perturbe            package:compositions            R Documentation

_P_e_r_t_u_r_b_a_t_i_o_n _o_f _c_o_m_p_o_s_i_t_i_o_n_s

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

     The perturbation is the addition operation in the Aitchison
     geometry of the simplex.

_U_s_a_g_e:

               perturbe(x,y)
               x + y
               x - y
               - x

_A_r_g_u_m_e_n_t_s:

       x: compositions of class 'acomp'

       y: compositions of class 'acomp'

_D_e_t_a_i_l_s:

     The perturbation is the basic addition operation of the Aitichson
     simplex as a vector space. It is defined by:

                    (x+y)_i = clo( (x_iy_i)_i )_i

     'permute' and '+' compute this operation. The only difference is
     that '+' checks the class of its argument, while 'permute' does
     not check the type of the arguments and can thus directly be
     applied to a composition in any form (unclassed, acomp, rcomp).
      The '-' operation is the inverse of the addition in the usual way
     and defined by:

                    (x-y)_i:=clo( (x_i/y_i)_i )_i

     and as unary operation respectively as: 

                      (-x)_i:=clo( (1/y_i)_i )_i

_V_a_l_u_e:

     An 'acomp' vector or matrix.

_R_e_f_e_r_e_n_c_e_s:

     Aitchison, J. (1986) _The Statistical Analysis of Compositional
     Data_ Monographs on Statistics and Applied Probability. Chapman &
     Hall Ltd., London (UK). 416p.

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

     'acomp', '*.aplus', '+.rplus'

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

     tmp <- -acomp(1:3)
     tmp + acomp(1:3)

