AMD

Given a square sparse matrix, compute an approximate minimum degree ordering. This package is an interface to the AMD library (Amestoy, Davis and Duff) and COLAMD library (Liromore, Davis, Gilberg an Ng).

Installing

julia> ]
pkg> add AMD
pkg> test AMD

Algorithms

amd: an approximate minimum degree ordering algorithm for the sparse factorization of square matrices.

symamd: an approximate minimum degree ordering algorithm for the sparse factorization of symmetric matrices.

colamd: an approximate minimum degree column ordering algorithm for the sparse factorization of arbitrary, square or rectangular, matrices.

Examples

In the simplest case:

using AMD
A = sprand(10, 10, .5)
p_amd = amd(A)
p_symamd = symamd(A)
p_colamd = colamd(A)

If statistics on the permutation are of interest and/or for changing the default control parameters:

julia> meta = Amd{Clong}();  # because A's index type is Int64 on my platform
julia> # optionally change meta.control: ?Amd
julia> p = amd(A, meta)
julia> print(meta)
Control:
  dense row parameter: 10.0
  aggressive absorption: 1.0
Info:
  status: ok
  matrix size: 10.0
  number of nonzeros: 54.0
  pattern symmetry: 0.5
  number of nonzeros on diagonal: 6.0
  number of nonzeros in A + A': 72.0
  number of dense columns: 0.0
  memory used: 1408.0
  number of garbage collections: 0.0
  approx number of nonzers in factor: 38.0
  number of float divides: 38.0
  number of float * or - for LDL: 114.0
  number of float * or - for LU: 190.0
  max nonzeros in any column of factor: 8.0

The amd algorithm computes a fill-reducing permutation based on the sparsity pattern of A + Aᵀ. The input pattern can be anything: diagonal entries will be ignored and the rest will be used to implicitly work on the pattern of A + Aᵀ. Thus if A is symmetric, it is sufficient to supply the strict lower or upper triangle only.

References

1. P. R. Amestoy, T. A. Davis and I. S. Duff. An Approximate Minimum Degree Ordering Algorithm. SIAM Journal on Matrix Analysis and Applications, 17(4), pp. 886–905, 1996. DOI 10.1137/S0895479894278952
2. P. R. Amestoy, T. A. Davis, and I. S. Duff. Algorithm 837: An approximate minimum degree ordering algorithm. ACM Transactions on Mathematical Software, 30(3), pp. 381–388, 2004. DOI 10.1145/1024074.1024081
3. T. A. Davis, J. R. Gilbert, S. Larimore, E. Ng. Algorithm 836: COLAMD, an approximate column minimum degree ordering algorithm, ACM Transactions on Mathematical Software, 30(3), pp. 377–380, 2004. DOI 10.1145/1024074.1024080