txlyre
/
avram


			
				
					
						
						
							123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081
							<html lang="en">
<head>
<title>glpk input parameters - avram - a virtual machine code interpreter</title>
<meta http-equiv="Content-Type" content="text/html">
<meta name="description" content="avram - a virtual machine code interpreter">
<meta name="generator" content="makeinfo 4.13">
<link title="Top" rel="start" href="index.html#Top">
<link rel="up" href="glpk.html#glpk" title="glpk">
<link rel="prev" href="glpk.html#glpk" title="glpk">
<link rel="next" href="glpk-output.html#glpk-output" title="glpk output">
<link href="http://www.gnu.org/software/texinfo/" rel="generator-home" title="Texinfo Homepage">
<meta http-equiv="Content-Style-Type" content="text/css">
<style type="text/css"><!--
  pre.display { font-family:inherit }
  pre.format  { font-family:inherit }
  pre.smalldisplay { font-family:inherit; font-size:smaller }
  pre.smallformat  { font-family:inherit; font-size:smaller }
  pre.smallexample { font-size:smaller }
  pre.smalllisp    { font-size:smaller }
  span.sc    { font-variant:small-caps }
  span.roman { font-family:serif; font-weight:normal; } 
  span.sansserif { font-family:sans-serif; font-weight:normal; } 
--></style>
</head>
<body>
<div class="node">
<a name="glpk-input-parameters"></a>
<p>
Next:&nbsp;<a rel="next" accesskey="n" href="glpk-output.html#glpk-output">glpk output</a>,
Previous:&nbsp;<a rel="previous" accesskey="p" href="glpk.html#glpk">glpk</a>,
Up:&nbsp;<a rel="up" accesskey="u" href="glpk.html#glpk">glpk</a>
<hr>
</div>

<h4 class="subsection">D.4.1 <code>glpk</code> input parameters</h4>

<p>The argument must be a triple of the form,
<code>(</code><var>c</var><code>,(</code><var>m</var><code>,</code><var>y</var><code>))</code>, subject to the following specification.

     <ul>
<li><var>c</var>
is a list of cost function coefficients as floating point numbers (see
<a href="math.html#math">math</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. 
<li><var>m</var>
is a sparse matrix represented as a list of triples in the form
<a name="index-sparse-matrix-715"></a>
     <pre class="example">          &lt;((<var>i</var>,<var>j</var>),<var>a</var>)...&gt;
</pre>
     <p class="noindent">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>((</code><var>i</var><code>,</code><var>j</var><code>),</code><var>a</var><code>)</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>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. 
<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>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>((</code><var>i</var><code>,</code><var>j</var><code>),</code><var>a</var><code>)</code> in <var>m</var>, if any, and <var>xj</var> is
the <var>j</var>-th variable of the solution. 
</ul>

   </body></html>