packedMatrix-class: Virtual Class '"packedMatrix"' of Packed Dense Matrices
In Matrix: Sparse and Dense Matrix Classes and Methods

packedMatrix-class

R Documentation

Virtual Class `"packedMatrix"` of Packed Dense Matrices

Description

Class "packedMatrix" is the virtual class of dense symmetric or triangular matrices in "packed" format, storing only the choose(n+1,2) == n*(n+1)/2 elements of the upper or lower triangle of an n-by-n matrix. It is used to define common methods for efficient subsetting, transposing, etc. of its proper subclasses: currently "[dln]spMatrix" (packed symmetric), "[dln]tpMatrix" (packed triangular), and subclasses of these, such as "dppMatrix".

Slots

uplo:: "character"; either "U", for upper triangular, and "L", for lower.
Dim, Dimnames:: as all Matrix objects.

Extends

Class "denseMatrix", directly. Class "Matrix", by class "denseMatrix", distance 2.

Methods

pack: signature(x = "packedMatrix"): ...
unpack: signature(x = "packedMatrix"): ...
isSymmetric: signature(object = "packedMatrix"): ...
isTriangular: signature(object = "packedMatrix"): ...
isDiagonal: signature(object = "packedMatrix"): ...
t: signature(x = "packedMatrix"): ...
diag: signature(x = "packedMatrix"): ...
diag<-: signature(x = "packedMatrix"): ...

Author(s)

Mikael Jagan

Examples

showClass("packedMatrix")
showMethods(classes = "packedMatrix")


(s0 <- new("nsyMatrix"))

(M2 <- Matrix(c(TRUE, NA, FALSE, FALSE), 2, 2)) # logical dense (ltr)
(sM <- M2 & t(M2))                       # -> "lge"
class(sM <- as(sM, "nMatrix"))           # -> "nge"
     (sM <- as(sM, "symmetricMatrix"))   # -> "nsy"
str(sM <- as(sM, "packedMatrix")) # -> "nsp", i.e., packed symmetric


(M2 <- Matrix(c(TRUE, NA, FALSE, FALSE), 2, 2)) # logical dense (ltr)
str(M2)
# can
(sM <- M2 | t(M2)) # "lge"
as(sM, "symmetricMatrix")
str(sM <- as(sM, "packedMatrix")) # packed symmetric


## Only upper triangular part matters (when uplo == "U" as per default)
(sy2 <- new("dsyMatrix", Dim = as.integer(c(2,2)), x = c(14, NA,32,77)))
str(t(sy2)) # uplo = "L", and the lower tri. (i.e. NA is replaced).

chol(sy2) #-> "Cholesky" matrix
(sp2 <- pack(sy2)) # a "dspMatrix"

## Coercing to dpoMatrix gives invalid object:
sy3 <- new("dsyMatrix", Dim = as.integer(c(2,2)), x = c(14, -1, 2, -7))
try(as(sy3, "dpoMatrix")) # -> error: not positive definite


## 4x4 example
m <- matrix(0,4,4); m[upper.tri(m)] <- 1:6
(sym <- m+t(m)+diag(11:14, 4))
(S1 <- pack(sym))
(S2 <- t(S1))
stopifnot(all(S1 == S2)) # equal "seen as matrix", but differ internally :
str(S1)
S2@x


showClass("ntrMatrix")

str(new("ntpMatrix"))
(nutr <- as(upper.tri(matrix(, 4, 4)), "ndenseMatrix"))
str(nutp <- pack(nutr)) # packed matrix: only 10 = 4*(4+1)/2 entries
!nutp # the logical negation (is *not* logical triangular !)
## but this one is:
stopifnot(all.equal(nutp, pack(!!nutp)))


showClass("ltrMatrix")

str(new("ltpMatrix"))
(lutr <- as(upper.tri(matrix(, 4, 4)), "ldenseMatrix"))
str(lutp <- pack(lutr)) # packed matrix: only 10 = 4*(4+1)/2 entries
!lutp # the logical negation (is *not* logical triangular !)
## but this one is:
stopifnot(all.equal(lutp, pack(!!lutp)))


(m <- rbind(2:3, 0:-1))
(M <- as(m, "generalMatrix"))

(T <- as(M, "triangularMatrix")) # formally upper triangular
(T2 <- as(t(M), "triangularMatrix"))
stopifnot(T@uplo == "U", T2@uplo == "L", identical(T2, t(T)))

m <- matrix(0,4,4); m[upper.tri(m)] <- 1:6
(t1 <- Matrix(m+diag(,4)))
str(t1p <- pack(t1))
(t1pu <- diagN2U(t1p))
stopifnot(exprs = {
   inherits(t1 , "dtrMatrix"); validObject(t1)
   inherits(t1p, "dtpMatrix"); validObject(t1p)
   inherits(t1pu,"dtCMatrix"); validObject(t1pu)
   t1pu@x == 1:6
   all(t1pu == t1p)
   identical((t1pu - t1)@x, numeric())# sparse all-0
})


showClass("dtpMatrix")

(p1 <- pack(T2))
str(p1)
(pp <- pack(T))
ip1 <- solve(p1)
stopifnot(length(p1@x) == 3, length(pp@x) == 3,
          p1 @ uplo == T2 @ uplo, pp @ uplo == T @ uplo,
	  identical(t(pp), p1), identical(t(p1), pp),
	  all((l.d <- p1 - T2) == 0), is(l.d, "dtpMatrix"),
	  all((u.d <- pp - T ) == 0), is(u.d, "dtpMatrix"),
	  l.d@uplo == T2@uplo, u.d@uplo == T@uplo,
	  identical(t(ip1), solve(pp)), is(ip1, "dtpMatrix"),
	  all.equal(as(solve(p1,p1), "diagonalMatrix"), Diagonal(2)))

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