Boolean Arithmetic Matrix Products: %&% and Methods

Description

For boolean or “pattern” matrices, i.e., R objects of class nMatrix, it is natural to allow matrix products using boolean instead of numerical arithmetic.

In package Matrix, we use the binary operator %&% (aka “infix”) function) for this and provide methods for all our matrices and the traditional R matrices (see matrix).

Value

a pattern matrix, i.e., inheriting from "nMatrix", or an "ldiMatrix" in case of a diagonal matrix.

Methods

We provide methods for both the “traditional” (R base) matrices and numeric vectors and conceptually all matrices and sparseVectors in package Matrix.

signature(x = "ANY", y = "ANY")
signature(x = "ANY", y = "Matrix")
signature(x = "Matrix", y = "ANY")
signature(x = "mMatrix", y = "mMatrix")
signature(x = "nMatrix", y = "nMatrix")
signature(x = "nMatrix", y = "nsparseMatrix")
signature(x = "nsparseMatrix", y = "nMatrix")
signature(x = "nsparseMatrix", y = "nsparseMatrix")
signature(x = "sparseVector", y = "mMatrix")
signature(x = "mMatrix", y = "sparseVector")
signature(x = "sparseVector", y = "sparseVector")

Note

The current implementation ends up coercing both x and y to (virtual) class nsparseMatrix which may be quite inefficient. A future implementation may well return a matrix with different class, but the “same” content, i.e., the same matrix entries m[i,j].

Examples

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set.seed(7)
L <- Matrix(rnorm(20) > 1,    4,5)
(N <- as(L, "nMatrix"))
D <- Matrix(round(rnorm(30)), 5,6) # -> values in -1:1 (for this seed)
L %&% D
stopifnot(identical(L %&% D, N %&% D),
          all(L %&% D == as((L %*% abs(D)) > 0, "sparseMatrix")))

## cross products , possibly with  boolArith = TRUE :
crossprod(N)     # -> sparse patter'n' (TRUE/FALSE : boolean arithmetic)
crossprod(N  +0) # -> numeric Matrix (with same "pattern")
stopifnot(all(crossprod(N) == t(N) %&% N),
          identical(crossprod(N), crossprod(N +0, boolArith=TRUE)),
          identical(crossprod(L), crossprod(N   , boolArith=FALSE)))
crossprod(D, boolArith =  TRUE) # pattern: "nsCMatrix"
crossprod(L, boolArith =  TRUE) #  ditto
crossprod(L, boolArith = FALSE) # numeric: "dsCMatrix"

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