EW_Fi_MLM_func          function to generate the expected fisher
                        information at one design point xi for
                        multinomial logit models
EW_ForLion_GLM_Optimal
                        EW ForLion for generalized linear models
EW_ForLion_MLM_Optimal
                        EW ForLion function for multinomial logit
                        models
EW_Xw_maineffects_self
                        function for calculating X=h(x) and
                        E_w=E(nu(beta^T h(x))) given a design point
                        x=(1,x1,...,xd)^T
EW_design_initial_GLM   function to generate a initial EW Design for
                        generalized linear models
EW_design_initial_MLM   function to generate a initial EW Design for
                        multinomial logistic models
EW_dprime_func_self     function to calculate dEu/dx in the gradient of
                        d(x, Xi), will be used in EW_ForLion_MLM_func()
                        function
EW_liftoneDoptimal_GLM_func
                        EW Lift-one algorithm for D-optimal approximate
                        design
EW_liftoneDoptimal_MLM_func
                        function of EW liftone for multinomial logit
                        model
EW_liftoneDoptimal_log_GLM_func
                        EW Lift-one algorithm for D-optimal approximate
                        design in log scale
Fi_MLM_func             function to generate fisher information at one
                        design point xi for multinomial logit models
ForLion_GLM_Optimal     ForLion for generalized linear models
ForLion_MLM_Optimal     ForLion function for multinomial logit models
GLM_Exact_Design        rounding algorithm for generalized linear
                        models
MLM_Exact_Design        rounding algorithm for multinomial logit models
Xw_maineffects_self     function for calculating X=h(x) and w=nu(beta^T
                        h(x)) given a design point x = (x1,...,xd)^T
design_initial_self     function to generate initial design with design
                        points and the approximate allocation
discrete_rv_self        function to generate discrete uniform random
                        variables for initial random design points in
                        ForLion
dprime_func_self        function to calculate du/dx in the gradient of
                        d(x, Xi), will be used in ForLion_MLM_func()
                        function, details see Appendix C in Huang, Li,
                        Mandal, Yang (2024)
liftoneDoptimal_GLM_func
                        Lift-one algorithm for D-optimal approximate
                        design
liftoneDoptimal_MLM_func
                        function of liftone for multinomial logit model
liftoneDoptimal_log_GLM_func
                        Lift-one algorithm for D-optimal approximate
                        design in log scale
nu1_cauchit_self        function to calculate first derivative of nu
                        function given eta for cauchit link
nu1_identity_self       function to calculate first derivative of nu
                        function given eta for identity link
nu1_log_self            function to calculate first derivative of nu
                        function given eta for log link
nu1_logit_self          function to calculate the first derivative of
                        nu function given eta for logit link
nu1_loglog_self         function to calculate the first derivative of
                        nu function given eta for log-log link
nu1_probit_self         function to calculate the first derivative of
                        nu function given eta for probit link
nu2_cauchit_self        function to calculate the second derivative of
                        nu function given eta for cauchit link
nu2_identity_self       function to calculate the second derivative of
                        nu function given eta for identity link
nu2_log_self            function to calculate the second derivative of
                        nu function given eta for log link
nu2_logit_self          function to calculate the second derivative of
                        nu function given eta for logit link
nu2_loglog_self         function to calculate the second derivative of
                        nu function given eta for loglog link
nu2_probit_self         function to calculate the second derivative of
                        nu function given eta for probit link
nu_cauchit_self         function to calculate w = nu(eta) given eta for
                        cauchit link
nu_identity_self        function to calculate w = nu(eta) given eta for
                        identity link
nu_log_self             function to calculate w = nu(eta) given eta for
                        log link
nu_logit_self           function to calculate w = nu(eta) given eta for
                        logit link
nu_loglog_self          function to calculate w = nu(eta) given eta for
                        loglog link
nu_probit_self          function to calculate w = nu(eta) given eta for
                        probit link
polynomial_sol_J3       functions to solve 2th order polynomial
                        function given coefficients
polynomial_sol_J4       functions to solve 3th order polynomial
                        function given coefficients
polynomial_sol_J5       functions to solve 4th order polynomial
                        function given coefficients
print.design_output     Print Method for Design Output from ForLion
                        Algorithms
print.list_output       Print Method for list_output Objects
svd_inverse             SVD Inverse Of A Square Matrix
xmat_discrete_self      Generate initial designs within ForLion
                        algorithms
