Elastic Functional Tolerance Bounds¶
Functional Tolerance Bounds using SRSF
moduleauthor:: J. Derek Tucker <jdtuck@sandia.gov>
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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
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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
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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
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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