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", ...)' or by calls of the form 'chol(pm)'
     where 'pm' inherits from the '"dpoMatrix"' 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))

