rmultscalarproduct       package:compositions       R Documentation

_i_n_n_e_r _p_r_o_d_u_c_t _f_o_r _d_a_t_a_s_e_t_s _w_i_t_h _v_e_c_t_o_r _s_c_a_l_e

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

     An rmult object is considered as a sequence of vectors. The '%*%'
     is considered as the inner multiplication. An inner multiplication
     with another vector is the scalar product. an inner multiplication
     with a matrix is a matrix multiplication, where the rmult-vectors
     are either considered as row or as column vector.

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

     '  x %*% y '
      '   x %*% v'
      '   v %*% x'
      '   x %*% A'
      '   A %*% x'
      '   w %*% A'
      '   A %*% w'
      '   w %*% x'
      '   x %*% w'


       x: an rmult vector or dataset of vectors 

       y: an rmult vector or dataset of vectors 

       v: a numeric vector of length 'gsi.getD(x)'

       w: a numeric vector of length 'gsi.getD(x)'

       A: a matrix

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

     The operators try to minic the behavior of '%*%' on 'c()'-vectors
     as inner product applied in parallel to all vectors of the
     dataset. Thus the product of a vector with another 'rmult' object
     or unclassed vector v results in the scalar product. For the
     multiplication with a matrix each vector is considered as a row or
     column, whatever is more appropriate.

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

     an object of class '"rmult"' or a numeric vector containing the
     result of the corresponding inner products.

_N_o_t_e:

     The product 'x %*% A %*% y' is associative.

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

     'rmult', '%*%.rmult'

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

     x <- rmult(matrix( sqrt(1:12), ncol= 3 ))
     x%*%x
     A <- matrix( 1:9,nrow=3)
     x %*% A %*% x
     x %*% A
     A %*% x
     x %*% 1:3
     x %*% 1:3
     1:3 %*% x 

