Cody

# Problem 485. Fletcher-Reeves Conjugate Gradient Method

Solution 666969

Submitted on 7 May 2015 by Ashley
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### Test Suite

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

Â Â Â iter alpha f(alpha)Â Â 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=[ 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)

Â Â Â iter alpha f(alpha)Â Â norm(c) 0 0.000 1.0000 2.0000 2 0.010 0.6238 7.5242 xmin = 0.2926 0.0505 fmin = 0.6238

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);

Â Â Â iter alpha f(alpha)Â Â norm(c) 0 0.000 9.6200 150.0119 4 0.001 0.0000 0.0099 xmin = 0.9991 0.9982 fmin = 8.1952e-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);

Â Â Â iter alpha f(alpha)Â Â norm(c) 0 0.000 1.0000 2.0000 12 0.001 0.0001 0.0096 xmin = 1.0106 1.0214 fmin = 1.1304e-04

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))

Â Â Â iter alpha f(alpha)Â Â norm(c) 0 0.000 267.6200 1270.8691 80 0.001 0.0000 0.0005 xmin = 1.0005 1.0011 fmin = 3.0282e-07

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