orthobasis               package:ade4               R Documentation

_O_r_t_h_o_n_o_r_m_a_l _b_a_s_i_s _f_o_r _o_r_t_h_o_n_o_r_m_a_l _t_r_a_n_s_f_o_r_m

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

     These functions returns object of class ''orthobasis'' that
     contains data frame with _n_ rows and _n-1_ columns. Each data
     frame defines an orthonormal basis for the uniform weights.

     'orthobasic.neig' returns the eigen vectors of the matrix N-M
     where M is the symmetric _n_ by _n_ matrix of the between-sites
     neighbouring graph and N is the diagonal matrix of neighbour
     numbers. 
      'orthobasis.line' returns the analytical solution for the linear
     neighbouring graph. 
      'orthobasic.circ' returns the analytical solution for the
     circular neighbouring graph. 
      'orthobsic.mat' returns the eigen vectors of the general link
     matrix M. 
      'orthobasis.listw' returns the eigen vectors of the general link
     matrix M associated to a 'listw' object. 
      'orthobasis.haar' returns wavelet haar basis.

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

     orthobasis.neig(neig)
     orthobasis.line(n)
     orthobasis.circ(n)
     orthobasis.mat(mat, cnw=TRUE)
     orthobasis.listw(listw)
     orthobasis.haar(n)
     print.orthobasis(x,...)

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

    neig: is an object of class 'neig'

       n: is an integer that defines length of vectors

     mat: is a _n_ by _n_ phylogenetic or spatial link matrix

   listw: is a ''listw'' object

     cnw: if TRUE, the matrix of the neighbouring graph is modified to
          give Constant Neighbouring Weights

       x: is an object of class 'orthobasis'

     ...: : further arguments passed to or from other methods

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

     All the functions excepted 'print.ortobasis' return an object of
     class 'orthobasis' containing a data frame. This data frame
     defines an orthonormal basis with _n-1_ vectors of length _n_.
     Various attributes are associated to it : 


   names: : names of the vectors

row.names: : row names of the data frame

   class: : class

  values: : row weights (uniform weights)

 weights: : numeric values to class vectors according to their
          quadratic forms (Moran ones)

    call: : call

_N_o_t_e:

     the function 'orthobasis.haar' uses function 'wavelet.filter' from
     package waveslim.

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

     Sbastien Ollier ollier@biomserv.univ-lyon1.fr 
      Daniel Chessel chessel@biomserv.univ-lyon1.fr

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

     Misiti, M., Misiti, Y., Oppenheim, G. and Poggi, J.M. (1993)
     Analyse de signaux classiques par dcomposition en ondelettes. 
     _Revue de Statistique Applique_, *41*, 5-32.

     Cornillon, P.A. (1998) _Prise en compte de proximits en analyse
     factorielle et comparative_. Thse, Ecole Nationale Suprieure
     Agronomique, Montpellier.

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

     'gridrowcol' that defines an orthobasis for square grid, 'phylog'
     that defines an orthobasis for phylogenetic tree, 'orthogram' and
     'mld'

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

     # a 2D spatial orthobasis
     par(mfrow = c(4,4))
     w <- gridrowcol(8,8)
      for (k in 1:16)
         s.value(w$xy, w$orthobasis[,k], cleg = 0, csi = 2, incl = FALSE,
          addax = FALSE, sub = k, csub = 4, ylim = c(0,10), cgri = 0)
     par(mfrow = c(1,1))
     barplot(attr(w$orthobasis, "values"))

     # Haar 1D orthobasis
     w <- orthobasis.haar(32)
     par(mfrow = c(8,4))
     par(mar = c(0.1,0.1,0.1,0.1))
      for (k in 1:31) {
         plot(w[,k], type="S",xlab = "", ylab = "", xaxt = "n",
          yaxt = "n", xaxs = "i", yaxs = "i",ylim=c(-4.5,4.5))
         points(w[,k], type = "p", pch = 20, cex = 1.5)
     }

     # a 1D orthobasis
     w <- orthobasis.line(n = 33)
     par(mfrow = c(8,4))
     par(mar = c(0.1,0.1,0.1,0.1))
      for (k in 1:32) {
         plot(w[,k], type="l",xlab = "", ylab = "", xaxt = "n",
          yaxt = "n", xaxs = "i", yaxs = "i",ylim=c(-1.5,1.5))
         points(w[,k], type = "p", pch = 20, cex = 1.5)
     }

     par(mfrow = c(1,1))
     barplot(attr(w, "values"))

     w <- orthobasis.circ(n = 26)
     #par(mfrow = c(5,5))
     #par(mar = c(0.1,0.1,0.1,0.1))
     # for (k in 1:25) 
     #    dotcircle(w[,k], xlim = c(-1.5,1.5), cleg = 0)

     par(mfrow = c(1,1))
     #barplot(attr(w, "values"))

     ## Not run: 
     # a spatial orthobasis
     data(mafragh)
     w <- orthobasis.neig(mafragh$neig)
     par(mfrow = c(4,2))
     for (k in 1:8)
         s.value(mafragh$xy, w[,k],cleg = 0, sub = as.character(k),
          csub = 3)

     par(mfrow = c(1,1))
     barplot(attr(w, "values"))

     # a phylogenetic orthobasis
     data(njplot)
     phy <- newick2phylog(njplot$tre)
     wA <- phy$Ascores
     wW <- phy$Wscores
     table.phylog(phylog = phy, wA, clabel.row = 0, clabel.col  = 0.5)
     table.phylog(phylog = phy, wW, clabel.row = 0, clabel.col  = 0.5)

     ## End(Not run)

