MATLAB Function Reference |
Column approximate minimum degree permutation
Syntax
Description
p = colamd(S)
returns the column approximate minimum degree permutation vector for the sparse matrix S
. For a non-symmetric matrix S
, S(:,p)
tends to have sparser LU factors than S
. The Cholesky factorization of S(:,p)' * S(:,p)
also tends to be sparser than that of S'*S
.
knobs
is a two-element vector. If S is m
-by-n
, then rows with more than (knobs(1))*n
entries are ignored. Columns with more than (knobs(2))*m
entries are removed prior to ordering, and ordered last in the output permutation p
. If the knobs
parameter is not present, then knobs(1)
= knobs(2) = spparms('wh_frac')
.
stats
is an optional vector that provides data about the ordering and the validity of the matrix S
.
Although, MATLAB built-in functions generate valid sparse matrices, a user may construct an invalid sparse matrix using the MATLAB C or Fortran APIs and pass it to colamd
. For this reason, colamd
verifies that S
is valid:
colamd
ignores the duplicate entries, continues processing, and provides information about the duplicate entries in stats(4:7)
.
colamd
sorts each column of its internal copy of the matrix S
(but does not repair the input matrix S
), continues processing, and provides information about the out-of-order entries in stats(4:7)
.
S
is invalid in any other way, colamd
cannot continue. It prints an error message, and returns no output arguments (p
or stats
) .
The ordering is followed by a column elimination tree post-ordering.
Examples
The Harwell-Boeing collection of sparse matrices and the MATLAB demos directory include a test matrix west0479
. It is a matrix of order 479 resulting from a model due to Westerberg of an eight-stage chemical distillation column. The spy plot shows evidence of the eight stages. The colamd
ordering scrambles this structure.
load west0479 A = west0479; p = colamd(A); subplot(1,2,1), spy(A,4), title('A') subplot(1,2,2), spy(A(:,p),4), title('A(:,p)')
Comparing the spy plot of the LU factorization of the original matrix with that of the reordered matrix shows that minimum degree reduces the time and storage requirements by better than a factor of 2.8. The nonzero counts are 16777 and 5904, respectively.
See Also
colmmd
, colperm
, spparms
, symamd
, symmmd
, symrcm
References
[1] The authors of the code for colamd
are Stefan I. Larimore and Timothy A.
Davis (davis@cise.ufl.edu
), University of Florida. The algorithm was
developed in collaboration with John Gilbert, Xerox PARC, and Esmond Ng,
Oak Ridge National Laboratory. Sparse Matrix Algorithms Research at the
University of Florida: http://www.cise.ufl.edu/research/sparse/
cmopts | colmmd |
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