mld2p4-2:

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Doc fixes.
stopcriterion
Salvatore Filippone 9 years ago
parent ed62c7d467
commit 758164ff20

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@ -726,7 +726,7 @@ $w = y_1$;
\begin{tabbing} \begin{tabbing}
\quad \=\quad... \quad \=\quad...
...= y_l+r_l$\\ ...= y_l+r_l$\\
\textbf{endfor} \\ [1mm] \textbf{endfor} [1mm]
$w = y_1$; $w = y_1$;
\end{tabbing}} \end{tabbing}}
\end{minipage}}"> \end{minipage}}">

@ -163,10 +163,13 @@ preconditioner, which uses block Jacobi with ILU(0) on the
local blocks as post-smoother, has a coarsest matrix replicated on the processors, 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 and solves the coarsest-level system with the LU factorization from UMFPACK&nbsp;[<A
HREF="node25.html#UMFPACK">9</A>]. HREF="node25.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 Figure&nbsp;<A HREF="#fig:ex_3lhm">4</A> shows how to set a three-level preconditioner
HREF="node25.html#UMFPACK">9</A>]. similar to the one of&nbsp;<A HREF="#fig:ex_3lh">3</A>, but the coarsest-level
Note that MUMPS can be used on both replicated and distributed coarsest level matrices, systems is solved with the multifrontal factorization from
as a global and local solver respectively. MUMPS&nbsp;[<A
HREF="node25.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 The number of levels is specified by using <code>mld_precinit</code>; the other
preconditioner parameters are set by calling <code>mld_precset</code>. Note that preconditioner parameters are set by calling <code>mld_precset</code>. Note that
the type of multilevel framework (i.e. multiplicative among the levels the type of multilevel framework (i.e. multiplicative among the levels
@ -183,13 +186,14 @@ solver. Again, <code>mld_precset</code> is used only to set
non-default values of the parameters (see Tables&nbsp;<A HREF="#tab:p_type">2</A>-<A HREF="#tab:p_coarse">5</A>). non-default values of the parameters (see Tables&nbsp;<A HREF="#tab:p_type">2</A>-<A HREF="#tab:p_coarse">5</A>).
In both cases, the construction and the application of the preconditioner In both cases, the construction and the application of the preconditioner
are carried out as for the default multi-level preconditioner. are carried out as for the default multi-level preconditioner.
The code fragments shown in in Figures&nbsp;<A HREF="#fig:ex_3lh">3</A>&nbsp;<A HREF="#fig:ex_3lhm">4</A>-<A HREF="#fig:ex_3la">5</A> are The code fragments shown in in
included in the example program file <code>mld_dexample_ml.f90</code> too. Figures&nbsp;<A HREF="#fig:ex_3lh">3</A>&nbsp;<A HREF="#fig:ex_3lhm">4</A>-<A HREF="#fig:ex_3la">5</A> are
included in the example program file <code>mld_dexample_ml.f90</code> too.
<P> <P>
Finally, Figure&nbsp;<A HREF="#fig:ex_1l">6</A> shows the setup of a one-level Finally, Figure&nbsp;<A HREF="#fig:ex_1l">6</A> shows the setup of a one-level
additive Schwarz preconditioner, i.e. RAS with overlap 2. The corresponding additive Schwarz preconditioner, i.e. RAS with overlap 2. The
example program is available in <code>mld_dexample_</code> <code>1lev.f90</code>. corresponding example program is available in <code>mld_dexample_1lev.f90</code>.
<P> <P>
For all the previous preconditioners, example programs where the sparse matrix and For all the previous preconditioners, example programs where the sparse matrix and

@ -57,10 +57,11 @@ User Interface
</H1> </H1>
<P> <P>
The basic user interface of MLD2P4 consists of six routines. The four routines <code>mld_</code> <code>precinit</code>, The basic user interface of MLD2P4 consists of six routines. The four
<code>mld_precset</code>, <code>mld_precbld</code> and <code>mld_precaply</code> encapsulate all the functionalities routines <code>mld_</code> <code>precinit</code>, <code>mld_precset</code>,
for the setup and the application of any one-level and multi-level <code>mld_precbld</code> and <code>mld_precaply</code> encapsulate all the
preconditioner implemented in the package. functionalities for the setup and the application of any one-level and
multi-level preconditioner implemented in the package.
The routine <code>mld_precfree</code> deallocates the preconditioner data structure, while The routine <code>mld_precfree</code> deallocates the preconditioner data structure, while
<code>mld_precdescr</code> prints a description of the preconditioner setup by the user. <code>mld_precdescr</code> prints a description of the preconditioner setup by the user.

@ -71,7 +71,7 @@ contained in <code>val</code>.
The routine may also be invoked as a method The routine may also be invoked as a method
of the preconditioner object as in the following: of the preconditioner object as in the following:
<DIV ALIGN="CENTER"> <DIV ALIGN="CENTER">
<code>call p%set(what,val,info [,ilev])</code> <code>call p%set(what,val,info [,ilev, pos])</code>
<BR> <BR>
</DIV> </DIV>
In this case it is also possible to specify an optional <code>ilev</code> In this case it is also possible to specify an optional <code>ilev</code>
@ -84,8 +84,8 @@ solver by extending one of the base MLD2P4 types, and has declared a
variable of the new type in the main program, it is possible to pass variable of the new type in the main program, it is possible to pass
the new smoother/solver variable to the setup routine as follows: the new smoother/solver variable to the setup routine as follows:
<DIV ALIGN="CENTER"> <DIV ALIGN="CENTER">
<code>call p%set(smoother,info [,ilev])</code> <code>call p%set(smoother,info [,ilev ,pos])</code>
<BR><code>call p%set(solver,info [,ilev])</code> <BR><code>call p%set(solver,info [,ilev ,poss])</code>
</DIV> </DIV>
In this way, the variable will act as a <I>mold</I> to which the In this way, the variable will act as a <I>mold</I> to which the
@ -202,7 +202,7 @@ according to their needs.
<P> <P>
<BR><P></P> <BR><P></P>
<DIV ALIGN="CENTER"><A NAME="1302"></A> <DIV ALIGN="CENTER"><A NAME="1306"></A>
<TABLE> <TABLE>
<CAPTION><STRONG>Table 2:</STRONG> <CAPTION><STRONG>Table 2:</STRONG>
Parameters defining the type of multi-level preconditioner. Parameters defining the type of multi-level preconditioner.
@ -246,7 +246,7 @@ Parameters defining the type of multi-level preconditioner.
<P> <P>
<BR><P></P> <BR><P></P>
<DIV ALIGN="CENTER"><A NAME="1304"></A> <DIV ALIGN="CENTER"><A NAME="1308"></A>
<TABLE> <TABLE>
<CAPTION><STRONG>Table 3:</STRONG> <CAPTION><STRONG>Table 3:</STRONG>
Parameters defining the one-level preconditioner used as smoother. Parameters defining the one-level preconditioner used as smoother.
@ -288,13 +288,17 @@ Parameters defining the one-level preconditioner used as smoother.
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=99><code>mld_sub_solve_</code> <BR><code>SUB_SOLVE</code></TD> <TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=99><code>mld_sub_solve_</code> <BR><code>SUB_SOLVE</code></TD>
<TD ALIGN="LEFT"><code>character(len=*)</code></TD> <TD ALIGN="LEFT"><code>character(len=*)</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91><TT>'DIAG'</TT> <TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91><TT>'DIAG'</TT>
<TT>'GS'</TT> <TT>'GS'</TT> <TT>'BWGS'</TT>
<TT>'ILU'</TT> <TT>'ILU'</TT>
<TT>'MILU'</TT> <TT>'ILUT'</TT> <TT>'MILU'</TT> <TT>'ILUT'</TT>
<TT>'UMF'</TT> <TT>'SLU'</TT></TD>
<TT>'UMF'</TT>
<TT>'SLU'</TT>
<TT>'MUMPS'</TT></TD>
<TD ALIGN="LEFT"><TT>'ILU'</TT></TD> <TD ALIGN="LEFT"><TT>'ILU'</TT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142>Predefined local solver: pointwise Jacobi <TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142>Predefined local solver: pointwise Jacobi
(diagonal scaling), (diagonal scaling),
(forward) Gauss-Seidel, Backward
Gauss-Seidel, ILU(<IMG Gauss-Seidel, ILU(<IMG
WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img35.png" SRC="img35.png"
@ -305,8 +309,8 @@ Parameters defining the one-level preconditioner used as smoother.
ILU(<IMG ILU(<IMG
WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img36.png" SRC="img36.png"
ALT="$p,t$">), LU from UMFPACK, LU from ALT="$p,t$">), LU from UMFPACK, LU from
SuperLU (plus triangular solve).</TD> SuperLU (plus triangular solve), LU from MUMPS.</TD>
</TR> </TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=99><code>mld_sub_fillin_</code> <BR><code>SUB_FILLIN</code></TD> <TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=99><code>mld_sub_fillin_</code> <BR><code>SUB_FILLIN</code></TD>
<TD ALIGN="LEFT"><code>integer</code></TD> <TD ALIGN="LEFT"><code>integer</code></TD>
@ -362,7 +366,7 @@ Parameters defining the one-level preconditioner used as smoother.
<P> <P>
<BR><P></P> <BR><P></P>
<DIV ALIGN="CENTER"><A NAME="1306"></A> <DIV ALIGN="CENTER"><A NAME="1310"></A>
<TABLE> <TABLE>
<CAPTION><STRONG>Table 4:</STRONG> <CAPTION><STRONG>Table 4:</STRONG>
Parameters defining the aggregation algorithm. Parameters defining the aggregation algorithm.
@ -397,7 +401,7 @@ Parameters defining the aggregation algorithm.
</TR> </TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142><code>mld_aggr_ord_</code> <BR><code>AGGR_ORD</code></TD> <TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142><code>mld_aggr_ord_</code> <BR><code>AGGR_ORD</code></TD>
<TD ALIGN="LEFT"><code>character(len=*)</code></TD> <TD ALIGN="LEFT"><code>character(len=*)</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68><TT>'NAT'</TT></TD> <TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68><TT>'NATURAL'</TT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68><TT>'DEGREE'</TT></TD> <TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68><TT>'DEGREE'</TT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=170>Initial ordering of indices for aggregation <TD ALIGN="LEFT" VALIGN="TOP" WIDTH=170>Initial ordering of indices for aggregation
algorithm: natural ordering or sorted by algorithm: natural ordering or sorted by
@ -503,7 +507,7 @@ Parameters defining the aggregation algorithm.
<P> <P>
<BR><P></P> <BR><P></P>
<DIV ALIGN="CENTER"><A NAME="1309"></A> <DIV ALIGN="CENTER"><A NAME="1313"></A>
<TABLE> <TABLE>
<CAPTION><STRONG>Table 5:</STRONG> <CAPTION><STRONG>Table 5:</STRONG>
Parameters defining the coarse-space correction at the coarsest Parameters defining the coarse-space correction at the coarsest

@ -70,7 +70,7 @@ This routine computes <!-- MATH
<IMG <IMG
WIDTH="118" HEIGHT="39" ALIGN="MIDDLE" BORDER="0" WIDTH="118" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
SRC="img100.png" SRC="img100.png"
ALT="$y = op(M^{-1})\, x$">, where <IMG ALT="$y = op(M^{-1}) x$">, where <IMG
WIDTH="23" HEIGHT="15" ALIGN="BOTTOM" BORDER="0" WIDTH="23" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="img60.png" SRC="img60.png"
ALT="$M$"> is a previously built ALT="$M$"> is a previously built

@ -63,7 +63,7 @@ Mathematics Department, Macquarie University, Sydney.
The command line arguments were: <BR> The command line arguments were: <BR>
<STRONG>latex2html</STRONG> <TT>-local_icons -noaddress -dir ../../html userhtml.tex</TT> <STRONG>latex2html</STRONG> <TT>-local_icons -noaddress -dir ../../html userhtml.tex</TT>
<P> <P>
The translation was initiated by Salvatore Filippone on 2016-05-09 The translation was initiated by Salvatore Filippone on 2016-05-18
<BR><HR> <BR><HR>
</BODY> </BODY>

@ -103,7 +103,7 @@ as algebraic coarsening strategy&nbsp;[<A
</UL> </UL>
<P> <P>
Version 2.0 of the package is written in <I>Fortran&nbsp;2003</I>, following an Version 2.1 of the package is written in <I>Fortran&nbsp;2003</I>, following an
<I>object-oriented design</I> through the exploitation of features <I>object-oriented design</I> through the exploitation of features
such as abstract data type creation, functional overloading and such as abstract data type creation, functional overloading and
dynamic memory management. The parallel implementation is based on a Single Program Multiple Data dynamic memory management. The parallel implementation is based on a Single Program Multiple Data
@ -149,11 +149,12 @@ by expert users to build new versions of multi-level Schwarz preconditioners.
We provide here a description of the upper-layer routines, but not of the We provide here a description of the upper-layer routines, but not of the
medium-layer ones. medium-layer ones.
<P> <P>
The user interface of version 2.0 is essentially identical to that of The user interface of version 2.1 is essentially identical (except for
the support of additional solvers) to that of
version 1.1. The internal implementation however has been changed version 1.1. The internal implementation however has been changed
significantly; as a result, it has become much easier to extend the library by significantly; as a result, it has become much easier to extend the library by
adding new smoothers and/or solvers, thanks to the Fortran&nbsp;2003 features adding new smoothers and/or solvers, thanks to the Fortran&nbsp;2003 features
exploited in the design of PSBLAS&nbsp;3.0. exploited in the design of PSBLAS&nbsp;3.
<P> <P>
This guide is organized as follows. General information on the distribution of the source code This guide is organized as follows. General information on the distribution of the source code

@ -89,7 +89,7 @@ constant
</DIV> </DIV>
<BR CLEAR="ALL"> <BR CLEAR="ALL">
<P></P> <P></P>
whose current value is <code>2.0.0</code> whose current value is <code>2.1.0</code>
<BR><HR> <BR><HR>
</BODY> </BODY>

@ -66,11 +66,10 @@ to build the software.
MLD2P4 is implemented almost entirely in Fortran&nbsp;2003, with some MLD2P4 is implemented almost entirely in Fortran&nbsp;2003, with some
interfaces to external libraries in C; the Fortran compiler interfaces to external libraries in C; the Fortran compiler
must support the Fortran&nbsp;2003 standard plus the extension <code>MOLD=</code> must support the Fortran&nbsp;2003 standard plus the extension <code>MOLD=</code>
feature, which feature, which enhances the usability of <code>ALLOCATE</code>.
enhances the usability of <code>ALLOCATE</code>.
Many compiles do this; in particular, this is Many compiles do this; in particular, this is
supported by the GNU Fortran compiler, for which we supported by the GNU Fortran compiler, for which we
recommend to use at least version 4.7.2. recommend to use at least version 4.8.
The software defines data types and interfaces for The software defines data types and interfaces for
real and complex data, in both single and double precision. real and complex data, in both single and double precision.

@ -88,7 +88,7 @@ The following base libraries are needed:
HREF="node25.html#psblas_00">18</A>] Parallel Sparse BLAS is HREF="node25.html#psblas_00">18</A>] Parallel Sparse BLAS is
available from available from
<BR><code>http://www.ce.uniroma2.it/psblas</code>; version <BR><code>http://www.ce.uniroma2.it/psblas</code>; version
3.3 (or later) is required. Indeed, all the prerequisites 3.4.0 (or later) is required. Indeed, all the prerequisites
listed so far are also prerequisites of PSBLAS. listed so far are also prerequisites of PSBLAS.
</DD> </DD>
</DL> </DL>

@ -144,6 +144,15 @@ Optional Packages:
--with-extra-libs List additional link flags here. For example, --with-extra-libs List additional link flags here. For example,
--with-extra-libs=-lspecial_system_lib or --with-extra-libs=-lspecial_system_lib or
--with-extra-libs=-L/path/to/libs --with-extra-libs=-L/path/to/libs
--with-mumps=LIBNAME Specify the libname for MUMPS. Default: "-lsmumps
-ldmumps -lcmumps -lzmumps -lmumps_common -lpord"
--with-mumpsdir=DIR Specify the directory for MUMPS library and
includes. Note: you will need to add auxiliary
libraries with --extra-libs; this depends on how
MUMPS was configured and installed, at a minimum you
will need SCALAPACK and BLAS
--with-mumpsincdir=DIR Specify the directory for MUMPS includes.
--with-mumpslibdir=DIR Specify the directory for MUMPS library.
--with-umfpack=LIBNAME Specify the library name for UMFPACK and its support --with-umfpack=LIBNAME Specify the library name for UMFPACK and its support
libraries. Default: "-lumfpack -lamd" libraries. Default: "-lumfpack -lamd"
--with-umfpackdir=DIR Specify the directory for UMFPACK library and --with-umfpackdir=DIR Specify the directory for UMFPACK library and
@ -194,12 +203,12 @@ it to find libraries and programs with nonstandard names/locations.
Report bugs to &lt;bugreport@mld2p4.it&gt;. Report bugs to &lt;bugreport@mld2p4.it&gt;.
</PRE> </PRE>
For instance, if a user has built and installed PSBLAS 3.3 under the For instance, if a user has built and installed PSBLAS 3.4 under the
<code>/opt</code> directory and is <code>/opt</code> directory and is
using the SuiteSparse package (which includes UMFPACK), then MLD2P4 using the SuiteSparse package (which includes UMFPACK), then MLD2P4
might be configured with: might be configured with:
<PRE> <PRE>
./configure --with-psblas=/opt/psblas-3.3/ \ ./configure --with-psblas=/opt/psblas-3.4/ \
--with-umfpackincdir=/usr/include/suitesparse --with-umfpackincdir=/usr/include/suitesparse
</PRE> </PRE>
Once the configure script has completed execution, it will have Once the configure script has completed execution, it will have
@ -208,8 +217,13 @@ Makefiles in the directory tree; this file will be copied in the
install directory under the name <code>Make.inc.MLD2P4</code>. install directory under the name <code>Make.inc.MLD2P4</code>.
<P> <P>
In order to use the MUMPS solver based on multifrontal factorization, the user has to add MUMPS flags, include directories and libraries in the Make.inc file. To use the MUMPS solver package,
The necessary MUMPS libraries are <code>-ldmumps, -lsmumps -lzmumps -lzmumps -mumps_common -lpord</code>. The flag <code>-DHAVE_MUMPS_</code> is mandatory too. Since MUMPS uses openmp and ScaLAPACK, <code>LINKOPT=-fonemp</code> must be added as well, along with the ScaLAPACK flags, include directories and library (which can be set using the configure script). the user has to add the appropriate options to the configure script;
by default we are looking for the libraries
<code>-ldmumps -lsmumps -lzmumps -lzmumps -mumps_common -lpord</code>.
MUMPS often uses additional packages such as ScaLAPACK, ParMETIS,
SCOTCH, as well as enabling OpenMP; in such cases it is necessary to
add linker options with the <code>--with-extra-libs</code> configure option.
<P> <P>
To build the library the user will now enter To build the library the user will now enter

@ -133,7 +133,7 @@ BT
0 g 0 G 0 g 0 G
[-431(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ [-431(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
0 g 0 G 0 g 0 G
[-1780(8)]TJ [-1780(9)]TJ
0 g 0 G 0 g 0 G
0 0 1 rg 0 0 1 RG 0 0 1 rg 0 0 1 RG
0 -13.549 Td [(3.5)-1022(Example)-333(and)-334(test)-333(programs)]TJ 0 -13.549 Td [(3.5)-1022(Example)-333(and)-334(test)-333(programs)]TJ
@ -328,7 +328,7 @@ BT
1 0 0 rg 1 0 0 RG 1 0 0 rg 1 0 0 RG
[-284(27)]TJ [-284(27)]TJ
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q q
1 0 0 1 306.627 932.783 cm 1 0 0 1 306.627 946.332 cm
[]0 d 0 J 0.398 w 0 0 m 565.57 0 l S []0 d 0 J 0.398 w 0 0 m 565.57 0 l S
Q Q
q q
1 0 0 1 306.627 905.485 cm 1 0 0 1 306.627 919.035 cm
[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S []0 d 0 J 0.398 w 0 0 m 0 27.098 l S
Q Q
BT BT
/F44 10.9091 Tf 312.605 923.099 Td [(mld_sub_ovr_)]TJ 0 -13.549 Td [(SUB_OVR)]TJ /F44 10.9091 Tf 312.605 936.649 Td [(mld_sub_ovr_)]TJ 0 -13.55 Td [(SUB_OVR)]TJ
ET ET
q q
1 0 0 1 417.795 905.485 cm 1 0 0 1 417.795 919.035 cm
[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S []0 d 0 J 0.398 w 0 0 m 0 27.098 l S
Q Q
BT BT
/F44 10.9091 Tf 423.773 923.099 Td [(integer)]TJ /F44 10.9091 Tf 423.773 936.649 Td [(integer)]TJ
ET ET
q q
1 0 0 1 536.768 905.485 cm 1 0 0 1 536.768 919.035 cm
[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S []0 d 0 J 0.398 w 0 0 m 0 27.098 l S
Q Q
BT BT
/F15 10.9091 Tf 542.746 923.099 Td [(an)28(y)-333(in)27(t.)-333(n)28(um.)]TJ/F25 10.9091 Tf 67.879 0 Td [(\025)]TJ/F15 10.9091 Tf 11.515 0 Td [(0)]TJ /F15 10.9091 Tf 542.746 936.649 Td [(an)28(y)-333(in)27(t.)-333(n)28(um.)]TJ/F25 10.9091 Tf 67.879 0 Td [(\025)]TJ/F15 10.9091 Tf 11.515 0 Td [(0)]TJ
ET ET
q q
1 0 0 1 639.432 905.485 cm 1 0 0 1 639.432 919.035 cm
[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S []0 d 0 J 0.398 w 0 0 m 0 27.098 l S
Q Q
BT BT
/F15 10.9091 Tf 645.41 923.099 Td [(1)]TJ /F15 10.9091 Tf 645.41 936.649 Td [(1)]TJ
ET ET
q q
1 0 0 1 718.51 905.485 cm 1 0 0 1 718.51 919.035 cm
[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S []0 d 0 J 0.398 w 0 0 m 0 27.098 l S
Q Q
BT BT
/F15 10.9091 Tf 724.488 923.099 Td [(Num)28(b)-28(er)-333(of)-334(o)28(v)28(erlap)-333(la)28(y)27(ers.)]TJ /F15 10.9091 Tf 724.488 936.649 Td [(Num)28(b)-28(er)-333(of)-334(o)28(v)28(erlap)-333(la)28(y)27(ers.)]TJ
ET ET
q q
1 0 0 1 872.198 905.485 cm 1 0 0 1 872.198 919.035 cm
[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S []0 d 0 J 0.398 w 0 0 m 0 27.098 l S
Q Q
q q
1 0 0 1 306.627 905.286 cm 1 0 0 1 306.627 918.835 cm
[]0 d 0 J 0.398 w 0 0 m 565.57 0 l S []0 d 0 J 0.398 w 0 0 m 565.57 0 l S
Q Q
q q
1 0 0 1 306.627 850.89 cm 1 0 0 1 306.627 864.439 cm
[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S []0 d 0 J 0.398 w 0 0 m 0 54.197 l S
Q Q
BT BT
/F44 10.9091 Tf 312.605 895.603 Td [(mld_sub_restr_)]TJ 0 -13.55 Td [(SUB_RESTR)]TJ /F44 10.9091 Tf 312.605 909.152 Td [(mld_sub_restr_)]TJ 0 -13.549 Td [(SUB_RESTR)]TJ
ET ET
q q
1 0 0 1 417.795 850.89 cm 1 0 0 1 417.795 864.439 cm
[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S []0 d 0 J 0.398 w 0 0 m 0 54.197 l S
Q Q
BT BT
/F44 10.9091 Tf 423.773 895.603 Td [(character\050len=*\051)]TJ /F44 10.9091 Tf 423.773 909.152 Td [(character\050len=*\051)]TJ
ET ET
q q
1 0 0 1 536.768 850.89 cm 1 0 0 1 536.768 864.439 cm
[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S []0 d 0 J 0.398 w 0 0 m 0 54.197 l S
Q Q
BT BT
/F44 10.9091 Tf 542.746 895.603 Td [('HALO')]TJ 0 -13.55 Td [('NONE')]TJ /F44 10.9091 Tf 542.746 909.152 Td [('HALO')]TJ 0 -13.549 Td [('NONE')]TJ
ET ET
q q
1 0 0 1 639.432 850.89 cm 1 0 0 1 639.432 864.439 cm
[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S []0 d 0 J 0.398 w 0 0 m 0 54.197 l S
Q Q
BT BT
/F44 10.9091 Tf 645.41 895.603 Td [('HALO')]TJ /F44 10.9091 Tf 645.41 909.152 Td [('HALO')]TJ
ET ET
q q
1 0 0 1 718.51 850.89 cm 1 0 0 1 718.51 864.439 cm
[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S []0 d 0 J 0.398 w 0 0 m 0 54.197 l S
Q Q
BT BT
/F15 10.9091 Tf 724.488 895.603 Td [(T)28(yp)-28(e)-501(of)-501(restriction)-501(op)-28(erator:)]TJ/F44 10.9091 Tf 0 -13.55 Td [('HALO')]TJ/F15 10.9091 Tf 42.331 0 Td [(for)-731(taking)-730(in)27(to)-730(ac-)]TJ -42.331 -13.549 Td [(coun)28(t)-354(the)-354(o)28(v)28(erlap,)]TJ/F44 10.9091 Tf 90.45 0 Td [('NONE')]TJ/F15 10.9091 Tf 38.222 0 Td [(for)]TJ -128.672 -13.549 Td [(neglecting)-333(it.)]TJ /F15 10.9091 Tf 724.488 909.152 Td [(T)28(yp)-28(e)-501(of)-501(restriction)-501(op)-28(erator:)]TJ/F44 10.9091 Tf 0 -13.549 Td [('HALO')]TJ/F15 10.9091 Tf 42.331 0 Td [(for)-731(taking)-730(in)27(to)-730(ac-)]TJ -42.331 -13.55 Td [(coun)28(t)-354(the)-354(o)28(v)28(erlap,)]TJ/F44 10.9091 Tf 90.45 0 Td [('NONE')]TJ/F15 10.9091 Tf 38.222 0 Td [(for)]TJ -128.672 -13.549 Td [(neglecting)-333(it.)]TJ
ET ET
q q
1 0 0 1 872.198 850.89 cm 1 0 0 1 872.198 864.439 cm
[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S []0 d 0 J 0.398 w 0 0 m 0 54.197 l S
Q Q
q q
1 0 0 1 306.627 850.691 cm 1 0 0 1 306.627 864.24 cm
[]0 d 0 J 0.398 w 0 0 m 565.57 0 l S []0 d 0 J 0.398 w 0 0 m 565.57 0 l S
Q Q
q q
1 0 0 1 306.627 796.295 cm 1 0 0 1 306.627 809.844 cm
[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S []0 d 0 J 0.398 w 0 0 m 0 54.197 l S
Q Q
BT BT
/F44 10.9091 Tf 312.605 841.007 Td [(mld_sub_prol_)]TJ 0 -13.549 Td [(SUB_PROL)]TJ /F44 10.9091 Tf 312.605 854.556 Td [(mld_sub_prol_)]TJ 0 -13.549 Td [(SUB_PROL)]TJ
ET ET
q q
1 0 0 1 417.795 796.295 cm 1 0 0 1 417.795 809.844 cm
[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S []0 d 0 J 0.398 w 0 0 m 0 54.197 l S
Q Q
BT BT
/F44 10.9091 Tf 423.773 841.007 Td [(character\050len=*\051)]TJ /F44 10.9091 Tf 423.773 854.556 Td [(character\050len=*\051)]TJ
ET ET
q q
1 0 0 1 536.768 796.295 cm 1 0 0 1 536.768 809.844 cm
[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S []0 d 0 J 0.398 w 0 0 m 0 54.197 l S
Q Q
BT BT
/F44 10.9091 Tf 542.746 841.007 Td [('SUM')]TJ 0 -13.549 Td [('NONE')]TJ /F44 10.9091 Tf 542.746 854.556 Td [('SUM')]TJ 0 -13.549 Td [('NONE')]TJ
ET ET
q q
1 0 0 1 639.432 796.295 cm 1 0 0 1 639.432 809.844 cm
[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S []0 d 0 J 0.398 w 0 0 m 0 54.197 l S
Q Q
BT BT
/F44 10.9091 Tf 645.41 841.007 Td [('NONE')]TJ /F44 10.9091 Tf 645.41 854.556 Td [('NONE')]TJ
ET ET
q q
1 0 0 1 718.51 796.295 cm 1 0 0 1 718.51 809.844 cm
[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S []0 d 0 J 0.398 w 0 0 m 0 54.197 l S
Q Q
BT BT
/F15 10.9091 Tf 724.488 841.007 Td [(T)28(yp)-28(e)-560(of)-561(prolon)1(gation)-561(op)-27(e)-1(r)1(a-)]TJ 0 -13.549 Td [(tor:)]TJ/F44 10.9091 Tf 21.445 0 Td [('SUM')]TJ/F15 10.9091 Tf 31.465 0 Td [(for)-259(adding)-260(th)1(e)-260(con-)]TJ -52.91 -13.549 Td [(tributions)-622(from)-623(t)1(he)-623(o)28(v)28(erlap,)]TJ/F44 10.9091 Tf 0 -13.549 Td [('NONE')]TJ/F15 10.9091 Tf 37.999 0 Td [(for)-333(neglecting)-334(them.)]TJ /F15 10.9091 Tf 724.488 854.556 Td [(T)28(yp)-28(e)-560(of)-561(prolon)1(gation)-561(op)-27(e)-1(r)1(a-)]TJ 0 -13.549 Td [(tor:)]TJ/F44 10.9091 Tf 21.445 0 Td [('SUM')]TJ/F15 10.9091 Tf 31.465 0 Td [(for)-259(adding)-260(th)1(e)-260(con-)]TJ -52.91 -13.549 Td [(tributions)-622(from)-623(t)1(he)-623(o)28(v)28(erlap,)]TJ/F44 10.9091 Tf 0 -13.549 Td [('NONE')]TJ/F15 10.9091 Tf 37.999 0 Td [(for)-333(neglecting)-334(them.)]TJ
ET ET
q q
1 0 0 1 872.198 796.295 cm 1 0 0 1 872.198 809.844 cm
[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S []0 d 0 J 0.398 w 0 0 m 0 54.197 l S
Q Q
q q
1 0 0 1 306.627 796.096 cm 1 0 0 1 306.627 809.645 cm
[]0 d 0 J 0.398 w 0 0 m 565.57 0 l S []0 d 0 J 0.398 w 0 0 m 565.57 0 l S
Q Q
q q
1 0 0 1 306.627 701.052 cm 1 0 0 1 306.627 687.503 cm
[]0 d 0 J 0.398 w 0 0 m 0 94.844 l S []0 d 0 J 0.398 w 0 0 m 0 121.943 l S
Q Q
BT BT
/F44 10.9091 Tf 312.605 786.412 Td [(mld_sub_solve_)]TJ 0 -13.549 Td [(SUB_SOLVE)]TJ /F44 10.9091 Tf 312.605 799.961 Td [(mld_sub_solve_)]TJ 0 -13.549 Td [(SUB_SOLVE)]TJ
ET ET
q q
1 0 0 1 417.795 701.052 cm 1 0 0 1 417.795 687.503 cm
[]0 d 0 J 0.398 w 0 0 m 0 94.844 l S []0 d 0 J 0.398 w 0 0 m 0 121.943 l S
Q Q
BT BT
/F44 10.9091 Tf 423.773 786.412 Td [(character\050len=*\051)]TJ /F44 10.9091 Tf 423.773 799.961 Td [(character\050len=*\051)]TJ
ET ET
q q
1 0 0 1 536.768 701.052 cm 1 0 0 1 536.768 687.503 cm
[]0 d 0 J 0.398 w 0 0 m 0 94.844 l S []0 d 0 J 0.398 w 0 0 m 0 121.943 l S
Q Q
BT BT
/F44 10.9091 Tf 542.746 786.412 Td [('DIAG')]TJ 0 -13.549 Td [('GS')]TJ 0 -13.549 Td [('ILU')]TJ 0 -13.55 Td [('MILU')]TJ 0 -13.549 Td [('ILUT')]TJ 0 -13.549 Td [('UMF')]TJ 0 -13.549 Td [('SLU')]TJ /F44 10.9091 Tf 542.746 799.961 Td [('DIAG')]TJ 0 -13.549 Td [('GS')]TJ 0 -13.549 Td [('BWGS')]TJ 0 -13.549 Td [('ILU')]TJ 0 -13.55 Td [('MILU')]TJ 0 -13.549 Td [('ILUT')]TJ 0 -13.549 Td [('UMF')]TJ 0 -13.549 Td [('SLU')]TJ 0 -13.549 Td [('MUMPS')]TJ
ET ET
q q
1 0 0 1 639.432 701.052 cm 1 0 0 1 639.432 687.503 cm
[]0 d 0 J 0.398 w 0 0 m 0 94.844 l S []0 d 0 J 0.398 w 0 0 m 0 121.943 l S
Q Q
BT BT
/F44 10.9091 Tf 645.41 786.412 Td [('ILU')]TJ /F44 10.9091 Tf 645.41 799.961 Td [('ILU')]TJ
ET ET
q q
1 0 0 1 718.51 701.052 cm 1 0 0 1 718.51 687.503 cm
[]0 d 0 J 0.398 w 0 0 m 0 94.844 l S []0 d 0 J 0.398 w 0 0 m 0 121.943 l S
Q Q
BT BT
/F15 10.9091 Tf 724.488 786.412 Td [(Prede\014ned)-264(lo)-28(cal)-265(solv)28(er:)-410(p)-28(oin)28(t-)]TJ 0 -13.549 Td [(wise)-785(Jacobi)-786(\050diagonal)-785(scal-)]TJ 0 -13.549 Td [(ing\051,)-951(Gauss-Seidel,)-950(ILU\050)]TJ/F22 10.9091 Tf 128.971 0 Td [(p)]TJ/F15 10.9091 Tf 5.488 0 Td [(\051,)]TJ -134.459 -13.55 Td [(MILU\050)]TJ/F22 10.9091 Tf 33.182 0 Td [(p)]TJ/F15 10.9091 Tf 5.488 0 Td [(\051,)-431(ILU\050)]TJ/F22 10.9091 Tf 35.162 0 Td [(p;)-167(t)]TJ/F15 10.9091 Tf 14.277 0 Td [(\051,)-431(LU)-412(from)]TJ -88.109 -13.549 Td [(UMFP)83(A)28(CK,)-908(LU)-909(f)1(rom)-909(Su-)]TJ 0 -13.549 Td [(p)-28(erLU)-301(\050plus)-301(triangular)-301(solv)28(e\051.)]TJ /F15 10.9091 Tf 724.488 799.961 Td [(Prede\014ned)-264(lo)-28(cal)-265(solv)28(er:)-410(p)-28(oin)28(t-)]TJ 0 -13.549 Td [(wise)-230(Jacobi)-230(\050diagon)1(al)-230(scaling\051,)]TJ 0 -13.549 Td [(\050forw)28(ard\051)-293(Gauss-Seidel,)-301(Bac)28(k-)]TJ 0 -13.549 Td [(w)28(ard)-819(Gauss-Seidel,)-941(ILU\050)]TJ/F22 10.9091 Tf 128.971 0 Td [(p)]TJ/F15 10.9091 Tf 5.488 0 Td [(\051,)]TJ -134.459 -13.55 Td [(MILU\050)]TJ/F22 10.9091 Tf 33.182 0 Td [(p)]TJ/F15 10.9091 Tf 5.488 0 Td [(\051,)-431(ILU\050)]TJ/F22 10.9091 Tf 35.162 0 Td [(p;)-167(t)]TJ/F15 10.9091 Tf 14.277 0 Td [(\051,)-431(LU)-412(from)]TJ -88.109 -13.549 Td [(UMFP)83(A)28(CK,)-908(LU)-909(f)1(rom)-909(Su-)]TJ 0 -13.549 Td [(p)-28(erLU)-301(\050plus)-301(triangular)-301(solv)28(e\051,)]TJ 0 -13.549 Td [(LU)-333(from)-334(MUMPS)1(.)]TJ
ET ET
q q
1 0 0 1 872.198 701.052 cm 1 0 0 1 872.198 687.503 cm
[]0 d 0 J 0.398 w 0 0 m 0 94.844 l S []0 d 0 J 0.398 w 0 0 m 0 121.943 l S
Q Q
q q
1 0 0 1 306.627 700.853 cm 1 0 0 1 306.627 687.304 cm
[]0 d 0 J 0.398 w 0 0 m 565.57 0 l S []0 d 0 J 0.398 w 0 0 m 565.57 0 l S
Q Q
q q
1 0 0 1 306.627 673.555 cm 1 0 0 1 306.627 660.006 cm
[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S []0 d 0 J 0.398 w 0 0 m 0 27.098 l S
Q Q
BT BT
/F44 10.9091 Tf 312.605 691.169 Td [(mld_sub_fillin_)]TJ 0 -13.549 Td [(SUB_FILLIN)]TJ /F44 10.9091 Tf 312.605 677.62 Td [(mld_sub_fillin_)]TJ 0 -13.549 Td [(SUB_FILLIN)]TJ
ET ET
q q
1 0 0 1 417.795 673.555 cm 1 0 0 1 417.795 660.006 cm
[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S []0 d 0 J 0.398 w 0 0 m 0 27.098 l S
Q Q
BT BT
/F44 10.9091 Tf 423.773 691.169 Td [(integer)]TJ /F44 10.9091 Tf 423.773 677.62 Td [(integer)]TJ
ET ET
q q
1 0 0 1 536.768 673.555 cm 1 0 0 1 536.768 660.006 cm
[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S []0 d 0 J 0.398 w 0 0 m 0 27.098 l S
Q Q
BT BT
/F15 10.9091 Tf 542.746 691.169 Td [(An)28(y)-333(in)27(t.)-333(n)28(um.)]TJ/F25 10.9091 Tf 70.606 0 Td [(\025)]TJ/F15 10.9091 Tf 11.515 0 Td [(0)]TJ /F15 10.9091 Tf 542.746 677.62 Td [(An)28(y)-333(in)27(t.)-333(n)28(um.)]TJ/F25 10.9091 Tf 70.606 0 Td [(\025)]TJ/F15 10.9091 Tf 11.515 0 Td [(0)]TJ
ET ET
q q
1 0 0 1 639.432 673.555 cm 1 0 0 1 639.432 660.006 cm
[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S []0 d 0 J 0.398 w 0 0 m 0 27.098 l S
Q Q
BT BT
/F15 10.9091 Tf 645.41 691.169 Td [(0)]TJ /F15 10.9091 Tf 645.41 677.62 Td [(0)]TJ
ET ET
q q
1 0 0 1 718.51 673.555 cm 1 0 0 1 718.51 660.006 cm
[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S []0 d 0 J 0.398 w 0 0 m 0 27.098 l S
Q Q
BT BT
/F15 10.9091 Tf 724.488 691.169 Td [(Fill-in)-550(lev)27(el)]TJ/F22 10.9091 Tf 62.164 0 Td [(p)]TJ/F15 10.9091 Tf 11.495 0 Td [(of)-551(th)1(e)-551(incom-)]TJ -73.659 -13.549 Td [(plete)-333(LU)-334(factorizations.)]TJ /F15 10.9091 Tf 724.488 677.62 Td [(Fill-in)-550(lev)27(el)]TJ/F22 10.9091 Tf 62.164 0 Td [(p)]TJ/F15 10.9091 Tf 11.495 0 Td [(of)-551(th)1(e)-551(incom-)]TJ -73.659 -13.549 Td [(plete)-333(LU)-334(factorizations.)]TJ
ET ET
q q
1 0 0 1 872.198 673.555 cm 1 0 0 1 872.198 660.006 cm
[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S []0 d 0 J 0.398 w 0 0 m 0 27.098 l S
Q Q
q q
1 0 0 1 306.627 673.356 cm 1 0 0 1 306.627 659.807 cm
[]0 d 0 J 0.398 w 0 0 m 565.57 0 l S []0 d 0 J 0.398 w 0 0 m 565.57 0 l S
Q Q
q q
1 0 0 1 306.627 646.058 cm 1 0 0 1 306.627 632.509 cm
[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S []0 d 0 J 0.398 w 0 0 m 0 27.098 l S
Q Q
BT BT
/F44 10.9091 Tf 312.605 663.672 Td [(mld_sub_iluthrs_)]TJ 0 -13.549 Td [(SUB_ILUTHRS)]TJ /F44 10.9091 Tf 312.605 650.123 Td [(mld_sub_iluthrs_)]TJ 0 -13.549 Td [(SUB_ILUTHRS)]TJ
ET ET
q q
1 0 0 1 417.795 646.058 cm 1 0 0 1 417.795 632.509 cm
[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S []0 d 0 J 0.398 w 0 0 m 0 27.098 l S
Q Q
BT BT
/F44 10.9091 Tf 423.773 663.672 Td [(real\050)]TJ/F18 10.9091 Tf 28.636 0 Td [(kind)]TJ /F44 10.9091 Tf 423.773 650.123 Td [(real\050)]TJ/F18 10.9091 Tf 28.636 0 Td [(kind)]TJ
ET ET
q q
1 0 0 1 473.15 663.872 cm 1 0 0 1 473.15 650.322 cm
[]0 d 0 J 0.398 w 0 0 m 3.345 0 l S []0 d 0 J 0.398 w 0 0 m 3.345 0 l S
Q Q
BT BT
/F18 10.9091 Tf 476.496 663.672 Td [(p)51(ar)51(ameter)]TJ/F44 10.9091 Tf 48.568 0 Td [(\051)]TJ /F18 10.9091 Tf 476.496 650.123 Td [(p)51(ar)51(ameter)]TJ/F44 10.9091 Tf 48.568 0 Td [(\051)]TJ
ET ET
q q
1 0 0 1 536.768 646.058 cm 1 0 0 1 536.768 632.509 cm
[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S []0 d 0 J 0.398 w 0 0 m 0 27.098 l S
Q Q
BT BT
/F15 10.9091 Tf 542.746 663.672 Td [(An)28(y)-333(re)-1(al)-333(n)28(um.)]TJ/F25 10.9091 Tf 72.152 0 Td [(\025)]TJ/F15 10.9091 Tf 11.515 0 Td [(0)]TJ /F15 10.9091 Tf 542.746 650.123 Td [(An)28(y)-333(re)-1(al)-333(n)28(um.)]TJ/F25 10.9091 Tf 72.152 0 Td [(\025)]TJ/F15 10.9091 Tf 11.515 0 Td [(0)]TJ
ET ET
q q
1 0 0 1 639.432 646.058 cm 1 0 0 1 639.432 632.509 cm
[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S []0 d 0 J 0.398 w 0 0 m 0 27.098 l S
Q Q
BT BT
/F15 10.9091 Tf 645.41 663.672 Td [(0)]TJ /F15 10.9091 Tf 645.41 650.123 Td [(0)]TJ
ET ET
q q
1 0 0 1 718.51 646.058 cm 1 0 0 1 718.51 632.509 cm
[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S []0 d 0 J 0.398 w 0 0 m 0 27.098 l S
Q Q
BT BT
/F15 10.9091 Tf 724.488 663.672 Td [(Drop)-1063(tol)1(e)-1(r)1(ance)]TJ/F22 10.9091 Tf 90.366 0 Td [(t)]TJ/F15 10.9091 Tf 15.532 0 Td [(in)-1063(t)1(he)]TJ -105.898 -13.549 Td [(ILU\050)]TJ/F22 10.9091 Tf 23.182 0 Td [(p;)-167(t)]TJ/F15 10.9091 Tf 14.276 0 Td [(\051)-333(factorization.)]TJ /F15 10.9091 Tf 724.488 650.123 Td [(Drop)-1063(tol)1(e)-1(r)1(ance)]TJ/F22 10.9091 Tf 90.366 0 Td [(t)]TJ/F15 10.9091 Tf 15.532 0 Td [(in)-1063(t)1(he)]TJ -105.898 -13.549 Td [(ILU\050)]TJ/F22 10.9091 Tf 23.182 0 Td [(p;)-167(t)]TJ/F15 10.9091 Tf 14.276 0 Td [(\051)-333(factorization.)]TJ
ET ET
q q
1 0 0 1 872.198 646.058 cm 1 0 0 1 872.198 632.509 cm
[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S []0 d 0 J 0.398 w 0 0 m 0 27.098 l S
Q Q
q q
1 0 0 1 306.627 645.859 cm 1 0 0 1 306.627 632.31 cm
[]0 d 0 J 0.398 w 0 0 m 565.57 0 l S []0 d 0 J 0.398 w 0 0 m 565.57 0 l S
Q Q
q q
1 0 0 1 306.627 564.365 cm 1 0 0 1 306.627 550.815 cm
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