pdFactor                package:nlme                R Documentation

_S_q_u_a_r_e-_R_o_o_t _F_a_c_t_o_r _o_f _a _P_o_s_i_t_i_v_e-_D_e_f_i_n_i_t_e _M_a_t_r_i_x

_D_e_s_c_r_i_p_t_i_o_n:

     A square-root factor of the positive-definite matrix represented
     by 'object' is obtained. Letting S denote a positive-definite
     matrix, a square-root factor of S is any square matrix L such that
     S = L'L. This function extracts L.

_U_s_a_g_e:

     pdFactor(object)

_A_r_g_u_m_e_n_t_s:

  object: an object inheriting from class 'pdMat', representing a
          positive definite matrix, which must have been initialized
          (i.e. 'length(coef(object)) > 0').

_V_a_l_u_e:

     a vector with a square-root factor of the positive-definite matrix
     associated with 'object' stacked column-wise.

_N_o_t_e:

     This function is used intensively in optimization algorithms and
     its value is returned as a vector for efficiency reasons. The
     'pdMatrix' function can be used to obtain square-root factors in
     matrix form.

_A_u_t_h_o_r(_s):

     Jose Pinheiro Jose.Pinheiro@pharma.novartis.com and Douglas Bates
     bates@stat.wisc.edu

_R_e_f_e_r_e_n_c_e_s:

     Pinheiro, J.C., and Bates, D.M. (2000) "Mixed-Effects Models in S
     and S-PLUS", Springer.

_S_e_e _A_l_s_o:

     'pdMatrix'

_E_x_a_m_p_l_e_s:

     pd1 <- pdCompSymm(4 * diag(3) + 1)
     pdFactor(pd1)

