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: tryqalt.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 [itest, gq, hq, pq] = tryqalt(idz, fval, ratio, smat, zmat, itest, gq, hq, pq, debugflag)
    n = length(gq);
    npt = length(pq);
    % TRYQALT tests whether to replace Q by the alternative model, namely the model that minimizes

    
function [itest, gq, hq, pq] = tryqalt(idz, fval, ratio, smat, zmat, itest, gq, hq, pq, debugflag)
    n = length(gq);
    npt = length(pq);
    % TRYQALT tests whether to replace Q by the alternative model, namely the model that minimizes
    % the F-norm of the Hessian subject to the interpolation conditions. It does the replacement
    % when certain criteria are satisfied (i.e., when ITEST = 3). Note that SMAT = BMAT(:, 1:NPT)
    %
    % See Section 8 of the NEWUOA paper.

    % N.B.:
    % GQ, HQ, and PQ should be IN10T(INOUT) instead of IN10T(OUT). According to the Fortran 2018
    % standard, an IN10T(OUT) dummy argument becomes undefined on invocation of the procedure.
    % Therefore, if the procedure does not define such an argument, its value becomes undefined,
    % which is the case for HQ and PQ when ITEST < 3 at exit. In addition, the information in GQ is
    % needed for defining ITEST, so it must be IN10T(INOUT).

    % Local variables
    galt = NaN(length(gq), 1);
    funname = 'TRYQALT';

    % Get and verify the sizes.

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