For loop of symbolic variables extracting symbolic coefficients

I want to create a certain number of symbolic variables without having to define them individually. I want to basically do something as the follows

for i = 1:length(m)+1 %m is some matrix input to a larger problem

syms x(i)

end

so that lets say if m has length 2 i can create 3 symbolic variables x1 x2 x3. Again these problems are larger than 2x2 and can grow and I would like to be able to automate the creation of the symbolic variables if possible.

The other questions I have is once I have created these symbolic variables and done some computations and create a matrix of symbolic equations is there a way to extract the coefficients of the symbolic matrix to another matrix?

Answer 1

[Walter Roberson]

This is seldom a good idea, for reasons similar to those described in http://matlab.wikia.com/wiki/FAQ#How_can_I_create_variables_A1.2C_A2.2C....2CA10_in_a_loop.3F

Have you considered symbolic arrays? R2010b and later gives an easy way to create those, http://www.mathworks.com/help/toolbox/symbolic/sym.html

A = sym('A',[m n]) creates a m-by-n matrix of symbolic variables. The dimensions m and n of a matrix must be integers. You can use this syntax to create a 1-by-n or an n-by-1 vector. The sym function does not allow you to use symbolic variables without assigned numeric values as dimensions. By default, the generated names of elements of a vector use the form Ak, and the generated names of elements of a matrix use the form Ai_j. The base, A, must be a valid variable name. (To verify whether the name is a valid variable name, use isvarname.) The values of k, i, and j range from 1 to m or 1 to n. To specify other form for generated names of matrix elements, use '%d' in the first input. For example, A = sym('A%d%d', [3 3]) generates the 3-by-3 symbolic matrix A with the elements A11, A12, ..., A33.

If you need a 3D array or you are using an earlier symbolic toolbox, then see http://www.mathworks.com/matlabcentral/answers/2521-creating-vector-of-symbols

For extracting coefficients: see coeff() and coeffs() and map(), especially within MuPAD itself: http://www.mathworks.com/help/toolbox/mupad/stdlib/ You may need to use feval() or evalin() in order to invoke these from MuPAD. For example,

evalin(symengine, 'map', 'coeff', AA, 'x2', 1)

Answer 2

[Nick Drake]

m = 6;

mv = sym(zeros(1, m));

for k=1:m

mv(k) = sym(sprintf('m%d', k));

end

This is what I found and it works great. I do not have that new of a version of Matlab. I have tried using the coeff and coeffs but I have struggled to get the syntax correct. I will look more into this I will try and post and example that might be more easily worked on. give me a little more time.

Answer 3

[Andrew Newell]

See How to generate symbolic variables dynamically at run-time?

Answer 4

[Nick Drake]

Ok, I have been trying to use coeffs here is what I am currently have a problem with, although I have 5 symbolic variables, not all show up in every equation so when I try and gather coeffients I would like to be able to catch even the 0 values. heres what I have so far.

clc
clear 
m= [2 -3 ; 3 -2];
q = [ -1 -1]';
xv = sym('x1');
lm = length(m);
yv = sym(zeros(1, lm))';
zv = sym(zeros(1, lm))';
for k=1:lm
yv(k) = sym(sprintf('x%d', k+1));
zv(k) = sym(sprintf('x%d', k+lm+1));
end
A = [-(m*yv+xv*q);m*yv+xv*q-zv; yv-zv;zv-yv];
Aineq=zeros;
temp = zeros;
for i=1:length(A)
  temp=coeffs(A(i,:))
  for j=1:length(temp)
      Aineq(i,j)=temp(j)
  end
end
Aineq

the last nested for was my attempt to gather the coefficients. I but I cannot place them in the right way this way. Any suggestions? I have looked at ineval and feval but I do not see the how to use these tools

Oh this is what my output looks like A =

   -2*x2+3*x3+x1
   -3*x2+2*x3+x1
 2*x2-3*x3-x1-x4
 3*x2-2*x3-x1-x5
           x2-x4
           x3-x5
           x4-x2
           x5-x3  
  Aineq =

     1    -2     3     0
     1    -3     2     0
    -1     2    -3    -1
    -1     3    -2    -1
     1    -1     0     0
     1    -1     0     0
    -1     1     0     0
    -1     1     0     0  
So this is where I am stuck at this point.

[Paul]

m = [2 -3 ; 3 -2];
q = [ -1 -1]';
xv = sym('x1');
lm = length(m);  % use size() instead?
Xv = sym('x',[2*lm+1 1]);
xv = Xv(1);
yv = Xv(2:lm+1);
zv = Xv(lm+2:end);
A = [-(m*yv+xv*q);m*yv+xv*q-zv; yv-zv;zv-yv]

A = 

Aineq = zeros(size(A,1),numel(Xv));
for ii = 1:size(A,1)
    [c,t] = coeffs(A(ii,:));
    [tf,locb] = ismember(t,Xv);
    Aineq(ii,locb) = c;
end
Aineq

Aineq = 8×5

1 -2 3 0 0 1 -3 2 0 0 -1 2 -3 -1 0 -1 3 -2 0 -1 0 1 0 -1 0 0 0 1 0 -1 0 -1 0 1 0 0 0 -1 0 1

Answer 5

[Nick Drake]

Ok so part of the problems that I think that I am having is that in my workspace there is no symbolic variable x1,x2.... defined. So i cant collect the coefficients i on the other hand have xv, yv,zv defined and I cannot seem to use coeffs with those symbolic vectors. Any help would be great.