boolmatmult-methods: Boolean Arithmetic Matrix Products: '%&%' and Methods In Matrix: Sparse and Dense Matrix Classes and Methods

 boolmatmult-methods R Documentation

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 `sparseVector`s in package Matrix.

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

Note

These boolean arithmetic matrix products had been newly introduced for Matrix 1.2.0 (March 2015). Its implementation has still not been tested extensively.

Originally, it was left unspecified how non-structural zeros, i.e., `0`'s as part of the `M@x` slot should be treated for numeric (`"dMatrix"`) and logical (`"lMatrix"`) sparse matrices. We now specify that boolean matrix products should behave as if applied to `drop0(M)`, i.e., as if dropping such zeros from the matrix before using it.
Equivalently, for all matrices `M`, boolean arithmetic should work as if applied to `M != 0` (or `M != FALSE`).

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

`%*%`, `crossprod()`, or `tcrossprod()`, for (regular) matrix product methods.

Examples

``````
set.seed(7)
L <- Matrix(rnorm(20) > 1,    4,5)
(N <- as(L, "nMatrix"))
L. <- L; L.[1:2,1] <- TRUE; L.@x[1:2] <- FALSE; L. # has "zeros" to drop0()
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"
``````

Matrix documentation built on May 29, 2024, 1:20 a.m.