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
