R: inner product for datasets with a vector space structure

acompscalarproduct {compositions} | R Documentation

## 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 class 'acomp'
    x %*% y
    ## S3 method for class '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

### 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.

### 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.

### Author(s)

K.Gerald v.d. Boogaart http://www.stat.boogaart.de

### See Also

`%*%.rmult`

### Examples

    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

[Package compositions version 1.40-5 Index]