| | DEFUN_DLD (ccolamd, args, nargout,"-*- texinfo -*-\n\
@deftypefn {Loadable Function} {@var{p} =} ccolamd (@var{s})\n\
@deftypefnx {Loadable Function} {@var{p} =} ccolamd (@var{s}, @var{knobs})\n\
@deftypefnx {Loadable Function} {@var{p} =} ccolamd (@var{s}, @var{knobs}, @var{cmember})\n\
@deftypefnx {Loadable Function} {[@var{p}, @var{stats}] =} ccolamd (@dots{})\n\
\n\
Constrained column approximate minimum degree permutation. @code{@var{p} =\n\
ccolamd (@var{s})} returns the column approximate minimum degree permutation\n\
vector for the sparse matrix @var{s}. For a non-symmetric matrix @var{s},\n\
@code{@var{s} (:, @var{p})} tends to have sparser LU factors than @var{s}.\n\
@code{chol (@var{s} (:, @var{p})' * @var{s} (:, @var{p}))} also tends to be\n\
sparser than @code{chol (@var{s}' * @var{s})}. @code{@var{p} = ccolamd\n\
(@var{s}, 1)} optimizes the ordering for @code{lu (@var{s} (:, @var{p}))}.\n\
The ordering is followed by a column elimination tree post-ordering.\n\
\n\
@var{knobs} is an optional one- to five-element input vector, with a default\n\
value of @code{[0 10 10 1 0]} if not present or empty. Entries not present\n\
are set to their defaults.\n\
\n\
@table @code\n\
@item @var{knobs}(1)\n\
if nonzero, the ordering is optimized for @code{lu (S (:, p))}. It will be a\n\
poor ordering for @code{chol (@var{s} (:, @var{p})' * @var{s} (:,\n\
@var{p}))}. This is the most important knob for ccolamd.\n\
\n\
@item @var{knob}(2)\n\
if @var{s} is m-by-n, rows with more than @code{max (16, @var{knobs} (2) *\n\
sqrt (n))} entries are ignored.\n\
\n\
@item @var{knob}(3)\n\
columns with more than @code{max (16, @var{knobs} (3) * sqrt (min (@var{m},\n\
@var{n})))} entries are ignored and ordered last in the output permutation\n\
(subject to the cmember constraints).\n\
\n\
@item @var{knob}(4)\n\
if nonzero, aggressive absorption is performed.\n\
\n\
@item @var{knob}(5)\n\
if nonzero, statistics and knobs are printed.\n\
\n\
@end table\n\
\n\
@var{cmember} is an optional vector of length n. It defines the constraints\n\
on the column ordering. If @code{@var{cmember} (j) = @var{c}}, then column\n\
@var{j} is in constraint set @var{c} (@var{c} must be in the range 1 to\n\
@var{n}). In the output permutation @var{p}, all columns in set 1 appear\n\
first, followed by all columns in set 2, and so on. @code{@var{cmember} =\n\
ones(1,n)} if not present or empty. @code{ccolamd (@var{s}, [], 1 :\n\
@var{n})} returns @code{1 : @var{n}}\n\
\n\
@code{@var{p} = ccolamd (@var{s})} is about the same as @code{@var{p} =\n\
colamd (@var{s})}. @var{knobs} and its default values differ. @code{colamd}\n\
always does aggressive absorption, and it finds an ordering suitable for\n\
both @code{lu (@var{s} (:, @var{p}))} and @code{chol (@var{S} (:, @var{p})'\n\
* @var{s} (:, @var{p}))}; it cannot optimize its ordering for\n\
@code{lu (@var{s} (:, @var{p}))} to the extent that\n\
@code{ccolamd (@var{s}, 1)} can.\n\
\n\
@var{stats} is an optional 20-element output vector that provides data\n\
about the ordering and the validity of the input matrix @var{s}. Ordering\n\
statistics are in @code{@var{stats} (1 : 3)}. @code{@var{stats} (1)} and\n\
@code{@var{stats} (2)} are the number of dense or empty rows and columns\n\
ignored by CCOLAMD and @code{@var{stats} (3)} is the number of garbage\n\
collections performed on the internal data structure used by CCOLAMD\n\
(roughly of size @code{2.2 * nnz (@var{s}) + 4 * @var{m} + 7 * @var{n}}\n\
integers).\n\
\n\
@code{@var{stats} (4 : 7)} provide information if CCOLAMD was able to\n\
continue. The matrix is OK if @code{@var{stats} (4)} is zero, or 1 if\n\
invalid. @code{@var{stats} (5)} is the rightmost column index that is\n\
unsorted or contains duplicate entries, or zero if no such column exists.\n\
@code{@var{stats} (6)} is the last seen duplicate or out-of-order row\n\
index in the column index given by @code{@var{stats} (5)}, or zero if no\n\
such row index exists. @code{@var{stats} (7)} is the number of duplicate\n\
or out-of-order row indices. @code{@var{stats} (8 : 20)} is always zero in\n\
the current version of CCOLAMD (reserved for future use).\n\
\n\
The authors of the code itself are S. Larimore, T. Davis (Uni of Florida)\n\
and S. Rajamanickam in collaboration with J. Bilbert and E. Ng. Supported\n\
by the National Science Foundation (DMS-9504974, DMS-9803599, CCR-0203270),\n\
and a grant from Sandia National Lab. See\n\
@url{http://www.cise.ufl.edu/research/sparse} for ccolamd, csymamd, amd,\n\
colamd, symamd, and other related orderings.\n\
@seealso{colamd, csymamd}\n\
@end deftypefn") |
| | DEFUN_DLD (csymamd, args, nargout,"-*- texinfo -*-\n\
@deftypefn {Loadable Function} {@var{p} =} csymamd (@var{s})\n\
@deftypefnx {Loadable Function} {@var{p} =} csymamd (@var{s}, @var{knobs})\n\
@deftypefnx {Loadable Function} {@var{p} =} csymamd (@var{s}, @var{knobs}, @var{cmember})\n\
@deftypefnx {Loadable Function} {[@var{p}, @var{stats}] =} csymamd (@dots{})\n\
\n\
For a symmetric positive definite matrix @var{s}, returns the permutation\n\
vector @var{p} such that @code{@var{s}(@var{p},@var{p})} tends to have a\n\
sparser Cholesky factor than @var{s}. Sometimes @code{csymamd} works well\n\
for symmetric indefinite matrices too. The matrix @var{s} is assumed to\n\
be symmetric; only the strictly lower triangular part is referenced.\n\
@var{s} must be square. The ordering is followed by an elimination tree\n\
post-ordering.\n\
\n\
@var{knobs} is an optional one- to three-element input vector, with a\n\
default value of @code{[10 1 0]} if present or empty. Entries not\n\
present are set to their defaults.\n\
\n\
@table @code\n\
@item @var{knobs}(1)\n\
If @var{s} is n-by-n, then rows and columns with more than\n\
@code{max(16,@var{knobs}(1)*sqrt(n))} entries are ignored, and ordered\n\
last in the output permutation (subject to the cmember constraints).\n\
\n\
@item @var{knobs}(2)\n\
If nonzero, aggressive absorption is performed.\n\
\n\
@item @var{knobs}(3)\n\
If nonzero, statistics and knobs are printed.\n\
\n\
@end table\n\
\n\
@var{cmember} is an optional vector of length n. It defines the constraints\n\
on the ordering. If @code{@var{cmember}(j) = @var{s}}, then row/column j is\n\
in constraint set @var{c} (@var{c} must be in the range 1 to n). In the\n\
output permutation @var{p}, rows/columns in set 1 appear first, followed\n\
by all rows/columns in set 2, and so on. @code{@var{cmember} = ones(1,n)}\n\
if not present or empty. @code{csymamd(@var{s},[],1:n)} returns @code{1:n}.\n\
\n\
@code{@var{p} = csymamd(@var{s})} is about the same as @code{@var{p} =\n\
symamd(@var{s})}. @var{knobs} and its default values differ.\n\
\n\
@code{@var{stats} (4:7)} provide information if CCOLAMD was able to\n\
continue. The matrix is OK if @code{@var{stats} (4)} is zero, or 1 if\n\
invalid. @code{@var{stats} (5)} is the rightmost column index that is\n\
unsorted or contains duplicate entries, or zero if no such column exists.\n\
@code{@var{stats} (6)} is the last seen duplicate or out-of-order row\n\
index in the column index given by @code{@var{stats} (5)}, or zero if no\n\
such row index exists. @code{@var{stats} (7)} is the number of duplicate\n\
or out-of-order row indices. @code{@var{stats} (8:20)} is always zero in\n\
the current version of CCOLAMD (reserved for future use).\n\
\n\
The authors of the code itself are S. Larimore, T. Davis (Uni of Florida)\n\
and S. Rajamanickam in collaboration with J. Bilbert and E. Ng. Supported\n\
by the National Science Foundation (DMS-9504974, DMS-9803599, CCR-0203270),\n\
and a grant from Sandia National Lab. See\n\
@url{http://www.cise.ufl.edu/research/sparse} for ccolamd, csymamd, amd,\n\
colamd, symamd, and other related orderings.\n\
@seealso{symamd, ccolamd}\n\
@end deftypefn") |
