diagonalMatrix-class: Class "diagonalMatrix" of Diagonal Matrices
In Matrix: Sparse and Dense Matrix Classes and Methods

diagonalMatrix-class

R Documentation

Class "diagonalMatrix" of Diagonal Matrices

Description

Class "diagonalMatrix" is the virtual class of all diagonal matrices.

Objects from the Class

A virtual Class: No objects may be created from it.

Slots

diag:: character string, either "U" or "N", where "U" means ‘unit-diagonal’.
Dim:: matrix dimension, and
Dimnames:: the dimnames, a list, see the Matrix class description. Typically list(NULL,NULL) for diagonal matrices.

Extends

Class "sparseMatrix", directly.

Methods

These are just a subset of the signature for which defined methods. Currently, there are (too) many explicit methods defined in order to ensure efficient methods for diagonal matrices.

coerce: signature(from = "matrix", to = "diagonalMatrix"): ...
coerce: signature(from = "Matrix", to = "diagonalMatrix"): ...
coerce: signature(from = "diagonalMatrix", to = "generalMatrix"): ...
coerce: signature(from = "diagonalMatrix", to = "triangularMatrix"): ...
coerce: signature(from = "diagonalMatrix", to = "nMatrix"): ...
coerce: signature(from = "diagonalMatrix", to = "matrix"): ...
coerce: signature(from = "diagonalMatrix", to = "sparseVector"): ...
t: signature(x = "diagonalMatrix"): ...

and many more methods

solve: signature(a = "diagonalMatrix", b, ...): is trivially implemented, of course; see also solve-methods.
which: signature(x = "nMatrix"), semantically equivalent to base function which(x, arr.ind).
"Math": signature(x = "diagonalMatrix"): all these group methods return a "diagonalMatrix", apart from cumsum() etc which return a vector also for base matrix.
*: signature(e1 = "ddiMatrix", e2="denseMatrix"): arithmetic and other operators from the Ops group have a few dozen explicit method definitions, in order to keep the results diagonal in many cases, including the following:
/: signature(e1 = "ddiMatrix", e2="denseMatrix"): the result is from class ddiMatrix which is typically very desirable. Note that when e2 contains off-diagonal zeros or NAs, we implicitly use 0 / x = 0, hence differing from traditional R arithmetic (where 0 / 0 \mapsto \mbox{NaN}), in order to preserve sparsity.
summary: (object = "diagonalMatrix"): Returns an object of S3 class "diagSummary" which is the summary of the vector object@x plus a simple heading, and an appropriate print method.

Examples

I5 <- Diagonal(5)
D5 <- Diagonal(x = 10*(1:5))
## trivial (but explicitly defined) methods:
stopifnot(identical(crossprod(I5), I5),
          identical(tcrossprod(I5), I5),
          identical(crossprod(I5, D5), D5),
          identical(tcrossprod(D5, I5), D5),
          identical(solve(D5), solve(D5, I5)),
          all.equal(D5, solve(solve(D5)), tolerance = 1e-12)
          )
solve(D5)# efficient as is diagonal

# an unusual way to construct a band matrix:
rbind2(cbind2(I5, D5),
       cbind2(D5, I5))


(lM <- Diagonal(x = c(TRUE,FALSE,FALSE)))
str(lM)#> gory details (slots)

crossprod(lM) # numeric
(nM <- as(lM, "nMatrix"))
crossprod(nM) # pattern sparse


(d2 <- Diagonal(x = c(10,1)))
str(d2)
## slightly larger in internal size:
str(as(d2, "sparseMatrix"))

M <- Matrix(cbind(1,2:4))
M %*% d2 #> `fast' multiplication

chol(d2) # trivial
stopifnot(is(cd2 <- chol(d2), "ddiMatrix"),
          all.equal(cd2@x, c(sqrt(10),1)))

Matrix documentation built on Aug. 13, 2024, 3:01 p.m.