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<a name="umf-input-parameters"></a>
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<hr size="1">
<a name="umf-input-parameters-1"></a>
<h3 class="subsection">D.17.1 <code>umf</code> input parameters</h3>

<p>For a square matrix <var>A</var> and a column vector <var>b</var>, the
<code>umf</code> functions find the solution <var>x</var> to the matrix equation
<var>M</var> <var>x</var> = <var>b</var>, where <var>M</var> is either <var>A</var>, the
transpose of <var>A</var>, or its conjugate transpose. As noted above, the
choice is determined by whether the the function name is of the form
*<code>_a_</code>*, *<code>_t_</code>*, or *<code>_c_</code>* respectively.
</p>
<p>The argument to any of these functions is a pair
<code>(<var>A</var>,<var>b</var>)</code>, where <var>A</var> represents the matrix
mentioned above and <var>b</var> represents the column vector.
</p>
<p>The parameter <var>b</var> is required to be a list of numbers whose length
matches the number of rows in the matrix. The numbers are either real
numbers for the <code>di_</code>* functions (<a href="math.html#math"><code>math</code></a>), or complex
for the <code>zi_</code>* functions (<a href="complex.html#complex"><code>complex</code></a>).
</p>
<p>There is a choice of representations for the parameter <var>A</var>,
depending on whether the function being called is one of the *<code>_trp</code>
functions or one of the *<code>_col</code> functions.
</p>
<p>For the *<code>_trp</code> functions, <var>A</var> is represented as a non-empty
list of triples <code>&lt;((<var>i</var>,<var>j</var>),<var>v</var>)...&gt;</code>, where each
item of the list corresponds to a non-zero entry in the matrix.
</p>
<ul>
<li>
The parameters <var>i</var> and <var>j</var> are natural numbers as in
<a href="Representation-of-Numeric-and-Textual-Data.html#Representation-of-Numeric-and-Textual-Data">Representation of Numeric and Textual Data</a>. 
</li><li>
The value <var>v</var> is a real number for the <code>di_</code>*<code>_trp</code> functions or a
complex number for the <code>zi_</code>*<code>_trp</code> functions.
</li><li>
The presence of a triple ((<var>i</var>,<var>j</var>),<var>v</var>) in the list
signifies that the <var>i</var>,<var>j</var>-th entry in the matrix <var>A</var>
(numbered from zero) has a value of <var>v</var>.
</li></ul>

<p>For the *<code>_col</code> functions, the representation of <var>A</var> is more
complicated but has a slight advantage in memory usage. It may also
have an advantage in speed unless more time is wasted on the virtual
side transforming a matrix to this representation than it saves.
</p>
<p>In this case, <var>A</var> is represented by a triple of the form
<code>((<var>p</var>,<var>i</var>),<var>v</var>)</code>. The parameters <var>p</var> and <var>i</var>
are lists of natural numbers. The parameter <var>v</var> is a list of real
numbers for the <code>di_</code>*<code>_col</code> functions and complex numbers
for the <code>zi_</code>*<code>_col</code> functions. They have the following
interpretations.
</p>
<ul>
<li> <var>v</var>
is the list of non-zero entries in the matrix in
<a name="index-column-major-order-4"></a>
column major order.
</li><li> <var>i</var>
has the same length as <var>v</var>, and each item of <var>i</var> is the row
index of the corresponding item in <var>v</var>, numbered from zero.
</li><li> <var>p</var>
has the length of the number of columns in the matrix, and each
item identifies the starting position of a column in <var>v</var> and
<var>i</var>, numbered from zero.
</li></ul>

<p>The first item of <var>p</var> is always zero. Further explanation of this
format in terms of an array representation can be found in the file
&lsquo;<tt>UMFPACK_UserGuide.pdf</tt>&rsquo;, available from the <code>umf</code> library
home page at <a href="http://www.cise.ufl.edu/research/sparse/SuiteSparse/current/SuiteSparse/">http://www.cise.ufl.edu/research/sparse/SuiteSparse/current/SuiteSparse/</a>.
</p>

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