matlab: creating a symbolic vector

Question

I am trying to create a function using the symbolic toolbox in matlab. I have been having trouble creating a symbolic vector (not a vector of symbolic variables). Do you guys know a way to do this without creating and editing a text-like matlab function file in your path?

*After creating the symbolic variables and all I use 'matlabFunction' to create and save the function.

Example:

Function:

function f=test1(x,a) {
   f=x(1)/a(1)+x(2)/a(2);
}

Code:

a = sym('a', [1 2]);
x = sym('x', [1 2]);
% f(x, a) = sym('f(x, a)');
r=x(1)/a(1)+x(2)/a(2);
% f(x,a)=r;
% handle=matlabFunction(f(x,a),'file','test1');
handle=matlabFunction(r,'file','test1');

The problem is that the code seen above creates a function with the set of input arguments (x1, x2, a1, a2) instead of (x,a) and I can't change the form of input arguments, it must be uniform.
In reality I am trying to write a function that will create a polynomial of specified degree and save it to the path so I could use 'eval' with it (which doesn't support polyval), but it will probably be useful for more.

Amro · Accepted Answer · 2013-09-06 16:18:41Z

7

Try:

>> x = sym('x',[1 2])
x =
[ x1, x2]

>> x(1)
ans =
x1

>> x(2)
ans =
x2

>> whos x
  Name      Size            Bytes  Class    Attributes

  x         1x2               112  sym

This is similar to writing:

>> syms a1 a2
>> a = [a1 a2]

EDIT:

First we build an expression from the symbolic variables:

a = sym('a', [1 2]);
x = sym('x', [1 2]);
expr = x(1)/a(1)+x(2)/a(2);

Next we convert it to a regular MATLAB function:

fh = matlabFunction(expr, 'file','test1', 'vars',{a,x});

The generated function is:

function expr = test1(in1,in2)
    a1 = in1(:,1);
    a2 = in1(:,2);
    x1 = in2(:,1);
    x2 = in2(:,2);
    expr = x1./a1+x2./a2;
end

Initially I was thinking of using regular expressions to fix the function handle generated. This is a much dirtier hack, so I recommend using the previous approach instead:

% convert to a function handle as string
fh = matlabFunction(expr);
str = char(fh);

% separate the header from the body of the function handle
T = regexp(char(fh), '@\((.*)\)(.*)', 'tokens', 'once');
[args,body] = deal(T{:});

% extract the name of the unique arguments (without the index number)
args = regexp(args, '(\w+)\d+', 'tokens');
args = unique([args{:}], 'stable');

% convert arguments from: x1 into x(1)
r = sprintf('%s|', args{:}); r = r(1:end-1);
body = regexprep(body, ['(' r ')(\d+)'], '$1($2)');

% build the arguments list of the new function: @(a,b,c)
head = sprintf('%s,', args{:}); head = head(1:end-1);

% put things back together to form a function handle
f = str2func(['@(' head ') ' body])

The resulting function handle:

>> f
f = 
    @(a,x)x(1)./a(1)+x(2)./a(2)

edited Sep 6, 2013 at 16:18

answered Sep 6, 2013 at 13:24

Amro

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7 Comments

Avico Over a year ago

tried it before, doesn't work. it creates a function with 4 input arguments: 'test1(x1, x2, a1, a2)' instead of 'test1(x, a)'.

Amro Over a year ago

I dont follow, the above doesnt create a function, only the symbolic variables. Those will be the input to your functions that you will have to write.. Perhaps you could explain further exactly what you are doing

Avico Over a year ago

after you create those symbolic variables and use them to create a function using 'matlabFunction' the function that it will create will have 4 input arguments (x1, x2, a1, a2) instead of (x, a), it will treat every cell in the vectors x and a as an individual variable and it won't except 2 vectors as needed, but 4 arguments instead.

Amro Over a year ago

@Avico: ah now I understand, you didnt initially mention matlabFunction. Can you post the exact expression you are converting into a function handle? I'm thinking we can fix it by using some regular expression...

Amro Over a year ago

@Avico: try this: fh = matlabFunction(r, 'file','test1', 'vars',{a,x}) (you could reverse the order {x,a} if you like). This tells MATLAB to use vectors as input

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