How to find all coordinates of extremes of two variable function?

Hello,

I can't figure out how to find all coordinates of extremes of two variable function.

x=1:12;
y=[-0.1 0.01 0.05 -0.2 0.13 -0.19 0.2 -0.11 0.02 0 -0.1 -0.02];
p=polyfit(x, y, 6);
pol = @(x) p(1)*x.^6+p(2)*x.^5+p(3)*x.^4+p(4)*x.^3+p(5)*x.^2+p(6)*x+p(7);

x=1:0.25:12;
y=1:0.25:12;
[X,Y]=meshgrid(x,y);
k=0.55;
sk = numel(X);
matrix(X,sk);
P = k.*pol(X)-(1-k).*pol(Y);
subplot(1,2,2);
surf(X, Y, P)
xlabel('x'); ylabel('y'); zlabel('z')

function ma = matrix(X, sk)
num=floor(sk/2);
M=X;
while num > 0
    x_temp=M(num);
    M(num)=M(sk-num+1);
    M(sk-num+1)=x_temp;
    num=num-1;
end
X=M;
end

[dpb]

What's the purpose of function matrix? As is now, it's doing nothing as you don't return the result so might as well not exist. But, it isn't clear what it is trying to compute???

As to the Q? posed,

[mx1,imx1]=max(P);

will return index of largest row by column as well as maximum in first dimension;

[mx2,imx2]=max(P,[],2);

the same info by row.

Finding other local maxima is a slightly different if this isn't the actual objective (is isn't quite clear)...

Answer 1

[Walter Roberson]

https://www.mathworks.com/help/matlab/ref/polyder.html and roots()

[pragiedruliai]

Thank you.

I've tried, but it doesn't work with two variables.

[Walter Roberson]

You have no cross-products between X and Y. You can fully separate it out to the sum of two independent polynomials, each of which can be solved by the above process.

In fact, because it is the same polynomial each time (just with different constant coefficients multiplied by each part) the extrema are the same for X and Y, so you only need to solve one part.