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<h3 class="section">D.17 <code>umf</code></h3>

<p>Systems of equations described by sparse matrices (i.e., matrices
<a name="index-sparse-matrices-813"></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>A virtual code interface to functions for solving sparse systems of
equations by these methods is afforded by library functions of the form

<pre class="example">     library('umf',f)
</pre>
   <p class="noindent">where the library function name, <code>f</code> is a character string
of the form <var>tt</var><code>_</code><var>m</var><code>_</code><var>rrr</var>.

     <ul>
<li><var>tt</var>
can be either <code>di</code> for real matrices, or <code>zi</code> for complex. 
<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-814"></a>corresponding to mnemonics <code>A</code>, <code>Aat</code> and <code>At</code> used in
the C language API. 
<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. 
</ul>

   <p>The complete set of function names for this library interface is as
follows.

<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>
   <p class="noindent">Not all combinations are represented, because the conjugate transpose
is relevant only to complex matrices.

<ul class="menu">
<li><a accesskey="1" href="umf-input-parameters.html#umf-input-parameters">umf input parameters</a>
<li><a accesskey="2" href="umf-output.html#umf-output">umf output</a>
<li><a accesskey="3" href="umf-exceptions.html#umf-exceptions">umf exceptions</a>
<li><a accesskey="4" href="Additional-umf-notes.html#Additional-umf-notes">Additional umf notes</a>
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