Matrix (version 1.2-8)

lsparseMatrix-classes: Sparse logical matrices

Description

The lsparseMatrix class is a virtual class of sparse matrices with TRUE/FALSE or NA entries. Only the positions of the elements that are TRUE are stored.

These can be stored in the “triplet” form (class TsparseMatrix, subclasses lgTMatrix, lsTMatrix, and ltTMatrix) or in compressed column-oriented form (class CsparseMatrix, subclasses lgCMatrix, lsCMatrix, and ltCMatrix) or--rarely--in compressed row-oriented form (class RsparseMatrix, subclasses lgRMatrix, lsRMatrix, and ltRMatrix). The second letter in the name of these non-virtual classes indicates general, symmetric, or triangular.

Objects from the Class

Objects can be created by calls of the form new("lgCMatrix", ...) and so on. More frequently objects are created by coercion of a numeric sparse matrix to the logical form, e.g. in an expression x != 0. The logical form is also used in the symbolic analysis phase of an algorithm involving sparse matrices. Such algorithms often involve two phases: a symbolic phase wherein the positions of the non-zeros in the result are determined and a numeric phase wherein the actual results are calculated. During the symbolic phase only the positions of the non-zero elements in any operands are of interest, hence any numeric sparse matrices can be treated as logical sparse matrices.

Slots

Methods

Details

Note that triplet stored (TsparseMatrix) matrices such as lgTMatrix may contain duplicated pairs of indices $(i,j)$ as for the corresponding numeric class dgTMatrix where for such pairs, the corresponding x slot entries are added. For logical matrices, the x entries corresponding to duplicated index pairs $(i,j)$ are “added” as well if the addition is defined as logical $or$, i.e., “TRUE + TRUE |-> TRUE” and “TRUE + FALSE |-> TRUE”. Note the use of uniqTsparse() for getting an internally unique representation without duplicated $(i,j)$ entries.

See Also

the class dgCMatrix and dgTMatrix

Examples

(m <- Matrix(c(0,0,2:0), 3,5, dimnames=list(LETTERS[1:3],NULL)))
(lm <- (m > 1)) # lgC
!lm     # no longer sparse
stopifnot(is(lm,"lsparseMatrix"),
          identical(!lm, m <= 1))

data(KNex)
str(mmG.1 <- (KNex $ mm) > 0.1)# "lgC..."
table(mmG.1@x)# however with many ``non-structural zeros''
## from logical to nz_pattern -- okay when there are no NA's :
nmG.1 <- as(mmG.1, "nMatrix") # <<< has "TRUE" also where mmG.1 had FALSE
## from logical to "double"
dmG.1 <- as(mmG.1, "dMatrix") # has '0' and back:
lmG.1 <- as(dmG.1, "lMatrix") # has no extra FALSE, i.e. drop0() included
stopifnot(identical(nmG.1, as((KNex $ mm) != 0,"nMatrix")),
          validObject(lmG.1), all(lmG.1@x),
          # same "logical" but lmG.1 has no 'FALSE' in x slot:
          all(lmG.1 == mmG.1))

class(xnx <- crossprod(nmG.1))# "nsC.."
class(xlx <- crossprod(mmG.1))# "dsC.." : numeric
is0 <- (xlx == 0)
mean(as.vector(is0))# 99.3% zeros: quite sparse, but
table(xlx@x == 0)# more than half of the entries are (non-structural!) 0
stopifnot(isSymmetric(xlx), isSymmetric(xnx),
          ## compare xnx and xlx : have the *same* non-structural 0s :
          sapply(slotNames(xnx),
                 function(n) identical(slot(xnx, n), slot(xlx, n))))

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