Matrix Diagonals

Description

Extract or replace the diagonal of a matrix, or construct a diagonal matrix.

Usage

diag(x = 1, nrow, ncol, names = TRUE)
diag(x) <- value

Arguments

Details

diag has four distinct usages:

1. x is a matrix, when it extracts the diagonal.

2. x is missing and nrow is specified, it returns an identity matrix.

3. x is a scalar (length-one vector) and the only argument, it returns a square identity matrix of size given by the scalar.

4. x is a ‘numeric’ (complex, numeric, integer, logical, or raw) vector, either of length at least 2 or there were further arguments. This returns a matrix with the given diagonal and zero off-diagonal entries.

It is an error to specify nrow or ncol in the first case.

Value

If x is a matrix then diag(x) returns the diagonal of x. The resulting vector will have names if names is true and if the matrix x has matching column and rownames.

The replacement form sets the diagonal of the matrix x to the given value(s).

In all other cases the value is a diagonal matrix with nrow rows and ncol columns (if ncol is not given the matrix is square). Here nrow is taken from the argument if specified, otherwise inferred from x: if that is a vector (or 1D array) of length two or more, then its length is the number of rows, but if it is of length one and neither nrow nor ncol is specified, nrow = as.integer(x).

When a diagonal matrix is returned, the diagonal elements are one except in the fourth case, when x gives the diagonal elements: it will be recycled or truncated as needed, but fractional recycling and truncation will give a warning.

Note

Using diag(x) can have unexpected effects if x is a vector that could be of length one. Use diag(x, nrow = length(x)) for consistent behaviour.

References

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.

See Also

upper.tri, lower.tri, matrix.

Examples

dim(diag(3))
diag(10, 3, 4) # guess what?
all(diag(1:3) == {m <- matrix(0,3,3); diag(m) <- 1:3; m})

## other "numeric"-like diagonal matrices :
diag(c(1i,2i))    # complex
diag(TRUE, 3)     # logical
diag(as.raw(1:3)) # raw
(D2 <- diag(2:1, 4)); typeof(D2) # "integer"

require(stats)
## diag(<var-cov-matrix>) = variances
diag(var(M <- cbind(X = 1:5, Y = rnorm(5))))
#-> vector with names "X" and "Y"
rownames(M) <- c(colnames(M), rep("", 3))
M; diag(M) #  named as well
diag(M, names = FALSE) # w/o names