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Added texinfo header.

time-shift
Stéphane Adjemian (Charybdis) 2012-07-11 16:30:01 +02:00
parent a86a904823
commit 47e543409c
1 changed files with 44 additions and 11 deletions
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55
matlab/cycle_reduction.m
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@ -1,14 +1,47 @@
function [X, info] = cycle_reduction(A0, A1, A2, cvg_tol, ch)
% function [X, info] = cycle_reduction(A0,A1,A2,A3, cvg_tolch)
%
% Solves Polynomial Equation:
% A0 + A1 * X + A2 * X² = 0
% Using Cyclic Reduction algorithm
% - D.A. Bini, G. Latouche, B. Meini (2002), "Solving matrix polynomial equations arising in
% queueing problems", Linear Algebra and its Applications 340 (2002) 225–244
% - D.A. Bini, B. Meini, On the solution of a nonlinear matrix equation arising in queueing problems,
% SIAM J. Matrix Anal. Appl. 17 (1996) 906–926.
% =================================================================
%@info:
%! @deftypefn {Function File} {[@var{X}, @var{info}] =} cycle_reduction (@var{A0},@var{A1},@var{A2},@var{cvg_tol},@var{ch})
%! @anchor{cycle_reduction}
%! @sp 1
%! Solves the quadratic matrix equation A2*X^2 + A1*X + A0 = 0.
%! @sp 2
%! @strong{Inputs}
%! @sp 1
%! @table @ @var
%! @item A0
%! Square matrix of doubles, n*n.
%! @item A1
%! Square matrix of doubles, n*n.
%! @item A2
%! Square matrix of doubles, n*n.
%! @item cvg_tol
%! Scalar double, tolerance parameter.
%! @item ch
%! Any matlab object, if not empty the solution is checked.
%! @end table
%! @sp 1
%! @strong{Outputs}
%! @sp 1
%! @table @ @var
%! @item X
%! Square matrix of doubles, n*n, solution of the matrix equation.
%! @item info
%! Scalar integer, if nonzero the algorithm failed in finding the solution of the matrix equation.
%! @end table
%! @sp 2
%! @strong{This function is called by:}
%! @sp 2
%! @strong{This function calls:}
%! @sp 2
%! @strong{References:}
%! @sp 1
%! D.A. Bini, G. Latouche, B. Meini (2002), "Solving matrix polynomial equations arising in queueing problems", Linear Algebra and its Applications 340, pp. 222-244
%! @sp 1
%! D.A. Bini, B. Meini (1996), "On the solution of a nonlinear matrix equation arising in queueing problems", SIAM J. Matrix Anal. Appl. 17, pp. 906-926.
%! @sp 2
%! @end deftypefn
%@eod:
% Copyright (C) 2012 Dynare Team
%
@ -59,7 +92,7 @@ end
X = -A_0\A0;
if (nargin == 5 && ~isempty( ch ) == 1 )
if (nargin == 5 && ~isempty(ch) )
%check the solution
res = A0 + A1 * X + A2 * X * X;
if (sum(sum(abs(res))) > cvg_tol)