how to create symbolic function for vector input?

I'm new to Matlab and I wonder how to input a vector to a symbolic function. It is said in the document that creating vectors by x = sym('x',[50 1]) and use it for generate objective function f(x), but it doesn't work if I want to test the value of function when x = ones(50,1) since the input expects 50 variables.

How can I change my code to achieve that?

m = 100;

n = 50;

A = rand(m,n);

b = rand(m,1);

c = rand(n,1);



% initialize objective function

syms x

f = symfun([c'* x - sum(log(A*x + b))],x);

tolerance = 1e-6


% Max iterations

N =1000;

% start point

xstart = ones(n,1)

% Method: gradient descent

% store step history 

xg =  zeros(n,N);

% initial point

xg(:,1) = xstart;


fprintf('Starting gradient descent.')';

for k = 1:(N-1)
    
d = - gradient(f,xg(:,k));
    
if norm(d) < tolearance
        
xg = xg(:,1:k);
        
break;
    
end

Answer 1

[Walter Roberson]

Symbolic functions cannot handle vectors of inputs as separate variables. For symbolic functions, input vectors or arrays are always treated as requests to vectorize the calculation.

Work-around:

x = sym('x',[50 1]);
f = c'* x - sum(log(A*x + b));

then

xc = num2cell(xg(:,k));
d = - gradient(f, xc{:});

[Jiayan Yang]

Thanks for your advice.It works when computing value in terms of point but fails to compute gradient says,

Error using sym/gradient

Too many input arguments.

It is really troublesome since the calculation such as gradient(f,x) or f(x) involves later.

I also tried this form f = @(x) c'* x - sum(log(A*x + b)); it is easier to calculate f(x) but it is hard to calculate the gradient at certain point.

[Walter Roberson]

If you want to evaluate the gradient at a particular point, then

fg = gradient(f, x);
g = matlabFunction(fg, 'vars', {x});

after which

d = -g(xg(:,k));

There is a variation of this but it is only worth doing if you are going to be testing the gradient of a lot of points:

g = matlabFunction(fg, 'vars', {x}, 'file', 'fgrad.m', 'optimize', true);

I will update with relative timings when I have them.

[Walter Roberson]

47 seconds to creat the unoptimized MATLAB Function (not stored on disk, so would only persist between seconds if save/load)

0.0149 seconds to execute the non-optimized MATLAB version

705 seconds to create the optimized MATLAB function (stored on disk, so would persist between sessions)

0.000115 seconds to execute the optimized MATLAB function.

Improvement ratio: about 129

But to make up the extra 658 seconds of optimizing, you would need to be calling the function close to 6 million times. Not impossible, certainly.