You are an expert in writing code in many different languages. Your goal is to perform code completion for the following code, keeping in mind the rest of the code and the file meta data.
    Metadata details:
    filename: trsapp.m
    path of file: ./repos/prima/benchmark/rescue_idz/norma/matlab/interfaces/+newuoa_norma_mat/private
    
    the code of the file until where you have to start completion: function [crvmin, s, info] = trsapp(delta, gq, hq, pq, tol, x, xpt, debugflag)
    n = size(xpt, 1);
    npt = size(xpt, 2);
    % TRSAPP finds an approximate solution to the N-dimensional trust
    % region subproblem
    %
    % min <X+S, GQ> + 0.5*<X+S, HESSIAN*(X+S)> s.t. ||S|| <= DELTA
    %
    % Note that the HESSIAN here is the sum of an explicit part HQ and
    % an implicit part (PQ, XPT):
    %
    % HESSIAN = HQ + sum_K=1^NPT PQ(K)*XPT(:, K)*XPT(:, K)' .
    %
    % At return, S will be the approximate solution. CRVMIN will be
    % set to the least curvature of HESSIAN along the conjugate
    % directions that occur, except that it is set to 0 if S goes
    % all the way to the trust region boundary. QRED is the reduction
    % of Q achieved by S. INFO is an exit flag:
    % INFO = 0: an approximate solution satisfying one of the
    % following conditions is found:
    % 1. ||G+HS||/||GBEG|| <= TOL,
    % 2. ||S|| = DELTA and <S, -(G+HS)> >= (1 - TOL)*||S||*||G+HS||,
    % where TOL is a tolerance that is set to 1e-2 in NEWUOA.
    % INFO = 1: the iteration is reducing Q only slightly;
    % INFO = 2: the maximal number of iterations is attained;
    % INFO = -1: too much rounding error to continue

    % The calculation of S begins with the truncated conjugate
    % gradient method. If the boundary of the trust region is reached,
    % then further changes to S may be made, each one being in the 2D
    % space spanned by the current S and the corresponding gradient of
    % Q. Thus S should provide a substantial reduction to Q within the
    % trust region.

    
function [crvmin, s, info] = trsapp(delta, gq, hq, pq, tol, x, xpt, debugflag)
    n = size(xpt, 1);
    npt = size(xpt, 2);
    % TRSAPP finds an approximate solution to the N-dimensional trust
    % region subproblem
    %
    % min <X+S, GQ> + 0.5*<X+S, HESSIAN*(X+S)> s.t. ||S|| <= DELTA
    %
    % Note that the HESSIAN here is the sum of an explicit part HQ and
    % an implicit part (PQ, XPT):
    %
    % HESSIAN = HQ + sum_K=1^NPT PQ(K)*XPT(:, K)*XPT(:, K)' .
    %
    % At return, S will be the approximate solution. CRVMIN will be
    % set to the least curvature of HESSIAN along the conjugate
    % directions that occur, except that it is set to 0 if S goes
    % all the way to the trust region boundary. QRED is the reduction
    % of Q achieved by S. INFO is an exit flag:
    % INFO = 0: an approximate solution satisfying one of the
    % following conditions is found:
    % 1. ||G+HS||/||GBEG|| <= TOL,
    % 2. ||S|| = DELTA and <S, -(G+HS)> >= (1 - TOL)*||S||*||G+HS||,
    % where TOL is a tolerance that is set to 1e-2 in NEWUOA.
    % INFO = 1: the iteration is reducing Q only slightly;
    % INFO = 2: the maximal number of iterations is attained;
    % INFO = -1: too much rounding error to continue

    % The calculation of S begins with the truncated conjugate
    % gradient method. If the boundary of the trust region is reached,
    % then further changes to S may be made, each one being in the 2D
    % space spanned by the current S and the corresponding gradient of
    % Q. Thus S should provide a substantial reduction to Q within the
    % trust region.
    %
    % See Section 5 of the NEWUOA paper.

    s = NaN(n, 1);

    % Local variables
    funname = 'TRSAPP';

    % Get and verify the sizes.

    if debugflag
        if n == 0 || npt < n + 2
            error('Error: %s: SIZE(XPT) is invalid.', funname);
        end