pdLogChol-class            package:Matrix            R Documentation

_C_l_a_s_s "_p_d_L_o_g_C_h_o_l", _p_o_s_i_t_i_v_e-_d_e_f_i_n_i_t_e _m_a_t_r_i_c_e_s

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

     A class of general, positive-definite symmetric matrices
     parameterized by the non-zero elements in the Cholesky
     decomposition.  The diagonal elements are represented by their
     logarithms in the first 'q' positions of the parameter vector. 
     The strict upper triangle of the factor is in the last 'q(q-1)/2'
     positions.

_O_b_j_e_c_t_s _f_r_o_m _t_h_e _C_l_a_s_s:

     Objects of class 'pdLogChol' can be created by calls of the form
     'new("pdLogChol", ...)' or by the generic constructor function
     'pdLogChol'.  Frequently the constructor is given a formula only,
     creating an uninitialized 'pdLogChol' object which is later
     assigned a value.

     'pdLogChol' objects are primarily used to represent the
     variance-covariance matrix or the precision matrix of
     random-effects terms in mixed-effects models.

_S_l_o_t_s:

     '_f_o_r_m': Object of class '"formula", from class "pdMat"', a formula
          for the object

     '_N_a_m_e_s': Object of class '"character", from class "pdMat"', names
          for the rows (and columns) of the positive-definite matrix.

     '_p_a_r_a_m': Object of class '"numeric", from class "pdMat"', a
          parameter vector of length [q(q+1)]/2 where q is 'Ncol', the
          number of columns (and rows) in the positive-definite matrix.

     '_N_c_o_l': Object of class '"integer", from class "pdMat"', number of
          columns (and rows) in the positive-definite matrix.

     '_f_a_c_t_o_r': Object of class '"matrix", from class "pdMat"', a square
          root factor of the positive-definite matrix.

     '_l_o_g_D_e_t': Object of class '"numeric", from class "pdMat"' the
          logarithm of the absolute value of the determinant of the
          square root factor or, equivalently, half the logarithm of
          the determinant of the positive-definite matrix.

_E_x_t_e_n_d_s:

     Class '"pdMat"', directly.

_M_e_t_h_o_d_s:

     _E_M_u_p_d_a_t_e<- 'signature(x = "pdLogChol", nlev = "numeric", value =
          "matrix")': update the 'pdLogChol' object in the EM algorithm
          for a mixed-effects model.

     _L_M_E_g_r_a_d_i_e_n_t 'signature(x = "pdLogChol", A = "matrix", nlev =
          "numeric")': evaluate the gradient of the log-likelihood in a
          linear mixed-effects model.

     _c_o_e_f<- 'signature(object = "pdLogChol", value = "numeric")':
          assign the parameter.

     _c_o_e_r_c_e 'signature(from = "pdLogChol", to = "pdmatrix")': extract
          the positive-definite matrix represented by the object.

     _p_d_g_r_a_d_i_e_n_t 'signature(x = "pdLogChol")': the gradient of the
          positive definite matrix with respect to the parameter
          vector.

     _s_o_l_v_e 'signature(a = "pdLogChol", b = "missing")': a 'pdLogChol'
          object representing the inverse of the positive-definite
          matrix represented by this object.

     _s_u_m_m_a_r_y 'signature(object = "pdLogChol")': summarize the object.

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

     'pdMat-class'

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

     m1 <- pdLogChol(~ age)
     coef(m1) <- rnorm(3)
     print(m1)
     solve(m1)

