Meshgrid and contours

A common task is a graphical representation of a scalar function over a rectangle:

For this, first we have to generate a grid on the rectangle [a,b] x [c,d]. This is done using the meshgrid command:

n = ... # number of discretization points along the x-axis
m = ... # number of discretization points along the x-axis 
X,Y = meshgrid(linspace(a,b,n), linspace(c,d,m))

X and Y are arrays with (n,m) shape such that  contains the coordinates of the grid point as shown in the next figure (Figure 6.6):

Figure 6.6: A rectangle discretized by meshgrid

A rectangle discretized by meshgrid will be used  to visualize the behavior of an iteration. Bur first we will use it to plot level curves of a function. This is done by the command contour.

As an example we choose Rosenbrock's banana function:

It is used to challenge optimization methods. The function values descend towards a banana-shaped valley, which itself decreases slowly towards the function’s global minimum at...