BunchKaufman-methods         package:Matrix         R Documentation

_B_u_n_c_h-_K_a_u_f_m_a_n _D_e_c_o_m_p_o_s_i_t_i_o_n _M_e_t_h_o_d_s

_D_e_s_c_r_i_p_t_i_o_n:

     The Bunch-Kaufman Decomposition of a square symmetric matrix A is
     A = P LDL' P' where P is a permutation matrix, L is _unit_-lower
     triangular and D is _block_-diagonal with blocks of dimension 1 x
     1 or 2 x 2.

_U_s_a_g_e:

     BunchKaufman(x, ...)

_A_r_g_u_m_e_n_t_s:

       x: a symmetric square matrix.

     ...: potentially further arguments passed to methods.

_M_e_t_h_o_d_s:

     Currently, only methods for *dense* numeric symmetric matrices are
     implemented.

     '_x = "_d_s_p_M_a_t_r_i_x"' ...

     '_x = "_d_s_y_M_a_t_r_i_x"' ...

     These rely on the Lapack routines 'dsptrf' and 'dsytrf',
     respectively.

_S_e_e _A_l_s_o:

     The resulting class, 'BunchKaufman'. Related decompositions are
     the LU,  'lu', and the Cholesky, 'chol' (and for _sparse_
     matrices, 'Cholesky').

_E_x_a_m_p_l_e_s:

     data(CAex)
     dim(CAex)
     isSymmetric(CAex)# TRUE
     CAs <- as(CAex, "symmetricMatrix")
     if(FALSE) # no method defined yet for *sparse* :
        bk. <- BunchKaufman(CAs)
     ## does apply to *dense* symmetric matrices:
     bkCA <- BunchKaufman(as(CAs, "denseMatrix"))
     bkCA

