Adaptive Robust Numerical Differentiation
27 Dec 2006
01 Jun 2011)
Numerical derivative of an analytically supplied function, also gradient, Jacobian & Hessian
function [dd,err,finaldelta] = directionaldiff(fun,x0,vec)
% directionaldiff: estimate of the directional derivative of a function of n variables
% usage: [grad,err,finaldelta] = directionaldiff(fun,x0,vec)
% Uses derivest to provide both a directional derivative
% estimates plus an error estimates. fun needs not be vectorized.
% arguments: (input)
% fun - analytical function to differentiate. fun must
% be a function of the vector or array x0. Fun needs
% not be vectorized.
% x0 - vector location at which to differentiate fun
% If x0 is an nxm array, then fun is assumed to be
% a function of n*m variables.
% vec - vector defining the line along which to take the
% derivative. Vec should be the same size as x0. It
% need not be a vector of unit length.
% arguments: (output)
% dd - scalar estimate of the first derivative of fun
% in the SPECIFIED direction.
% err - error estimate of the directional derivative
% finaldelta - vector of final step sizes chosen for
% each partial derivative.
% At the global minimizer (1,1) of the Rosenbrock function,
% compute the directional derivative in the direction [1 2]
% It should be 0.
% rosen = @(x) (1-x(1)).^2 + 105*(x(2)-x(1).^2).^2;
% [dd,err] = directionaldiff(rosen,[1 1])
% dd =
% err =
% See also: derivest, gradest, gradient
% Author: John D'Errico
% e-mail: firstname.lastname@example.org
% Release: 1.0
% Release date: 3/5/2007
% get the size of x0 so we can make sure vec is
% the same shape.
sx = size(x0);
error 'vec and x0 must be the same sizes'
vec = vec(:);
vec = vec/norm(vec);
vec = reshape(vec,sx);
[dd,err,finaldelta] = derivest(@(t) fun(x0+t*vec), ...
end % mainline function end