MGH17                package: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 _1_7

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

     The `MGH17' data frame has 33 rows and 2 columns

_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.

     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:

     Osborne, M. R. (1972).   Some aspects of nonlinear least squares 
     calculations.  In Numerical Methods for Nonlinear  Optimization,
     Lootsma (Ed).   New York, NY:  Academic Press, pp. 171-189.

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

     data(MGH17)
     plot(y ~ x, data = MGH17)

     ## Starting values here are ridiculous
     fm1 <- nls(y ~ b1 + b2*exp(-x*b4) + b3*exp(-x*b5),
                data = MGH17, trace = TRUE,
                start = c(b1 = 50, b2 = 150, b3 = -100, b4 = 1, b5 = 2))

     fm2 <- nls(y ~ b1 + b2*exp(-x*b4) + b3*exp(-x*b5),
                data = MGH17, trace = TRUE,
                start = c(b1 = 0.5, b2 = 1.5, b3 = -1, b4 = 0.01, b5 = 0.02))

     fm3 <- nls(y ~ cbind(1, exp(-x*b4), exp(-x*b5)),
                data = MGH17, trace = TRUE, algorithm = "plinear",
                start = c(b4 = 1, b5 = 2))

     fm4 <- nls(y ~ cbind(1, exp(-x*b4), exp(-x*b5)),
                data = MGH17, trace = TRUE, algorithm = "plinear",
                start = c(b4 = 0.01, b5 = 0.02))

