chol                  package:base                  R Documentation

_T_h_e _C_h_o_l_e_s_k_i _D_e_c_o_m_p_o_s_i_t_i_o_n

_D_e_s_c_r_i_p_t_i_o_n:

     Compute the Choleski factorization of a symmetric (Hermitian),
     positive definite square matrix.

_U_s_a_g_e:

     chol(x)

_A_r_g_u_m_e_n_t_s:

       x: a symmetric, positive definite matrix.

_V_a_l_u_e:

     The upper triangular factor of the Choleski decomposition, i.e.,
     the matrix R such that R'R = x (see example).

     Note that effectively, only the upper triangular part of `x' is
     used such that the above only holds when `x' is symmetric.

_R_e_f_e_r_e_n_c_e_s:

     Dongarra, J. J., Bunch, J. R., Moler, C. B. and Stewart, G. W.
     (1978) LINPACK Users Guide.  Philadelphia: SIAM Publications.

_S_e_e _A_l_s_o:

     `chol2inv' for its inverse, `backsolve' for solving linear systems
     with upper triangular left sides.

     `qr', `svd' for related matrix factorizations.

_E_x_a_m_p_l_e_s:

     ( m <- matrix(c(5,1,1,3),2,2) )
     ( cm <- chol(m) )
     t(cm) %*% cm  #-- = 'm'
     all(abs(m  -  t(cm) %*% cm) < 100* .Machine$double.eps) # TRUE

