Generate array of y values, from the numerical solution of f(y)=x, where x is an array of numbers

How can I generate array of y values, from the numerical solution of , where x is an array of numbers, if I assume that: a. for each x there is only a single y and vice-verse, and b. I cannot invert and isolate explicitly?

For example, let

This is a monotonically decending function of x, for any .

If I have the vector , how can I obtain the vector of the y values corresponding to these xs ?

• I want the array y to contains real numbers, that I can later use for calculations.
• Speed matters, I prefer to find the fastest solution.

Thanks!

Answer 1

[Star Strider]

There are likely at least two solutions because of the term. I did not exhaustively analyse the function.

Try this:

f = @(y) exp(-y).*(-1+exp(y)-y)./y.^2;

x=[1 2 3 4 5];

for k = 1:numel(x)
    ys(k) = fsolve(@(y) f(y)-x(k), 1);
end

Experiment to get different results. The fzero function is also an option, however fsolve is more robust.

[Erez]

There is a unique solution, since f(y) is monotoic. Thanks, your code works.

Is there a way to do this without the loop?

[Stephen23]

"Is there a way to do this without the loop? "

>> x = [1,2,3,4,5];
>> f = @(y) exp(-y).*(-1+exp(y)-y)./y.^2;
>> y = arrayfun(@(v)fzero(@(z)f(z)-v,1),x)
y =
           -1      -1.9375      -2.4647       -2.831      -3.1113

But an explicit loop would most likely be faster.

[Star Strider]

As always, my pleasure!

The loop is required, since fsolve (and all the others that I am aware of) can only solve for one value at a time.

For example:

ys = fsolve(@(y) f(y)-x, 1)

only solves for ‘x=3’, and none of the others.