Hello Octave Developers,
I would like to submit a new function for consideration of
inclusion. My SourceForge username is kwinfree. This function,
gramian.m, is different from gram.m in that it computes the general
Gramian for a set of vectors. This does not necessarily pertain to
control of systems.
If accepted, I would like to register as an octave-forge developer.
Thank you,
Kyle W
Index: main/linear-algebra/inst/gramian.m
===================================================================
--- main/linear-algebra/inst/gramian.m (revision 0)
+++ main/linear-algebra/inst/gramian.m (revision 0)
@@ -0,0 +1,49 @@
+ % Copyright (C) 2010 Kyle Winfree <[email protected]>
+%
+% This program is free software; you can redistribute it and/or modify
+% it under the terms of the GNU General Public License as published by
+% the Free Software Foundation; either version 3 of the License, or
+% any later version.
+%
+% This program is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+% GNU General Public License for more details.
+%
+% You should have received a copy of the GNU General Public License
+% along with this program; if not, see <http://www.gnu.org/licenses/>.
+%
+% This program computes the Gramian of a given set of vectors.
+% This is found as G = [ <xi, xj> ]
+% The function must be supplied either a single matrix with columns
+% equal to the vectors in question, or with a series of column vectors
+% all the same size. Linear independence can then be determined if
+% det(G) ~= 0. This is just one use of the Gramian matrix.
+
+function [G, M] = gramian(varargin)
+ switch(length(varargin))
+ case 1
+ % a matrix has been given such that each column is a vector
+ M = varargin{1};
+ otherwise
+ % separate vectors have been given, first check to ensure they all
have the same dimension.
+ sz = size(varargin{1});
+ M = zeros(sz(1),length(varargin));
+ for(n=1:length(varargin))
+ if(size(varargin{n},1) ~= sz(1) || size(varargin{n},2) ~= 1)
+ fprintf('Sorry, there was an error with your input (vector
%i). Please ensure the vectors all have the same number of rows.\n', n);
+ M = [];
+ G = [];
+ return
+ end
+ M(:,n) = varargin{n};
+ end
+ end
+ n = size(M,2);
+ for(i=1:n)
+ for(j=i:n)
+ G(i,j) = dot(M(:,i), M(:,j));
+ end
+ end
+ G = G + G' - eye(size(G)).*G; % mirror the top to the bottom, without
doubling the diagonal
+end
\ No newline at end of file
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