How can I define norm of a vector as a symbolic function?

I have defined the symbolic function as follows:

syms g(x,w)
g(x,w) = norm(w);

Then I have tested it using a symbolic variable:

v = sym('v', [1,2]);
g(x,v)

It only gives me the magnitude of of each entry of the vector, rather than the magnitude of the whole vector which is what I want:

ans =
 
[ (abs(v1)^2)^(1/2), (abs(v2)^2)^(1/2)]

How can I change it so it yields the norm of the whole vector? I would greatly appreciate your help!

Answer 1

[Stephan]

Hi,

try:

syms g(x,v)
v = sym('v', [1,3]);
g(x,v) = norm(v)

g(x, v1, v2, v3) =
 
(abs(v1)^2 + abs(v2)^2 + abs(v3)^2)^(1/2)

>> pretty(g)
         2       2       2
sqrt(|v1|  + |v2|  + |v3| )

Best regards

Stephan

[Jeff Lau]

Thanks for your comment. Also,I would like to be able to alter the size of the vector. (i.e v could be [1,4], [1,20] or even [1,100] etc.) Is there a way so that you don't need to specify the entries of v? (It would be quite time-consuming to type v1 up to v100 haha)

[Stephan]

You can:

v_elements = 10
syms g(x,v)
v = sym('v', [1,v_elements]);
g(x,v) = norm(v)
pretty(g)

with result:

         2       2       2       2       2       2       2       2       2        2
sqrt(|v1|  + |v2|  + |v3|  + |v4|  + |v5|  + |v6|  + |v7|  + |v8|  + |v9|  + |v10| )

If needed you could write a function with the length of v as input argument and as the result it gives the symbolic expression back:

result = give_symbolic_norm(6)

function result =  give_symbolic_norm(num_v_elements)
syms g(x,v)
v = sym('v', [1,num_v_elements]);
g(x,v) = norm(v);
result = g;
end

With result:

result(x, v1, v2, v3, v4, v5, v6) =
 
(abs(v1)^2 + abs(v2)^2 + abs(v3)^2 + abs(v4)^2 + abs(v5)^2 + abs(v6)^2)^(1/2)
 

This has the advantage, that your base workspace keeps clean and only the resulting symbolic function is in it:

>> whos
  Name        Size            Bytes  Class     Attributes

  result      1x1                 8  symfun