parLimNat

Below is a demonstration of the features of the parLimNat function

Contents

Syntax

[xx,S]=parLimNat(xx_c,[xx_min xx_max],x);

Description

The parLimNat function can be used to constrain parameters from [-inf,inf] to the range [xx_min xx_max] with the values xx_c at its centre. The constraining can be used in combination with optimization routinges that do not naturally handle parameter constraints.

Examples

clear; close all; clc;

PLOT SETTINGS

fontSize=25;
fontSize2=15;
markerSize=45;
lineWidth1=2;
lineWidth2=1;

Example: Constraining parameters (normal centre)

xx_c=5;
xx_min=4;
xx_max=10;
x=linspace(xx_c-10,xx_c+10,250);
[xx,S]=parLimNat(xx_c,[xx_min xx_max],x);

hf1=cFigure; hold on; grid on;
title('Constraining using parLimNat','FontSize',fontSize);
xlabel('"free" x','FontSize',fontSize); ylabel('constrained x','FontSize',fontSize);

hf=plot(x,xx,'r-','LineWidth',lineWidth1);
hf=plot(xx_min,xx_min,'k.','markerSize',markerSize);
hf=plot(xx_max,xx_max,'k.','markerSize',markerSize);
plot(xx_c,xx_c,'k.','markerSize',markerSize);

text(xx_c+0.5,xx_c,'xx_c = centre','Interpreter','none','FontSize',fontSize2);
text(xx_max,xx_max-0.5,'xx_max = upper bound','Interpreter','none','FontSize',fontSize2);
text(xx_min-2.5,xx_min+0.5,'xx_min = lower bound','Interpreter','none','FontSize',fontSize2);

axis tight; axis equal;
set(gca,'FontSize',fontSize);
drawnow;

Example: Constraining parameters (out of centre centre)

xx_c=2;
xx_min=0;
xx_max=10;
x=linspace(xx_c-10,xx_c+15,100);
[xx,S]=parLimNat(xx_c,[xx_min xx_max],x);

hf1=cFigure; hold on; grid on;
title('Constraining using parLimNat','FontSize',fontSize);
xlabel('"free" x','FontSize',fontSize); ylabel('constrained x','FontSize',fontSize);

hf=plot(x,xx,'r-','LineWidth',lineWidth1);
hf=plot(xx_min,xx_min,'k.','markerSize',markerSize);
hf=plot(xx_max,xx_max,'k.','markerSize',markerSize);
plot(xx_c,xx_c,'k.','markerSize',markerSize);

text(xx_c+0.5,xx_c,'xx_c = centre','Interpreter','none','FontSize',fontSize2);
text(xx_max,xx_max-0.5,'xx_max = upper bound','Interpreter','none','FontSize',fontSize2);
text(xx_min-2.5,xx_min+0.5,'xx_min = lower bound','Interpreter','none','FontSize',fontSize2);

axis tight; axis equal;
set(gca,'FontSize',fontSize);
drawnow;

GIBBON www.gibboncode.org

Kevin Mattheus Moerman, [email protected]

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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) 2017 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.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/.