## Copyright (C) 1998 Auburn University.  All rights reserved.
##
## This file is part of Octave.
##
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## under the terms of the GNU General Public License as published by the
## Free Software Foundation; either version 2, or (at your option) any
## later version.
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## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
## FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
## for more details.
##
## You should have received a copy of the GNU General Public License
## along with Octave; see the file COPYING.  If not, write to the Free
## Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
## 02110-1301 USA.

## -*- texinfo -*-
## @deftypefn {Function File} {[@var{mag}, @var{phase}, @var{w}] =} nichols (@var{sys}, @var{w}, @var{outputs}, @var{inputs})
## Produce Nichols plot of a system.
##
## @strong{Inputs}
## @table @var
## @item sys
## System data structure (must be either purely continuous or discrete; 
## see @command{is_digital}).
## @item w
## Frequency values for evaluation.
## @itemize
## @item if sys is continuous, then nichols evaluates @math{G(jw)}.
## @item if sys is discrete, then nichols evaluates @math{G(exp(jwT))}, 
## where @var{T}=@var{sys}. @var{tsam} is the system sampling time.
## @item the default frequency range is selected as follows (These
##        steps are @strong{not} performed if @var{w} is specified):
## @enumerate
## @item via routine @command{__bodquist__}, isolate all poles and zeros away from
## @var{w}=0 (@math{jw=0} or @math{exp(jwT)=1}) and select the frequency range 
## based on the breakpoint locations of the frequencies.
## @item if sys is discrete time, the frequency range is limited to jwT in 
## @iftex
## @tex
## $ [0, 2p\pi] $.
## @end tex
## @end iftex
## @ifinfo
## [0,2p*pi].
## @end ifinfo
## @item A ``smoothing'' routine is used to ensure that the plot phase does
## not change excessively from point to point and that singular points 
## (e.g., crossovers from +/- 180) are accurately shown.
## @end enumerate
## @end itemize
## @item outputs
## @itemx inputs
## the names or indices of the output(s) and input(s) to be used in the 
## frequency response; see @command{sysprune}.
## @end table
## @strong{Outputs}
## @table @var
## @item mag
## @itemx phase
## The magnitude and phase of the frequency response @math{G(jw)} or 
## @math{G(exp(jwT))} at the selected frequency values.
## @item w
## The vector of frequency values used.
## @end table
## If no output arguments are given, @command{nichols} plots the results to the screen.
## Descriptive labels are automatically placed. See @command{xlabel}, 
## @command{ylabel}, @command{title}, and @command{replot}.
##
## Note: if the requested plot is for an @acronym{MIMO} system, @var{mag} is set to
## @iftex
## @tex
## $ \Vert G(jw) \Vert $ or $ \Vert G( {\rm exp}(jwT) \Vert $
## @end tex
## @end iftex
## @ifinfo
## ||G(jw)|| or ||G(exp(jwT))||
## @end ifinfo
## and phase information is not computed.
## @end deftypefn

function [mag, phase, w] = nichols (sys, w, outputs, inputs)

  ## check number of input arguments given
  if (nargin < 1 | nargin > 4)
    usage("[mag,phase,w] = nichols(sys[,w,outputs,inputs])");
  endif
  if(nargin < 2)
    w = [];
  endif
  if(nargin < 3)
    outputs = [];
  endif
  if(nargin < 4)
    inputs = [];
  endif

  [f, w, sys] = __bodquist__ (sys, w, outputs, inputs, "nichols");

  [stname,inname,outname] = sysgetsignals(sys);
  systsam = sysgettsam(sys);

  ## Get the magnitude and phase of f.
  mag = abs(f);
  phase = arg(f)*180.0/pi;

  if (nargout < 1),
    ## Plot the information
    oneplot();
    __gnuplot_set__ autoscale;
    __gnuplot_set__ nokey;
    clearplot();
    grid("on");
    __gnuplot_set__ data style lines;
    if(is_digital(sys))
      tistr = "(exp(jwT)) ";
    else
      tistr = "(jw)";
    endif
    xlabel("Phase (deg)");
    if(is_siso(sys))
      title(["Nichols plot of |[Y/U]",tistr,"|, u=", ...
        sysgetsignals(sys,"in",1,1), ", y=",sysgetsignals(sys,"out",1,1)]);
    else
      title([ "||Y(", tistr, ")/U(", tistr, ")||"]);
      printf("MIMO plot from\n%s\nto\n%s\n",__outlist__(inname,"    "), ...
        __outlist__(outname,"       "));
    endif
    if(max(mag) > 0)
      ylabel("Gain in dB");
      md = 20*log10(mag);
    else
      ylabel("Gain |Y/U|")
      md = mag;
    endif

    axvec = axis2dlim([vec(phase),vec(md)]);
    axis(axvec);
    plot(phase,md);
    mag = phase = w = [];
  endif
endfunction