Cody

# Problem 485. Fletcher-Reeves Conjugate Gradient Method

Solution 63108

Submitted on 19 Mar 2012 by Scott Bacvinskas
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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

iter alpha f(alpha) norm(c) 0 0.000 267.6200 1270.8691 1 0.003 0.6068 1270.8691 1 0.003 0.6068 1270.8691 xmin = 1.7064 2.9446 fmin = 0.6068

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)

iter alpha f(alpha) norm(c) 0 0.000 1.0000 2.0000 1 0.081 0.7711 2.0000 2 0.010 0.6236 5.1997 xmin = 0.2927 0.0506 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);

iter alpha f(alpha) norm(c) 0 0.000 9.6200 150.0119 1 0.001 0.0006 150.0119 5 0.001 0.0000 0.0040 xmin = 0.9992 0.9983 fmin = 6.8127e-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);

iter alpha f(alpha) norm(c) 0 0.000 1.0000 2.0000 1 0.081 0.7711 2.0000 13 0.009 0.0001 0.0094 xmin = 1.0104 1.0209 fmin = 1.0792e-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))

iter alpha f(alpha) norm(c) 0 0.000 267.6200 1270.8691 1 0.003 0.6068 1270.8691 23 0.210 0.0000 0.0001 xmin = 0.9999 0.9997 fmin = 2.4635e-08

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