how to make a table of iterations
18 views (last 30 days)
Show older comments
i need help to make table of iterations to this code
tic
clear; clc; close all;
syms f(x,y) ph
% f(x,y)
f(x,y)=3*x^2+y^2;
% Initial Guess:
x0=[4;4];
% Gradient Computation:
g(x,y)=[diff(f(x,y),x) ; diff(f(x,y),y)];
fprintf('========================================\n');
g0=g(x0(1),x0(2));
XX=[x0(1)];
YY=[x0(2)];
ff=[f(x0(1),x0(2))];
fprintf('Loop 1\n');
x2(ph)=x0(1)-ph*g0(1);
y2(ph)=x0(2)-ph*g0(2);
G=-g(x2(ph),y2(ph)).*g0;
G=G(1)+G(2);
phsol=solve(G,ph);
X=x0(1)-phsol*g0(1);% New x value
Y=x0(2)-phsol*g0(2);% New y value
m=(Y-x0(2))/(X-x0(1));
%error=10^-20
err=10^-20;
ii=2;
fprintf('alpha=%.3f\n',phsol);
fprintf('x=%.3f y=%.3f\n',X,Y);
fprintf('f(Xnew,Ynew)=%.3f\n',f(X,Y));
fprintf('m=%.3f\n',m);
%relative norm
relnorm=sqrt((X-x0(1))^2/x0(1)^2 + (Y-x0(2))^2/x0(2)^2 );
fprintf('relative norm=%.3f\n',relnorm);
XX=[XX X];
YY=[YY Y];
ff=[ff f(X,Y)];
fprintf('========================================\n');
while(abs(f(X,Y) - f(x0(1),x0(2))) > err)
x0=[X,Y];
g0=g(x0(1),x0(2));
fprintf('Loop%d\n',ii);
x2(ph)=x0(1)-ph*g0(1);
y2(ph)=x0(2)-ph*g0(2);
G=-g(x2(ph),y2(ph)).*g0;
G=G(1)+G(2);
phsol=solve(G,ph);
X=x0(1)-phsol*g0(1);
Y=x0(2)-phsol*g0(2);
ii=ii+1;
% Output results
fprintf('alpha=%.3f\n',phsol);
fprintf('x=%.3f y=%.3f\n',X,Y);
fprintf('f(Xnew,Ynew)=%.3f\n',f(X,Y));
% m
m=(Y-x0(2))/(X-x0(1));
fprintf('m=%.3f\n',m);
% relative norm
relnorm=sqrt((X-x0(1))^2/x0(1)^2 + (Y-x0(2))^2/x0(2)^2 );
fprintf('relative norm=%.3f\n',relnorm);
XX=[XX X];
YY=[YY Y];
ff=[ff f(X,Y)];
fprintf('========================================\n');
end
% Plot Contour
xx=linspace(-5,5);
yy=linspace(-5,5);
[xx,yy] = meshgrid(xx,yy);
ff=3*xx.^2+yy.^2;
[x,y,z] = peaks(100);
v=[0.5,1,1.5,2,2.5];
[C,h] = contour(xx,yy,ff,[-90,-80 -70 -60 -50 -40 30 -20 -10 -5 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 5 10 20 30 40 50 60 70 80 90],'lineWidth',1.5);
clabel(C,h)
hold on
plot(XX,YY,'*-r');
xlabel('X')
ylabel('Y')
hold off
xlabel ('x')
ylabel ('y')
grid
fprintf('initial guess = (4,4)\n');
fprintf('error = 10^-20\n');
fprintf('Number of iteration = %d\n',ii-1);
toc
0 Comments
Answers (1)
KSSV
on 27 Apr 2023
The vairable T at the end is the required table. If you want it as an array check the variable iwant.
tic
clear; clc; close all;
syms f(x,y) ph
count = 1 ;
iwant = zeros([],7) ;
% f(x,y)
f(x,y)=3*x^2+y^2;
% Initial Guess:
x0=[4;4];
% Gradient Computation:
g(x,y)=[diff(f(x,y),x) ; diff(f(x,y),y)];
fprintf('========================================\n');
g0=g(x0(1),x0(2));
XX=[x0(1)];
YY=[x0(2)];
ff=[f(x0(1),x0(2))];
fprintf('Loop 1\n');
x2(ph)=x0(1)-ph*g0(1);
y2(ph)=x0(2)-ph*g0(2);
G=-g(x2(ph),y2(ph)).*g0;
G=G(1)+G(2);
phsol=solve(G,ph);
X=x0(1)-phsol*g0(1);% New x value
Y=x0(2)-phsol*g0(2);% New y value
m=(Y-x0(2))/(X-x0(1));
%error=10^-20
err=10^-20;
ii=2;
fprintf('alpha=%.3f\n',phsol);
fprintf('x=%.3f y=%.3f\n',X,Y);
fprintf('f(Xnew,Ynew)=%.3f\n',f(X,Y));
fprintf('m=%.3f\n',m);
%relative norm
relnorm=sqrt((X-x0(1))^2/x0(1)^2 + (Y-x0(2))^2/x0(2)^2 );
fprintf('relative norm=%.3f\n',relnorm);
fprintf('========================================\n');
iwant(count,:) = [count phsol X Y f(X,Y) m relnorm] ;
while(abs(f(X,Y) - f(x0(1),x0(2))) > err)
count = count+1 ;
x0=[X,Y];
g0=g(x0(1),x0(2));
fprintf('Loop%d\n',ii);
x2(ph)=x0(1)-ph*g0(1);
y2(ph)=x0(2)-ph*g0(2);
G=-g(x2(ph),y2(ph)).*g0;
G=G(1)+G(2);
phsol=solve(G,ph);
X=x0(1)-phsol*g0(1);
Y=x0(2)-phsol*g0(2);
ii=ii+1;
% Output results
fprintf('alpha=%.3f\n',phsol);
fprintf('x=%.3f y=%.3f\n',X,Y);
fprintf('f(Xnew,Ynew)=%.3f\n',f(X,Y));
% m
m=(Y-x0(2))/(X-x0(1));
fprintf('m=%.3f\n',m);
% relative norm
relnorm=sqrt((X-x0(1))^2/x0(1)^2 + (Y-x0(2))^2/x0(2)^2 );
fprintf('relative norm=%.3f\n',relnorm);
% XX=[XX X];
% YY=[YY Y];
% ff=[ff f(X,Y)];
fprintf('========================================\n');
iwant(count,:) = [count phsol X Y f(X,Y) m relnorm] ;
end
% Plot Contour
xx=linspace(-5,5);
yy=linspace(-5,5);
[xx,yy] = meshgrid(xx,yy);
ff=3*xx.^2+yy.^2;
[x,y,z] = peaks(100);
v=[0.5,1,1.5,2,2.5];
[C,h] = contour(xx,yy,ff,[-90,-80 -70 -60 -50 -40 30 -20 -10 -5 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 5 10 20 30 40 50 60 70 80 90],'lineWidth',1.5);
clabel(C,h)
hold on
plot(XX,YY,'*-r');
xlabel('X')
ylabel('Y')
hold off
xlabel ('x')
ylabel ('y')
grid
fprintf('initial guess = (4,4)\n');
fprintf('error = 10^-20\n');
fprintf('Number of iteration = %d\n',ii-1);
toc
T = array2table(iwant) ;
T.Properties.VariableNames = {'Loop','alpha','x','y','f(x,y)','m','relative_norm'};
T
0 Comments
See Also
Categories
Find more on Assembly in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!