control_systems_torbox 0.2.1

Control systems toolbox
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<HTML>
<HEAD><TITLE>MC01PY - SLICOT Library Routine Documentation</TITLE>
</HEAD>
<BODY>

<H2><A Name="MC01PY">MC01PY</A></H2>
<H3>
Coefficients of a real polynomial, stored in decreasing order, given its zeros
</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 compute the coefficients of a real polynomial P(x) from its
  zeros. The coefficients are stored in decreasing order of the
  powers of x.

</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
      SUBROUTINE MC01PY( K, REZ, IMZ, P, DWORK, INFO )
C     .. Scalar Arguments ..
      INTEGER           INFO, K
C     .. Array Arguments ..
      DOUBLE PRECISION  DWORK(*), IMZ(*), P(*), REZ(*)

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

</PRE>
<B>Input/Output Parameters</B>
<PRE>
  K       (input) INTEGER
          The number of zeros (and hence the degree) of P(x).
          K &gt;= 0.

  REZ     (input) DOUBLE PRECISION array, dimension (K)
  IMZ     (input) DOUBLE PRECISION array, dimension (K)
          The real and imaginary parts of the i-th zero of P(x)
          must be stored in REZ(i) and IMZ(i), respectively, where
          i = 1, 2, ..., K. The zeros may be supplied in any order,
          except that complex conjugate zeros must appear
          consecutively.

  P       (output) DOUBLE PRECISION array, dimension (K+1)
          This array contains the coefficients of P(x) in decreasing
          powers of x.

</PRE>
<B>Workspace</B>
<PRE>
  DWORK   DOUBLE PRECISION array, dimension (K)
          If K = 0, this array is not referenced.

</PRE>
<B>Error Indicator</B>
<PRE>
  INFO    INTEGER
          = 0:  successful exit;
          &lt; 0:  if INFO = -i, the i-th argument had an illegal
                value;
          &gt; 0:  if INFO = i, (REZ(i),IMZ(i)) is a complex zero but
                (REZ(i-1),IMZ(i-1)) is not its conjugate.

</PRE>
<A name="Method"><B><FONT SIZE="+1">Method</FONT></B></A>
<PRE>
  The routine computes the coefficients of the real K-th degree
  polynomial P(x) as

     P(x) = (x - r(1)) * (x - r(2)) * ... * (x - r(K))

  where r(i) = (REZ(i),IMZ(i)).

  Note that REZ(i) = REZ(j) and IMZ(i) = -IMZ(j) if r(i) and r(j)
  form a complex conjugate pair (where i &lt;&gt; j), and that IMZ(i) = 0
  if r(i) is real.

</PRE>
<A name="Numerical Aspects"><B><FONT SIZE="+1">Numerical Aspects</FONT></B></A>
<PRE>
  None.

</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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