Symbolic Functions of Symbolic Vectors

I have a function where x and y are both vectors of an arbitrary length. The function d is a small part which appears many times in a larger function and I'd like to be able to have the derivatives of d show up as as opposed to the behavior that occurs if I fully define . However, if I try to do this with something like:

syms d(x,y) real

syms x y real [1 4]

I'll end up with vectors:

x = [x1, x2, x3, x4]

y = [y1, y2, y3, y4]

Which means that if I take the Jacobian of this function I get:

jacobian(d,x) = [0,0,0,0]

As opposed to something like:

jacobian(d,x) = [diff(d,x1), diff(d,x2), ....]

Which is my desired behavior.

Additionally, if I use syntax like:

syms x [1 4]

syms d(x) [1 4] matrix keepargs

jacobian(d,x)

I get the error:

Incorrect number or types of inputs or outputs for function 'jacobian'.

And if I use the syntax:

syms x [1 4] matrix

syms d(x) [1 4] matrix keepargs

diff(d,x)

I get the output:

diff(d(x), x)

Calling Jacobian gives the same error as before and attempting to differentiate w/r.t. any of the variables within symmatrix x throws an error saying it isn't a recognized variable.

Does anyone know how to get that behavior? In this case would I need to explicitly define something like ?

I'm working on r2023a right now if that helps.

Answer 1

[Raghvi]

I understand that you are trying to figure out the partial derivatives of your function using the “Jacobian” function, and your desired output is jacobian(d,x) = [diff(d,x1), diff(d,x2), ....]

The following piece of code worked for me:

>> syms x y [1 4] real 
>> d(x,y)= sqrt((x-x0).^2 + (y-y0).^2); 
>> jacobian(d,x) 

For more information on Jacobian, you can refer to the documentation:

https://www.mathworks.com/help/symbolic/sym.jacobian.html