| vars_matrices {sensobol} | R Documentation |
STAR-VARS sampling strategy
Description
It creates the STAR-VARS matrix needed to compute VARS-TO following Razavi and Gupta (2016).
Usage
vars_matrices(star.centers, params, h = 0.1, type = "QRN", ...)
Arguments
star.centers |
Positive integer, number of star centers. |
params |
Character vector with the name of the model inputs. |
h |
Distance between pairs. The user should select between 0.001, 0.002, 0.005, 0.01,
0.02, 0.05, 0.1, 0.2. Default is |
type |
Approach to construct the STAR-VARS. Options are:
|
... |
Further arguments in |
Details
The user randomly selects N_{star} points across the factor space using
either Sobol' Quasi Random Numbers (type = "QRN") or random numbers (type = "R").
These are the star centres and their location can be denoted as
\mathbf{s}_v = s_{v_1},...,s_{v_i}, ..., s_{v_k}, where v=1,2,...,N_{star}.
Then, for each star centre, the function generates a cross section of equally spaced points
\Delta h apart for each of the k model inputs, including and passing through the
star centre. The cross section is produced by fixing \mathbf{s}_{v_{\sim i}} and varying s_i.
Finally, for each factor all pairs of points with h values of \Delta h, 2\Delta h, 3\Delta h
and so on are extracted. The total computational cost of this design is
N_t=N_{star} (k (\frac{1}{\Delta h} - 1) + 1).
Value
A matrix where each column is a model input and each row a sampling point.
References
Razavi S, Gupta HV (2016).
“A new framework for comprehensive, robust, and efficient global sensitivity analysis: 2. Application.”
Water Resources Research, 52(1), 440–455.
doi:10.1002/2015WR017558, 2014WR016527.
Sobol' IM (1967).
“On the distribution of points in a cube and the approximate evaluation of integrals.”
USSR Computational Mathematics and Mathematical Physics, 7(4), 86–112.
doi:10.1016/0041-5553(67)90144-9.
Examples
# Define settings
star.centers <- 10; params <- paste("X", 1:5, sep = ""); h <- 0.1
# Create STAR-VARS
mat <- vars_matrices(star.centers = star.centers, params = params, h = h)