##### https://github.com/cran/multivariance
Tip revision: 223488f
multivariance.cpp
``````#include <Rcpp.h>
#include <float.h>
using namespace Rcpp;

//' fast Euclidean distance matrix
//'
//' @param x matrix with sample rows for which the distance matrix is computed (to use with vectors, use \code{as.matrix(x)})
//' @examples
//' #require(microbenchmark)
//' #x = rnorm(100)
//' #microbenchmark(fastdist(as.matrix(x)),as.matrix(dist(x)))
//' @export
// [[Rcpp::export]]
NumericMatrix fastdist (const NumericMatrix & x){
unsigned int outrows = x.nrow(), i = 0, j = 0;
double d;
Rcpp::NumericMatrix out(outrows,outrows);

for (i = 0; i < outrows - 1; i++){
Rcpp::NumericVector v1 = x.row(i);
for (j = i + 1; j < outrows ; j ++){
d = sqrt(sum(pow(v1-x.row(j), 2.0)));
out(j,i)=d;
out(i,j)=d;
}
}

return out;
}

//' double center a symmetric matrix
//'
//' @param x symmetric matrix
//' @param normalize boolean. If \code{TRUE} the matrix will be normalized to mean 1.
//' @keywords internal
// [[Rcpp::export]]
NumericMatrix doubleCenterSymMat(const NumericMatrix & x, bool & normalize) {
int i, j;
int N = x.nrow();
NumericVector colmeans(N);
NumericMatrix out(N, N);
double fullmean;
double tmp;

for (i=0; i<N; i++) {
colmeans(i) = sum(x(i,_))/(double)(N);
}
fullmean = sum(colmeans)/N;

if ( (fullmean == 0) | !normalize) {
// unnormalized centering
if (fullmean == 0) warning("It seems that one variable is constant. Constants are always independent. \n");
for (i=0; i<N; i++)
for (j=i; j<N; j++) {
tmp = - x(i, j) + colmeans(i) + colmeans(j) - fullmean;
out(j, i) = tmp;
out(i, j) = tmp;
}
} else { // normalized centering
for (i=0; i<N; i++)
for (j=i; j<N; j++) {
tmp = (- x(i, j) + colmeans(i) + colmeans(j) - fullmean)/fullmean;
out(j, i) = tmp;
out(i, j) = tmp;
}
}

return out;
}

//' fast centered Euclidean distance matrix
//'
//' @param x matrix with sample rows for which the distance matrix is computed (to use with vectors, use \code{as.matrix(x)})
//' @param normalize boolean. If \code{TRUE} the matrix will be normalized to mean 1.
//' @export
// [[Rcpp::export]]
NumericMatrix fastEuclideanCdm (const NumericMatrix & x, bool & normalize){
unsigned const int N = x.nrow();
unsigned int i = 0, j = 0;
NumericMatrix out(N,N);
NumericVector colmeans(N);
double tmp, m;

for (i = 0; i < N - 1; i++){ // row
NumericVector v1 = x.row(i);
for (j = i + 1; j < N ; j ++){ // column
tmp = sqrt(sum(pow(v1-x.row(j), 2.0)));
out(i,j) = tmp;
colmeans(i) += tmp;
colmeans(j) += tmp;
}
}

colmeans = colmeans/N;
m = sum(colmeans)/(double) N;

if ( (m == 0) | !normalize) {
// unnormalized centering
if (m == 0) warning("It seems that one variable is constant. Constants are always independent. \n");
for (i = 0; i < N-1; i++){ // row
for (j = i+1 ; j < N ; j++){ // column
tmp = -out(i,j) + colmeans(i) + colmeans(j) - m;
out(i,j) = tmp;
out(j,i) = tmp;

}
}

for (i = 0; i < N ; i++){ // diag
out(i,i) =  2*colmeans(i) - m;
}
} else {
// normalized centering
for (i = 0; i < N-1; i++){ // row
for (j = i+1 ; j < N ; j++){ // column
tmp = (-out(i,j) + colmeans(i) + colmeans(j) - m)/m;
out(i,j) = tmp;
out(j,i) = tmp;
}
}

for (i = 0; i < N ; i++){ // diag
out(i,i) =  (2*colmeans(i) - m)/m;
}
}
/* */
return out;
}

//' for the fast detection of the full dependence structure
//'
//' Returns the row indicies of matrix A which match with B
//'
//' @param A matrix
//' @param B matrix whose rows are subset of A
//'
//' @examples
//' # A = t(utils::combn(10,3))
//' # B = A[sort(sample.int(nrow(A),10)),]
//' # match_rows(A,B)
//'
//' @keywords internal
// [[Rcpp::export]]

NumericVector match_rows(NumericMatrix & A,NumericMatrix &B){
int i = 0, k;
NumericVector res (B.nrow());

for (k = 0; k < B.nrow(); k++) {
while( is_true(any(A.row(i) != B.row(k)))) {
i++;
}
res(k) = i;
}
return res+1;
}

//' bias corrected double centering
//' # included for speed comparison
//'
//' @keywords internal
// [[Rcpp::export]]
NumericMatrix doubleCenterBiasCorrected(const NumericMatrix & x) {
int i, j;
int N = x.nrow();
NumericVector colmeans(N);
NumericMatrix out(N, N);
double fullmean;
double tmp;

for (i=0; i<N; i++) {
colmeans(i) = sum(x(i,_))/(double)(N-2);
}
fullmean = sum(colmeans)/(N-1);

// unnormalized centering
for (i=0; i<N; i++)
for (j=i+1; j<N; j++) {
tmp = - x(i, j) + colmeans(i) + colmeans(j) - fullmean;
out(j, i) = tmp;
out(i, j) = tmp;
}

return out;
}

//' bias corrected double centering with normalizing
//' # included for speed comparison
//'
//' @keywords internal
// [[Rcpp::export]]
NumericVector doubleCenterBiasCorrectedUpper(const NumericMatrix & x) {
// returning a vector
int i, j, k = 0;
int N = x.nrow();
NumericVector colmeans(N);
NumericVector out(N*(N-1)/2);
const NumericVector zero(N*(N-1)/2);
double fullmean;
double tmp;
double centeredmean = 0.0;

for (i=0; i<N; i++) {
colmeans(i) = sum(x(i,_))/(double)(N-2);
}
fullmean = sum(colmeans)/(N-1);

// unnormalized centering
for (i=0; i<N; i++)
for (j=i+1; j<N; j++) {
tmp = - x(i, j) + colmeans(i) + colmeans(j) - fullmean;
centeredmean += pow(tmp, 2);
out(k) = tmp;
k += 1;
}

centeredmean = 2*centeredmean/(N*(N-3));

if (centeredmean < DBL_EPSILON) {
//    warning("A doubly centered distance matrix seems to have only zero entries. Maybe one variable is constant. Constants are always independent. \n");
return zero;
} else {
return out/pow(centeredmean, 0.5);
}
}

//' bias corrected double centering with normalizing constants for upper and lower bound
//'
//' @keywords internal
// [[Rcpp::export]]
List doubleCenterBiasCorrectedUpperLower(const NumericMatrix & x, const int & n) {
// returning a list, with vector instead of matrix
int i, j, k = 0;
int N = x.nrow();
NumericVector colmeans(N);
NumericVector out(N*(N-1)/2);
const NumericVector zero(N*(N-1)/2);
double fullmean;
double tmp;
double upper = 0.0, lower = 0.0;
List ret;

for (i=0; i<N; i++) {
colmeans(i) = sum(x(i,_))/(double)(N-2);
}
fullmean = sum(colmeans)/(N-1);

// unnormalized centering
for (i=0; i<N; i++)
for (j=i+1; j<N; j++) {
tmp = - x(i, j) + colmeans(i) + colmeans(j) - fullmean;
upper += pow(tmp, 2);
lower += fabs(pow(tmp, n));
out(k) = tmp;
k += 1;
}

upper = 2*upper/(N*(N-3));

if (upper < DBL_EPSILON) {
//    warning("A doubly centered distance matrix seems to have only zero entries. Maybe one variable is constant. Constants are always independent. \n");
out = zero;
upper = 1;  // to prevent division by 0
lower = 1;  // to prevent division by 0
}

ret["out"] = out;

ret["upper"] =  pow(upper, 0.5);

lower = 2*lower/(N*(N-3));
ret["lower"] =  pow(lower, (double)1/n);

return ret;
}

/*** R
*/
``````