chol.tensor {tensorA} | R Documentation |
A tensor can be seen as a linear mapping of a tensor to a tensor. This function computes its Cholesky decomposition.
chol.tensor(X,i,j,...,name="lambda")
X |
The tensor to be decomposed |
i |
The image dimensions of the linear mapping |
j |
The coimage dimensions of the linear mapping |
name |
The name of the eigenspace dimension. This is the dimension created by the decompositions, in which the eigenvectors are e_i |
... |
for generic use only |
A tensor can be seen as a linear mapping of a tensor to a tensor. Let denote R_i the space of real tensors with dimensions i_1...i_d.
chol.tensorComputes for a tensor a_{i_1...i_dj_1...j_d} representing a positive definit mapping form R_j to R_j with equal dimension structure in i and j its "Cholesky" decomposition L_{i_1...i_d lambda} such that
a_{i_1...i_dj_1...j_d}=∑_{λ{}} L_{i_1...i_d λ{}}L_{j_1...j_d λ{}}
a tensor
A by
argument is not necessary, since both processing
dimensions have to be given.
K. Gerald van den Boogaart
A <- to.tensor(rnorm(15),c(a=3,b=5)) AAt <- einstein.tensor(A,mark(A,i="a")) ch <- chol.tensor(AAt,"a","a'",name="lambda") #names(ch)[1]<-"lambda" einstein.tensor(ch,mark(ch,i="a")) # AAt A <- to.tensor(rnorm(30),c(a=3,b=5,c=2)) AAt <- einstein.tensor(A,mark(A,i="a"),by="c") ch <- chol.tensor(AAt,"a","a'",name="lambda") einstein.tensor(ch,mark(ch,i="a"),by="c") #AAt