0001 function realtest_AD1()
0002
0003
0004
0005 if isempty(which('spherefactory'))
0006 error(['You should first add Manopt to the Matlab path.\n' ...
0007 'Please run importmanopt.']);
0008 end
0009
0010
0011 assert(exist('dlarray', 'file') == 2, ['Deep learning tool box is '...
0012 'needed for automatic differentiation.\n Please install the'...
0013 'latest version of the deep learning tool box and \nupgrade to Matlab'...
0014 ' R2021b if possible.'])
0015
0016
0017 n = 100;
0018 A = randn(n);
0019 A = .5*(A+A');
0020
0021
0022 S = spherefactory(n);
0023 manifold.x = S;
0024 manifold.y = S;
0025 problem.M = productmanifold(manifold);
0026
0027
0028 problem.cost = @(X) -X.x'*(A*X.y);
0029
0030
0031 problem = manoptAD(problem);
0032
0033
0034 figure;
0035 checkgradient(problem);
0036 figure;
0037 checkhessian(problem);
0038
0039
0040 [x, xcost, info] = trustregions(problem);
0041
0042
0043 ground_truth = svd(A);
0044 distance = abs(ground_truth(1) - (-problem.cost(x)));
0045 fprintf('The distance between the ground truth and the solution is %e \n',distance);
0046
0047
0048 end