How to perform the derivation of a symbolic vector on an symbolic function?

Hello,

I would like to perform a derivation of a function containing symbolic vectors and matrices.

As an example:

a = sym('a', [3 3], 'real');
b = sym('b', [3 1], 'real');
c = sym('c', [3 1], 'real');

d = a*b + c

diff(d,c)

Here I get an error saying:

Error using sym/diff (line 70) Second argument must be a variable or a nonnegative integer specifying the number of differentiations.

The problem is that C is defined as:

c =

   c1
   c2
   c3

And this way I cannot differentiate for c. I also tried to define separate symbols c1 c2 c3 but this does not work either.

[Christopher Creutzig]

Are you maybe looking for jacobian(a*b+c,c)?

[Chris B]

Yes that was it, tank you.

Answer 1

[Birdman]

The error that you get actually tells you what to do: Variable d is not a function of variable c. You need to indicate that d(c) and then do the operations. For example, let's consider the possible approaches:

1- Your initial case:

a = sym('a', [3 3], 'real');
b = sym('b', [3 1], 'real');
c = sym('c', [3 1], 'real');
d = a*b + c
diff(d,c)

d is not dependent on any of those variables, therefore its change according to c will not mean anything, which will end up zero mathematically. This is normal.

2- d being dependent on c:

a = sym('a', [3 3], 'real');
b = sym('b', [3 1], 'real');
c = sym('c', [3 1], 'real');
d(c) = a*b + c
diff(d,c)

This will either not work because c contains three elements. You need to specify according to which element of c you are taking derivative. For instance:

 >> diff(d,c(1))

 ans(c1, c2, c3) =

 1
 0
 0

 >> diff(d,c(2))

 ans(c1, c2, c3) =

 0
 1
 0

Hope this helps.

[Christopher Creutzig]

The d(c) step is not needed. It's perfectly reasonable to call diff(a*b+c,c(1)).

[Birdman]

It is written to show how to define a function dependent on a variable symbolically. Of course, it can be eliminated.