matr_Symmetry {MultiStatM} | R Documentation |
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
matr_Symmetry(d, n, useSparse = FALSE)
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. |
A Symmetrizer matrix with order {d^n} \times d^n
. If useSparse=TRUE
an object of the class "dgCMatrix" is produced.
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)
Other Matrices and commutators:
indx_Commutator_Kmn()
,
indx_Commutator_Kperm()
,
indx_Commutator_Mixing()
,
indx_Commutator_Moment()
,
indx_Elimination()
,
indx_Qplication()
,
indx_Symmetry()
,
indx_UnivMomCum()
,
matr_Commutator_Kmn()
,
matr_Commutator_Kperm()
,
matr_Commutator_Mixing()
,
matr_Commutator_Moment()
,
matr_Elimination()
,
matr_Qplication()
a<-c(1,2)
b<-c(2,3)
c<-kronecker(kronecker(a,a),b)
## The symmetrized version of c is
as.vector(matr_Symmetry(2,3)%*%c)