Extracting the base name and size of symbolic variables

Hello,

I have a simple question. Consider the following:

syms a [3 3] real 
syms x r [3 1] real 
mu(x) = (r.*x).*(1-a*x)

Now, I would like to know the symbolic variables and their sizes in the symbolic function mu(x). If I use symvar(mu) I can only get the

variables in a scalar form and this command does not help to get the size of matrixes and vectors. You might think that it should not be

a big deal to write a code for this. However, ingeneral this is not possible. Foe instance, consider the following example:

syms x beta0 w w0 w1 w2
mu(x) = x+beta0+w+w0+w1+w2

In this example there is not a unique interpretation of the variables in terms of matrices, vectors, and scalars. One interpretation is to consider w = [w1 w2] as a vector. But, another interpretation is to consider al w's as scalar (which is the correct interpretation).

Why I need this?

I am performing a parameter estimation procedure to estimate the parameters of a function like mu(x). When I want to represent the results I do not like to display them scalar-wiae. rather I prefer to display the outcomes based on their actual sizes.

I hope MATLAB has a command to handled this issue?

Thanks,

Babank

Answer 1

[Walter Roberson]

syms a [3 3] real 

That is equivalent to

a = sym('a', [3 3], 'real')
mu(x) = (r.*x).*(1-a*x)

When scanning that code, the value of a is substituted, as-if you had written

mu(x) = (r.*x).*(1-sym('a', [3 3], 'real')*x)

The code does not remember that the value came from the variable a

So what you want to do is not possible.

[Walter Roberson]

You can potentially use symmatrix()

a = symmatrix('a', [3, 3])
syms x
r = symmatrix('r', [3, 1])
mu(x) = (r.*repmat(x,[3 1])) .* (repmat(1, 3,3) - a*repmat(x,3,3))

but

symvar(mu)

Error using symbolic.mixin.symbolicmatrix/symvar (line 862)
Convert input of class 'symmatrix' to 'sym' using 'symmatrix2sym' before applying function 'symvar'.

At the moment I do not know of any way to get the size of symmatrix, except by using whos()

[Mohammad Shojaei Arani]

Thanks Walter,

Do you, like me, think that it is needed to have a built-in matlab command to save such information. I believe it can simply be done in a more advanced symvar (perhaps symvar can be a structure where its fields can be the size of the corresponding symbolic variable).

In different areas of math/statistics we are concerned with estimating a function which can have many parameters where some of such oarameters can be matrices or vectors (or even tensors). In the following case, for instance, we have

syms a [3 3] real

syms x r s [3 1] real

mu(x) = (r.*x).*(1-a*x);

Now, imagine someone is going to make a MATLAB package (I am doing this now). At the end the user expect to se an elegant representation as follows:

Estimated paramers as as follows:

r is estimated to be : xxx

a is estimated to be: xxx

But, now imagine that we are going to do parameter estimation for the following function:

syms a [3 3] real

syms r1 r2 r3 real

mu(x) = (1-a*x)+r1+r2+r3;

Then the user expects the following output:

a is estimated to be:

r1 is estimated to be:

r2 is estimated to be:

r3 is estimated to be:

So, the package should respect the way a user likes to define his/her function (vectors, matrices, scalars). There are more complicated examples.

Best,

Babak

[Walter Roberson]

The substitution of the value for the variable is inherent in how symbolic mathematics works. There is no chance that you would be able to recover variable a from mu(x) = (r.*x).*(1-a*x);

[Mohammad Shojaei Arani]

You are right.

My point was about displaying the results in an elegant way which corresponds with the way the function is defined.