scrypy package

Submodules

scrypy.figure_choice_shares_over_time module

scrypy.figure_cone_plot_choice_shares module

scrypy.jac_estimation_chol module

Estimates covariance matrix for KW94 Dataset 1 with Simulated Max. Likelihood.

scrypy.jac_estimation_chol.chol_reindex_params(params_sdcorr)

Creates the params Df with Cholesky factors and the right indices for respy. This transformation holds only true for the parametrization in KW94 Dataset 1. Thus, this function simply changes SD-Corr indices to cholesky indices. Without the slicing and merging, index (‘maximum_exp’, ‘edu’) yields an uniqueness error for the second index when (…, ‘sd_edu’) is set to (…, ‘edu’). Yet, because we have double_indices the indices ARE unique.

Parameters

params_sdcorrDataFrame

Parameters DataFrame in respy format with SD-Corr matrix elements

Returns

params_cholDataFrame

Parameters DataFrame in respy format with matrix elements from Choleksy decomposition of covariance matrix that underlies the SD-Corr matrix.

scrypy.jac_estimation_chol.jac_estimation_chol(save=False)

Estimates covariance matrix for KW94 Dataset 1 with Simulated Max. Likelihood. The Jacobian matrix is used instead of Hessian because it yields no inversion error. The parameters contain Cholesky factors instead of SD-Corr-Matrix because these factors are unconstrained. Therefore, their distribution can be estimated by an unconstrained normal distribution.

Parameters

savebool

Indicates wether to save data.

Returns

par_estimates_chol_dfDataFrame

Contains the estimates parameters and the not estimates fixed parameters in respy format.

rand_par_chol_dfDataFrame

Df containing variable parameters, SDs and lower and upper bound in estimagic format. It can be post-processed with surface/topography plot.

cov_chol_dfDataFrame

Df containing the covariance matrix.

corr_chol_dfDataFrame

DF containing the correlation matrix.

scrypy.multi_quantities_of_interest module

Besides the difference in mean age of education, this module also generates two Dataframes for a second QoI: The difference in education shares over time for a sample of agents. The second quantity is used to create the cone plot.

scrypy.multi_quantities_of_interest.model_wrapper_kw_94(input_params, base_options, tuition_subsidy)

Wrapper around respy to compute the mean number of years in education.

Parameters

input_paramsDataframe

Contains the complete respy vector of input parameters with indices.

base_optionsdict

Contains the options for the sumulation of agents.

tuition_subsidyfloat

tuition subsidy that is added to the respective paramter.

add_qoi_edu_choicesbool

Specifies whether to compute the addition QoIs, education choice shares in the sample over time, to depict a cone plot (confidence interval plot).

Returns

edufloat

Mean number of years in education.

occ_shares_dfDataFrame

Occupation shares over all ages.

policy_dfDataframe

Dataframe of occupation choices of sample of agents of time.

scrypy.multi_quantities_of_interest.multi_quantities_of_interest(input_params, *args)

Computes the Quantity of Interest.

Parameters

input_paramsndarray

Unindexed input parameters.

multi_qoisbool

Option to compute policy_occ_shares_df and base_occ_shares_df.

Returns

change_mean_edufloat

Quantity of Interest. Mean changes in education years of population.

policy_occ_shares_dfDataFrame

Occupation shares over all ages for the policy scenario.

base_occ_shares_dfDataFrame

Occupation shares over all ages for the base scenario.

scrypy.multi_quantities_of_interest.transform_params_kw94_respy(params_idx)

Converts indexed Series of non-constant input paramters to a Dataframe and adds three constant factors to achieve respy format.

Parameters

params_idxSeries

Non-constant input paramters with correct indices

Returns

rp_params_dfDataframe

Input parameters in respy format.

Raises

AssertionError

If the lenght of the paramter vector is incorrect.

scrypy.plots module

scrypy.sampling_schemes module

Functions that create random samples in trajectory and radial design.

scrypy.sampling_schemes.morris_trajectory(n_inputs, n_levels, seed=123, normal=False, numeric_zero=0.01, step_function=<function stepsize at 0x7f3a908b8ef0>, stairs=True)

Creates random sample in trajectory design.

This function creates a random sample for a number of function parameters (columns). The sample itself consists of the number plus one vectors of parameter draws (rows). It also computes the steps taken by each element.

Parameters

n_inputsint

Number of input paramters / columns / rows - 1.

n_levelsint

Number of distict grid points.

seedint

Random seed.

normalbool

Indicates whether to transform points by scipy.normal.ppt

numeric_zerofloat

if normal is True: Prevents scipy.normal.ppt to return -Inf and Inf for 0 and 1.

step_functionfunction

Constant step as function of n_levels added to lower half of point grid.

stairsbool

if False: Randomly shuffle columns, dissolves stairs shape.

Returns

B_randomndarray

Random sample in trajectory design. Dimension n_inputs x n_inputs + 1.

trans_stepsndarray

Column vector of steps added to base value point. Sorted by parameter/column. Dimension n_inputs x 1.

See also

stepsize

See parameter step_function.

transform_uniform_stnormal_uncorr

See parameter numeric_zero.

Notes

The method is described in [1]. This function follows the notation therein. The idea is tailored to compute a random sample of function arguments to compute local derivates. First, a random row of paramters is drawn. Then, one parameter is changed by a fixed step in each row. The local derivatives can be computed by subtracting the function evaluations of each row from its upper row, thereby obtaining one local derivative for each parameter. The order of rows and columns may be shuffled. Shuffling rows creates a negative stepsize. By default, the shuffling of columns is turned off to facilitate post-processing.

Importantly, an additional option is to evaluate the points by the inverse normal cdf to account for normally distributed input paramters vice versa uniformly distributed ones. For this purpose, zeros and ones are slighly shifted towards the centre of [0,1], so that no infinite values arise. Given the shape of the inverse cdf, the specific transformation choice has large influences on the stepsize and therefore the Elementary Effects. To account for transformations, the step is recomputed for each parameter by subtracting the last first row from the last row.

References

[1] Morris, M. D. (1991). Factorial sampling plans for preliminary computational experiments. Technometrics 33 (2), 161–174.

scrypy.sampling_schemes.radial_sample(n_rad, n_inputs, normal=False, sequence='S')

Generates sample in radial design as described in [1].

For each subsample, there are n_inputs + 1 rows and n_inputs colums. Each row is identical except of the diagonal of the sample w/o the first row.

Parameters

n_radint

Number of subsamples.

n_inputsint

Number of input paramters / columns / rows - 1.

seedint

Random seed.

normalbool

Indicates whether to transform points by scipy.normal.ppt

numeric_zerofloat

if normal is True: Prevents scipy.normal.ppt to return -Inf and Inf for 0 and 1.

sequencestring

Type of quasi-random sequence.

Returns

samplendarray

Random sample in radial design. Dimension n_inputs x n_inputs + 1.

trans_stepsndarray

Column vector of steps added to base value point. Sorted by parameter/column. Dimension n_inputs x 1.

Notes

See [2] for abbreviations of the different sequence types.

In contrary to the trajectory design, the stepsize differs right from the start by design and only one element changes in each row compared to the first row.

All distict elements in the whole sample are drawn at once because the default Sobol’ sequence can not be reseeded.

References

[1] Ge, Q. and M. Menendez (2017). Extending morris method for qualitative global sensitivityanalysis of models with dependent inputs. Reliability Engineering & System Safety 100 (162), 28–39.

[1] https://github.com/jonathf/chaospy/blob/master/chaospy/distributions/sampler/generator.py#L62

scrypy.sampling_schemes.stepsize(n_levels)

Computes stepsize to create equiprobable sample points for the trajectory design.

Parameters

n_levelsint

Number of points in a trajectory sample.

Returns

stepfloat

Step added to each lower half point of the point grid.

Raises

AssertionError

If the number of levels is not an even integer.

Notes

This function, published in [1], assumes that the number of sample points called “levels” is an even integer. The first row in the trajectory is initialized with the lower half of the desired equispaced points between 0 and 1. Given the below formula, the step added to the lowest, second lowest, …, highest point in the lower half creates the lowest, second lowest, …, highest point in the upper half of the point grid.

References

[1] Morris, M. D. (1991). Factorial sampling plans for preliminary computational experiments. Technometrics 33 (2), 161–174.

scrypy.sampling_schemes.trajectory_sample(n_traj, n_inputs, n_levels, seed=123, normal=False, numeric_zero=0.01, step_function=<function stepsize at 0x7f3a908b8ef0>, stairs=True)

Loops over morris_sample.

Parameters

n_inputsint

Number if input paramters.

n_levelsint

Number of distict grid points.

seedint

Random seed.

normalbool

Indicates whether to transform points by scipy.normal.ppt

numeric_zerofloat

if normal is True: Prevents scipy.normal.ppt to return -Inf and Inf for 0 and 1.

step_functionfunction

Constant step as function of n_levels added to lower half of point grid.

stairsbool

if False: Randomly shuffle columns, dissolves stairs shape.

Returns

sample_traj_listlist of ndarrays

Set of trajectories.

steps_listlist of ndarrays

Set of steps taken by each base row.

scrypy.sandbox module

scrypy.screening_measures module

Computes the screening measures for correlated inputs that I improved upon [1] by adjusting the step in the denumeroter to the transformed step in the nominator in order to not violate the definition of the function derivative.

References

[1] Ge, Q. and M. Menendez (2017). Extending morris method for qualitative global sensitivityanalysis of models with dependent inputs. Reliability Engineering & System Safety 100 (162), 28–39.

scrypy.screening_measures.compute_measures(ee_i, sd_x=1, sd_y=1, sigma_norm=False, ub=False)

Compute aggregate measures based on (individual) Elementary Effects.

Returns

measures_list: list

contains:

ee_meanndarray

Mean Elementary Effect for each parameter.

ee_abs_meanndarray

Mean absolute correlated Elementary Effect for each parameter.

ee_sdndarray

SD of correlated Elementary Effects for each parameter.

Notes

ub follows http://www.andreasaltelli.eu/file/repository/DGSA_MATCOM_2009.pdf.

scrypy.screening_measures.screening_measures(function, traj_list, step_list, cov, mu, radial=False)

Computes screening measures for a set of paramters.

Parameters

functionfunction

Function or Model of which its parameters are subject to screening.

traj_listlist of ndarrays

List of transformed trajectories according to [1].

step_listlist of ndarrays

List of steps that each parameter takes in each trajectory.

covndarray

Covariance matrix of the input parameters.

mundarray

Expectation values of the input parameters.

radialbool

Sample is in trajectory or radial design.

Returns

measures_list: list

contains:

ee_uncorrndarray

Mean uncorrelated Elementary Effect for each parameter.

ee_corrndarray

Mean correlated Elementary Effect for each parameter.

abs_ee_uncorrndarray

Mean absolute uncorrelated Elementary Effect for each parameter.

abs_ee_corrndarray

Mean absolute correlated Elementary Effect for each parameter.

sd_ee_uncorrndarray

SD of uncorrelated Elementary Effects for each parameter.

sd_ee_corrndarray

SD of correlated Elementary Effects for each parameter.

obs_list: list

contains

ee_uncorr_indarray

Observations of uncorrelated Elementary Effects.

ee_corr_indarray

Observations of correlated Elementary Effects.

Notes

The samples can be in trajectory or in radial design and the deviates can be from an arbitrary (correlated) normal distribution or an uncorrelated Uniform[0,1] distribution.

Unorrelated uniform paramters require different interpretion of mu as a scaling summand rather than the expectation value.

It might be necessary to multiply the SDs by (n_trajs/(n_trajs - 1)) for the precise formula. However, this leads to problems for the case of only one trajectory - which is used in test_screening_measures_uncorrelated_g_function.

scrypy.script_uncertainty_propagation module

Script for Uncertainty Propagation. The structure is adapted to parallel computing.

scrypy.script_uncertainty_propagation.propagate_mean_estimates()

Evaluates the QoI at the mean estimates. Called in run.

Returns

mean_edu_dfDataFrame

Difference in mean years of education between policy and base scenario.

base_occ_shares_dfDataFrame

Occupation shares over all ages for the policy scenario.

policy_occ_shares_dfDataFrame

Occupation shares over all ages for the base scenario.

scrypy.script_uncertainty_propagation.run(args)

Creates and saves the inputs and the outputs of the Uncertainty Propgation.

In context of parallel computing, this function also protects the “entry point” of new programs to not produce endlessly many entries. See [1].

Parameters

number_drawsint

Number of draws of random input paramter vector from the respective distribution.

seedint

Random seed.

Raises

AssertionError

If tempory output array temp_array contains NaNs, and +/- Infs.

References

[1] https://docs.python.org/3/library/multiprocessing.html#multiprocessing-programming.

scrypy.select_sample_set module

Functions that decrease a set of sample sets in order to increase its representativeness. These are developed in the context of the trajectory design because it can not cover the space very densely. The methods are taken from the effective screening design in [1] and the efficient screening design in [2]

References

[1] Campolongo, F., J. Cariboni, and A. Saltelli (2007). An effective screening design for sensitivity analysis of large models. Environmental modelling & software 22 (10), 1509– 1518. [2] Ge, Q. and M. Menendez (2014). An efficient sensitivity analysis approach for computationally expensive microscopic traffic simulation models. International Journal of Transportation 2 (2), 49–64.

scrypy.select_sample_set.campolongo_2007(sample_traj_list, n_traj)

Implements the post-selected sample set in [1].

Takes a list of Morris trajectories and selects the n_traj trajectories with the largest distance between them. Returns the selection as array with n_inputs at the verical and n_traj at the horizontal axis and as a list. It also returns the diagonal matrix that contains the pair distance between each trajectory pair.

Parameters

sample_traj_listlist of ndarrays

Set of samples.

n_trajint

Number of samples to choose from sample_traj_list.

Returns

sample_traj_listlist of ndarrays

Set of trajectories.

select_dist_matrixndarray

Symmetric distance_matrix of selection.

select_indiceslist

Indices of selected samples.

scrypy.select_sample_set.combi_wrapper(iterable, r)

Wrapper around itertools.combinations, written in C, see [1].

Parameters

iterableiterable object

Hashable container like a list of distinct elements to combine.

rint

Number to draw from iterable with putting back and regarding the order.

Returns

list_listlist of lists

All possible combinations in ascending order.

References

[1] https://docs.python.org/2/library/itertools.html#itertools.combinations.

scrypy.select_sample_set.compute_pair_distance(sample_0, sample_1)

Computes the distance measure between a pair of samples.

The aggregate distance between sum of the root of the square distance between each parameter vector of one sample to each vector of the other sample.

Parameters

sample_0ndarray

Sample with paramters in cols and draws as rows.

sample_1ndarray

Sample with paramters in cols and draws as rows.

Returns

distancefloat

Pair distance.

Raises

AssertionError

If sample is not in trajectory or radial design shape.

AssertionError

If the sample shapes differ.

Notes

The distance between two samples is sum of the root of the square distance between each parameter vector of one sample to each vector of the other sample.

scrypy.select_sample_set.distance_matrix(sample_list)

Computes symmetric matrix of pair distances for a list of samples.

Parameters

sample_listlist of ndarrays

Set of samples.

Returns

distance_matrixndarry

Symmatric matrix of pair distances.

scrypy.select_sample_set.final_ge_menendez_2014(sample_traj_list, n_traj)

Implements both “improvements” in [2] vis-a-vis [1].

Parameters

sample_traj_listlist of ndarrays

Set of samples.

n_trajint

Number of samples to choose from sample_traj_list.

Returns

sample_traj_listlist of ndarrays

Set of trajectories.

select_dist_matrixndarray

Symmetric distance_matrix of selection.

select_indiceslist

Indices of selected samples.

See also

next_combi_total_distance_gm14

Notes

This function, is in fact much slower than intermediate_ge_menendez_2014 because it uses more for loops to get the pair distances from the right combinations that must be subtracted from the total distances.

This function selects n_traj trajectories from n_traj_sample trajectories by iteratively selecting n_traj_sample - i for i = 1,…,n_traj_sample - n-traj. For this purpose, next_combi_total_distance_gm14 computes the total distance of each trajectory combination by using the total distance of each combination in the previous step and subtracting each pair distance with the dropped trajectory, that yielded the lowest total distance combinations in the previous step.

scrypy.select_sample_set.intermediate_ge_menendez_2014(sample_traj_list, n_traj)

Implements the essential of the two “improvements” in[2] vis-a-vis [1].

This is basically a wrapper around select_trajectories_wrapper_iteration.

Parameters

sample_traj_listlist of ndarrays

Set of samples.

n_trajint

Number of samples to choose from sample_traj_list.

Returns

sample_traj_listlist of ndarrays

Set of trajectories.

select_dist_matrixndarray

Symmetric distance_matrix of selection.

select_indiceslist

Indices of selected samples.

See also

select_trajectories_wrapper_iteration

Notes

Oftentimes this function leads to diffent combinations than select_trajectories. However, their total distance is very close to the optimal solution.

scrypy.select_sample_set.next_combi_total_distance_gm14(combi_total_distance, pair_dist_matrix, lost_index)

Selects the set of samples minus one sample.

Based on the algorithmic computation of the total_distance proposed by [2]. I.e. by re-using and adjusting the first combi_total_distance matrix each iteration. Used for selecting iteratively rather than by brute force.

Parameters

combi_total_distance_nextndarray

Matrix with n_traj + 1 rows. The first n_traj cols are filled with indices of samples and the last column is the total_distance of the combinations of samples marked by indices in the same row and the columns before.

pair_dist_matrixndarray

Distance matrix of all combinations and their total_distance.

lost_indexint

index of the sample that will be dropped from the samples in the above objects.

Returns

combi_total_distance_nextndarray

combi_total_distance without the dropped sample.

pair_dist_matrix_nextndarray

pair_dist_matrix without the dropped sample.

lost_indexndarray

lost_index without the dropped sample one iteration before.

Notes

The function computes the total distance of each trajectory combination by using the total distance of each combination in the previous step and subtracting each pair distance with the dropped trajectory, that yielded the lowest total distance combinations in the previous step.

This function, is in fact much slower than select_trajectories_wrapper_iteration because it uses more for loops to get the pair distances from the right combinations that must be subtracted from the total distances.

scrypy.select_sample_set.select_sample_set_normal(samp_list, n_select, numeric_zero)

Post-select set of samples based on [0,1] and transform it to stnormal space.

Parameters

samp_listlist of ndarrays

Sub-samples.

n_selectint

Number of sub-samples to select from samp_list.

numeric_zerofloat

if normal is True: Prevents scipy.normal.ppt to return -Inf and Inf for 0 and 1.

Returns

samp_listlist of ndarrays

steps_listlist of ndarrays

See also

intermediate_ge_menendez_2014

Notes

Function for post-selection is intermediate_ge_menendez_2014 because it is the fastest.

scrypy.select_sample_set.select_trajectories(pair_dist_matrix, n_traj)

Computes total distance for each n_traj combinations of a set of samples.

Parameters

pair_dist_matrixndarray

distance_matrix for a sample set.

n_trajint

Number of sample combinations for which the total_distance is computed.

Returns

max_dist_indiceslist of ints

Indices of samples in pair_dist_matrix that are part of the combination with the largest total_distance.

combi_total_distancendarray

Matrix with n_traj + 1 rows. The first n_traj cols are filled with indices of samples and the last column is the total_distance of the combinations of samples marked by indices in the same row and the columns before.

Raises

AssertionError

If pair_dist_matrix is not symmetric.

AssertionError

If the number of combinations does not correspong to the combinations indicated by the size of pair_dist_matrix.

Notes

This function can be very slow because it computes distances between np.binomial(len(pair_dist_matrix, n_traj) pairs of trajectories. Example: np.biomial(30,15) = 155117520.

This selection function yields precise results because each total distance for each possible combination of trajectories is computed directly. The faster, iterative methods can yield different results that are, however, close in the total distance. The total distances tend to differentiate clearly. Therefore, the optimal combination is precisely determined.

scrypy.select_sample_set.select_trajectories_wrapper_iteration(pair_dist_matrix, n_traj)

Selects the set of samples minus one sample.

Used for selecting iteratively rather than by brute force. Implements the main step of the essential of the two “improvements” from [2] to [1].

Parameters

pair_dist_matrixndarray

Distance matrix of all combinations and their total_distance.

n_trajint

number of samples to choose from a set of samples based on their total_distance.

Returns

tracker_keep_indiceslist

Indices of samples part of the selection.

combi_total_distancendarray

Matrix with n_traj + 1 rows. The first n_traj cols are filled with indices of samples and the last column is the total_distance of the combinations of samples marked by indices in the same row and the columns before.

See also

select_trajectories

Notes

Oftentimes this function leads to diffent combinations than select_trajectories. The reason seems to be that this function deviates from the optimal path due to numerical reasons as different combinations may be very close (see [2]). However, the total sum of the returned combinations are close. Therefore, the total_distance loss is negligible compared to the speed gain for large numbers of trajectory combinations.

This implies that, combi_total_distance always differs from the one in select_trajectories because it only contains the combination indices from the last iteration if n_traj is smaller than the sample set minus 1.

The trick using tracker_keep_indices is an elegant solution.

scrypy.select_sample_set.total_distance(distance_matrix)

Computes the total distance measure of all pairs of samples in a set.

The equation corresponds to Equation (10) in [2].

Parameters

distance_matrixndarray

diagonal matrix of distances for sample pairs.

Returns

total_distance: float

total distance measure of all pairs of samples in a set.

scrypy.transform_distributions module

Functions for the inverse Rosenblatt / inverse Nataf transformation from uniform to normal distribution.

scrypy.transform_distributions.covariance_to_correlation(cov)

Converts covariance matrix to correlation matrix.

Parameters

covndarray

Covariance matrix.

Returns

corrndarray

Correlation matrix.

scrypy.transform_distributions.transform_stnormal_normal_corr(z_row, cov, mu)

Transformation from standard normal to multivariate normal space with given correlations following [1], page 77-102.

Step 1) Compute correlation matrix. Step 2) Introduce dependencies to standard normal sample. Step 3) De-standardize sample to normal space.

Parameters

z_rowndarray

Row of uncorrelated standard normal deviates.

covndarray

Covariance matrix of correlated normal deviates.

mundarray

Expectation values of correlated normal deviates

Returns

x_norm_rowndarray

Row of correlated normal deviates.

correlate_stepfloat

Lower right corner element of the lower Cholesky matrix.

Notes

Importantly, the step in the numerator of the uncorrelated Elementary Effect is multiplied by correlate_step. Therefore, this factor has to multiply the step in the denominator as well to not violate the definition of the function derivation.

This method is equivalent to the one in [2], page 199 which uses the Cholesky decomposition of the covariance matrix directly. This saves the scaling by SD and expectation.

This method is simpler and slightly more precise than the one in [3], page 33, for normally distributed paramters.

[1] explains how Rosenblatt and Nataf transformation are equal for normally distributed deviates.

References

[1] Lemaire, M. (2013). Structural reliability. John Wiley & Sons. [2] Gentle, J. E. (2006). Random number generation and Monte Carlo methods. Springer Science & Business Media. [3] Ge, Q. and M. Menendez (2017). Extending morris method for qualitative global sensitivity analysis of models with dependent inputs. Reliability Engineering & System Safety 100 (162), 28–39.

scrypy.transform_distributions.transform_uniform_stnormal_uncorr(uniform_deviates, numeric_zero=0.005)

Converts sample from uniform distribution to standard normal space without regarding correlations.

Parameters

uniform_deviatesndarray

Draws from Uniform[0,1].

numeric_zerofloat

Used to substitute zeros and ones before applying scipy.stats.norm to not obtain -Inf and Inf.

Returns

stnormal_deviatesndarray

uniform deviates converted to standard normal space without correlations.

See also

morris_trajectory

Notes

This transformation is already applied as option in morris_trajectory. The reason is that scipy.stats.norm transforms the random draws from the unit cube non-linearily including the addition of the step. To obtain non-distorted screening measures, it is important to also account for this transformation of the step in the denominator to not violate the definition of the function derivation.

The parameter numeric_zero can be highly influential. I prefer it to be relatively large to put more proportional, i.e. less weight on the extremes.

scrypy.transform_reorder module

Functions for reordering the sample rows following [1].

The intuition behind the reordering in general is the following: To compute the uncorrelated Elementary Effects, one moves the sampled elements that have been changed by step to the back of the row. For the correlated EE, one leaves the newly changed element in front, but moves the elements that were changed in rows above to the end. These compose the left parts of the numerator in the EE definition. One then subtracts the same row, except that the changed element is unchanged. The reason for these reorderings is that the correlation technique works hierarchically, like Dominoes. The element before is unaffected by the correlation of the elements thereafter. This implies that the first element is unchanged, as for the correlated EE. Therefore, the step is involved in correlating the other elements without becoming changed itself. The opposite is true for the uncorrelated EE. The above procedure is dervied from the ordering in trajectory samples. It also works for the radial design. Other functions order the expectations and covariance matrix accordingly. They are also used to initialize the correlating loops in the two functions in transform_ee.py in the right order.

References

[1] Ge, Q. and M. Menendez (2017). Extending morris method for qualitative global sensitivityanalysis of models with dependent inputs. Reliability Engineering & System Safety 100 (162), 28–39.

scrypy.transform_reorder.ee_corr_reorder_sample(sample)

For each row i (non-pythonic), move the first i-1 elements to the back.

Parameters

samplendarray

sample.

row_plus_onebool

Add 1 to row index, i.e. start with second row.

Returns

sample_reorderedndarray

Reordered sample.

Notes

There is no row_plus_one=False option because this is equivalent with uncorr_reorder_sample(sample, row_plus_one=True).

scrypy.transform_reorder.ee_uncorr_reorder_sample(sample, row_plus_one=True)

For each row i (non-pythonic), move the first i elements to the back.

Parameters

samplendarray

sample.

row_plus_onebool

Add 1 to row index, i.e. start with second row.

Returns

sample_reorderedndarray

Reordered sample.

scrypy.transform_reorder.reorder_cov(cov)

Arrange covariance matrix according to the expectation vector when the first element is moved to the end.

Parameters

covndarray

Covariance matrix of row.

Returns

cov_reorderedndarray

Reordered covariance matrix of row.

scrypy.transform_reorder.reorder_mu(mu)

Move the first element of the expectation vector to the end.

Parameters

mundarray

Expectation values of row.

Returns

mu_reorderedndarray

Reordered expectation values of row.

scrypy.transform_reorder.reverse_ee_corr_reorder_sample(sample_reordered)

Reverse of function corr_reorder_sample.

Parameters

sample_reorderedndarray

Reordered sample.

Returns

samplendarray

Trjectory in original order.

scrypy.transform_reorder.reverse_ee_uncorr_reorder_sample(sample_reordered, row_plus_one=True)

Reverse of function uncorr_reorder_sample.

Parameters

sample_reorderedndarray

Reordered sample.

Returns

samplendarray

Trjectory in original order.

scrypy.transform_reorder.reverse_reorder_cov(cov_reordered)

Reverse of function reorder_cov.

Parameters

cov_reorderedndarray

Reordered covariance matrix.

Returns

covndarray

Covarince matrix in original order.

scrypy.transform_reorder.reverse_reorder_mu(mu_reordered)

Reverse of function reorder_mu.

Parameters

mu_reorderedndarray

Reordered expectation values of row.

Returns

mundarray

Expectation values of row in original order.

scrypy.transform_traj_elementary_effects module

Module contents