needed dtw like in R package - c++

Question

There is a function of the dtw package
dtw(x, y=NULL, dist.method="Euclidean", step.pattern=symmetric2, window.type="none", keep.internals=FALSE, distance.only=FALSE, open.end=FALSE, open.begin=FALSE, ... )
In the function, there are three methods of calculating distances
symmetric1 , symmetric2 , asymmetric
I am interested in the method step.pattern = symmetric2.
I have a C ++ function that works exactly like symmetric1
#include <Rcpp.h>
using namespace Rcpp;
// [[Rcpp::export]]
double dtw_rcpp(const NumericVector& x, const NumericVector& y) {
size_t n = x.size(), m = y.size();
NumericMatrix res = no_init(n + 1, m + 1);
std::fill(res.begin(), res.end(), R_PosInf);
res(0, 0) = 0;
double cost = 0;
size_t w = std::abs(static_cast<int>(n - m));
for (size_t i = 1; i <= n; ++i) {
for (size_t j = std::max(1, static_cast<int>(i - w)); j <= std::min(m, i + w); ++j) {
cost = std::abs(x[i - 1] - y[j - 1]);
res(i, j) = cost + std::min(std::min(res(i - 1, j), res(i, j - 1)), res(i - 1, j - 1));
}
}
return res(n, m);
}
What do I need to change in this с++ function that it considered the method of distance symmetric2.
I do not understand how it works symmetric2.
here it is said very little about it
1. Well-known step patterns
These common transition types are used in quite a lot of implementations.
symmetric1 (or White-Neely) is the commonly used quasi-symmetric, no local constraint, non-normalizable. It is biased in favor of oblique steps. symmetric2 is normalizable, symmetric, with no local slope constraints. Since one diagonal step costs as much as the two equivalent steps along the sides, it can be normalized dividing by N+M (query+reference lengths).
in the source code, I could not understand because I am a beginner programmer
I do not speak English so forgive me for the mistakes.
thank you

Answer 1

OP is asking about dynamic time warping alignments in R. Printing the symmetric2 object should clarify the recursion rule:
g[i,j] = min(
g[i-1,j-1] + 2 * d[i ,j ] ,
g[i ,j-1] + d[i ,j ] ,
g[i-1,j ] + d[i ,j ] ,
)
g is the global cost matrix, d the local distance. I can't comment on the rest of your code.
If you only need the distance value under this specific step pattern, and no other features, the code may be much simplified (see e.g. the pseudocode on Wikipedia).