Question

I am trying to differentiate the following symbolic expression using a created symbolic vector but I keep getting errors. That is, I would like df/dx1, df/dx2, and df/dx3. Here is what I have tried:

>> x = sym('x', [3 1])

x =

 x1
 x2
 x3

>> symbolic = 0.5*transpose(x)*eye(1)*x + [1 1 1]*x

symbolic =

x1^2/2 + x1 + x2^2/2 + x2 + x3^2/2 + x3

>> diff(symbolic, x)
Error using mupadmex
Error in MuPAD command: Invalid argument. [contains]

  Evaluating: (Dom::Matrix(Dom::ExpressionField()))::_mult1

Error in sym/diff (line 44)
    R = mupadmex('symobj::diff', S.s, x.s, int2str(n));

>> diff(symbolic, x.x1)
Error using sym/subsref
Too many output arguments.

Any assistance would be greatly appreciated. Thanks!

Answer 1

You can try one of these two options:

% option 1
x = sym('x', [3 1]);
f = 0.5*transpose(x)*eye(1)*x + [1 1 1]*x;

for i=1:3
    Df(1,i) = diff(f, x(i));
end

% I do not like this option because I do not know 
% how to evaluate the expressions with numeric values
x(1) = 1;
eval(Df)

I prefer the ‘option 2’, because it is easier to evaluate expressions.

% option 2
syms x1 x2 x3 real; % 'real' fixes x1 x2 x3 as real numbers (not complex ones)
x = [x1 x2 x3]'; % '
f = 0.5*transpose(x)*eye(1)*x + [1 1 1]*x;

for i=1:3
    eval(['Df(1,i) = diff(f,x',num2str(i),');']);
end

% To eval at a certain value
x1 = 1;
x2 = 2;
x3 = 3;
eval(Df)

I think that eval has only the two functions I used above:

1. To eval symbolic expressions to specific values of the symbolic variables, like when I wrote eval(Df).

2. You can use eval to evaluate a matlab command written as a string, as if you were writing it as normal code. Try this to see what I mean:

   a = 1; % set value of a to 1

   eval(‘a = 2’); % change value of a to 2

   eval([‘a = ‘,num2str(5)]); % set value of a to 5;

Hope this helps,