

MGH09(NISTnls)                               R Documentation

_M_o_r_e_, _G_a_b_r_o_w _a_n_d _H_i_l_l_s_t_r_o_m _e_x_a_m_p_l_e _9

_D_e_s_c_r_i_p_t_i_o_n_:

     The `MGH09' data frame has 11 rows and 2 columns giving

_A_r_g_u_m_e_n_t_s_:

       y: A numeric vector of response values.

       x: A numeric vector of input values.

_F_o_r_m_a_t_:

     This data frame contains the following columns:

_D_e_t_a_i_l_s_:

     This problem was found to be difficult for some very
     good algorithms.  There is a local minimum at (+inf,
     -14.07..., -inf, -inf) with final sum of squares
     0.00102734....

     See More, J. J., Garbow, B. S., and Hillstrom, K. E.
     (1981).  Testing unconstrained optimization software.
     ACM Transactions on Mathematical Software. 7(1): pp.
     17-41.

_S_o_u_r_c_e_:

     Kowalik, J.S., and M. R. Osborne, (1978).  Methods for
     Unconstrained Optimization Problems.  New York, NY:
     Elsevier North-Holland.

_E_x_a_m_p_l_e_s_:

     library(NISTnls)
     data(MGH09)
     plot(y ~ x, data = MGH09)
     ## starting values for this attempt are ridiculous
     fm1 <- nls(y ~ b1*(x**2+x*b2) / (x**2+x*b3+b4),
                data = MGH09, trace = TRUE,
                start = c(b1 = 25, b2 = 39, b3 = 41.5, b4 = 39),
                warnOnly = TRUE)
     fm2 <- nls(y ~ b1*(x**2+x*b2) / (x**2+x*b3+b4),
                data = MGH09, trace = TRUE,
                start = c(b1 = 0.25, b2 = 0.39, b3 = 0.415, b4 = 0.39))
     fm3 <- nls(y ~ cbind(x, x**2) / (x**2+x*b3+b4),
                data = MGH09, trace = TRUE, algorithm = "plinear",
                start = c(b3 = 41.5, b4 = 39),
                warnOnly = TRUE)
     fm4 <- nls(y ~ cbind(x, x**2) / (x**2+x*b3+b4),
                data = MGH09, trace = TRUE, algorithm = "plinear",
                start = c(b3 = 0.415, b4 = 0.39),
                warnOnly = TRUE)

