compositions (version 2.0-0)

acompscalarproduct: inner product for datasets with a vector space structure

Description

acomp and aplus objects are considered as (sets of) vectors. The %*% is considered as the inner multiplication. An inner multiplication with another vector is the scalar product. An inner multiplication with a matrix is a matrix multiplication, where the vectors are either considered as row or as column vector.

Usage

# S3 method for acomp
%*%(x,y)
# S3 method for aplus
%*%(x,y)

Arguments

x

a acomp or aplus object or a matrix interpreted in clr, ilr or ilt coordinates

y

a acomp or aplus object or a matrix interpreted in clr, ilr or ilt coordinates

Value

Either a numeric vector containing the scalar products, or an object of type acomp or aplus containing the vectors transformed with the given matrix.

Details

The operators try to mimic the behavior of %*% on c()-vectors as inner product, applied in parallel to all row-vectors of the dataset. Thus the product of a vector with a vector of the same type results in the scalar product of both. For the multiplication with a matrix each vector is considered as a row or column, whatever is more appropriate. The matrix itself is considered as representing a linear mapping (endomorphism) of the vector space to a space of the same type. The mapping is represented in clr, ilr or ilt coordinates. Which of the aforementioned coordinate systems is used is judged from the type of x and from the dimensions of the A.

See Also

%*%.rmult

Examples

# NOT RUN {
x <- acomp(matrix( sqrt(1:12), ncol= 3 ))
x%*%x
A <- matrix( 1:9,nrow=3)
x %*% A %*% x
x %*% A
A %*% x
A <- matrix( 1:4,nrow=2)
x %*% A %*% x
x %*% A
A %*% x
x <- aplus(matrix( sqrt(1:12), ncol= 3 ))
x%*%x
A <- matrix( 1:9,nrow=3)
x %*% A %*% x
x %*% A
A %*% x
# }