control_systems_torbox 0.2.1

Control systems toolbox
Documentation 
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<HTML>
<HEAD><TITLE>IB01OD - SLICOT Library Routine Documentation</TITLE>
</HEAD>
<BODY>

<H2><A Name="IB01OD">IB01OD</A></H2>
<H3>
Estimating the system order
</H3>
<A HREF ="#Specification"><B>[Specification]</B></A>
<A HREF ="#Arguments"><B>[Arguments]</B></A>
<A HREF ="#Method"><B>[Method]</B></A>
<A HREF ="#References"><B>[References]</B></A>
<A HREF ="#Comments"><B>[Comments]</B></A>
<A HREF ="#Example"><B>[Example]</B></A>

<P>
<B><FONT SIZE="+1">Purpose</FONT></B>
<PRE>
  To estimate the system order, based on the singular values of the
  relevant part of the triangular factor of the concatenated block
  Hankel matrices.

</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
      SUBROUTINE IB01OD( CTRL, NOBR, L, SV, N, TOL, IWARN, INFO )
C     .. Scalar Arguments ..
      DOUBLE PRECISION   TOL
      INTEGER            INFO, IWARN, L, N, NOBR
      CHARACTER          CTRL
C     .. Array Arguments ..
      DOUBLE PRECISION   SV(*)

</PRE>
<A name="Arguments"><B><FONT SIZE="+1">Arguments</FONT></B></A>
<P>

<B>Mode Parameters</B>
<PRE>
  CTRL    CHARACTER*1
          Specifies whether or not the user's confirmation of the
          system order estimate is desired, as follows:
          = 'C':  user's confirmation;
          = 'N':  no confirmation.
          If  CTRL = 'C',  a reverse communication routine,  IB01OY,
          is called, and, after inspecting the singular values and
          system order estimate,  n,  the user may accept  n  or set
          a new value.
          IB01OY  is not called by the routine if CTRL = 'N'.

</PRE>
<B>Input/Output Parameters</B>
<PRE>
  NOBR    (input) INTEGER
          The number of block rows,  s,  in the processed input and
          output block Hankel matrices.  NOBR &gt; 0.

  L       (input) INTEGER
          The number of system outputs.  L &gt; 0.

  SV      (input) DOUBLE PRECISION array, dimension ( L*NOBR )
          The singular values of the relevant part of the triangular
          factor from the QR factorization of the concatenated block
          Hankel matrices.

  N       (output) INTEGER
          The estimated order of the system.

</PRE>
<B>Tolerances</B>
<PRE>
  TOL     DOUBLE PRECISION
          Absolute tolerance used for determining an estimate of
          the system order. If  TOL &gt;= 0,  the estimate is
          indicated by the index of the last singular value greater
          than or equal to  TOL.  (Singular values less than  TOL
          are considered as zero.) When  TOL = 0,  an internally
          computed default value,  TOL = NOBR*EPS*SV(1),  is used,
          where  SV(1)  is the maximal singular value, and  EPS  is
          the relative machine precision (see LAPACK Library routine
          DLAMCH). When  TOL &lt; 0,  the estimate is indicated by the
          index of the singular value that has the largest
          logarithmic gap to its successor.

</PRE>
<B>Warning Indicator</B>
<PRE>
  IWARN   INTEGER
          = 0:  no warning;
          = 3:  all singular values were exactly zero, hence  N = 0.
                (Both input and output were identically zero.)

</PRE>
<B>Error Indicator</B>
<PRE>
  INFO    INTEGER
          = 0:  successful exit;
          &lt; 0:  if INFO = -i, the i-th argument had an illegal
                value.

</PRE>
<A name="Method"><B><FONT SIZE="+1">Method</FONT></B></A>
<PRE>
  The singular values are compared to the given, or default TOL, and
  the estimated order  n  is returned, possibly after user's
  confirmation.

</PRE>

<A name="Comments"><B><FONT SIZE="+1">Further Comments</FONT></B></A>
<PRE>
  None
</PRE>

<A name="Example"><B><FONT SIZE="+1">Example</FONT></B></A>
<P>
<B>Program Text</B>
<PRE>
  None
</PRE>
<B>Program Data</B>
<PRE>
  None
</PRE>
<B>Program Results</B>
<PRE>
  None
</PRE>

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