facmul                package:Matrix                R Documentation

_M_u_l_t_i_p_l_i_c_a_t_i_o_n _b_y _D_e_c_o_m_p_o_s_i_t_i_o_n _F_a_c_t_o_r_s

_D_e_s_c_r_i_p_t_i_o_n:

     Performs multiplication by factors for certain decompositions (and
     allows explicit formation of those factors).

_U_s_a_g_e:

     facmul(x, factor, y, transpose, left, ...)

_A_r_g_u_m_e_n_t_s:

       x: a matrix decomposition.  No missing values or IEEE special
          values are allowed. 

  factor: an indicator for selecting a particular factor for
          multiplication. 

       y: a matrix or vector to be multiplied by the factor or its
          transpose. No missing values or IEEE special values are
          allowed. 

transpose: a logical value.  When 'FALSE' (the default) the factor is
          applied.  When 'TRUE' the transpose of the factor is applied. 

    left: a logical value.  When 'TRUE' (the default) the factor is
          applied from the left.  When 'FALSE' the factor is applied
          from the right. 

     ...: the method for '"qr.Matrix"' has additional arguments. 

_V_a_l_u_e:

     the product of the selected factor (or its transpose) and 'y'

_N_O_T_E:

     Factors for decompositions such as 'lu' and 'qr' can be stored in
     a compact form. The function 'facmul' allows multiplication
     without explicit formation of the factors, saving both storage and
     operations.

_R_e_f_e_r_e_n_c_e_s:

     Golub, G., and Van Loan, C. F. (1989). _Matrix Computations,_ 2nd
     edition, Johns Hopkins, Baltimore.

_E_x_a_m_p_l_e_s:

     library(Matrix)
     x <- Matrix(rnorm(9), 3, 3)
     ## Not run: 
     qrx <- qr(x)                      # QR factorization of x
     y <- rnorm(3)
     facmul( qr(x), factor = "Q", y)   # form Q y
     ## End(Not run)