%Ch 6: Numerical Techniques for Unconstrained Optimization
% Optimzation with MATLAB, Section 6.5.3
% copyright (code) Dr. P.Venkataraman
%
% Example 6.5.3 - Curfitting using Bezier curves
%
%
%************************************
% requires: DFP.m
% UpperBound_nVar.m
% GoldSection_nVar.m
%
% The example m-file: Example6_4.m
%
% This is run as a stand alone program
% The Bezier calculations are handles in
% Curve_fit.m
% Bez_Sq_Err.m
% Coefficient in coeff.m which requires
% Combination.m
% Factorial.m
%
%***************************************
% data must be available in an ascii File in which is
% two column of numeric data starting from the first row
% this file will be will be selected through a file selection box
%
global nBez A XX YY
global xv1 yv1 xv2 yv2
%********************************
% use a file selection box
%***********************************
[file,path] = uigetfile('*.txt','File of type text .txt ',200,200);
if isstr(file)
loadpathfile= ['load ',path,file];
eval(loadpathfile);
newname = strrep(file,'.txt','');
Data = eval(newname);
XX=Data(:,1);
YY=Data(:,2);
clear path loadpathfilename newname
end
nTotal =0;
nBez = 0;
nTotal = length(XX);
NTOTAL = num2str(nTotal);
%***************************************
% use an input dialg box to obtain order of curve
% String input must be converted to number
%^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Prompt ={'Enter the order of Bezier curve (between 2 and 10) used to track data'};
Title='Order of the Bezier curve';
Lineno = 1;
ok = 1;
while (ok)
answer = inputdlg(Prompt,Title,Lineno);
NBEZ = answer{1,1};
nBez = str2num(NBEZ);
if (nBez > 2) & (nBez < 10)
break;
else
Prompt ={'Please enter an order between 2 and 10'};
end
end
clear Prompt Title Lineno
% calculate Bezier Coeffifient matrix
% this depends on order and will not change for the rest of the calculations
A = coeff(nBez);
%*******************************************
% The design variables are the vertices of the
% Bezier polygons (except for the first and last vertices)
% Automatically guess the initial design using curve data
%*****************************************
XV(1) = XX(1);
xv1 = XV(1); % first vertex used elsewhere
XV(nBez+1) = XX(nTotal);
xv2 = XV(nBez+1); % last vertex - useful elsewhere
YV(1) = YY(1);
yv1 = YV(1);
YV(nBez+1) = YY(nTotal);
yv2 = YV(nBez+1);
for i = 2:nBez
ii = round((i-1)*(nTotal/nBez));
XV(i) = XX(ii);
%XVO(i)=XV(i);
YV(i) = YY(ii)*1.1;
%YVO(i) = YV(i);
end
% call the curve_fit routine
% this will call the DFP method
%
[VX,VY]= Curve_Fit(XV,YV);
DX = 1.0/(nTotal-1);
for i = 1:nTotal
gam = (i - 1)*DX;
for j = 1:nBez+ 1
k = nBez+1 - j;
GAM(j) = gam^k;
end
XYVert=[VX;VY]';
Xfit = GAM*A*XYVert;
XF(i) = Xfit(1);
YF(i) = Xfit(2);
end
plot(XX,YY,'ro',XF,YF,'b--')
title('Example 6-4: Curfit using Bezier curves')
xlabel('x - data (read from file)')
ylabel('y - data (read from file)')
grid
