# HG changeset patch
# User jwe
# Date 1173306262 0
# Node ID a8dd70bacc1e707db97d5d9e7d325dedb30a9f61
# Parent  df3445687c6efd8910d5337a387330cd1b2724cb
[project @ 2007-03-07 22:22:12 by jwe]

diff -r df3445687c6e -r a8dd70bacc1e scripts/ChangeLog
--- a/scripts/ChangeLog	Wed Mar 07 20:29:28 2007 +0000
+++ b/scripts/ChangeLog	Wed Mar 07 22:24:22 2007 +0000
@@ -1,5 +1,18 @@
 2007-03-07  John W. Eaton  <jwe@octave.org>
 
+	* control/base/rlocus.m: Update for current plotting functions.
+
+2007-03-07  A. S. Hodel  <a.s.hodel@eng.auburn.edu>
+
+	* control/base/rlocus.m: Improve display.
+
+2007-03-07  John W. Eaton  <jwe@octave.org>
+
+	* plot/legend.m: Only handle positions -1:4.
+	* plot/__pltopt1__.m: Don't set linestyle if only marker style is
+	found in option string
+	* plot/__uiobject_draw_axes__.m: Handle key position.
+
 	* plot/newplot.m: Always reset next line color.
 
 	* testfun/assert.m: Check that number of dimensions match before
@@ -1222,7 +1235,7 @@
 
 	* time/datevec.m: Add additional compatible default parsing strings.
 
-2006-10-09  Bill Denney  <denney@seas.upenn.edu><
+2006-10-09  Bill Denney  <denney@seas.upenn.edu>
 
 	* pkg/pkg.m: Remove trailing "\n" from error messages.
 	Remove compare_versions subfunction.
diff -r df3445687c6e -r a8dd70bacc1e scripts/control/base/rlocus.m
--- a/scripts/control/base/rlocus.m	Wed Mar 07 20:29:28 2007 +0000
+++ b/scripts/control/base/rlocus.m	Wed Mar 07 22:24:22 2007 +0000
@@ -18,7 +18,7 @@
 ## 02110-1301 USA.
 
 ## -*- texinfo -*-
-## @deftypefn {Function File} {[@var{rldata}, @var{k_break}, @var{rlpol}, @var{gvec}, @var{real_ax_pts}] =} rlocus (@var{sys}[, @var{increment}, @var{min_k}, @var{max_k}])
+## @deftypefn {Function File} {[@var{rldata}, @var{k}] =} rlocus (@var{sys}[, @var{increment}, @var{min_k}, @var{max_k}])
 ##
 ## Display root locus plot of the specified @acronym{SISO} system.
 ## @example
@@ -49,15 +49,8 @@
 ## @table @var 
 ## @item rldata
 ## Data points plotted: in column 1 real values, in column 2 the imaginary values.
-## @item k_break
+## @item k
 ## Gains for real axis break points.
-## @item rlpol
-## Closed-loop roots for each gain value: 1 locus branch per row; 1 pole
-## set per column
-## @item gvec
-## Gains vector
-## @item real_ax_pts
-## Real axis breakpoints
 ## @end table
 ## @end deftypefn
 
@@ -68,65 +61,98 @@
 
 function [rldata, k_break, rlpol, gvec, real_ax_pts] = rlocus (sys, increment, min_k, max_k)
 
-  if (nargin < 1) | (nargin > 4)
+  if (nargin < 1 || nargin > 4)
     print_usage ();
   endif
 
   ## Convert the input to a transfer function if necessary
-
   [num,den] = sys2tf(sys);               # extract numerator/denom polyomials
-  lnum = length(num);      lden = length(den);
+  lnum = length(num);      
+  lden = length(den);
+  # equalize length of num, den polynomials
   if(lden < 2)
-    error(sprintf("length of derivative=%d, doesn't make sense",lden));
-  elseif(lnum == 1)
-    num = [0, num];     # so that derivative is shortened by one
+    error("system has no poles");
+  elseif(lnum < lden)
+    num = [zeros(1,lden-lnum), num];  # so that derivative is shortened by one
+  endif
+
+  olpol = roots(den);
+  olzer = roots(num);
+  nas = lden -lnum; # number of asymptotes
+  maxk = 0;
+  if(nas > 0)
+    cas = ( sum(olpol) - sum(olzer) )/nas;
+    angles = (2*[1:nas]-1)*pi/nas;
+    # printf("rlocus: there are %d asymptotes centered at %f\n", nas, cas);
+  else
+    cas = angles = [];
+    maxk = 100*den(1)/num(1);
   endif
 
-  ## root locus plot axis limits
 
-  ## compute real axis locus breakpoints
-  ## compute the derivative of the numerator and the denominator
-  dern=polyderiv(num);        derd=polyderiv(den);
-
-  ## compute real axis breakpoints
-  real_ax_pol = conv(den,dern) - conv(num,derd);
-  real_ax_pts = roots(real_ax_pol);
-  if(isempty(real_ax_pts))
-    k_break = [];
-    maxk = 0;
+  # compute real axis break points and corresponding gains
+  dnum=polyderiv(num);
+  dden=polyderiv(den);
+  brkp = conv(den, dnum) - conv(num, dden);
+  real_ax_pts = roots(brkp);
+  real_ax_pts = real_ax_pts(find(imag(real_ax_pts) == 0));
+  k_break = -polyval(den,real_ax_pts) ./ polyval(num, real_ax_pts);
+  idx = find(k_break >= 0);
+  k_break = k_break(idx);
+  real_ax_pts = real_ax_pts(idx);
+  if(!isempty(k_break))
+    maxk = max(max(k_break),maxk);
+  endif
+  
+  if(nas == 0)
+    maxk = max(1, 2*maxk);  % get at least some root locus
   else
-    ## compute gains that achieve the breakpoints
-    c1 = polyval(num,real_ax_pts);
-    c2 = polyval(den,real_ax_pts);
-    k_break = -real(c2 ./ c1);
-    maxk = max(max(k_break,0));
+    # get distance from breakpoints, poles, and zeros to center of asymptotes
+    dmax = 3*max(abs( [vec(olzer); vec(olpol); vec(real_ax_pts)] - cas ));
+    if(dmax == 0)
+      dmax = 1;
+    endif
+ 
+    # get gain for dmax along each asymptote, adjust maxk if necessary
+    svals = cas + dmax*exp(j*angles);
+    kvals = -polyval(den,svals) ./ polyval(num, svals);
+    maxk = max(maxk, max(real(kvals)));
+  end
+  
+  ## check for input arguments:
+  if (nargin > 2)
+    mink = min_k;
+  else
+    mink = 0;
   endif
-
-  ## compute gain ranges based on computed K values
-  if(maxk == 0)     maxk = 1;
-  else              maxk = 1.1*maxk;        endif
-  mink = 0;
-  ngain = 20;
-
-  ## check for input arguments:
-  if (nargin > 2)       mink = min_k;          endif
-  if (nargin > 3)       maxk = max_k;          endif
+  if (nargin > 3)
+    maxk = max_k;
+  endif
   if (nargin > 1)
-    if(increment <= 0)  error("increment must be positive");
+    if(increment <= 0)
+      error("increment must be positive");
     else
       ngain = (maxk-mink)/increment;
     endif
+  else
+    ngain = 30;
   endif
 
   ## vector of gains
-  ngain = max(3,ngain);
+  ngain = max(30,ngain);
   gvec = linspace(mink,maxk,ngain);
+  if(length(k_break))
+    gvec = sort([gvec, vec(k_break)']);
+  endif
 
   ## Find the open loop zeros and the initial poles
   rlzer = roots(num);
 
   ## update num to be the same length as den
-  lnum = length(num);  if(lnum < lden) num = [zeros(1,lden - lnum),num];  endif
+  lnum = length(num);  
+  if(lnum < lden)
+    num = [zeros(1,lden - lnum),num];
+  endif
 
   ## compute preliminary pole sets
   nroots = lden-1;
@@ -135,57 +161,40 @@
    rlpol(1:nroots,ii)  = vec(sortcom(roots(den + gain*num)));
   endfor
 
-  ## compute axis limits (isolate asymptotes)
-  olpol = roots(den);
-  real_axdat = union(real(rlzer), real(union(olpol,real_ax_pts)) );
-  rmin = min(real_axdat);      rmax = max(real_axdat);
+  ## set smoothing tolerance 
+  smtolx = 0.01*( max(max(real(rlpol))) - min(min(real(rlpol))));
+  smtoly = 0.01*( max(max(imag(rlpol))) - min(min(imag(rlpol))));
+  smtol = max(smtolx, smtoly);
+  rlpol = sort_roots(rlpol,smtolx, smtoly);   % sort according to nearest-neighbor
 
-  rlpolv = [vec(rlpol); vec(real_axdat)];
-  idx = find(real(rlpolv) >= rmin & real(rlpolv) <= rmax);
-  axlim = axis2dlim([real(rlpolv(idx)),imag(rlpolv(idx))]);
-  xmin = axlim(1);
-  xmax = axlim(2);
-
-  ## set smoothing tolerance per axis limits
-  smtol = 0.01*max(abs(axlim));
-
-  ## smooth poles if necessary, up to maximum of 1000 gain points
-  ## only smooth points within the axis limit window
-  ## smoothing done if max_k not specified as a command argument
   done=(nargin == 4);    # perform a smoothness check
   while((!done) & ngain < 1000)
     done = 1 ;      # assume done
     dp = abs(diff(rlpol'))';
-    maxd = max(dp);
-    ## search for poles in the real axis limits whose neighbors are distant
-    idx = find(maxd > smtol);
-    for ii=1:length(idx)
-      i1 = idx(ii);      g1 = gvec(i1);       p1 = rlpol(:,i1);
-      i2 = idx(ii)+1;    g2 = gvec(i2);       p2 = rlpol(:,i2);
+    maxdp = max(dp);
+    
+    ## search for poles whose neighbors are distant
+    if(lden == 2)
+      idx = find(dp > smtol);
+    else
+      idx = find(maxdp > smtol);
+    endif
 
-      ## isolate poles in p1, p2 that are inside the real axis limits
-      bidx = find( (real(p1) >= xmin & real(p1) <= xmax)  ...
-          | (real(p2) >= xmin & real(p2) <= xmax) );
-      if(!isempty(bidx))
-        p1 = p1(bidx);
-        p2 = p2(bidx);
-        if( max(abs(p2-p1)) > smtol)
-          newg = linspace(g1,g2,5);
-          newg = newg(2:4);
-          if(isempty(newg))
-            printf("rlocus: empty newg")
-            g1
-            g2
-            i1
-            i2
-            idx_i1 = idx(ii)
-            gvec_i1 = gvec(i1:i2)
-            delta_vec_i1 = diff(gvec(i1:i2))
-            prompt
-          endif
-          gvec =  [gvec,newg];
-          done = 0;             # need to process new gains
-        endif
+    for ii=1:length(idx)
+      i1 = idx(ii);
+      g1 = gvec(i1);
+      p1 = rlpol(:,i1);
+
+      i2 = idx(ii)+1;
+      g2 = gvec(i2);
+      p2 = rlpol(:,i2);
+
+      ## isolate poles in p1, p2 
+      if( max(abs(p2-p1)) > smtol)
+        newg = linspace(g1,g2,5);
+        newg = newg(2:4);
+        gvec =  [gvec,newg];
+        done = 0;             # need to process new gains
       endif
     endfor
 
@@ -199,32 +208,87 @@
     [gvec,idx] = sort(gvec);
     rlpol = rlpol(:,idx);
     ngain = length(gvec);
+    rlpol = sort_roots(rlpol,smtolx, smtoly);   % sort according to nearest-neighbor
   endwhile
+  rldata = rlpol;
 
   ## Plot the data
   if(nargout  == 0)
     rlpolv = vec(rlpol);
-    idx = find(real(rlpolv) >= xmin & real(rlpolv) <= xmax);
-    axdata = [real(rlpolv(idx)),imag(rlpolv(idx))];
+    axdata = [real(rlpolv),imag(rlpolv); real(olzer), imag(olzer)];
     axlim = axis2dlim(axdata);
-    axlim(1:2) = [xmin, xmax];
-    __gnuplot_set__ nologscale xy;
-    grid("on");
     rldata = [real(rlpolv), imag(rlpolv) ];
-    axis(axlim);
     [stn,inname,outname] = sysgetsignals(sys);
-    xlabel(sprintf("Root locus from %s to %s, gain=[%f,%f]: Real axis", ...
-        inname{1}, outname{1},gvec(1),gvec(ngain)));
-    ylabel("Imag. axis");
+
+    ## build plot command args pole by pole
 
-    if(isempty(rlzer))
-      plot(real(rlpolv),imag(rlpolv),".1;locus points;", ...
-           real(olpol),imag(olpol),"x2;open loop poles;");
-    else
-      plot(real(rlpolv),imag(rlpolv),".1;locus points;", ...
-           real(olpol),imag(olpol),"x2;open loop poles;", ...
-           real(rlzer),imag(rlzer),"o3;zeros;");
+    n_rlpol = rows(rlpol);
+    nelts = n_rlpol+1;
+    if (! isempty (rlzer))
+      nelts++;
     endif
+    args = cell (3, nelts);
+    for kk=1:rows(rlpol)
+      args{1,kk} = real (rlpol (kk,:));
+      args{2,kk} = imag (rlpol (kk,:));
+      args{3,kk} = "b-";
+    endfor
+    args{1,n_rlpol+1} = real(olpol);
+    args{2,n_rlpol+1} = imag(olpol);
+    args{3,n_rlpol+1} = "rx;open loop poles;";
+
+    if (! isempty(rlzer))
+      args{1,n_rlpol+2} = real(rlzer);
+      args{2,n_rlpol+2} = imag(rlzer);
+      args{3,n_rlpol+2} = "go;zeros;";
+    endif
+
+    plot (args{:})
+    legend ("boxon", 2);
+    grid ("on");
+    axis (axlim);
+    xlabel (sprintf ("Root locus from %s to %s, gain=[%f,%f]: Real axis",
+		     inname{1}, outname{1}, gvec(1), gvec(ngain)));
+    ylabel ("Imag. axis");
     rldata = [];
   endif
 endfunction
+
+function rlpol = sort_roots (rlpol,tolx, toly)
+  # no point sorting of you've only got one pole!
+  if(rows(rlpol) == 1)
+    return
+  endif
+
+  # reorder entries in each column of rlpol to be by their nearest-neighbors
+  dp = diff(rlpol')';
+  drp = max(real(dp));
+  dip = max(imag(dp));
+  idx = find( drp > tolx | dip > toly );
+  if(isempty(idx) )
+    return
+  endif
+
+  [np,ng] = size(rlpol);  # num poles, num gains
+  for jj = idx
+    vals = rlpol(:,[jj,jj+1]);
+    jdx = (jj+1):ng;
+    for ii=1:rows(rlpol-1)
+      rdx = ii:np;
+      dval = abs(rlpol(rdx,jj+1)-rlpol(ii,jj));
+      mindist = min(dval);
+      sidx = min( find ( dval == mindist)) + ii - 1;
+      if( sidx != ii)
+        c1 = norm(diff(vals'));
+        [vals(ii,2), vals(sidx,2)] = swap( vals(ii,2), vals(sidx,2));
+        c2 = norm(diff(vals'));
+        if(c1 > c2 )
+          # perform the swap
+          [rlpol(ii,jdx), rlpol(sidx,jdx)] = swap( rlpol(ii,jdx), rlpol(sidx,jdx));
+          vals = rlpol(:,[jj,jj+1]);
+        endif
+      endif
+    endfor
+  endfor
+
+endfunction
diff -r df3445687c6e -r a8dd70bacc1e scripts/plot/__pltopt1__.m
--- a/scripts/plot/__pltopt1__.m	Wed Mar 07 20:29:28 2007 +0000
+++ b/scripts/plot/__pltopt1__.m	Wed Mar 07 22:24:22 2007 +0000
@@ -41,6 +41,9 @@
     return;
   endif
 
+  have_linestyle = false;
+  have_marker = false;
+
   while (! isempty (opt))
     if (strncmp (opt, "--", 2) || strncmp (opt, "-.", 2))
       options.linestyle = opt(1:2);
@@ -49,12 +52,14 @@
       topt = opt(1);
       n = 1;
       if (topt == "-" || topt == ":")
+	have_linestyle = true;
 	options.linestyle = topt;
       elseif (topt == "+" || topt == "o" || topt == "*"
 	      || topt == "." || topt == "x" || topt == "s"
 	      || topt == "d" || topt == "^" || topt == "v"
 	      || topt == ">" || topt == "<" || topt == "p"
 	      || topt == "h")
+	have_marker = true;
 	options.marker = topt;
       elseif (topt == "k")
 	options.color = [0, 0, 0];
@@ -89,4 +94,8 @@
     opt(1:n) = [];
   endwhile
 
+  if (have_marker && ! have_linestyle)
+    options.linestyle = "";
+  endif
+
 endfunction
diff -r df3445687c6e -r a8dd70bacc1e scripts/plot/__uiobject_draw_axes__.m
--- a/scripts/plot/__uiobject_draw_axes__.m	Wed Mar 07 20:29:28 2007 +0000
+++ b/scripts/plot/__uiobject_draw_axes__.m	Wed Mar 07 22:24:22 2007 +0000
@@ -32,6 +32,8 @@
 
     parent_figure_obj = get (axis_obj.parent);
 
+    have_newer_gnuplot = compare_versions (__gnuplot_version__ (), "4.0", ">");
+
     ## Set axis properties here?
 
     if (! isempty (axis_obj.outerposition))
@@ -633,10 +635,30 @@
 
     if (strcmp (axis_obj.key, "on"))
       if (strcmp (axis_obj.keybox, "on"))
-	fputs (plot_stream, "set key box;\n");
+	box = "box";
       else
-	fputs (plot_stream, "set key nobox;\n");
+	box = "nobox";
       endif
+      inout = "inside";
+      switch (axis_obj.keypos)
+	case -1
+	  pos = "right bottom";
+	  inout = "outside";
+	case 1
+	  pos = "right top";
+	case 2
+	  pos = "left top";
+	case 3
+	  pos = "left bottom";
+	case 4
+	  pos = "right bottom";
+	otherwise
+	  pos = "";
+      endswitch
+      if (! have_newer_gnuplot)
+	inout = "";
+      endif
+      fprintf (plot_stream, "set key %s %s %s;\n", inout, pos, box);
     else
       fputs (plot_stream, "unset key;\n");
     endif
diff -r df3445687c6e -r a8dd70bacc1e scripts/plot/legend.m
--- a/scripts/plot/legend.m	Wed Mar 07 20:29:28 2007 +0000
+++ b/scripts/plot/legend.m	Wed Mar 07 22:24:22 2007 +0000
@@ -29,6 +29,8 @@
 ## @var{pos} optionally  places the legend in the specified location:
 ##
 ## @multitable @columnfractions 0.1 0.1 0.8
+## @item @tab -1 @tab
+##   To the top right of the plot
 ## @item @tab 0 @tab
 ##   Don't move the legend box (default)
 ## @item @tab 1 @tab
@@ -39,14 +41,6 @@
 ##   Lower left-hand corner
 ## @item @tab 4 @tab
 ##   Lower right-hand corner
-## @item @tab -1 @tab
-##   To the top right of the plot
-## @item @tab -2 @tab
-##   To the bottom right of the plot
-## @item @tab -3 @tab
-##   To the bottom of the plot
-## @item @tab [@var{x}, @var{y}] @tab
-##   To the arbitrary postion in plot [@var{x}, @var{y}]
 ## @end multitable
 ##
 ## Some specific functions are directely avaliable using @var{func}:
@@ -79,7 +73,7 @@
   if (nargs > 0)
     pos = varargin{nargs};
     if (isnumeric (pos) && isscalar (pos) && round (pos) == pos)
-      if (pos >= -3 && pos <= 4)
+      if (pos >= -1 && pos <= 4)
 	set (ca, "keypos", pos);
 	nargs--;
       else