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Test Suite

Test
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]=BFGS_Quasi_Newton(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=[
    0.2927
    0.0506];
fcorrect=0.63;
[xmin,fmin]=BFGS_Quasi_Newton(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 =
    0.6237
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 = [0;0];
xcorrect = [1;1;];
fcorrect = 0;
[xmin,fmin]=BFGS_Quasi_Newton(F,gradF,x0)
assert(norm(xmin-xcorrect)<0.01)
assert(abs(fmin-fcorrect)<0.01);
xmin =
    0.9999
    0.9999
fmin =
   4.8016e-09
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)];
HessF=@(x) 200*[4*x(1).^2-2*(x(2)-x(1).^2)+1/100, -2*x(1);
                -2*x(1), 1];
xcorrect = [1;1];
fcorrect = 0;
x0 = [-1.9; 2];
[xmin,fmin]=BFGS_Quasi_Newton(F,gradF,x0,1e-4)
assert(isequal(round(xmin),xcorrect))
assert(isequal(round(fmin),fcorrect))
xmin =
    0.8262
    0.6697
fmin =
    0.0470