##### 22.6.2.2 ccolamd

— Loadable Function: p = ccolamd (s)
— Loadable Function: p = ccolamd (s, knobs)
— Loadable Function: p = ccolamd (s, knobs, cmember)
— Loadable Function: [p, stats] = ccolamd (...)

> Constrained column approximate minimum degree permutation. p`= ccolamd (`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. `chol (`s`(:,`p`)'*`s`(:,`p`))` also tends to be sparser than `chol (`s`'*`s`)`. p`= ccolamd (`s`,1)` optimizes the ordering for `lu (`s`(:,`p`))`. The ordering is followed by a column elimination tree post-ordering.

> knobs is an optional one- to five-element input vector, with a default value of `[0 10 10 1 0]` if not present or empty. Entries not present are set to their defaults.

> knobs`(1)`
>   if nonzero, the ordering is optimized for `lu(S(:,p))`. It will be a poor ordering for `chol(`s`(:,`p`)'*`s`(:,`p`))`. This is the most important knob for ccolamd.
> knob`(2)`
>   if s is m-by-n, rows with more than `max(16,`knobs`(2)* sqrt(n))` entries are ignored.
> knob`(3)`
>   columns with more than `max(16,`knobs`(3)*sqrt(min(m,n)))` entries are ignored and ordered last in the output permutation (subject to the cmember constraints).
> knob`(4)`
>   if nonzero, aggressive absorption is performed.
> knob`(5)`
>   if nonzero, statistics and knobs are printed.

> cmember is an optional vector of length n. It defines the constraints on the column ordering. If cmember`(j) =` c, then column j is in constraint set c (c must be in the range 1 to n). In the output permutation p, all columns in set 1 appear first, followed by all columns in set 2, and so on. cmember`= ones(1,n)` if not present or empty. `ccolamd (`s`,[],1:n)` returns `1:n`

> p`= ccolamd(`s`)` is about the same as p`= colamd(`s`)`. knobs and its default values differ. `colamd` always does aggressive absorption, and it finds an ordering suitable for both `lu(`s`(:,`p`))` and `chol(`S`(:,`p`)'*` s`(:,`p`))`; it cannot optimize its ordering for `lu(`s`(:,`p`))` to the extent that `ccolamd(`s`,1)` can.

> stats is an optional 20-element output vector that provides data about the ordering and the validity of the input matrix s. Ordering statistics are in stats`(1:3)`. stats`(1)` and stats`(2)` are the number of dense or empty rows and columns ignored by CCOLAMD and stats`(3)` is the number of garbage collections performed on the internal data structure used by CCOLAMD (roughly of size `2.2 * nnz(`s`) + 4 *` m`+ 7 *` n integers).

> stats`(4:7)` provide information if CCOLAMD was able to continue. The matrix is OK if stats`(4)` is zero, or 1 if invalid. stats`(5)` is the rightmost column index that is unsorted or contains duplicate entries, or zero if no such column exists. stats`(6)` is the last seen duplicate or out-of-order row index in the column index given by stats`(5)`, or zero if no such row index exists. stats`(7)` is the number of duplicate or out-of-order row indices. stats`(8:20)` is always zero in the current version of CCOLAMD (reserved for future use).

> The authors of the code itself are S. Larimore, T. Davis (Uni of Florida) and S. Rajamanickam in collaboration with J. Bilbert and E. Ng. Supported by the National Science Foundation (DMS-9504974, DMS-9803599, CCR-0203270), and a grant from Sandia National Lab. See http://www.cise.ufl.edu/research/sparse for ccolamd, csymamd, amd, colamd, symamd, and other related orderings.

> See also: colamd, csymamd.