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function X = pinv(A,varargin)
%PINV Pseudoinverse.
% X = PINV(A) produces a matrix X of the same dimensions
% as A' so that A*X*A = A, X*A*X = X and A*X and X*A
% are Hermitian. The computation is based on SVD(A) and any
% singular values less than a tolerance are treated as zero.
% The default tolerance is MAX(SIZE(A)) * NORM(A) * EPS.
%
% PINV(A,TOL) uses the tolerance TOL instead of the default.
%
% Class support for input A:
% float: double, single
%
% See also RANK.
% Copyright 1984-2004 The MathWorks, Inc.
% $Revision: 5.12.4.1 $ $Date: 2004/03/02 21:47:30 $
[m,n] = size(A);
if n > m
X = pinv(A',varargin{:})';
else
[U,S,V] = svd(A,0);
if m > 1, s = diag(S);
elseif m == 1, s = S(1);
else s = 0;
end
if nargin == 2
tol = varargin{1};
else
tol = max(m,n) * eps(max(s));
end
r = sum(s > tol);
if (r == 0)
X = zeros(size(A'),class(A));
else
s = diag(ones(r,1)./s(1:r));
X = V(:,1:r)*s*U(:,1:r)';
end
end |
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