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<a name="glpk-input-parameters"></a>
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<a name="glpk-input-parameters-1"></a>
<h3 class="subsection">D.4.1 <code>glpk</code> input parameters</h3>

<p>The argument must be a triple of the form,
<code>(<var>c</var>,(<var>m</var>,<var>y</var>))</code>, subject to the following specification.
</p>
<ul>
<li> <var>c</var>
is a list of cost function coefficients as floating point numbers (see
<a href="math.html#math"><code>math</code></a>). There should be one item of <var>c</var> for each variable in
the linear programming problem (Note that there is no additive
constant, which would require one extra).

<p>The interpretation of <var>c</var> is that an assignment of non-negative
values to the variables <var>x</var> is sought to make the vector inner
product <var>c</var> <var>x</var> as small as possible.
</p></li><li> <var>m</var>
is a sparse matrix represented as a list of triples in the form
<a name="index-sparse-matrix"></a>

<table><tr><td>&nbsp;</td><td><pre class="example">&lt;((<var>i</var>,<var>j</var>),<var>a</var>)...&gt;
</pre></td></tr></table>

<p>where <var>i</var> and <var>j</var> are row and column indices as natural
numbers starting from 0 and <var>a</var> is a non-zero floating point
number. The presence of a triple <code>((<var>i</var>,<var>j</var>),<var>a</var>)</code> in
the list indicates that the <var>i</var>,<var>j</var>-th entry in the matrix has
a value of <var>a</var>.  Missing combinations of <var>i</var> and <var>j</var>
indicate that the corresponding entry is zero.
</p>
<p>The interpretation of <var>m</var> is that together with <var>y</var> it
specifies a system of equations the variables in the solution <var>x</var>
must satisfy simultaneously, as explained below.
</p></li><li> <var>y</var>
is a list of floating point numbers, with one number for each distinct value of
<var>i</var> in <var>m</var>, above, needed to complete the equations.

<p>The interpretation of <var>y</var> is that in matrix notation, the
condition <var>m</var> <var>x</var> = <var>y</var> must be met by any acceptable
solution <var>x</var>.
</p>
<p>To put it another way, for each distinct value of <var>i</var>, the <var>i</var>-th item
of <var>y</var> has to equal the sum over all <var>j</var> of <var>xj</var> <var>a</var>,
where <var>a</var> is the real number appearing in the triple
<code>((<var>i</var>,<var>j</var>),<var>a</var>)</code> in <var>m</var>, if any, and <var>xj</var> is
the <var>j</var>-th variable of the solution.
</p></li></ul>

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