echo on; clc;
%---------------------------------------------------------------------------
%A5_3 MATLAB script file for implementing Algorithm 5.3
%
% NUMERICAL METHODS: MATLAB Programs, (c) John H. Mathews 1995
% To accompany the text:
% NUMERICAL METHODS for Mathematics, Science and Engineering, 2nd Ed, 1992
% Prentice Hall, Englewood Cliffs, New Jersey, 07632, U.S.A.
% Prentice Hall, Inc.; USA, Canada, Mexico ISBN 0-13-624990-6
% Prentice Hall, International Editions: ISBN 0-13-625047-5
% This free software is compliments of the author.
% E-mail address: in%"mathews@fullerton.edu"
%
% Algorithm 5.3 (Non-linear Curve Fitting).
% Section 5.2, Curve Fitting, Page 280
%---------------------------------------------------------------------------
clc; clear all; format short;
% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
%
% This program performs curve fitting, by using
%
% the method of data linearization. Given a set of
%
% data points { (x , y ), (x , y ) ,..., (x , y ) }.
% 1 1 2 2 n n
%
% The abscissas and ordinates are stored in X and Y, respectively.
%
% X = [x , x ,..., x ]; Y = [y , y ,..., y ];
% 1 2 n 1 2 n
%
% Remark. crvfit.m crvfun.m crvnam.m are used for Algorithm 5.3
pause % Press any key to continue.
clc;
% - - - - - - - - - - - - - - - - - - - - - - - - - -
%
% Example, page 280 Find the least squares curve(s).
%
% Enter the abscissas for the points in X.
%
% Enter the ordinates for the points in Y.
X = [0.0001 1.0 2.0 3.0 4.0];
Y = [1.5000 2.5 3.5 5.0 7.5];
pause % Press any key to graph data points.
clc; figure(1); clf;
%~~~~~~~~~~~~~~~~~~~~~~~
% Begin graphics section
%~~~~~~~~~~~~~~~~~~~~~~~
a = min(X)-0.2;
b = max(X)+0.2;
c = min(Y)-1.0;
d = max(Y)+1.0;
whitebg('w');
plot([a b],[0 0],'b',[0 0],[c d],'b');
axis([a b c d]);
axis(axis);
hold on;
plot(X,Y,'or');
xlabel('x');
ylabel('y');
title('The given x-y data points.');
grid;
hold off;
figure(gcf); pause % Press any key to continue.
points = [X;Y];
clc;
%............................................
% Begin section to print the results.
% Diary commands are included which write all
% the results to the Matlab textfile output
%............................................
clc,disp('The given x-y points:'),...
disp(' x y'),disp(points')
pause % Press any key for the menu of curves.
clc;
Mx1=' Available curves are:';
Mx2='(1) y = A/x + B (2) y = D/(x + C) (3) y = 1/(Ax + B)';
Mx3='(4) y = x/(A + Bx) (5) y = A ln(X) + B (6) y = C exp(Ax)';
Mx4='(7) y = C x^A (8) y = 1/(Ax + B)^2';
Mx5='(9) y = C x exp(-Dx) (10) y = L/(1 + C exp(Ax))';
clc,disp(''),disp(Mx1),disp(''),disp(Mx2),disp(''),...
disp(Mx3),disp(''),disp(Mx4),disp(''),disp(Mx5),...
ct = input(' Enter the curve type <1-10> ');
pause % Press any key to fit the curve.
clc;
% ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
% Prepare graphics arrays
% ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
if length(ct)==0, ct=2; end
Clist = crvfit(X,Y,ct);
h = (b-a)/200;
Xs = a:h:b;
Ys = crvfun(Clist,ct,Xs);
clc; figure(2); clf;
%~~~~~~~~~~~~~~~~~~~~~~~
% Begin graphics section
%~~~~~~~~~~~~~~~~~~~~~~~
whitebg('w');
plot([a b],[0 0],'b',[0 0],[c d],'b');
axis([a b c d]);
axis(axis);
hold on;
plot(X,Y,'or',Xs,Ys,'-g');
xlabel('x');
ylabel('y');
title(crvnam(Clist,ct)); end;
grid;
hold off;
figure(gcf); pause % Press any key to continue.
% .. .. .. .. ..
% Prepare results
% .. .. .. .. ..
points = [X;Y;crvfun(Clist,ct,X);Y-Crvfun(Clist,ct,X)]';
clc;
%............................................
% Begin section to print the results.
% Diary commands are included which write all
% the results to the Matlab textfile output
%............................................
Mx1 = crvnam(Clist,ct);
Mx2 = 'The given x-y points:';
clc,echo off,diary output,...
disp(''),disp(Mx1),disp(''),disp(Mx2),...
disp(' x y'),disp(points'),diary off,echo on
pause % Press any key to continue.
Mx3=' x(k) y(k) f(x(k)) error';
clc,echo off,diary output,disp(''),...
disp([' ',Mx1]),disp(Mx3),disp(points),diary off, echo on
