0001 function realtest_AD2()
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 problem.M = powermanifold(S,2);
0024
0025
0026 problem.cost = @(X) -X{1}'*(A*X{2});
0027
0028
0029 problem = manoptAD(problem);
0030
0031
0032 figure;
0033 checkgradient(problem);
0034 figure;
0035 checkhessian(problem);
0036
0037
0038 [x, xcost, info] = trustregions(problem);
0039
0040
0041 ground_truth = svd(A);
0042 distance = abs(ground_truth(1) - (-problem.cost(x)));
0043 fprintf('The distance between the ground truth and the solution is %e \n',distance);
0044
0045
0046 end