Cholesky               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 _o_f _a _S_p_a_r_s_e _M_a_t_r_i_x

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

     Computes the Cholesky decomposition of a sparse, symmetric,
     positive-definite matrix.

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

     Cholesky(A, perm, LDL, super, ...)

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

       A: sparse symmetric matrix.  No missing values or IEEE special
          values are allowed.

    perm: logical scalar indicating if a fill-reducing permutation
          should be computed and applied to the rows and columns of
          'A'. Default is 'TRUE'.

     LDL: logical scalar indicating if the decomposition should be
          computed as LDL' where 'L' is a unit lower triangular matrix.
          The alternative is LL' where 'L' is lower triangular with
          arbitrary diagonal elements.  Default is 'TRUE'.

   super: logical scalar indicating is a supernodal decomposition
          should be created.  The alternative is a simplicial
          decomposition. Default is 'FALSE'.

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

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

     This is a generic function with special methods for different
     types of matrices.  Use 'showMethods("Cholesky")' to list all the
     methods for the 'Cholesky' generic.

     The method for class 'dsCMatrix' of sparse matrices is based on
     functions from the CHOLMOD library.

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

     an object of class '"CHMfactor"'.

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

     Tim Davis (2005) _{CHOLMOD}: sparse supernodal {Cholesky}
     factorization and update/downdate_ <URL:
     http://www.cise.ufl.edu/research/sparse/cholmod/>

     Timothy A. Davis (2006) _Direct Methods for Sparse Linear
     Systems_, SIAM Series "Fundamentals of Algorithms".

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

     Class definitions 'CHMfactor' and 'dsCMatrix' and function
     'expand'.

     Note that 'chol()' returns matrices (inheriting from '"Matrix"')
     whereas 'Cholesky()' returns a '"CHMfactor"' object.

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

     data(KNex)
     mtm <- with(KNex, crossprod(mm))
     Cholesky(mtm)             # uses show(<MatrixFactorization>)
     Cholesky(mtm, super = TRUE)

