How can I get a proper double form for a symbolic matrix?

How can I get a proper double form from this symbolic Matrix in MatLab? I've tried everything but I prefer not using feval or inline function as they're not recommended

This is the code to get the matrix

    function T = Romberg (a, b, m, f)

    T = zeros(m, m);
    T = sym(T);

    syms f(x) c h;

    f(x) = f;

    c = (subs(f,a)+subs(f,b)) / 2;

    h = b - a;

    T(1,1) = h * c;

    som = 0 ;

    n = 2;

    for i = 2 : m

        h = h / 2;

        for r = 1 : n/2

            som = som + subs(f,(a + 2*(r-1)*h));

            T(i,1) = h * (c + som);

            n = 2*n;

        end

    end

    r = 1;

    for j = 2 : m

        r = 4*r;

        for i = j : m

            T(i,j) = (r * T(i, j-1) - T(i-1,j-1)/(r-1)); 
        end

    end

    end

And with an input like this

    Romberg(0, 1, 4, '2*x')

I get a symbolic matrix output with all the

    3 * f(3)/2 + f(1)/2 + f(5)/2

I would like to have a double output.

Can you please help me? Thank you very much in advance!

Answer 1

[Steven Lord]

Rather than perform the calculations symbolically, why not just write a numeric Romberg integration function? Pass your f input argument as a function handle:

f = @(x) 2*x;
Romberg(0, 1, 4, f)

You'd need to replace your symbolic subs calls with function handle evaluation like f(1) but at first glance it looks like that's the only change you would need to make.

[PaoloV]

Didn't know function handle! Thank you very much!

This is the final version of the function hoping this may help someone having the same problem.

I used str2func in order to pass the function as a normal string.

function T = Romberg (a, b, m, f)

%pass the function as string

f = str2func(['@(x) ' f]);

T = zeros(m, m);

c = (f(a)+f(b)) / 2;

h = b - a;

T(1,1) = h * c;

som = 0 ;

n = 2;

for i = 2 : m

      h = h / 2;

      for r = 1 : n/2

          som = som + subs(f,(a + 2*(r-1)*h));

          T(i,1) = h * (c + som);

          n = 2*n;

      end

end

r = 1;

for j = 2 : m

      r = 4*r;

      for i = j : m

          T(i,j) = (r * T(i, j-1) - T(i-1,j-1)/(r-1)); 
      end
  end
  end

Answer 2

[Kiran Prasad]

Just from my limited experience using symbolic equations to get double answers, I would suggest maybe using the double function on each of the elements at the end if using double on the whole thing won't work. If that doesn't work I would create a small new function that just converts T to numeric. You can try using sym2cell and then cell2mat as that has worked for me before. Hopefully, this helps you-I'm by no means an expert.

[PaoloV]

Thanks for your answer,

I tried at the end of the function writing

T = cell2mat(sym2cell(T));

but MatLab prompted me

Error using cell2mat (line 52)
CELL2MAT does not support cell arrays containing cell arrays or objects.

    Error in Romberg (line 47)
    T = cell2mat(sym2cell(T));

Answer 3

[Walter Roberson]

You have an input parameter named f, and then you have

syms f(x) c h;

The first part of that,

syms f(x)

is equivalent to

f = sym('f(x)');
x = sym('x');

which clobbers the meaning of f as being from the input parameter and redefines it as being symbolic. After, places where you thought you were referring to the input parameter become references to the symbolic function.

If you are deliberately ignoring the input parameter then you should use ~ instead of giving it a name, as you are going to confuse readers. And if you are not deliberately ignoring the input parameter then you should be using a different name for f(x) compared to f.

If the idea is to indicate that the input is already a symbolic function then do not declare it with syms: MATLAB would already know it is a symbolic function because it knows the data type of the value that was passed in. But in that case you might still want to syms x