eFAST Method

struct eFAST <: GSAMethod
    num_harmonics::Int
end

The eFAST object has num_harmonics as the only field, which is the number of harmonics to sum in the Fourier series decomposition, this defaults to 4.

eFAST Method Details

eFAST offers a robust, especially at low sample size, and computationally efficient procedure to get the first and total order indices as discussed in Sobol. It utilizes monodimensional Fourier decomposition along a curve exploring the parameter space. The curve is defined by a set of parametric equations,

\[x_{i}(s) = G_{i}(sin ω_{i}s), ∀ i=1,2 ,..., n,\]

where s is a scalar variable varying over the range $-∞ < s < +∞$, $G_{i}$ are transformation functions and ${ω_{i}}, ∀ i=1,2,...,n$ is a set of different (angular) frequencies, to be properly selected, associated with each factor. For more details on the transformation used and other implementation details you can go through A. Saltelli et al..

API

function gsa(f, method::eFAST, p_range::AbstractVector; n::Int=1000, batch=false, distributed::Val{SHARED_ARRAY} = Val(false), kwargs...) where {SHARED_ARRAY}

Example

Below we show use of eFAST on the Ishigami function.

using GlobalSensitivity, QuasiMonteCarlo

function ishi(X)
    A= 7
    B= 0.1
    sin(X[1]) + A*sin(X[2])^2+ B*X[3]^4 *sin(X[1])
end

lb = -ones(4)*π
ub = ones(4)*π

res1 = gsa(ishi,eFAST(),[[lb[i],ub[i]] for i in 1:4],n=15000)

##with batching
function ishi_batch(X)
    A= 7
    B= 0.1
    @. sin(X[1,:]) + A*sin(X[2,:])^2+ B*X[3,:]^4 *sin(X[1,:])
end

res2 = gsa(ishi_batch,eFAST(),[[lb[i],ub[i]] for i in 1:4],n=15000,batch=true)