otaf.distribution package

Module contents

otaf.distribution.compute_sup_inf_distributions(distributions, x_min=-10, x_max=10, n_points=10000)[source]

Compute the supremum (sup) and infimum (inf) CDFs for a list of distributions.

This function evaluates the Cumulative Distribution Functions (CDFs) at n_points evenly spaced points between x_min and x_max for a given list of distributions. It then computes the pointwise supremum and infimum of the CDFs across the distributions at each of these points.

Parameters:

distributionslist

A list of objects where each object has a computeCDF(x) method to evaluate the CDF at a point x.

x_minfloat

The lower bound of the x values over which the CDFs are evaluated.

x_maxfloat

The upper bound of the x values over which the CDFs are evaluated.

n_pointsint, optional

The number of points at which the CDFs are evaluated between x_min and x_max. Default is 10,000.

Returns:

: sup_data : np.ndarray

A 2D array with shape (n_points, 2), where the first column is the x values and the second column contains the pointwise supremum of the CDFs at each x.

inf_datanp.ndarray

A 2D array with shape (n_points, 2), where the first column is the x values and the second column contains the pointwise infimum of the CDFs at each x.

otaf.distribution.generate_correlated_samples(mu1=0, mu2=0, sigma1=1, sigma2=1, corr=0, N=1)[source]

Generate bivariate correlated samples.

otaf.distribution.get_composed_normal_defect_distribution(defect_names, mu_list=[], sigma_list=[], mu_dict={}, sigma_dict={})[source]

Create a composed distribution of defects based on their names and associated standard deviations.

Parameters:

  • defect_names (list) – A list of defect variable names (symbols).

  • mu_list (list, optional) – List of means for each defect. If not provided, defaults to 0.0 for all defects.

  • sigma_list (list, optional) – List of standard deviations for each defect. If not provided, defaults to 1.0 for all defects.

  • mu_dict (dict, optional) – Dictionary mapping defect names to their mean values.

  • sigma_dict (dict, optional) – Dictionary mapping defect names to their standard deviation values.

Returns:

A composed distribution object.

Return type:

ot.ComposedDistribution

Notes

  • The defect names are expected to have specific prefixes to identify their type:

    • u_ for translation along the x-axis

    • v_ for translation along the y-axis

    • w_ for translation along the z-axis

    • alpha_ for rotation around the x-axis

    • beta_ for rotation around the y-axis

    • gamma_ for rotation around the z-axis

  • This has to be reflected in the mu_dict/sigma_dict if provided, e.g., sigma_dict = {'u':1.0}.

otaf.distribution.get_means_standards_composed_distribution(composed_distribution)[source]

Extracts the means and standard deviations from the composed distribution. Assumes all distributions are normal (mean/std).

Parameters:

composed_distribution – The composed distribution of normal distributions.

Returns:

A list of the means of the distributions. stds: A list of the standard deviations of the distributions.

Return type:

means

otaf.distribution.get_prob_below_threshold(data_inf_sup, threshold=0)[source]

Get the probability of the gap statistic being below a specified threshold.

This function finds the element in the array data_inf_sup where the absolute value of the difference between the first column and the threshold is the smallest, and then returns the corresponding value from the second column.

Parameters: data_inf_sup : numpy array

Array where the first column contains gap values and the second column contains probabilities.

thresholdfloat, optional

The threshold to check against (default is 0).

Returns: float

The probability corresponding to the gap closest to the threshold.

otaf.distribution.multiply_composed_distribution_standard_with_constants(composed_distribution, constants)[source]

Multiply the standard deviations of each sub-distribution by corresponding constants.

This function assumes each sub-distribution is a Normal distribution, where each distribution’s parameters are in the form [mean, std, mean, std, …].

Parameters:

  • composed_distribution (ot.ComposedDistribution) – The original composed distribution.

  • constants (list[float]) – A list of constants to multiply each distribution’s standard deviation.

Returns:

A copy of the original composed distribution, with updated standard deviations.

Return type:

ot.ComposedDistribution

otaf.distribution.multiply_composed_distribution_with_constant(composed_distribution, constant)[source]

Multiply all parameters in a ComposedDistribution by a constant.

Parameters:

  • composed_distribution (ot.ComposedDistribution) – The original composed distribution.

  • constant (float) – The constant value by which to multiply all parameters.

Returns:

A copy of the original composed distribution, with its parameters scaled by the given constant.

Return type:

ot.ComposedDistribution