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Description</th>
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<td class="tabxpl">clean is used to remove base matrices in an
<a href="reference.htm#sdpvar">sdpvar</a> object that are small (mainly
used together with <a href="reference.htm#solvesos">solvesos</a>)</td>
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Examples</th>
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<td class="tabxpl"><p>Removing nuisance variables</p><table cellpadding="10" width="100%">
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<td class="xmpcode">
<pre>x1 = sdpvar(n,1);
x2 = sdpvar(n,1);
x = x1+1e-8*x2;
y = clean(x,1e-6);
sdisplay(y)
<font color="#000000">ans
'x1'</font></pre>
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Related commands</th>
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<td class="tabxpl"><a href="reference.htm#sos">sos</a>,
<a href="reference.htm#sdpvar">sdpvar</a></td>
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</table>
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<p> </p>
<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933" id="table19">
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<td class="tableheader">
<p class="tableheader"><a name="coefficients">COEFFICIENTS</a></p>
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<table cellspacing="0" cellpadding="4" width="100%" border="0" id="table20">
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Syntax<p> </p>
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<td class="code" valign="top" nowrap width="100%"><code>[c,v] =
coefficients(p,x)</code></td>
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<td class="tabxpl">
<table border="0" id="table21">
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<p align="right"><font face="Courier New">c</font><font face="Courier New" size="2">:</font></p>
</td>
<td>Coefficients (sdpvar object)</td>
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<td>
<p align="right"><font face="Courier New" size="2">v:</font></p>
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<td>Monomials (sdpvar object)</td>
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<p align="right"><font face="Courier New" size="2">p:</font></p>
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<td>Polynomials (sdpvar object)</td>
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<p align="right"><font face="Courier New">x</font><font face="Courier New" size="2">:</font></p>
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<td>Variables (sdpvar object)</td>
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Description</th>
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<td class="tabxpl">coefficients is used to extract the
coefficients of a polynomials.</td>
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<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
Examples</th>
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<td class="tabxpl">Define a polynomial in variables <b>x</b> and
<b>y</b>, with coefficients parameterized by <b>s</b> and <b>t</b>.<table cellpadding="10" width="100%" id="table22">
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<td class="xmpcode">
<pre>sdpvar x y s t
p = x^2+x*y*(s+t)+s^2+t^2;</pre>
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<p>The coefficients are easily recovered</p>
<table cellpadding="10" width="100%" id="table23">
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<td class="xmpcode">
<pre>c = coefficients(p,[x y]);
sdisplay(c)
<font color="#000000">ans =
's^2+t^2'
's+t'
'1'</font></pre>
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<p>By adding a second output, the monomial basis is returned also.</p>
<table cellpadding="10" width="100%" id="table24">
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<td class="xmpcode">
<pre>[c,v] = coefficients(p,[x y]);
sdisplay([c v])
<font color="#000000">ans =
's^2+t^2' '1'
's+t' 'xy'
'1' 'x^2'</font></pre>
<pre>p-c'*v
<font color="#000000">ans =
0</font></pre>
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<p>Of-course, we might just as well consider this to be a
polynomial in <b>s</b> and <b>t</b> with coefficients
parameterized by <b>x</b> and
<b>y</b>.<table cellpadding="10" width="100%" id="table25">
<tr>
<td class="xmpcode">
<pre>[c,v] = coefficients(p,[s t]);
sdisplay([c v])
<font color="#000000">ans =
'x^2' '1'
'xy' 't'
'1' 't^2'
'xy' 's'
'1' 's^2'</font></pre>
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<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
Related commands</th>
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<td class="tabxpl"><a href="reference.htm#sdpvar">sdpvar</a></td>
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</table>
</td>
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</table>
<p> </p>
<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933">
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<td class="tableheader">
<p class="tableheader"><a name="cone">CONE</a></p>
</td>
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<table cellspacing="0" cellpadding="4" width="100%" border="0">
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<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2"> <p> </p>
</th>
<td class="code" valign="top" nowrap width="100%"><code>c = cone(x,y)</code></td>
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<td class="tabxpl">
<table border="0">
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<td>
<p align="right"><font face="Courier New" size="2">c:</font></p>
</td>
<td>sdpvar object (only useful in set object)</td>
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<td>
<p align="right"><font face="Courier New" size="2">x:</font></p>
</td>
<td>sdpvar object (vector)</td>
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<td>
<p align="right"><font face="Courier New" size="2">y:</font></p>
</td>
<td>sdpvar object (scalar)</td>
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</table>
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<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
Description</th>
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<td class="tabxpl">cone is used to define the constraints <b>
<font face="Tahoma">||x||</font>≤<font face="Tahoma">y</font></b></td>
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<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
Examples</th>
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<td class="tabxpl"><p>Constraining the Euclidean norm of a vector to
be less than 1 is done with</p><table cellpadding="10" width="100%">
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<td class="xmpcode">
<pre>x = sdpvar(n,1);
F = set(cone(x,1));</pre>
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</table>
<p>Of-course, arbitrary complicated constructs are possible, such
as constraining the norm of the diagonal to be less than the sum of
the off-diagonal terms in a matrix! </p>
<table cellpadding="10" width="100%">
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<td class="xmpcode">
<pre>x = sdpvar(n,n);
F = set(cone(diag(x),sum(sum(x-diag(diag(x))))))</pre>
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<p>An alternative is to use the nonlinear norm operator instead
(see the examples on <a href="extoperators.htm">nonlinear
operators</a> for details)</p>
<table cellpadding="10" width="100%">
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<td class="xmpcode">
<pre>x = sdpvar(n,n);
F = set(norm(diag(x)) < sum(sum(x-diag(diag(x)))))</pre>
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<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
Related commands</th>
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<td class="tabxpl"><a href="reference.htm#rcone">rcone</a>,
<a href="#set">set</a>, <a href="reference.htm#sdpvar">sdpvar</a></td>
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</table>
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<p> </p>
<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933">
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<td class="tableheader">
<p class="tableheader"><a name="cut">CUT</a></p>
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<table cellspacing="0" cellpadding="4" width="100%" border="0">
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<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
Syntax<p> </p>
</th>
<td class="code" valign="top" nowrap width="100%"><code>F = cut(X,'tag')</code></td>
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<td class="tabxpl">
<table border="0">
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<p align="right"><font face="Courier New" size="2">F:</font></p>
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<td>set object</td>
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<td>
<p align="right"><font face="Courier New" size="2">X:</font></p>
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<td>sdpvar or constraint object, or string</td>
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<td>
<p align="right"><font face="Courier New" size="2">'tag':</font></p>
</td>
<td>char</td>
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</table>
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<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
Description</th>
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<td class="tabxpl">cut is used to define user-specified cuts for the
global BMI solver.</td>
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<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
Example</th>
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<td class="tabxpl"><p>The result from this command is nothing but a
<a href="#set">set</a> object.</p>
<table cellpadding="10" width="100%">
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<td class="xmpcode">
<pre>P = sdpvar(2,2);
F = cut((P-eye(2))*(P-eye(2))>0);
<font color="#000000">+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
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