Description

Module contains code to define Smolyak Grids and construct corresponding Interpolating Smolyak Polynomials. Both Anisotrophic and Isotrophic Grids/Polynomials are supported and are constructed efficiently following the methodology outlined in Judd, Maliar, Maliar, Valero (2014).

The code is designed for Julia version: 0.5.

The module has 3 main components with corresponding types:

• SmolyakGrid : Smolyak Grid
• SmolyakBasis : Smolyak Basis
• SmolyakPoly : Smolyak Polynomial

See help functions in REPL for details.

Example

Below is an example of how to use module to:

1. Create a Smolyak Grid
2. Define Smolyak Basis functions of an Interpolating Smolyak Polynomial on the Smolyak Grid
3. Create and evaluate the Smolyak Polynomial

using Smolyak
mu = [2,2,2]
lb = -2.*ones(length(mu))
ub = 3.*ones(length(mu))
sg = SmolyakGrid(mu,lb,ub)
sb = SmolyakBasis(sg)
makeBasis!(sb)
sp = SmolyakPoly(sb)
makeValue!(sp,sb)
makeGrad!(sp,sb)
makeHess!(sp,sb)

Further examples can be found in help files in REPL and at Interpolation Example.