Question

Plot the contour plot and the gradient (shown by arrows) for the function

f(x, y) = -x2 + 2xy + 3y2

Answer 1

Consider the function f(x, y) = -x2 + 2xy + 3y2

 

The objective is to draw the contour plot.

 

Firstly, generate a set of data for x and y range a using ‘meshgrid’ command.

 

Then based on these, calculate the data function and obtain differential x and y.

 

Using these differential values and ‘gradient’ command first order derivatives can be found.

 

The contour is plotted using ‘contour’ command for x, y and function values. Then for the contour and gradient, arrows are shown using ‘quiver’ command.

 

Mat-lab code for above problem is provided below.

Save this program as ‘Required problem’.

% Plot the contour plot and gradient (shown by arrows) for the function

clc; clear;

[x,y] = meshgrid(-2:0.25:2);

f=-x.^2+2*x.*y+3*y.^2;

dx = x(1,2) - x(1,1);

dy = y(2,1) - y(1,1);

[df_dx,df_dy] = gradient(f, dx, dy);

contour(x,y,f);

xlabel(\'x\');

ylabel(\'y\');

hold on;

quiver(x,y,df_dx,df_dy);

hold off;

The output of the code ‘Above problem’ in the figure window is shown below.