Sparse "pattern" Matrices

Description

The nsparseMatrix class is a virtual class of sparse “pattern” matrices, i.e., binary matrices conceptually with TRUE/FALSE entries. Only the positions of the elements that are TRUE are stored. These can be stored in the “triplet” form (classes ngTMatrix, nsTMatrix, and ntTMatrix which really contain pairs, not triplets) or in compressed column-oriented form (classes ngCMatrix, nsCMatrix, and ntCMatrix) or in compressed row-oriented form (classes ngRMatrix, nsRMatrix, and ntRMatrix). 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("ngCMatrix", ...) and so on. More frequently objects are created by coercion of a numeric sparse matrix to the pattern form for use 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 numeric sparse matrices can be treated as sparse pattern matrices.

Slots

uplo:

Object of class "character". Must be either "U", for upper triangular, and "L", for lower triangular. Present in the triangular and symmetric classes but not in the general class.

diag:

Object of class "character". Must be either "U", for unit triangular (diagonal is all ones), or "N" for non-unit. The implicit diagonal elements are not explicitly stored when diag is "U". Present in the triangular classes only.

p:

Object of class "integer" of pointers, one for each column (row), to the initial (zero-based) index of elements in the column. Present in compressed column-oriented and compressed row-oriented forms only.

i:

Object of class "integer" of length nnzero (number of non-zero elements). These are the row numbers for each TRUE element in the matrix. All other elements are FALSE. Present in triplet and compressed column-oriented forms only.

j:

Object of class "integer" of length nnzero (number of non-zero elements). These are the column numbers for each TRUE element in the matrix. All other elements are FALSE. Present in triplet and compressed column-oriented forms only.

Dim:

Object of class "integer" - the dimensions of the matrix.

Methods

coerce

signature(from = "dgCMatrix", to = "ngCMatrix"), and many similar ones; typically you should coerce to "nsparseMatrix" (or "nMatrix"). Note that coercion to a sparse pattern matrix records all the potential non-zero entries, i.e., explicit (“non-structural”) zeroes are coerced to TRUE, not FALSE, see the example.

t

signature(x = "ngCMatrix"): returns the transpose of x

which

signature(x = "lsparseMatrix"), semantically equivalent to base function which(x, arr.ind); for details, see the lMatrix class documentation.

See Also

the class dgCMatrix

Examples

(m <- Matrix(c(0,0,2:0), 3,5, dimnames=list(LETTERS[1:3],NULL)))
## ``extract the nonzero-pattern of (m) into an nMatrix'':
nm <- as(m, "nsparseMatrix") ## -> will be a "ngCMatrix"
str(nm) # no 'x' slot
nnm <- !nm     # no longer sparse
(nnm <- as(nnm, "sparseMatrix"))# "lgCMatrix"
## consistency check:
stopifnot(xor(as( nm, "matrix"),
              as(nnm, "matrix")))

## low-level way of adding "non-structural zeros" :
nnm@x[2:4] <- c(FALSE,NA,NA)
nnm
as(nnm, "nMatrix") # NAs *and* non-structural 0  |--->  'TRUE'

data(KNex)
nmm <- as(KNex $ mm, "ngCMatrix")
str(xlx <- crossprod(nmm))# "nsCMatrix"
stopifnot(isSymmetric(xlx))
image(xlx, main=paste("crossprod(nmm) : Sparse", class(xlx)))