Problem: Plot a color map and a contour plot of a function, and a histogram

Here we want to define a function z of x and y coordinates:

=sincos(+)+z=sinAxcos(y+r)B+x

where =2+2r=x2+y2, A and B are constants. We then plot the function with a colour map and make a histogram giving some details about the map. In particular, please do the following:

• Introduce a Python function that does the following: (1) defines Numpy arrays x and y from a to b with N elements each; (2) computes the values of the function z as defined above; (3) accepts N, a and b as arguments and A and B as keywords with default values =1,=0A=1,B=0; (4) return arrays x, y and the 2D Numpy array z.

• Produce a figure with two panels side by side horisontally. The left hand side panel should show the colour map image and a contour plot (on the same image) of function z for =1A=1, =1B=1, =100N=100, =0a=0, =2b=2. The right hand panel should show the histogram of the values of z for all the (NN) pixels. Make sure that you plot looks professional, e.g., has labels and the title. Test that your code works for B between 0 and 2.

• Compute and print in one line the mean of the function (,)z(x,y) on the domain defined above. Use .format statement and the scientific notation with 4 digits after the floating point.