opChol.m

classdef opChol < opFactorization
%opCHOL  Operator representing the Cholesky factorization of a
%        symmetric and definite matrix with optional iterative
%        refinement. Only the lower triangle of the input matrix
%        is referenced.
%
%   opChol(A) creates an operator for multiplication by the
%   inverse of the matrix A implicitly represented by its Cholesky
%   factorization. Optionally, iterative refinement is performed.
%   Note that A is an explicit matrix.
%
%   The following attributes may be changed by the user:
%    * nitref : the maximum number of iterative refinement steps (3)
%    * itref_tol : iterative refinement tolerance (1.0e-8)
%    * force_itref : force iterative refinement (false)
%
%   See also chol.
%
%   Dominique Orban <dominique.orban@gerad.ca>, 2014.
%
%   Copyright 2009, Ewout van den Berg and Michael P. Friedlander
%   See the file COPYING.txt for full copyright information.
%   Use the command 'spot.gpl' to locate this file.

%   http://www.cs.ubc.ca/labs/scl/spot

  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  % Properties
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  properties( SetAccess = private )
    L             % Lower triangular Cholesky factor
  end

  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  % Methods - Public
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  methods

    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    % opChol. Constructor
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    function op = opChol(A)
      if nargin ~= 1
        error('Invalid number of arguments.');
      end

      [m,n] = size(A);

      % Construct operator
      op = op@opFactorization('Chol', m, n);
      B  = A;
      if ~issparse(A)
       B             = sparse(A);
      end
      op.A           = opHermitian(B);
      op.L           = chol(B, 'lower');
      op.Ainv        = inv(op.L') * inv(op.L);
      op.cflag       = ~isreal(A);
    end % function opChol

    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    % transpose
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    function opOut = transpose(op)
       opOut = inv(op.L.') * inv(op.L);
    end

    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    % conj
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    function opOut = conj(op)
       opOut = inv(conj(op.L')) * inv(conj(op.L));
    end

    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    % ctranpose
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    function opOut = ctranspose(op)
       opOut = inv(op.L') * inv(op.L);
    end

  end % methods - public

end % classdef