DIRDIFF

Directional derivative

Description

Xpf = dirdiff(X,f,p)

generates directional derivative of symbolic scalar function f at the point p in the direction of symbolic vector X(p). p must be a cell array {p1,p2,..pn} of doubles or symbolic variables.

examples
syms x1 x2 x3 y1 y2 y3
X = [ 2*x3 - x1^2 ; x1^3 - x3^2 ; x2^4 ] ;
f = x1^2 + x2^2 + x3^2 ;
dirdiff(X,f,{2,0,3}) returns Xpf = 3.5777
dirdiff(X,f,{y1,0,0}) returns Xpf = -2*y1^3/(y1^4+y1^6)^(1/2)

• Required Products: Symbolic Math Toolbox
• MATLAB release: MATLAB 7 (R14)

[Centi Riccardo]

Function directionally derivative can be calcolated faster in the following way

syms a;
syms f1;
f1 = subs(f,x + a*X);
Xpdf = subs(diff ((f1-f),a),a,0)

[Riccardo Centi]

% if F is a surface its directional
% derivative at the point x in the
% direction r can be expressed
% DF(x,r) = D(F(x+a*r,r) - F(x))/da with a = 0

syms a;
syms f1;
f1 = subs(f,x,x + a*r);
Xpdf = subs(diff ((f1-f),a),a,0)