Add examples for armax, armax1 & initstate
[scilab.git] / scilab / modules / cacsd / help / en_US / inistate.xml
index d06696c..d8999e5 100644 (file)
  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
  *
  -->
-<refentry version="5.0-subset Scilab" xml:id="inistate" xml:lang="en"
-          xmlns="http://docbook.org/ns/docbook"
-          xmlns:xlink="http://www.w3.org/1999/xlink"
-          xmlns:svg="http://www.w3.org/2000/svg"
-          xmlns:ns4="http://www.w3.org/1999/xhtml"
-          xmlns:mml="http://www.w3.org/1998/Math/MathML"
-          xmlns:db="http://docbook.org/ns/docbook">
-  <info>
-    <pubdate>$LastChangedDate$</pubdate>
-  </info>
-
-  <refnamediv>
-    <refname>inistate</refname>
-
-    <refpurpose>Estimates the initial state of a discrete-time
-    system</refpurpose>
-  </refnamediv>
-
-  <refsynopsisdiv>
-    <title>Calling Sequence</title>
-
-    <synopsis>X0 = inistate(SYS,Y,U,TOL,PRINTW)
-X0 = inistate(A,B,C,Y,U);
-X0 = inistate(A,C,Y);
-
-[x0,V,rcnd] = inistate(SYS,Y,U,TOL,PRINTW)</synopsis>
-  </refsynopsisdiv>
-
-  <refsection>
-    <title>Parameters</title>
-
-    <variablelist>
-      <varlistentry>
-        <term>SYS</term>
-
-        <listitem>
-          <para>given system, syslin(dt,A,B,C,D)</para>
-        </listitem>
-      </varlistentry>
-
-      <varlistentry>
-        <term>Y</term>
-
-        <listitem>
-          <para>the output of the system</para>
-        </listitem>
-      </varlistentry>
-
-      <varlistentry>
-        <term>U</term>
-
-        <listitem>
-          <para>the input of the system</para>
-        </listitem>
-      </varlistentry>
-
-      <varlistentry>
-        <term>TOL</term>
-
-        <listitem>
-          <para>TOL is the tolerance used for estimating the rank of matrices.
-          If TOL &gt; 0, then the given value of TOL is used as a lower bound
-          for the reciprocal condition number.</para>
-
-          <para>Default: prod(size(matrix))*epsilon_machine where
-          epsilon_machine is the relative machine precision.</para>
-        </listitem>
-      </varlistentry>
-
-      <varlistentry>
-        <term>PRINTW</term>
-
-        <listitem>
-          <para>PRINTW is a switch for printing the warning messages.</para>
-
-          <variablelist>
+<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="inistate">
+    <refnamediv>
+        <refname>inistate</refname>
+        <refpurpose>Estimates the initial state of a discrete-time system</refpurpose>
+    </refnamediv>
+    <refsynopsisdiv>
+        <title>Calling Sequence</title>
+        <synopsis>X0 = inistate(SYS,Y,U,TOL,PRINTW)
+            X0 = inistate(A,B,C,Y,U);
+            X0 = inistate(A,C,Y);
+            
+            [x0,V,rcnd] = inistate(SYS,Y,U,TOL,PRINTW)
+        </synopsis>
+    </refsynopsisdiv>
+    <refsection>
+        <title>Arguments</title>
+        <variablelist>
             <varlistentry>
-              <term>=</term>
-
-              <listitem>
-                <para>1: print warning messages;</para>
-              </listitem>
+                <term>SYS</term>
+                <listitem>
+                    <para>given system, syslin(dt,A,B,C,D)</para>
+                </listitem>
             </varlistentry>
-
             <varlistentry>
-              <term>=</term>
-
-              <listitem>
-                <para>0: do not print warning messages.</para>
-              </listitem>
+                <term>Y</term>
+                <listitem>
+                    <para>the output of the system</para>
+                </listitem>
             </varlistentry>
-          </variablelist>
-
-          <para>Default: PRINTW = 0.</para>
-        </listitem>
-      </varlistentry>
-
-      <varlistentry>
-        <term>X0</term>
-
-        <listitem>
-          <para>the estimated initial state vector</para>
-        </listitem>
-      </varlistentry>
-
-      <varlistentry>
-        <term>V</term>
-
-        <listitem>
-          <para>orthogonal matrix which reduces the system state matrix A to a
-          real Schur form</para>
-        </listitem>
-      </varlistentry>
-
-      <varlistentry>
-        <term>rcnd</term>
-
-        <listitem>
-          <para>estimate of the reciprocal condition number of the coefficient
-          matrix of the least squares problem solved.</para>
-        </listitem>
-      </varlistentry>
-    </variablelist>
-  </refsection>
-
-  <refsection>
-    <title>Description</title>
-
-    <para>inistate Estimates the initial state of a discrete-time system,
-    given the (estimated) system matrices, and a set of input/output
-    data.</para>
-
-    <para>X0 = inistate(SYS,Y,U,TOL,PRINTW) estimates the initial state X0 of
-    the discrete-time system SYS = (A,B,C,D), using the output data Y and the
-    input data U. The model structure is :</para>
-
-    <programlisting> 
-x(k+1) = Ax(k) + Bu(k),   k &gt;= 1,
+            <varlistentry>
+                <term>U</term>
+                <listitem>
+                    <para>the input of the system</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>TOL</term>
+                <listitem>
+                    <para>TOL is the tolerance used for estimating the rank of matrices.  If  TOL &gt; 0,  then the given value of  TOL  is used as a lower bound for the reciprocal condition number.</para>
+                    <para>
+                        Default:    prod(size(matrix))*epsilon_machine where epsilon_machine is the relative machine precision. 
+                    </para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>PRINTW</term>
+                <listitem>
+                    <para>PRINTW is a switch for printing the warning messages.</para>
+                    <variablelist>
+                        <varlistentry>
+                            <term>=  </term>
+                            <listitem>
+                                <para>1: print warning messages;</para>
+                            </listitem>
+                        </varlistentry>
+                        <varlistentry>
+                            <term>=  </term>
+                            <listitem>
+                                <para>0: do not print warning messages.</para>
+                            </listitem>
+                        </varlistentry>
+                    </variablelist>
+                    <para>
+                        Default:    PRINTW = 0.
+                    </para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>X0</term>
+                <listitem>
+                    <para>the estimated initial state vector</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>V</term>
+                <listitem>
+                    <para>orthogonal matrix which reduces the system state matrix A to  a real Schur form</para>
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>rcnd</term>
+                <listitem>
+                    <para>estimate of the reciprocal condition number of the coefficient matrix of the least squares problem solved.</para>
+                </listitem>
+            </varlistentry>
+        </variablelist>
+    </refsection>
+    <refsection>
+        <title>Description</title>
+        <para>
+            inistate  Estimates the initial state of a discrete-time system, given the 
+            (estimated) system matrices, and a set of input/output data.
+        </para>
+        <para>
+            X0 = inistate(SYS,Y,U,TOL,PRINTW)  estimates the initial state X0 of 
+            the discrete-time system SYS = (A,B,C,D), using the output data Y
+            and the input data U. The model structure is :
+        </para>
+        <programlisting role=""><![CDATA[ 
+x(k+1) = Ax(k) + Bu(k),   k >= 1,
 y(k)   = Cx(k) + Du(k),
-      </programlisting>
-
-    <para>The vectors y(k) and u(k) are transposes of the k-th rows of Y and
-    U, respectively.</para>
-
-    <para>Instead of the first input parameter SYS (an syslin object),
-    equivalent information may be specified using matrix parameters, for
-    instance, X0 = inistate(A,B,C,Y,U); or X0 = inistate(A,C,Y);</para>
-
-    <para>[x0,V,rcnd] = inistate(SYS,Y,U,TOL,PRINTW) returns, besides x0, the
-    orthogonal matrix V which reduces the system state matrix A to a real
-    Schur form, as well as an estimate of the reciprocal condition number of
-    the coefficient matrix of the least squares problem solved.</para>
-  </refsection>
-
-  <refsection>
-    <title>See Also</title>
-
-    <simplelist type="inline">
-      <member><link linkend="findBD">findBD</link></member>
-
-      <member><link linkend="findx0BD">findx0BD</link></member>
-    </simplelist>
-  </refsection>
+ ]]></programlisting>
+        <para>
+            The vectors y(k) and u(k) are transposes of the k-th rows of Y and U,
+            respectively.
+        </para>
+        <para>
+            Instead of the first input parameter SYS (an syslin object), equivalent
+            information may be specified using matrix parameters, for instance,
+            X0 = inistate(A,B,C,Y,U);   or   X0 = inistate(A,C,Y);
+        </para>
+        <para>
+            [x0,V,rcnd] = inistate(SYS,Y,U,TOL,PRINTW) returns, besides x0, 
+            the orthogonal matrix V which reduces the system state matrix A to 
+            a real Schur form, as well as an estimate of the reciprocal condition
+            number of the coefficient matrix of the least squares problem solved.
+        </para>
+    </refsection>
+    <refsection>
+        <title>Examples</title>
+        <programlisting role="example"><![CDATA[ 
+//generate data from a given linear system
+A = [ 0.5, 0.1,-0.1, 0.2;
+      0.1, 0,  -0.1,-0.1;      
+     -0.4,-0.6,-0.7,-0.1;  
+      0.8, 0,  -0.6,-0.6];      
+B = [0.8;0.1;1;-1];
+C = [1 2 -1 0];
+SYS=syslin(0.1,A,B,C);
+nsmp=100;
+U=prbs_a(nsmp,nsmp/5);
+Y=(flts(U,SYS)+0.3*rand(1,nsmp,'normal'));
+
+// Compute R
+S=15;
+[R,N1,SVAL] = findR(S,Y',U');
+N=3;
+SYS1 = findABCD(S,N,1,R) ;
+SYS1.dt=0.1;
+
+inistate(SYS1,Y',U')
+
+]]></programlisting>
+    </refsection>
+    <refsection role="see also">
+        <title>See Also</title>
+        <simplelist type="inline">
+            <member>
+                <link linkend="findBD">findBD</link>
+            </member>
+            <member>
+                <link linkend="findx0BD">findx0BD</link>
+            </member>
+        </simplelist>
+    </refsection>
 </refentry>