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<a name="umf"></a>
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<hr size="1">
<a name="umf-1"></a>
<h2 class="section">D.17 <code>umf</code></h2>

<p>Systems of equations described by sparse matrices (i.e., matrices
<a name="index-sparse-matrices"></a>
containing mostly zeros) arise in certain practical problems. The
usual array representation in which zeros are explicitly stored would
be prohibitive for large matrices occurring in many problems of
interest. A more sophisticated approach is used by the <code>umf</code>
library to manage memory efficiently, which is documented at
<a href="http://www.cise.ufl.edu/research/sparse/SuiteSparse/current/SuiteSparse/UMFPACK/Doc/">http://www.cise.ufl.edu/research/sparse/SuiteSparse/current/SuiteSparse/UMFPACK/Doc/</a>.
</p>


<p>A virtual code interface to functions for solving sparse systems of
equations by these methods is afforded by library functions of the form
</p>
<table><tr><td>&nbsp;</td><td><pre class="example">library('umf',f)
</pre></td></tr></table>

<p>where the library function name, <code>f</code> is a character string
of the form <code><var>tt</var>_<var>m</var>_<var>rrr</var></code>.
</p>
<ul>
<li> <var>tt</var>
can be either <code>di</code> for real matrices, or <code>zi</code> for complex.
</li><li> <var>m</var>
can be one of <code>a</code>, <code>t</code>, or <code>c</code> for solving a system
given either by a matrix, its transpose, or its conjugate transpose,
respectively,
<a name="index-conjugate-transpose"></a>
corresponding to mnemonics <code>A</code>, <code>Aat</code> and <code>At</code> used in
the C language API.
</li><li> <var>rrr</var>
is either <code>trp</code> or <code>col</code>, to indicate a sparse matrix expressed
either as a list of triples, or in packed column form, as documented below.
</li></ul>

<p>The complete set of function names for this library interface is as
follows.
</p>
<table><tr><td>&nbsp;</td><td><pre class="example">di_a_trp      di_a_col       zi_a_trp       zi_a_col
di_t_trp      di_t_col       zi_t_trp       zi_t_col
                             zi_c_trp       zi_c_col
</pre></td></tr></table>

<p>Not all combinations are represented, because the conjugate transpose
is relevant only to complex matrices.
</p>
<table class="menu" border="0" cellspacing="0">
<tr><td align="left" valign="top"><a href="umf-input-parameters.html#umf-input-parameters">D.17.1 <code>umf</code> input parameters</a></td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top"><a href="umf-output.html#umf-output">D.17.2 <code>umf</code> output</a></td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top"><a href="umf-exceptions.html#umf-exceptions">D.17.3 <code>umf</code> exceptions</a></td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top"><a href="Additional-umf-notes.html#Additional-umf-notes">D.17.4 Additional <code>umf</code> notes</a></td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
</table>

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