sparseLU-class            package:Matrix            R Documentation

_S_p_a_r_s_e _L_U _d_e_c_o_m_p_o_s_i_t_i_o_n _o_f _a _s_q_u_a_r_e _s_p_a_r_s_e _m_a_t_r_i_x

_D_e_s_c_r_i_p_t_i_o_n:

     Objects of this class contain the components of the LU
     decomposition of a sparse square matrix.

_O_b_j_e_c_t_s _f_r_o_m _t_h_e _C_l_a_s_s:

     Objects can be created by calls of the form 'new("sparseLU", ...)'
     but are more commonly created by function 'lu()' applied to a
     sparse matrix, such as a matrix of class 'dgCMatrix'.

_S_l_o_t_s:


     '_L': Object of class '"dtCMatrix"', the lower triangular factor
          from the left.

     '_U': Object of class '"dtCMatrix"', the upper triangular factor
          from the right.

     '_p': Object of class '"integer"', permutation applied from the
          left. 

     '_q': Object of class '"integer"', permutation applied from the
          right.

     '_D_i_m': the dimension of the original matrix; inherited from class
          'MatrixFactorization'.

_E_x_t_e_n_d_s:

     Class '"LU"', directly. Class '"MatrixFactorization"', by class
     '"LU"'.

_M_e_t_h_o_d_s:


     _e_x_p_a_n_d 'signature(x = "sparseLU")' Returns a list with components
          'P', 'L', 'U', and 'Q', where P and Q represent fill-reducing
          permutations, and L, and U the lower and upper triangular
          matrices of the decomposition.  The original matrix
          corresponds to the product PLUQ.

_N_o_t_e:

     The decomposition is of the form

                               A = PLUQ

     where all matrices are sparse and of size n by n. The matrices P
     and Q are permutation matrices, L is lower triangular and U is
     upper triangular.

_S_e_e _A_l_s_o:

     'lu', 'solve', 'dgCMatrix'

_E_x_a_m_p_l_e_s:

       ## see  examples(lu)