How to generate symbolic variables dynamically at run-time?

I am trying to generate a set of equations for user input matrices.

For example, if the user inputs:

 [0 1 0 1;
  1 0 1 0;
  0 0 1 1];

I want to generate equations

Y1 = Q12 + Q44
Y2 = Q21 + Q31
Y3 = Q33 + Q44

and assign these equations to symbolic vars y1, y2, and y3.

 .

In addition, at some other point I want to be able to substitute values symbolic values for Q12 = P12 + R1, etc, and have all the equations automatically update all the symbolic values.

 .

I have tried to use:

y = sym(sprintf('q%d%d', [m k]))

method described here, but the matrix elements q12, q44, etc are not substitutable. These vars are not symbolic variable in themselves.

 .

The 'eval(..)' function and other symbolic manipulation functions cannot be used to simply/substitute other values.

I can do something like this:

syms q11, q12, q13, .. q44 etc

for all positions of the matrix, and then do:

Y = [q11, q12,..; ... q44]

but this is tedious and does not allow for a general function that handles any matrix of any size.

I guess, my question is how to dynamically create symbolic variables. I can generate a character string 'Q12', but then I can't seem to be able to convert it to a symbolic variable.

For example, if vars = {'Q12'}, then

char(vars(1)) = sym(char(vars(1)), 'real')

gives an error

"Conversion to double from cell is not possible."

[Christopher Creutzig]

What exactly do you mean by “assign these equations to symbolic vars y1, y2, and y3”? Also note that you can set Y = sym('q', [4 4]) as a shorthand for your tedious definition of Y.

Answer 1

[Kenneth Eaton]

You can generate your system of equations from a matrix of zeroes and ones using just the SYM function and some basic arithmetic operations like SUM and .* that are overloaded for symbolic objects:

>> C = [0 1 0 1; 1 0 1 0; 0 0 1 1];      % The sample input matrix
>> Q = sym(sym('Q%d%d',size(C)),'real')  % Create a matrix of Qxy variables

Q =

[ Q11, Q12, Q13, Q14]
[ Q21, Q22, Q23, Q24]
[ Q31, Q32, Q33, Q34]

>> Y = sum(sym(C).*Q,2)  % Perform element-wise multiplication of Q by a
                         %   symbolic version of C, then sum the result
Y =                      %   along the rows

   Q12 + Q14
   Q21 + Q23
   Q33 + Q34

[Andrew Newell]

The matrix Y behaves strangely if substitutions are attempted. For example:

syms P12 R1

subs(Y,Q12,P12+R1)

??? Undefined function or variable 'Q12'.

But this works:

syms Q12

subs(Y,Q12,P12+R1)

ans =

P12 + Q14 + R1

Q21 + Q23

Q33 + Q34

[Kenneth Eaton]

Andrew, you can do the substitution like so:

>> syms P12 R1

>> subs(Y,'Q12',P12+R1)

ans =

P12 + Q14 + R1

Q21 + Q23

Q33 + Q34

Note that Q12 is in quotes.

[Andrew Newell]

Interesting. Any idea why it won't accept Q12 without quotes?

[Kenneth Eaton]

I guess it doesn't accept Q12 because that isn't a symbolic variable *in the workspace*, just a symbolic variable *within the set of equations* in Y.

Answer 2

[Walter Roberson]

Your code,

if vars = {'Q12'}, then char(vars(1)) = sym(char(vars(1)), 'real')

would need to be

if isequal(vars, {'Q12'}), then char(vars(1)) = sym(char(vars{1}), 'real')

in order to be consistent.

Have you consider using

Q = sym('Q', size(UserMatrix));

Your example equations look inconsistent to me, by the way. I do not see how Q44 can occur in two of them.

[Ali]

Hello Walter,

Thank you for your reply.

The equations are inconsistent, it was a typo. It was a quick example I made up to describe what I was doing. The number of equations that I have is much larger.

The use of eval(sprintf(...)) I found to be very helpful in doing what I wanted Matlab to do.

I did try:

char(vars(1)) = sym(char(vars{1}), 'real')

but I still got am error.

But thank you for the reply.

Ali

[Walter Roberson]

Note: that sym() syntax with a size is R2010b or later.

Answer 3

[Viki]

Consider a symbolic matrix created as,

S = sym('s%d%d',[3,3], 'real');

It would fetch you

S =
 
[ s11, s12, s13]
[ s21, s22, s23]
[ s31, s32, s33]

Now, if you want to have each element of the symbolic matrix S as an independent symbolic variable; use the following code

for i = 1:3
    for j = 1:3
        feval('syms',S(i,j));
    end
end

[Steven Lord]

Doing this "poofs" variables into the workspace and should be discouraged for the reasons given here.