Trouble with using the function 'solve' to obtain decision boundary

I need to find the point where the decision boundary occurs for a single feature of the iris data set. I am certain i need to solve the equation P(x/SWL) = P(x/VWL) and obtain the solutions for x.I get an error for the code i tried below. The error states x is an undefined variable. Can you tell me where i am going wrong?

load fisheriris
SWL=meas(1:50,1)
VWL=meas(51:100,1)
V1 = var(SWL);
V2 = var(VWL);
M1 = mean(SWL);
M2 = mean(VWL);
P1 = (1/(sqrt(2*pi*V1))*(exp(((x-M1)^2)/(2*V1))));
P2 = (1/(sqrt(2*pi*V2))*(exp(((x-M2)^2)/(2*V2))));
solve(P1-P2);

Answer 1

[Star Strider]

The easiest way is to use the fzero function:

P1 = @(x) (1/(sqrt(2*pi*V1))*(exp(((x-M1)^2)/(2*V1))));     % ‘P1’ As Anonymous Function
P2 = @(x) (1/(sqrt(2*pi*V2))*(exp(((x-M2)^2)/(2*V2))));     % ‘P2’ As Anonymous Function
X = fzero(@(x) P1(x)-P2(x), 1)                              % Create Anonymous Funciton, Solve For ‘x’

produces:

X =

       3.0804

[nazneen]

Thank you. I just learnt something new.

[Star Strider]

My pleasure!

That occurs frequently for all of us here on MATLAB Answers!

[nazneen]

Is there an another way of solving this equation since fzero gives me the correct answer only if i know that the solution i need lies closer to 5 instead of 1. Is there a way to obtain multiple solutions?

[Star Strider]

The best way to obtain multiple solutions from fzero is to iterate in a for loop, with a different initial guess at each iteration.

For example:

IV = linspace(0, 10, 20);                           % Vector Of Initial Guesses
for k1 = 1:length(IV)
    X(k1) = fzero(@(x) P1(x)-P2(x), IV(k1));        % Create Anonymous Function, Solve For ‘x’
end
Xu = unique(fix(X*1E+4)/1E+4);                      % Find Unique Elements Of ‘X’

produces:

Xu =

       3.0803     5.3062

It is necessary to use a ‘roundoff’ approximation with the unique function because the inherent approximation errors in floating-point calculations do not guarantee that every solution near 3 or 5 will be exactly the same to full floating point precision.

[nazneen]

Thank you

[Star Strider]

My pleasure!