error_A: The l_1 distance between two thin matrices up to a column permuation
Description
This function computes l_1 distance between two thin matrices up to a column permuation,
that is to find the smallest sum of absolute value entry-wise difference between two matrices
over all possible permutations over the columns of the first matrix. This can be done
either universially or greedily.
Usage
error_A(A, A_hat, type = "u")
Arguments
A
The first p-by-K matrix.
A_hat
The second p-by-K matrix.
type
The search type for the best permutation. If it's 'u', the search is
done universially, that is over all possible permuations of the columns of A.
If it's 'g', the search is done greedily, that is at kth step find the closest
column in the remaining columns of A to the kth column of A_hat in terms of l_1 distance. Greedy search may
result in sub-optimal solutions, but it can be computed much faster than
the universal way when K is large. The default value is 'u'.
# NOT RUN {# The example uses the runif() function in the 'stats' packageA <- matrix(runif(10*3),10,3)
A_hat <- A + 0.1*matrix(runif(10*3),10,3)
error_A(A, A_hat)
error_A(A, A_hat, type='g')
# }