Skip to content
Switch branches/tags

Name already in use

A tag already exists with the provided branch name. Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. Are you sure you want to create this branch?
Go to file
Cannot retrieve contributors at this time
function checkgradient(problem, x, d)
% Checks the consistency of the cost function and the gradient.
% function checkgradient(problem)
% function checkgradient(problem, x)
% function checkgradient(problem, x, d)
% checkgradient performs a numerical test to check that the gradient
% defined in the problem structure agrees up to first order with the cost
% function at some point x, along some direction d. The test is based on a
% truncated Taylor series (see online Manopt documentation).
% It is also tested that the gradient is indeed a tangent vector.
% Both x and d are optional and will be sampled at random if omitted.
% See also: checkdiff checkhessian
% This file is part of Manopt:
% Original author: Nicolas Boumal, Dec. 30, 2012.
% Contributors:
% Change log:
% April 3, 2015 (NB):
% Works with the new StoreDB class system.
% Nov. 1, 2016 (NB):
% Now calls checkdiff with force_gradient = true, instead of doing an
% rmfield of problem.diff. This became necessary after getGradient
% was updated to know how to compute the gradient from directional
% derivatives.
% Verify that the problem description is sufficient.
if ~canGetCost(problem)
% The call to canGetPartialGradient will readily issue a warning if
% problem.ncostterms is not defined even though it is expected.
if ~canGetPartialGradient(problem)
error('getCost:checkgradient', 'It seems no cost was provided.');
error('getCost:stochastic', ['It seems no cost was provided.\n' ...
'If you intend to use a stochastic solver, you still\n' ...
'need to define problem.cost to use checkgradient.']);
if ~canGetGradient(problem)
warning('manopt:checkgradient:nograd', ...
'It seems no gradient was provided.');
x_isprovided = exist('x', 'var') && ~isempty(x);
d_isprovided = exist('d', 'var') && ~isempty(d);
if ~x_isprovided && d_isprovided
error('If d is provided, x must be too, since d is tangent at x.');
% If x and / or d are not specified, pick them at random.
if ~x_isprovided
x = problem.M.rand();
if ~d_isprovided
d = problem.M.randvec(x);
%% Check that the gradient yields a first order model of the cost.
% Call checkdiff with force_gradient set to true, to force that
% function to make a gradient call.
checkdiff(problem, x, d, true);
title(sprintf(['Gradient check.\nThe slope of the continuous line ' ...
'should match that of the dashed\n(reference) line ' ...
'over at least a few orders of magnitude for h.']));
ylabel('Approximation error');
%% Try to check that the gradient is a tangent vector.
if isfield(problem.M, 'tangent')
storedb = StoreDB();
key = storedb.getNewKey();
grad = getGradient(problem, x, storedb, key);
pgrad = problem.M.tangent(x, grad);
residual = problem.M.lincomb(x, 1, grad, -1, pgrad);
err = problem.M.norm(x, residual);
fprintf('The residual should be 0, or very close. Residual: %g.\n', err);
fprintf('If it is far from 0, then the gradient is not in the tangent space.\n');
fprintf('In certain cases (e.g., hyperbolicfactory), the tangency test is inconclusive.\n');
fprintf(['Unfortunately, Manopt was unable to verify that the '...
'gradient is indeed a tangent vector.\nPlease verify ' ...
'this manually or implement the ''tangent'' function ' ...
'in your manifold structure.']);