How do I know if an element in a syms vector is assigned (MATLAB)?

Question

Define a syms vector

f = sym('f', [1 100]);

Define a syms variable x

syms x

The elements in vector f may be accessed and assigned, e.g.,

f(i) = x

Given any k, then how do I know if f(k) is assigned?

Answer 1

Short answer

Let k be the index of the entry of f to be inspected. Then

isAssigned = ~isempty(whos(char(f(k))));

is true (or 1) if the k-th entry of f has been assigned and false (or 0) otherwise.

Long answer

From the documentation (boldface added)

A = sym('a',[m,n]) creates an m-by-n symbolic matrix filled with automatically generated elements. The generated elements do not appear in the MATLAB workspace.

For example,

>> clear all
>> f = sym('f', [1 10])
>> f =
[ f1, f2, f3, f4, f5, f6, f7, f8, f9, f10]
>> whos
  Name      Size            Bytes  Class    Attributes

  f         1x10              112  sym

which indeed shows that f1, f2 etc don't appear in the workspace. However, if you then assign

>> syms x;
>> f(3) = x
f =
[ f1, f2, x, f4, f5, f6, f7, f8, f9, f10]

the variable x of course does appear in the workspace:

>> whos
  Name      Size            Bytes  Class    Attributes

  f         1x10              112  sym                
  x         1x1               112  sym   

So, a way to check if a particular entry of f has been assigned is to check for its existence in the workspace using the functional form of whos. Compare

>> whos('f2') %// produces no output because no variable f2 exists in the workspace

and

>> whos('x') %// produces output because variable x exists in the workspace
  Name      Size            Bytes  Class    Attributes

  x         1x1               112  sym                

Given the index k of the entry of f to be inspected, you can automatically generate the corresponding string ('f2' or 'x' in the above example) using char(f(k)):

>> k = 2;
>> char(f(k))
ans =
f2

>> k = 3;
>> char(f(k))
ans =
x    

It only remains to assign the output of whos(char(f(k))) to a variable, which will be empty if f(k) has not been assigned, and non-empty if it has been assigned:

>> k = 2;
>> t = whos(char(f(k)))
t = 
0x1 struct array with fields:
    name
    size
    bytes
    class
    global
    sparse
    complex
    nesting
    persistent

>> k = 3;
>> t = whos(char(f(k)))
t = 
          name: 'x'
          size: [1 1]
         bytes: 112
         class: 'sym'
        global: 0
        sparse: 0
       complex: 0
       nesting: [1x1 struct]
    persistent: 0

Thus, applying ~isempty to this t produces true (1) if the k-th entry of f has been assigned and false (0) otherwise:

>> k = 2;
>> isAssigned = ~isempty(whos(char(f(k))))
isAssigned =
     0

>> k = 3;
>> isAssigned = ~isempty(whos(char(f(k))))
isAssigned =
     1