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<title>YALMIP Example : Advanced programming</title>
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<h2>Advanced YALMIP programming</h2>
<hr noShade SIZE="1" color="#000000">
<p>In some cases, it might be necessary to do more advanced YALMIP coding.
YALMIP 3 comes with a number of commands to facilitate this.</p>
<p>Let us begin by defining a set of variables.</p>
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<pre>x = sdpvar(2,1);
y = x'*randn(2)*x;</pre>
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<p>A common task is to find variables used in an expression. To do this, there are
two important commands, <code>depends.m </code>and <code>getvariables.m</code>.</p>
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<pre>depends(x)
<font color="#000000">ans =
1 2</font>
depends(y)
<font color="#000000"> ans =
1 2</font>
getvariables(x)
<font color="#000000"> ans =
1 2</font>
getvariables(y)
<font color="#000000"> ans =
3 4 5</font></pre>
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<p>The command <code>depends.m</code> gives the actual linear independent variables, while <code>getvariables.m</code> returns the
variable indices to the so called relaxed variables used in YALMIP. When
a nonlinear expression is defined in YALMIP, a new variable is introduced
for every monomial term. For our quadratic variable y, we need 3 monomials.</p>
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<pre>getvariables(x(1)^2)
<font color="#000000"> ans =
3</font>
getvariables(x(2)^2)
<font color="#000000">ans =
4</font></pre>
<pre>getvariables(x(1)*x(2))
<font color="#000000"> ans =
5</font></pre>
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<p>The commands above only give the internal identifiers. To create an
<a href="reference.htm#sdpvar">sdpvar</a> variable using these variables,
we use the command <code>recover.m</code></p>
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<pre>variables_in_y = recover(depends(y))
<font color="#000000">Linear matrix variable 2x1 (full, real)</font></pre>
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<p>All <a href="reference.htm#sdpvar">sdpvar</a>
objects are defined by their variables obtained with <code>getvariables.m</code>,
and a basis. Let us begin with scalar variables to explain the concepts.
The basis with respect to all variables returned from <code>getvariables.m </code>
is obtained using <code>getbase.m</code></p>
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<pre>x = sdpvar(1,1);
y = sdpvar(1,1);
z = pi+2*x+3*y;
full(getbase(z))
<font color="#000000">
ans =
3.1416 2.0000 3.0000</font></pre>
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<p>A basis with respect to a particular variable is obtained using <code>getbasematrix.m.</code></p>
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<pre>full(getbasematrix(z,getvariables(x)))
<font color="#000000">
ans =
2
</font>
full(getbasematrix(z,0))
<font color="#000000">
ans =
3.1416</font>
full(getbasematrix(z,123456789))
<font color="#000000">
ans =
0</font></pre>
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<p>Matrix variables are defined in the same way, except that all basis
matrices are stored in a vectorized format.</p>
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<pre>x = pi*eye(2)+5*sdpvar(2,2);
base = full(getbase(x))
<font color="#000000"> base =
3.1416 5.0000 0 0
0 0 5.0000 0
0 0 5.0000 0
3.1416 0 0 5.0000</font>
reshape(base(:,1),2,2)
<font color="#000000"> ans =
3.1416 0
0 3.1416</font></pre>
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<p>The command <a href="reference.htm#is">is</a> can be useful to select
parts of <a href="reference.htm#set">set</a> objects</p>
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<pre>F = set(x>0) + lmi(x*x' > 0);
F_linear = F(find(is(F,'linear')))</pre>
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<p><code>replace.m</code> can be useful in some situations to replace an
<a href="reference.htm#sdpvar">sdpvar</a> inside an
<a href="reference.htm#sdpvar">sdpvar</a> or <a href="reference.htm#set">
set</a>.</p>
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<pre>F0 = replace(F,x(1),0);
y0 = replace(y,x(1),0);</pre>
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<p>The terms in a <a href="reference.htm#set">set</a> object can be
extracted and converted to <a href="reference.htm#sdpvar">sdpvar</a>
objects.</p>
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<pre>xtimesx = sdpvar(F(2));</pre>
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<p>More to come...</td>
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