| SymMatr {MultiStatM} | R Documentation |
Symmetrizer Matrix
Description
Based on Chacon and Duong (2015) efficient recursive algorithms for functionals based on higher order derivatives. An option for sparse matrix is provided. By using sparse matrices far less memory is required and faster computation times are obtained
Usage
SymMatr(d, n, useSparse = FALSE)
Arguments
d |
dimension of a vector x |
n |
power of the Kronecker product |
useSparse |
TRUE or FALSE. If TRUE an object of the class "dgCMatrix" is produced. |
Value
A Symmetrizer matrix with order {d^n} \times d^n. If useSparse=TRUE
an object of the class "dgCMatrix" is produced.
References
Chacon, J. E., and Duong, T. (2015). Efficient recursive algorithms for functionals based on higher order derivatives of the multivariate Gaussian density. Statistics and Computing, 25(5), 959-974.
Gy. Terdik, Multivariate statistical methods - going beyond the linear, Springer 2021.Section 1.3.1 Symmetrization, p.14. (1.29)
See Also
Other Matrices and commutators:
EliminIndx(),
EliminMatr(),
QplicIndx(),
QplicMatr(),
SymIndx(),
UnivMomCum()
Examples
a<-c(1,2)
b<-c(2,3)
c<-kronecker(kronecker(a,a),b)
## The symmetrized version of c is
as.vector(SymMatr(2,3)%*%c)