dCholCMatrix-class          package:Matrix          R Documentation

_C_h_o_l_e_s_k_y _D_e_c_o_m_p_o_s_i_t_i_o_n_s _o_f _d_s_C_M_a_t_r_i_x _O_b_j_e_c_t_s

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

     '"dCholCMatrix"' is class of Cholesky decompositions of symmetric,
     sparse, compressed, column-oriented matrices (the '"dsCMatrix"'
     class).  '"lCholCMatrix"' is class showing the logical structure
     (positions of the non-zeros) of these Cholesky decompositions.

_O_b_j_e_c_t_s _f_r_o_m _t_h_e _C_l_a_s_s:

     Objects can be created by calls of the form 'new("dCholCMatrix",
     ...)' but are more commonly created from 'chol' applied to
     'dsCMatrix' or 'lsCMatrix' objects.

_S_l_o_t_s:

     '_p_e_r_m': Object of class '"integer"' giving the permutation of the
          rows and columns chosen to minimize fill-in. If pivoting has
          not been applied this will be an integer vector of length 0.

     '_d_i_a_g': A character object indicating if the triangular matrix is
          unit triangular or not.  This slot is inherited from the
          '"dtCMatrix"' class.  It is always '"N"' for this class.

     '_u_p_l_o': A character object indicating if the upper triangle ('"U"'
          or '"u"') or the lower triangle ('"L"' or '"l"') is stored. 
          At present only the lower triangle form is allowed.

     '_p': Object of class '"integer"' of pointers, one for each column,
          to the initial (zero-based) index of elements in the column.

     '_i': Object of class '"integer"' of length nnzero (number of
          non-zero elements).  These are the row numbers for each
          non-zero element in the matrix.

     '_x': Object of class '"numeric"' - the non-zero elements of the
          matrix.  Present only in the '"dCholCMatrix"' class.

     '_f_a_c_t_o_r_s': Object of class '"list"' - a list of factorizations of
          the matrix. 

     '_D_i_m': Object of class '"integer"' - the dimensions of the matrix
          - must be an integer vector with exactly two non-negative
          values.

     '_D_i_m_n_a_m_e_s': list of length two; inherited from the '"Matrix"'
          class, see 'Matrix'.

     '_D': Object of class '"numeric"' - the diagonal elements of the
          matrix D in the LDL' decomposition. Present only in the
          '"dCholCMatrix"' class.

     '_P_a_r_e_n_t': Object of class '"integer"' - the elimination tree of
          the (possibly permuted) symmetric matrix.

_E_x_t_e_n_d_s:

     Class '"dtCMatrix"', directly. Class '"dgCMatrix"', by class
     '"dtCMatrix"'.

_M_e_t_h_o_d_s:

     No methods defined with class "dCholCMatrix" in the signature.

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

     Class 'dgCMatrix'

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

     data(KNex)
     xpx <- with(KNex, crossprod(mm))
     str(xpx)
     str(ch <- chol(xpx))

     ## Visualize the sparseness:
     dq <- function(ch) paste('"',ch,'"', sep="") ## dQuote(<UTF-8>) gives bad plots
     image(xpx, main=paste("crossprod(mm) : Sparse", dq(class(xpx))))
     image(ch, main= paste("chol (crossprod(mm)) : Sparse", dq(class(ch))))

