MATLAB: How to write x as a function of f(x)

polynomialpolynomialsswitch function

Hi, I was wondering if there exists some code or function to change for example:

f(x) = (x^2 – 1); or any other polynomial

x = sqrt(f(x) + 1) This is just an example.

Basically i would want any function written as f(x) in function of x changed to x in function of f(x).

Best Answer

The Symbolic Math Toolbox has the finverse function:

syms x 
f(x) = (x^2 - 1);
finv = finverse(f)

producing:

finv(x) = 
(x + 1)^(1/2)

To do this numerically, use the fsolve function, for example:

x = fsolve(@(x)(x.^2-1) - y, x0)

where ‘y’ is the value to solve ‘x’ for, and ‘x0’ is the intial estimate.

Related Solutions

MATLAB: Symbolic differentiation with fminunc


function [f,g] = rosenbrockwithgrad_s(x)
X = sym('x', [1 2]);
% Calculate objective f

F = 100*(X(2) - X(1)^2)^2 + (1-X(1))^2;
f = double( subs(F, X, x) );
if nargout > 1 % gradient required
   G = diff(F);
   g = double( subs(G, X, x) );
end

However, this would involve repeated calculation of diff(F) symbolically, which is pointless. Instead you would do something like,

    function [f, g] = f_and_g(x, F, G)
        f = F(x);
        if nargout > 1
            g = G(x);
        end
    end

together with (outside)

X = sym('x', [1 2]);
% Calculate objective f
f = 100*(X(2) - X(1)^2)^2 + (1-X(1))^2;
g = diff(f);
F = matlabFunction(f, 'vars', {X});
G = matlabFunction(g, 'vars', {X});
x = fminunc( @(x) f_and_g(x, F, G), x0 )

MATLAB: Create An Array That Contains All the Values of F(x)? Help!

And to be complete:

y = x.^2;
y(x < 1) = x(x < 1);

Best Answer

Related Solutions

MATLAB: Symbolic differentiation with fminunc

MATLAB: Create An Array That Contains All the Values of F(x)? Help!

Related Question