I'm using Ds instead of S, for saving memory
double alpha = 1.0, beta = 0.0;
char transA = 'T', transB = 'N';
F77_NAME(dgemm)( &transA, &transB, &dim, &dim, n, &alpha, Z, n, Z, n, &beta, &S[0], &dim );
#pragma omp parallel for
for( int i = 0; i < dim * dim; i++ )
Ds[ i ] = D[ i ] + S[ i ];
}
