Discover MakerZone

MATLAB and Simulink resources for Arduino, LEGO, and Raspberry Pi

Learn more

Discover what MATLAB® can do for your career.

Opportunities for recent engineering grads.

Apply Today

Correct

106Size
This is the leading solution.
This solution is locked. To view this solution, you need to provide a solution of the same size or smaller.

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]=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 =
    0.9994
    0.9987
fmin =
   4.0173e-07