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Use it in GENPDE. Update docs
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Salvatore Filippone
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@@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
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<B> Previous:</B> <A NAME="tex2html1816"
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<B> <A NAME="tex2html1824"
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HREF="node126.html">Iterative Methods</A>
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<B> Previous:</B> <A NAME="tex2html1821"
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HREF="node126.html">Iterative Methods</A>
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<B> <A NAME="tex2html1827"
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HREF="node1.html">Contents</A></B>
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<BR><BR>
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<BR>
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<BR>
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<!--End of Navigation Panel-->
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<H2><A NAME="SECTION000130000000000000000">
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Bibliography</A>
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</H2><DL COMPACT><DD><P></P><DT><A NAME="DesPat:11">1</A>
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<DD>
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D. Barbieri, V. Cardellini, S. Filippone and D. Rouson
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<EM>Design Patterns for Scientific Computations on Sparse Matrices</EM>,
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HPSS 2011, Algorithms and Programming Tools for Next-Generation High-Performance Scientific Software, Bordeaux, Sep. 2011
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<P>
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<P></P><DT><A NAME="PARA04FOREST">2</A>
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<DD>
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G. Bella, S. Filippone, A. De Maio and M. Testa,
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<EM>A Simulation Model for Forest Fires</EM>,
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in J. Dongarra, K. Madsen, J. Wasniewski, editors,
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Proceedings of PARA 04 Workshop on State of the Art
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in Scientific Computing, pp. 546-553, Lecture Notes in Computer Science,
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Springer, 2005.
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<P></P><DT><A NAME="2007d">3</A>
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<DD> A. Buttari, D. di Serafino, P. D'Ambra, S. Filippone,<BR>
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2LEV-D2P4: a package of high-performance preconditioners,<BR>
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Applicable Algebra in Engineering, Communications and Computing,
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Volume 18, Number 3, May, 2007, pp. 223-239
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<P></P><DT><A NAME="2007c">4</A>
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<DD> P. D'Ambra, S. Filippone, D. Di Serafino<BR>
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On the Development of PSBLAS-based Parallel Two-level Schwarz Preconditioners
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<H2><A NAME="SECTION000121000000000000000"></A><A NAME="krylov"></A>
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<BR>
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Applied Numerical Mathematics, Elsevier Science,
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Volume 57, Issues 11-12, November-December 2007, Pages 1181-1196.
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psb_krylov -- Krylov Methods Driver
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Routine
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</H2>
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<P>
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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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<P>
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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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<BR><P></P>
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<DIV ALIGN="CENTER">
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<!-- MATH
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\begin{displaymath}
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err = \frac{\|r_i\|}{(\|A\|\|x_i\|+\|b\|)} < eps
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\end{displaymath}
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-->
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<IMG
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WIDTH="204" HEIGHT="44" BORDER="0"
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SRC="img156.png"
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ALT="\begin{displaymath}err = \frac{\Vert r_i\Vert}{(\Vert A\Vert\Vert x_i\Vert+\Vert b\Vert)} < eps \end{displaymath}">
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</DIV>
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<BR CLEAR="ALL">
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<P></P>
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or the 2-norm residual reduction
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<BR><P></P>
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<DIV ALIGN="CENTER">
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<!-- MATH
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\begin{displaymath}
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err = \frac{\|r_i\|}{\|b\|_2} < eps
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\end{displaymath}
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-->
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<IMG
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WIDTH="121" HEIGHT="44" BORDER="0"
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SRC="img157.png"
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ALT="\begin{displaymath}err = \frac{\Vert r_i\Vert}{\Vert b\Vert _2} < eps \end{displaymath}">
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</DIV>
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<BR CLEAR="ALL">
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<P></P>
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according to the value passed through the istop argument (see
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later). In the above formulae, <IMG
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WIDTH="18" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img158.png"
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ALT="$x_i$"> is the tentative solution and
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<IMG
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WIDTH="91" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img159.png"
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ALT="$r_i=b-Ax_i$"> the corresponding residual at the <IMG
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WIDTH="9" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
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SRC="img4.png"
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ALT="$i$">-th iteration.
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<P>
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<P></P><DT><A NAME="BLAS2">5</A>
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<DD>
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Dongarra, J. J., DuCroz, J., Hammarling, S. and Hanson, R.,
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An Extended Set of Fortran Basic Linear Algebra Subprograms,
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ACM Trans. Math. Softw. vol. 14, 1-17, 1988.
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<P></P><DT><A NAME="BLAS3">6</A>
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<DD>
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Dongarra, J., DuCroz, J., Hammarling, S. and Duff, I.,
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A Set of level 3 Basic Linear Algebra Subprograms,
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ACM Trans. Math. Softw. vol. 16, 1-17, 1990.
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<P></P><DT><A NAME="BLACS">7</A>
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<DD>
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J. J. Dongarra and R. C. Whaley,
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<EM>A User's Guide to the BLACS v. 1.1</EM>,
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Lapack Working Note 94, Tech. Rep. UT-CS-95-281, University of
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Tennessee, March 1995 (updated May 1997).
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<P></P><DT><A NAME="sblas97">8</A>
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<DD>
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I. Duff, M. Marrone, G. Radicati and C. Vittoli,
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<EM>Level 3 Basic Linear Algebra Subprograms for Sparse Matrices:
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a User Level Interface</EM>,
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ACM Transactions on Mathematical Software, 23(3), pp. 379-401, 1997.
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<P></P><DT><A NAME="sblas02">9</A>
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<DD>
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I. Duff, M. Heroux and R. Pozo,
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<EM>An Overview of the Sparse Basic Linear
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Algebra Subprograms: the New Standard from the BLAS Technical Forum</EM>,
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ACM Transactions on Mathematical Software, 28(2), pp. 239-267, 2002.
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<P></P><DT><A NAME="PSBLAS">10</A>
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<DD>
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S. Filippone and M. Colajanni,
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<EM>PSBLAS: A Library for Parallel Linear Algebra
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Computation on Sparse Matrices</EM>,
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<BR>
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ACM Transactions on Mathematical Software, 26(4), pp. 527-550, 2000.
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<P></P><DT><A NAME="Sparse03">11</A>
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<DD>
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S. Filippone and A. Buttari,
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<EM>Object-Oriented Techniques for Sparse Matrix Computations in Fortran 2003</EM>,
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<IMG
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WIDTH="482" HEIGHT="35" ALIGN="BOTTOM" BORDER="0"
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SRC="img160.png"
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ALT="\begin{lstlisting}
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call psb_krylov(method,a,prec,b,x,eps,desc_a,info,&
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& itmax,iter,err,itrace,irst,istop,cond)
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\end{lstlisting}">
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<BR>
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ACM Transactions on Mathematical Software, 38(4), 2012.
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<P></P><DT><A NAME="KIVA3PSBLAS">12</A>
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<DD>
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S. Filippone, P. D'Ambra, M. Colajanni,
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<EM>Using a Parallel Library of Sparse Linear Algebra in a Fluid Dynamics
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||||
Applications Code on Linux Clusters</EM>,
|
||||
in G. Joubert, A. Murli, F. Peters, M. Vanneschi, editors,
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Parallel Computing - Advances & Current Issues,
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pp. 441-448, Imperial College Press, 2002.
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<P></P><DT><A NAME="DesignPatterns">13</A>
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<DD>
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Gamma, E., Helm, R., Johnson, R., and Vlissides,
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J. 1995.
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<EM>Design Patterns: Elements of Reusable Object-Oriented Software</EM>.
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Addison-Wesley.
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<P>
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<P></P><DT><A NAME="METIS">14</A>
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<DL>
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<DT><STRONG>Type:</STRONG></DT>
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<DD>Synchronous.
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</DD>
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<DT><STRONG><B>On Entry</B></STRONG></DT>
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<DD>
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||||
Karypis, G. and Kumar, V.,
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||||
<EM>METIS: Unstructured Graph Partitioning and Sparse Matrix
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||||
Ordering System</EM>.
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||||
Minneapolis, MN 55455: University of Minnesota, Department of
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||||
Computer Science, 1995.
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||||
Internet Address: <code>http://www.cs.umn.edu/~karypis</code>.
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<P></P><DT><A NAME="BLAS1">15</A>
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<DD>
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Lawson, C., Hanson, R., Kincaid, D. and Krogh, F.,
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||||
Basic Linear Algebra Subprograms for Fortran usage,
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||||
ACM Trans. Math. Softw. vol. 5, 38-329, 1979.
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</DD>
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<DT><STRONG>method</STRONG></DT>
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<DD>a string that defines the iterative method to be
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used. Supported values are:
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<DL>
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<DT><STRONG>CG:</STRONG></DT>
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<DD>the Conjugate Gradient method;
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</DD>
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<DT><STRONG>CGS:</STRONG></DT>
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<DD>the Conjugate Gradient Stabilized method;
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<P>
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<P></P><DT><A NAME="machiels">16</A>
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<DD>
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Machiels, L. and Deville, M.
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<EM>Fortran 90: An entry to object-oriented programming for the solution
|
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of partial differential equations.</EM>
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||||
ACM Trans. Math. Softw. vol. 23, 32-49.
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<P></P><DT><A NAME="metcalf">17</A>
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<DD>
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Metcalf, M., Reid, J. and Cohen, M.
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<EM>Fortran 95/2003 explained.</EM>
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Oxford University Press, 2004.
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||||
<P></P><DT><A NAME="RouXiaXu:11">18</A>
|
||||
<DD>
|
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Rouson, D.W.I., Xia, J., Xu, X.: Scientific Software Design: The
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Object-Oriented Way. Cambridge University Press (2011)
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</DD>
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<DT><STRONG>BICG:</STRONG></DT>
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<DD>the Bi-Conjugate Gradient method;
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</DD>
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<DT><STRONG>BICGSTAB:</STRONG></DT>
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<DD>the Bi-Conjugate Gradient Stabilized method;
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</DD>
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<DT><STRONG>BICGSTABL:</STRONG></DT>
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<DD>the Bi-Conjugate Gradient Stabilized method with restarting;
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</DD>
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<DT><STRONG>RGMRES:</STRONG></DT>
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<DD>the Generalized Minimal Residual method with restarting.
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</DD>
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</DL>
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</DD>
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<DT><STRONG>a</STRONG></DT>
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<DD>the local portion of global sparse matrix
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<IMG
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WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img1.png"
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ALT="$A$">.
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<BR>
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Scope: <B>local</B>
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<BR>
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Type: <B>required</B>
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<BR>
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Intent: <B>in</B>.
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<BR>
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Specified as: a structured data of type spdata<TT>psb_Tspmat_type</TT>.
|
||||
</DD>
|
||||
<DT><STRONG>prec</STRONG></DT>
|
||||
<DD>The data structure containing the preconditioner.
|
||||
<BR>
|
||||
Scope: <B>local</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR>
|
||||
Specified as: a structured data of type precdata<TT>psb_prec_type</TT>.
|
||||
</DD>
|
||||
<DT><STRONG>b</STRONG></DT>
|
||||
<DD>The RHS vector.
|
||||
<BR>
|
||||
Scope: <B>local</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR>
|
||||
Specified as: a rank one array or an object of type vdata<TT>psb_T_vect_type</TT>.
|
||||
</DD>
|
||||
<DT><STRONG>x</STRONG></DT>
|
||||
<DD>The initial guess.
|
||||
<BR>
|
||||
Scope: <B>local</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>inout</B>.
|
||||
<BR>
|
||||
Specified as: a rank one array or an object of type vdata<TT>psb_T_vect_type</TT>.
|
||||
</DD>
|
||||
<DT><STRONG>eps</STRONG></DT>
|
||||
<DD>The stopping tolerance.
|
||||
<BR>
|
||||
Scope: <B>global</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR>
|
||||
Specified as: a real number.
|
||||
</DD>
|
||||
<DT><STRONG>desc_a</STRONG></DT>
|
||||
<DD>contains data structures for communications.
|
||||
<BR>
|
||||
Scope: <B>local</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR>
|
||||
Specified as: a structured data of type descdata<TT>psb_desc_type</TT>.
|
||||
</DD>
|
||||
<DT><STRONG>itmax</STRONG></DT>
|
||||
<DD>The maximum number of iterations to perform.
|
||||
<BR>
|
||||
Scope: <B>global</B>
|
||||
<BR>
|
||||
Type: <B>optional</B>
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR>
|
||||
Default: <IMG
|
||||
WIDTH="100" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img161.png"
|
||||
ALT="$itmax = 1000$">.
|
||||
<BR>
|
||||
Specified as: an integer variable <IMG
|
||||
WIDTH="75" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img162.png"
|
||||
ALT="$itmax \ge 1$">.
|
||||
</DD>
|
||||
<DT><STRONG>itrace</STRONG></DT>
|
||||
<DD>If <IMG
|
||||
WIDTH="29" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img111.png"
|
||||
ALT="$>0$"> print out an informational message about
|
||||
convergence every <IMG
|
||||
WIDTH="46" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img163.png"
|
||||
ALT="$itrace$"> iterations.
|
||||
<BR>
|
||||
Scope: <B>global</B>
|
||||
<BR>
|
||||
Type: <B>optional</B>
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR></DD>
|
||||
<DT><STRONG>irst</STRONG></DT>
|
||||
<DD>An integer specifying the restart parameter.
|
||||
<BR>
|
||||
Scope: <B>global</B>
|
||||
<BR>
|
||||
Type: <B>optional</B>.
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR>
|
||||
Values: <IMG
|
||||
WIDTH="59" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img164.png"
|
||||
ALT="$irst>0$">. This is employed for the BiCGSTABL or RGMRES
|
||||
methods, otherwise it is ignored.
|
||||
|
||||
<P>
|
||||
<P></P><DT><A NAME="MPI1">19</A>
|
||||
</DD>
|
||||
<DT><STRONG>istop</STRONG></DT>
|
||||
<DD>An integer specifying the stopping criterion.
|
||||
<BR>
|
||||
Scope: <B>global</B>
|
||||
<BR>
|
||||
Type: <B>optional</B>.
|
||||
<BR>
|
||||
Intent: <B>in</B>.
|
||||
<BR>
|
||||
Values: 1: use the normwise backward error, 2: use the scaled 2-norm
|
||||
of the residual. Default: 2.
|
||||
</DD>
|
||||
<DT><STRONG><B>On Return</B></STRONG></DT>
|
||||
<DD>
|
||||
M. Snir, S. Otto, S. Huss-Lederman, D. Walker and J. Dongarra,
|
||||
<EM>MPI: The Complete Reference. Volume 1 - The MPI Core</EM>, second edition,
|
||||
MIT Press, 1998.
|
||||
</DD>
|
||||
<DT><STRONG>x</STRONG></DT>
|
||||
<DD>The computed solution.
|
||||
<BR>
|
||||
Scope: <B>local</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>inout</B>.
|
||||
<BR>
|
||||
Specified as: a rank one array or an object of type vdata<TT>psb_T_vect_type</TT>.
|
||||
</DD>
|
||||
<DT><STRONG>iter</STRONG></DT>
|
||||
<DD>The number of iterations performed.
|
||||
<BR>
|
||||
Scope: <B>global</B>
|
||||
<BR>
|
||||
Type: <B>optional</B>
|
||||
<BR>
|
||||
Intent: <B>out</B>.
|
||||
<BR>
|
||||
Returned as: an integer variable.
|
||||
</DD>
|
||||
<DT><STRONG>err</STRONG></DT>
|
||||
<DD>The convergence estimate on exit.
|
||||
<BR>
|
||||
Scope: <B>global</B>
|
||||
<BR>
|
||||
Type: <B>optional</B>
|
||||
<BR>
|
||||
Intent: <B>out</B>.
|
||||
<BR>
|
||||
Returned as: a real number.
|
||||
</DD>
|
||||
<DT><STRONG>cond</STRONG></DT>
|
||||
<DD>An estimate of the condition number of matrix <IMG
|
||||
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img1.png"
|
||||
ALT="$A$">; only
|
||||
available with the <IMG
|
||||
WIDTH="29" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img165.png"
|
||||
ALT="$CG$"> method.
|
||||
<BR>
|
||||
Scope: <B>global</B>
|
||||
<BR>
|
||||
Type: <B>optional</B>
|
||||
<BR>
|
||||
Intent: <B>out</B>.
|
||||
<BR>
|
||||
Returned as: a real number.
|
||||
</DD>
|
||||
<DT><STRONG>info</STRONG></DT>
|
||||
<DD>Error code.
|
||||
<BR>
|
||||
Scope: <B>local</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>out</B>.
|
||||
<BR>
|
||||
An integer value; 0 means no error has been detected.
|
||||
</DD>
|
||||
</DL>
|
||||
|
||||
<P>
|
||||
<BR><HR>
|
||||
|
||||
<P>
|
||||
|
||||
<P>
|
||||
|
||||
<P>
|
||||
<HR>
|
||||
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|
||||
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|
||||
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||||
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||||
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||||
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||||
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||||
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|
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Reference in New Issue
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