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How to generate symbolic variables dynamically at run-time?

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Ali
Ali 2011-1-21
评论： Steven Lord 2019-4-8
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."
  1 个评论
Christopher Creutzig
Christopher Creutzig 2011-1-24
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.

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采纳的回答

Kenneth Eaton
Kenneth Eaton 2011-1-24
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
  4 个评论
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Andrew Newell
Andrew Newell 2011-1-26
Interesting. Any idea why it won't accept Q12 without quotes?
Kenneth Eaton
Kenneth Eaton 2011-1-26
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.

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更多回答（2 个）

Walter Roberson
Walter Roberson 2011-1-21
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.
  2 个评论
Ali
Ali 2011-1-24
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

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Viki
Viki 2019-4-8
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

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