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<div class="section" id="getting-started">
<span id="sec-getting-started"></span><h1>Getting Started<a class="headerlink" href="#getting-started" title="Permalink to this headline">¶</a></h1>
<p>PETSc consists of a collection of classes,
which are discussed in detail in later parts of the manual (<a class="reference internal" href="programming.html"><span class="doc">Programming with PETSc</span></a> and <a class="reference internal" href="additional.html"><span class="doc">Additional Information</span></a>).
The important PETSc classes include</p>
<ul class="simple">
<li><p>index sets (<code class="docutils literal notranslate"><span class="pre"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/IS/IS.html#IS">IS</a></span></code>), including permutations, for indexing into
vectors, renumbering, etc;</p></li>
<li><p>vectors (<code class="docutils literal notranslate"><span class="pre"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/Vec.html#Vec">Vec</a></span></code>);</p></li>
<li><p>matrices (<code class="docutils literal notranslate"><span class="pre"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/Mat.html#Mat">Mat</a></span></code>) (generally sparse);</p></li>
<li><p>over thirty Krylov subspace methods (<code class="docutils literal notranslate"><span class="pre"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSP.html#KSP">KSP</a></span></code>);</p></li>
<li><p>dozens of preconditioners, including multigrid, block solvers, and
sparse direct solvers (<code class="docutils literal notranslate"><span class="pre"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/PC/PC.html#PC">PC</a></span></code>);</p></li>
<li><p>nonlinear solvers (<code class="docutils literal notranslate"><span class="pre"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/SNES/SNES.html#SNES">SNES</a></span></code>);</p></li>
<li><p>timesteppers for solving time-dependent (nonlinear) PDEs, including
support for differential algebraic equations, and the computation of
adjoints (sensitivities/gradients of the solutions) (<code class="docutils literal notranslate"><span class="pre"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/TS/TS.html#TS">TS</a></span></code>);</p></li>
<li><p>managing interactions between mesh data structures and vectors,
matrices, and solvers (<code class="docutils literal notranslate"><span class="pre"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/DM/DM.html#DM">DM</a></span></code>);</p></li>
<li><p>scalable optimization algorithms (<code class="docutils literal notranslate"><span class="pre"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Tao/Tao.html#Tao">Tao</a></span></code>).</p></li>
</ul>
<p>Each class consist of an abstract interface (simply a set of calling
sequences; an abstract base class in C++) and an implementation for each algorithm and data structure.
Thus, PETSc provides clean and effective codes for the
various phases of solving PDEs, with a uniform approach for each type
of problem. This design enables easy comparison and use of different
algorithms (for example, to experiment with different Krylov subspace
methods, preconditioners, or truncated Newton methods). Hence, PETSc
provides a rich environment for modeling scientific applications as well
as for rapid algorithm design and prototyping.</p>
<p>The classes enable easy customization and extension of both algorithms
and implementations. This approach promotes code reuse and flexibility,
and also separates the issues of parallelism from the choice of algorithms.
The PETSc infrastructure creates a foundation for building large-scale
applications.</p>
<p>It is useful to consider the interrelationships among different pieces
of PETSc. <a class="reference internal" href="#fig-library"><span class="std std-ref">Numerical Libraries in PETSc</span></a> is a diagram of some
of these pieces. The figure illustrates the library’s hierarchical
organization, which enables users to employ the solvers that are most
appropriate for a particular problem.</p>
<div class="figure align-default" id="fig-library">
<img alt="PETSc numerical libraries" src="../_images/library_structure.svg" /><p class="caption"><span class="caption-number">Fig. 1 </span><span class="caption-text">Numerical Libraries in PETSc</span><a class="headerlink" href="#fig-library" title="Permalink to this image">¶</a></p>
</div>
<div class="section" id="suggested-reading">
<h2>Suggested Reading<a class="headerlink" href="#suggested-reading" title="Permalink to this headline">¶</a></h2>
<p>The manual is divided into three parts:</p>
<ul class="simple">
<li><p><a class="reference internal" href="introduction.html"><span class="doc">Introduction to PETSc</span></a></p></li>
<li><p><a class="reference internal" href="programming.html"><span class="doc">Programming with PETSc</span></a></p></li>
<li><p><a class="reference internal" href="additional.html"><span class="doc">Additional Information</span></a></p></li>
</ul>
<p><a class="reference internal" href="introduction.html"><span class="doc">Introduction to PETSc</span></a> describes the basic procedure for using the PETSc library and
presents two simple examples of solving linear systems with PETSc. This
section conveys the typical style used throughout the library and
enables the application programmer to begin using the software
immediately.</p>
<p><a class="reference internal" href="programming.html"><span class="doc">Programming with PETSc</span></a> explains in detail the use of the various PETSc libraries, such
as vectors, matrices, index sets, linear and nonlinear solvers, and
graphics. <a class="reference internal" href="additional.html"><span class="doc">Additional Information</span></a> describes a variety of useful information, including
profiling, the options database, viewers, error handling, and some
details of PETSc design.</p>
<p>PETSc has evolved to become quite a comprehensive package, and therefore
this manual can be rather intimidating for new users. Bear in mind that PETSc can be used
efficiently before one understands all of the material presented here.
Furthermore, the definitive reference for any PETSc function is always
the online manual page.
Manual pages for all PETSc functions can be accessed at
<a class="reference external" href="https://www.mcs.anl.gov/petsc/documentation/">www.mcs.anl.gov/petsc/documentation</a>.
The manual pages provide hyperlinked indices (organized by both concept
and routine name) to the tutorial examples and enable easy movement
among related topics.</p>
<p><a class="reference external" href="https://code.visualstudio.com/">Visual Studio Code</a> , Eclipse, Emacs, and Vim users may find their development environment’s options for
searching in the source code (for example, <code class="docutils literal notranslate"><span class="pre">etags</span></code> <code class="docutils literal notranslate"><span class="pre">ctags</span></code> for Emacs and Vim) are
extremely useful for exploring the PETSc source code. Details of these
feature are provided in <a class="reference internal" href="other.html#sec-emacs"><span class="std std-ref">Emacs Users</span></a>.</p>
<p>The complete PETSc distribution, manual pages, and additional information are available via the
<a class="reference external" href="https://www.mcs.anl.gov/petsc">PETSc home page</a>. The PETSc
home page also contains details regarding installation, new features and
changes in recent versions of PETSc, machines that we currently support,
and a frequently asked questions (FAQ) list.</p>
<p><strong>Note to Fortran Programmers</strong>: In most of the manual, the examples and calling sequences are given
for the C/C++ family of programming languages. However, Fortran
programmers can use all of the functionality of PETSc from Fortran,
with only minor differences in the user interface.
<a class="reference internal" href="fortran.html#chapter-fortran"><span class="std std-ref">PETSc for Fortran Users</span></a> provides a discussion of the differences between
using PETSc from Fortran and C, as well as several complete Fortran
examples.</p>
<p><strong>Note to Python Programmers</strong>: To program with PETSc in Python you need to install the
PETSc4py package developed by Lisandro Dalcin. This can be done by
configuring PETSc with the option <code class="docutils literal notranslate"><span class="pre">--download-petsc4py</span></code>. See the
<a class="reference external" href="https://www.mcs.anl.gov/petsc/documentation/installation.html">PETSc installation guide</a>
for more details.</p>
</div>
<div class="section" id="running-petsc-programs">
<span id="sec-running"></span><h2>Running PETSc Programs<a class="headerlink" href="#running-petsc-programs" title="Permalink to this headline">¶</a></h2>
<p>Before using PETSc, the user must first set the environmental variable
<code class="docutils literal notranslate"><span class="pre">PETSC_DIR</span></code>, indicating the full path of the PETSc home directory. For
example, under the UNIX bash shell a command of the form</p>
<div class="highlight-bash notranslate"><div class="highlight"><pre><span></span><span class="nb">export</span> <span class="nv">PETSC_DIR</span><span class="o">=</span><span class="nv">$HOME</span>/petsc
</pre></div>
</div>
<p>can be placed in the user’s <code class="docutils literal notranslate"><span class="pre">.bashrc</span></code> or other startup file. In
addition, the user may need to set the environment variable
<code class="docutils literal notranslate"><span class="pre">PETSC_ARCH</span></code> to specify a particular configuration of the PETSc
libraries. Note that <code class="docutils literal notranslate"><span class="pre">PETSC_ARCH</span></code> is just a name selected by the
installer to refer to the libraries compiled for a particular set of
compiler options and machine type. Using different values of
<code class="docutils literal notranslate"><span class="pre">PETSC_ARCH</span></code> allows one to switch between several different sets (say
debug and optimized) of libraries easily. To determine if you need to
set <code class="docutils literal notranslate"><span class="pre">PETSC_ARCH</span></code>, look in the directory indicated by <code class="docutils literal notranslate"><span class="pre">PETSC_DIR</span></code>, if
there are subdirectories beginning with <code class="docutils literal notranslate"><span class="pre">arch</span></code> then those
subdirectories give the possible values for <code class="docutils literal notranslate"><span class="pre">PETSC_ARCH</span></code>.</p>
<p>All PETSc programs use the MPI (Message Passing Interface) standard for
message-passing communication <span id="id1">[<a class="reference internal" href="#id201"><span>For94</span></a>]</span>. Thus, to
execute PETSc programs, users must know the procedure for beginning MPI
jobs on their selected computer system(s). For instance, when using the
<a class="reference external" href="https://www.mpich.org/">MPICH</a> implementation of MPI and many
others, the following command initiates a program that uses eight
processors:</p>
<div class="highlight-bash notranslate"><div class="highlight"><pre><span></span>mpiexec -n <span class="m">8</span> ./petsc_program_name petsc_options
</pre></div>
</div>
<p>PETSc also comes with a script that automatically uses the correct
<code class="docutils literal notranslate"><span class="pre">mpiexec</span></code> for your configuration.</p>
<div class="highlight-bash notranslate"><div class="highlight"><pre><span></span><span class="si">${</span><span class="nv">PETSC_DIR</span><span class="si">}</span>/lib/petsc/bin/petscmpiexec -n <span class="m">8</span> ./petsc_program_name petsc_options
</pre></div>
</div>
<p>All PETSc-compliant programs support the use of the <code class="docutils literal notranslate"><span class="pre">-help</span></code>
option as well as the <code class="docutils literal notranslate"><span class="pre">-version</span></code> option.</p>
<p>Certain options are supported by all PETSc programs. We list a few
particularly useful ones below; a complete list can be obtained by
running any PETSc program with the option <code class="docutils literal notranslate"><span class="pre">-help</span></code>.</p>
<ul class="simple">
<li><p><code class="docutils literal notranslate"><span class="pre">-log_view</span></code> - summarize the program’s performance (see <a class="reference internal" href="profiling.html#ch-profiling"><span class="std std-ref">Profiling</span></a>)</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">-fp_trap</span></code> - stop on floating-point exceptions; for example divide
by zero</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">-malloc_dump</span></code> - enable memory tracing; dump list of unfreed memory
at conclusion of the run, see
<a class="reference internal" href="performance.html#detecting-memory-problems"><span class="std std-ref">Detecting Memory Allocation Problems</span></a>,</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">-malloc_debug</span></code> - enable memory debugging (by default this is
activated for the debugging version of PETSc), see
<a class="reference internal" href="performance.html#detecting-memory-problems"><span class="std std-ref">Detecting Memory Allocation Problems</span></a>,</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">-start_in_debugger</span></code> <code class="docutils literal notranslate"><span class="pre">[noxterm,gdb,lldb]</span></code>
<code class="docutils literal notranslate"><span class="pre">[-display</span> <span class="pre">name]</span></code> - start all processes in debugger. See
<a class="reference internal" href="other.html#sec-debugging"><span class="std std-ref">Debugging</span></a>, for more information on
debugging PETSc programs.</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">-on_error_attach_debugger</span></code> <code class="docutils literal notranslate"><span class="pre">[noxterm,gdb,lldb]</span></code>
<code class="docutils literal notranslate"><span class="pre">[-display</span> <span class="pre">name]</span></code> - start debugger only on encountering an error</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">-info</span></code> - print a great deal of information about what the program
is doing as it runs</p></li>
</ul>
</div>
<div class="section" id="writing-petsc-programs">
<span id="sec-writing"></span><h2>Writing PETSc Programs<a class="headerlink" href="#writing-petsc-programs" title="Permalink to this headline">¶</a></h2>
<p>Most PETSc programs begin with a call to</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscInitialize.html#PetscInitialize">PetscInitialize</a></span><span class="p">(</span><span class="kt">int</span> <span class="o">*</span><span class="n">argc</span><span class="p">,</span><span class="kt">char</span> <span class="o">***</span><span class="n">argv</span><span class="p">,</span><span class="kt">char</span> <span class="o">*</span><span class="n">file</span><span class="p">,</span><span class="kt">char</span> <span class="o">*</span><span class="n">help</span><span class="p">);</span><span class="k">if</span> <span class="p">(</span><span class="n">ierr</span><span class="p">)</span> <span class="k">return</span> <span class="n">ierr</span><span class="p">;</span>
</pre></div>
</div>
<p>which initializes PETSc and MPI. The arguments <code class="docutils literal notranslate"><span class="pre">argc</span></code> and <code class="docutils literal notranslate"><span class="pre">argv</span></code> are
the command line arguments delivered in all C and C++ programs. The
argument <code class="docutils literal notranslate"><span class="pre">file</span></code> optionally indicates an alternative name for the PETSc
options file, <code class="docutils literal notranslate"><span class="pre">.petscrc</span></code>, which resides by default in the user’s home
directory. <a class="reference internal" href="other.html#sec-options"><span class="std std-ref">Runtime Options</span></a> provides details
regarding this file and the PETSc options database, which can be used
for runtime customization. The final argument, <code class="docutils literal notranslate"><span class="pre">help</span></code>, is an optional
character string that will be printed if the program is run with the
<code class="docutils literal notranslate"><span class="pre">-help</span></code> option. In Fortran the initialization command has the form</p>
<div class="highlight-fortran notranslate"><div class="highlight"><pre><span></span><span class="k">call </span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscInitialize.html#PetscInitialize">PetscInitialize</a></span><span class="p">(</span><span class="kt">character</span><span class="p">(</span><span class="o">*</span><span class="p">)</span> <span class="k">file</span><span class="p">,</span><span class="kt">integer </span><span class="n">ierr</span><span class="p">)</span>
</pre></div>
</div>
<p><code class="docutils literal notranslate"><span class="pre"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscInitialize.html#PetscInitialize">PetscInitialize</a>()</span></code> automatically calls <code class="docutils literal notranslate"><span class="pre"><a href="http://www.mpich.org/static/docs/latest/www3/MPI_Init.html#MPI_Init">MPI_Init</a>()</span></code> if MPI has not
been not previously initialized. In certain circumstances in which MPI
needs to be initialized directly (or is initialized by some other
library), the user can first call <code class="docutils literal notranslate"><span class="pre"><a href="http://www.mpich.org/static/docs/latest/www3/MPI_Init.html#MPI_Init">MPI_Init</a>()</span></code> (or have the other
library do it), and then call <code class="docutils literal notranslate"><span class="pre"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscInitialize.html#PetscInitialize">PetscInitialize</a>()</span></code>. By default,
<code class="docutils literal notranslate"><span class="pre"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscInitialize.html#PetscInitialize">PetscInitialize</a>()</span></code> sets the PETSc “world” communicator
<code class="docutils literal notranslate"><span class="pre"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PETSC_COMM_WORLD.html#PETSC_COMM_WORLD">PETSC_COMM_WORLD</a></span></code> to <code class="docutils literal notranslate"><span class="pre">MPI_COMM_WORLD</span></code>.</p>
<p>For those not familiar with MPI, a <em>communicator</em> is a way of indicating
a collection of processes that will be involved together in a
calculation or communication. Communicators have the variable type
<code class="docutils literal notranslate"><span class="pre"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/MPI_Comm.html#MPI_Comm">MPI_Comm</a></span></code>. In most cases users can employ the communicator
<code class="docutils literal notranslate"><span class="pre"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PETSC_COMM_WORLD.html#PETSC_COMM_WORLD">PETSC_COMM_WORLD</a></span></code> to indicate all processes in a given run and
<code class="docutils literal notranslate"><span class="pre"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PETSC_COMM_SELF.html#PETSC_COMM_SELF">PETSC_COMM_SELF</a></span></code> to indicate a single process.</p>
<p>MPI provides routines for generating new communicators consisting of
subsets of processors, though most users rarely need to use these. The
book <em>Using MPI</em>, by Lusk, Gropp, and Skjellum
<span id="id2">[<a class="reference internal" href="#id292"><span>GLS94</span></a>]</span> provides an excellent introduction to the
concepts in MPI. See also the <a class="reference external" href="https://www.mcs.anl.gov/research/projects/mpi/">MPI homepage</a>.
Note that PETSc users
need not program much message passing directly with MPI, but they must
be familiar with the basic concepts of message passing and distributed
memory computing.</p>
<p>All PETSc routines return a <code class="docutils literal notranslate"><span class="pre"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscErrorCode.html#PetscErrorCode">PetscErrorCode</a></span></code>, which is an integer
indicating whether an error has occurred during the call. The error code
is set to be nonzero if an error has been detected; otherwise, it is
zero. For the C/C++ interface, the error variable is the routine’s
return value, while for the Fortran version, each PETSc routine has as
its final argument an integer error variable.</p>
<p>All PETSc programs should call <code class="docutils literal notranslate"><span class="pre"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscFinalize.html#PetscFinalize">PetscFinalize</a>()</span></code> as their final (or
nearly final) statement, as given below in the C/C++ and Fortran
formats, respectively:</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscFinalize.html#PetscFinalize">PetscFinalize</a></span><span class="p">();</span>
<span class="k">return</span> <span class="n">ierr</span><span class="p">;</span>
</pre></div>
</div>
<div class="highlight-fortran notranslate"><div class="highlight"><pre><span></span><span class="k">call </span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscFinalize.html#PetscFinalize">PetscFinalize</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">)</span>
</pre></div>
</div>
<p>This routine handles options to be called at the conclusion of the
program, and calls <code class="docutils literal notranslate"><span class="pre"><a href="http://www.mpich.org/static/docs/latest/www3/MPI_Finalize.html#MPI_Finalize">MPI_Finalize</a>()</span></code> if <code class="docutils literal notranslate"><span class="pre"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscInitialize.html#PetscInitialize">PetscInitialize</a>()</span></code> began
MPI. If MPI was initiated externally from PETSc (by either the user or
another software package), the user is responsible for calling
<code class="docutils literal notranslate"><span class="pre"><a href="http://www.mpich.org/static/docs/latest/www3/MPI_Finalize.html#MPI_Finalize">MPI_Finalize</a>()</span></code>.</p>
</div>
<div class="section" id="simple-petsc-examples">
<span id="sec-simple"></span><h2>Simple PETSc Examples<a class="headerlink" href="#simple-petsc-examples" title="Permalink to this headline">¶</a></h2>
<p>To help the user start using PETSc immediately, we begin with a simple
uniprocessor example that
solves the one-dimensional Laplacian problem with finite differences.
This sequential code, which can be found in
<code class="docutils literal notranslate"><span class="pre">$PETSC_DIR/src/ksp/ksp/tutorials/ex1.c</span></code>, illustrates the solution of
a linear system with <code class="docutils literal notranslate"><span class="pre"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSP.html#KSP">KSP</a></span></code>, the interface to the preconditioners,
Krylov subspace methods, and direct linear solvers of PETSc. Following
the code we highlight a few of the most important parts of this example.</p>
<div class="admonition-listing-src-ksp-ksp-tutorials-ex1-c admonition" id="ksp-ex1">
<p class="admonition-title">Listing: <code class="docutils literal notranslate"><span class="pre">src/ksp/ksp/tutorials/ex1.c</span></code></p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span>
<span class="k">static</span> <span class="kt">char</span> <span class="n">help</span><span class="p">[]</span> <span class="o">=</span> <span class="s">"Solves a tridiagonal linear system with <a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSP.html#KSP">KSP</a>.</span><span class="se">\n\n</span><span class="s">"</span><span class="p">;</span>
<span class="cm">/*T</span>
<span class="cm"> Concepts: <a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSP.html#KSP">KSP</a>^solving a system of linear equations</span>
<span class="cm"> Processors: 1</span>
<span class="cm">T*/</span>
<span class="cm">/*</span>
<span class="cm"> Include "petscksp.h" so that we can use <a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSP.html#KSP">KSP</a> solvers. Note that this file</span>
<span class="cm"> automatically includes:</span>
<span class="cm"> petscsys.h - base PETSc routines petscvec.h - vectors</span>
<span class="cm"> petscmat.h - matrices petscpc.h - preconditioners</span>
<span class="cm"> petscis.h - index sets</span>
<span class="cm"> petscviewer.h - viewers</span>
<span class="cm"> Note: The corresponding parallel example is ex23.c</span>
<span class="cm">*/</span>
<span class="cp">#include</span> <span class="cpf"><petscksp.h></span><span class="cp"></span>
<span class="kt">int</span> <span class="nf">main</span><span class="p">(</span><span class="kt">int</span> <span class="n">argc</span><span class="p">,</span><span class="kt">char</span> <span class="o">**</span><span class="n">args</span><span class="p">)</span>
<span class="p">{</span>
<span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/Vec.html#Vec">Vec</a></span> <span class="n">x</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">u</span><span class="p">;</span> <span class="cm">/* approx solution, RHS, exact solution */</span>
<span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/Mat.html#Mat">Mat</a></span> <span class="n">A</span><span class="p">;</span> <span class="cm">/* linear system matrix */</span>
<span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSP.html#KSP">KSP</a></span> <span class="n">ksp</span><span class="p">;</span> <span class="cm">/* linear solver context */</span>
<span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/PC/PC.html#PC">PC</a></span> <span class="n">pc</span><span class="p">;</span> <span class="cm">/* preconditioner context */</span>
<span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscReal.html#PetscReal">PetscReal</a></span> <span class="n">norm</span><span class="p">;</span> <span class="cm">/* norm of solution error */</span>
<span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscErrorCode.html#PetscErrorCode">PetscErrorCode</a></span> <span class="n">ierr</span><span class="p">;</span>
<span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscInt.html#PetscInt">PetscInt</a></span> <span class="n">i</span><span class="p">,</span><span class="n">n</span> <span class="o">=</span> <span class="mi">10</span><span class="p">,</span><span class="n">col</span><span class="p">[</span><span class="mi">3</span><span class="p">],</span><span class="n">its</span><span class="p">;</span>
<span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscMPIInt.html#PetscMPIInt">PetscMPIInt</a></span> <span class="n">size</span><span class="p">;</span>
<span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscScalar.html#PetscScalar">PetscScalar</a></span> <span class="n">value</span><span class="p">[</span><span class="mi">3</span><span class="p">];</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscInitialize.html#PetscInitialize">PetscInitialize</a></span><span class="p">(</span><span class="o">&</span><span class="n">argc</span><span class="p">,</span><span class="o">&</span><span class="n">args</span><span class="p">,(</span><span class="kt">char</span><span class="o">*</span><span class="p">)</span><span class="mi">0</span><span class="p">,</span><span class="n">help</span><span class="p">);</span><span class="k">if</span> <span class="p">(</span><span class="n">ierr</span><span class="p">)</span> <span class="k">return</span> <span class="n">ierr</span><span class="p">;</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="http://www.mpich.org/static/docs/latest/www3/MPI_Comm_size.html#MPI_Comm_size">MPI_Comm_size</a></span><span class="p">(</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PETSC_COMM_WORLD.html#PETSC_COMM_WORLD">PETSC_COMM_WORLD</a></span><span class="p">,</span><span class="o">&</span><span class="n">size</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="k">if</span> <span class="p">(</span><span class="n">size</span> <span class="o">!=</span> <span class="mi">1</span><span class="p">)</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/SETERRQ.html#SETERRQ">SETERRQ</a></span><span class="p">(</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PETSC_COMM_WORLD.html#PETSC_COMM_WORLD">PETSC_COMM_WORLD</a></span><span class="p">,</span><span class="n">PETSC_ERR_WRONG_MPI_SIZE</span><span class="p">,</span><span class="s">"This is a uniprocessor example only!"</span><span class="p">);</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscOptionsGetInt.html#PetscOptionsGetInt">PetscOptionsGetInt</a></span><span class="p">(</span><span class="nb">NULL</span><span class="p">,</span><span class="nb">NULL</span><span class="p">,</span><span class="s">"-n"</span><span class="p">,</span><span class="o">&</span><span class="n">n</span><span class="p">,</span><span class="nb">NULL</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="cm">/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -</span>
<span class="cm"> Compute the matrix and right-hand-side vector that define</span>
<span class="cm"> the linear system, Ax = b.</span>
<span class="cm"> - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */</span>
<span class="cm">/*</span>
<span class="cm"> Create vectors. Note that we form 1 vector from scratch and</span>
<span class="cm"> then duplicate as needed.</span>
<span class="cm"> */</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecCreate.html#VecCreate">VecCreate</a></span><span class="p">(</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PETSC_COMM_WORLD.html#PETSC_COMM_WORLD">PETSC_COMM_WORLD</a></span><span class="p">,</span><span class="o">&</span><span class="n">x</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscObjectSetName.html#PetscObjectSetName">PetscObjectSetName</a></span><span class="p">((</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscObject.html#PetscObject">PetscObject</a></span><span class="p">)</span> <span class="n">x</span><span class="p">,</span> <span class="s">"Solution"</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecSetSizes.html#VecSetSizes">VecSetSizes</a></span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PETSC_DECIDE.html#PETSC_DECIDE">PETSC_DECIDE</a></span><span class="p">,</span><span class="n">n</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecSetFromOptions.html#VecSetFromOptions">VecSetFromOptions</a></span><span class="p">(</span><span class="n">x</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecDuplicate.html#VecDuplicate">VecDuplicate</a></span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="o">&</span><span class="n">b</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecDuplicate.html#VecDuplicate">VecDuplicate</a></span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="o">&</span><span class="n">u</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="cm">/*</span>
<span class="cm"> Create matrix. When using <a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatCreate.html#MatCreate">MatCreate</a>(), the matrix format can</span>
<span class="cm"> be specified at runtime.</span>
<span class="cm"> Performance tuning note: For problems of substantial size,</span>
<span class="cm"> preallocation of matrix memory is crucial for attaining good</span>
<span class="cm"> performance. See the matrix chapter of the users manual for details.</span>
<span class="cm"> */</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatCreate.html#MatCreate">MatCreate</a></span><span class="p">(</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PETSC_COMM_WORLD.html#PETSC_COMM_WORLD">PETSC_COMM_WORLD</a></span><span class="p">,</span><span class="o">&</span><span class="n">A</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatSetSizes.html#MatSetSizes">MatSetSizes</a></span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PETSC_DECIDE.html#PETSC_DECIDE">PETSC_DECIDE</a></span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PETSC_DECIDE.html#PETSC_DECIDE">PETSC_DECIDE</a></span><span class="p">,</span><span class="n">n</span><span class="p">,</span><span class="n">n</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatSetFromOptions.html#MatSetFromOptions">MatSetFromOptions</a></span><span class="p">(</span><span class="n">A</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatSetUp.html#MatSetUp">MatSetUp</a></span><span class="p">(</span><span class="n">A</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="cm">/*</span>
<span class="cm"> Assemble matrix</span>
<span class="cm"> */</span>
<span class="n">value</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="mf">-1.0</span><span class="p">;</span> <span class="n">value</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="mf">2.0</span><span class="p">;</span> <span class="n">value</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="mf">-1.0</span><span class="p">;</span>
<span class="k">for</span> <span class="p">(</span><span class="n">i</span><span class="o">=</span><span class="mi">1</span><span class="p">;</span> <span class="n">i</span><span class="o"><</span><span class="n">n</span><span class="mi">-1</span><span class="p">;</span> <span class="n">i</span><span class="o">++</span><span class="p">)</span> <span class="p">{</span>
<span class="n">col</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">i</span><span class="mi">-1</span><span class="p">;</span> <span class="n">col</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">i</span><span class="p">;</span> <span class="n">col</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">;</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatSetValues.html#MatSetValues">MatSetValues</a></span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="o">&</span><span class="n">i</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="n">col</span><span class="p">,</span><span class="n">value</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/INSERT_VALUES.html#INSERT_VALUES">INSERT_VALUES</a></span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="p">}</span>
<span class="n">i</span> <span class="o">=</span> <span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">;</span> <span class="n">col</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">n</span> <span class="o">-</span> <span class="mi">2</span><span class="p">;</span> <span class="n">col</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">;</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatSetValues.html#MatSetValues">MatSetValues</a></span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="o">&</span><span class="n">i</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="n">col</span><span class="p">,</span><span class="n">value</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/INSERT_VALUES.html#INSERT_VALUES">INSERT_VALUES</a></span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="n">i</span> <span class="o">=</span> <span class="mi">0</span><span class="p">;</span> <span class="n">col</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span><span class="p">;</span> <span class="n">col</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span><span class="p">;</span> <span class="n">value</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="mf">2.0</span><span class="p">;</span> <span class="n">value</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="mf">-1.0</span><span class="p">;</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatSetValues.html#MatSetValues">MatSetValues</a></span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="o">&</span><span class="n">i</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="n">col</span><span class="p">,</span><span class="n">value</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/INSERT_VALUES.html#INSERT_VALUES">INSERT_VALUES</a></span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatAssemblyBegin.html#MatAssemblyBegin">MatAssemblyBegin</a></span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatAssemblyType.html#MatAssemblyType">MAT_FINAL_ASSEMBLY</a></span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatAssemblyEnd.html#MatAssemblyEnd">MatAssemblyEnd</a></span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatAssemblyType.html#MatAssemblyType">MAT_FINAL_ASSEMBLY</a></span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="cm">/*</span>
<span class="cm"> Set exact solution; then compute right-hand-side vector.</span>
<span class="cm"> */</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecSet.html#VecSet">VecSet</a></span><span class="p">(</span><span class="n">u</span><span class="p">,</span><span class="mf">1.0</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatMult.html#MatMult">MatMult</a></span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="n">u</span><span class="p">,</span><span class="n">b</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="cm">/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -</span>
<span class="cm"> Create the linear solver and set various options</span>
<span class="cm"> - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSPCreate.html#KSPCreate">KSPCreate</a></span><span class="p">(</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PETSC_COMM_WORLD.html#PETSC_COMM_WORLD">PETSC_COMM_WORLD</a></span><span class="p">,</span><span class="o">&</span><span class="n">ksp</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="cm">/*</span>
<span class="cm"> Set operators. Here the matrix that defines the linear system</span>
<span class="cm"> also serves as the matrix that defines the preconditioner.</span>
<span class="cm"> */</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSPSetOperators.html#KSPSetOperators">KSPSetOperators</a></span><span class="p">(</span><span class="n">ksp</span><span class="p">,</span><span class="n">A</span><span class="p">,</span><span class="n">A</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="cm">/*</span>
<span class="cm"> Set linear solver defaults for this problem (optional).</span>
<span class="cm"> - By extracting the <a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSP.html#KSP">KSP</a> and <a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/PC/PC.html#PC">PC</a> contexts from the <a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSP.html#KSP">KSP</a> context,</span>
<span class="cm"> we can then directly call any <a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSP.html#KSP">KSP</a> and <a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/PC/PC.html#PC">PC</a> routines to set</span>
<span class="cm"> various options.</span>
<span class="cm"> - The following four statements are optional; all of these</span>
<span class="cm"> parameters could alternatively be specified at runtime via</span>
<span class="cm"> <a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSPSetFromOptions.html#KSPSetFromOptions">KSPSetFromOptions</a>();</span>
<span class="cm"> */</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSPGetPC.html#KSPGetPC">KSPGetPC</a></span><span class="p">(</span><span class="n">ksp</span><span class="p">,</span><span class="o">&</span><span class="n">pc</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/PC/PCSetType.html#PCSetType">PCSetType</a></span><span class="p">(</span><span class="n">pc</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/PC/PCJACOBI.html#PCJACOBI">PCJACOBI</a></span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSPSetTolerances.html#KSPSetTolerances">KSPSetTolerances</a></span><span class="p">(</span><span class="n">ksp</span><span class="p">,</span><span class="mf">1.</span><span class="n">e</span><span class="mi">-5</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PETSC_DEFAULT.html#PETSC_DEFAULT">PETSC_DEFAULT</a></span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PETSC_DEFAULT.html#PETSC_DEFAULT">PETSC_DEFAULT</a></span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PETSC_DEFAULT.html#PETSC_DEFAULT">PETSC_DEFAULT</a></span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="cm">/*</span>
<span class="cm"> Set runtime options, e.g.,</span>
<span class="cm"> -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol></span>
<span class="cm"> These options will override those specified above as long as</span>
<span class="cm"> <a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSPSetFromOptions.html#KSPSetFromOptions">KSPSetFromOptions</a>() is called _after_ any other customization</span>
<span class="cm"> routines.</span>
<span class="cm"> */</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSPSetFromOptions.html#KSPSetFromOptions">KSPSetFromOptions</a></span><span class="p">(</span><span class="n">ksp</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="cm">/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -</span>
<span class="cm"> Solve the linear system</span>
<span class="cm"> - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSPSolve.html#KSPSolve">KSPSolve</a></span><span class="p">(</span><span class="n">ksp</span><span class="p">,</span><span class="n">b</span><span class="p">,</span><span class="n">x</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="cm">/*</span>
<span class="cm"> View solver info; we could instead use the option -ksp_view to</span>
<span class="cm"> print this info to the screen at the conclusion of <a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSPSolve.html#KSPSolve">KSPSolve</a>().</span>
<span class="cm"> */</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSPView.html#KSPView">KSPView</a></span><span class="p">(</span><span class="n">ksp</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Viewer/PETSC_VIEWER_STDOUT_WORLD.html#PETSC_VIEWER_STDOUT_WORLD">PETSC_VIEWER_STDOUT_WORLD</a></span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="cm">/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -</span>
<span class="cm"> Check the solution and clean up</span>
<span class="cm"> - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecAXPY.html#VecAXPY">VecAXPY</a></span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="mf">-1.0</span><span class="p">,</span><span class="n">u</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecNorm.html#VecNorm">VecNorm</a></span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/NORM_2.html#NORM_2">NORM_2</a></span><span class="p">,</span><span class="o">&</span><span class="n">norm</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSPGetIterationNumber.html#KSPGetIterationNumber">KSPGetIterationNumber</a></span><span class="p">(</span><span class="n">ksp</span><span class="p">,</span><span class="o">&</span><span class="n">its</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscPrintf.html#PetscPrintf">PetscPrintf</a></span><span class="p">(</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PETSC_COMM_WORLD.html#PETSC_COMM_WORLD">PETSC_COMM_WORLD</a></span><span class="p">,</span><span class="s">"Norm of error %g, Iterations %D</span><span class="se">\n</span><span class="s">"</span><span class="p">,(</span><span class="kt">double</span><span class="p">)</span><span class="n">norm</span><span class="p">,</span><span class="n">its</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="cm">/*</span>
<span class="cm"> Free work space. All PETSc objects should be destroyed when they</span>
<span class="cm"> are no longer needed.</span>
<span class="cm"> */</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecDestroy.html#VecDestroy">VecDestroy</a></span><span class="p">(</span><span class="o">&</span><span class="n">x</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span> <span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecDestroy.html#VecDestroy">VecDestroy</a></span><span class="p">(</span><span class="o">&</span><span class="n">u</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecDestroy.html#VecDestroy">VecDestroy</a></span><span class="p">(</span><span class="o">&</span><span class="n">b</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span> <span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatDestroy.html#MatDestroy">MatDestroy</a></span><span class="p">(</span><span class="o">&</span><span class="n">A</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSPDestroy.html#KSPDestroy">KSPDestroy</a></span><span class="p">(</span><span class="o">&</span><span class="n">ksp</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="cm">/*</span>
<span class="cm"> Always call <a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscFinalize.html#PetscFinalize">PetscFinalize</a>() before exiting a program. This routine</span>
<span class="cm"> - finalizes the PETSc libraries as well as MPI</span>
<span class="cm"> - provides summary and diagnostic information if certain runtime</span>
<span class="cm"> options are chosen (e.g., -log_view).</span>
<span class="cm"> */</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscFinalize.html#PetscFinalize">PetscFinalize</a></span><span class="p">();</span>
<span class="k">return</span> <span class="n">ierr</span><span class="p">;</span>
<span class="p">}</span>
</pre></div>
</div>
</div>
<div class="section" id="include-files">
<h3>Include Files<a class="headerlink" href="#include-files" title="Permalink to this headline">¶</a></h3>
<p>The C/C++ include files for PETSc should be used via statements such as</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="cp">#include</span> <span class="cpf"><petscksp.h></span><span class="cp"></span>
</pre></div>
</div>
<p>where <code class="docutils literal notranslate"><span class="pre">petscksp.h</span></code> is the include file for the linear solver library.
Each PETSc program must specify an include file that corresponds to the
highest level PETSc objects needed within the program; all of the
required lower level include files are automatically included within the
higher level files. For example, <code class="docutils literal notranslate"><span class="pre">petscksp.h</span></code> includes <code class="docutils literal notranslate"><span class="pre">petscmat.h</span></code>
(matrices), <code class="docutils literal notranslate"><span class="pre">petscvec.h</span></code> (vectors), and <code class="docutils literal notranslate"><span class="pre">petscsys.h</span></code> (base PETSc
file). The PETSc include files are located in the directory
<code class="docutils literal notranslate"><span class="pre">${PETSC_DIR}/include</span></code>. See <a class="reference internal" href="fortran.html#sec-fortran-includes"><span class="std std-ref">Fortran Include Files</span></a>
for a discussion of PETSc include files in Fortran programs.</p>
</div>
<div class="section" id="the-options-database">
<h3>The Options Database<a class="headerlink" href="#the-options-database" title="Permalink to this headline">¶</a></h3>
<p>As shown in <a class="reference internal" href="#sec-simple"><span class="std std-ref">Simple PETSc Examples</span></a>, the user can
input control data at run time using the options database. In this
example the command <code class="docutils literal notranslate"><span class="pre"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscOptionsGetInt.html#PetscOptionsGetInt">PetscOptionsGetInt</a>(NULL,NULL,"-n",&n,&flg);</span></code>
checks whether the user has provided a command line option to set the
value of <code class="docutils literal notranslate"><span class="pre">n</span></code>, the problem dimension. If so, the variable <code class="docutils literal notranslate"><span class="pre">n</span></code> is set
accordingly; otherwise, <code class="docutils literal notranslate"><span class="pre">n</span></code> remains unchanged. A complete description
of the options database may be found in <a class="reference internal" href="other.html#sec-options"><span class="std std-ref">Runtime Options</span></a>.</p>
</div>
<div class="section" id="vectors">
<span id="sec-vecintro"></span><h3>Vectors<a class="headerlink" href="#vectors" title="Permalink to this headline">¶</a></h3>
<p>One creates a new parallel or sequential vector, <code class="docutils literal notranslate"><span class="pre">x</span></code>, of global
dimension <code class="docutils literal notranslate"><span class="pre">M</span></code> with the commands</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecCreate.html#VecCreate">VecCreate</a></span><span class="p">(</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/MPI_Comm.html#MPI_Comm">MPI_Comm</a></span> <span class="n">comm</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/Vec.html#Vec">Vec</a></span> <span class="o">*</span><span class="n">x</span><span class="p">);</span>
<span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecSetSizes.html#VecSetSizes">VecSetSizes</a></span><span class="p">(</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/Vec.html#Vec">Vec</a></span> <span class="n">x</span><span class="p">,</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscInt.html#PetscInt">PetscInt</a></span> <span class="n">m</span><span class="p">,</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscInt.html#PetscInt">PetscInt</a></span> <span class="n">M</span><span class="p">);</span>
</pre></div>
</div>
<p>where <code class="docutils literal notranslate"><span class="pre">comm</span></code> denotes the MPI communicator and <code class="docutils literal notranslate"><span class="pre">m</span></code> is the optional
local size which may be <code class="docutils literal notranslate"><span class="pre"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PETSC_DECIDE.html#PETSC_DECIDE">PETSC_DECIDE</a></span></code>. The type of storage for the
vector may be set with either calls to <code class="docutils literal notranslate"><span class="pre"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecSetType.html#VecSetType">VecSetType</a>()</span></code> or
<code class="docutils literal notranslate"><span class="pre"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecSetFromOptions.html#VecSetFromOptions">VecSetFromOptions</a>()</span></code>. Additional vectors of the same type can be
formed with</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecDuplicate.html#VecDuplicate">VecDuplicate</a></span><span class="p">(</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/Vec.html#Vec">Vec</a></span> <span class="n">old</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/Vec.html#Vec">Vec</a></span> <span class="o">*</span><span class="n">new</span><span class="p">);</span>
</pre></div>
</div>
<p>The commands</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecSet.html#VecSet">VecSet</a></span><span class="p">(</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/Vec.html#Vec">Vec</a></span> <span class="n">x</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscScalar.html#PetscScalar">PetscScalar</a></span> <span class="n">value</span><span class="p">);</span>
<span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecSetValues.html#VecSetValues">VecSetValues</a></span><span class="p">(</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/Vec.html#Vec">Vec</a></span> <span class="n">x</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscInt.html#PetscInt">PetscInt</a></span> <span class="n">n</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscInt.html#PetscInt">PetscInt</a></span> <span class="o">*</span><span class="n">indices</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscScalar.html#PetscScalar">PetscScalar</a></span> <span class="o">*</span><span class="n">values</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/INSERT_VALUES.html#INSERT_VALUES">INSERT_VALUES</a></span><span class="p">);</span>
</pre></div>
</div>
<p>respectively set all the components of a vector to a particular scalar
value and assign a different value to each component. More detailed
information about PETSc vectors, including their basic operations,
scattering/gathering, index sets, and distributed arrays, is discussed
in Chapter <a class="reference internal" href="vec.html#chapter-vectors"><span class="std std-ref">Vectors and Parallel Data</span></a>.</p>
<p>Note the use of the PETSc variable type <code class="docutils literal notranslate"><span class="pre"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscScalar.html#PetscScalar">PetscScalar</a></span></code> in this example.
The <code class="docutils literal notranslate"><span class="pre"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscScalar.html#PetscScalar">PetscScalar</a></span></code> is simply defined to be <code class="docutils literal notranslate"><span class="pre">double</span></code> in C/C++ (or
correspondingly <code class="docutils literal notranslate"><span class="pre">double</span> <span class="pre">precision</span></code> in Fortran) for versions of PETSc
that have <em>not</em> been compiled for use with complex numbers. The
<code class="docutils literal notranslate"><span class="pre"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscScalar.html#PetscScalar">PetscScalar</a></span></code> data type enables identical code to be used when the
PETSc libraries have been compiled for use with complex numbers.
<a class="reference internal" href="other.html#sec-complex"><span class="std std-ref">Numbers</span></a> discusses the use of complex
numbers in PETSc programs.</p>
</div>
<div class="section" id="matrices">
<span id="sec-matintro"></span><h3>Matrices<a class="headerlink" href="#matrices" title="Permalink to this headline">¶</a></h3>
<p>Usage of PETSc matrices and vectors is similar. The user can create a
new parallel or sequential matrix, <code class="docutils literal notranslate"><span class="pre">A</span></code>, which has <code class="docutils literal notranslate"><span class="pre">M</span></code> global rows
and <code class="docutils literal notranslate"><span class="pre">N</span></code> global columns, with the routines</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatCreate.html#MatCreate">MatCreate</a></span><span class="p">(</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/MPI_Comm.html#MPI_Comm">MPI_Comm</a></span> <span class="n">comm</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/Mat.html#Mat">Mat</a></span> <span class="o">*</span><span class="n">A</span><span class="p">);</span>
<span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatSetSizes.html#MatSetSizes">MatSetSizes</a></span><span class="p">(</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/Mat.html#Mat">Mat</a></span> <span class="n">A</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PETSC_DECIDE.html#PETSC_DECIDE">PETSC_DECIDE</a></span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PETSC_DECIDE.html#PETSC_DECIDE">PETSC_DECIDE</a></span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscInt.html#PetscInt">PetscInt</a></span> <span class="n">M</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscInt.html#PetscInt">PetscInt</a></span> <span class="n">N</span><span class="p">);</span>
</pre></div>
</div>
<p>where the matrix format can be specified at runtime via the options
database. The user could alternatively specify each processes’ number of
local rows and columns using <code class="docutils literal notranslate"><span class="pre">m</span></code> and <code class="docutils literal notranslate"><span class="pre">n</span></code>.</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatSetSizes.html#MatSetSizes">MatSetSizes</a></span><span class="p">(</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/Mat.html#Mat">Mat</a></span> <span class="n">A</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscInt.html#PetscInt">PetscInt</a></span> <span class="n">m</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscInt.html#PetscInt">PetscInt</a></span> <span class="n">n</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PETSC_DETERMINE.html#PETSC_DETERMINE">PETSC_DETERMINE</a></span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PETSC_DETERMINE.html#PETSC_DETERMINE">PETSC_DETERMINE</a></span><span class="p">);</span>
</pre></div>
</div>
<p>Generally one then sets the “type” of the matrix, with, for example,</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatSetType.html#MatSetType">MatSetType</a></span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MATAIJ.html#MATAIJ">MATAIJ</a></span><span class="p">);</span>
</pre></div>
</div>
<p>This causes the matrix <code class="docutils literal notranslate"><span class="pre">A</span></code> to used the compressed sparse row storage
format to store the matrix entries. See <code class="docutils literal notranslate"><span class="pre"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatType.html#MatType">MatType</a></span></code> for a list of all
matrix types. Values can then be set with the command</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatSetValues.html#MatSetValues">MatSetValues</a></span><span class="p">(</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/Mat.html#Mat">Mat</a></span> <span class="n">A</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscInt.html#PetscInt">PetscInt</a></span> <span class="n">m</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscInt.html#PetscInt">PetscInt</a></span> <span class="o">*</span><span class="n">im</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscInt.html#PetscInt">PetscInt</a></span> <span class="n">n</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscInt.html#PetscInt">PetscInt</a></span> <span class="o">*</span><span class="n">in</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscScalar.html#PetscScalar">PetscScalar</a></span> <span class="o">*</span><span class="n">values</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/INSERT_VALUES.html#INSERT_VALUES">INSERT_VALUES</a></span><span class="p">);</span>
</pre></div>
</div>
<p>After all elements have been inserted into the matrix, it must be
processed with the pair of commands</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatAssemblyBegin.html#MatAssemblyBegin">MatAssemblyBegin</a></span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatAssemblyType.html#MatAssemblyType">MAT_FINAL_ASSEMBLY</a></span><span class="p">);</span>
<span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatAssemblyEnd.html#MatAssemblyEnd">MatAssemblyEnd</a></span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatAssemblyType.html#MatAssemblyType">MAT_FINAL_ASSEMBLY</a></span><span class="p">);</span>
</pre></div>
</div>
<p><a class="reference internal" href="mat.html#chapter-matrices"><span class="std std-ref">Matrices</span></a> discusses various matrix formats as
well as the details of some basic matrix manipulation routines.</p>
</div>
<div class="section" id="linear-solvers">
<h3>Linear Solvers<a class="headerlink" href="#linear-solvers" title="Permalink to this headline">¶</a></h3>
<p>After creating the matrix and vectors that define a linear system,
<code class="docutils literal notranslate"><span class="pre">Ax</span></code> <span class="math">\(=\)</span> <code class="docutils literal notranslate"><span class="pre">b</span></code>, the user can then use <code class="docutils literal notranslate"><span class="pre"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSP.html#KSP">KSP</a></span></code> to solve the
system with the following sequence of commands:</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSPCreate.html#KSPCreate">KSPCreate</a></span><span class="p">(</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/MPI_Comm.html#MPI_Comm">MPI_Comm</a></span> <span class="n">comm</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSP.html#KSP">KSP</a></span> <span class="o">*</span><span class="n">ksp</span><span class="p">);</span>
<span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSPSetOperators.html#KSPSetOperators">KSPSetOperators</a></span><span class="p">(</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSP.html#KSP">KSP</a></span> <span class="n">ksp</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/Mat.html#Mat">Mat</a></span> <span class="n">Amat</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/Mat.html#Mat">Mat</a></span> <span class="n">Pmat</span><span class="p">);</span>
<span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSPSetFromOptions.html#KSPSetFromOptions">KSPSetFromOptions</a></span><span class="p">(</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSP.html#KSP">KSP</a></span> <span class="n">ksp</span><span class="p">);</span>
<span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSPSolve.html#KSPSolve">KSPSolve</a></span><span class="p">(</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSP.html#KSP">KSP</a></span> <span class="n">ksp</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/Vec.html#Vec">Vec</a></span> <span class="n">b</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/Vec.html#Vec">Vec</a></span> <span class="n">x</span><span class="p">);</span>
<span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSPDestroy.html#KSPDestroy">KSPDestroy</a></span><span class="p">(</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSP.html#KSP">KSP</a></span> <span class="n">ksp</span><span class="p">);</span>
</pre></div>
</div>
<p>The user first creates the <code class="docutils literal notranslate"><span class="pre"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSP.html#KSP">KSP</a></span></code> context and sets the operators
associated with the system (matrix that defines the linear system,
<code class="docutils literal notranslate"><span class="pre">Amat</span></code> and matrix from which the preconditioner is constructed,
<code class="docutils literal notranslate"><span class="pre">Pmat</span></code>). The user then sets various options for customized solution,
solves the linear system, and finally destroys the <code class="docutils literal notranslate"><span class="pre"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSP.html#KSP">KSP</a></span></code> context. We
emphasize the command <code class="docutils literal notranslate"><span class="pre"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSPSetFromOptions.html#KSPSetFromOptions">KSPSetFromOptions</a>()</span></code>, which enables the user to
customize the linear solution method at runtime by using the options
database, which is discussed in <a class="reference internal" href="other.html#sec-options"><span class="std std-ref">Runtime Options</span></a>. Through this database, the
user not only can select an iterative method and preconditioner, but
also can prescribe the convergence tolerance, set various monitoring
routines, etc. (see, e.g., <a class="reference internal" href="#sec-profiling-programs"><span class="std std-ref">Profiling Programs</span></a>).</p>
<p><a class="reference internal" href="ksp.html#chapter-ksp"><span class="std std-ref">KSP: Linear System Solvers</span></a> describes in detail the <code class="docutils literal notranslate"><span class="pre"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSP.html#KSP">KSP</a></span></code> package,
including the <code class="docutils literal notranslate"><span class="pre"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/PC/PC.html#PC">PC</a></span></code> and <code class="docutils literal notranslate"><span class="pre"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSP.html#KSP">KSP</a></span></code> packages for preconditioners and Krylov
subspace methods.</p>
</div>
<div class="section" id="nonlinear-solvers">
<h3>Nonlinear Solvers<a class="headerlink" href="#nonlinear-solvers" title="Permalink to this headline">¶</a></h3>
<p>Most PDE problems of interest are inherently nonlinear. PETSc provides
an interface to tackle the nonlinear problems directly called <code class="docutils literal notranslate"><span class="pre"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/SNES/SNES.html#SNES">SNES</a></span></code>.
<a class="reference internal" href="snes.html#chapter-snes"><span class="std std-ref">SNES: Nonlinear Solvers</span></a> describes the nonlinear
solvers in detail. We recommend most PETSc users work directly with
<code class="docutils literal notranslate"><span class="pre"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/SNES/SNES.html#SNES">SNES</a></span></code>, rather than using PETSc for the linear problem within a
nonlinear solver.</p>
</div>
<div class="section" id="error-checking">
<h3>Error Checking<a class="headerlink" href="#error-checking" title="Permalink to this headline">¶</a></h3>
<p>All PETSc routines return an integer indicating whether an error has
occurred during the call. The PETSc macro <code class="docutils literal notranslate"><span class="pre"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a>(ierr)</span></code> checks the
value of <code class="docutils literal notranslate"><span class="pre">ierr</span></code> and calls the PETSc error handler upon error
detection. <code class="docutils literal notranslate"><span class="pre"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a>(ierr)</span></code> should be used in all subroutines to enable
a complete error traceback. Below, we indicate a traceback
generated by error detection within a sample PETSc program. The error
occurred on line 3618 of the file
<code class="docutils literal notranslate"><span class="pre">${PETSC_DIR}/src/mat/impls/aij/seq/aij.c</span></code> and was caused by trying to
allocate too large an array in memory. The routine was called in the
program <code class="docutils literal notranslate"><span class="pre">ex3.c</span></code> on line 66. See
<a class="reference internal" href="fortran.html#sec-fortran-errors"><span class="std std-ref">Error Checking</span></a> for details regarding error checking
when using the PETSc Fortran interface.</p>
<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>$ cd $PETSC_DIR/src/ksp/ksp/tutorials
$ make ex3
$ mpiexec -n 1 ./ex3 -m 100000
[0]PETSC ERROR: --------------------- Error Message --------------------------------
[0]PETSC ERROR: Out of memory. This could be due to allocating
[0]PETSC ERROR: too large an object or bleeding by not properly
[0]PETSC ERROR: destroying unneeded objects.
[0]PETSC ERROR: Memory allocated 11282182704 Memory used by process 7075897344
[0]PETSC ERROR: Try running with -malloc_dump or -malloc_view for info.
[0]PETSC ERROR: Memory requested 18446744072169447424
[0]PETSC ERROR: See https://www.mcs.anl.gov/petsc/documentation/faq.html for trouble shooting.
[0]PETSC ERROR: Petsc Development GIT revision: v3.7.1-224-g9c9a9c5 GIT Date: 2016-05-18 22:43:00 -0500
[0]PETSC ERROR: ./ex3 on a arch-darwin-double-debug named Patricks-MacBook-Pro-2.local by patrick Mon Jun 27 18:04:03 2016
[0]PETSC ERROR: Configure options PETSC_DIR=/Users/patrick/petsc PETSC_ARCH=arch-darwin-double-debug --download-mpich --download-f2cblaslapack --with-cc=clang --with-cxx=clang++ --with-fc=gfortran --with-debugging=1 --with-precision=double --with-scalar-type=real --with-viennacl=0 --download-c2html -download-sowing
[0]PETSC ERROR: #1 MatSeqAIJSetPreallocation_SeqAIJ() line 3618 in /Users/patrick/petsc/src/mat/impls/aij/seq/aij.c
[0]PETSC ERROR: #2 PetscTrMallocDefault() line 188 in /Users/patrick/petsc/src/sys/memory/mtr.c
[0]PETSC ERROR: #3 MatSeqAIJSetPreallocation_SeqAIJ() line 3618 in /Users/patrick/petsc/src/mat/impls/aij/seq/aij.c
[0]PETSC ERROR: #4 <a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatSeqAIJSetPreallocation.html#MatSeqAIJSetPreallocation">MatSeqAIJSetPreallocation</a>() line 3562 in /Users/patrick/petsc/src/mat/impls/aij/seq/aij.c
[0]PETSC ERROR: #5 main() line 66 in /Users/patrick/petsc/src/ksp/ksp/tutorials/ex3.c
[0]PETSC ERROR: PETSc Option Table entries:
[0]PETSC ERROR: -m 100000
[0]PETSC ERROR: ----------------End of Error Message ------- send entire error message to petsc-maint@mcs.anl.gov----------
</pre></div>
</div>
<p>When running the debug version of the PETSc libraries, it does a great
deal of checking for memory corruption (writing outside of array bounds
etc). The macro <code class="docutils literal notranslate"><span class="pre"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKMEMQ.html#CHKMEMQ">CHKMEMQ</a></span></code> can be called anywhere in the code to check
the current status of the memory for corruption. By putting several (or
many) of these macros into your code you can usually easily track down
in what small segment of your code the corruption has occured. One can
also use Valgrind to track down memory errors; see the <a class="reference external" href="https://www.mcs.anl.gov/petsc/documentation/faq.html">FAQ</a>.</p>
</div>
<div class="section" id="parallel-programming">
<span id="sec-parallel"></span><h3>Parallel Programming<a class="headerlink" href="#parallel-programming" title="Permalink to this headline">¶</a></h3>
<p>Since PETSc uses the message-passing model for parallel programming and
employs MPI for all interprocessor communication, the user is free to
employ MPI routines as needed throughout an application code. However,
by default the user is shielded from many of the details of message
passing within PETSc, since these are hidden within parallel objects,
such as vectors, matrices, and solvers. In addition, PETSc provides
tools such as generalized vector scatters/gathers to assist in the
management of parallel data.</p>
<p>Recall that the user must specify a communicator upon creation of any
PETSc object (such as a vector, matrix, or solver) to indicate the
processors over which the object is to be distributed. For example, as
mentioned above, some commands for matrix, vector, and linear solver
creation are:</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatCreate.html#MatCreate">MatCreate</a></span><span class="p">(</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/MPI_Comm.html#MPI_Comm">MPI_Comm</a></span> <span class="n">comm</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/Mat.html#Mat">Mat</a></span> <span class="o">*</span><span class="n">A</span><span class="p">);</span>
<span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecCreate.html#VecCreate">VecCreate</a></span><span class="p">(</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/MPI_Comm.html#MPI_Comm">MPI_Comm</a></span> <span class="n">comm</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/Vec.html#Vec">Vec</a></span> <span class="o">*</span><span class="n">x</span><span class="p">);</span>
<span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSPCreate.html#KSPCreate">KSPCreate</a></span><span class="p">(</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/MPI_Comm.html#MPI_Comm">MPI_Comm</a></span> <span class="n">comm</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSP.html#KSP">KSP</a></span> <span class="o">*</span><span class="n">ksp</span><span class="p">);</span>
</pre></div>
</div>
<p>The creation routines are collective over all processors in the
communicator; thus, all processors in the communicator <em>must</em> call the
creation routine. In addition, if a sequence of collective routines is
being used, they <em>must</em> be called in the same order on each processor.</p>
<p>The next example, given below,
illustrates the solution of a linear system in parallel. This code,
corresponding to
<cite>KSP Tutorial ex2 <https://www.mcs.anl.gov/petsc/petsc-current/src/ksp/ksp/tutorials/ex2.c.html></cite>,
handles the two-dimensional Laplacian discretized with finite
differences, where the linear system is again solved with KSP. The code
performs the same tasks as the sequential version within
<a class="reference internal" href="#sec-simple"><span class="std std-ref">Simple PETSc Examples</span></a>. Note that the user interface
for initiating the program, creating vectors and matrices, and solving
the linear system is <em>exactly</em> the same for the uniprocessor and
multiprocessor examples. The primary difference between the examples in
<a class="reference internal" href="#sec-simple"><span class="std std-ref">Simple PETSc Examples</span></a> and
here is that each processor forms only its
local part of the matrix and vectors in the parallel case.</p>
<div class="admonition-listing-src-ksp-ksp-tutorials-ex2-c admonition" id="ksp-ex2">
<p class="admonition-title">Listing: <code class="docutils literal notranslate"><span class="pre">src/ksp/ksp/tutorials/ex2.c</span></code></p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span>
<span class="k">static</span> <span class="kt">char</span> <span class="n">help</span><span class="p">[]</span> <span class="o">=</span> <span class="s">"Solves a linear system in parallel with <a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSP.html#KSP">KSP</a>.</span><span class="se">\n</span><span class="s">\</span>
<span class="s">Input parameters include:</span><span class="se">\n</span><span class="s">\</span>
<span class="s"> -view_exact_sol : write exact solution vector to stdout</span><span class="se">\n</span><span class="s">\</span>
<span class="s"> -m <mesh_x> : number of mesh points in x-direction</span><span class="se">\n</span><span class="s">\</span>
<span class="s"> -n <mesh_y> : number of mesh points in y-direction</span><span class="se">\n\n</span><span class="s">"</span><span class="p">;</span>
<span class="cm">/*T</span>
<span class="cm"> Concepts: <a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSP.html#KSP">KSP</a>^basic parallel example;</span>
<span class="cm"> Concepts: <a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSP.html#KSP">KSP</a>^Laplacian, 2d</span>
<span class="cm"> Concepts: Laplacian, 2d</span>
<span class="cm"> Processors: n</span>
<span class="cm">T*/</span>
<span class="cm">/*</span>
<span class="cm"> Include "petscksp.h" so that we can use <a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSP.html#KSP">KSP</a> solvers.</span>
<span class="cm">*/</span>
<span class="cp">#include</span> <span class="cpf"><petscksp.h></span><span class="cp"></span>
<span class="kt">int</span> <span class="nf">main</span><span class="p">(</span><span class="kt">int</span> <span class="n">argc</span><span class="p">,</span><span class="kt">char</span> <span class="o">**</span><span class="n">args</span><span class="p">)</span>
<span class="p">{</span>
<span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/Vec.html#Vec">Vec</a></span> <span class="n">x</span><span class="p">,</span><span class="n">b</span><span class="p">,</span><span class="n">u</span><span class="p">;</span> <span class="cm">/* approx solution, RHS, exact solution */</span>
<span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/Mat.html#Mat">Mat</a></span> <span class="n">A</span><span class="p">;</span> <span class="cm">/* linear system matrix */</span>
<span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSP.html#KSP">KSP</a></span> <span class="n">ksp</span><span class="p">;</span> <span class="cm">/* linear solver context */</span>
<span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscReal.html#PetscReal">PetscReal</a></span> <span class="n">norm</span><span class="p">;</span> <span class="cm">/* norm of solution error */</span>
<span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscInt.html#PetscInt">PetscInt</a></span> <span class="n">i</span><span class="p">,</span><span class="n">j</span><span class="p">,</span><span class="n">Ii</span><span class="p">,</span><span class="n">J</span><span class="p">,</span><span class="n">Istart</span><span class="p">,</span><span class="n">Iend</span><span class="p">,</span><span class="n">m</span> <span class="o">=</span> <span class="mi">8</span><span class="p">,</span><span class="n">n</span> <span class="o">=</span> <span class="mi">7</span><span class="p">,</span><span class="n">its</span><span class="p">;</span>
<span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscErrorCode.html#PetscErrorCode">PetscErrorCode</a></span> <span class="n">ierr</span><span class="p">;</span>
<span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscBool.html#PetscBool">PetscBool</a></span> <span class="n">flg</span><span class="p">;</span>
<span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscScalar.html#PetscScalar">PetscScalar</a></span> <span class="n">v</span><span class="p">;</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscInitialize.html#PetscInitialize">PetscInitialize</a></span><span class="p">(</span><span class="o">&</span><span class="n">argc</span><span class="p">,</span><span class="o">&</span><span class="n">args</span><span class="p">,(</span><span class="kt">char</span><span class="o">*</span><span class="p">)</span><span class="mi">0</span><span class="p">,</span><span class="n">help</span><span class="p">);</span><span class="k">if</span> <span class="p">(</span><span class="n">ierr</span><span class="p">)</span> <span class="k">return</span> <span class="n">ierr</span><span class="p">;</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscOptionsGetInt.html#PetscOptionsGetInt">PetscOptionsGetInt</a></span><span class="p">(</span><span class="nb">NULL</span><span class="p">,</span><span class="nb">NULL</span><span class="p">,</span><span class="s">"-m"</span><span class="p">,</span><span class="o">&</span><span class="n">m</span><span class="p">,</span><span class="nb">NULL</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscOptionsGetInt.html#PetscOptionsGetInt">PetscOptionsGetInt</a></span><span class="p">(</span><span class="nb">NULL</span><span class="p">,</span><span class="nb">NULL</span><span class="p">,</span><span class="s">"-n"</span><span class="p">,</span><span class="o">&</span><span class="n">n</span><span class="p">,</span><span class="nb">NULL</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="cm">/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -</span>
<span class="cm"> Compute the matrix and right-hand-side vector that define</span>
<span class="cm"> the linear system, Ax = b.</span>
<span class="cm"> - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */</span>
<span class="cm">/*</span>
<span class="cm"> Create parallel matrix, specifying only its global dimensions.</span>
<span class="cm"> When using <a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatCreate.html#MatCreate">MatCreate</a>(), the matrix format can be specified at</span>
<span class="cm"> runtime. Also, the parallel partitioning of the matrix is</span>
<span class="cm"> determined by PETSc at runtime.</span>
<span class="cm"> Performance tuning note: For problems of substantial size,</span>
<span class="cm"> preallocation of matrix memory is crucial for attaining good</span>
<span class="cm"> performance. See the matrix chapter of the users manual for details.</span>
<span class="cm"> */</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatCreate.html#MatCreate">MatCreate</a></span><span class="p">(</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PETSC_COMM_WORLD.html#PETSC_COMM_WORLD">PETSC_COMM_WORLD</a></span><span class="p">,</span><span class="o">&</span><span class="n">A</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatSetSizes.html#MatSetSizes">MatSetSizes</a></span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PETSC_DECIDE.html#PETSC_DECIDE">PETSC_DECIDE</a></span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PETSC_DECIDE.html#PETSC_DECIDE">PETSC_DECIDE</a></span><span class="p">,</span><span class="n">m</span><span class="o">*</span><span class="n">n</span><span class="p">,</span><span class="n">m</span><span class="o">*</span><span class="n">n</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatSetFromOptions.html#MatSetFromOptions">MatSetFromOptions</a></span><span class="p">(</span><span class="n">A</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatMPIAIJSetPreallocation.html#MatMPIAIJSetPreallocation">MatMPIAIJSetPreallocation</a></span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span><span class="nb">NULL</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span><span class="nb">NULL</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatSeqAIJSetPreallocation.html#MatSeqAIJSetPreallocation">MatSeqAIJSetPreallocation</a></span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span><span class="nb">NULL</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatSeqSBAIJSetPreallocation.html#MatSeqSBAIJSetPreallocation">MatSeqSBAIJSetPreallocation</a></span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span><span class="nb">NULL</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatMPISBAIJSetPreallocation.html#MatMPISBAIJSetPreallocation">MatMPISBAIJSetPreallocation</a></span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span><span class="nb">NULL</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span><span class="nb">NULL</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatMPISELLSetPreallocation.html#MatMPISELLSetPreallocation">MatMPISELLSetPreallocation</a></span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span><span class="nb">NULL</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span><span class="nb">NULL</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatSeqSELLSetPreallocation.html#MatSeqSELLSetPreallocation">MatSeqSELLSetPreallocation</a></span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span><span class="nb">NULL</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="cm">/*</span>
<span class="cm"> Currently, all PETSc parallel matrix formats are partitioned by</span>
<span class="cm"> contiguous chunks of rows across the processors. Determine which</span>
<span class="cm"> rows of the matrix are locally owned.</span>
<span class="cm"> */</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatGetOwnershipRange.html#MatGetOwnershipRange">MatGetOwnershipRange</a></span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="o">&</span><span class="n">Istart</span><span class="p">,</span><span class="o">&</span><span class="n">Iend</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="cm">/*</span>
<span class="cm"> Set matrix elements for the 2-D, five-point stencil in parallel.</span>
<span class="cm"> - Each processor needs to insert only elements that it owns</span>
<span class="cm"> locally (but any non-local elements will be sent to the</span>
<span class="cm"> appropriate processor during matrix assembly).</span>
<span class="cm"> - Always specify global rows and columns of matrix entries.</span>
<span class="cm"> Note: this uses the less common natural ordering that orders first</span>
<span class="cm"> all the unknowns for x = h then for x = 2h etc; Hence you see J = Ii +- n</span>
<span class="cm"> instead of J = I +- m as you might expect. The more standard ordering</span>
<span class="cm"> would first do all variables for y = h, then y = 2h etc.</span>
<span class="cm"> */</span>
<span class="k">for</span> <span class="p">(</span><span class="n">Ii</span><span class="o">=</span><span class="n">Istart</span><span class="p">;</span> <span class="n">Ii</span><span class="o"><</span><span class="n">Iend</span><span class="p">;</span> <span class="n">Ii</span><span class="o">++</span><span class="p">)</span> <span class="p">{</span>
<span class="n">v</span> <span class="o">=</span> <span class="mf">-1.0</span><span class="p">;</span> <span class="n">i</span> <span class="o">=</span> <span class="n">Ii</span><span class="o">/</span><span class="n">n</span><span class="p">;</span> <span class="n">j</span> <span class="o">=</span> <span class="n">Ii</span> <span class="o">-</span> <span class="n">i</span><span class="o">*</span><span class="n">n</span><span class="p">;</span>
<span class="k">if</span> <span class="p">(</span><span class="n">i</span><span class="o">></span><span class="mi">0</span><span class="p">)</span> <span class="p">{</span><span class="n">J</span> <span class="o">=</span> <span class="n">Ii</span> <span class="o">-</span> <span class="n">n</span><span class="p">;</span> <span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatSetValues.html#MatSetValues">MatSetValues</a></span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="o">&</span><span class="n">Ii</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="o">&</span><span class="n">J</span><span class="p">,</span><span class="o">&</span><span class="n">v</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/ADD_VALUES.html#ADD_VALUES">ADD_VALUES</a></span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);}</span>
<span class="k">if</span> <span class="p">(</span><span class="n">i</span><span class="o"><</span><span class="n">m</span><span class="mi">-1</span><span class="p">)</span> <span class="p">{</span><span class="n">J</span> <span class="o">=</span> <span class="n">Ii</span> <span class="o">+</span> <span class="n">n</span><span class="p">;</span> <span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatSetValues.html#MatSetValues">MatSetValues</a></span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="o">&</span><span class="n">Ii</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="o">&</span><span class="n">J</span><span class="p">,</span><span class="o">&</span><span class="n">v</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/ADD_VALUES.html#ADD_VALUES">ADD_VALUES</a></span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);}</span>
<span class="k">if</span> <span class="p">(</span><span class="n">j</span><span class="o">></span><span class="mi">0</span><span class="p">)</span> <span class="p">{</span><span class="n">J</span> <span class="o">=</span> <span class="n">Ii</span> <span class="o">-</span> <span class="mi">1</span><span class="p">;</span> <span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatSetValues.html#MatSetValues">MatSetValues</a></span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="o">&</span><span class="n">Ii</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="o">&</span><span class="n">J</span><span class="p">,</span><span class="o">&</span><span class="n">v</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/ADD_VALUES.html#ADD_VALUES">ADD_VALUES</a></span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);}</span>
<span class="k">if</span> <span class="p">(</span><span class="n">j</span><span class="o"><</span><span class="n">n</span><span class="mi">-1</span><span class="p">)</span> <span class="p">{</span><span class="n">J</span> <span class="o">=</span> <span class="n">Ii</span> <span class="o">+</span> <span class="mi">1</span><span class="p">;</span> <span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatSetValues.html#MatSetValues">MatSetValues</a></span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="o">&</span><span class="n">Ii</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="o">&</span><span class="n">J</span><span class="p">,</span><span class="o">&</span><span class="n">v</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/ADD_VALUES.html#ADD_VALUES">ADD_VALUES</a></span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);}</span>
<span class="n">v</span> <span class="o">=</span> <span class="mf">4.0</span><span class="p">;</span> <span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatSetValues.html#MatSetValues">MatSetValues</a></span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="o">&</span><span class="n">Ii</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="o">&</span><span class="n">Ii</span><span class="p">,</span><span class="o">&</span><span class="n">v</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/ADD_VALUES.html#ADD_VALUES">ADD_VALUES</a></span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="p">}</span>
<span class="cm">/*</span>
<span class="cm"> Assemble matrix, using the 2-step process:</span>
<span class="cm"> <a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatAssemblyBegin.html#MatAssemblyBegin">MatAssemblyBegin</a>(), <a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatAssemblyEnd.html#MatAssemblyEnd">MatAssemblyEnd</a>()</span>
<span class="cm"> Computations can be done while messages are in transition</span>
<span class="cm"> by placing code between these two statements.</span>
<span class="cm"> */</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatAssemblyBegin.html#MatAssemblyBegin">MatAssemblyBegin</a></span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatAssemblyType.html#MatAssemblyType">MAT_FINAL_ASSEMBLY</a></span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatAssemblyEnd.html#MatAssemblyEnd">MatAssemblyEnd</a></span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatAssemblyType.html#MatAssemblyType">MAT_FINAL_ASSEMBLY</a></span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="cm">/* A is symmetric. Set symmetric flag to enable ICC/Cholesky preconditioner */</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatSetOption.html#MatSetOption">MatSetOption</a></span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatOption.html#MatOption">MAT_SYMMETRIC</a></span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PETSC_TRUE.html#PETSC_TRUE">PETSC_TRUE</a></span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="cm">/*</span>
<span class="cm"> Create parallel vectors.</span>
<span class="cm"> - We form 1 vector from scratch and then duplicate as needed.</span>
<span class="cm"> - When using <a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecCreate.html#VecCreate">VecCreate</a>(), <a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecSetSizes.html#VecSetSizes">VecSetSizes</a> and <a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecSetFromOptions.html#VecSetFromOptions">VecSetFromOptions</a>()</span>
<span class="cm"> in this example, we specify only the</span>
<span class="cm"> vector's global dimension; the parallel partitioning is determined</span>
<span class="cm"> at runtime.</span>
<span class="cm"> - When solving a linear system, the vectors and matrices MUST</span>
<span class="cm"> be partitioned accordingly. PETSc automatically generates</span>
<span class="cm"> appropriately partitioned matrices and vectors when <a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatCreate.html#MatCreate">MatCreate</a>()</span>
<span class="cm"> and <a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecCreate.html#VecCreate">VecCreate</a>() are used with the same communicator.</span>
<span class="cm"> - The user can alternatively specify the local vector and matrix</span>
<span class="cm"> dimensions when more sophisticated partitioning is needed</span>
<span class="cm"> (replacing the <a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PETSC_DECIDE.html#PETSC_DECIDE">PETSC_DECIDE</a> argument in the <a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecSetSizes.html#VecSetSizes">VecSetSizes</a>() statement</span>
<span class="cm"> below).</span>
<span class="cm"> */</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecCreate.html#VecCreate">VecCreate</a></span><span class="p">(</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PETSC_COMM_WORLD.html#PETSC_COMM_WORLD">PETSC_COMM_WORLD</a></span><span class="p">,</span><span class="o">&</span><span class="n">u</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecSetSizes.html#VecSetSizes">VecSetSizes</a></span><span class="p">(</span><span class="n">u</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PETSC_DECIDE.html#PETSC_DECIDE">PETSC_DECIDE</a></span><span class="p">,</span><span class="n">m</span><span class="o">*</span><span class="n">n</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecSetFromOptions.html#VecSetFromOptions">VecSetFromOptions</a></span><span class="p">(</span><span class="n">u</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecDuplicate.html#VecDuplicate">VecDuplicate</a></span><span class="p">(</span><span class="n">u</span><span class="p">,</span><span class="o">&</span><span class="n">b</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecDuplicate.html#VecDuplicate">VecDuplicate</a></span><span class="p">(</span><span class="n">b</span><span class="p">,</span><span class="o">&</span><span class="n">x</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="cm">/*</span>
<span class="cm"> Set exact solution; then compute right-hand-side vector.</span>
<span class="cm"> By default we use an exact solution of a vector with all</span>
<span class="cm"> elements of 1.0;</span>
<span class="cm"> */</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecSet.html#VecSet">VecSet</a></span><span class="p">(</span><span class="n">u</span><span class="p">,</span><span class="mf">1.0</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatMult.html#MatMult">MatMult</a></span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="n">u</span><span class="p">,</span><span class="n">b</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="cm">/*</span>
<span class="cm"> View the exact solution vector if desired</span>
<span class="cm"> */</span>
<span class="n">flg</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PETSC_FALSE.html#PETSC_FALSE">PETSC_FALSE</a></span><span class="p">;</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscOptionsGetBool.html#PetscOptionsGetBool">PetscOptionsGetBool</a></span><span class="p">(</span><span class="nb">NULL</span><span class="p">,</span><span class="nb">NULL</span><span class="p">,</span><span class="s">"-view_exact_sol"</span><span class="p">,</span><span class="o">&</span><span class="n">flg</span><span class="p">,</span><span class="nb">NULL</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="k">if</span> <span class="p">(</span><span class="n">flg</span><span class="p">)</span> <span class="p">{</span><span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecView.html#VecView">VecView</a></span><span class="p">(</span><span class="n">u</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Viewer/PETSC_VIEWER_STDOUT_WORLD.html#PETSC_VIEWER_STDOUT_WORLD">PETSC_VIEWER_STDOUT_WORLD</a></span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);}</span>
<span class="cm">/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -</span>
<span class="cm"> Create the linear solver and set various options</span>
<span class="cm"> - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSPCreate.html#KSPCreate">KSPCreate</a></span><span class="p">(</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PETSC_COMM_WORLD.html#PETSC_COMM_WORLD">PETSC_COMM_WORLD</a></span><span class="p">,</span><span class="o">&</span><span class="n">ksp</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="cm">/*</span>
<span class="cm"> Set operators. Here the matrix that defines the linear system</span>
<span class="cm"> also serves as the preconditioning matrix.</span>
<span class="cm"> */</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSPSetOperators.html#KSPSetOperators">KSPSetOperators</a></span><span class="p">(</span><span class="n">ksp</span><span class="p">,</span><span class="n">A</span><span class="p">,</span><span class="n">A</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="cm">/*</span>
<span class="cm"> Set linear solver defaults for this problem (optional).</span>
<span class="cm"> - By extracting the <a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSP.html#KSP">KSP</a> and <a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/PC/PC.html#PC">PC</a> contexts from the <a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSP.html#KSP">KSP</a> context,</span>
<span class="cm"> we can then directly call any <a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSP.html#KSP">KSP</a> and <a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/PC/PC.html#PC">PC</a> routines to set</span>
<span class="cm"> various options.</span>
<span class="cm"> - The following two statements are optional; all of these</span>
<span class="cm"> parameters could alternatively be specified at runtime via</span>
<span class="cm"> <a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSPSetFromOptions.html#KSPSetFromOptions">KSPSetFromOptions</a>(). All of these defaults can be</span>
<span class="cm"> overridden at runtime, as indicated below.</span>
<span class="cm"> */</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSPSetTolerances.html#KSPSetTolerances">KSPSetTolerances</a></span><span class="p">(</span><span class="n">ksp</span><span class="p">,</span><span class="mf">1.</span><span class="n">e</span><span class="mi">-2</span><span class="o">/</span><span class="p">((</span><span class="n">m</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span><span class="o">*</span><span class="p">(</span><span class="n">n</span><span class="o">+</span><span class="mi">1</span><span class="p">)),</span><span class="mf">1.</span><span class="n">e</span><span class="mi">-50</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PETSC_DEFAULT.html#PETSC_DEFAULT">PETSC_DEFAULT</a></span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PETSC_DEFAULT.html#PETSC_DEFAULT">PETSC_DEFAULT</a></span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="cm">/*</span>
<span class="cm"> Set runtime options, e.g.,</span>
<span class="cm"> -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol></span>
<span class="cm"> These options will override those specified above as long as</span>
<span class="cm"> <a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSPSetFromOptions.html#KSPSetFromOptions">KSPSetFromOptions</a>() is called _after_ any other customization</span>
<span class="cm"> routines.</span>
<span class="cm"> */</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSPSetFromOptions.html#KSPSetFromOptions">KSPSetFromOptions</a></span><span class="p">(</span><span class="n">ksp</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="cm">/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -</span>
<span class="cm"> Solve the linear system</span>
<span class="cm"> - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSPSolve.html#KSPSolve">KSPSolve</a></span><span class="p">(</span><span class="n">ksp</span><span class="p">,</span><span class="n">b</span><span class="p">,</span><span class="n">x</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="cm">/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -</span>
<span class="cm"> Check the solution and clean up</span>
<span class="cm"> - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecAXPY.html#VecAXPY">VecAXPY</a></span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="mf">-1.0</span><span class="p">,</span><span class="n">u</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecNorm.html#VecNorm">VecNorm</a></span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/NORM_2.html#NORM_2">NORM_2</a></span><span class="p">,</span><span class="o">&</span><span class="n">norm</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSPGetIterationNumber.html#KSPGetIterationNumber">KSPGetIterationNumber</a></span><span class="p">(</span><span class="n">ksp</span><span class="p">,</span><span class="o">&</span><span class="n">its</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="cm">/*</span>
<span class="cm"> Print convergence information. <a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscPrintf.html#PetscPrintf">PetscPrintf</a>() produces a single</span>
<span class="cm"> print statement from all processes that share a communicator.</span>
<span class="cm"> An alternative is <a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscFPrintf.html#PetscFPrintf">PetscFPrintf</a>(), which prints to a file.</span>
<span class="cm"> */</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscPrintf.html#PetscPrintf">PetscPrintf</a></span><span class="p">(</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PETSC_COMM_WORLD.html#PETSC_COMM_WORLD">PETSC_COMM_WORLD</a></span><span class="p">,</span><span class="s">"Norm of error %g iterations %D</span><span class="se">\n</span><span class="s">"</span><span class="p">,(</span><span class="kt">double</span><span class="p">)</span><span class="n">norm</span><span class="p">,</span><span class="n">its</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="cm">/*</span>
<span class="cm"> Free work space. All PETSc objects should be destroyed when they</span>
<span class="cm"> are no longer needed.</span>
<span class="cm"> */</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSPDestroy.html#KSPDestroy">KSPDestroy</a></span><span class="p">(</span><span class="o">&</span><span class="n">ksp</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecDestroy.html#VecDestroy">VecDestroy</a></span><span class="p">(</span><span class="o">&</span><span class="n">u</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span> <span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecDestroy.html#VecDestroy">VecDestroy</a></span><span class="p">(</span><span class="o">&</span><span class="n">x</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecDestroy.html#VecDestroy">VecDestroy</a></span><span class="p">(</span><span class="o">&</span><span class="n">b</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span> <span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatDestroy.html#MatDestroy">MatDestroy</a></span><span class="p">(</span><span class="o">&</span><span class="n">A</span><span class="p">);</span><span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/CHKERRQ.html#CHKERRQ">CHKERRQ</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">);</span>
<span class="cm">/*</span>
<span class="cm"> Always call <a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscFinalize.html#PetscFinalize">PetscFinalize</a>() before exiting a program. This routine</span>
<span class="cm"> - finalizes the PETSc libraries as well as MPI</span>
<span class="cm"> - provides summary and diagnostic information if certain runtime</span>
<span class="cm"> options are chosen (e.g., -log_view).</span>
<span class="cm"> */</span>
<span class="n">ierr</span> <span class="o">=</span> <span class="n"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Sys/PetscFinalize.html#PetscFinalize">PetscFinalize</a></span><span class="p">();</span>
<span class="k">return</span> <span class="n">ierr</span><span class="p">;</span>
<span class="p">}</span>
</pre></div>
</div>
</div>
</div>
<div class="section" id="compiling-and-running-programs">
<h3>Compiling and Running Programs<a class="headerlink" href="#compiling-and-running-programs" title="Permalink to this headline">¶</a></h3>
<p>The output below illustrates compiling and running a
PETSc program using MPICH on an OS X laptop. Note that different
machines will have compilation commands as determined by the
configuration process. See <a class="reference internal" href="#sec-writing-application-codes"><span class="std std-ref">Writing Application Codes with PETSc</span></a> for
a discussion about how to compile your PETSc programs. Users who are
experiencing difficulties linking PETSc programs should refer to the FAQ
on the PETSc website <a class="reference external" href="https://www.mcs.anl.gov/petsc">https://www.mcs.anl.gov/petsc</a> or given in the file
<code class="docutils literal notranslate"><span class="pre">$PETSC_DIR/docs/faq.html</span></code>.</p>
<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>$ cd $PETSC_DIR/src/ksp/ksp/tutorials
$ make ex2
/Users/patrick/petsc/arch-darwin-double-debug/bin/mpicc -o ex2.o -c -Wall -Wwrite-strings -Wno-strict-aliasing -Wno-unknown-pragmas -Qunused-arguments -fvisibility=hidden -g3 -I/Users/patrick/petsc/include -I/Users/patrick/petsc/arch-darwin-double-debug/include -I/opt/X11/include -I/opt/local/include `pwd`/ex2.c
/Users/patrick/petsc/arch-darwin-double-debug/bin/mpicc -Wl,-multiply_defined,suppress -Wl,-multiply_defined -Wl,suppress -Wl,-commons,use_dylibs -Wl,-search_paths_first -Wl,-multiply_defined,suppress -Wl,-multiply_defined -Wl,suppress -Wl,-commons,use_dylibs -Wl,-search_paths_first -Wall -Wwrite-strings -Wno-strict-aliasing -Wno-unknown-pragmas -Qunused-arguments -fvisibility=hidden -g3 -o ex2 ex2.o -Wl,-rpath,/Users/patrick/petsc/arch-darwin-double-debug/lib -L/Users/patrick/petsc/arch-darwin-double-debug/lib -lpetsc -Wl,-rpath,/Users/patrick/petsc/arch-darwin-double-debug/lib -lf2clapack -lf2cblas -Wl,-rpath,/opt/X11/lib -L/opt/X11/lib -lX11 -lssl -lcrypto -Wl,-rpath,/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/lib/clang/7.0.2/lib/darwin -L/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/lib/clang/7.0.2/lib/darwin -lmpifort -lgfortran -Wl,-rpath,/opt/local/lib/gcc5/gcc/x86_64-apple-darwin14/5.3.0 -L/opt/local/lib/gcc5/gcc/x86_64-apple-darwin14/5.3.0 -Wl,-rpath,/opt/local/lib/gcc5 -L/opt/local/lib/gcc5 -lgfortran -lgcc_ext.10.5 -lquadmath -lm -lclang_rt.osx -lmpicxx -lc++ -Wl,-rpath,/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/../lib/clang/7.0.2/lib/darwin -L/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/../lib/clang/7.0.2/lib/darwin -lclang_rt.osx -Wl,-rpath,/Users/patrick/petsc/arch-darwin-double-debug/lib -L/Users/patrick/petsc/arch-darwin-double-debug/lib -ldl -lmpi -lpmpi -lSystem -Wl,-rpath,/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/../lib/clang/7.0.2/lib/darwin -L/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/../lib/clang/7.0.2/lib/darwin -lclang_rt.osx -ldl
/bin/rm -f ex2.o
$ $PETSC_DIR/lib/petsc/bin/petscmpiexec -n 1 ./ex2
Norm of error 0.000156044 iterations 6
$ $PETSC_DIR/lib/petsc/bin/petscmpiexec -n 2 ./ex2
Norm of error 0.000411674 iterations 7
</pre></div>
</div>
</div>
</div>
<div class="section" id="profiling-programs">
<span id="sec-profiling-programs"></span><h2>Profiling Programs<a class="headerlink" href="#profiling-programs" title="Permalink to this headline">¶</a></h2>
<p>The option
<code class="docutils literal notranslate"><span class="pre">-log_view</span></code> activates printing of a performance summary, including
times, floating point operation (flop) rates, and message-passing
activity. <a class="reference internal" href="profiling.html#ch-profiling"><span class="std std-ref">Profiling</span></a> provides details about
profiling, including interpretation of the output data below.
This particular example involves
the solution of a linear system on one processor using GMRES and ILU.
The low floating point operation (flop) rates in this example are due to
the fact that the code solved a tiny system. We include this example
merely to demonstrate the ease of extracting performance information.</p>
<div class="highlight-none notranslate" id="listing-exprof"><div class="highlight"><pre><span></span>$ $PETSC_DIR/lib/petsc/bin/petscmpiexec -n 1 ./ex1 -n 1000 -pc_type ilu -ksp_type gmres -ksp_rtol 1.e-7 -log_view
...
------------------------------------------------------------------------------------------------------------------------
Event Count Time (sec) Flops --- Global --- --- Stage ---- Total
Max Ratio Max Ratio Max Ratio Mess AvgLen Reduct %T %F %M %L %R %T %F %M %L %R Mflop/s
------------------------------------------------------------------------------------------------------------------------
--- Event Stage 0: Main Stage
<a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecMDot.html#VecMDot">VecMDot</a> 1 1.0 3.2830e-06 1.0 2.00e+03 1.0 0.0e+00 0.0e+00 0.0e+00 0 5 0 0 0 0 5 0 0 0 609
<a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecNorm.html#VecNorm">VecNorm</a> 3 1.0 4.4550e-06 1.0 6.00e+03 1.0 0.0e+00 0.0e+00 0.0e+00 0 14 0 0 0 0 14 0 0 0 1346
<a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecScale.html#VecScale">VecScale</a> 2 1.0 4.0110e-06 1.0 2.00e+03 1.0 0.0e+00 0.0e+00 0.0e+00 0 5 0 0 0 0 5 0 0 0 499
<a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecCopy.html#VecCopy">VecCopy</a> 1 1.0 3.2280e-06 1.0 0.00e+00 0.0 0.0e+00 0.0e+00 0.0e+00 0 0 0 0 0 0 0 0 0 0 0
<a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecSet.html#VecSet">VecSet</a> 11 1.0 2.5537e-05 1.0 0.00e+00 0.0 0.0e+00 0.0e+00 0.0e+00 2 0 0 0 0 2 0 0 0 0 0
<a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecAXPY.html#VecAXPY">VecAXPY</a> 2 1.0 2.0930e-06 1.0 4.00e+03 1.0 0.0e+00 0.0e+00 0.0e+00 0 10 0 0 0 0 10 0 0 0 1911
<a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecMAXPY.html#VecMAXPY">VecMAXPY</a> 2 1.0 1.1280e-06 1.0 4.00e+03 1.0 0.0e+00 0.0e+00 0.0e+00 0 10 0 0 0 0 10 0 0 0 3546
<a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecNormalize.html#VecNormalize">VecNormalize</a> 2 1.0 9.3970e-06 1.0 6.00e+03 1.0 0.0e+00 0.0e+00 0.0e+00 1 14 0 0 0 1 14 0 0 0 638
<a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatMult.html#MatMult">MatMult</a> 2 1.0 1.1177e-05 1.0 9.99e+03 1.0 0.0e+00 0.0e+00 0.0e+00 1 24 0 0 0 1 24 0 0 0 894
<a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatSolve.html#MatSolve">MatSolve</a> 2 1.0 1.9933e-05 1.0 9.99e+03 1.0 0.0e+00 0.0e+00 0.0e+00 1 24 0 0 0 1 24 0 0 0 501
MatLUFactorNum 1 1.0 3.5081e-05 1.0 4.00e+03 1.0 0.0e+00 0.0e+00 0.0e+00 2 10 0 0 0 2 10 0 0 0 114
MatILUFactorSym 1 1.0 4.4259e-05 1.0 0.00e+00 0.0 0.0e+00 0.0e+00 0.0e+00 3 0 0 0 0 3 0 0 0 0 0
<a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatAssemblyBegin.html#MatAssemblyBegin">MatAssemblyBegin</a> 1 1.0 8.2015e-08 1.0 0.00e+00 0.0 0.0e+00 0.0e+00 0.0e+00 0 0 0 0 0 0 0 0 0 0 0
<a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatAssemblyEnd.html#MatAssemblyEnd">MatAssemblyEnd</a> 1 1.0 3.3536e-05 1.0 0.00e+00 0.0 0.0e+00 0.0e+00 0.0e+00 2 0 0 0 0 2 0 0 0 0 0
<a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatGetRowIJ.html#MatGetRowIJ">MatGetRowIJ</a> 1 1.0 1.5960e-06 1.0 0.00e+00 0.0 0.0e+00 0.0e+00 0.0e+00 0 0 0 0 0 0 0 0 0 0 0
<a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/MatOrderings/MatGetOrdering.html#MatGetOrdering">MatGetOrdering</a> 1 1.0 3.9791e-05 1.0 0.00e+00 0.0 0.0e+00 0.0e+00 0.0e+00 3 0 0 0 0 3 0 0 0 0 0
<a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatView.html#MatView">MatView</a> 2 1.0 6.7909e-05 1.0 0.00e+00 0.0 0.0e+00 0.0e+00 0.0e+00 5 0 0 0 0 5 0 0 0 0 0
KSPGMRESOrthog 1 1.0 7.5970e-06 1.0 4.00e+03 1.0 0.0e+00 0.0e+00 0.0e+00 1 10 0 0 0 1 10 0 0 0 526
<a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSPSetUp.html#KSPSetUp">KSPSetUp</a> 1 1.0 3.4424e-05 1.0 0.00e+00 0.0 0.0e+00 0.0e+00 0.0e+00 2 0 0 0 0 2 0 0 0 0 0
<a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSPSolve.html#KSPSolve">KSPSolve</a> 1 1.0 2.7264e-04 1.0 3.30e+04 1.0 0.0e+00 0.0e+00 0.0e+00 19 79 0 0 0 19 79 0 0 0 121
<a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/PC/PCSetUp.html#PCSetUp">PCSetUp</a> 1 1.0 1.5234e-04 1.0 4.00e+03 1.0 0.0e+00 0.0e+00 0.0e+00 11 10 0 0 0 11 10 0 0 0 26
<a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/PC/PCApply.html#PCApply">PCApply</a> 2 1.0 2.1022e-05 1.0 9.99e+03 1.0 0.0e+00 0.0e+00 0.0e+00 1 24 0 0 0 1 24 0 0 0 475
------------------------------------------------------------------------------------------------------------------------
Memory usage is given in bytes:
Object Type Creations Destructions Memory Descendants' Mem.
Reports information only for process 0.
--- Event Stage 0: Main Stage
Vector 8 8 76224 0.
Matrix 2 2 134212 0.
Krylov Solver 1 1 18400 0.
Preconditioner 1 1 1032 0.
Index Set 3 3 10328 0.
Viewer 1 0 0 0.
========================================================================================================================
...
</pre></div>
</div>
</div>
<div class="section" id="writing-application-codes-with-petsc">
<span id="sec-writing-application-codes"></span><h2>Writing Application Codes with PETSc<a class="headerlink" href="#writing-application-codes-with-petsc" title="Permalink to this headline">¶</a></h2>
<p>The examples throughout the library demonstrate the software usage and
can serve as templates for developing custom applications. We suggest
that new PETSc users examine programs in the directories
<code class="docutils literal notranslate"><span class="pre">${PETSC_DIR}/src/<library>/tutorials</span></code> where <code class="docutils literal notranslate"><span class="pre"><library></span></code> denotes any
of the PETSc libraries (listed in the following section), such as
<code class="docutils literal notranslate"><span class="pre"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/SNES/SNES.html#SNES">SNES</a></span></code> or <code class="docutils literal notranslate"><span class="pre"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSP.html#KSP">KSP</a></span></code> or <code class="docutils literal notranslate"><span class="pre"><a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/TS/TS.html#TS">TS</a></span></code>. The manual pages located at
<code class="docutils literal notranslate"><span class="pre">${PETSC_DIR}/docs/index.htm</span></code> or
<a class="reference external" href="https://www.mcs.anl.gov/petsc/documentation/">https://www.mcs.anl.gov/petsc/documentation/</a> provide links (organized by
both routine names and concepts) to the tutorial examples.</p>
<p>To write a new application program using PETSc, we suggest the following
procedure:</p>
<ol class="arabic simple">
<li><p>Install and test PETSc according to the instructions at the PETSc web
site.</p></li>
<li><p>Make a working directory for your source code: for example,
<code class="docutils literal notranslate"><span class="pre">mkdir</span> <span class="pre">$HOME/application</span></code></p></li>
<li><p>Change to that working directory; for
example,<code class="docutils literal notranslate"><span class="pre">cd</span> <span class="pre">$HOME/application</span></code></p></li>
<li><p>Copy one of the examples in the directory that corresponds to the
class of problem of interest into your working directory, for
example, <code class="docutils literal notranslate"><span class="pre">cp</span> <span class="pre">$PETSC_DIR/src/snes/tutorials/ex19.c</span> <span class="pre">ex19.c</span></code></p></li>
<li><p>Copy $PETSC_DIR/share/petsc/Makefile.user to your working directory,
for example, <code class="docutils literal notranslate"><span class="pre">cp</span> <span class="pre">$PETSC_DIR/share/petsc/Makefile.user</span> <span class="pre">Makefile</span></code></p></li>
<li><p>Compile and run the example program, for example,
<code class="docutils literal notranslate"><span class="pre">make</span> <span class="pre">ex19;</span> <span class="pre">./ex19</span></code></p></li>
<li><p>Use the example program as a starting point for developing a custom
code.</p></li>
</ol>
<p>We highly recommend against the following since it requires changing
your makefile for each new configuration/computing system but if you do
not wish to include any PETSc utilities in your makefile, you can use
the following commands in the PETSc root directory to get the
information needed by your makefile:</p>
<div class="highlight-bash notranslate"><div class="highlight"><pre><span></span>make getlinklibs getincludedirs getcflags getcxxflags getfortranflags getccompiler getfortrancompiler getcxxcompiler
</pre></div>
</div>
<p>All the libraries listed need to be linked into your executable and the
include directories and flags need to be passed to the compiler. Usually
this is done with <code class="docutils literal notranslate"><span class="pre">CFLAGS=<list</span> <span class="pre">of</span> <span class="pre">-I</span> <span class="pre">and</span> <span class="pre">other</span> <span class="pre">flags></span></code> and
<code class="docutils literal notranslate"><span class="pre">FFLAGS=<list</span> <span class="pre">of</span> <span class="pre">-I</span> <span class="pre">and</span> <span class="pre">other</span> <span class="pre">flags></span></code> in your makefile.</p>
</div>
<div class="section" id="citing-petsc">
<h2>Citing PETSc<a class="headerlink" href="#citing-petsc" title="Permalink to this headline">¶</a></h2>
<p>If you use the TS component of PETSc please cite the following:</p>
<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>@article{abhyankar2018petsc,
title={PETSc/<a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/TS/TS.html#TS">TS</a>: A Modern Scalable ODE/DAE Solver Library},
author={Abhyankar, Shrirang and Brown, Jed and Constantinescu, Emil M and Ghosh, Debojyoti and Smith, Barry F and Zhang, Hong},
journal={arXiv preprint arXiv:1806.01437},
year={2018}
}
</pre></div>
</div>
<p>When citing PETSc in a publication please cite the following:</p>
<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>@Misc{petsc-web-page,
Author = "Satish Balay and Shrirang Abhyankar and Mark~F. Adams and Jed Brown
and Peter Brune and Kris Buschelman and Lisandro Dalcin and Alp Dener and Victor Eijkhout
and William~D. Gropp and Dinesh Kaushik and Matthew~G. Knepley and Dave~A. May
and Lois Curfman McInnes and Richard Tran Mills and Todd Munson and Karl Rupp
and Patrick Sanan and Barry~F. Smith and Stefano Zampini and Hong Zhang and Hong Zhang",
Title = "{PETS}c {W}eb page",
Note = "https://www.mcs.anl.gov/petsc",
Year = "2020"}
@TechReport{petsc-user-ref,
Author = "Satish Balay and Shrirang Abhyankar and Mark~F. Adams and Jed Brown
and Peter Brune and Kris Buschelman and Lisandro Dalcin and Alp Dener and Victor Eijkhout
and William~D. Gropp and Dinesh Kaushik and Matthew~G. Knepley and Dave~A. May
and Lois Curfman McInnes and Richard Tran Mills and Todd Munson and Karl Rupp
and Patrick Sanan and Barry~F. Smith and Stefano Zampini and Hong Zhang and Hong Zhang",
Title = "{PETS}c Users Manual",
Number = "ANL-95/11 - Revision 3.13",
Institution = "Argonne National Laboratory",
Year = "2020"}
@InProceedings{petsc-efficient,
Author = "Satish Balay and William D. Gropp and Lois C. McInnes and Barry F. Smith",
Title = "Efficient Management of Parallelism in Object Oriented
Numerical Software Libraries",
Booktitle = "Modern Software Tools in Scientific Computing",
Editor = "E. Arge and A. M. Bruaset and H. P. Langtangen",
Pages = "163--202",
Publisher = "Birkhauser Press",
Year = "1997"}
</pre></div>
</div>
</div>
<div class="section" id="directory-structure">
<span id="sec-directory"></span><h2>Directory Structure<a class="headerlink" href="#directory-structure" title="Permalink to this headline">¶</a></h2>
<p>We conclude this introduction with an overview of the organization of
the PETSc software. The root directory of PETSc contains the following
directories:</p>
<ul class="simple">
<li><p><code class="docutils literal notranslate"><span class="pre">docs</span></code> (only in the tarball distribution of PETSc; not the git
repository) - All documentation for PETSc. The files <code class="docutils literal notranslate"><span class="pre">manual.pdf</span></code>
contains the hyperlinked users manual, suitable for printing or
on-screen viewering. Includes the subdirectory - <code class="docutils literal notranslate"><span class="pre">manualpages</span></code>
(on-line manual pages).</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">conf</span></code> - Base PETSc configuration files that define the standard
make variables and rules used by PETSc</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">include</span></code> - All include files for PETSc that are visible to the
user.</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">include/petsc/finclude</span></code> - PETSc include files for Fortran
programmers using the .F suffix (recommended).</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">include/petsc/private</span></code> - Private PETSc include files that should
<em>not</em> need to be used by application programmers.</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">share</span></code> - Some small test matrices in data files</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">src</span></code> - The source code for all PETSc libraries, which currently
includes</p>
<ul>
<li><p><code class="docutils literal notranslate"><span class="pre">vec</span></code> - vectors,</p>
<ul>
<li><p><code class="docutils literal notranslate"><span class="pre">is</span></code> - index sets,</p></li>
</ul>
</li>
<li><p><code class="docutils literal notranslate"><span class="pre">mat</span></code> - matrices,</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">ksp</span></code> - complete linear equations solvers,</p>
<ul>
<li><p><code class="docutils literal notranslate"><span class="pre">ksp</span></code> - Krylov subspace accelerators,</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">pc</span></code> - preconditioners,</p></li>
</ul>
</li>
<li><p><code class="docutils literal notranslate"><span class="pre">snes</span></code> - nonlinear solvers</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">ts</span></code> - ODE solvers and timestepping,</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">dm</span></code> - data management between meshes and solvers, vectors, and
matrices,</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">sys</span></code> - general system-related routines,</p>
<ul>
<li><p><code class="docutils literal notranslate"><span class="pre">logging</span></code> - PETSc logging and profiling routines,</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">classes</span></code> - low-level classes</p>
<ul>
<li><p><code class="docutils literal notranslate"><span class="pre">draw</span></code> - simple graphics,</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">viewer</span></code> - mechanism for printing and visualizing PETSc
objects,</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">bag</span></code> - mechanism for saving and loading from disk user
data stored in C structs.</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">random</span></code> - random number generators.</p></li>
</ul>
</li>
</ul>
</li>
</ul>
</li>
</ul>
<p>Each PETSc source code library directory has the following
subdirectories:</p>
<ul class="simple">
<li><dl class="simple">
<dt><code class="docutils literal notranslate"><span class="pre">tutorials</span></code> - Programs designed to teach users about PETSc.</dt><dd><p>These codes can serve as templates for the design of custom
applications.</p>
</dd>
</dl>
</li>
<li><dl class="simple">
<dt><code class="docutils literal notranslate"><span class="pre">tests</span></code> - Programs designed for thorough testing of PETSc. As</dt><dd><p>such, these codes are not intended for examination by users.</p>
</dd>
</dl>
</li>
<li><p><code class="docutils literal notranslate"><span class="pre">interface</span></code> - The calling sequences for the abstract interface to
the component. Code here does not know about particular
implementations.</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">impls</span></code> - Source code for one or more implementations.</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">utils</span></code> - Utility routines. Source here may know about the
implementations, but ideally will not know about implementations for
other components.</p></li>
</ul>
<hr><p id="id3"><dl class="citation">
<dt class="label" id="id201"><span class="brackets"><a class="fn-backref" href="#id1">For94</a></span></dt>
<dd><p>MPI Forum. MPI: a message-passing interface standard. <em>International J. Supercomputing Applications</em>, 1994.</p>
</dd>
<dt class="label" id="id292"><span class="brackets"><a class="fn-backref" href="#id2">GLS94</a></span></dt>
<dd><p>William Gropp, Ewing Lusk, and Anthony Skjellum. <em>Using MPI: Portable Parallel Programming with the Message Passing Interface</em>. MIT Press, 1994.</p>
</dd>
</dl>
</p>
<span class="target" id="id1253"></span></div>
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