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<!DOCTYPE MAN SYSTEM "../../manrev.dtd">
<MAN>
  <LANGUAGE>eng</LANGUAGE>
  <TITLE>portrait</TITLE>
  <TYPE>Scilab Function</TYPE>
  <DATE>April 1993</DATE>
  <SHORT_DESCRIPTION name="portrait"> 2 dimensional phase portrait.  </SHORT_DESCRIPTION>
  <CALLING_SEQUENCE>
    <CALLING_SEQUENCE_ITEM>[]=portrait(f,[odem,xdim,npts,pinit])  </CALLING_SEQUENCE_ITEM>
  </CALLING_SEQUENCE>
  <PARAM>
    <PARAM_INDENT>
      <PARAM_ITEM>
        <PARAM_NAME>f</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: a Scilab external which gives the field of the dynamical system. Hence  it can be a macro name which computes the field at time t and point x [y]=f(t,x,[u]) or a list list(f1,u1) where f1 is a macro of type [y]=f1(t,x,u) or a character string. The macro can be used to simulate a continuous or discrete system and in case  of discrete system the second parameter must be set to 'discrete'</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>options</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: The other parameters are optional. If omitted they will be asked interactively</SP>
          <PARAM_INDENT>
            <PARAM_ITEM>
              <PARAM_NAME>odem</PARAM_NAME>
              <PARAM_DESCRIPTION>
                <SP>: gives the integration method to use. The value &quot;default&quot; can be used,  otherwise see ode for a complete set of possibilities</SP>
              </PARAM_DESCRIPTION>
            </PARAM_ITEM>
            <PARAM_ITEM>
              <PARAM_NAME>npts</PARAM_NAME>
              <PARAM_DESCRIPTION>
                <SP>:  a vector of size (2,10) [number-of-points,step] gives the step
    for integration  and the number of requested points. The solution
    will be calculated and drawn  for
    time=0:step:(step*[number-of-points])</SP>
              </PARAM_DESCRIPTION>
            </PARAM_ITEM>
            <PARAM_ITEM>
              <PARAM_NAME>xdim</PARAM_NAME>
              <PARAM_DESCRIPTION>
                <SP>: [xmin,xmax,ymin,ymax,zmin,zmax] the boundaries of the graphic frame.</SP>
              </PARAM_DESCRIPTION>
            </PARAM_ITEM>
            <PARAM_ITEM>
              <PARAM_NAME>pinit</PARAM_NAME>
              <PARAM_DESCRIPTION>
                <SP>: initial values for integration. A set of initial points can be given in a matrix</SP>
                <VERBATIM>
<![CDATA[
      pinit = [x0(1), x1(1),...., xn(1)
               x0(2), x1(2),...., xn(2)
               x0(3), x1(3),...., xn(3)].
   ]]>
                </VERBATIM>
              </PARAM_DESCRIPTION>
            </PARAM_ITEM>
          </PARAM_INDENT>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
    </PARAM_INDENT>
  </PARAM>
  <DESCRIPTION>
    <P>
    Interactive integration and display of a 2 dimensional phase portrait
    of a dynamical system  dx/dt=f(t,x,[u]) (where u is an optional parameter )</P>
  </DESCRIPTION>
  <EXAMPLE>
<![CDATA[
a=rand(2,2)
deff('[ydot]=l_s(t,y)','ydot=a*y')
portrait(l_s)
 ]]>
  </EXAMPLE>
  <SEE_ALSO>
    <SEE_ALSO_ITEM>
      <LINK>ode</LINK>
    </SEE_ALSO_ITEM>
  </SEE_ALSO>
</MAN>
