full_rank_ness() [1/4]

double syten::full_rank_ness

(

DenseTensor< 2, double > &&

a

)

Estimates the full-rank-ness of a real matrix A (compared to its smaller dimension) using QR with pivoting.

Does not perform row sorting or row pivoting. For optimal stability, you should do both, using scale_columns_2norm and sort_rows_infnorm.

Returns the ratio of largest to smallest (absolute-value-wise) diagonal element of R. A ratio of 1 indicates an identity matrix, a very large ratio a near-degenerate matrix and a value of inf a matrix not of full rank.

References abs(), syten::DynArray< Type >::begin(), syten::DynArray< Type >::end(), logGE(), std::min(), syten::DynArray< Type >::size(), and std::sort().

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