Elastic Functional Tolerance Bounds

Functional Tolerance Bounds using SRSF

moduleauthor:: J. Derek Tucker <jdtuck@sandia.gov>

tolerance.bootTB(f, time, a=0.5, p=0.99, B=500, no=5, parallel=True)[source]

This function computes tolerance bounds for functional data containing phase and amplitude variation using bootstrap sampling

Parameters:
  • f (np.ndarray) – numpy ndarray of shape (M,N) of N functions with M samples
  • time (np.ndarray) – vector of size M describing the sample points
  • a – confidence level of tolerance bound (default = 0.05)
  • p – coverage level of tolerance bound (default = 0.99)
  • B – number of bootstrap samples (default = 500)
  • no – number of principal components (default = 5)
  • parallel – enable parallel processing (default = T)
Return type:

tuple of boxplot objects

Return amp:

amplitude tolerance bounds

Rtype out_med:

ampbox object

Return ph:

phase tolerance bounds

Rtype out_med:

phbox object

Return out_med:

alignment results

Rtype out_med:

fdawarp object

tolerance.mvtol_region(x, alpha, P, B)[source]

Computes tolerance factor for multivariate normal

Krishnamoorthy, K. and Mondal, S. (2006), Improved Tolerance Factors for Multivariate Normal Distributions, Communications in Statistics - Simulation and Computation, 35, 461–478.

Parameters:
  • x – (M,N) matrix defining N variables of M samples
  • alpha – confidence level
  • P – coverage level
  • B – number of bootstrap samples
Return type:

double

Return tol:

tolerance factor

tolerance.pcaTB(f, time, a=0.5, p=0.99, no=5, parallel=True)[source]

This function computes tolerance bounds for functional data containing phase and amplitude variation using fPCA

Parameters:
  • f (np.ndarray) – numpy ndarray of shape (M,N) of N functions with M samples
  • time (np.ndarray) – vector of size M describing the sample points
  • a – confidence level of tolerance bound (default = 0.05)
  • p – coverage level of tolerance bound (default = 0.99)
  • no – number of principal components (default = 5)
  • parallel – enable parallel processing (default = T)
Return type:

tuple of boxplot objects

Return warp:

alignment data from time_warping

Return pca:

functional pca from jointFPCA

Return tol:

tolerance factor

tolerance.rwishart(df, p)[source]

Computes a random wishart matrix

Parameters:
  • df – degree of freedom
  • p – number of dimensions
Return type:

double

Return R:

matrix