# 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;
```

GIBBON www.gibboncode.org

Kevin Mattheus Moerman, gibbon.toolbox@gmail.com

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GIBBON: The Geometry and Image-based Bioengineering add-On. A toolbox for image segmentation, image-based modeling, meshing, and finite element analysis.

Copyright (C) 2019 Kevin Mattheus Moerman

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

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