COMPDIR computes a search direction in a subspace defined by Z.　
% [SD,dirType] = compdir(Z,H,gf,nvars,f) returns a search direction for the
% subproblem 0.5*Z'*H*Z + Z'*gf. Helper function for NLCONST. SD is Newton
% direction if possible. SD is a direction of negative curvature if the
% Cholesky factorization of Z'*H*Z fails. If the negative curvature
% direction isn't negative "enough", SD is the steepest descent direction.
% For singular Z'*H*Z, SD is the steepest descent direction even if small,
% or even zero, magnitude.