

chol {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

_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_:

     This function computes the Choleski factorization of
     the square matrix `x'.  It returns the upper triangular
     factor of the 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., J. R. Bunch, C. B. Moler and G. W.
     Stewart (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

