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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: 2012-2014 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.
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Returns: | the list of samples for which the experiment have not been evaluated yet. |
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Returns: | the list of results of the evaluation of f on the samples. |
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Returns: | the list of samples for which the experiment have been evaluated already. |
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Evaluate the function f on the samples.
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Sample from the multidimensional distribution defined by the dists.
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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. |
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Samples size realizations from the multidimensional distribution using the Latin Hyper Cube method.
Parameters: | size (int) – number of samples |
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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.
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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.
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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.
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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 cut-HDMR based on spectral methods from the module SpectralToolbox.Spectral1D. Additionally the cut-HDMR can be used to compute the associated ANOVA-HDMR.
Provided a Covariance function and discretization points, it generates the Gaussian fields.
Parameters: | C (function) – Covariance function C(x1,x2) |
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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 |
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Generates random fields from the input variables (Normally distributed)
Parameters: | xi (np.ndarray) – 1 or 2 dimensional array containing the generating variables. If 2-dimensional, each row should contain a different sample. |
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Returns: | the realizations of the random field |
Return type: | np.ndarray |
KLExpansion: Computes the 1D KL expansion of the covariance matrix C, using the Legendre-Gauss-Loabatto rule for the solution to the generalized eigenvalue problem A * u = lmb * M * u. The KLExpansion of d-dimensional random fields is obtained by tensor product.
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Note : | Deprecated. Use the class KLExpansion instead |
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Scramble function as in Owen (1997)
Reference:
[1] | Saltelli, A., Chan, K., Scott, E.M., “Sensitivity Analysis” |