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603 lines
20 KiB
TeX
603 lines
20 KiB
TeX
\section{Iterative Methods}
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\label{sec:methods}
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In this chapter we provide routines for preconditioners and iterative
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methods. The interfaces for Krylov subspace methods are available in
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the module \verb|psb_krylov_mod|.
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%
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% Krylov Methods driver routine
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%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subroutine{psb\_krylov \label{krylov}}{Krylov Methods Driver Routine}
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This subroutine is a driver that provides a general interface for all
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the Krylov-Subspace family methods implemented in PSBLAS version 2.
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The stopping criterion is the normwise backward error, in the infinity
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norm, i.e. the iteration is stopped when
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\[ err = \frac{\|r_i\|}{(\|A\|\|x_i\|+\|b\|)} < eps \]
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or the 2-norm residual reduction
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\[ err = \frac{\|r_i\|}{\|b\|_2} < eps \]
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according to the value passed through the istop argument (see
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later). In the above formulae, $x_i$ is the tentative solution and
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$r_i=b-Ax_i$ the corresponding residual at the $i$-th iteration.
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\syntax{call psb\_krylov}{method,a,prec,b,x,eps,desc\_a,info,itmax,iter,err,itrace,irst,istop}
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\begin{description}
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\item[Type:] Synchronous.
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\item[\bf On Entry]
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\item[method] a string that defines the iterative method to be
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used. Supported values are:
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\begin{description}
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\item[CG]: the Conjugate Gradient method;
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\item[CGS]:the Conjugate Gradient Stabilized method;
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\item[BICG]: the Bi-Conjugate Gradient method;
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\item[BICGSTAB]: the Bi-Conjugate Gradient Stabilized method;
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\item[BICGSTABL]: the Bi-Conjugate Gradient Stabilized method with restarting;
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\item[RGMRES]: the Generalized Minimal Residual method with restarting.
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\end{description}
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\item[a] the local portion of global sparse matrix
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$A$. \\
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Scope: {\bf local} \\
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Type: {\bf required}\\
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Intent: {\bf in}.\\
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Specified as: a structured data of type \spdata.
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\item[prec] The data structure containing the preconditioner.\\
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Scope: {\bf local} \\
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Type: {\bf required}\\
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Intent: {\bf in}.\\
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Specified as: a structured data of type \precdata.
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\item[b] The RHS vector. \\
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Scope: {\bf local} \\
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Type: {\bf required}\\
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Intent: {\bf in}.\\
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Specified as: a rank one array.
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\item[x] The initial guess. \\
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Scope: {\bf local} \\
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Type: {\bf required}\\
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Intent: {\bf inout}.\\
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Specified as: a rank one array.
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\item[eps] The stopping tolerance. \\
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Scope: {\bf global} \\
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Type: {\bf required}\\
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Intent: {\bf in}.\\
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Specified as: a real number.
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\item[desc\_a] contains data structures for communications.\\
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Scope: {\bf local} \\
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Type: {\bf required}\\
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Intent: {\bf in}.\\
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Specified as: a structured data of type \descdata.
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\item[itmax] The maximum number of iterations to perform.\\
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Scope: {\bf global} \\
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Type: {\bf optional}\\
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Intent: {\bf in}.\\
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Default: $itmax = 1000$.\\
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Specified as: an integer variable $itmax \ge 1$.
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\item[itrace] If $>0$ print out an informational message about
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convergence every $itrace$ iterations.\\
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Scope: {\bf global} \\
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Type: {\bf optional}\\
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Intent: {\bf in}.\\
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\item[irst] An integer specifying the restart parameter.\\
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Scope: {\bf global} \\
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Type: {\bf optional}.\\
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Intent: {\bf in}.\\
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Values: $irst>0$. This is employed for the BiCGSTABL or RGMRES
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methods, otherwise it is ignored.
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\item[istop] An integer specifying the stopping criterion.\\
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Scope: {\bf global} \\
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Type: {\bf optional}.\\
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Intent: {\bf in}.\\
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Values: 1: use the normwise backward error, 2: use the scaled 2-norm
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of the residual. Default: 1.
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\item[\bf On Return]
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\item[x] The computed solution. \\
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Scope: {\bf local} \\
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Type: {\bf required}\\
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Intent: {\bf inout}.\\
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Specified as: a rank one array.
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\item[iter] The number of iterations performed.\\
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Scope: {\bf global} \\
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Type: {\bf optional}\\
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Intent: {\bf out}.\\
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Returned as: an integer variable.
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\item[err] The convergence estimate on exit.\\
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Scope: {\bf global} \\
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Type: {\bf optional}\\
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Intent: {\bf out}.\\
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Returned as: a real number.
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\item[info] Error code.\\
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Scope: {\bf local} \\
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Type: {\bf required} \\
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Intent: {\bf out}.\\
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An integer value; 0 means no error has been detected.
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\end{description}
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%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%% %
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%% % CG
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%% %
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%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%% \subroutine{psb\_cg \label{cg}}{CG Iterative Method}
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%% This subroutine implements the CG method with restarting. The
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%% stopping criterion is the normwise backward error, in the infinity
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%% norm, i.e. the iteration is stopped when
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%% \[ \frac{\|r\|}{(\|A\|\|x\|+\|b\|)} < eps \]
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%% or
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%% \[ \frac{\|r_i\|}{\|b\|_2} < eps \]
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%% according to the value passed through the istop argument (see later).
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%% \syntax{call psb\_cg}{a,prec,b,x,eps,desc\_a,info,itmax,iter,err,itrace,istop}
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%% \begin{description}
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%% \item[\bf On Entry]
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%% \item[a] the local portion of global sparse matrix
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%% $A$. \\
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%% Scope: {\bf local} \\
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%% Type: {\bf required}\\
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%% Specified as: a structured data of type \spdata.
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%% \item[prec] The data structure containing the preconditioner.\\
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%% Scope: {\bf local} \\
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%% Type: {\bf required}\\
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%% Specified as: a structured data of type \precdata.
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%% \item[b] The RHS vector. \\
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%% Scope: {\bf local} \\
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%% Type: {\bf required}\\
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%% Specified as: a rank one array.
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%% \item[x] The initial guess. \\
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%% Scope: {\bf local} \\
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%% Type: {\bf required}\\
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%% Specified as: a rank one array.
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%% \item[eps] The stopping tolerance. \\
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%% Scope: {\bf global} \\
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%% Type: {\bf required}\\
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%% Specified as: a real number.
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%% \item[desc\_a] contains data structures for communications.\\
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%% Scope: {\bf local} \\
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%% Type: {\bf required}\\
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%% Specified as: a structured data of type \descdata.
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%% \item[itmax] The maximum number of iterations to perform.\\
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%% Scope: {\bf global} \\
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%% Type: {\bf optional}\\
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%% Default: $itmax = 1000$.\\
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%% Specified as: an integer variable $itmax \ge 1$.
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%% \item[itrace] If $>0$ print out an informational message about
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%% convergence every $itrace$ iterations.\\
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%% Scope: {\bf global} \\
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%% Type: {\bf optional}\\
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%% \item[istop] An integer specifying the stopping criterion.\\
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%% Scope: {\bf global} \\
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%% Type: {\bf optional}\\
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%% \item[\bf On Return]
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%% \item[x] The computed solution. \\
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%% Scope: {\bf local} \\
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%% Type: {\bf required}\\
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%% Specified as: a rank one array.
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%% \item[iter] The number of iterations performed.\\
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%% Scope: {\bf global} \\
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%% Type: {\bf optional}\\
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%% Returned as: an integer variable.
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%% \item[err] The error estimate on exit.\\
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%% Scope: {\bf global} \\
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%% Type: {\bf optional}\\
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%% Returned as: a real number.
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%% \item[info] Error code.\\
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%% Scope: {\bf local} \\
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%% Type: {\bf required} \\
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%% An integer value; 0 means no error has been detected.
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%% \end{description}
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%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%% %
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%% % CGS
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%% %
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%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%% \subroutine{psb\_cgs \label{cgs}}{CGS Iterative Method}
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%% This subroutine implements the CGS method with restarting. The
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%% stopping criterion is the normwise backward error, in the infinity
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%% norm, i.e. the iteration is stopped when
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%% \[ \frac{\|r\|}{(\|A\|\|x\|+\|b\|)} < eps \]
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%% or
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%% \[ \frac{\|r_i\|}{\|b\|_2} < eps \]
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%% according to the value passed through the istop argument (see later).
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%% \syntax{call psb\_cgs}{a,prec,b,x,eps,desc\_a,info,itmax,iter,err,itrace,istop}
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%% \begin{description}
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%% \item[\bf On Entry]
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%% \item[a] the local portion of global sparse matrix
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%% $A$. \\
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%% Scope: {\bf local} \\
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%% Type: {\bf required}\\
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%% Specified as: a structured data of type \spdata.
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%% \item[prec] The data structure containing the preconditioner.\\
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%% Scope: {\bf local} \\
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%% Type: {\bf required}\\
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%% Specified as: a structured data of type \precdata.
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%% \item[b] The RHS vector. \\
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%% Scope: {\bf local} \\
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%% Type: {\bf required}\\
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%% Specified as: a rank one array.
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%% \item[x] The initial guess. \\
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%% Scope: {\bf local} \\
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%% Type: {\bf required}\\
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%% Specified as: a rank one array.
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%% \item[eps] The stopping tolerance. \\
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%% Scope: {\bf global} \\
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%% Type: {\bf required}\\
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%% Specified as: a real number.
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%% \item[desc\_a] contains data structures for communications.\\
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%% Scope: {\bf local} \\
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%% Type: {\bf required}\\
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%% Specified as: a structured data of type \descdata.
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%% \item[itmax] The maximum number of iterations to perform.\\
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%% Scope: {\bf global} \\
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%% Type: {\bf optional}\\
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%% Default: $itmax = 1000$.\\
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%% Specified as: an integer variable $itmax \ge 1$.
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%% \item[itrace] If $>0$ print out an informational message about
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%% convergence every $itrace$ iterations.\\
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%% Scope: {\bf global} \\
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%% Type: {\bf optional}\\
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%% \item[istop] An integer specifying the stopping criterion.\\
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%% Scope: {\bf global} \\
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%% Type: {\bf optional}\\
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%% \item[\bf On Return]
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%% \item[x] The computed solution. \\
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%% Scope: {\bf local} \\
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%% Type: {\bf required}\\
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%% Specified as: a rank one array.
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%% \item[iter] The number of iterations performed.\\
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%% Scope: {\bf global} \\
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%% Type: {\bf optional}\\
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%% Returned as: an integer variable.
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%% \item[err] The error estimate on exit.\\
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%% Scope: {\bf global} \\
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%% Type: {\bf optional}\\
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%% Returned as: a real number.
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%% \item[info] Error code.\\
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%% Scope: {\bf local} \\
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%% Type: {\bf required} \\
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%% An integer value; 0 means no error has been detected.
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%% \end{description}
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%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%% %
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%% % BiCG
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%% %
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%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%% \subroutine{psb\_bicg \label{bicg}}{BiCG Iterative Method}
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%% This subroutine implements the BiCG method with restarting. The
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%% stopping criterion is the normwise backward error, in the infinity
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%% norm, i.e. the iteration is stopped when
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%% \[ \frac{\|r\|}{(\|A\|\|x\|+\|b\|)} < eps \]
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%% or
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%% \[ \frac{\|r_i\|}{\|b\|_2} < eps \]
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%% according to the value passed through the istop argument (see later).
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%% \syntax{call psb\_bicg}{a,prec,b,x,eps,desc\_a,info,itmax,iter,err,itrace,istop}
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%% \begin{description}
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%% \item[\bf On Entry]
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%% \item[a] the local portion of global sparse matrix
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%% $A$. \\
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%% Scope: {\bf local} \\
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%% Type: {\bf required}\\
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%% Specified as: a structured data of type \spdata.
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%% \item[prec] The data structure containing the preconditioner.\\
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%% Scope: {\bf local} \\
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%% Type: {\bf required}\\
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%% Specified as: a structured data of type \precdata.
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%% \item[b] The RHS vector. \\
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%% Scope: {\bf local} \\
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%% Type: {\bf required}\\
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%% Specified as: a rank one array.
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%% \item[x] The initial guess. \\
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%% Scope: {\bf local} \\
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%% Type: {\bf required}\\
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%% Specified as: a rank one array.
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%% \item[eps] The stopping tolerance. \\
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%% Scope: {\bf global} \\
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%% Type: {\bf required}\\
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%% Specified as: a real number.
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%% \item[desc\_a] contains data structures for communications.\\
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%% Scope: {\bf local} \\
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%% Type: {\bf required}\\
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%% Specified as: a structured data of type \descdata.
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%% \item[itmax] The maximum number of iterations to perform.\\
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%% Scope: {\bf global} \\
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%% Type: {\bf optional}\\
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%% Default: $itmax = 1000$.\\
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%% Specified as: an integer variable $itmax \ge 1$.
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%% \item[itrace] If $>0$ print out an informational message about
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%% convergence every $itrace$ iterations.\\
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%% Scope: {\bf global} \\
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%% Type: {\bf optional}\\
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%% \item[istop] An integer specifying the stopping criterion.\\
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%% Scope: {\bf global} \\
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%% Type: {\bf optional}\\
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%% \item[\bf On Return]
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%% \item[x] The computed solution. \\
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%% Scope: {\bf local} \\
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%% Type: {\bf required}\\
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%% Specified as: a rank one array.
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%% \item[iter] The number of iterations performed.\\
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%% Scope: {\bf global} \\
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%% Type: {\bf optional}\\
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%% Returned as: an integer variable.
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%% \item[err] The error estimate on exit.\\
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%% Scope: {\bf global} \\
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%% Type: {\bf optional}\\
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%% Returned as: a real number.
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%% \item[info] Error code.\\
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%% Scope: {\bf local} \\
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%% Type: {\bf required} \\
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%% An integer value; 0 means no error has been detected.
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%% \end{description}
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%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%% %
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%% % BiCGSTAB
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%% %
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%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%% \subroutine{psb\_bicgstab \label{bicgstab}}{BiCGSTAB Iterative Method}
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%% This subroutine implements the BiCGSTAB method with restarting. The
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%% stopping criterion is the normwise backward error, in the infinity
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%% norm, i.e. the iteration is stopped when
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%% \[ \frac{\|r\|}{(\|A\|\|x\|+\|b\|)} < eps \]
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%% or
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%% \[ \frac{\|r_i\|}{\|b\|_2} < eps \]
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%% according to the value passed through the istop argument (see later).
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%% \syntax{call psb\_bicgstab}{a,prec,b,x,eps,desc\_a,info,itmax,iter,err,itrace,istop}
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%% \begin{description}
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%% \item[\bf On Entry]
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%% \item[a] the local portion of global sparse matrix
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%% $A$. \\
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%% Scope: {\bf local} \\
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%% Type: {\bf required}\\
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%% Specified as: a structured data of type \spdata.
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%% \item[prec] The data structure containing the preconditioner.\\
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%% Scope: {\bf local} \\
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%% Type: {\bf required}\\
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%% Specified as: a structured data of type \precdata.
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%% \item[b] The RHS vector. \\
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%% Scope: {\bf local} \\
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%% Type: {\bf required}\\
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%% Specified as: a rank one array.
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%% \item[x] The initial guess. \\
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%% Scope: {\bf local} \\
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%% Type: {\bf required}\\
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%% Specified as: a rank one array.
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%% \item[eps] The stopping tolerance. \\
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%% Scope: {\bf global} \\
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%% Type: {\bf required}\\
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%% Specified as: a real number.
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%% \item[desc\_a] contains data structures for communications.\\
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%% Scope: {\bf local} \\
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%% Type: {\bf required}\\
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%% Specified as: a structured data of type \descdata.
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%% \item[itmax] The maximum number of iterations to perform.\\
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%% Scope: {\bf global} \\
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%% Type: {\bf optional}\\
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|
%% Default: $itmax = 1000$.\\
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%% Specified as: an integer variable $itmax \ge 1$.
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%% \item[itrace] If $>0$ print out an informational message about
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%% convergence every $itrace$ iterations.\\
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%% Scope: {\bf global} \\
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%% Type: {\bf optional}\\
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%% \item[istop] An integer specifying the stopping criterion.\\
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%% Scope: {\bf global} \\
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%% Type: {\bf optional}\\
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%% \item[\bf On Return]
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%% \item[x] The computed solution. \\
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%% Scope: {\bf local} \\
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%% Type: {\bf required}\\
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%% Specified as: a rank one array.
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%% \item[iter] The number of iterations performed.\\
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%% Scope: {\bf global} \\
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%% Type: {\bf optional}\\
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%% Returned as: an integer variable.
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%% \item[err] The error estimate on exit.\\
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%% Scope: {\bf global} \\
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%% Type: {\bf optional}\\
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%% Returned as: a real number.
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%% \item[info] Error code.\\
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%% Scope: {\bf local} \\
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%% Type: {\bf required} \\
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%% An integer value; 0 means no error has been detected.
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%% \end{description}
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%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%% %
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%% % BiCGSTAB(L)
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%% %
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%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%% \subroutine{psb\_bicgstabl \label{bicgstabl}}{BiCGSTAB-$l$ Iterative Method}
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%% This subroutine implements the BiCGSTAB-$l$ method with restarting. The
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%% stopping criterion is the normwise backward error, in the infinity
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%% norm, i.e. the iteration is stopped when
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%% \[ \frac{\|r\|}{(\|A\|\|x\|+\|b\|)} < eps \]
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%% or
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%% \[ \frac{\|r_i\|}{\|b\|_2} < eps \]
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%% according to the value passed through the istop argument (see later).
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|
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%% \syntax{call psb\_bicgstab}{a,prec,b,x,eps,desc\_a,info,itmax,iter,err,itrace,irst,istop}
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%% \begin{description}
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%% \item[\bf On Entry]
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|
%% \item[a] the local portion of global sparse matrix
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%% $A$. \\
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%% Scope: {\bf local} \\
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|
%% Type: {\bf required}\\
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|
%% Specified as: a structured data of type \spdata.
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%% \item[prec] The data structure containing the preconditioner.\\
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%% Scope: {\bf local} \\
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|
%% Type: {\bf required}\\
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%% Specified as: a structured data of type \precdata.
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%% \item[b] The RHS vector. \\
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%% Scope: {\bf local} \\
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%% Type: {\bf required}\\
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%% Specified as: a rank one array.
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|
%% \item[x] The initial guess. \\
|
|
%% Scope: {\bf local} \\
|
|
%% Type: {\bf required}\\
|
|
%% Specified as: a rank one array.
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|
%% \item[eps] The stopping tolerance. \\
|
|
%% Scope: {\bf global} \\
|
|
%% Type: {\bf required}\\
|
|
%% Specified as: a real number.
|
|
%% \item[desc\_a] contains data structures for communications.\\
|
|
%% Scope: {\bf local} \\
|
|
%% Type: {\bf required}\\
|
|
%% Specified as: a structured data of type \descdata.
|
|
%% \item[itmax] The maximum number of iterations to perform.\\
|
|
%% Scope: {\bf global} \\
|
|
%% Type: {\bf optional}\\
|
|
%% Default: $itmax = 1000$.\\
|
|
%% Specified as: an integer variable $itmax \ge 1$.
|
|
%% \item[itrace] If $>0$ print out an informational message about
|
|
%% convergence every $itrace$ iterations.\\
|
|
%% Scope: {\bf global} \\
|
|
%% Type: {\bf optional}\\
|
|
%% \item[irst] An integer specifying the restarting iteration.\\
|
|
%% Scope: {\bf global} \\
|
|
%% Type: {\bf optional}\\
|
|
%% \item[istop] An integer specifying the stopping criterion.\\
|
|
%% Scope: {\bf global} \\
|
|
%% Type: {\bf optional}\\
|
|
|
|
%% \item[\bf On Return]
|
|
%% \item[x] The computed solution. \\
|
|
%% Scope: {\bf local} \\
|
|
%% Type: {\bf required}\\
|
|
%% Specified as: a rank one array.
|
|
%% \item[iter] The number of iterations performed.\\
|
|
%% Scope: {\bf global} \\
|
|
%% Type: {\bf optional}\\
|
|
%% Returned as: an integer variable.
|
|
%% \item[err] The error estimate on exit.\\
|
|
%% Scope: {\bf global} \\
|
|
%% Type: {\bf optional}\\
|
|
%% Returned as: a real number.
|
|
%% \item[info] Error code.\\
|
|
%% Scope: {\bf local} \\
|
|
%% Type: {\bf required} \\
|
|
%% An integer value; 0 means no error has been detected.
|
|
%% \end{description}
|
|
|
|
|
|
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
%% %
|
|
%% % GMRES
|
|
%% %
|
|
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
%% \subroutine{psb\_gmres \label{gmres}}{GMRES Iterative Method}
|
|
|
|
%% This subroutine implements the GMRES method with restarting. The
|
|
%% stopping criterion is the normwise backward error, in the infinity
|
|
%% norm, i.e. the iteration is stopped when
|
|
%% \[ \frac{\|r\|}{(\|A\|\|x\|+\|b\|)} < eps \]
|
|
%% or
|
|
%% \[ \frac{\|r_i\|}{\|b\|_2} < eps \]
|
|
%% according to the value passed through the istop argument (see later).
|
|
|
|
|
|
%% \syntax{call psb\_gmres}{a,prec,b,x,eps,desc\_a,info,itmax,iter,err,itrace,irst,istop}
|
|
|
|
%% \begin{description}
|
|
%% \item[\bf On Entry]
|
|
%% \item[a] the local portion of global sparse matrix
|
|
%% $A$. \\
|
|
%% Scope: {\bf local} \\
|
|
%% Type: {\bf required}\\
|
|
%% Specified as: a structured data of type \spdata.
|
|
%% \item[prec] The data structure containing the preconditioner.\\
|
|
%% Scope: {\bf local} \\
|
|
%% Type: {\bf required}\\
|
|
%% Specified as: a structured data of type \precdata.
|
|
%% \item[b] The RHS vector. \\
|
|
%% Scope: {\bf local} \\
|
|
%% Type: {\bf required}\\
|
|
%% Specified as: a rank one array.
|
|
%% \item[x] The initial guess. \\
|
|
%% Scope: {\bf local} \\
|
|
%% Type: {\bf required}\\
|
|
%% Specified as: a rank one array.
|
|
%% \item[eps] The stopping tolerance. \\
|
|
%% Scope: {\bf global} \\
|
|
%% Type: {\bf required}\\
|
|
%% Specified as: a real number.
|
|
%% \item[desc\_a] contains data structures for communications.\\
|
|
%% Scope: {\bf local} \\
|
|
%% Type: {\bf required}\\
|
|
%% Specified as: a structured data of type \descdata.
|
|
%% \item[itmax] The maximum number of iterations to perform.\\
|
|
%% Scope: {\bf global} \\
|
|
%% Type: {\bf optional}\\
|
|
%% Default: $itmax = 1000$.\\
|
|
%% Specified as: an integer variable $itmax \ge 1$.
|
|
%% \item[itrace] If $>0$ print out an informational message about
|
|
%% convergence every $itrace$ iterations.\\
|
|
%% Scope: {\bf global} \\
|
|
%% Type: {\bf optional}\\
|
|
%% \item[irst] An integer specifying the restart iteration.\\
|
|
%% Scope: {\bf global} \\
|
|
%% Type: {\bf optional}\\
|
|
%% \item[istop] An integer specifying the stopping criterion.\\
|
|
%% Scope: {\bf global} \\
|
|
%% Type: {\bf optional}\\
|
|
|
|
%% \item[\bf On Return]
|
|
%% \item[x] The computed solution. \\
|
|
%% Scope: {\bf local} \\
|
|
%% Type: {\bf required}\\
|
|
%% Specified as: a rank one array.
|
|
%% \item[iter] The number of iterations performed.\\
|
|
%% Scope: {\bf global} \\
|
|
%% Type: {\bf optional}\\
|
|
%% Returned as: an integer variable.
|
|
%% \item[err] The error estimate on exit.\\
|
|
%% Scope: {\bf global} \\
|
|
%% Type: {\bf optional}\\
|
|
%% Returned as: a real number.
|
|
%% \item[info] Error code.\\
|
|
%% Scope: {\bf local} \\
|
|
%% Type: {\bf required} \\
|
|
%% An integer value; 0 means no error has been detected.
|
|
%% \end{description}
|
|
|
|
|
|
|
|
|
|
|
|
%%% Local Variables:
|
|
%%% mode: latex
|
|
%%% TeX-master: "userguide"
|
|
%%% End:
|