Random orthogonal matrix

Generate a random orthogonal basis matrix of dimension \((nrow x ncol)\) using the method in Heiberger (1978).

Usage

randomOrthogonalMatrix(nrow, ncol, n = nrow, d = ncol, seed = NULL)

Arguments

nrow

the number of rows of the resulting orthogonal matrix.

ncol

the number of columns of the resulting orthogonal matrix.

n

deprecated. See nrow above.

d

deprecated. See ncol above.

seed

an optional integer argument to use in set.seed() for reproducibility. By default the current seed will be used. Reproducibility can also be achieved by calling set.seed() before calling this function.

Details

The use of arguments n and d is deprecated and they will be removed in the future.

Value

An orthogonal matrix of dimension \(nrow x ncol\) such that each column is orthogonal to the other and has unit lenght. Because of the latter, it is also called orthonormal.

See also

coordProj

References

Heiberger R. (1978) Generation of random orthogonal matrices. Journal of the Royal Statistical Society. Series C (Applied Statistics), 27(2), 199-206.

Examples

B <- randomOrthogonalMatrix(10,3)
zapsmall(crossprod(B))
#>      [,1] [,2] [,3]
#> [1,]    1    0    0
#> [2,]    0    1    0
#> [3,]    0    0    1