solve                  package:base                  R Documentation

_S_o_l_v_e _a _S_y_s_t_e_m _o_f _E_q_u_a_t_i_o_n_s

_D_e_s_c_r_i_p_t_i_o_n:

     This generic function solves the equation `a %*% x = b' for `x',
     where `b' can be either a vector or a matrix.

_U_s_a_g_e:

     solve(a, b, tol = 1e-7)

_A_r_g_u_m_e_n_t_s:

       a: a numeric matrix containing the coefficients of the linear
          system.

       b: a numeric vector or matrix giving the right-hand side(s) of
          the linear system.  If omitted, `b' is taken to be an
          identity matrix and `solve' will return the inverse of `a'.

     tol: the tolerance for detecting linear dependencies in the
          columns of `a'.

_S_e_e _A_l_s_o:

     `backsolve', `qr.solve'.

_E_x_a_m_p_l_e_s:

     hilbert <- function(n) { i <- 1:n; 1 / outer(i - 1, i, "+") }
     h8 <- hilbert(8); h8
     solve(h8) # gives error: `singular'
     sh8 <- solve(h8, tol = 1e-10)
     round(sh8 %*% h8, 3)

