/usr/share/freemat/toolbox/matrix/det.m is in freemat-data 4.0-5.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 | % DET DET Determinant of a Matrix
%
% Usage
%
% Calculates the determinant of a matrix. Note that for all but
% very small problems, the determinant is not particularly useful.
% The condition number cond gives a more reasonable estimate as
% to the suitability of a matrix for inversion than comparing det(A)
% to zero. In any case, the syntax for its use is
%
% y = det(A)
%
% where A is a square matrix.
% Copyright (c) 2002-2007 Samit Basu
% Licensed under the GPL
function y = det(A)
if (~isnumeric(A))
error('Argument to det must be numeric');
end
if (ndims(A) ~= 2)
error('argument to det must be 2D matrix');
end
if (size(A,1) ~= size(A,2))
error('argument to det must be square');
end
if (isscalar(A))
y = A;
return;
end
N = size(A,1);
[L,U,P] = lu(A);
o = (1:N)';
p = P*o;
exchange_count = det_exchange_count(p);
y = prod(diag(U));
if (mod(exchange_count,2) ~= 0)
y = -y;
end
function exchange_count = det_exchange_count(pivot)
exchange_count = 0;
for i=1:numel(pivot)
if (pivot(i) ~= i)
k = find(pivot == i);
p = pivot(i);
pivot(i) = i;
pivot(k) = p;
exchange_count = exchange_count + 1;
end
end
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