# HG changeset patch # User John W. Eaton # Date 1315081964 14400 # Node ID 1bf456b4e51cc4f0f88236eaede6bbdd17fc7a4b # Parent 59def8890992295cb6a14a13fde0ea5e09e1bf17 maint: style fixes for cgs * cgs.m: Style fixes. diff -r 59def8890992 -r 1bf456b4e51c scripts/sparse/cgs.m --- a/scripts/sparse/cgs.m Sat Sep 03 16:25:48 2011 -0400 +++ b/scripts/sparse/cgs.m Sat Sep 03 16:32:44 2011 -0400 @@ -22,92 +22,96 @@ ## @deftypefn {Function File} {@var{x} =} cgs (@var{A}, @var{b}, @var{rtol}, @var{maxit}, @var{M1}, @var{M2}, @var{x0}) ## @deftypefnx {Function File} {@var{x} =} cgs (@var{A}, @var{b}, @var{rtol}, @var{maxit}, @var{P}) ## @deftypefnx {Function File} {[@var{x}, @var{flag}, @var{relres}, @var{iter}, @var{resvec}] =} cgs (@var{A}, @var{b}, ...) -## -## Solve @code{A x = b}, where @var{A} is a square matrix, using the Conjugate Gradients Squared method. +## Solve @code{A x = b}, where @var{A} is a square matrix, using the +## Conjugate Gradients Squared method. ## -## @itemize @minus -## @item @var{rtol} is the relative tolerance, if not given or set to [] the default value 1e-6 is used. -## @item @var{maxit} the maximum number of outer iterations, if not given or set to [] the default value @code{min (20, numel (b))} is used. -## @item @var{x0} the initial guess, if not given or set to [] the default value @code{zeros (size (b))} is used. -## @end itemize +## @itemize @minus +## @item @var{rtol} is the relative tolerance, if not given or set to [] +## the default value 1e-6 is used. +## @item @var{maxit} the maximum number of outer iterations, if not +## given or set to [] the default value @code{min (20, numel (b))} is +## used. +## @item @var{x0} the initial guess, if not given or set to [] the +## default value @code{zeros (size (b))} is used. +## @end itemize ## -## @var{A} can be passed as a matrix or as a function handle or -## inline function @code{f} such that @code{f(x) = A*x}. -## -## The preconditioner @var{P} is given as @code{P = M1 * M2}. -## Both @var{M1} and @var{M2} can be passed as a matrix or as a function handle or -## inline function @code{g} such that @code{g(x) = M1 \ x} or @code{g(x) = M2 \ x}. +## @var{A} can be passed as a matrix or as a function handle or +## inline function @code{f} such that @code{f(x) = A*x}. ## -## If called with more than one output parameter +## The preconditioner @var{P} is given as @code{P = M1 * M2}. +## Both @var{M1} and @var{M2} can be passed as a matrix or as a function +## handle or inline function @code{g} such that @code{g(x) = M1 \ x} or +## @code{g(x) = M2 \ x}. +## +## If called with more than one output parameter ## -## @itemize @minus -## @item @var{flag} indicates the exit status: -## @itemize @minus -## @item 0: iteration converged to the within the chosen tolerance -## @item 1: the maximum number of iterations was reached before convergence -## @item 3: the algorithm reached stagnation -## @end itemize -## (the value 2 is unused but skipped for compatibility). -## @item @var{relres} is the final value of the relative residual. -## @item @var{iter} is the number of iterations performed. -## @item @var{resvec} is a vector containing the relative residual at each iteration. -## @end itemize +## @itemize @minus +## @item @var{flag} indicates the exit status: +## @itemize @minus +## @item 0: iteration converged to the within the chosen tolerance +## @item 1: the maximum number of iterations was reached before convergence +## @item 3: the algorithm reached stagnation +## @end itemize +## (the value 2 is unused but skipped for compatibility). +## @item @var{relres} is the final value of the relative residual. +## @item @var{iter} is the number of iterations performed. +## @item @var{resvec} is a vector containing the relative residual at +## each iteration. +## @end itemize ## -## @seealso{pcg,bicgstab,bicg,gmres} -## +## @seealso{pcg,bicgstab,bicg,gmres} ## @end deftypefn function [x, flag, relres, iter, resvec] = cgs (A, b, tol, maxit, M1, M2, x0) - if ((nargin >= 2) && (nargin <= 7) && isvector (full (b))) + if (nargin >= 2 && nargin <= 7 && isvector (full (b))) if (ischar (A)) A = str2func (A); elseif (ismatrix (A)) - Ax = @(x) A * x; + Ax = @(x) A * x; elseif (isa (A, "function_handle")) - Ax = @(x) feval (A, x); + Ax = @(x) feval (A, x); else error (["cgs: first argument is expected to "... "be a function or a square matrix"]); endif - if ((nargin < 3) || (isempty (tol))) + if (nargin < 3 || isempty (tol)) tol = 1e-6; endif - if ((nargin < 4) || (isempty (maxit))) + if (nargin < 4 || isempty (maxit)) maxit = min (rows (b), 20); endif - if ((nargin < 5) || isempty (M1)) + if (nargin < 5 || isempty (M1)) M1m1x = @(x) x; elseif (ischar (M1)) M1m1x = str2func (M1); elseif (ismatrix (M1)) - M1m1x = @(x) M1 \ x; + M1m1x = @(x) M1 \ x; elseif (isa (M1, "function_handle")) - M1m1x = @(x) feval (M1, x); + M1m1x = @(x) feval (M1, x); else - error (["cgs: preconditioner is expected "... - "to be a function or matrix"]); + error ("cgs: preconditioner is expected to be a function or matrix"); endif - if ((nargin < 6) || isempty (M2)) + if (nargin < 6 || isempty (M2)) M2m1x = @(x) x; elseif (ischar (M2)) M2m1x = str2func (M2); elseif (ismatrix (M2)) - M2m1x = @(x) M2 \ x; + M2m1x = @(x) M2 \ x; elseif (isa (M2, "function_handle")) - M2m1x = @(x) feval (M2, x); + M2m1x = @(x) feval (M2, x); else error ("cgs: preconditioner is expected to be a function or matrix"); endif - precon = @(x) M2m1x (M1m1x (x)); + precon = @(x) M2m1x (M1m1x (x)); - if ((nargin < 7) || (isempty (x0))) + if (nargin < 7 || isempty (x0)) x0 = zeros (size (b)); endif @@ -117,11 +121,11 @@ res = b - Ax (x); norm_b = norm (b); ## Vector of the residual norms for each iteration. - resvec = [ norm(res)/norm_b ]; + resvec = norm (res) / norm_b; ro = 0; ## Default behavior we don't reach tolerance tol within maxit iterations. flag = 1; - for iter = 1 : maxit + for iter = 1:maxit z = precon (res); @@ -140,36 +144,34 @@ x = x + alpha * p; res = res - alpha * q; - relres = norm(res) / norm_b; - resvec = [resvec;relres]; + relres = norm (res) / norm_b; + resvec = [resvec; relres]; if (relres <= tol) ## We reach tolerance tol within maxit iterations. flag = 0; - break; + break elseif (resvec (end) == resvec (end - 1)) ## The method stagnates. flag = 3; - break; + break endif - endfor; + endfor if (nargout < 1) - if ( flag == 0 ) - printf (["cgs converged at iteration %i ", - "to a solution with relative residual %e\n"],iter,relres); + if (flag == 0) + printf ("cgs converged at iteration %i to a solution with relative residual %e\n", + iter, relres); elseif (flag == 3) - printf (["cgs stopped at iteration %i ", - "without converging to the desired tolerance %e\n", + printf (["cgs stopped at iteration %i without converging to the desired tolerance %e\n", "because the method stagnated.\n", "The iterate returned (number %i) has relative residual %e\n"], - iter,tol,iter,relres); + iter, tol, iter, relres); else - printf (["cgs stopped at iteration %i ", - "without converging to the desired tolerance %e\n", + printf (["cgs stopped at iteration %i without converging to the desired tolerance %e\n", "because the maximum number of iterations was reached.\n", "The iterate returned (number %i) has relative residual %e\n"], - iter,tol,iter,relres); + iter, tol, iter, relres); endif endif