MATLAB Function Reference    

Symmetric approximate minimum degree permutation



p = symamd(S) for a symmetric positive definite matrix S, returns the permutation vector p such that S(p,p) tends to have a sparser Cholesky factor than S. To find the ordering for S, symamd constructs a matrix M such that spones(M'*M) = spones (S), and then computes p = colamd(M). The symamd function may also work well for symmetric indefinite matrices.

S must be square; only the strictly lower triangular part is referenced.

knobs is a scalar. If S is n-by-n, rows and columns with more than knobs*n entries are removed prior to ordering, and ordered last in the output permutation p. If the knobs parameter is not present, then knobs = spparms('wh_frac').

stats is an optional vector that provides data about the ordering and the validity of the matrix S.

Number of dense or empty rows ignored by symamd
Number of dense or empty columns ignored by symamd
Number of garbage collections performed on the internal data structure used by symamd (roughly of size 8.4*nnz(tril(S,-1)) + 9n integers)
0 if the matrix is valid, or 1 if invalid
Rightmost column index that is unsorted or contains duplicate entries, or 0 if no such column exists
Last seen duplicate or out-of-order row index in the column index given by stats(5), or 0 if no such row index exists
Number of duplicate and out-of-order row indices

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 symamd. For this reason, symamd verifies that S is valid:

The ordering is followed by a symmetric elimination tree post-ordering.

See Also

colamd, colmmd, colperm, spparms, symmmd, symrcm


The authors of the code for symamd are Stefan I. Larimore and Timothy A. Davis (, 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:

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