Utility Functions

Utility functions for SRSF Manipulations

moduleauthor:: Derek Tucker <dtucker@stat.fsu.edu>

utility_functions.SqrtMean(gam)

calculates the srsf of warping functions with corresponding shooting vectors

Parameters:gam – numpy ndarray of shape (M,N) of M warping functions with N samples Return type:2 numpy ndarray and vector Return mu:Karcher mean psi function Return gam_mu:vector of dim N which is the Karcher mean warping function Return psi:numpy ndarray of shape (M,N) of M SRSF of the warping functions Return vec:numpy ndarray of shape (M,N) of M shooting vectors

utility_functions.SqrtMeanInverse(gam)

finds the inverse of the mean of the set of the diffeomorphisms gamma

Parameters:gam – numpy ndarray of shape (M,N) of M warping functions with N samples Return type:vector Return gamI:inverse of gam

utility_functions.cumtrapzmid(x, y, c)

cummulative trapzodial numerical integration taken from midpoint

Parameters:

• x – vector of size N descibing the time samples
• y – vector of size N describing the function
• c – midpoint

Return type:

vector

Return fa:

cummulative integration

utility_functions.elastic_distance(f1, f2, time, lam=0.0)

” calculates the distnaces between function, where f1 is aligned to f2. In other words caluclates the elastic distances

Parameters:

• f1 – vector of size N
• f2 – vector of size N
• time – vector of size N describing the sample points
• lam – controls the elasticity (default = 0.0)

Return type:

scalar

Return Dy:

amplitude distance

Return Dx:

phase distance

utility_functions.f_to_srvf(f, time)

converts f to a square-root slope function (SRSF)

Parameters:

• f – vector of size N samples
• time – vector of size N describing the sample points

Return type:

vector

Return q:

srsf of f

utility_functions.gradient_spline(time, f)

This function takes the gradient of f using b-spline smoothing

Parameters:

• time – vector of size N describing the sample points
• f – numpy ndarray of shape (M,N) of M functions with N samples

Return type:

tuple of numpy ndarray

Return f0:

smoothed functions functions

Return g:

first derivative of each function

Return g2:

second derivative of each function

utility_functions.invertGamma(gam)

finds the inverse of the diffeomorphism gamma

Parameters:gam – vector describing the warping function Return type:vector Return gamI:inverse of gam

utility_functions.optimum_reparam(q1, time, q2, lam=0.0)

calculates the warping to align srsf q2 to q1

Parameters:

• q1 – vector of size N or array of NxM samples of first SRSF
• time – vector of size N describing the sample points
• q2 – vector of size N or array of NxM samples samples of second SRSF
• lam – controls the amount of elasticity (default = 0.0)

Return type:

vector

Return gam:

describing the warping function used to align q2 with q1

utility_functions.outlier_detection(q, time, mq, k=1.5)

calculates outlier’s using geodesci distnaces of the SRSFs from the median

Parameters:

• q – numpy ndarray of N x M of M SRS functions with N samples
• time – vector of size N describing the sample points
• mq – median calculated using time_warping.srsf_align()
• k – cutoff threshold (default = 1.5)

Returns:

q_outlier: outlier functions

utility_functions.rgam(N, sigma, num)

Generates random warping functions

Parameters:

• N – length of warping function
• sigma – variance of warping functions
• num – number of warping functions

Returns:

gam: numpy ndarray of warping functions

utility_functions.smooth_data(f, sparam)

This function smooths a collection of functions using a box filter

Parameters:

• f – numpy ndarray of shape (M,N) of M functions with N samples
• sparam – Number of times to run box filter (default = 25)

Return type:

numpy ndarray

Return f:

smoothed functions functions