Partial differentiation/gradient of anonymous function with array input - arrays

Question

I have following anonymous function (with x as an array):
f = #(x) 312*x(2) - 240*x(1) + 30*x(3) - 24*x(4) + 282*x(1)*x(2) + 30*x(1)*x(3) + 18*x(1)*x(4) + 54*x(2)*x(3) + 6*x(2)*x(4) + 6*x(3)*x(4) + 638*x(1)^2 + 207*x(2)^2 + 6*x(3)^2 + 3*x(4)^2 + 4063
I want to make gradient of this function and save it for future use. Also with array input.
X = [ 0;...
0;...
0;...
0];
F = f(X)
G = g(X)
Is it possible to archive this with this type of function? Or maybe it is possible to somehow make it via diff command? Something like this:
g = [diff(f, x(1));...
diff(f, x(2));...
diff(f, x(3));...
diff(f, x(4))]

Answer 1

I guess the following is what you want. I'm afraid, you need the Symbolic Math Toolbox for a simple solution, otherwise I'd rather calculate the derivatives by hand.
x = [1 2 3 4];
%// define function
syms a b c d
f = 312*b - 240*a + 30*c - 24*d + 282*a*b + 30*a*c + 18*a*d + 54*b*c + ...
6*b*d + 6*c*d + 638*a^2 + 207*b^2 + 6*c^2 + 3*d^2 + 4063
%// symbolic gradient
g = gradient(f,[a,b,c,d])
%// eval symbolic function
F = subs(f,[a,b,c,d],x)
G = subs(g,[a,b,c,d],x)
%// convert symbolic value to double
Fd = double(F)
Gd = double(G)
or alternatively:
%// convert symbolic function to anonymous function
fd = matlabFunction(f)
gd = matlabFunction(g)
%// eval anonymous function
x = num2cell(x)
Fd = fd(x{:})
Gd = gd(x{:})
f =
638*a^2 + 282*a*b + 30*a*c + 18*a*d - 240*a + 207*b^2 + 54*b*c +
6*b*d + 312*b + 6*c^2 + 6*c*d + 30*c + 3*d^2 - 24*d + 4063
g =
1276*a + 282*b + 30*c + 18*d - 240
282*a + 414*b + 54*c + 6*d + 312
30*a + 54*b + 12*c + 6*d + 30
18*a + 6*b + 6*c + 6*d - 24
F =
7179
G =
1762
1608
228
48
fd =
#(a,b,c,d)a.*-2.4e2+b.*3.12e2+c.*3.0e1-d.*2.4e1+a.*b.*2.82e2+a.*c.*3.0e1+a.*d.*1.8e1+b.*c.*5.4e1+b.*d.*6.0+c.*d.*6.0+a.^2.*6.38e2+b.^2.*2.07e2+c.^2.*6.0+d.^2.*3.0+4.063e3
gd =
#(a,b,c,d)[a.*1.276e3+b.*2.82e2+c.*3.0e1+d.*1.8e1-2.4e2;a.*2.82e2+b.*4.14e2+c.*5.4e1+d.*6.0+3.12e2;a.*3.0e1+b.*5.4e1+c.*1.2e1+d.*6.0+3.0e1;a.*1.8e1+b.*6.0+c.*6.0+d.*6.0-2.4e1]
x =
[1] [2] [3] [4]
Fd =
7179
Gd =
1762
1608
228
48