Contents:
Created on Wed Jul 11 10:40:30 2012
@author: Daniele Bigoni (dabi@imm.dtu.dk)
UncertaintyQuantificationToolbox is the collection of tools for Uncertainty Quantification.
@copyright: 20122014 The Technical University of Denmark
This class is devoted to the sampling from a multi dimensional distribution and the evaluation of a function f on it.
Parameters: 


Returns:  the list of samples for which the experiment have not been evaluated yet. 

Returns:  the list of results of the evaluation of f on the samples. 

Returns:  the list of samples for which the experiment have been evaluated already. 

Evaluate the function f on the samples.
Parameters: 

Sample from the multidimensional distribution defined by the dists.
Parameters: 


Note :  If the Experiments object has been reloaded using pickle, the dists parameters should be reset using set_dists. 
Run Latin Hyper Cube Simulations
..deprecated:: 0.1.5
Run Monte Carlo Simulations
..deprecated:: 0.1.5
Tensor construction of a multidimensional distribution
Parameters:  dists (list) – list of distributions along each dimension. 

Samples size realizations from the multidimensional distribution using the Latin Hyper Cube method.
Parameters:  size (int) – number of samples 

Returns:  list of samples 
Run Quasi Monte Carlo Simulations
..deprecated:: 0.1.5
Compute the Experiments f on the samples. The implementation uses MPI for parallel computations.
Parameters: 


Returns:  Array of computed values, ordered by the first dimension of the array. 
..deprecated:: 0.1.5
Generates the full tensor grid using the list of distributions of the parameters space approximated by the selected polynomials.
Parameters: 


Returns:  dictionary with the following attributes ‘x’: tensor product of collocation points in the standard distributions ‘w’: tensor product of the weights for cubature/projection rules (sum to 1 or prod(gamma0) respectively) ‘vals’: tensor product of collocation points ‘V’: tensor basis functions 
Generates the Multi Index basis Vandermonde matrix using the list of distributions of the parameters space approximated by the selected polynomials.
Parameters: 


Returns:  dictionary with the following attributes x: tensor product of collocation points in the standard distributions w: tensor product of the weights for cubature/projection rules (sum to 1 or prod(gamma0) respectively) vals: tensor product of collocation points V: Pascal’s simplex of the basis functions 
Created on Wed Mar 13 09:03:41 2013
@author: Daniele Bigoni (dabi@dtu.dk)
This module is used to construct High Dimensionar Model Representation using cutHDMR based on spectral methods from the module SpectralToolbox.Spectral1D. Additionally the cutHDMR can be used to compute the associated ANOVAHDMR.
Provided a Covariance function and discretization points, it generates the Gaussian fields.
Parameters:  C (function) – Covariance function C(x1,x2) 

Given some discretization points, it finds the Cholesky factorization to be used for the simulation of the random field
Parameters:  x (np.ndarray) – array containing the discretization points 

Generates random fields from the input variables (Normally distributed)
Parameters:  xi (np.ndarray) – 1 or 2 dimensional array containing the generating variables. If 2dimensional, each row should contain a different sample. 

Returns:  the realizations of the random field 
Return type:  np.ndarray 
KLExpansion: Computes the 1D KL expansion of the covariance matrix C, using the LegendreGaussLoabatto rule for the solution to the generalized eigenvalue problem A * u = lmb * M * u. The KLExpansion of ddimensional random fields is obtained by tensor product.
Parameters: 

Note :  Deprecated. Use the class KLExpansion instead 

Parameters: 

Scramble function as in Owen (1997)
Reference:
[1]  Saltelli, A., Chan, K., Scott, E.M., “Sensitivity Analysis” 