plotprofile

 Plot the cost function along a geodesic or a retraction path.

 function plotprofile(problem)
 function plotprofile(problem, x)
 function plotprofile(problem, x, d)
 function plotprofile(problem, x, d, t)
 function plotprofile(problem, x, [], t)
 function plotprofile(problem, [], [], t)

 function costs = plotprofile(problem, x, d, t)

 Plot profile evaluates the cost function along a geodesic gamma(t) such
 that gamma(0) = x and the derivative of gamma at 0 is the direction d.
 The input t is a vector specifying for which values of t we must evaluate
 f(gamma(t)) (it may include negative values).

 If the function is called with an output, the plot is not drawn and the
 values of the cost are returned for the instants t.

 If x is omitted, a random point is picked. If d is omitted, a random
 tangent vector at x is picked. If t is omitted, it is generated as a
 linspace over [-1, 1].

0001 function cost = plotprofile(problem, x, d, t)
0002 % Plot the cost function along a geodesic or a retraction path.
0003 %
0004 % function plotprofile(problem)
0005 % function plotprofile(problem, x)
0006 % function plotprofile(problem, x, d)
0007 % function plotprofile(problem, x, d, t)
0008 % function plotprofile(problem, x, [], t)
0009 % function plotprofile(problem, [], [], t)
0010 %
0011 % function costs = plotprofile(problem, x, d, t)
0012 %
0013 % Plot profile evaluates the cost function along a geodesic gamma(t) such
0014 % that gamma(0) = x and the derivative of gamma at 0 is the direction d.
0015 % The input t is a vector specifying for which values of t we must evaluate
0016 % f(gamma(t)) (it may include negative values).
0017 %
0018 % If the function is called with an output, the plot is not drawn and the
0019 % values of the cost are returned for the instants t.
0020 %
0021 % If x is omitted, a random point is picked. If d is omitted, a random
0022 % tangent vector at x is picked. If t is omitted, it is generated as a
0023 % linspace over [-1, 1].
0024 
0025 % This file is part of Manopt: www.manopt.org.
0026 % Original author: Nicolas Boumal, Jan. 9, 2013.
0027 % Contributors:
0028 % Change log:
0029 %
0030 %   April 3, 2015 (NB):
0031 %       Works with the new StoreDB class system.
0032 %
0033 %   Nov. 12, 2016 (NB):
0034 %       Making more inputs optional.
0035 
0036     % Verify that the problem description is sufficient.
0037     if ~canGetCost(problem)
0038         error('It seems no cost was provided.');  
0039     end
0040     
0041     if ~exist('x', 'var') || isempty(x)
0042         x = problem.M.rand();
0043         if exist('d', 'var') && ~isempty(d)
0044             error('If x is omitted, d should not be specified.');
0045         end
0046     end
0047     if ~exist('d', 'var') || isempty(d)
0048         d = problem.M.randvec(x);
0049     end
0050     if ~exist('t', 'var') || isempty(t)
0051         t = linspace(-1, 1, 101);
0052     end
0053     
0054     if isfield(problem.M, 'exp')
0055         expo = problem.M.exp;
0056         str = 'Exp';
0057     else
0058         expo = problem.M.retr;
0059         str = 'Retr';
0060     end
0061     
0062     storedb = StoreDB();
0063     linesearch_fun = @(t) getCost(problem, expo(x, d, t), storedb);
0064     
0065     cost = zeros(size(t));
0066     for i = 1 : numel(t)
0067         cost(i) = linesearch_fun(t(i));
0068     end
0069     
0070     if nargout == 0
0071         plot(t, cost);
0072         xlabel('t');
0073         ylabel(['f(' str '_x(t*d))']);
0074     end
0075     
0076 end