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SLM - Shape Language Modeling

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SLM - Shape Language Modeling

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15 Jun 2009 (Updated )

Least squares spline modeling using shape primitives

plotslm(slm)
function hfig = plotslm(slm)
% plotslm: plots a Shape Language Model (slm) or its derivatives
% usage: plotslm(slm)
% usage: hfig = plotslm(slm)
%
%
% arguments: (input)
%  slm - slm struct, as returned by slmengine or slmfit,
%        or evaluated by slmeval
%
%
% arguments: (output)
%  hfig - figure handle. Only returned if an output argument
%        is requested
%
%
% Example:
%  Plot of a fit to exponential data
%  x = 0:.1:1;
%  y = exp(x) + randn(size(x))/10;
%  slm = slmengine(x,y);
%  plotslm(slm)
%
%
% See also: slmset, slmengine, slmeval, ppval, slmfit
%
%
% Author: John D'Errico
% E-mail: woodchips@rochester.rr.com
% Release: 1.0
% Release date: 2/6/07

% initial plot parameters
params.LineStyle = '-';
params.LineColor = 'r';
params.LineWidth = 0.5;

params.DataMarker = 'o';
params.DataColor = 'b';
params.DataSize = 3;

params.KnotStyle = '--';
params.KnotColor = 'g';

params.Grid = 'off';

params.NumberOfPoints = 1001;

% is it a slm or pp or old style hermite form?
if isstruct(slm)
  % this covers both the pp or slm forms
  params.model = slm;
  
  if strcmp(slm.form,'slm')
    params.Degree = slm.degree;
  else
    % its a pp
    params.Degree = slm.order - 1;
  end
elseif isa(slm,'double') && ismember(size(slm,2),[2 3])
  % It must have been a linear or cubic Hermite array form.
  % Be friendly, and convert to a slm.
  params.model = hermite2slm(slm);
  
  % define linear as first order, cubic is third
  params.Degree = params.model.degree;
end

% do we have any data?
if isfield(params.model,'x') && ~isempty(params.model.x)
  params.DataExists = true;
else
  params.DataExists = false;
end

% which style will we use initially
if params.DataExists
  params.PlotStyle = 'fundata';
else
  params.PlotStyle = 'fun';
end

% generate plot figure
figuregen

% and plot the model. The options will be
% 'fundata', 'fun', 'residuals', 'dy', 'dy2', 'dy3', 'integral'
plotcurve(params.PlotStyle)

% any further interactions will be by callbacks.

% do we return the figure handle?
if nargout > 0
  hfig = params.handles.figure;
end

% ===============================================
%    nested functions - initial plot figure
% ===============================================
function figuregen
  % generates/initializes the plot gui
  
  % a new figure
  params.handles.figure = figure;
  
  % generate the plot menu
  h=uimenu(params.handles.figure,'Label','Plot');
  uimenu(h,'Label','Curve only','Callback',@(s,e) plotcurve('fun'));
  if params.DataExists
    uimenu(h,'Label','Curve & Data','Callback',@(s,e) plotcurve('fundata'));
    uimenu(h,'Label','Residuals','Callback',@(s,e) plotcurve('residuals'));
  end
  if params.Degree > 0
    uimenu(h,'Label','First derivative','Callback',@(s,e) plotcurve('dy'));
  end
  if params.Degree > 1
    uimenu(h,'Label','Second derivative','Callback',@(s,e) plotcurve('dy2'));
    uimenu(h,'Label','Third derivative','Callback',@(s,e) plotcurve('dy3'));
  end
  uimenu(h,'Label','Integral','Callback',@(s,e) plotcurve('integral'));
  
  
  if params.DataExists
    hh=uimenu(h,'Label','Data points','Separator','on');
    hhh=uimenu(hh,'Label','Data markers');
    uimenu(hhh,'Label','o','Callback',@(s,e) setplotparam('DataMarker','o'));
    uimenu(hhh,'Label','+','Callback',@(s,e) setplotparam('DataMarker','+'));
    uimenu(hhh,'Label','x','Callback',@(s,e) setplotparam('DataMarker','x'));
    uimenu(hhh,'Label','.','Callback',@(s,e) setplotparam('DataMarker','.'));
    uimenu(hhh,'Label','Triangle','Callback',@(s,e) setplotparam('DataMarker','v'));
    uimenu(hhh,'Label','Square','Callback',@(s,e) setplotparam('DataMarker','s'));
    uimenu(hhh,'Label','Pentagram','Callback',@(s,e) setplotparam('DataMarker','p'));
    uimenu(hhh,'Label','Hexagram','Callback',@(s,e) setplotparam('DataMarker','h'));
    uimenu(hhh,'Label','None','Callback',@(s,e) setplotparam('DataMarker',''));
    
    hhh=uimenu(hh,'Label','Symbol color');
    uimenu(hhh,'Label','Red','Callback',@(s,e) setplotparam('DataColor','r'));
    uimenu(hhh,'Label','Green','Callback',@(s,e) setplotparam('DataColor','g'));
    uimenu(hhh,'Label','Blue','Callback',@(s,e) setplotparam('DataColor','b'));
    uimenu(hhh,'Label','Cyan','Callback',@(s,e) setplotparam('DataColor','c'));
    uimenu(hhh,'Label','Magenta','Callback',@(s,e) setplotparam('DataColor','m'));
    uimenu(hhh,'Label','Yellow','Callback',@(s,e) setplotparam('DataColor','y'));
    uimenu(hhh,'Label','Black','Callback',@(s,e) setplotparam('DataColor','k'));
    
    hhh=uimenu(hh,'Label','Symbol size');
    uimenu(hhh,'Label','1','Callback',@(s,e) setplotparam('DataSize',1));
    uimenu(hhh,'Label','2','Callback',@(s,e) setplotparam('DataSize',2));
    uimenu(hhh,'Label','3','Callback',@(s,e) setplotparam('DataSize',3));
    uimenu(hhh,'Label','4','Callback',@(s,e) setplotparam('DataSize',4));
    uimenu(hhh,'Label','6','Callback',@(s,e) setplotparam('DataSize',6));
    uimenu(hhh,'Label','10','Callback',@(s,e) setplotparam('DataSize',10));
    uimenu(hhh,'Label','20','Callback',@(s,e) setplotparam('DataSize',20));
  end
  
  hh=uimenu(h,'Label','Knots/Breaks');
  hhh=uimenu(hh,'Label','Line style');
  uimenu(hhh,'Label','Solid','Callback',@(s,e) setplotparam('KnotStyle','-'));
  uimenu(hhh,'Label','Dotted','Callback',@(s,e) setplotparam('KnotStyle',':'));
  uimenu(hhh,'Label','Dash/dot','Callback',@(s,e) setplotparam('KnotStyle','-.'));
  uimenu(hhh,'Label','Dashed','Callback',@(s,e) setplotparam('KnotStyle','--'));
  uimenu(hhh,'Label','None','Callback',@(s,e) setplotparam('KnotStyle','none'));
  
  hhh=uimenu(hh,'Label','Line color');
  uimenu(hhh,'Label','Red','Callback',@(s,e) setplotparam('KnotColor','r'));
  uimenu(hhh,'Label','Green','Callback',@(s,e) setplotparam('KnotColor','g'));
  uimenu(hhh,'Label','Blue','Callback',@(s,e) setplotparam('KnotColor','b'));
  uimenu(hhh,'Label','Cyan','Callback',@(s,e) setplotparam('KnotColor','c'));
  uimenu(hhh,'Label','Magenta','Callback',@(s,e) setplotparam('KnotColor','m'));
  uimenu(hhh,'Label','Yellow','Callback',@(s,e) setplotparam('KnotColor','y'));
  uimenu(hhh,'Label','Black','Callback',@(s,e) setplotparam('KnotColor','k'));
  
  hh=uimenu(h,'Label','Curve');
  hhh=uimenu(hh,'Label','Line style');
  uimenu(hhh,'Label','Solid','Callback',@(s,e) setplotparam('LineStyle','-'));
  uimenu(hhh,'Label','Dotted','Callback',@(s,e) setplotparam('LineStyle',':'));
  uimenu(hhh,'Label','Dash/dot','Callback',@(s,e) setplotparam('LineStyle','-.'));
  uimenu(hhh,'Label','Dashed','Callback',@(s,e) setplotparam('LineStyle','--'));
  uimenu(hhh,'Label','None','Callback',@(s,e) setplotparam('LineStyle','none'));
  
  hhh=uimenu(hh,'Label','Line color');
  uimenu(hhh,'Label','Red','Callback',@(s,e) setplotparam('LineColor','r'));
  uimenu(hhh,'Label','Green','Callback',@(s,e) setplotparam('LineColor','g'));
  uimenu(hhh,'Label','Blue','Callback',@(s,e) setplotparam('LineColor','b'));
  uimenu(hhh,'Label','Cyan','Callback',@(s,e) setplotparam('LineColor','c'));
  uimenu(hhh,'Label','Magenta','Callback',@(s,e) setplotparam('LineColor','m'));
  uimenu(hhh,'Label','Yellow','Callback',@(s,e) setplotparam('LineColor','y'));
  uimenu(hhh,'Label','Black','Callback',@(s,e) setplotparam('LineColor','k'));
  
  hh=uimenu(h,'Label','Interrogate data by mouse','Separator','on');
  uimenu(hh,'Label','Label a point by mouse','Callback',@(s,e) selectp('remove'));
  uimenu(hh,'Label','Permanent Label','Callback',@(s,e) selectp('permanent'));
  
  hh=uimenu(h,'Label','Toggle grid','Separator','on','Callback',@(s,e) togglegrid);
  
  
end % figuregen
  
% ===============================================
%    nested functions - set plot parameters
% ===============================================
function setplotparam(parameter,val)
% sets plot parameters from callbacks
switch parameter
  case 'DataMarker'
    params.DataMarker = val;
  case 'DataColor'
    params.DataColor = val;
  case 'DataSize'
    params.DataSize = val;

  case 'KnotStyle'
    params.KnotStyle = val;
  case 'KnotColor'
    params.KnotColor = val;
    
  case 'LineStyle'
    params.LineStyle = val;
  case 'LineColor'
    params.LineColor = val;
    
end

% and regenerate the figure to reflect the change
plotcurve(params.PlotStyle)

end


% ===============================================
%    nested functions - plots function/data/derivatives
% ===============================================
function selectp(action)
  % uses selectdata to flag a point
  
  switch action
    case 'remove'
      removelabel = 'on';
    case 'permanent'
      removelabel = 'off';
  end
  
  selectdata('selectionmode','c','label','on','removelabel',removelabel);
  
end % 

% ===============================================
%    nested functions - plots function/data/derivatives
% ===============================================
function togglegrid
  
  if strcmp(params.Grid,'on')
    params.Grid = 'off';
    grid off
  else
    params.Grid = 'on';
    grid on
  end
  
end % 

% ===============================================
%    nested functions - plots function/data/derivatives
% ===============================================
function plotcurve(plotstyle)
% plots the data and model. The options will be
% 'fundata', 'fun', 'residuals', 'dy', 'dy2', 'dy3', 'integral'

% make sure the figure is on top
figure(params.handles.figure)

% which plot was called for?
switch plotstyle
  case {'fundata' 'fun'}
    % plot the function itself. we will add the
    % data later if appropriate
    if strcmpi(params.model.form,'slm')
      xrange = params.model.knots([1,end]);
    else
      xrange = params.model.breaks([1,end]);
    end
    
    xev = linspace(xrange(1),xrange(2),params.NumberOfPoints);
    
    % evaluate
    if strcmpi(params.model.form,'slm')
      ypred = slmeval(xev,params.model);
    else
      ypred = ppval(params.model,xev);
    end
    
    % plot the curve
    h = plot(xev,ypred);
    set(h,'Marker','none', ...
      'Color',params.LineColor, ...
      'LineStyle',params.LineStyle, ...
      'LineWidth',params.LineWidth)
      
    hold on
    
    % plot the vertical knot marker lines    
    axlim = axis;
    yrange = axlim(3:4);
    
    if strcmpi(params.model.form,'slm')
      knots = params.model.knots(:);
    else
      knots = params.model.breaks(:);
    end
    
    h = plot(repmat(knots',2,1),yrange(:));
    set(h,'Marker','none', ...
      'Color',params.KnotColor, ...
      'LineStyle',params.KnotStyle)
    
    % release the hold
    hold off
    
    xlabel 'X'
    ylabel 'f(X)'
    title 'Function plot'
    
  case 'residuals'
    % only a residual plot, no function at all
    
    if isfield(params.model,'x') && ~isempty(params.model.x)
      % get the residuals
      if strcmpi(params.model.form,'slm')
        % a slm form
        yhat = slmeval(params.model.x,params.model);
      else
        % it was a pp form
        yhat = ppval(params.model,params.model.x);
      end
      resid = yhat - params.model.y;
      
      % plot them
      h = plot(params.model.x,resid);
      set(h,'Marker',params.DataMarker, ...
        'Color',params.DataColor, ...
        'MarkerSize',params.DataSize, ...
        'LineStyle','none')
      
      hold on
      
      % knots too
      if strcmpi(params.model.form,'slm')
        knots = params.model.knots(:);
      else
        knots = params.model.breaks(:);
      end
      
      axlim = axis;
      
      h = plot(repmat(knots',2,1),axlim(3:4));
      set(h,'Marker','none', ...
        'Color',params.KnotColor, ...
        'LineStyle',params.KnotStyle)
      
      % plot a reference line at zero residual
      plot([min(axlim(1),knots(1)),max(axlim(2),knots(end))],[0 0],'g-')
      
      % release the hold
      hold off
      
      xlabel 'X'
      ylabel 'f(X)'
      title 'Residual error plot'
      
    end
    
  case {'dy' 'dy2' 'dy3'}
    % plot the k'th derivative
    switch plotstyle
      case 'dy'
        k = 1;
      case 'dy2'
        k = 2;
      case 'dy3'
        k = 3;
    end
    
    if strcmpi(params.model.form,'slm')
      xrange = params.model.knots([1,end]);
    else
      xrange = params.model.breaks([1,end]);
    end
    
    xev = linspace(xrange(1),xrange(2),params.NumberOfPoints);
    
    % evaluate
    if strcmpi(params.model.form,'slm')
      ypred = slmeval(xev,params.model,k);
    else
      pp = params.model;
      % differentiate the model
      order = size(pp.coefs,2);
      for j = 1:k
        pp.coefs = pp.coefs*diag((order-1):-1:1,1);
      end
      ypred = ppval(pp,xev);
    end
    
    % plot the curve
    h = plot(xev,ypred);
    set(h,'Marker','none', ...
      'Color',params.LineColor, ...
      'LineStyle',params.LineStyle, ...
      'LineWidth',params.LineWidth)
      
    hold on
    
    % plot the vertical knot marker lines    
    axlim = axis;
    yrange = axlim(3:4);
    
    if strcmpi(params.model.form,'slm')
      knots = params.model.knots(:);
    else
      knots = params.model.breaks(:);
    end
    
    h = plot(repmat(knots',2,1),yrange(:));
    set(h,'Marker','none', ...
      'Color',params.KnotColor, ...
      'LineStyle',params.KnotStyle)
    
    % release the hold
    hold off

    xlabel 'X'
    switch plotstyle
      case 'dy'
        ylabel 'f''(X)'
        title '1st derivative plot'
      case 2
        ylabel 'f''''(X)'
        title '2nd derivative plot'
      case 3
        ylabel 'f''''''(X)'
        title '3rd derivative plot'
    end
    
  case 'integral'
    % plot the cumulative integral
    
    % if its a slm, easiest is to convert to a
    % pp form, then integrate that
    if strcmpi(params.model.form,'slm')
      pp = slm2pp(params.model);
    else
      % it already was a pp
      pp = params.model;
    end
    
    xrange = pp.breaks([1,end]);
    xev = linspace(xrange(1),xrange(2),params.NumberOfPoints);
    
    % integrate (once)
    order = size(pp.coefs,2);
    op = diag(1./(order:-1:1),-1);
    op(1,:) = [];
    pp.coefs = pp.coefs*op;
    pp.order = pp.order + 1;
    % offset the constant terms to make the integral cumulative
    % Just use horner's rule to evaluate at the upper endpoint
    % of each interval
    knots = pp.breaks';
    dx = diff(knots); %#ok
    offset = pp.coefs(:,1);
    for j = 2:(order+1)
      offset = offset.*dx + pp.coefs(:,j);
    end
    pp.coefs(2:end,end) = pp.coefs(2:end,end) + ...
      cumsum(offset(1:(end-1)));
    
    % evaluate
    ypred = ppval(pp,xev);
    
    % plot the curve
    h = plot(xev,ypred);
    set(h,'Marker','none', ...
      'Color',params.LineColor, ...
      'LineStyle',params.LineStyle, ...
      'LineWidth',params.LineWidth)
      
    hold on
    
    % plot the vertical knot marker lines    
    axlim = axis;
    yrange = axlim(3:4);
    knots = pp.breaks(:);
    
    h = plot(repmat(knots',2,1),yrange(:));
    set(h,'Marker','none', ...
      'Color',params.KnotColor, ...
      'LineStyle',params.KnotStyle)
    
    % release the hold
    hold off
    
    xlabel 'X'
    ylabel 'f''(X)'
    title 'Cumulative integral function'
    
end

if strcmp(plotstyle,'fundata')
  % we must also plot the data
  if isfield(params.model,'x') && ~isempty(params.model.x)
    hold on
    h = plot(params.model.x,params.model.y);
    
    set(h,'LineStyle','none', ...
      'Marker',params.DataMarker, ...
      'Color',params.DataColor, ...
      'MarkerSize',params.DataSize)
    hold off
  end
  
  if isfield(params.model,'prescription') && ~isempty(params.model.prescription.ErrorBar)
    hold on
    errorbar(params.model.x,params.model.y, ...
      params.model.prescription.ErrorBar(:,1), ...
      params.model.prescription.ErrorBar(:,2), ...
      'LineStyle','none', ...
      'Marker',params.DataMarker, ...
      'Color',params.DataColor, ...
      'MarkerSize',params.DataSize)
    hold off
  end
end

% do we need the grid plotted?
if strcmp(params.Grid,'on')
  grid on
end  

end % plotcurve

% ===============================================
%    end mainline
% ===============================================
end

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