something strange with test 2, my implementation fails on this test (because two iterations take me considerably closer to the minimum), perhaps this is something to do with the different forms of linesearch we are using?
Test case 2 is changed to account for your subsequent comment and to also to be far enough away from the solution so that it cannot converge in 2 iterations.
Test | Status | Code Input and Output |
---|---|---|
1 | Pass |
%%
% Rosenbrock's banana function
F=@(x) 100*(x(2)-x(1).^2).^2 + (1-x(1)).^2;
gradF=@(x) [100*(4*x(1).^3-4*x(1).*x(2))+2*x(1)-2; 100*(2*x(2)-2*x(1).^2)];
x0 = [-1.9; 2.0];
x1=[
-1.4478
2.1184];
x2=[
1.7064
2.9446];
f1=6.0419;
f2=0.6068;
[xmin,fmin]=ConjGrad(F,gradF,x0,0.01,1) % single steepest descent
assert(norm(xmin-x1)<0.2||norm(xmin-x2)<0.2)
assert( abs(fmin-f1)<0.5|| abs(fmin-f2)<0.5) % 2 local min
xmin =
-1.4522
2.1173
fmin =
6.0204
|
2 | Pass |
%%
% Rosenbrock's banana function
F=@(x) 100*(x(2)-x(1).^2).^2 + (1-x(1)).^2;
gradF=@(x) [100*(4*x(1).^3-4*x(1).*x(2))+2*x(1)-2; 100*(2*x(2)-2*x(1).^2)];
x0 = [0; 0];
xcorrect=[
0.2926
0.0505];
fcorrect=0.6238;
[xmin,fmin]=ConjGrad(F,gradF,x0,1e-2,2) % two iterations
assert(norm(xmin-xcorrect)<0.1)
assert( abs(fmin-fcorrect)<0.01)
xmin =
0.2931
0.0507
fmin =
0.6236
|
3 | Pass |
%%
% Rosenbrock's banana function
F=@(x) 100*(x(2)-x(1).^2).^2 + (1-x(1)).^2;
gradF=@(x) [100*(4*x(1).^3-4*x(1).*x(2))+2*x(1)-2; 100*(2*x(2)-2*x(1).^2)];
x0 = [1.1;0.9];
xcorrect = [1;1];
fcorrect = 0;
[xmin,fmin]=ConjGrad(F,gradF,x0) % default 20 iterations
assert(norm(xmin-xcorrect)<0.1)
assert(abs(fmin-fcorrect)<0.01);
xmin =
1.0005
1.0010
fmin =
2.5719e-07
|
4 | Pass |
%%
% Rosenbrock's banana function
F=@(x) 100*(x(2)-x(1).^2).^2 + (1-x(1)).^2;
gradF=@(x) [100*(4*x(1).^3-4*x(1).*x(2))+2*x(1)-2; 100*(2*x(2)-2*x(1).^2)];
x0 = [0; 0];
xcorrect = [1;1];
fcorrect = 0;
[xmin,fmin]=ConjGrad(F,gradF,x0,0.01,100) % Convergence before 100 iterations
assert(norm(xmin-xcorrect)<0.1)
assert(abs(fmin-fcorrect)<0.01);
xmin =
0.9989
0.9977
fmin =
1.3062e-06
|
5 | Pass |
%%
% Rosenbrock's banana function
F=@(x) 100*(x(2)-x(1).^2).^2 + (1-x(1)).^2;
gradF=@(x) [100*(4*x(1).^3-4*x(1).*x(2))+2*x(1)-2; 100*(2*x(2)-2*x(1).^2)];
x0 = [-1.9; 2];
xcorrect = [1;1];
fcorrect = 0;
[xmin,fmin]=ConjGrad(F,gradF,x0,1e-3,200)
assert(isequal(round(xmin),xcorrect))
assert(isequal(round(fmin),fcorrect))
xmin =
0.9998
0.9997
fmin =
2.4865e-08
|
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