How do you create a symbolic function of symbolic vectors?

What I'm trying to write is this:

syms T real
r=sym('r', [1 3], 'real');
v=sym('v', [1 3], 'real');
pv=sym('pv', [1 3], 'real');
pr=sym('pr', [1 3], 'real');
u=sym('u', [1 3], 'real');
syms Drag(r,v)
f = dot(pr, v) + dot(pv,( - 1/norm(r)^3 * r + T * u - Drag))

Error using dot
A and B must be same size.

subexpr(simplify(-gradient(f,[r])))
subexpr(simplify(-gradient(f,[v])))

What I want is to get an expression out that has the partial derivatives of the Drag function with respect to r and v (allowing me to divide-and-conquer and go on and symbolically differentiate the actual Drag function).

What I'm getting is that the syms Drag(r,v) line replaces the definitions that I have of r and v with 1x1 symbols and then the dot(pr,v) operation fails with "A and B must be the same size".

I'm not sure that the question that I've asked is correct, but I'd like Drag to be a vector-valued function of the r and v vectors (without giving the actual expression for Drag).

Answer 1

[Walter Roberson]

Have a look at this:

syms x [1,2]
syms y [1,2]
f(x,y) = x.^2 + y.^2

f(x1, x2, y1, y2) = 

Notice that the resulting function is a function with four inputs, not a function with two inputs.

It is not possible in MATLAB to define a symbolic function that accepts vectors in positions and treats them as vectors in the calculations.

You can define

syms X
g(X) = X.^2

g(X) = 

g(x)

ans = 

That is, you can define a function that operates on scalar variables but when called with vectors does element-wise calculations (under restrictions -- there are definitely times this does not work out.) You can use vector-valued names in a function -- but if you use the vector-valued variables as the dummy variables standing in for what is being passed in, then the function will treat each one as a separate parameter.

You can use the relatively new symmatrix to write formulas in which the names are understood to stand in for fixed-sized vectors or arrays -- however, you cannot create a function from them. You can symmatrix2sym to convert to something that can appear on the right side of a symbolic function definition... but as soon as you convert the left side as well, you run into the problem that the names will each expand to a separate parameter.