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New interfaces for building hierachy and preconditioner.
stopcriterion
Salvatore Filippone 9 years ago
parent d989714ee9
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@ -126,21 +126,25 @@ Mar. 31, 2016
<LI><A NAME="tex2html35"
HREF="node19.html">Subroutine mld_precbld</A>
<LI><A NAME="tex2html36"
HREF="node20.html">Subroutine mld_precaply</A>
HREF="node20.html">Subroutine mld_hierarchy_bld</A>
<LI><A NAME="tex2html37"
HREF="node21.html">Subroutine mld_precfree</A>
HREF="node21.html">Subroutine mld_ml_prec_bld</A>
<LI><A NAME="tex2html38"
HREF="node22.html">Subroutine mld_precdescr</A>
</UL>
<BR>
HREF="node22.html">Subroutine mld_precaply</A>
<LI><A NAME="tex2html39"
HREF="node23.html">Error Handling</A>
HREF="node23.html">Subroutine mld_precfree</A>
<LI><A NAME="tex2html40"
HREF="node24.html">License</A>
HREF="node24.html">Subroutine mld_precdescr</A>
</UL>
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HREF="node25.html">Error Handling</A>
<LI><A NAME="tex2html42"
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@ -26,26 +26,26 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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@ -88,26 +88,26 @@ the user interface of MLD2P4.
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@ -68,15 +68,15 @@ into subdomains, e.g. in a PDE discretization, to (approximately) solving the
subproblems corresponding to the subdomains and to building an approximate
solution of the original problem from the local solutions
[<A
HREF="node25.html#Cai_Widlund_92">6</A>,<A
HREF="node25.html#dd1_94">7</A>,<A
HREF="node25.html#dd2_96">23</A>].
HREF="node27.html#Cai_Widlund_92">6</A>,<A
HREF="node27.html#dd1_94">7</A>,<A
HREF="node27.html#dd2_96">23</A>].
<P>
<I>Additive Schwarz</I> preconditioners are DD preconditioners using overlapping
submatrices, i.e. with some common rows, to couple the local information
related to the submatrices (see, e.g., [<A
HREF="node25.html#dd2_96">23</A>]).
HREF="node27.html#dd2_96">23</A>]).
The main motivation for choosing Additive Schwarz preconditioners is their
intrinsic parallelism. A drawback of these
preconditioners is that the number of iterations of the preconditioned solvers
@ -95,7 +95,7 @@ correction. In this context, the one-level preconditioner is often
called `smoother'. Different two-level preconditioners are obtained by varying the
choice of the smoother and of the coarse-level correction, and the
way they are combined [<A
HREF="node25.html#dd2_96">23</A>]. The same reasoning can be applied starting
HREF="node27.html#dd2_96">23</A>]. The same reasoning can be applied starting
from the coarse-level system, i.e. a coarse-space correction can be built
from this system, thus obtaining <I>multi-level</I> preconditioners.
@ -119,25 +119,25 @@ are considered. The algebraic approach builds coarse-space corrections using onl
information. It performs a fully automatic coarsening and enforces the interplay between
the fine and coarse levels by suitably choosing the coarse space and the coarse-to-fine
interpolation [<A
HREF="node25.html#StubenGMD69_99">25</A>].
HREF="node27.html#StubenGMD69_99">25</A>].
<P>
MLD2P4 uses a pure algebraic approach for building the sequence of coarse matrices
starting from the original matrix. The algebraic approach is based on the <I>smoothed
aggregation</I> algorithm [<A
HREF="node25.html#BREZINA_VANEK">1</A>,<A
HREF="node25.html#VANEK_MANDEL_BREZINA">27</A>]. A decoupled version
HREF="node27.html#BREZINA_VANEK">1</A>,<A
HREF="node27.html#VANEK_MANDEL_BREZINA">27</A>]. A decoupled version
of this algorithm is implemented, where the smoothed aggregation is applied locally
to each submatrix [<A
HREF="node25.html#TUMINARO_TONG">26</A>]. In the next two subsections we provide
HREF="node27.html#TUMINARO_TONG">26</A>]. In the next two subsections we provide
a brief description of the multi-level Schwarz preconditioners and of the smoothed
aggregation technique as implemented in MLD2P4. For further details the reader
is referred to [<A
HREF="node25.html#para_04">2</A>,<A
HREF="node25.html#aaecc_07">3</A>,<A
HREF="node25.html#apnum_07">4</A>,<A
HREF="node25.html#MLD2P4_TOMS">8</A>,<A
HREF="node25.html#dd2_96">23</A>].
HREF="node27.html#para_04">2</A>,<A
HREF="node27.html#aaecc_07">3</A>,<A
HREF="node27.html#apnum_07">4</A>,<A
HREF="node27.html#MLD2P4_TOMS">8</A>,<A
HREF="node27.html#dd2_96">23</A>].
<P>
<BR><HR>
@ -145,34 +145,34 @@ is referred to [<A
<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
<UL>
<LI><A NAME="tex2html199"
<LI><A NAME="tex2html203"
HREF="node12.html">Multi-level Schwarz Preconditioners</A>
<LI><A NAME="tex2html200"
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HREF="node13.html">Smoothed Aggregation</A>
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@ -295,15 +295,15 @@ ILU(<IMG
WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img36.png"
ALT="$p,t$">) [<A
HREF="node25.html#Saad_book">22</A>, Chapter 10].
HREF="node27.html#Saad_book">22</A>, Chapter 10].
<P>
A variant of the classical AS preconditioner that outperforms it
in terms of convergence rate and of computation and communication
time on parallel distributed-memory computers is the so-called <I>Restricted AS
(RAS)</I> preconditioner&nbsp;[<A
HREF="node25.html#CAI_SARKIS">5</A>,<A
HREF="node25.html#EFSTATHIOU">15</A>]. It
HREF="node27.html#CAI_SARKIS">5</A>,<A
HREF="node27.html#EFSTATHIOU">15</A>]. It
is obtained by zeroing the components of <IMG
WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img33.png"
@ -386,8 +386,8 @@ of <IMG
WIDTH="23" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
SRC="img11.png"
ALT="$W$"> increases [<A
HREF="node25.html#dd1_94">7</A>,<A
HREF="node25.html#dd2_96">23</A>]. To reduce the dependency
HREF="node27.html#dd1_94">7</A>,<A
HREF="node27.html#dd2_96">23</A>]. To reduce the dependency
of the number of iterations on the degree of parallelism we may
introduce a global coupling among the overlapping partitions by defining
a coarse-space approximation <IMG
@ -642,12 +642,12 @@ in which the coarse-level correction is re-applied starting from the current
coarse-level system. The corresponding preconditioners, called <I>multi-level</I>
preconditioners, can significantly reduce the computational cost of preconditioning
with respect to the two-level case (see [<A
HREF="node25.html#dd2_96">23</A>, Chapter 3]).
HREF="node27.html#dd2_96">23</A>, Chapter 3]).
Additive and hybrid multilevel preconditioners
are obtained as direct extensions of the two-level counterparts.
For a detailed descrition of them, the reader is
referred to [<A
HREF="node25.html#dd2_96">23</A>, Chapter 3].
HREF="node27.html#dd2_96">23</A>, Chapter 3].
The algorithm for the application of a multi-level hybrid
post-smoothed preconditioner <IMG
WIDTH="23" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
@ -738,26 +738,26 @@ $w = y_1$;
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@ -65,8 +65,8 @@ the coarse-level matrix <IMG
SRC="img44.png"
ALT="$A_C$">, MLD2P4 uses the <I>smoothed aggregation</I>
algorithm described in [<A
HREF="node25.html#BREZINA_VANEK">1</A>,<A
HREF="node25.html#VANEK_MANDEL_BREZINA">27</A>].
HREF="node27.html#BREZINA_VANEK">1</A>,<A
HREF="node27.html#VANEK_MANDEL_BREZINA">27</A>].
The basic idea of this algorithm is to build a coarse set of vertices
<IMG
WIDTH="32" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
@ -114,8 +114,8 @@ Three main steps can be identified in the smoothed aggregation procedure:
<P>
To perform the coarsening step, we have implemented the aggregation algorithm sketched
in [<A
HREF="node25.html#apnum_07">4</A>]. According to [<A
HREF="node25.html#VANEK_MANDEL_BREZINA">27</A>], a modification of
HREF="node27.html#apnum_07">4</A>]. According to [<A
HREF="node27.html#VANEK_MANDEL_BREZINA">27</A>], a modification of
this algorithm has been actually considered,
in which each aggregate <IMG
WIDTH="26" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
@ -171,9 +171,9 @@ dependent on the number of processors and on the initial partitioning of the mat
Nevertheless, this algorithm has been chosen for the implementation in MLD2P4,
since it has been shown to produce good results in practice
[<A
HREF="node25.html#aaecc_07">3</A>,<A
HREF="node25.html#apnum_07">4</A>,<A
HREF="node25.html#TUMINARO_TONG">26</A>].
HREF="node27.html#aaecc_07">3</A>,<A
HREF="node27.html#apnum_07">4</A>,<A
HREF="node27.html#TUMINARO_TONG">26</A>].
<P>
The prolongator <IMG
@ -251,8 +251,8 @@ P_C = S P,
in order to remove oscillatory components from the range of the prolongator
and hence to improve the convergence properties of the multi-level
Schwarz method [<A
HREF="node25.html#BREZINA_VANEK">1</A>,<A
HREF="node25.html#StubenGMD69_99">25</A>].
HREF="node27.html#BREZINA_VANEK">1</A>,<A
HREF="node27.html#StubenGMD69_99">25</A>].
A simple choice for <IMG
WIDTH="16" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
SRC="img84.png"
@ -284,30 +284,30 @@ using some estimate of the spectral radius of <IMG
WIDTH="50" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
SRC="img87.png"
ALT="$D^{-1}A$"> [<A
HREF="node25.html#BREZINA_VANEK">1</A>].
HREF="node27.html#BREZINA_VANEK">1</A>].
<P>
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@ -59,7 +59,7 @@ Getting Started
<P>
We describe the basics for building and applying MLD2P4 one-level and multi-level
Schwarz preconditioners with the Krylov solvers included in PSBLAS [<A
HREF="node25.html#PSBLASGUIDE">16</A>].
HREF="node27.html#PSBLASGUIDE">16</A>].
The following steps are required:
<OL>
@ -80,6 +80,18 @@ The following steps are required:
Note that these strings are valid also if uppercase letters are substituted by
corresponding lowercase ones.
</LI>
<LI><I>Modify the aggregation parameters.</I> This is performed by
the routine <code>mld_precset</code>.
This routine must be called only if the user wants to modify the default values
of the parameters associated to the aggregation hierarchy construction.
Examples of use of <code>mld_precset</code> are given in
Section&nbsp;<A HREF="node15.html#sec:examples">5.1</A>; a complete list of all the
preconditioner parameters and their allowed and default values is provided in
Section&nbsp;<A HREF="node16.html#sec:userinterface">6</A>, Tables&nbsp;<A HREF="#tab:p_type">2</A>-<A HREF="#tab:p_coarse">6</A>.
</LI>
<LI><I>Build the aggregation hierarchy for a given matrix.</I> This is performed by
the routine <code>mld_hierarchy_bld</code>.
</LI>
<LI><I>Modify the selected preconditioner type, by properly setting
preconditioner parameters.</I> This is performed by the routine <code>mld_precset</code>.
This routine must be called only if the user wants to modify the default values
@ -90,7 +102,7 @@ The following steps are required:
Section&nbsp;<A HREF="node16.html#sec:userinterface">6</A>, Tables&nbsp;<A HREF="#tab:p_type">2</A>-<A HREF="#tab:p_coarse">6</A>.
</LI>
<LI><I>Build the preconditioner for a given matrix.</I> This is performed by
the routine <code>mld_precbld</code>.
the routine <code>mld_ml_prec_bld</code>.
</LI>
<LI><I>Apply the preconditioner at each iteration of a Krylov solver.</I>
This is performed by the routine <code>mld_precaply</code>. When using the PSBLAS Krylov solvers,
@ -121,8 +133,8 @@ machines, it often leads to the smallest execution time when applied to
linear systems coming from finite-difference discretizations of basic
elliptic PDE problems, considered as standard tests for multi-level Schwarz
preconditioners [<A
HREF="node25.html#aaecc_07">3</A>,<A
HREF="node25.html#apnum_07">4</A>]. However, this solver does
HREF="node27.html#aaecc_07">3</A>,<A
HREF="node27.html#apnum_07">4</A>]. However, this solver does
not necessarily correspond to the smallest number of iterations of the
preconditioned Krylov method, which is usually obtained by applying
a direct solver to the coarsest-level system, e.g. based on the LU
@ -131,7 +143,7 @@ for the coarsest-level solvers available in MLD2P4).
<P>
<BR><P></P>
<DIV ALIGN="CENTER"><A NAME="943"></A>
<DIV ALIGN="CENTER"><A NAME="949"></A>
<TABLE>
<CAPTION><STRONG>Table 1:</STRONG>
Preconditioner types, corresponding strings and default choices.
@ -198,32 +210,32 @@ Preconditioner types, corresponding strings and default choices.
<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
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HREF="node15.html">Examples</A>
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@ -25,26 +25,26 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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@ -75,7 +75,7 @@ in the directory <code>examples/fileread</code> of the MLD2P4 tree (see
Section&nbsp;<A HREF="node10.html#sec:ex_and_test">3.5</A>).
For details on the use of the PSBLAS routines, see the PSBLAS User's
Guide [<A
HREF="node25.html#PSBLASGUIDE">16</A>].
HREF="node27.html#PSBLASGUIDE">16</A>].
<P>
The setup and application of the default multi-level
@ -86,7 +86,7 @@ the corresponding Fortran 95 codes are available in <code>examples/fileread/</co
<P>
<DIV ALIGN="CENTER"><A NAME="fig:ex_default"></A><A NAME="946"></A>
<DIV ALIGN="CENTER"><A NAME="fig:ex_default"></A><A NAME="952"></A>
<TABLE>
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 2:</STRONG>
Setup and application of the default multi-level Schwarz preconditioner.
@ -128,7 +128,9 @@ Setup and application of the default multi-level Schwarz preconditioner.
call mld_precinit(P,'ML',info)
!
! build the preconditioner
call mld_precbld(A,desc_A,P,info)
call mld_hierarchy_bld(A,desc_A,P,info)
call mld_ml_prec_bld(A,desc_A,P,info)
!
! set the solver parameters and the initial guess
... ...
@ -162,12 +164,12 @@ Figure&nbsp;<A HREF="#fig:ex_3lh">3</A> shows how to set a three-level hybrid Sc
preconditioner, which uses block Jacobi with ILU(0) on the
local blocks as post-smoother, has a coarsest matrix replicated on the processors,
and solves the coarsest-level system with the LU factorization from UMFPACK&nbsp;[<A
HREF="node25.html#UMFPACK">9</A>].
HREF="node27.html#UMFPACK">9</A>].
Figure&nbsp;<A HREF="#fig:ex_3lhm">4</A> shows how to set a three-level preconditioner
similar to the one of&nbsp;<A HREF="#fig:ex_3lh">3</A>, but the coarsest-level
systems is solved with the multifrontal factorization from
MUMPS&nbsp;[<A
HREF="node25.html#UMFPACK">9</A>].
HREF="node27.html#UMFPACK">9</A>].
Note that MUMPS can be used on both replicated and distributed
coarsest level matrices, as a global and local solver respectively.
The number of levels is specified by using <code>mld_precinit</code>; the other
@ -202,7 +204,7 @@ boundary conditions are also available in the directory <code>examples/pdegen</c
<P>
<DIV ALIGN="CENTER"><A NAME="fig:ex_3lh"></A><A NAME="948"></A>
<DIV ALIGN="CENTER"><A NAME="fig:ex_3lh"></A><A NAME="954"></A>
<TABLE>
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 3:</STRONG>
Setup of a hybrid three-level Schwarz preconditioner.</CAPTION>
@ -216,11 +218,14 @@ Setup of a hybrid three-level Schwarz preconditioner.</CAPTION>
! block Jacobi (with ILU(0) on the blocks) as post-smoother,
! a coarsest matrix replicated on the processors, and the
! LU factorization from UMFPACK as coarse-level solver
call mld_precinit(P,'ML',info,nlev=3)
call mld_precinit(P,'ML',info)
call mld_hierarchy_bld(A,desc_A,P,info)
call_mld_precset(P,'SMOOTHER_TYPE','BJAC',info)
call_mld_precset(P,'SMOOTHER_POS,'POST'w,info)
call mld_precset(P,'COARSE_MAT','REPL',info)
call mld_precset(P,'COARSE_SOLVE','UMF',info)
call mld_ml_prec_bld(A,desc_A,P,info)
... ...
</PRE>
</TD></TR>
@ -235,7 +240,7 @@ Setup of a hybrid three-level Schwarz preconditioner.</CAPTION>
<P>
<DIV ALIGN="CENTER"><A NAME="fig:ex_3lhm"></A><A NAME="950"></A>
<DIV ALIGN="CENTER"><A NAME="fig:ex_3lhm"></A><A NAME="956"></A>
<TABLE>
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 4:</STRONG>
Setup of a hybrid three-level Schwarz preconditioner.</CAPTION>
@ -251,10 +256,12 @@ Setup of a hybrid three-level Schwarz preconditioner.</CAPTION>
! multifrontal solver in MUMPS as coarse-level solver
call mld_precinit(P,'ML',info,nlev=3)
call mld_hierarchy_bld(A,desc_A,P,info)
call mld_precset(P,mld_smoother_type_,'BJAC',info)
call mld_precset(P,mld_coarse_mat_,'REPL',info)
call mld_precset(P,mld_coarse_solve_,'MUMPS',info)
call mld_ml_prec_bld(A,desc_A,P,info)
... ...
</PRE>
</TD></TR>
@ -269,7 +276,7 @@ Setup of a hybrid three-level Schwarz preconditioner.</CAPTION>
<P>
<DIV ALIGN="CENTER"><A NAME="fig:ex_3la"></A><A NAME="952"></A>
<DIV ALIGN="CENTER"><A NAME="fig:ex_3la"></A><A NAME="958"></A>
<TABLE>
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 5:</STRONG>
Setup of an additive three-level Schwarz preconditioner.</CAPTION>
@ -284,9 +291,11 @@ Setup of an additive three-level Schwarz preconditioner.</CAPTION>
! post-smoother, and 5 block-Jacobi sweeps (with UMFPACK LU
! on the blocks) as distributed coarsest-level solver
call mld_precinit(P,'ML',info,nlev=3)
call mld_ml_prec_bld(A,desc_A,P,info)
call mld_precset(P,'ML_TYPE','ADD',info)
call_mld_precset(P,'SMOOTHER_POS','TWOSIDE',info)
call mld_precset(P,'COARSE_SWEEPS',5,info)
call mld_ml_prec_bld(A,desc_A,P,info)
... ...
</PRE>
</TD></TR>
@ -301,7 +310,7 @@ Setup of an additive three-level Schwarz preconditioner.</CAPTION>
<P>
<DIV ALIGN="CENTER"><A NAME="fig:ex_1l"></A><A NAME="954"></A>
<DIV ALIGN="CENTER"><A NAME="fig:ex_1l"></A><A NAME="960"></A>
<TABLE>
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 6:</STRONG>
Setup of a one-level Schwarz preconditioner.</CAPTION>
@ -314,6 +323,7 @@ Setup of a one-level Schwarz preconditioner.</CAPTION>
! set RAS with overlap 2 and ILU(0) on the local blocks
call mld_precinit(P,'AS',info)
call mld_precset(P,'SUB_OVR',2,info)
call mld_precbld(A,desc_A,P,info)
... ...
</PRE>
</TD></TR>
@ -327,26 +337,26 @@ Setup of a one-level Schwarz preconditioner.</CAPTION>
<P>
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@ -113,42 +113,46 @@ A description of each routine is given in the remainder of this section.
<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
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<LI><A NAME="tex2html266"
HREF="node21.html">Subroutine mld_ml_prec_bld</A>
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@ -94,7 +94,7 @@ according to the preconditioner type chosen by the user.
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>integer, intent(out)</code>.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>Error code. If no error, 0 is returned. See Section&nbsp;<A HREF="node23.html#sec:errors">7</A> for details.</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>Error code. If no error, 0 is returned. See Section&nbsp;<A HREF="node25.html#sec:errors">7</A> for details.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>nlev</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>integer, optional, intent(in)</code>.</TD>
@ -114,26 +114,26 @@ according to the preconditioner type chosen by the user.
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@ -144,7 +144,7 @@ modified, and thus has no direct knowledge about the new type.
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>integer, intent(out)</code>.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>Error code. If no error, 0 is returned. See Section&nbsp;<A HREF="node23.html#sec:errors">7</A>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>Error code. If no error, 0 is returned. See Section&nbsp;<A HREF="node25.html#sec:errors">7</A>
for details.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>pos</code></TD>
@ -209,7 +209,7 @@ according to their needs.
<P>
<BR><P></P>
<DIV ALIGN="CENTER"><A NAME="1324"></A>
<DIV ALIGN="CENTER"><A NAME="1363"></A>
<TABLE>
<CAPTION><STRONG>Table 2:</STRONG>
Parameters defining the type of multi-level preconditioner.
@ -253,7 +253,7 @@ Parameters defining the type of multi-level preconditioner.
<P>
<BR><P></P>
<DIV ALIGN="CENTER"><A NAME="1326"></A>
<DIV ALIGN="CENTER"><A NAME="1365"></A>
<TABLE>
<CAPTION><STRONG>Table 3:</STRONG>
Parameters defining the one-level preconditioner used as smoother.
@ -405,7 +405,7 @@ Parameters defining the one-level preconditioner used as smoother.
<P>
<BR><P></P>
<DIV ALIGN="CENTER"><A NAME="1328"></A>
<DIV ALIGN="CENTER"><A NAME="1367"></A>
<TABLE>
<CAPTION><STRONG>Table 4:</STRONG>
Parameters defining the aggregation algorithm.
@ -490,7 +490,7 @@ Parameters defining the aggregation algorithm.
<P>
<BR><P></P>
<DIV ALIGN="CENTER"><A NAME="1330"></A>
<DIV ALIGN="CENTER"><A NAME="1369"></A>
<TABLE>
<CAPTION><STRONG>Table 5:</STRONG>
Parameters defining the aggregation algorithm.
@ -602,7 +602,7 @@ Parameters defining the aggregation algorithm.
<P>
<BR><P></P>
<DIV ALIGN="CENTER"><A NAME="1333"></A>
<DIV ALIGN="CENTER"><A NAME="1372"></A>
<TABLE>
<CAPTION><STRONG>Table 6:</STRONG>
Parameters defining the coarse-space correction at the coarsest
@ -717,26 +717,26 @@ level.</CAPTION>
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@ -67,6 +67,9 @@ This routine builds the preconditioner according to the requirements made by
the user through the routines <code>mld_precinit</code> and <code>mld_precset</code>.
<P>
For multilevel preconditioner this routine is supported for backward
compatibility, but we recommend to use the routines of
Sec.&nbsp;<A HREF="node20.html#sec:hier_bld">6.4</A> and&nbsp;<A HREF="node21.html#sec:ml_prec_bld">6.5</A>.
<FONT SIZE="+1"><B>Arguments</B></FONT>
<P>
@ -80,7 +83,7 @@ the user through the routines <code>mld_precinit</code> and <code>mld_precset</c
to the real/complex,
single/double precision version of MLD2P4 under use.
See the PSBLAS User's Guide for details [<A
HREF="node25.html#PSBLASGUIDE">16</A>].</TD>
HREF="node27.html#PSBLASGUIDE">16</A>].</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>desc_a</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(psb_desc_type), intent(in)</code>.</TD>
@ -88,7 +91,7 @@ single/double precision version of MLD2P4 under use.
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The communication descriptor of <code>a</code>. See the PSBLAS User's Guide for
details [<A
HREF="node25.html#PSBLASGUIDE">16</A>].</TD>
HREF="node27.html#PSBLASGUIDE">16</A>].</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>p</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(mld_</code><I>x</I><code>prec_type), intent(inout)</code>.</TD>
@ -101,34 +104,33 @@ single/double precision version of MLD2P4 under use.
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>integer, intent(out)</code>.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>Error code. If no error, 0 is returned. See Section&nbsp;<A HREF="node23.html#sec:errors">7</A> for details.</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>Error code. If no error, 0 is returned. See Section&nbsp;<A HREF="node25.html#sec:errors">7</A> for details.</TD>
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<LI><A NAME="tex2html79"
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<LI><A NAME="tex2html80"
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<LI><A NAME="tex2html81"
HREF="node19.html">Subroutine mld_precbld</A>
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HREF="node18.html">Subroutine mld_precset</A>
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HREF="node19.html">Subroutine mld_precbld</A>
<LI><A NAME="tex2html84"
HREF="node22.html">Subroutine mld_precdescr</A>
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<BR>
HREF="node20.html">Subroutine mld_hierarchy_bld</A>
<LI><A NAME="tex2html85"
HREF="node23.html">Error Handling</A>
HREF="node21.html">Subroutine mld_ml_prec_bld</A>
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HREF="node22.html">Subroutine mld_precaply</A>
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@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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<H2><A NAME="SECTION00084000000000000000"></A><A NAME="sec:precaply"></A>
<H2><A NAME="SECTION00084000000000000000"></A><A NAME="sec:hier_bld"></A>
<BR>
Subroutine mld_precaply
Subroutine mld_hierarchy_bld
</H2>
<P>
<DIV ALIGN="CENTER">
<code>mld_precaply(p,x,y,desc_a,info)</code>
<BR><code>mld_precaply(p,x,y,desc_a,info,trans,work)</code>
<code>mld_hierachy_bld(a,desc_a,p,info)</code>
<BR>
</DIV>
<P>
This routine computes <!-- MATH
$y = op(M^{-1})\, x$
-->
<IMG
WIDTH="118" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
SRC="img101.png"
ALT="$y = op(M^{-1}) x$">, where <IMG
WIDTH="23" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="img60.png"
ALT="$M$"> is a previously built
preconditioner, stored into <code>p</code>, and <IMG
WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img102.png"
ALT="$op$">
denotes the preconditioner itself or its transpose, according to
the value of <code>trans</code>.
Note that, when MLD2P4 is used with a Krylov solver from PSBLAS,
<code>mld_precaply</code> is called within the PSBLAS routine <code>psb_krylov</code>
and hence it is completely transparent to the user.
This routine builds the aggregation hierarchy according to the requirements made by
the user through the routines <code>mld_precinit</code> and <code>mld_precset</code>.
<P>
<FONT SIZE="+1"><B>Arguments</B></FONT>
<P>
<TABLE CELLPADDING=3>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>p</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(mld_</code><I>x</I><code>prec_type), intent(inout)</code>.</TD>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>a</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(psb_</code><I>x</I><code>spmat_type), intent(in)</code>.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The preconditioner data structure, containing the local part of <IMG
WIDTH="23" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="img60.png"
ALT="$M$">.
Note that <I>x</I> must be chosen according
to the real/complex, single/double precision version of MLD2P4 under use.</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The sparse matrix structure containing the local part of the
matrix to be preconditioned. Note that <I>x</I> must be chosen according
to the real/complex,
single/double precision version of MLD2P4 under use.
See the PSBLAS User's Guide for details [<A
HREF="node27.html#PSBLASGUIDE">16</A>].</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>x</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><I>type</I><code>(</code><I>kind_parameter</I><code>), dimension(:), intent(in)</code>.</TD>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>desc_a</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(psb_desc_type), intent(in)</code>.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The local part of the vector <IMG
WIDTH="15" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
SRC="img103.png"
ALT="$x$">. Note that <I>type</I> and
<I>kind_parameter</I> must be chosen according
to the real/complex, single/double precision version of MLD2P4 under use.</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The communication descriptor of <code>a</code>. See the PSBLAS User's Guide for
details [<A
HREF="node27.html#PSBLASGUIDE">16</A>].</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>y</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><I>type</I><code>(</code><I>kind_parameter</I><code>), dimension(:), intent(out)</code>.</TD>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>p</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(mld_</code><I>x</I><code>prec_type), intent(inout)</code>.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The local part of the vector <IMG
WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img104.png"
ALT="$y$">. Note that <I>type</I> and
<I>kind_parameter</I> must be chosen according
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The preconditioner data structure. Note that <I>x</I> must be chosen according
to the real/complex, single/double precision version of MLD2P4 under use.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>desc_a</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(psb_desc_type), intent(in)</code>.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The communication descriptor associated to the matrix to be
preconditioned.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>info</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>integer, intent(out)</code>.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>Error code. If no error, 0 is returned. See Section&nbsp;<A HREF="node23.html#sec:errors">7</A> for details.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>trans</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>character(len=1), optional, intent(in).</code></TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>If <code>trans</code> = <code>'N','n'</code> then <!-- MATH
$op(M^{-1}) = M^{-1}$
-->
<IMG
WIDTH="132" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
SRC="img105.png"
ALT="$op(M^{-1}) = M^{-1}$">;
if <code>trans</code> = <code>'T','t'</code> then <!-- MATH
$op(M^{-1}) = M^{-T}$
-->
<IMG
WIDTH="135" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
SRC="img106.png"
ALT="$op(M^{-1}) = M^{-T}$">
(transpose of <IMG
WIDTH="48" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
SRC="img107.png"
ALT="$M^{-1})$">; if <code>trans</code> = <code>'C','c'</code> then <!-- MATH
$op(M^{-1}) = M^{-C}$
-->
<IMG
WIDTH="136" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
SRC="img108.png"
ALT="$op(M^{-1}) = M^{-C}$">
(conjugate transpose of <IMG
WIDTH="48" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
SRC="img107.png"
ALT="$M^{-1})$">.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>work</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><I>type</I><code>(</code><I>kind_parameter</I><code>), dimension(:), optional, target</code>.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>Workspace. Its size should be at
least <code>4 * psb_cd_get_local_</code> <code>cols(desc_a)</code> (see the PSBLAS User's Guide).
Note that <I>type</I> and <I>kind_parameter</I> must be chosen according
to the real/complex, single/double precision version of MLD2P4 under use.</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>Error code. If no error, 0 is returned. See Section&nbsp;<A HREF="node25.html#sec:errors">7</A> for details.</TD>
</TR>
</TABLE>
<P>
<P>
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<H2><A NAME="SECTION00085000000000000000"></A><A NAME="sec:precfree"></A>
<H2><A NAME="SECTION00085000000000000000"></A><A NAME="sec:ml_prec_bld"></A>
<BR>
Subroutine mld_precfree
Subroutine mld_ml_prec_bld
</H2>
<P>
<DIV ALIGN="CENTER">
<code>mld_precfree(p,info)</code>
<code>mld_ml_prec_bld(a,desc_a,p,info)</code>
<BR>
</DIV>
<P>
This routine deallocates the preconditioner data structure.
This routine builds the preconditioner according to the requirements made by
the user through the routines <code>mld_precinit</code> and
<code>mld_precset</code>, based on the aggregation hierahy produced by a
previous call to <code>mld_hierarchy_bld</code> (see
Sec.&nbsp;<A HREF="node20.html#sec:hier_bld">6.4</A>).
<P>
<FONT SIZE="+1"><B>Arguments</B></FONT>
<P>
<TABLE CELLPADDING=3>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>a</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(psb_</code><I>x</I><code>spmat_type), intent(in)</code>.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The sparse matrix structure containing the local part of the
matrix to be preconditioned. Note that <I>x</I> must be chosen according
to the real/complex,
single/double precision version of MLD2P4 under use.
See the PSBLAS User's Guide for details [<A
HREF="node27.html#PSBLASGUIDE">16</A>].</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>desc_a</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(psb_desc_type), intent(in)</code>.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The communication descriptor of <code>a</code>. See the PSBLAS User's Guide for
details [<A
HREF="node27.html#PSBLASGUIDE">16</A>].</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>p</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=298><code>type(mld_</code><I>x</I><code>prec_type), intent(inout)</code>.</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(mld_</code><I>x</I><code>prec_type), intent(inout)</code>.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=298>The preconditioner data structure. Note that <I>x</I> must be chosen according
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The preconditioner data structure. Note that <I>x</I> must be chosen according
to the real/complex, single/double precision version of MLD2P4 under use.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>info</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=298><code>integer, intent(out)</code>.</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>integer, intent(out)</code>.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=298>Error code. If no error, 0 is returned. See Section&nbsp;<A HREF="node23.html#sec:errors">7</A> for details.</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>Error code. If no error, 0 is returned. See Section&nbsp;<A HREF="node25.html#sec:errors">7</A> for details.</TD>
</TR>
</TABLE>
<P>
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<H2><A NAME="SECTION00086000000000000000"></A><A NAME="sec:precdescr"></A>
<H2><A NAME="SECTION00086000000000000000"></A><A NAME="sec:precaply"></A>
<BR>
Subroutine mld_precdescr
Subroutine mld_precaply
</H2>
<P>
<DIV ALIGN="CENTER">
<code>mld_precdescr(p,info)</code>
<BR><code>mld_precdescr(p,info,iout)</code>
<code>mld_precaply(p,x,y,desc_a,info)</code>
<BR><code>mld_precaply(p,x,y,desc_a,info,trans,work)</code>
<BR>
</DIV>
<P>
This routine prints a description of the preconditioner to the standard output or
to a file. It must be called after <code>mld_precbld</code> has been called.
This routine computes <!-- MATH
$y = op(M^{-1})\, x$
-->
<IMG
WIDTH="118" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
SRC="img101.png"
ALT="$y = op(M^{-1}) x$">, where <IMG
WIDTH="23" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="img60.png"
ALT="$M$"> is a previously built
preconditioner, stored into <code>p</code>, and <IMG
WIDTH="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img102.png"
ALT="$op$">
denotes the preconditioner itself or its transpose, according to
the value of <code>trans</code>.
Note that, when MLD2P4 is used with a Krylov solver from PSBLAS,
<code>mld_precaply</code> is called within the PSBLAS routine <code>psb_krylov</code>
and hence it is completely transparent to the user.
<P>
<FONT SIZE="+1"><B>Arguments</B></FONT>
@ -72,29 +90,122 @@ to a file. It must be called after <code>mld_precbld</code> has been called.
<P>
<TABLE CELLPADDING=3>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>p</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(mld_</code><I>x</I><code>prec_type), intent(in)</code>.</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(mld_</code><I>x</I><code>prec_type), intent(inout)</code>.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The preconditioner data structure. Note that <I>x</I> must be chosen according
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The preconditioner data structure, containing the local part of <IMG
WIDTH="23" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="img60.png"
ALT="$M$">.
Note that <I>x</I> must be chosen according
to the real/complex, single/double precision version of MLD2P4 under use.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>x</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><I>type</I><code>(</code><I>kind_parameter</I><code>), dimension(:), intent(in)</code>.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The local part of the vector <IMG
WIDTH="15" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
SRC="img103.png"
ALT="$x$">. Note that <I>type</I> and
<I>kind_parameter</I> must be chosen according
to the real/complex, single/double precision version of MLD2P4 under use.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>y</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><I>type</I><code>(</code><I>kind_parameter</I><code>), dimension(:), intent(out)</code>.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The local part of the vector <IMG
WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img104.png"
ALT="$y$">. Note that <I>type</I> and
<I>kind_parameter</I> must be chosen according
to the real/complex, single/double precision version of MLD2P4 under use.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>desc_a</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(psb_desc_type), intent(in)</code>.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The communication descriptor associated to the matrix to be
preconditioned.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>info</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>integer, intent(out)</code>.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>Error code. If no error, 0 is returned. See Section&nbsp;<A HREF="node23.html#sec:errors">7</A> for details.</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>Error code. If no error, 0 is returned. See Section&nbsp;<A HREF="node25.html#sec:errors">7</A> for details.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>trans</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>character(len=1), optional, intent(in).</code></TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>If <code>trans</code> = <code>'N','n'</code> then <!-- MATH
$op(M^{-1}) = M^{-1}$
-->
<IMG
WIDTH="132" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
SRC="img105.png"
ALT="$op(M^{-1}) = M^{-1}$">;
if <code>trans</code> = <code>'T','t'</code> then <!-- MATH
$op(M^{-1}) = M^{-T}$
-->
<IMG
WIDTH="135" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
SRC="img106.png"
ALT="$op(M^{-1}) = M^{-T}$">
(transpose of <IMG
WIDTH="48" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
SRC="img107.png"
ALT="$M^{-1})$">; if <code>trans</code> = <code>'C','c'</code> then <!-- MATH
$op(M^{-1}) = M^{-C}$
-->
<IMG
WIDTH="136" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
SRC="img108.png"
ALT="$op(M^{-1}) = M^{-C}$">
(conjugate transpose of <IMG
WIDTH="48" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
SRC="img107.png"
ALT="$M^{-1})$">.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>iout</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>integer, intent(in), optional</code>.</TD>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>work</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><I>type</I><code>(</code><I>kind_parameter</I><code>), dimension(:), optional, target</code>.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The id of the file where the preconditioner description
will be printed; the default is the standard output.</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>Workspace. Its size should be at
least <code>4 * psb_cd_get_local_</code> <code>cols(desc_a)</code> (see the PSBLAS User's Guide).
Note that <I>type</I> and <I>kind_parameter</I> must be chosen according
to the real/complex, single/double precision version of MLD2P4 under use.</TD>
</TR>
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<H1><A NAME="SECTION00090000000000000000"></A><A NAME="sec:errors"></A>
<H2><A NAME="SECTION00087000000000000000"></A><A NAME="sec:precfree"></A>
<BR>
Subroutine mld_precfree
</H2>
<P>
<DIV ALIGN="CENTER">
<code>mld_precfree(p,info)</code>
<BR>
Error Handling
</H1>
</DIV>
<P>
The error handling in MLD2P4 is based on the PSBLAS (version 2) error
handling. Error conditions are signaled via an integer argument
<code>info</code>; whenever an error condition is detected, an error trace
stack is built by the library up to the top-level, user-callable
routine. This routine will then decide, according to the user
preferences, whether the error should be handled by terminating the
program or by returning the error condition to the user code, which
will then take action, and whether
an error message should be printed. These options may be set by using
the PSBLAS error handling routines; for further details see the PSBLAS
User's Guide [<A
HREF="node25.html#PSBLASGUIDE">16</A>].
This routine deallocates the preconditioner data structure.
<P>
<FONT SIZE="+1"><B>Arguments</B></FONT>
<P>
<TABLE CELLPADDING=3>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>p</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=298><code>type(mld_</code><I>x</I><code>prec_type), intent(inout)</code>.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=298>The preconditioner data structure. Note that <I>x</I> must be chosen according
to the real/complex, single/double precision version of MLD2P4 under use.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>info</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=298><code>integer, intent(out)</code>.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=298>Error code. If no error, 0 is returned. See Section&nbsp;<A HREF="node25.html#sec:errors">7</A> for details.</TD>
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<H1><A NAME="SECTION000100000000000000000"></A><A NAME="sec:license"></A>
<H2><A NAME="SECTION00088000000000000000"></A><A NAME="sec:precdescr"></A>
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License
</H1>
Subroutine mld_precdescr
</H2>
<P>
The MLD2P4 is freely distributable under the following copyright
terms: <PRE>
<DIV ALIGN="CENTER">
<code>mld_precdescr(p,info)</code>
<BR><code>mld_precdescr(p,info,iout)</code>
<BR>
</DIV>
MLD2P4 version 2.0
MultiLevel Domain Decomposition Parallel Preconditioners Package
based on PSBLAS (Parallel Sparse BLAS version 3.3)
(C) Copyright 2008, 2010, 2012, 2015
<P>
This routine prints a description of the preconditioner to the standard output or
to a file. It must be called after <code>mld_precbld</code> has been called.
Salvatore Filippone University of Rome Tor Vergata
Alfredo Buttari CNRS-IRIT, Toulouse
Pasqua D'Ambra ICAR-CNR, Naples
Daniela di Serafino Second University of Naples
<P>
<FONT SIZE="+1"><B>Arguments</B></FONT>
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions
are met:
1. Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright
notice, this list of conditions, and the following disclaimer in the
documentation and/or other materials provided with the distribution.
3. The name of the MLD2P4 group or the names of its contributors may
not be used to endorse or promote products derived from this
software without specific written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE MLD2P4 GROUP OR ITS CONTRIBUTORS
BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
POSSIBILITY OF SUCH DAMAGE.
</PRE>
<P>
<TABLE CELLPADDING=3>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>p</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(mld_</code><I>x</I><code>prec_type), intent(in)</code>.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The preconditioner data structure. Note that <I>x</I> must be chosen according
to the real/complex, single/double precision version of MLD2P4 under use.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>info</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>integer, intent(out)</code>.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>Error code. If no error, 0 is returned. See Section&nbsp;<A HREF="node25.html#sec:errors">7</A> for details.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>iout</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>integer, intent(in), optional</code>.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The id of the file where the preconditioner description
will be printed; the default is the standard output.</TD>
</TR>
</TABLE>
<P>
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<H2><A NAME="SECTION000110000000000000000">
Bibliography</A>
</H2><DL COMPACT><DD>
<P>
<P></P><DT><A NAME="BREZINA_VANEK">1</A>
<DD>
M.&nbsp;Brezina, P.&nbsp;Vanek,
<EM>A Black-Box Iterative Solver Based on a Two-Level Schwarz Method</EM>,
Computing, 63, 1999, 233-263.<P></P><DT><A NAME="para_04">2</A>
<DD>
A.&nbsp;Buttari, P.&nbsp;D'Ambra, D.&nbsp;di Serafino, S.&nbsp;Filippone,
<EM>Extending PSBLAS to Build Parallel Schwarz Preconditioners</EM>,
in , J.&nbsp;Dongarra, K.&nbsp;Madsen, J.&nbsp;Wasniewski, editors,
Proceedings of PARA&nbsp;04 Workshop on State of the Art
in Scientific Computing, Lecture Notes in Computer Science,
Springer, 2005, 593-602.<P></P><DT><A NAME="aaecc_07">3</A>
<DD>
A.&nbsp;Buttari, P.&nbsp;D'Ambra, D.&nbsp;di&nbsp;Serafino, S.&nbsp;Filippone,
<EM>2LEV-D2P4: a package of high-performance preconditioners
for scientific and engineering applications</EM>,
Applicable Algebra in Engineering, Communications and Computing,
18, 3, 2007, 223-239.<P></P><DT><A NAME="apnum_07">4</A>
<DD> P.&nbsp;D'Ambra, S.&nbsp;Filippone, D.&nbsp;di&nbsp;Serafino,
<EM>On the Development of PSBLAS-based Parallel Two-level Schwarz Preconditioners</EM>,
Applied Numerical Mathematics, Elsevier Science,
57, 11-12, 2007, 1181-1196.
<P>
<P></P><DT><A NAME="CAI_SARKIS">5</A>
<DD>
X.&nbsp;C.&nbsp;Cai, M.&nbsp;Sarkis,
<EM>A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems</EM>,
SIAM Journal on Scientific Computing, 21, 2, 1999, 792-797.<P></P><DT><A NAME="Cai_Widlund_92">6</A>
<DD>
X.&nbsp;C.&nbsp;Cai, O.&nbsp;B.&nbsp;Widlund,
<EM>Domain Decomposition Algorithms for Indefinite Elliptic Problems</EM>,
SIAM Journal on Scientific and Statistical Computing, 13, 1, 1992, 243-258.<P></P><DT><A NAME="dd1_94">7</A>
<DD>
T.&nbsp;Chan and T.&nbsp;Mathew,
<EM>Domain Decomposition Algorithms</EM>,
in A.&nbsp;Iserles, editor, Acta Numerica 1994, 61-143.
Cambridge University Press.<P></P><DT><A NAME="MLD2P4_TOMS">8</A>
<DD>
P.&nbsp;D'Ambra, D.&nbsp;di&nbsp;Serafino, S.&nbsp;Filippone,
<I>MLD2P4: a Package of Parallel Multilevel
Algebraic Domain Decomposition Preconditioners
in Fortran 95</I>, ACM Trans. Math. Softw., 37(3), 2010.<P></P><DT><A NAME="UMFPACK">9</A>
<DD>
T.A.&nbsp;Davis,
<EM>Algorithm 832: UMFPACK - an Unsymmetric-pattern Multifrontal
Method with a Column Pre-ordering Strategy</EM>,
ACM Transactions on Mathematical Software, 30, 2004, 196-199.
(See also <TT>http://www.cise.ufl.edu/&nbsp;davis/</TT>)
<P>
<P></P><DT><A NAME="MUMPS">10</A>
<DD>
P.R.&nbsp;Amestoy, C.&nbsp;Ashcraft, O.&nbsp;Boiteau, A.&nbsp;Buttari, J.&nbsp;L'Excellent, C.&nbsp;Weisbecker
<EM>Improving multifrontal methods by means of block low-rank representations</EM>,
SIAM SISC, volume 37, number 3, pages A1452-A1474.
(See also <TT>http://mumps.enseeiht.fr</TT>)
<P>
<P></P><DT><A NAME="SUPERLU">11</A>
<DD>
J.W.&nbsp;Demmel, S.C.&nbsp;Eisenstat, J.R.&nbsp;Gilbert, X.S.&nbsp;Li and J.W.H.&nbsp;Liu,
A supernodal approach to sparse partial pivoting,
SIAM Journal on Matrix Analysis and Applications, 20, 3, 1999, 720-755.<P></P><DT><A NAME="blas3">12</A>
<DD>
J.&nbsp;J.&nbsp;Dongarra, J.&nbsp;Du Croz, I.&nbsp;S.&nbsp;Duff, S.&nbsp;Hammarling,
<I>A set of Level 3 Basic Linear Algebra Subprograms</I>,
ACM Transactions on Mathematical Software, 16, 1990, 1-17.<P></P><DT><A NAME="blas2">13</A>
<DD>
J.&nbsp;J.&nbsp;Dongarra, J.&nbsp;Du Croz, S.&nbsp;Hammarling, R.&nbsp;J.&nbsp;Hanson,
<I>An extended set of FORTRAN Basic Linear Algebra Subprograms</I>,
ACM Transactions on Mathematical Software, 14, 1988, 1-17.<P></P><DT><A NAME="BLACS">14</A>
<DD>
J.&nbsp;J.&nbsp;Dongarra and R.&nbsp;C.&nbsp;Whaley,
<EM>A User's Guide to the BLACS v.&nbsp;1.1</EM>,
Lapack Working Note 94, Tech. Rep. UT-CS-95-281, University of
Tennessee, March 1995 (updated May 1997).<P></P><DT><A NAME="EFSTATHIOU">15</A>
<DD>
E.&nbsp;Efstathiou, J.&nbsp;G.&nbsp;Gander,
<EM>Why Restricted Additive Schwarz Converges Faster than Additive Schwarz</EM>,
BIT Numerical Mathematics, 43, 2003, 945-959.<P></P><DT><A NAME="PSBLASGUIDE">16</A>
<DD>
S.&nbsp;Filippone, A.&nbsp;Buttari,
<EM>PSBLAS-3.0 User's Guide. A Reference Guide for the Parallel Sparse BLAS Library</EM>, 2012,
available from <TT>http://www.ce.uniroma2.it/psblas/</TT>.
<P>
<P></P><DT><A NAME="PSBLAS3">17</A>
<DD>
Salvatore Filippone and Alfredo Buttari.
<EM>Object-Oriented Techniques for Sparse Matrix Computations in Fortran
2003.</EM>
ACM Trans. on Math Software, 38(4), 2012.
<H1><A NAME="SECTION00090000000000000000"></A><A NAME="sec:errors"></A>
<BR>
Error Handling
</H1>
<P>
<P></P><DT><A NAME="psblas_00">18</A>
<DD>
S.&nbsp;Filippone, M.&nbsp;Colajanni,
<EM>PSBLAS: A Library for Parallel Linear Algebra
Computation on Sparse Matrices</EM>,
ACM Transactions on Mathematical Software, 26, 4, 2000, 527-550.<P></P><DT><A NAME="MPI2">19</A>
<DD>
W.&nbsp;Gropp, S.&nbsp;Huss-Lederman, A.&nbsp;Lumsdaine, E.&nbsp;Lusk, B.&nbsp;Nitzberg, W.&nbsp;Saphir, M.&nbsp;Snir,
<EM>MPI: The Complete Reference. Volume 2 - The MPI-2 Extensions</EM>,
MIT Press, 1998.<P></P><DT><A NAME="blas1">20</A>
<DD>
C.&nbsp;L.&nbsp;Lawson, R.&nbsp;J.&nbsp;Hanson, D.&nbsp;Kincaid, F.&nbsp;T.&nbsp;Krogh,
<I>Basic Linear Algebra Subprograms for FORTRAN usage</I>,
ACM Transactions on Mathematical Software, 5, 1979, 308-323.<P></P><DT><A NAME="SUPERLUDIST">21</A>
<DD>
X.&nbsp;S.&nbsp;Li, J.&nbsp;W.&nbsp;Demmel, <EM>SuperLU_DIST: A Scalable Distributed-memory
Sparse Direct Solver for Unsymmetric Linear Systems</EM>,
ACM Transactions on Mathematical Software, 29, 2, 2003, 110-140.<P></P><DT><A NAME="Saad_book">22</A>
<DD>
Y.&nbsp;Saad,
<I>Iterative methods for sparse linear systems</I>, 2nd edition,
SIAM, 2003
The error handling in MLD2P4 is based on the PSBLAS (version 2) error
handling. Error conditions are signaled via an integer argument
<code>info</code>; whenever an error condition is detected, an error trace
stack is built by the library up to the top-level, user-callable
routine. This routine will then decide, according to the user
preferences, whether the error should be handled by terminating the
program or by returning the error condition to the user code, which
will then take action, and whether
an error message should be printed. These options may be set by using
the PSBLAS error handling routines; for further details see the PSBLAS
User's Guide [<A
HREF="node27.html#PSBLASGUIDE">16</A>].
<P>
<P></P><DT><A NAME="dd2_96">23</A>
<DD>
B.&nbsp;Smith, P.&nbsp;Bjorstad, W.&nbsp;Gropp,
<EM>Domain Decomposition: Parallel Multilevel Methods for Elliptic
Partial Differential Equations</EM>,
Cambridge University Press, 1996.<P></P><DT><A NAME="MPI1">24</A>
<DD>
M.&nbsp;Snir, S.&nbsp;Otto, S.&nbsp;Huss-Lederman, D.&nbsp;Walker, J.&nbsp;Dongarra,
<EM>MPI: The Complete Reference. Volume 1 - The MPI Core</EM>, second edition,
MIT Press, 1998.<P></P><DT><A NAME="StubenGMD69_99">25</A>
<DD>
K.&nbsp;St&#252;ben,
<EM>Algebraic Multigrid (AMG): an Introduction with Applications</EM>,
in A.&nbsp;Sch&#252;ller, U.&nbsp;Trottenberg, C.&nbsp;Oosterlee, editors, Multigrid,
Academic Press, 2000.<P></P><DT><A NAME="TUMINARO_TONG">26</A>
<DD>
R.&nbsp;S.&nbsp;Tuminaro, C.&nbsp;Tong,
<EM>Parallel Smoothed Aggregation Multigrid: Aggregation Strategies on Massively Parallel Machines</EM>,
in J. Donnelley, editor, Proceedings of SuperComputing 2000, Dallas, 2000.<P></P><DT><A NAME="VANEK_MANDEL_BREZINA">27</A>
<DD>
P.&nbsp;Vanek, J.&nbsp;Mandel and M.&nbsp;Brezina,
<EM>Algebraic Multigrid by Smoothed Aggregation for Second and Fourth Order Elliptic Problems</EM>,
Computing, 56, 1996, 179-196.
<P>
</DL>
<P>
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Copyright &#169; 1993, 1994, 1995, 1996,
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Computer Based Learning Unit, University of Leeds.
<H1><A NAME="SECTION000100000000000000000"></A><A NAME="sec:license"></A>
<BR>
Copyright &#169; 1997, 1998, 1999,
<A HREF="http://www.maths.mq.edu.au/~ross/">Ross Moore</A>,
Mathematics Department, Macquarie University, Sydney.
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The command line arguments were: <BR>
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License
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The translation was initiated by Salvatore Filippone on 2016-05-23
The MLD2P4 is freely distributable under the following copyright
terms: <PRE>
MLD2P4 version 2.0
MultiLevel Domain Decomposition Parallel Preconditioners Package
based on PSBLAS (Parallel Sparse BLAS version 3.3)
(C) Copyright 2008, 2010, 2012, 2015
Salvatore Filippone University of Rome Tor Vergata
Alfredo Buttari CNRS-IRIT, Toulouse
Pasqua D'Ambra ICAR-CNR, Naples
Daniela di Serafino Second University of Naples
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions
are met:
1. Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright
notice, this list of conditions, and the following disclaimer in the
documentation and/or other materials provided with the distribution.
3. The name of the MLD2P4 group or the names of its contributors may
not be used to endorse or promote products derived from this
software without specific written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE MLD2P4 GROUP OR ITS CONTRIBUTORS
BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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<H2><A NAME="SECTION000110000000000000000">
Bibliography</A>
</H2><DL COMPACT><DD>
<H1><A NAME="SECTION000120000000000000000">
About this document ...</A>
</H1>
<P>
This document was generated using the
<A HREF="http://www.latex2html.org/"><STRONG>LaTeX</STRONG>2<tt>HTML</tt></A> translator Version 2002-2-1 (1.71)
<P>
Copyright &#169; 1993, 1994, 1995, 1996,
<A HREF="http://cbl.leeds.ac.uk/nikos/personal.html">Nikos Drakos</A>,
Computer Based Learning Unit, University of Leeds.
<BR>
Copyright &#169; 1997, 1998, 1999,
<A HREF="http://www.maths.mq.edu.au/~ross/">Ross Moore</A>,
Mathematics Department, Macquarie University, Sydney.
<P></P><DT><A NAME="BREZINA_VANEK">1</A>
<DD>
M.&nbsp;Brezina, P.&nbsp;Vanek,
<EM>A Black-Box Iterative Solver Based on a Two-Level Schwarz Method</EM>,
Computing, 63, 1999, 233-263.<P></P><DT><A NAME="para_04">2</A>
<DD>
A.&nbsp;Buttari, P.&nbsp;D'Ambra, D.&nbsp;di Serafino, S.&nbsp;Filippone,
<EM>Extending PSBLAS to Build Parallel Schwarz Preconditioners</EM>,
in , J.&nbsp;Dongarra, K.&nbsp;Madsen, J.&nbsp;Wasniewski, editors,
Proceedings of PARA&nbsp;04 Workshop on State of the Art
in Scientific Computing, Lecture Notes in Computer Science,
Springer, 2005, 593-602.<P></P><DT><A NAME="aaecc_07">3</A>
<DD>
A.&nbsp;Buttari, P.&nbsp;D'Ambra, D.&nbsp;di&nbsp;Serafino, S.&nbsp;Filippone,
<EM>2LEV-D2P4: a package of high-performance preconditioners
for scientific and engineering applications</EM>,
Applicable Algebra in Engineering, Communications and Computing,
18, 3, 2007, 223-239.<P></P><DT><A NAME="apnum_07">4</A>
<DD> P.&nbsp;D'Ambra, S.&nbsp;Filippone, D.&nbsp;di&nbsp;Serafino,
<EM>On the Development of PSBLAS-based Parallel Two-level Schwarz Preconditioners</EM>,
Applied Numerical Mathematics, Elsevier Science,
57, 11-12, 2007, 1181-1196.
<P>
<P></P><DT><A NAME="CAI_SARKIS">5</A>
<DD>
X.&nbsp;C.&nbsp;Cai, M.&nbsp;Sarkis,
<EM>A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems</EM>,
SIAM Journal on Scientific Computing, 21, 2, 1999, 792-797.<P></P><DT><A NAME="Cai_Widlund_92">6</A>
<DD>
X.&nbsp;C.&nbsp;Cai, O.&nbsp;B.&nbsp;Widlund,
<EM>Domain Decomposition Algorithms for Indefinite Elliptic Problems</EM>,
SIAM Journal on Scientific and Statistical Computing, 13, 1, 1992, 243-258.<P></P><DT><A NAME="dd1_94">7</A>
<DD>
T.&nbsp;Chan and T.&nbsp;Mathew,
<EM>Domain Decomposition Algorithms</EM>,
in A.&nbsp;Iserles, editor, Acta Numerica 1994, 61-143.
Cambridge University Press.<P></P><DT><A NAME="MLD2P4_TOMS">8</A>
<DD>
P.&nbsp;D'Ambra, D.&nbsp;di&nbsp;Serafino, S.&nbsp;Filippone,
<I>MLD2P4: a Package of Parallel Multilevel
Algebraic Domain Decomposition Preconditioners
in Fortran 95</I>, ACM Trans. Math. Softw., 37(3), 2010.<P></P><DT><A NAME="UMFPACK">9</A>
<DD>
T.A.&nbsp;Davis,
<EM>Algorithm 832: UMFPACK - an Unsymmetric-pattern Multifrontal
Method with a Column Pre-ordering Strategy</EM>,
ACM Transactions on Mathematical Software, 30, 2004, 196-199.
(See also <TT>http://www.cise.ufl.edu/&nbsp;davis/</TT>)
<P>
<P></P><DT><A NAME="MUMPS">10</A>
<DD>
P.R.&nbsp;Amestoy, C.&nbsp;Ashcraft, O.&nbsp;Boiteau, A.&nbsp;Buttari, J.&nbsp;L'Excellent, C.&nbsp;Weisbecker
<EM>Improving multifrontal methods by means of block low-rank representations</EM>,
SIAM SISC, volume 37, number 3, pages A1452-A1474.
(See also <TT>http://mumps.enseeiht.fr</TT>)
<P>
<P></P><DT><A NAME="SUPERLU">11</A>
<DD>
J.W.&nbsp;Demmel, S.C.&nbsp;Eisenstat, J.R.&nbsp;Gilbert, X.S.&nbsp;Li and J.W.H.&nbsp;Liu,
A supernodal approach to sparse partial pivoting,
SIAM Journal on Matrix Analysis and Applications, 20, 3, 1999, 720-755.<P></P><DT><A NAME="blas3">12</A>
<DD>
J.&nbsp;J.&nbsp;Dongarra, J.&nbsp;Du Croz, I.&nbsp;S.&nbsp;Duff, S.&nbsp;Hammarling,
<I>A set of Level 3 Basic Linear Algebra Subprograms</I>,
ACM Transactions on Mathematical Software, 16, 1990, 1-17.<P></P><DT><A NAME="blas2">13</A>
<DD>
J.&nbsp;J.&nbsp;Dongarra, J.&nbsp;Du Croz, S.&nbsp;Hammarling, R.&nbsp;J.&nbsp;Hanson,
<I>An extended set of FORTRAN Basic Linear Algebra Subprograms</I>,
ACM Transactions on Mathematical Software, 14, 1988, 1-17.<P></P><DT><A NAME="BLACS">14</A>
<DD>
J.&nbsp;J.&nbsp;Dongarra and R.&nbsp;C.&nbsp;Whaley,
<EM>A User's Guide to the BLACS v.&nbsp;1.1</EM>,
Lapack Working Note 94, Tech. Rep. UT-CS-95-281, University of
Tennessee, March 1995 (updated May 1997).<P></P><DT><A NAME="EFSTATHIOU">15</A>
<DD>
E.&nbsp;Efstathiou, J.&nbsp;G.&nbsp;Gander,
<EM>Why Restricted Additive Schwarz Converges Faster than Additive Schwarz</EM>,
BIT Numerical Mathematics, 43, 2003, 945-959.<P></P><DT><A NAME="PSBLASGUIDE">16</A>
<DD>
S.&nbsp;Filippone, A.&nbsp;Buttari,
<EM>PSBLAS-3.0 User's Guide. A Reference Guide for the Parallel Sparse BLAS Library</EM>, 2012,
available from <TT>http://www.ce.uniroma2.it/psblas/</TT>.
<P>
The command line arguments were: <BR>
<STRONG>latex2html</STRONG> <TT>-noaddress -dir ../../html userhtml.tex</TT>
<P></P><DT><A NAME="PSBLAS3">17</A>
<DD>
Salvatore Filippone and Alfredo Buttari.
<EM>Object-Oriented Techniques for Sparse Matrix Computations in Fortran
2003.</EM>
ACM Trans. on Math Software, 38(4), 2012.
<P>
<P></P><DT><A NAME="psblas_00">18</A>
<DD>
S.&nbsp;Filippone, M.&nbsp;Colajanni,
<EM>PSBLAS: A Library for Parallel Linear Algebra
Computation on Sparse Matrices</EM>,
ACM Transactions on Mathematical Software, 26, 4, 2000, 527-550.<P></P><DT><A NAME="MPI2">19</A>
<DD>
W.&nbsp;Gropp, S.&nbsp;Huss-Lederman, A.&nbsp;Lumsdaine, E.&nbsp;Lusk, B.&nbsp;Nitzberg, W.&nbsp;Saphir, M.&nbsp;Snir,
<EM>MPI: The Complete Reference. Volume 2 - The MPI-2 Extensions</EM>,
MIT Press, 1998.<P></P><DT><A NAME="blas1">20</A>
<DD>
C.&nbsp;L.&nbsp;Lawson, R.&nbsp;J.&nbsp;Hanson, D.&nbsp;Kincaid, F.&nbsp;T.&nbsp;Krogh,
<I>Basic Linear Algebra Subprograms for FORTRAN usage</I>,
ACM Transactions on Mathematical Software, 5, 1979, 308-323.<P></P><DT><A NAME="SUPERLUDIST">21</A>
<DD>
X.&nbsp;S.&nbsp;Li, J.&nbsp;W.&nbsp;Demmel, <EM>SuperLU_DIST: A Scalable Distributed-memory
Sparse Direct Solver for Unsymmetric Linear Systems</EM>,
ACM Transactions on Mathematical Software, 29, 2, 2003, 110-140.<P></P><DT><A NAME="Saad_book">22</A>
<DD>
Y.&nbsp;Saad,
<I>Iterative methods for sparse linear systems</I>, 2nd edition,
SIAM, 2003
<P>
<P></P><DT><A NAME="dd2_96">23</A>
<DD>
B.&nbsp;Smith, P.&nbsp;Bjorstad, W.&nbsp;Gropp,
<EM>Domain Decomposition: Parallel Multilevel Methods for Elliptic
Partial Differential Equations</EM>,
Cambridge University Press, 1996.<P></P><DT><A NAME="MPI1">24</A>
<DD>
M.&nbsp;Snir, S.&nbsp;Otto, S.&nbsp;Huss-Lederman, D.&nbsp;Walker, J.&nbsp;Dongarra,
<EM>MPI: The Complete Reference. Volume 1 - The MPI Core</EM>, second edition,
MIT Press, 1998.<P></P><DT><A NAME="StubenGMD69_99">25</A>
<DD>
K.&nbsp;St&#252;ben,
<EM>Algebraic Multigrid (AMG): an Introduction with Applications</EM>,
in A.&nbsp;Sch&#252;ller, U.&nbsp;Trottenberg, C.&nbsp;Oosterlee, editors, Multigrid,
Academic Press, 2000.<P></P><DT><A NAME="TUMINARO_TONG">26</A>
<DD>
R.&nbsp;S.&nbsp;Tuminaro, C.&nbsp;Tong,
<EM>Parallel Smoothed Aggregation Multigrid: Aggregation Strategies on Massively Parallel Machines</EM>,
in J. Donnelley, editor, Proceedings of SuperComputing 2000, Dallas, 2000.<P></P><DT><A NAME="VANEK_MANDEL_BREZINA">27</A>
<DD>
P.&nbsp;Vanek, J.&nbsp;Mandel and M.&nbsp;Brezina,
<EM>Algebraic Multigrid by Smoothed Aggregation for Second and Fourth Order Elliptic Problems</EM>,
Computing, 56, 1996, 179-196.
<P>
</DL>
<P>
The translation was initiated by Salvatore Filippone on 2008-09-12
<BR><HR>
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* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
* with significant contributions from:
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<H1><A NAME="SECTION00090000000000000000"></A><A NAME="sec:errors"></A>
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Error Handling
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About this document ...</A>
</H1>
<P>
This document was generated using the
<A HREF="http://www.latex2html.org/"><STRONG>LaTeX</STRONG>2<tt>HTML</tt></A> translator Version 2012 (1.2)
<P>
The error handling in MLD2P4 is based on the PSBLAS (version 2) error
handling. Error conditions are signaled via an integer argument
<code>info</code>; whenever an error condition is detected, an error trace
stack is built by the library up to the top-level, user-callable
routine. This routine will then decide, according to the user
preferences, whether the error should be handled by terminating the
program or by returning the error condition to the user code, which
will then take action, and whether
an error message should be printed. These options may be set by using
the PSBLAS error handling routines; for further details see the PSBLAS
User's Guide [<A
HREF="node30.html#PSBLASGUIDE">14</A>].
Copyright &#169; 1993, 1994, 1995, 1996,
<A HREF="http://cbl.leeds.ac.uk/nikos/personal.html">Nikos Drakos</A>,
Computer Based Learning Unit, University of Leeds.
<BR>
Copyright &#169; 1997, 1998, 1999,
<A HREF="http://www.maths.mq.edu.au/~ross/">Ross Moore</A>,
Mathematics Department, Macquarie University, Sydney.
<P>
The command line arguments were: <BR>
<STRONG>latex2html</STRONG> <TT>-local_icons -noaddress -dir ../../html userhtml.tex</TT>
<P>
The translation was initiated by Salvatore Filippone on 2016-06-09
<BR><HR>
<ADDRESS>
Salvatore Filippone
2008-07-23
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@ -59,7 +59,7 @@ General Overview
<P>
The M<SMALL>ULTI-</SMALL>L<SMALL>EVEL </SMALL>D<SMALL>OMAIN </SMALL>D<SMALL>ECOMPOSITION </SMALL>P<SMALL>ARALLEL </SMALL>P<SMALL>RECONDITIONERS </SMALL>P<SMALL>ACKAGE BASED ON
</SMALL>PSBLAS (MLD2P4) provides <I>multi-level Schwarz preconditioners</I>&nbsp;[<A
HREF="node25.html#dd2_96">23</A>],
HREF="node27.html#dd2_96">23</A>],
to be used in the iterative solutions of sparse linear systems:
<BR>
<DIV ALIGN="RIGHT">
@ -97,8 +97,8 @@ generate a sequence of coarse-level corrections to a basic AS preconditioner, wi
explicitly using any information on the geometry of the original problem (e.g. the
discretization of a PDE). The <I>smoothed aggregation</I> technique is applied
as algebraic coarsening strategy&nbsp;[<A
HREF="node25.html#BREZINA_VANEK">1</A>,<A
HREF="node25.html#VANEK_MANDEL_BREZINA">27</A>].
HREF="node27.html#BREZINA_VANEK">1</A>,<A
HREF="node27.html#VANEK_MANDEL_BREZINA">27</A>].
</LI>
</UL>
@ -116,8 +116,8 @@ interface.
MLD2P4 has been designed to implement scalable and easy-to-use
multilevel preconditioners in the context of the <I>PSBLAS
(Parallel Sparse BLAS) computational framework</I>&nbsp;[<A
HREF="node25.html#psblas_00">18</A>,<A
HREF="node25.html#PSBLAS3">17</A>].
HREF="node27.html#psblas_00">18</A>,<A
HREF="node27.html#PSBLAS3">17</A>].
PSBLAS is a library originally developed to address the parallel implementation of
iterative solvers for sparse linear system, by providing basic linear algebra
operators and data management facilities for distributed sparse matrices; it
@ -130,10 +130,10 @@ portability, modularity ed extensibility in the development of the preconditione
package. On the other hand, the implementation of MLD2P4 has led to some
revisions and extentions of the PSBLAS kernels, leading to the
PSBLAS 2.0 version&nbsp;[<A
HREF="node25.html#PSBLASGUIDE">16</A>]. The inter-process comunication required
HREF="node27.html#PSBLASGUIDE">16</A>]. The inter-process comunication required
by MLD2P4 is encapsulated into the PSBLAS routines, except few cases where
MPI&nbsp;[<A
HREF="node25.html#MPI1">24</A>] is explicitly called. Therefore, MLD2P4 can be run on any parallel
HREF="node27.html#MPI1">24</A>] is explicitly called. Therefore, MLD2P4 can be run on any parallel
machine where PSBLAS and MPI implementations are available.
<P>
@ -167,32 +167,32 @@ with the Krylov solvers implemented in PSBLAS are reported in Section&nbsp;<A HR
Fortran codes of a few sample programs are also shown. A reference guide for
the upper-layer routines of MLD2P4, that are the user interface, is provided
in Section&nbsp;<A HREF="node16.html#sec:userinterface">6</A>. The error handling mechanism used by the package is briefly described
in Section&nbsp;<A HREF="node23.html#sec:errors">7</A>. The copyright terms concerning the distribution and modification
of MLD2P4 are reported in Appendix&nbsp;<A HREF="node24.html#sec:license">A</A>.
in Section&nbsp;<A HREF="node25.html#sec:errors">7</A>. The copyright terms concerning the distribution and modification
of MLD2P4 are reported in Appendix&nbsp;<A HREF="node26.html#sec:license">A</A>.
<P>
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@ -66,7 +66,7 @@ where contact points for further information can be also found.
<P>
The software is available under a modified BSD license, as specified
in Appendix&nbsp;<A HREF="node24.html#sec:license">A</A>; please note that some of the optional
in Appendix&nbsp;<A HREF="node26.html#sec:license">A</A>; please note that some of the optional
third party libraries may be licensed under a different and more
stringent license, most notably the GPL, and this should be taken into
account when treating derived works.

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@ -79,15 +79,15 @@ real and complex data, in both single and double precision.
<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
<UL>
<LI><A NAME="tex2html124"
<LI><A NAME="tex2html128"
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<LI><A NAME="tex2html132"
HREF="node10.html">Example and test programs</A>
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@ -60,9 +60,9 @@ The following base libraries are needed:
<DL>
<DT><STRONG>BLAS</STRONG></DT>
<DD>[<A
HREF="node25.html#blas3">12</A>,<A
HREF="node25.html#blas2">13</A>,<A
HREF="node25.html#blas1">20</A>] Many vendors provide optimized versions
HREF="node27.html#blas3">12</A>,<A
HREF="node27.html#blas2">13</A>,<A
HREF="node27.html#blas1">20</A>] Many vendors provide optimized versions
of the Basic Linear Algebra Subprograms; if no vendor version is
available for a given platform, the ATLAS software
(<code>http://math-atlas.sourceforge.net/</code>)
@ -77,15 +77,15 @@ The following base libraries are needed:
</DD>
<DT><STRONG>MPI</STRONG></DT>
<DD>[<A
HREF="node25.html#MPI2">19</A>,<A
HREF="node25.html#MPI1">24</A>] A version of MPI is available on most
HREF="node27.html#MPI2">19</A>,<A
HREF="node27.html#MPI1">24</A>] A version of MPI is available on most
high-performance computing systems;
</DD>
<DT><STRONG>PSBLAS</STRONG></DT>
<DD>[<A
HREF="node25.html#PSBLASGUIDE">16</A>,<A
HREF="node25.html#psblas_00">18</A>] Parallel Sparse BLAS is
HREF="node27.html#PSBLASGUIDE">16</A>,<A
HREF="node27.html#psblas_00">18</A>] Parallel Sparse BLAS is
available from
<BR><code>http://www.ce.uniroma2.it/psblas</code>; version
3.4.0 (or later) is required. Indeed, all the prerequisites

@ -26,26 +26,26 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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@ -64,7 +64,7 @@ for multilevel preconditioners may change to reflect their presence.
<DL>
<DT><STRONG>UMFPACK</STRONG></DT>
<DD>[<A
HREF="node25.html#UMFPACK">9</A>]
HREF="node27.html#UMFPACK">9</A>]
A sparse direct factorization package available from
<BR> <code>http://www.cise.ufl.edu/research/sparse/umfpack/</code>;
provides serial factorization and triangular system solution for double
@ -73,7 +73,7 @@ for multilevel preconditioners may change to reflect their presence.
</DD>
<DT><STRONG>SuperLU</STRONG></DT>
<DD>[<A
HREF="node25.html#SUPERLU">11</A>]
HREF="node27.html#SUPERLU">11</A>]
A sparse direct factorization package available from
<BR> <code>http://crd.lbl.gov/~xiaoye/SuperLU/</code>; provides serial
factorization and triangular system solution for single and double precision,
@ -82,7 +82,7 @@ for multilevel preconditioners may change to reflect their presence.
</DD>
<DT><STRONG>SuperLU_Dist</STRONG></DT>
<DD>[<A
HREF="node25.html#SUPERLUDIST">21</A>]
HREF="node27.html#SUPERLUDIST">21</A>]
A sparse direct factorization package available
from the same site as SuperLU; provides parallel factorization and
triangular system solution for double precision real and complex data.
@ -90,7 +90,7 @@ for multilevel preconditioners may change to reflect their presence.
</DD>
<DT><STRONG>MUMPS</STRONG></DT>
<DD>[<A
HREF="node25.html#MUMPS">10</A>]
HREF="node27.html#MUMPS">10</A>]
MUMPS (“MUltifrontal Massively Parallel Solver”) is a sparse, direct factorization
package available from
<BR> <code>http://mumps.enseeiht.fr/</code>.
@ -102,26 +102,26 @@ for multilevel preconditioners may change to reflect their presence.
</DD>
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@ -235,26 +235,26 @@ followed (optionally) by
make install
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@ -126,21 +126,25 @@ Mar. 31, 2016
<LI><A NAME="tex2html35"
HREF="node19.html">Subroutine mld_precbld</A>
<LI><A NAME="tex2html36"
HREF="node20.html">Subroutine mld_precaply</A>
HREF="node20.html">Subroutine mld_hierarchy_bld</A>
<LI><A NAME="tex2html37"
HREF="node21.html">Subroutine mld_precfree</A>
HREF="node21.html">Subroutine mld_ml_prec_bld</A>
<LI><A NAME="tex2html38"
HREF="node22.html">Subroutine mld_precdescr</A>
</UL>
<BR>
HREF="node22.html">Subroutine mld_precaply</A>
<LI><A NAME="tex2html39"
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@ -21,6 +21,16 @@ The following steps are required:
\verb|mld_precinit| to identify the preconditioner types are also given.
Note that these strings are valid also if uppercase letters are substituted by
corresponding lowercase ones.
\item \emph{Modify the aggregation parameters.} This is performed by
the routine \verb|mld_precset|.
This routine must be called only if the user wants to modify the default values
of the parameters associated to the aggregation hierarchy construction.
Examples of use of \verb|mld_precset| are given in
Section~\ref{sec:examples}; a complete list of all the
preconditioner parameters and their allowed and default values is provided in
Section~\ref{sec:userinterface}, Tables~\ref{tab:p_type}-\ref{tab:p_coarse}.
\item \emph{Build the aggregation hierarchy for a given matrix.} This is performed by
the routine \verb|mld_hierarchy_bld|.
\item \emph{Modify the selected preconditioner type, by properly setting
preconditioner parameters.} This is performed by the routine \verb|mld_precset|.
This routine must be called only if the user wants to modify the default values
@ -30,7 +40,7 @@ The following steps are required:
preconditioner parameters and their allowed and default values is provided in
Section~\ref{sec:userinterface}, Tables~\ref{tab:p_type}-\ref{tab:p_coarse}.
\item \emph{Build the preconditioner for a given matrix.} This is performed by
the routine \verb|mld_precbld|.
the routine \verb|mld_ml_prec_bld|.
\item \emph{Apply the preconditioner at each iteration of a Krylov solver.}
This is performed by the routine \verb|mld_precaply|. When using the PSBLAS Krylov solvers,
this step is completely transparent to the user, since \verb|mld_precaply| is called
@ -172,7 +182,9 @@ the corresponding Fortran 95 codes are available in \verb|examples/fileread/|.
call mld_precinit(P,'ML',info)
!
! build the preconditioner
call mld_precbld(A,desc_A,P,info)
call mld_hierarchy_bld(A,desc_A,P,info)
call mld_ml_prec_bld(A,desc_A,P,info)
!
! set the solver parameters and the initial guess
... ...
@ -257,11 +269,14 @@ boundary conditions are also available in the directory \verb|examples/pdegen|.
! block Jacobi (with ILU(0) on the blocks) as post-smoother,
! a coarsest matrix replicated on the processors, and the
! LU factorization from UMFPACK as coarse-level solver
call mld_precinit(P,'ML',info,nlev=3)
call mld_precinit(P,'ML',info)
call mld_hierarchy_bld(A,desc_A,P,info)
call_mld_precset(P,'SMOOTHER_TYPE','BJAC',info)
call_mld_precset(P,'SMOOTHER_POS,'POST'w,info)
call mld_precset(P,'COARSE_MAT','REPL',info)
call mld_precset(P,'COARSE_SOLVE','UMF',info)
call mld_ml_prec_bld(A,desc_A,P,info)
... ...
\end{verbatim}
}
@ -283,10 +298,12 @@ boundary conditions are also available in the directory \verb|examples/pdegen|.
! multifrontal solver in MUMPS as coarse-level solver
call mld_precinit(P,'ML',info,nlev=3)
call mld_hierarchy_bld(A,desc_A,P,info)
call mld_precset(P,mld_smoother_type_,'BJAC',info)
call mld_precset(P,mld_coarse_mat_,'REPL',info)
call mld_precset(P,mld_coarse_solve_,'MUMPS',info)
call mld_ml_prec_bld(A,desc_A,P,info)
... ...
\end{verbatim}
}
@ -308,9 +325,11 @@ boundary conditions are also available in the directory \verb|examples/pdegen|.
! post-smoother, and 5 block-Jacobi sweeps (with UMFPACK LU
! on the blocks) as distributed coarsest-level solver
call mld_precinit(P,'ML',info,nlev=3)
call mld_ml_prec_bld(A,desc_A,P,info)
call mld_precset(P,'ML_TYPE','ADD',info)
call_mld_precset(P,'SMOOTHER_POS','TWOSIDE',info)
call mld_precset(P,'COARSE_SWEEPS',5,info)
call mld_ml_prec_bld(A,desc_A,P,info)
... ...
\end{verbatim}
}
@ -329,6 +348,7 @@ boundary conditions are also available in the directory \verb|examples/pdegen|.
! set RAS with overlap 2 and ILU(0) on the local blocks
call mld_precinit(P,'AS',info)
call mld_precset(P,'SUB_OVR',2,info)
call mld_precbld(A,desc_A,P,info)
... ...
\end{verbatim}
}

@ -483,7 +483,7 @@ level.\label{tab:p_coarse}}
\clearpage
\subsection{Subroutine mld\_precbld\label{sec:precbld}}
\begin{center}
\verb|mld_precbld(a,desc_a,p,info)|\\
\end{center}
@ -492,6 +492,71 @@ level.\label{tab:p_coarse}}
This routine builds the preconditioner according to the requirements made by
the user through the routines \verb|mld_precinit| and \verb|mld_precset|.
For multilevel preconditioner this routine is supported for backward
compatibility, but we recommend to use the routines of
Sec.~\ref{sec:hier_bld} and~\ref{sec:ml_prec_bld}.
{\vskip2\baselineskip\noindent\large\bfseries Arguments}
\begin{tabular}{p{1.2cm}p{12cm}}
\verb|a| & \verb|type(psb_|\emph{x}\verb|spmat_type), intent(in)|. \\
& The sparse matrix structure containing the local part of the
matrix to be preconditioned. Note that \emph{x} must be chosen according
to the real/complex,
single/double precision version of MLD2P4 under use.
See the PSBLAS User's Guide for details \cite{PSBLASGUIDE}.\\
\verb|desc_a| & \verb|type(psb_desc_type), intent(in)|. \\
& The communication descriptor of \verb|a|. See the PSBLAS User's Guide for
details \cite{PSBLASGUIDE}.\\
\verb|p| & \verb|type(mld_|\emph{x}\verb|prec_type), intent(inout)|.\\
& The preconditioner data structure. Note that \emph{x} must be chosen according
to the real/complex, single/double precision version of MLD2P4 under use.\\
\verb|info| & \verb|integer, intent(out)|.\\
& Error code. If no error, 0 is returned. See Section~\ref{sec:errors} for details.\\
\end{tabular}
\subsection{Subroutine mld\_hierarchy\_bld\label{sec:hier_bld}}
\begin{center}
\verb|mld_hierachy_bld(a,desc_a,p,info)|\\
\end{center}
\noindent
This routine builds the aggregation hierarchy according to the requirements made by
the user through the routines \verb|mld_precinit| and \verb|mld_precset|.
{\vskip2\baselineskip\noindent\large\bfseries Arguments}
\begin{tabular}{p{1.2cm}p{12cm}}
\verb|a| & \verb|type(psb_|\emph{x}\verb|spmat_type), intent(in)|. \\
& The sparse matrix structure containing the local part of the
matrix to be preconditioned. Note that \emph{x} must be chosen according
to the real/complex,
single/double precision version of MLD2P4 under use.
See the PSBLAS User's Guide for details \cite{PSBLASGUIDE}.\\
\verb|desc_a| & \verb|type(psb_desc_type), intent(in)|. \\
& The communication descriptor of \verb|a|. See the PSBLAS User's Guide for
details \cite{PSBLASGUIDE}.\\
\verb|p| & \verb|type(mld_|\emph{x}\verb|prec_type), intent(inout)|.\\
& The preconditioner data structure. Note that \emph{x} must be chosen according
to the real/complex, single/double precision version of MLD2P4 under use.\\
\verb|info| & \verb|integer, intent(out)|.\\
& Error code. If no error, 0 is returned. See Section~\ref{sec:errors} for details.\\
\end{tabular}
\subsection{Subroutine mld\_ml\_prec\_bld\label{sec:ml_prec_bld}}
\begin{center}
\verb|mld_ml_prec_bld(a,desc_a,p,info)|\\
\end{center}
\noindent
This routine builds the preconditioner according to the requirements made by
the user through the routines \verb|mld_precinit| and
\verb|mld_precset|, based on the aggregation hierahy produced by a
previous call to \verb|mld_hierarchy_bld| (see
Sec.~\ref{sec:hier_bld}).
{\vskip2\baselineskip\noindent\large\bfseries Arguments}
\begin{tabular}{p{1.2cm}p{12cm}}

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