PCE

PCE#

class uqpce.pce.pce.PCE(**kwargs)#

The Polynomial Chaos Exapansion (PCE) model class. This class is intended to be an interface for programmers.

Parameters:

kwargs –

key word arguments used by UQPCE

input_file :: file containing variables
matrix_file :: file containing matrix elements
results_file :: file containing results
verification_results_file :: file containing verification results
verification_matrix_file :: file containing verification matrix elements
output_directory :: directory that the outputs will be put in
case :: case name of input data
significance :: significance level of the confidence interval
order :: order of polynomial chaos expansion
over_samp_ratio :: over sampling ratio; factor for how many points to be used in calculations
verify_over_samp_ratio :: over sampling ratio for verification; factor for how many points to be used in calculations
aleat_sub_samp_size :: the number of samples to check the new high and low intervals at for each individual curve
epist_sub_samp_size :: the number of curves to check the new high and low intervals at for a set of curves
conv_threshold_percent :: the percent of the response mean to be used as a threshold for tracking convergence
epist_samp_size :: the number of times to sample for each variable with epistemic uncertainty
aleat_samp_size :: the number of times to sample for each variable with aleatory uncertainty
version :: displays the version of the software
verbose :: increase output verbosity
verify :: allows verification of results
plot :: generates factor vs response plots, pbox plot, and error plots
plot_stand :: plots standardized variables
track_convergence_off :: allows users to converge on confidence interval until the change between the two iters is less than the threshold
model_conf_int :: includes uncertainties associated with the model itself
stats :: perform additional statistics for a more-comprehensive profile of the model
seed :: if UQPCE should use a seed for random values

add_variable(**kwargs) → None#

Adds a variable with kwargs to the PCE object.

Parameters:: kwargs – The input arguments required for the variable being added and the name of the distribution being added.

backward_elimination() → None#: Peforms backward elemination on the existing model.

build_basis(order: int) → None#

Builds the variable basis and norm squared for the model. This sets up the variable- and order- based information for the model that is independent of the response samples.

Parameters:: order – An int for the order of the model to build

check_fit() → str#: Provides statistics on the fit of the model.

check_variables(X: ndarray) → bool#

Saves figures for all of the variables with their values plotted on them, if the data is available, which serves as a check if the user’s run matrix does not match their distributions well.

Parameters:: X – The array of samples to check against the variable distributions

confidence_interval() → tuple#: Calls the ProbabilityBoxes class, resamples the model, and outputs the confidence interval at the set significance level.

fit(X: ndarray, y: ndarray) → ndarray#

Fits the PCE model and returns the matrix coefficients of the model.

Parameters:

X – An m-by-n matrix with the first dimension having the number of samples in the model (m) and the second having the number of variables in the model (n).
y – The 2D numpy array of responses from the user’s analytic tool.

from_yaml(input_file: str) → dict#

Update the PCE object from the UQPCE YAML file. Adds the variables to the object and updates the settings.

Parameters:: input_file – A string for the file name of the input yaml file

generate_responses(X, equation: str) → ndarray#

For testing purposes; allows users to generate samples according to an input function.

Parameters:

X – An m-by-n matrix with the first dimension having the number of samples in the model (m) and the second having the number of variables in the model (n).
equation – A string represenation of the desired equation, using x0 for the first variable, x1 for the second, and so on.

load_matrix_file(filename: str) → ndarray#

Loads and returns a matrix file.

Parameters:: filename – A string for the file name of the run matrix file

predict(X: ndarray, return_uncert: bool = False) → ndarray#

Predicts the model responses of an input matrix of values.

Parameters:

X – An m-by-n matrix with the first dimension having the number of samples in the model (m) and the second having the number of variables in the model (n).
return_uncert – Boolean for if the method should return the uncertainty associated with the predicted responses.

Returns:

resp_pred – the predicted value
uncert_mean – the uncertainty on the predicted value

print() → None#: Print the outputs for the model.

resample_surrogate() → ndarray#: Resamples the surrogate model.

sample(count: int = - 1, seed=None) → ndarray#

This method returns a matrix of samples from the input variables.

Parameters:: count – The number of samples to generate. A value of -1 creates a number of samples based on the attribute over_samp_ratio.

save_model() → bool#: Pickles the entire PCE object.

set_samples(X: ndarray) → None#: Sets the run matrix samples for the PCE model.

update_settings(**kwargs) → None#

A method to update the object attributes with the input kwargs.

Parameters:: kwargs – The key-value pairs for the keyword arguments to update for the PCE model

verification(X: ndarray, y: ndarray) → ndarray#

Predicts the response for the verification samples and compares the predicted responses to the user-provided verification response file.

Parameters:

X – An m-by-n matrix with the first dimension having the number of samples in the model (m) and the second having the number of variables in the model (n).
y – The 2D numpy array of responses from the user’s analytic tool.

Returns:

The error between the truth and the predicted reponses.

Return type:

ver_error

verify_sample(count: int = - 1, seed=None) → ndarray#

Sample the number of verification values according to the input count or the set attribute verify_over_samp_ratio.

Parameters:: count – The number of verification samples to generate. A value of -1 creates a number of samples based on the attribute verify_over_samp_ratio.

write_outputs() → None#: Writes all of the output files for all of the models associated with the PCE object.