function X = invert(A)
% Usage: X = invert(A)
%---------------------------------------------------------------------%
% Calculating the inverse of a matrix A                               %
%                                                                     %
% input                                                               %
%   A: a matrix to be inverted                                        %
%                                                                     %
% output                                                              %
%   X: the inverse of A, empty if A is numerically singular           %
%   recondA: an estimate of the reciprocal of the condition of A for  %
%      the linear system A*x = b, returned by decomp.                 %
%      If rcondA + 1.0 = 1.0, A is singular to the working precision  %
%                                                                     %
% dependency                                                          %
%   decomp.m, solve.m                                                 %
%---------------------------------------------------------------------%

n = length(A(:,1));

[A, rcondA, pvt] = decomp(A);

if ((1.0 + rcondA) == 1.0)
    X=[];
    display('singularity is detected.');
    return;
end

X = eye(n);
for k=1:n
    X(:,k) = solve(A, X(:,k), pvt);
end