function [gradient, delta] = gradchek(w, func, grad, varargin)%GRADCHEK Checks a user-defined gradient function using finite differences.%%	Description%	This function is intended as a utility for other netlab functions%	(particularly optimisation functions) to use.  It enables the user to%	check whether a gradient calculation has been correctly implmented%	for a given function. GRADCHEK(W, FUNC, GRAD) checks how accurate the%	gradient  GRAD of a function FUNC is at a parameter vector X.   A%	central difference formula with step size 1.0e-6 is used, and the%	results for both gradient function and finite difference%	approximation are printed. The optional return value GRADIENT is the%	gradient calculated using the function GRAD and the return value%	DELTA is the difference between the functional and finite difference%	methods of calculating the graident.%%	GRADCHEK(X, FUNC, GRAD, P1, P2, ...) allows additional arguments to%	be passed to FUNC and GRAD.%%	See also%	CONJGRAD, GRADDESC, HMC, OLGD, QUASINEW, SCG%%	Copyright (c) Ian T Nabney (1996-2001)% Reasonable value for step sizeepsilon = 1.0e-6;func = fcnchk(func, length(varargin));grad = fcnchk(grad, length(varargin));% Treatnparams = length(w);deltaf = zeros(1, nparams);step = zeros(1, nparams);for i = 1:nparams  % Move a small way in the ith coordinate of w  step(i) = 1.0;  fplus  = feval('linef', epsilon, func, w, step, varargin{:});  fminus = feval('linef', -epsilon, func, w, step, varargin{:});  % Use central difference formula for approximation  deltaf(i) = 0.5*(fplus - fminus)/epsilon;  step(i) = 0.0;endgradient = feval(grad, w, varargin{:});fprintf(1, 'Checking gradient ...\n\n');delta = gradient - deltaf;fprintf(1, '   analytic   diffs     delta\n\n');disp([gradient', deltaf', delta'])