Determine the rank (number of linearly independent columns) of a matrix.
Details
Implementation via the Armadillo C++ linear algebra library. The function
returns the rank of the matrix x. The computation is based on the
singular value decomposition of the matrix; a std::runtime_error exception
will be thrown if the decomposition fails. Any singular values less than
the tolerance are treated as zeros. The tolerance is
max(m, n) * max_sv * arma::datum::eps, where m is the number
of rows of x, n is the number of columns of x,
max_sv is the maximal singular value of x, and
arma::datum::eps is the difference between 1 and the least value
greater than 1 that is representable.
References
Conrad Sanderson and Ryan Curtin. Armadillo: a template-based C++ library for linear algebra. Journal of Open Source Software, Vol. 1, pp. 26, 2016.
Examples
# Check the rank of a matrix
set.seed(42)
mat <- matrix(rnorm(25000 * 120), nrow = 25000)
matrix_rank(mat) == ncol(mat)
#> [1] TRUE
matrix_rank(mat) == 120L
#> [1] TRUE
# A full rank B-spline basis
bmat <- bsplines(seq(0, 1, length = 100), df = 15)
#> Warning: At least one x value >= max(bknots)
matrix_rank(bmat) == 15L
#> [1] TRUE
# A rank deficient B-spline basis
bmat <- bsplines(seq(0, 1, length = 100), iknots = c(0.001, 0.002))
#> Warning: At least one x value >= max(bknots)
ncol(bmat) == 6L
#> [1] TRUE
matrix_rank(bmat) == 5L
#> [1] TRUE