projections              package:lspls              R Documentation

_P_r_o_j_e_c_t_i_o_n _a_n_d _O_r_t_h_o_g_o_n_a_l_i_s_a_t_i_o_n

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

     Functions to project one matrix onto another, or to ortghogonalise
     it against the other.

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

     project(M, N)
     orth(M, N)
     Corth(M, N)

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

       M: matrix to be projected or orthogonalised

       N: matrix to be projected onto or orthogonalised against

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

     'project(M, N)' calculates the projection of 'M' onto 'N', i.e., N
     (N' N)^(-1) N' M.

     'orth(M, N)' orthogonalises 'M' with respect to 'N', i.e., it
     calculates the projection of 'M' onto the orthogonal space of 'N':
     M - N (N' N)^(-1) N' M.

     'Corth(M, N)' calculates the coefficient matrix needed to
     orthogonalise future matrices, i.e., (N' N)^(-1) N' M.  Future
     matrices 'm' and 'n' can be orthogonalised with 'm - n %*%
     Corth(M, N)'.

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

     A matrix.

_N_o_t_e:

     The functions need to be opitmised, both for speed and numerical
     accurracy.

_A_u_t_h_o_r(_s):

     Bjrn-Helge Mevik

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

     'lspls', 'lsplsCv', 'predict.lspls'

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

     ##FIXME

