| diagonalMatrix-class {Matrix} | R Documentation |
Class "diagonalMatrix" is the virtual class of all diagonal matrices.
A virtual Class: No objects may be created from it.
diag:code"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.
Class "sparseMatrix", directly.
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.
signature(from = "matrix", to = "diagonalMatrix"): ...
signature(from = "Matrix", to = "diagonalMatrix"): ...
signature(from = "diagonalMatrix", to = "generalMatrix"): ...
signature(from = "diagonalMatrix", to = "triangularMatrix"): ...
signature(from = "diagonalMatrix", to = "nMatrix"): ...
signature(from = "diagonalMatrix", to = "matrix"): ...
signature(from = "diagonalMatrix", to = "sparseVector"): ...
signature(x = "diagonalMatrix"): ...
signature(x = "dgeMatrix", y = "diagonalMatrix"): ...
signature(x = "matrix", y = "diagonalMatrix"): ...
signature(x = "diagonalMatrix", y = "matrix"): ...
signature(x = "diagonalMatrix", y = "dgeMatrix"): ...
signature(x = "diagonalMatrix", y = "dgeMatrix"): ...
and many more methods
signature(a = "diagonalMatrix", b, ...): is
trivially implemented, of course.
signature(x = "nMatrix"), semantically
equivalent to base function which(x, arr.ind).
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 |-> NaN), in order to preserve sparsity.
ddiMatrix and ldiMatrix are
“actual” classes extending "diagonalMatrix".
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)), tol = 1e-12)
)
solve(D5)# efficient as is diagonal
# an unusual way to construct a band matrix:
rbind2(cbind2(I5, D5),
cbind2(D5, I5))