Computing the inverse of function in MATLAB

Question

How do you compute the inverse of a function in MATLAB? Say you want to compute the inverse of f(x)=e^x, what would be the code?

Answer 1

If the analytical approach fails (which is preferred whenever possible) use numerical approach:

Given y and guess x0 for the inverse

x = fzero( @(x)(f(x)-y), x0 ); 

or a low accuracy but faster method when the range of x known to be bounded in xmin...xmax

xx = linspace( xmin, xmax, N );
yy = f(xx);
x = interp1(yy, xx, y);

Of course, N has to be chosen according to the desired accuracy.

Answer 2

you can use finverse from the symbolic math toolbox http://www.mathworks.com/help/symbolic/finverse.html but for your example you can just do ln()?

Answer 3

Numerical inverse of a monotone Function: let v be a monotone ascending array of numbers (that means v=sort(v)). Then you can derive the inverse (vinv) very simple:

vinv=cumsum(hist(v,length(v)));

After this you can beautify the result with a bit of scaling, but basically the cumsum of hist -thingi does the trick.

You can test the following:

x=randn(1,1000);
v=sort(x);
plot(v);
vinv=cumsum(hist(v,1000));
figure(2);
plot(vinv);