Elastic Functional Tolerance Bounds#
Functional Tolerance Bounds using SRSF
moduleauthor:: J. Derek Tucker <jdtuck@sandia.gov>
- tolerance.bootTB(f, time, a=0.05, 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