how to find values of X and Y that satisfy condition Z(X,Y)>a

Dear Pros, I'm very new to Matlab, and I'm a chemist not a computer science guy or engineer so be gentle with me please :). I have a rather complicated function of 2 variables Z=f(X,Y). I wish to find all the X and Y combinations (all real and positive numbers) at which z is above a certain value, so I'm looking to solve the inequity Z > a for X and Y. X and Y are vectors so I'm looking for an output that would be a set of X and Y pairs that satisfy the condition. Preferably these X and Y's and a would be arguments in a function that would describe an analytic solution (as an equation for a sphere segment would define the solution of all the points in a sphere above a certain longitude). Thanks for your help in advance, Tim

Answer 1

[Giovanni Mottola]

Is it something like this you're looking for?

function [vec_pairs, num_pairs] = find_greater(X, Y, a)
len_X=length(X);
len_Y=length(Y);
num_pairs=0;   %   number of such pairs that have been found
for i=1:len_X
    for j=1:len_Y
        z=f(X(i), Y(j));    %    insert name of your function, as defined in another .m file
        if z>a
           num_pairs=num_pairs+1;
           vec_pairs(num_pairs, :)=[X(i), Y(j)];
        end
    end
end
end

Example:

X=[-1 -0.5 0 0.5 1];
Y=[-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1];

The function f is defined in another .m file:

function z=f(x, y)
z=sqrt(1+x^2+y^2);
end

Calling the function from the command window:

[v, n]=find_greater(X, Y, 1.5)

Results:

v= -1.0000   -1.0000
   -1.0000   -0.7500
   -1.0000    0.7500
   -1.0000    1.0000
    1.0000   -1.0000
    1.0000   -0.7500
    1.0000    0.7500
    1.0000    1.0000
n=    8