function [R, permB, spdB] = CHOLfactorB(B, cholB, permB, shiftAndInvert, spdB)

% Get the Cholesky factorization of B and determine if it is Hermitian

% Positive (semi) Definite

if isempty(B) 

    % Standard problem, set values to flow through

    R = []; 

    permB = []; 

    spdB = false; 

elseif cholB

    % We already have the Cholesky factor, store it in R

    R = B;

    spdB = true;

elseif ishermitian(B) && (isempty(spdB)|| (spdB && ~shiftAndInvert))

    % We need to see if B is SPD by using chol OR

    % We know B is SPD, and we need Cholesky decomposition

    if issparse(B)

        [R, idxB, permB] = chol(B);

    else

        [R, idxB] = chol(B);

    end

    if idxB == 0

        % B is SPD, no further check needed

        spdB = true;

    elseif shiftAndInvert && isreal(B)

        % Check whether B is positive SEMI-definite by checking D from the

        % whether the D LDL decomposition is positive semi-definite

        [~, D, ~] = ldl(B,'vector');

        % Check that diagonal elements are non-negative and 2x2 diagonal

        % blocks are positive semi-definite:

        alpha = diag(D);

        beta = diag(D,1);

        spdB = checkTridiagForHSD(alpha, beta);

    else

        if spdB

            error(message('MATLAB:eigs:IsSymmetricDefiniteNotPD'));

        else % spdB is false or []

            spdB = false;

        end

    end

    if shiftAndInvert || ~spdB

        % We do not actually need the Cholesky factor to solve the problem

        R = [];

        permB = [];

    end

else

    % We do not need chol

    R = [];

    permB = [];

    if isempty(spdB)

        % B is empty or not Hermitian

        spdB = false;

    end

    % else we take the user's input

end

end