R: Cross-product of transpose

tcrossprod {Matrix} | R Documentation

## Cross-product of transpose

### Description

Take 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)`.

### Usage

    tcrossprod(x, y = NULL)

### Arguments

`x` | a matrix-like object
`y` | a matrix-like object or `NULL` (by default); the latter case is formally equivalent to `y = x`.

### 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.

### Value

An object of an appropriate symmetric matrix class.

### Methods

x = "dgCMatrix"

  method for compressed, sparse, column-oriented matrices.

### See Also

`crossprod`

### Examples

     ## A random sparce "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]

[Package Matrix version 1.0-9 Index]