The Rosenbrock function is commonly used for testing optimization and uncertainty quantification software. The form we will use is
f(x,y) = 100*(y-x**2)**2 + (1-x)**2
This is a fourth order polynomial and its response surface looks like this:
UQ software should be able to build close approximations to this response surface given enough sample points. Our "Smolyak" method will reproduce this response exactly with a level 4 run.