Creating Symbolic Functions

Hey all. I'm new to Matlab and a first time poster here. I'm trying to create a multivariate symbolic polynomial and access its variables using the argnames function, which I found here:

http://www.mathworks.com/help/toolbox/symbolic/argnames.html

Running the example code at the linked page, I get the following:

>> syms f(x, y);
??? Error using ==> syms at 61
Not a valid variable name.

Then I looked at the documentation for sym here:

http://www.mathworks.com/help/toolbox/symbolic/sym.html

I tried running the example code for a symbolic function found there, which produced:

>> x = sym('x');
>> y = sym('y');
>> f(x, y) = x + y;
??? Error using ==> mupadmex
Error in MuPAD command: DOUBLE cannot convert the input expression into a double
array.
If the input expression contains a symbolic variable, use the VPA function instead.

Error in ==> sym.sym>sym.double at 936
          Xstr = mupadmex('symobj::double', S.s, 0);

Error in ==> sym.sym>privformatscalar at 2678
  x = double(x);

Error in ==> sym.sym>privformat at 2663
  s = privformatscalar(x);

Error in ==> sym.sym>sym.subsasgn at 1433
              [inds{k},refs{k}] = privformat(inds{k});

Then I tried the following, just to see if it would work (it didn't):

>> x = sym('x');
>> y = sym('y');
>> f = x+y;
>> argnames(f);
??? Undefined function or method 'argnames' for input arguments of type 'sym'.

What am I doing wrong?

[G A]

Itamar, which version of Matlab are you using?

[Walter Roberson]

What is shown would apply to all MATLAB versions that use the MuPAD symbolic engine. (Not that the Maple symbolic engine would work for those commands either, but the error messages for the Maple engine would not mention MuPAD.)

[G A]

Why then is it not written explicitly in the Matlab documentation that this and that do not work in Matlab with Mapple symbolic engine?

[Walter Roberson]

At the time of the switch over to MuPAD, the release notes had comparisons between the two. After that, everything to do with Maple was legacy except for the symengine command, and that _was_ specifically documented in the release notes when MATLAB changed to disallow changing symengine a few releases later.

MathWorks is not in the habit of specifically documenting that new features will not work with releases that predate the introduction of the feature.

None of the commands that Itamar tried were supported in the MATLAB interface to the Maple symbolic engine, and none of them are supported in the MATLAB interface to the MuPAD symbolic engine. The error messages produced in both cases would have had the same essential meaning, but you can be sure that the Maple error messages would not have included the word "MuPAD" such as in the phrasing "Error in MuPAD command". It might have said "Error in Maple command" for example.

[G A]

Thanks, Walter.

[Walter Roberson]

Dang, they introduced new functionality that used to be illegal.

Answer 1

[Alexander]

The concept of 'symbolic functions' including the function argnames have been introduced in MATLAB 2012a. You cannot use this feature in earlier versions.

[G A]

That was my feeling.

[Itamar]

I'm running MATLAB 7.12.0.635 (R2011a), so that explains it. I really should have checked what version of the software I was using. Thanks.

Answer 2

[Walter Roberson]

f = evalin(symengine, '(x,y) -> x+y;');

For something more complicated,

f = evalin(symengine, 'proc(x) local S, N; S := 0; for N to x do S := S + cos(Pi/N) end_do; S end_proc;');

Only parts of MuPAD have direct MATLAB interfaces, and creating new functions (procedures) does not have a direct interface, unfortunately. Though it could be that I have missed a trick.

[Itamar]

I only started using MATLAB relatively recently, and I don't have a very clear picture of how things are structured; in particular I didn't realize there was a separate system responsible for performing symbolic computations. I'll probably go take a look at some MuPAD documentation now. Thanks for the help.

Answer 3

[G A]

Could it be an alternative solution to use symvar() instead of argnames()?

syms x y
f = x+y;
symvar(f)

 ans =

[ x, y]

[Walter Roberson]

Plausibly.

On the other hand, symvar() will not return the variable names in any particular order, so if Itamar was trying to distinguish between f(x,y) = atan2(x,y) versus f(y,x) = atan2(x,y) (looks the same but the order of the parameters is important) then there could be problems.

But symvar() might be fine for what Itamar is doing.

[G A]

What about this way:

f = fittype( @(t, x) x+t );

argnames(f)

it does not work with y instead of t

[Walter Roberson]

fittype() does not return a function: it returns an object. I do not know whether there is an argnames() method defined for that kind of object. (I do not have the curvefitting toolbox to test with.)

[G A]

>> f = fittype( @(t, x) x+t );

argnames(f)

ans =

't'

'x'

>> f

f =

General model:

f(t,x) = x+t

[Itamar]

I think that symvar is probably fine for me. And if I'm reading the documentation correctly, then symvar should return the variable names in lexicographic order:

http://www.mathworks.com/help/toolbox/symbolic/symvar.html

Also, it doesn't seem as though function evaluation notation works for 'sym' objects; it looks like I would be using the 'subs' function (or something similar), i.e.:

>> x = sym('x');

>> y = sym('y');

>> f = x+y^2;

>> subs(f,[x,y],[1,2])

ans =

5

>> subs(f,[y,x],[2,1])

ans =

5

So it seems like I could distinguish between asymmetric functions in this context.

[Itamar]

And thanks!