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

Solution 172733

Submitted on 5 Dec 2012 by @bmtran

Correct

304Size
Leading solution size is 76.
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]=SteepestDescent(F,gradF,x0,0.01,1)
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
iter alpha f(alpha)  norm(c)
      0 0.000 267.6200 1270.8691
      1 0.000   6.0719  14.1065
xmin =
   -1.4452
    2.1191
fmin =
    6.0719
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=[1;1];
fcorrect=0;
[xmin,fmin]=SteepestDescent(F,gradF,x0) % 20 iterations default
assert(norm((xmin-xcorrect),inf)<1)
assert(abs(fmin-fcorrect)<0.8);
iter alpha f(alpha)  norm(c)
      0 0.000   1.0000   2.0000
     20 0.005   0.3983   1.2496
xmin =
    0.3689
    0.1360
fmin =
    0.3983
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]=SteepestDescent(F,gradF,x0,1e-2,2000)
assert(isequal(round(xmin),xcorrect))
assert(isequal(round(fmin),fcorrect))
iter alpha f(alpha)  norm(c)
      0 0.000   9.6200 150.0119
    298 0.001   0.0001   0.0100
xmin =
    0.9897
    0.9794
fmin =
   1.0730e-04