F11MDF computes a column permutation suitable for
LU
factorization (by
F11MEF) of a real sparse matrix in compressed column (Harwell–Boeing) format and applies it to the matrix. This routine must be called prior to
F11MEF.
Given a sparse matrix in compressed column (Harwell–Boeing) format
A and a choice of column permutation schemes, the routine computes those data structures that will be needed by the
LU
factorization routine
F11MEF and associated routines
F11MMF,
F11MFF and
F11MHF. The column permutation choices are:
- original order (that is, no permutation);
- user-supplied permutation;
- a permutation, computed by the routine, designed to minimize fill-in during the
LU
factorization.
The algorithm for this computed permutation is based on the approximate minimum degree column ordering algorithm COLAMD. The computed permutation is not sensitive to the magnitude of the nonzero values of A.
Amestoy P R, Davis T A and Duff I S (1996) An approximate minimum degree ordering algorithm
SIAM J. Matrix Anal. Appl. 17 886–905
Gilbert J R and Larimore S I (2004) A column approximate minimum degree ordering algorithm
ACM Trans. Math. Software 30,3 353–376
Gilbert J R, Larimore S I and Ng E G (2004) Algorithm 836: COLAMD, an approximate minimum degree ordering algorithm
ACM Trans. Math. Software 30, 3 377–380
If on entry
IFAIL=0 or
-1, explanatory error messages are output on the current error message unit (as defined by
X04AAF).
Not applicable. This computation does not use floating point numbers.
We recommend calling this routine with
SPEC='M' before calling
F11MEF. The COLAMD algorithm computes a sparsity-preserving permutation
Pc solely from the pattern of
A such that the
LU
factorization
Pr
A
Pc
=
LU
remains as sparse as possible, regardless of the subsequent choice of
Pr. The algorithm takes advantage of the existence of super-columns (columns with the same sparsity pattern) to reduce running time.
This example computes a sparsity preserving column permutation for the
LU factorization of the matrix
A, where