<?xml version="1.0" encoding="UTF-8"?>
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 * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
 * Copyright (C) INRIA - F.D
 * Copyright (C) 2012 - 2016 - Scilab Enterprises
 *
 * This file is hereby licensed under the terms of the GNU GPL v2.0,
 * pursuant to article 5.3.4 of the CeCILL v.2.1.
 * This file was originally licensed under the terms of the CeCILL v2.1,
 * and continues to be available under such terms.
 * For more information, see the COPYING file which you should have received
 * along with this program.
 *
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<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
          xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML"
          xmlns:db="http://docbook.org/ns/docbook"  xmlns:scilab="http://www.scilab.org"
          xml:lang="en" xml:id="svplot">
    <refnamediv>
        <refname>svplot</refname>
        <refpurpose>singular-value sigma-plot</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>Syntax</title>
        <synopsis>
            SVM = svplot(sl)
            SVM = svplot(sl, w)
        </synopsis>
    </refsynopsisdiv>
    <refsection role="parameters">
        <title>Arguments</title>
        <variablelist>
            <varlistentry>
                <term>sl</term>
                <listitem>
                    <para>
                        <literal>syslin</literal> list (continuous, discrete or sampled system)
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>w</term>
                <listitem>
                    <para>real vector (optional parameter)</para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection role="description">
        <title>Description</title>
        <para>
            computes for the system <literal>sl=(A,B,C,D)</literal>
            the singular values of its transfer function matrix:
        </para>
        <programlisting role="no-scilab-exec"><![CDATA[
             G(jw) = C(jw*I-A)B^-1+D
or
             G(exp(jw)) = C(exp(jw)*I-A)B^-1+D
or
             G(exp(jwT)) = C(exp(jw*T)*I-A)B^-1+D
 ]]></programlisting>
        <para>
            evaluated over the frequency range specified by <literal>w</literal>. (T is the sampling
            period, <literal>T=sl('dt')</literal> for sampled systems).
        </para>
        <para>
            <literal>sl</literal> is a <literal>syslin</literal> list representing the system
            <literal>[A,B,C,D]</literal> in state-space form. <literal>sl</literal> can be continuous or
            discrete time or sampled system.
        </para>
        <para>
            The <literal>i</literal>-th column of the output matrix <literal>SVM</literal> contains the singular
            values of <literal>G</literal> for the <literal>i</literal>-th frequency value <literal>w(i)</literal>.
        </para>
        <programlisting role="no-scilab-exec"><![CDATA[
SVM = svplot(sl)
 ]]></programlisting>
        <para>
            is equivalent to
        </para>
        <programlisting role="no-scilab-exec"><![CDATA[
SVM = svplot(sl,logspace(-3,3))  (continuous)
 ]]></programlisting>
        <programlisting role="no-scilab-exec"><![CDATA[
SVM = svplot(sl,logspace(-3,%pi)) (discrete)
 ]]></programlisting>
    </refsection>
    <refsection role="examples">
        <title>Examples</title>
        <programlisting role="example"><![CDATA[
x = logspace(-3,3);
y = svplot(ssrand(2,2,4),x);
clf()
plot2d("ln", x, 20*log(y')/log(10))
xgrid(12)
xtitle("Singular values plot","(Rd/sec)", "Db");
 ]]></programlisting>
        <scilab:image>
            x=logspace(-3,3);
            y=svplot(ssrand(2,2,4),x);
            clf()
            plot2d("ln", x, 20*log(y')/log(10))
            xgrid(12)
            xtitle("Singular values plot","(Rd/sec)", "Db");
        </scilab:image>
    </refsection>
</refentry>
