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[project @ 2007-11-06 20:31:33 by dbateman]
author dbateman
date Tue, 06 Nov 2007 20:32:25 +0000
parents a1dbe9d80eee
children b166043585a8
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7106:33ed85dcfaa8 7107:22397f0fb0b2
58 @deftypefnx {Loadable Function} {[@var{p}, @var{stats}] =} ccolamd (@dots{})\n\ 58 @deftypefnx {Loadable Function} {[@var{p}, @var{stats}] =} ccolamd (@dots{})\n\
59 \n\ 59 \n\
60 Constrained column approximate minimum degree permutation. @code{@var{p} =\n\ 60 Constrained column approximate minimum degree permutation. @code{@var{p} =\n\
61 ccolamd (@var{s})} returns the column approximate minimum degree permutation\n\ 61 ccolamd (@var{s})} returns the column approximate minimum degree permutation\n\
62 vector for the sparse matrix @var{s}. For a non-symmetric matrix @var{s},\n\ 62 vector for the sparse matrix @var{s}. For a non-symmetric matrix @var{s},\n\
63 @code{@var{s}(:,@var{p})} tends to have sparser LU factors than @var{s}.\n\ 63 @code{@var{s} (:, @var{p})} tends to have sparser LU factors than @var{s}.\n\
64 @code{chol (@var{s}(:,@var{p})'*@var{s}(:,@var{p}))} also tends to be\n\ 64 @code{chol (@var{s} (:, @var{p})' * @var{s} (:, @var{p}))} also tends to be\n\
65 sparser than @code{chol (@var{s}'*@var{s})}. @code{@var{p} = ccolamd\n\ 65 sparser than @code{chol (@var{s}' * @var{s})}. @code{@var{p} = ccolamd\n\
66 (@var{s},1)} optimizes the ordering for @code{lu (@var{s}(:,@var{p}))}.\n\ 66 (@var{s}, 1)} optimizes the ordering for @code{lu (@var{s} (:, @var{p}))}.\n\
67 The ordering is followed by a column elimination tree post-ordering.\n\ 67 The ordering is followed by a column elimination tree post-ordering.\n\
68 \n\ 68 \n\
69 @var{knobs} is an optional one- to five-element input vector, with a default\n\ 69 @var{knobs} is an optional one- to five-element input vector, with a default\n\
70 value of @code{[0 10 10 1 0]} if not present or empty. Entries not present\n\ 70 value of @code{[0 10 10 1 0]} if not present or empty. Entries not present\n\
71 are set to their defaults.\n\ 71 are set to their defaults.\n\
72 \n\ 72 \n\
73 @table @code\n\ 73 @table @code\n\
74 @item @var{knobs}(1)\n\ 74 @item @var{knobs}(1)\n\
75 if nonzero, the ordering is optimized for @code{lu(S(:,p))}. It will be a\n\ 75 if nonzero, the ordering is optimized for @code{lu (S (:, p))}. It will be a\n\
76 poor ordering for @code{chol(@var{s}(:,@var{p})'*@var{s}(:,@var{p}))}. This\n\ 76 poor ordering for @code{chol (@var{s} (:, @var{p})' * @var{s} (:,\n\
77 is the most important knob for ccolamd.\n\ 77 @var{p}))}. This is the most important knob for ccolamd.\n\
78 \n\ 78 \n\
79 @item @var{knob}(2)\n\ 79 @item @var{knob}(2)\n\
80 if @var{s} is m-by-n, rows with more than @code{max(16,@var{knobs}(2)*\n\ 80 if @var{s} is m-by-n, rows with more than @code{max (16, @var{knobs} (2) *\n\
81 sqrt(n))} entries are ignored.\n\ 81 sqrt (n))} entries are ignored.\n\
82 \n\ 82 \n\
83 @item @var{knob}(3)\n\ 83 @item @var{knob}(3)\n\
84 columns with more than @code{max(16,@var{knobs}(3)*sqrt(min(m,n)))}\n\ 84 columns with more than @code{max (16, @var{knobs} (3) * sqrt (min (@var{m},\n\
85 entries are ignored and ordered last in the output permutation (subject\n\ 85 @var{n})))} entries are ignored and ordered last in the output permutation\n\
86 to the cmember constraints).\n\ 86 (subject to the cmember constraints).\n\
87 \n\ 87 \n\
88 @item @var{knob}(4)\n\ 88 @item @var{knob}(4)\n\
89 if nonzero, aggressive absorption is performed.\n\ 89 if nonzero, aggressive absorption is performed.\n\
90 \n\ 90 \n\
91 @item @var{knob}(5)\n\ 91 @item @var{knob}(5)\n\
92 if nonzero, statistics and knobs are printed.\n\ 92 if nonzero, statistics and knobs are printed.\n\
93 \n\ 93 \n\
94 @end table\n\ 94 @end table\n\
95 \n\ 95 \n\
96 @var{cmember} is an optional vector of length n. It defines the constraints\n\ 96 @var{cmember} is an optional vector of length n. It defines the constraints\n\
97 on the column ordering. If @code{@var{cmember}(j) = @var{c}}, then column j\n\ 97 on the column ordering. If @code{@var{cmember} (j) = @var{c}}, then column\n\
98 is in constraint set @var{c} (@var{c} must be in the range 1 to n). In\n\ 98 @var{j} is in constraint set @var{c} (@var{c} must be in the range 1 to\n\
99 the output permutation @var{p}, all columns in set 1 appear first, followed\n\ 99 @var{n}). In the output permutation @var{p}, all columns in set 1 appear\n\
100 by all columns in set 2, and so on. @code{@var{cmember} = ones(1,n)} if\n\ 100 first, followed by all columns in set 2, and so on. @code{@var{cmember} =\n\
101 not present or empty. @code{ccolamd (@var{s},[],1:n)} returns @code{1:n}\n\ 101 ones(1,n)} if not present or empty. @code{ccolamd (@var{s}, [], 1 :\n\
102 \n\ 102 @var{n})} returns @code{1 : @var{n}}\n\
103 @code{@var{p} = ccolamd(@var{s})} is about the same as @code{@var{p} =\n\ 103 \n\
104 colamd(@var{s})}. @var{knobs} and its default values differ. @code{colamd}\n\ 104 @code{@var{p} = ccolamd (@var{s})} is about the same as @code{@var{p} =\n\
105 colamd (@var{s})}. @var{knobs} and its default values differ. @code{colamd}\n\
105 always does aggressive absorption, and it finds an ordering suitable for\n\ 106 always does aggressive absorption, and it finds an ordering suitable for\n\
106 both @code{lu(@var{s}(:,@var{p}))} and @code{chol(@var{S}(:,@var{p})'*\n\ 107 both @code{lu (@var{s} (:, @var{p}))} and @code{chol (@var{S} (:, @var{p})'\n\
107 @var{s}(:,@var{p}))}; it cannot optimize its ordering for @code{lu(@var{s}\n\ 108 * @var{s} (:, @var{p}))}; it cannot optimize its ordering for\n\
108 (:,@var{p}))} to the extent that @code{ccolamd(@var{s},1)} can.\n\ 109 @code{lu (@var{s} (:, @var{p}))} to the extent that\n\
110 @code{ccolamd (@var{s}, 1)} can.\n\
109 \n\ 111 \n\
110 @var{stats} is an optional 20-element output vector that provides data\n\ 112 @var{stats} is an optional 20-element output vector that provides data\n\
111 about the ordering and the validity of the input matrix @var{s}. Ordering\n\ 113 about the ordering and the validity of the input matrix @var{s}. Ordering\n\
112 statistics are in @code{@var{stats} (1:3)}. @code{@var{stats} (1)} and\n\ 114 statistics are in @code{@var{stats} (1 : 3)}. @code{@var{stats} (1)} and\n\
113 @code{@var{stats} (2)} are the number of dense or empty rows and columns\n\ 115 @code{@var{stats} (2)} are the number of dense or empty rows and columns\n\
114 ignored by CCOLAMD and @code{@var{stats} (3)} is the number of garbage\n\ 116 ignored by CCOLAMD and @code{@var{stats} (3)} is the number of garbage\n\
115 collections performed on the internal data structure used by CCOLAMD\n\ 117 collections performed on the internal data structure used by CCOLAMD\n\
116 (roughly of size @code{2.2 * nnz(@var{s}) + 4 * @var{m} + 7 * @var{n}}\n\ 118 (roughly of size @code{2.2 * nnz (@var{s}) + 4 * @var{m} + 7 * @var{n}}\n\
117 integers).\n\ 119 integers).\n\
118 \n\ 120 \n\
119 @code{@var{stats} (4:7)} provide information if CCOLAMD was able to\n\ 121 @code{@var{stats} (4 : 7)} provide information if CCOLAMD was able to\n\
120 continue. The matrix is OK if @code{@var{stats} (4)} is zero, or 1 if\n\ 122 continue. The matrix is OK if @code{@var{stats} (4)} is zero, or 1 if\n\
121 invalid. @code{@var{stats} (5)} is the rightmost column index that is\n\ 123 invalid. @code{@var{stats} (5)} is the rightmost column index that is\n\
122 unsorted or contains duplicate entries, or zero if no such column exists.\n\ 124 unsorted or contains duplicate entries, or zero if no such column exists.\n\
123 @code{@var{stats} (6)} is the last seen duplicate or out-of-order row\n\ 125 @code{@var{stats} (6)} is the last seen duplicate or out-of-order row\n\
124 index in the column index given by @code{@var{stats} (5)}, or zero if no\n\ 126 index in the column index given by @code{@var{stats} (5)}, or zero if no\n\
125 such row index exists. @code{@var{stats} (7)} is the number of duplicate\n\ 127 such row index exists. @code{@var{stats} (7)} is the number of duplicate\n\
126 or out-of-order row indices. @code{@var{stats} (8:20)} is always zero in\n\ 128 or out-of-order row indices. @code{@var{stats} (8 : 20)} is always zero in\n\
127 the current version of CCOLAMD (reserved for future use).\n\ 129 the current version of CCOLAMD (reserved for future use).\n\
128 \n\ 130 \n\
129 The authors of the code itself are S. Larimore, T. Davis (Uni of Florida)\n\ 131 The authors of the code itself are S. Larimore, T. Davis (Uni of Florida)\n\
130 and S. Rajamanickam in collaboration with J. Bilbert and E. Ng. Supported\n\ 132 and S. Rajamanickam in collaboration with J. Bilbert and E. Ng. Supported\n\
131 by the National Science Foundation (DMS-9504974, DMS-9803599, CCR-0203270),\n\ 133 by the National Science Foundation (DMS-9504974, DMS-9803599, CCR-0203270),\n\