# How to replace variables in symbolic function with values from a vector

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Suleyman Muti on 24 Oct 2016
Commented: Suleyman Muti on 25 Oct 2016
I am working on a simple optimization code that has to account for varying number of equations. Since the existence of a type of equation adds one more variable, and the code cannot know how many it will encounter, it creates variables based on the input.
For example, the symbolic function might be:
L = L(x1, x2, v1)
L = L(x1, x2, v1, u1, u2)
...
x = sym('x',[2 1]) % variables of objective function
v = sym('v',[p 1]) % input requires p more variables
v = sym('u',[m 1]) % input requires m more variables
k = vertcat(x,v,....) % all variables based on input
The code does symbolic differentiation on k(i), and after manipulations obtains a final function.
result = (x1 - 3)^2 + (x2 - 3)^2 - v1*(3*x2 - x1 + 1) + u1*(s1^2 + x1 + x2 - 4)
The code is able to calculate values for all of the variables that exist for a particular case.
k = [x1,x2, v1, u1, s1] = [ 13/4, 3/4, -5/4, 3/4, 0]
However, I was unable to substitute these values back in the symbolic functions "L", and "result" to calculate their actual numeric values at this point, and for plotting them.
I appreciate any help on this.

Marc Jakobi on 24 Oct 2016
You probably want the function
subs()

Suleyman Muti on 25 Oct 2016
How do I do this programmatically?
s1 is also a symbolic variable. So, if I have a result function like this at the workspace
result = x1^2 + x2^2 + v1 + v2 + u1 + s1
% then the variables are
xx = [x1;x2;v1;v2;u1;s1];
Number of u, v, and s variables depend on the particular problem that user inputs. I calculate the xx matrix values using solve(), and get the following which I convert to numerical values.
xx_result = [ 1, 2, 3, 4, 5, 6]
So, how do I programmatically substitude these into xx and calculate result function's value? I thought I could do
xx = xx_result;
and this would make symbolic values equal to their corresponding values. X1 = 1, x2 = 2, ... And then just type result and get its value. That did not work...
Thank you.
Marc Jakobi on 25 Oct 2016
subs(result, [x; v; u; s], k)
should work.
Suleyman Muti on 25 Oct 2016
Thank you Marc.