

pdFactor(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', repre-
          senting a positive definite matrix, which must
          have been initialized (i.e. `length(coef(object))
          > 0').

     ...: some methods for the generic function may require
          additional arguments.

_V_a_l_u_e_:

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

_N_o_t_e_:

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

_A_u_t_h_o_r_(_s_)_:

     Jose Pinheiro and Douglas Bates

_S_e_e _A_l_s_o_:

     `pdMatrix'

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

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

