AxisAlgorithms is a collection of filtering and linear algebra algorithms for multidimensional arrays. For algorithms that would typically apply along the columns of a matrix, you can instead pick an arbitrary axis (dimension).
Note that all functions come in two variants, a
! version that uses pre-allocated output (where the output is
the first argument) and a version that allocates the output. Below, the
! versions will be described.
Tridiagonal and Woodbury inversion
F is an LU-factorization of a tridiagonal matrix, or a Woodbury matrix created from such a factorization,
A_ldiv_B_md!(dest, F, src, axis) will solve the equation
F\b for 1-dimensional slices
Unlike many linear algebra algorithms, this one is safe to use as a mutating algorithm with
The tridiagonal case does not create temporaries, and it has excellent cache behavior.
Multiply a matrix
M to all 1-dimensional slices along a particular dimension.
Here you have two algorithms to choose from:
A_mul_B_perm!(dest, M, src, axis)uses
permutedimsand standard BLAS-accelerated routines; it allocates temporary storage.
A_mul_B_md!(dest, M, src, axis)is a non-allocating naive routine. This also has optimized implementations for sparse
Mand 2x2 matrices.
In general it is very difficult to get efficient cache behavior for multidimensional multiplication, and often using
A_mul_B_perm! is the best strategy.
However, there are cases where
A_mul_B_md! is faster.
It's a good idea to time both and see which works better for your case.