Cholesky-class            package:Matrix            R Documentation

_C_h_o_l_e_s_k_y _a_n_d _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_s

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

     The '"Cholesky"' class is the class of Cholesky decompositions of
     positive-semidefinite, real matrices.  The '"BunchKaufman"' class
     is the class of Bunch-Kaufman decompositions of symmetric, real
     matrices.  The '"pCholesky"' and '"pBunchKaufman"' classes are
     their _*p*acked_ storage versions.

_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("Cholesky", ...)'
     or 'new("BunchKaufman", ...)', etc, or rather by calls of the form
     'chol(pm)' or 'BunchKaufman(pm)' where 'pm' inherits from the
     '"dpoMatrix"' or '"dsyMatrix"' class or as a side-effect of other
     functions applied to '"dpoMatrix"' objects (see 'dpoMatrix').

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

     A Cholesky decomposition extends class 'MatrixFactorization' but
     is basically a triangular matrix extending the '"dtrMatrix"'
     class.

     '_u_p_l_o': inherited from the '"dtrMatrix"' class.

     '_d_i_a_g': inherited from the '"dtrMatrix"' class.

     '_x': inherited from the '"dtrMatrix"' class.

     '_D_i_m': inherited from the '"dtrMatrix"' class.

     '_D_i_m_n_a_m_e_s': inherited from the '"dtrMatrix"' class.

     A Bunch-Kaufman decomposition also extends the '"dtrMatrix"' class
     and has a 'perm' slot representing a permutation matrix. The
     packed versions extend the '"dtpMatrix"' class.

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

     Class '"MatrixFactorization"' and '"dtrMatrix"', directly. Class
     '"dgeMatrix"', by class '"dtrMatrix"'. Class '"Matrix"', by class
     '"dtrMatrix"'.

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

     No methods defined with class "Cholesky" in the signature.

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

     Classes 'dtrMatrix', 'dpoMatrix'; function 'chol'.

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

     (sm <- as(as(Matrix(diag(5) + 1), "dsyMatrix"), "dspMatrix"))
     signif(csm <- chol(sm), 4)

     (pm <- crossprod(Matrix(rnorm(18), nrow = 6, ncol = 3)))
     (ch <- chol(pm))
     if (toupper(ch@uplo) == "U") # which is TRUE
        crossprod(ch)
     stopifnot(all.equal(as(crossprod(ch), "matrix"),
                         as(pm, "matrix"), tol=1e-14))

