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<title>MvTools Help : Singular Values</title>
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<p align=center style='text-align:center'><span lang=EN-US><img width=371
height=55 id="_x0000_i1025" src="Immagini\logoana.jpg"></span></p>
<p align=center style='text-align:center'><span lang=EN-US><a
href="HelpDeskmvt.htm" title="MVTOOLS HELP DESK"><b><i>MvTools Help Desk</i></b></a></span></p>
<p align=center style='text-align:center'><span lang=EN-US><img border=0
width=530 height=5 id="_x0000_i1026" src="Immagini\riga.gif"></span></p>
<p align=center style='text-align:center'><span lang=EN-US>Subsection</span><span
lang=EN-US style='font-size:13.5pt'> </span><b><u><span lang=EN-US
style='font-size:13.5pt;color:red'>SINGULAR VALUES</span></u></b></p>
<p><span lang=EN-US><img border=0 width=13 height=12 id="_x0000_i1037"
src="Immagini\Bullet1.gif"> </span><span lang=EN-US style='color:blue'>Singular
Values<o:p></o:p></span></p>
<p style='text-align:justify'><span lang=EN-US>The first window of this
subsection displays the singular value (SV) plot of the frequency response of the
LTI current model (the frequency range is chosen automatically).</span></p>
<p><span lang=EN-US> </span></p>
<p><span lang=EN-US><img border=0 width=13 height=13 id="_x0000_i1028"
src="Immagini\Bullet1.gif"> </span><span lang=EN-US style='color:blue'>Singular
Vectors</span><a name=singvect></a><span lang=EN-US> </span></p>
<p style='text-align:justify'><span lang=EN-US>The button <b>S.Vectors</b>
opens the following window in which it's possible to analyze all the Singular
Vectors of the current model:</span></p>
<p align=center style='margin-left:36.0pt;text-align:center'><span lang=EN-US><img
border=0 width=371 height=249 id="_x0000_i1029" src="Immagini\anaf2.gif"></span></p>
<p style='text-align:justify'><span lang=EN-US>for every Singular Vector, the
two graphics represent the absolute value of its components along the system
outputs and inputs at the frequency </span><span lang=EN-US style='font-family:
Symbol'>w</span><span lang=EN-US style='font-size:8.0pt;mso-bidi-font-size:
12.0pt'>o</span><span lang=EN-US> indicated in the relative edit-field; the
text-fields <b>S.Vector</b> and <b>S.Value</b> indicate, respectively, the
index and the absolute value of the considered vector, while in the frame below
them is reported the rank of the transfer matrix of the model</span></p>
<p align=center style='text-align:center'><span lang=EN-US style='color:red'>G</span><span
lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:12.0pt;color:red'>s</span><span
lang=EN-US style='color:red'>(j</span><span lang=EN-US style='font-family:Symbol;
color:red'>w</span><span lang=EN-US style='font-size:8.0pt;mso-bidi-font-size:
12.0pt;font-family:Symbol;color:red'>o</span><span lang=EN-US style='color:
red'>) = C inv( j</span><span lang=EN-US style='font-family:Symbol;color:red'>w</span><span
lang=EN-US style='font-size:8.0pt;mso-bidi-font-size:12.0pt;color:red'>o</span><span
lang=EN-US style='color:red'> I - A) B + D<o:p></o:p></span></p>
<p style='margin:0cm;margin-bottom:.0001pt;text-align:justify'><span
lang=EN-US>and its 2-norm condition number that represents the ratio in dB of
the largest singular value to the smallest one (large condition numbers
indicate a nearly singular matrix G</span><span lang=EN-US style='font-size:
10.0pt;mso-bidi-font-size:12.0pt'>s</span><span lang=EN-US>). </span></p>
<p style='margin:0cm;margin-bottom:.0001pt;text-align:justify'><span
lang=EN-US>The buttons <b><<</b> and <b>>></b> select another
singular vector, while the button <b>SAME</b> allows to re-examine the same one
at a new frequency value.</span></p>
<p><span lang=EN-US> </span></p>
<p><span lang=EN-US><img border=0 width=13 height=13 id="_x0000_i1030"
src="Immagini\Bullet1.gif"> </span><span lang=EN-US style='color:blue'>Norm(G(j</span><span
lang=EN-US style='font-family:Symbol;color:blue'>w</span><span lang=EN-US
style='color:blue'>))<a name=normg></a><o:p></o:p></span></p>
<p style='margin:0cm;margin-bottom:.0001pt;text-align:justify'><span
lang=EN-US>The button <b>Norm(G(j</b></span><b><span lang=EN-US
style='font-family:Symbol'>w</span><span lang=EN-US>))</span></b><span
lang=EN-US> allows to visualize, in a new window, the graphic of the maximum
singular value of G</span><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:
12.0pt'>s</span><span lang=EN-US>(j</span><span lang=EN-US style='font-family:
Symbol'>w</span><span lang=EN-US style='font-size:8.0pt;mso-bidi-font-size:
12.0pt'>o</span><span lang=EN-US>) along the plane inputs-outputs (the default </span><span
lang=EN-US style='font-family:Symbol'>w</span><span lang=EN-US
style='font-size:8.0pt;mso-bidi-font-size:12.0pt'>o</span><span lang=EN-US> is
0.001). This graphic is a contour plot of the matrix G</span><span lang=EN-US
style='font-size:10.0pt;mso-bidi-font-size:12.0pt'>s</span><span lang=EN-US>(j</span><span
lang=EN-US style='font-family:Symbol'>w</span><span lang=EN-US
style='font-size:8.0pt;mso-bidi-font-size:12.0pt'>o</span><span lang=EN-US>)
that treats the value in Gs as heights above a plane and plot its level curves
with different colors chosen in accordance with the current color map (the
default color map is JET which ranges from blue to red, and passes through the
colors cyan, yellow, and orange).</span></p>
<p style='margin:0cm;margin-bottom:.0001pt;text-align:justify'><span
lang=EN-US>Inside the relative window, the user can modify the reference
frequency </span><span lang=EN-US style='font-family:Symbol'>w</span><span
lang=EN-US style='font-size:8.0pt;mso-bidi-font-size:12.0pt'>o</span><span
lang=EN-US> and view the new graphic pressing the <b>PLOT</b> button.</span></p>
<p align=center style='margin-left:36.0pt;text-align:center'><span lang=EN-US><img
border=0 width=371 height=249 id="_x0000_i1031" src="Immagini\anaf3.gif"></span></p>
<p align=center style='margin-left:36.0pt;text-align:center'><span lang=EN-US> </span></p>
<p><span lang=EN-US>Note:</span><span lang=EN-US style='font-size:10.0pt'> <i>all
the graphics are associated with a </i></span><i><span lang=EN-US
style='font-size:10.0pt;mso-bidi-font-size:12.0pt'><a href="mod04.htm"
title="POPUP MENU help page">popup menu</a></span></i><i><span lang=EN-US
style='font-size:10.0pt'> that can be activated pressing the right mouse button
over them.<o:p></o:p></span></i></p>
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width=536 height=5 id="_x0000_i1032" src="Immagini\riga.gif"></span></p>
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width=536 height=5 id="_x0000_i1033" src="Immagini\riga.gif"></span></p>
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