indx_Commutator_Moment {MultiStatM} | R Documentation |
For a d-variate distribution it provides the product Kx where K is the moment commutator as
produced by matr_Commutator_Moment
and x is a vector of appropriate dimension.
It avoids the construction of large commutators matrices working much faster
with respect to matr_Commutator_Moment
.
indx_Commutator_Moment(x, el_rm, d)
x |
a vector of length d^n where n is length of (el_rm) |
el_rm |
type of a partition |
d |
dimensionality of the underlying multivariate distribution |
A vector K x
Gy., Terdik, Multivariate statistical methods - going beyond the linear, Springer 2021, Section 2.4.3, p.100, Sect. A.2.1, p. 353., Corollary 2.6., p.95
Other Matrices and commutators:
indx_Commutator_Kmn()
,
indx_Commutator_Kperm()
,
indx_Commutator_Mixing()
,
indx_Elimination()
,
indx_Qplication()
,
indx_Symmetry()
,
indx_UnivMomCum()
,
matr_Commutator_Kmn()
,
matr_Commutator_Kperm()
,
matr_Commutator_Mixing()
,
matr_Commutator_Moment()
,
matr_Elimination()
,
matr_Qplication()
,
matr_Symmetry()
n=4; r=2 ; m=1 ; d=2;
PTA<-Partition_Type_All(n)
el_r<-PTA$eL_r[[r]][m,]
## el_r is a given type (always a vector)
x<-1:d^n
indx_Commutator_Moment(x,el_r,d)
# Same as
MC<- matr_Commutator_Moment(el_r,d)
as.vector(MC%*%x)