myorth: Rank and orthonormal basis

Description

myorth(X) makes an orthonormal basis for the space spanned by the columns of X. The number of columns returned equals myrank(X), which is the rank of X.

Usage

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myorth(X, tol_ = 1e-09)
myrank(X, tol_ = 1e-9)

Arguments

X

numeric matrix.

tol_

tuning parameter for the rank.

Details

The calculations are based on the singular value decomposition (svd). And myrank(X) is the number of singular values of X that are larger than max(dim(X))*svd(x)$d[1]*tol_.

Value

myorth returns a matrix, whose columns form an orthonormal basis.

myrank returns a single number, which is the rank of X.

Note

In the special case where X has a single column, myorth(X) returns c*X where c is a positive constant.

Author(s)

Øyvind Langsrud and Bjørn-Helge Mevik

See Also

svd


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