Matrix (version 1.2-8)

matrix-products: Matrix (Cross) Products (of Transpose)

Description

The basic matrix product, %*% is implemented for all our Matrix and also for sparseVector classes, fully analogously to R's base matrix and vector objects.

The functions crossprod and tcrossprod are matrix products or “cross products”, ideally implemented efficiently without computing t(.)'s unnecessarily. They also return symmetricMatrix classed matrices when easily detectable, e.g., in crossprod(m), the one argument case.

tcrossprod() takes the cross-product of the transpose of a matrix. tcrossprod(x) is formally equivalent to, but faster than, the call x %*% t(x), and so is tcrossprod(x, y) instead of x %*% t(y).

Boolean matrix products are computed via either %&% or boolArith = TRUE.

Usage

"%*%"(x, y)
"crossprod"(x, y = NULL, boolArith = NA, ...)
"crossprod"(x, y = NULL, boolArith = NA, ...) ## .... and for many more signatures
"tcrossprod"(x, y = NULL, boolArith = NA, ...)
"tcrossprod"(x, y = NULL, boolArith = NA, ...) ## .... and for many more signatures

Arguments

x

a matrix-like object

y

a matrix-like object, or for [t]crossprod() NULL (by default); the latter case is formally equivalent to y = x.

boolArith

logical, i.e., NA, TRUE, or FALSE. If true the result is (coerced to) a pattern matrix, i.e., "nMatrix", unless there are NA entries and the result will be a "lMatrix". If false the result is (coerced to) numeric. When NA, currently the default, the result is a pattern matrix when x and y are "nsparseMatrix" and numeric otherwise.

...

potentially more arguments passed to and from methods.

Value

A Matrix object, in the one argument case of an appropriate symmetric matrix class.

Methods

Details

For some classes in the Matrix package, such as dgCMatrix, it is much faster to calculate the cross-product of the transpose directly instead of calculating the transpose first and then its cross-product.

boolArith = TRUE for regular (“non cross”) matrix products, %*% cannot be specified. Instead, we provide the %&% operator for boolean matrix products.

See Also

tcrossprod in R's base, crossprod and %*%.

Examples

 ## A random sparse "incidence" matrix :
 m <- matrix(0, 400, 500)
 set.seed(12)
 m[runif(314, 0, length(m))] <- 1
 mm <- as(m, "dgCMatrix")
 object.size(m) / object.size(mm) # smaller by a factor of > 200

 ## tcrossprod() is very fast:
 system.time(tCmm <- tcrossprod(mm))# 0   (PIII, 933 MHz)
 system.time(cm <- crossprod(t(m))) # 0.16
 system.time(cm. <- tcrossprod(m))  # 0.02

 stopifnot(cm == as(tCmm, "matrix"))

 ## show sparse sub matrix
 tCmm[1:16, 1:30]