inner product for datasets with a vector space structure
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.
## S3 method for class 'acomp' x %*% y ## S3 method for class 'aplus' x %*% y
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 |
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.
Either a numeric vector containing the scalar products, or an object of type acomp or aplus containing the vectors transformed with the given matrix.
K.Gerald v.d. Boogaart http://www.stat.boogaart.de
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
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