Hi --
I have an application in mind where I desperately
need a faster implementation of the matrix methods:
matrix_from_columns
matrix_from_rows_and_columns
matrix_from_rows
I am aware that these will not be as fast as the submatrix method (for
contiguous
submatrices) but the above three methods are still too slow by far...
I'm hoping that someone could spend a little bit of time to write
faster versions of these (maybe
just cythonize them...)? I do not know how to do this myself or I'd
be glad to. Just to give an idea of how slow they are currently, see
below:
#my own ad hoc matrix_from_columns:
def My_matrix_from_columns(mat,cols):
set_all_cols = set(range(mat.ncols()))
set_compl_cols = set_all_cols.difference(set(cols))
compl_cols = list(set_compl_cols)
all_cols = cols + compl_cols
all_cols_one_up = [j+1 for j in all_cols]
p = sage.combinat.permutation.Permutation(all_cols_one_up)
p_matrix = p.to_matrix()
mat_perm = mat * p_matrix
return mat_perm.submatrix(0,0,mat_perm.nrows(),len(cols))
(I'm running sage-4.8, compiled from source on a pretty basic desktop
computer)
sage: M = Matrix(GF(2),5000,5000); M.randomize()
sage: L = range(5000); shuffle(L); L = L[:2500]
sage: time N = M.matrix_from_columns(L)
Time: CPU 2.72 s, Wall: 2.73 s
sage: time N2 = My_matrix_from_columns(M,L)
Time: CPU 0.43 s, Wall: 0.45 s
Surely, going to all the trouble of building that permutation matrix
after constructing
the complement to L in range(M.ncols()) (and adding one to get a valid
permutation
which unfortunately isn't 0-based), then,
multiplying by the permutation matrix,
then extracting the contiguous submatrix, seems like it should have
been slower
than the native method from the matrix class?
Thanks!
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