CODEWITHSUNDEEP
matlab
Michael L.
Michael L.

Reputation: 473

How to inverse inline function in Matlab?

If I have anonymous function, for example:

a=3;
b=4;
y = @(x) (x)./(a+b+x);

So I easily can find a for x=4, but how can I find an x that will give me y=0.4? I actual looking for an easy way to have x(y) instead of y(x).

Upvotes: 2

Views: 389

Answers (2)

SecretAgentMan
SecretAgentMan

Reputation: 2854

One approach is to use MATLAB's interpolation (1D) function interp1, but this works on your function for parameter values that ensure y(x) is a non-decreasing function. 

step = .01;                  % Control precision (smaller = more precise)
Xmax = 50;                   % Largest x of interest
X = [0:step:Xmax]'; 
Y = y(X);                    % Generate discrete approximation of function
yinvh=@(L) interp1(Y,X,L);

Targets = [0.25 0.4 0.75]';
yinvh(Targets)

This matches the results from Cris Luengo's approach. 

>> yinvh(Targets)'
ans =
    2.3333    4.6667   21.0000

Illustration of inverse function

figure, hold on, box on
plot(X,y(X))
plot(zeros(3,1),Targets,'rx')
plot(yinvh(Targets),zeros(3,1),'rx')
for k = 1:length(Targets)
    plot([0; yinvh(Targets(k))],Targets(k)*ones(2,1),'k--')
    plot(yinvh(Targets(k))*ones(2,1),[0 Targets(k)],'k--')
end

Upvotes: 1

Cris Luengo
Cris Luengo

Reputation: 60790

One trivial approach is to use a numeric algorithm to find the zero of y(x) - 0.4:

target = 0.4;
x = fzero(@(x) y(x)-target, 0)

Now, x is 4.6667 and y(x) returns 0.4.

Note that this is an easy approach, but it is not cheap computationally. Also, you need a suitable start point, which here I've set to 0. If your function has multiple points where it reaches 0.4, then you will get the one closest to this start point.

Upvotes: 3

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