ranges

Gaussian and/or Fourier-Motzkin elimination is used 
to derive upper and lower limits implied by a system of (in)equations.

Variable elimination (Gaussian elimination, Fourier-Motzkin elimination),
Moore-Penrose pseudoinverse, reduction to reduced row echelon form, value substitution,
projecting a vector on the convex polytope described by a system of (in)equations,
simplify systems by removing spurious columns and rows and collapse implied equalities,
test if a matrix is totally unimodular, compute variable ranges implied by linear
(in)equalities.

Mark der Loo

lintools

Manipulation of Linear Systems of (in)Equalities

Mark van der Loo

Edwin de Jonge

ranges function

<dl><dt>A</dt>
<dd><code>[numeric]</code> Matrix</dd>
<dt>b</dt>
<dd><code>[numeric]</code> vector</dd>
<dt>neq</dt>
<dd>[<code>numeric</code>] The first <code>neq</code> rows in <code>A</code> and
<code>b</code> are treated as linear equalities.</dd>
<dt>nleq</dt>
<dd>[<code>numeric</code>] The <code>nleq</code> rows after <code>neq</code> are treated as
inequations of the form <code>a.x&lt;=b</code>. All remaining rows are treated as strict inequations
of the form <code>a.x&lt;b</code>.</dd>
<dt>eps</dt>
<dd><code>[numeric]</code> Coefficients with absolute value <code>&lt;= eps</code> are treated as zero.
using Fourier-Motzkin elimination.</dd></dl>

Arguments

Derive variable ranges from linear restrictions — ranges

<dl>

<dt>A</dt>
<dd><code>[numeric]</code> Matrix</dd>


<dt>b</dt>
<dd><code>[numeric]</code> vector</dd>


<dt>neq</dt>
<dd>[<code>numeric</code>] The first <code>neq</code> rows in <code>A</code> and
<code>b</code> are treated as linear equalities.</dd>


<dt>nleq</dt>
<dd>[<code>numeric</code>] The <code>nleq</code> rows after <code>neq</code> are treated as
inequations of the form <code>a.x&lt;=b</code>. All remaining rows are treated as strict inequations
of the form <code>a.x&lt;b</code>.</dd>


<dt>eps</dt>
<dd><code>[numeric]</code> Coefficients with absolute value <code>&lt;= eps</code> are treated as zero.
using Fourier-Motzkin elimination.</dd>

</dl>

ranges: Derive variable ranges from linear restrictions

Description

Usage

Arguments