%% boxconstrain
% Below is a demonstration of the features of the |boxconstrain| function

%% Syntax
% |[xb]=boxconstrain(x,lb,ub,m,s);|

%% Description
% The |boxconstrain| function can be used to constrain parameters from
% [-inf,inf] to the range [lb ub]. The sigmoidal tanh function is used to
% do this mapping. The middle of the sigmoid, denoted by the parameter m
% need not be (lb+ub)/2. If x=m xb=m. 
% The optional parameter s sets the slope of the sigmoid at
% x=m, the default slope is 1. 

%% Examples

clear; close all; clc;

%% Example: Constraining parameters

m=5; %The middle
lb=0; %The lower bound
ub=10; %The upper bound
x=linspace(m-20,m+20,1000); % x paremeters for plotting
[y]=boxconstrain(x,lb,ub,m);

%%

cFigure; hold on;
xlabel('x'); ylabel('Constrained x'); 
h1=plot([min(x) max(x)],[ub ub],'b--','LineWidth',3);
h2=plot([min(x) max(x)],[lb lb],'r--','LineWidth',3);
h3=plot(m,m,'k.','MarkerSize',50);
h4=plot(x,y,'k-','MarkerSize',25,'LineWidth',3);

legend([h1;h2;h3;h4],{'Upper limit','Lower limit','Middle','Constrained'},'Location','Northwest');

axis tight; 
set(gca,'FontSize',25);
grid on; box on; 
drawnow; 

%% Example: Assymetric mappings

m=1; %The middle
lb=0; %The lower bound
ub=10; %The upper bound

x=linspace(m-20,m+20,1000); % x paremeters for plotting

[y]=boxconstrain(x,lb,ub,m);

%%

cFigure; hold on;
xlabel('x'); ylabel('Constrained x'); 
h1=plot([min(x) max(x)],[ub ub],'b--','LineWidth',3);
h2=plot([min(x) max(x)],[lb lb],'r--','LineWidth',3);
h3=plot(m,m,'k.','MarkerSize',50);
h4=plot(x,y,'k-','MarkerSize',25,'LineWidth',3);

legend([h1;h2;h3;h4],{'Upper limit','Lower limit','Middle','Constrained'},'Location','Northwest');

axis tight; 
set(gca,'FontSize',25);
grid on; box on; 
drawnow; 

%% Example: Custom slop

m=5; %The middle
lb=0; %The lower bound
ub=10; %The upper bound
s=0.5; %Slope at the middle

x=linspace(m-20,m+20,1000); % x paremeters for plotting

[y]=boxconstrain(x,lb,ub,m,s);

%%

cFigure; hold on;
xlabel('x'); ylabel('Constrained x'); 
h1=plot([min(x) max(x)],[ub ub],'b--','LineWidth',3);
h2=plot([min(x) max(x)],[lb lb],'r--','LineWidth',3);
h3=plot(m,m,'k.','MarkerSize',50);
h4=plot(x,y,'k-','MarkerSize',25,'LineWidth',3);

legend([h1;h2;h3;h4],{'Upper limit','Lower limit','Middle','Constrained'},'Location','Northwest');

axis tight; 
set(gca,'FontSize',25);
grid on; box on; 
drawnow; 

%% 
%
% <<gibbVerySmall.gif>>
% 
% _*GIBBON*_ 
% <www.gibboncode.org>
% 
% _Kevin Mattheus Moerman_, <gibbon.toolbox@gmail.com>
 
%% 
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% License: <https://github.com/gibbonCode/GIBBON/blob/master/LICENSE>
% 
% GIBBON: The Geometry and Image-based Bioengineering add-On. A toolbox for
% image segmentation, image-based modeling, meshing, and finite element
% analysis.
% 
% Copyright (C) 2006-2022 Kevin Mattheus Moerman and the GIBBON contributors
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% This program is free software: you can redistribute it and/or modify
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