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How to find the coordinate of the point on (180) contour line when y(max)?

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ly
ly 2024-1-24
编辑： Matt J 2024-1-24
How to find the coordinate of the point on (180) contour line when y(max)?
Code of the contour line:
clear
x = 0:0.1:3;
y = -2:0.1:3;
[X,Y] = meshgrid(x,y);
Z = 1000*(X.*exp(-X.^2-Y.^1));
contour(X,Y,Z,[90 180],'ShowText','on')

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回答（2 个）

John D'Errico
John D'Errico 2024-1-24
Easy.
  1. Use contourc to find that specific contour. It will be a piecewise linear curve.
  2. Find the point where y is maximum. That will also tell you the x coordinate at that point.
Matt J
Matt J 2024-1-24
编辑：Matt J 2024-1-24
Ran in:
You could do the calculus, or use the Symbolic toolbox to help you.
syms x y z(x,y)
z=1000*(x.*exp(-x.^2-y.^1));
G=gradient(z);
assume(x>0);
xy_max=solve([G(1)==0, z==180]), %location of max point
xy_max = struct with fields:
x: 2^(1/2)/2 y: - log((9*2^(1/2))/50) - 1/2

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