Problem 481. Rosenbrock's Banana Function and its derivatives

Solution 60678

Submitted on 13 Mar 2012 by Charles Eger

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Test	Status	Code Input and Output
1	Pass	%% assert(isempty(regexp(fileread('Rosenbrock_banana.m'),'assert.m')))
2	Pass	%% x = [0; 0]; assert(isequal(Rosenbrock_banana(x),1))
3	Pass	%% x = [1; 1]; assert(isequal(Rosenbrock_banana(x),0))
4	Pass	%% x = [1; -1]; assert(isequal(Rosenbrock_banana(x),400))
5	Pass	%% x = [-1; 0.5]; assert(isequal(Rosenbrock_banana(x),29))
6	Pass	%% x = [0; 0]; [~,grad]=Rosenbrock_banana(x); assert(isequal(grad,[-2; 0]))
7	Pass	%% x = [0; 0]; [~,~,Hess]=Rosenbrock_banana(x); assert(isequal(Hess,diag([2, 200])))
8	Pass	%% x = [1; 1]; [~,grad]=Rosenbrock_banana(x); assert(isequal(grad,[0; 0]))
9	Pass	%% x = [1; 1]; [~,~,Hess]=Rosenbrock_banana(x); assert(isequal(Hess,[802, -400; -400, 200]))
10	Pass	%% x = [-1.9; 2]; correct_value = 267.6200; correct_grad = -1e3*[1.2294; 0.3220]; correct_Hess = [3534, 760; 760, 200]; [val,grad,Hess]=Rosenbrock_banana(x); assert(isequal(str2num(num2str(val)),correct_value)) assert(isequal(str2num(num2str(grad)),correct_grad)) assert(all(max(abs(Hess-correct_Hess)<1e-8)))

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