function validateReducedSystem(stiffness, mass, analysisType)
%VALIDATEREDUCEDSYSTEM Reject mechanisms and invalid reduced matrices.

if isempty(stiffness)
    if strcmp(analysisType, 'static')
        return;
    end
    error('MKEF:NoFreeDOFs', ...
        'The model has no free degrees of freedom for %s analysis.', ...
        analysisType);
end

if any(~isfinite(stiffness(:)))
    error('MKEF:InvalidReducedSystem', ...
        'The reduced stiffness matrix contains non-finite entries.');
end

symStiffness = (stiffness + stiffness.') / 2;
diagonal = diag(symStiffness);
stiffnessFailure = any(diagonal <= 0);
if ~stiffnessFailure
    % Diagonal scaling avoids comparing translation and rotation units.
    % Exact mechanisms can leave a tiny positive Cholesky pivot after rounding.
    scale = spdiags(1./sqrt(diagonal),0,size(stiffness,1),size(stiffness,1));
    [factor, stiffnessFailure] = chol(scale*symStiffness*scale);
    if stiffnessFailure == 0
        stiffnessFailure = any(abs(diag(factor)) <= sqrt(100*eps));
    end
end
if stiffnessFailure ~= 0
    error('MKEF:SingularStiffness', ...
        ['The reduced stiffness matrix is singular or not positive definite. ' ...
         'Check for insufficient supports or a structural mechanism.']);
end

if strcmp(analysisType, 'static')
    return;
end
if isempty(mass) || any(~isfinite(mass(:)))
    error('MKEF:InvalidReducedSystem', ...
        'The reduced mass matrix is empty or contains non-finite entries.');
end

symMass = (mass + mass.') / 2;
[~, massFailure] = chol(symMass);
if massFailure ~= 0
    error('MKEF:SingularMass', ...
        ['The reduced mass matrix is singular or not positive definite. ' ...
         'Check element connectivity and material density.']);
end
end