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function cholcheck(L,A,tol,meth)
% CHOLCHECK(L,A,tol,meth)
%
% Checks the Cholesky factorization of a two-by-two symmetric matrix of
% wavenumbers, noting that L is LOWER-triangular, so A=L*L^T.
%
% INPUT:
%
% L The purported determinant Cholesky factorization [Nx3]
% A The actual matrix whose factorization this should be [Nx3]
% tol The negative of the tolerance exponent [be explicit~]
% meth 1 By multiplication and comparing against itself
% 2 By using Matlab's function CHOL at a random wavenumber
%
% If it passes, no output, if it doesn't, get an error
%
% Last modified by fjsimons-at-alum.mit.edu, 02/27/2012
switch meth
case 1
difer(L(:,1).*L(:,1)-A(:,1),tol,[],NaN)
difer(L(:,1).*L(:,2)-A(:,2),tol,[],NaN)
% This element is the biggest with very little variance
% so special rules apply to the tolerance
difer([L(:,2).*L(:,2)+L(:,3).*L(:,3)-A(:,3)]./...
A(:,3)/length(A(:,3)),tol,[],NaN)
case 2
randi=ceil(rand*length(A));
Arand=[A(randi,1) A(randi,2) ; A(randi,2) A(randi,3)];
Lrand=[L(randi,1) 0 ; L(randi,2) L(randi,3)];
try
difer(chol(Arand)'-Lrand,tol,1,NaN);
catch
% This may have a small imaginary part
difer(imag(Arand),tol,[],NaN)
try
% But it should be positive definite if f2 is also positive
difer(chol(real(Arand))'-Lrand,tol,[],NaN);
catch
% If not, let it go but make a note of it
disp('Cholesky not happy; most likely claims not positive definite')
end
end
otherwise
error('Specify valid method')
end