teetool.helpers Namespace Reference

Functions
def	getDistinctColours (ncolours, colour=None)
	a function to obtain n distinct colours (based on the colourspace spread into hue space), inspired by https://stackoverflow.com/questions/470690/how-to-automatically-generate-n-distinct-colors More...
def	find_nearest (original_values, target_values)
	function to find nearest values in an array, perfect for reducing the number of datapoints More...
def	nearest_spd (A)
	nearestSPD - the nearest (in Frobenius norm) Symmetric Positive Definite matrix to A More...
def	get_trajectories (ntype=0, ndim=3, ntraj=50, npoints=100, noise_std=.5)
	function to generate some distributed trajectories More...
def	in_hull (p, hull)
	Test if points in p are in hull More...
def	unique_rows (a)
	function to find unique rows More...
def	gauss_logp (y, ndim, c, A)
	function to evaluate the Gaussian log likelihood More...
def	gauss (y, ndim, c, A)
	function to evaluate the Gaussian (normal distribution) More...
def	gauss_logLc (y, ndim, cc, cA)
	function to evaluate the Gaussian log likelihood in cell-form More...
def	getMaxOutline (ndim)
	simple function to obtain infinite outline based on dimensionality More...
def	getGridFromResolution (outline, resolution)
	function to generate a grid based on outline and resolution More...
def	getDimension (cluster_data)
	finds dimension D based on cluster_data More...
def	getMinMax (cluster_data)
	find minimum/maximum of the cluster data (x, Y), x-component. More...
def	normalise_data (cluster_data)
	normalise the cluster_data in x-domain More...
def	getNorm (x, tuple_min_max)
	returns a normalised array based on a specified minimum/maximum More...
def	get_cluster_data_outline (cluster_data)
	returns the outline based on cluster_data More...
def	get_cluster_data_norm (cluster_data, outline=None)
	returns a normalised cluster_data based on outline More...

Function Documentation

find_nearest()

def teetool.helpers.find_nearest	(		original_values,
			target_values
	)

function to find nearest values in an array, perfect for reducing the number of datapoints

Parameters

original_values	an array of original values
target_values	an array of desired values

Returns

idx returns a list of indices of points that hold the nearest values

gauss()

def teetool.helpers.gauss	(		y,
			ndim,
			c,
			A
	)

function to evaluate the Gaussian (normal distribution)

Parameters

y	data-point
ndim	dimensionality of y
c	mean vector
A	convariance matrix

Returns

value value of Gaussian at point y

gauss_logLc()

def teetool.helpers.gauss_logLc	(		y,
			ndim,
			cc,
			cA
	)

function to evaluate the Gaussian log likelihood in cell-form

Parameters

y	data-point
ndim	dimensionality of y
cc	mean vector cells
cA	convariance matrix cells

Returns

loglikelihood maximum log likelihood of Gaussian, based on models found in cells

returns the log likelihood of a position based on model (in cells)

gauss_logp()

def teetool.helpers.gauss_logp	(		y,
			ndim,
			c,
			A
	)

function to evaluate the Gaussian log likelihood

Parameters

y	data-point
ndim	dimensionality of y
c	mean vector
A	convariance matrix

Returns

loglikelihood log likelihood of Gaussian

get_cluster_data_norm()

def teetool.helpers.get_cluster_data_norm	(		cluster_data,
			outline = None
	)

returns a normalised cluster_data based on outline

Parameters

cluster_data	list of (x, Y) trajectory data
outline	array specifying an pre-set outline, otherwise the outline is calculated from the cluster_data

Returns

cluster_data_norm list of (x, Y), where all Y and x fit in [0, 1] domain

specifying an outline is useful when wanting to normalise based on multiple clusters

get_cluster_data_outline()

def teetool.helpers.get_cluster_data_outline

(

cluster_data

)

returns the outline based on cluster_data

Parameters

cluster_data

list of (x, Y) trajectory data

Returns

outline [min, max]*ndim for outline

get_trajectories()

def teetool.helpers.get_trajectories	(		ntype = 0,
			ndim = 3,
			ntraj = 50,
			npoints = 100,
			noise_std = .5
	)

function to generate some distributed trajectories

Parameters

ntype	type of trajectory (0 or 1)
ndim	dimensionality of trajectories (2 or 3)
ntraj	number of trajectories desired
npoints	how many points each trajectory has
noise_std	includes normal distributed (Gaussian) noise to the trajectory data-points return cluster_data a list of (x, Y) trajectory data

getDimension()

def teetool.helpers.getDimension

(

cluster_data

)

finds dimension D based on cluster_data

Parameters

cluster_data

list of (x, Y) format

Returns

D dimensionality of trajectory data

getDistinctColours()

def teetool.helpers.getDistinctColours	(		ncolours,
			colour = None
	)

a function to obtain n distinct colours (based on the colourspace spread into hue space), inspired by https://stackoverflow.com/questions/470690/how-to-automatically-generate-n-distinct-colors

Parameters

ncolours	integer with number of distinct colours
colour	when colour is specified, this overrides any distinct colour

Returns

rgb_tuples a list of tuples with (R, G, B) in the [0,1] domain

getGridFromResolution()

def teetool.helpers.getGridFromResolution	(		outline,
			resolution
	)

function to generate a grid based on outline and resolution

Parameters

outline	[ndim x 2], minimum and maximum values
resolution	can be a scalar [1x1] or specified per dimension [ndim x 1]

Returns

xx x grid

yy y grid

zz (optional) z grid

getMaxOutline()

def teetool.helpers.getMaxOutline

(

ndim

)

simple function to obtain infinite outline based on dimensionality

Parameters

ndim	number of dimensions

Returns

outline [ndim x 2], for minimum and maximum

getMinMax()

def teetool.helpers.getMinMax

(

cluster_data

)

find minimum/maximum of the cluster data (x, Y), x-component.

The tuple is used to normalise the data

Parameters

cluster_data

list of (x, Y)

Returns

xmin minimum value of x

xmax maximum value of x

getNorm()

def teetool.helpers.getNorm	(		x,
			tuple_min_max
	)

returns a normalised array based on a specified minimum/maximum

Parameters

x	input array
tuple_min_max	a tuple with minimum and maximum specified

Returns

x_norm a normalised array x

in_hull()

def teetool.helpers.in_hull	(		p,
			hull
	)

Test if points in p are in hull

Parameters

p	an array of points
hull	points for hull, if not hull, make a hull from points

Returns

p_bool an array with bools whether or not the points are inside the hull

p should be a NxK coordinates of N points in K dimensions hull is either a scipy.spatial.Delaunay object or the MxK array of the coordinates of M points in Kdimensions for which Delaunay triangulation will be computed

https://stackoverflow.com/questions/16750618/whats-an-efficient-way-to-find-if-a-point-lies-in-the-convex-hull-of-a-point-cl

nearest_spd()

def teetool.helpers.nearest_spd

(

A

)

nearestSPD - the nearest (in Frobenius norm) Symmetric Positive Definite matrix to A

Parameters

A	input matrix

Returns

Ahat nearest SPD matrix to A

nearestSPD - the nearest (in Frobenius norm) Symmetric Positive Definite matrix to A usage: Ahat = nearestSPD(A)

From Higham: "The nearest symmetric positive semidefinite matrix in the Frobenius norm to an arbitrary real matrix A is shown to be (B + H)/2, where H is the symmetric polar factor of B=(A + A')/2."

http://www.sciencedirect.com/science/article/pii/0024379588902236

arguments: (input) A - square matrix, which will be converted to the nearest Symmetric Positive Definite Matrix.

Arguments: (output) Ahat - The matrix chosen as the nearest SPD matrix to A.

RE-CODED FROM MATLAB nearestSPD http://uk.mathworks.com/matlabcentral/fileexchange/42885-nearestspd

normalise_data()

def teetool.helpers.normalise_data

(

cluster_data

)

normalise the cluster_data in x-domain

Parameters

cluster_data

list of (x, Y) data

Returns

cluster_data_norm list of (x, Y) data with normalised x

unique_rows()

def teetool.helpers.unique_rows

(

a

)

function to find unique rows

Parameters

a

matrix

Returns

unique_A the matrix a with only unique rows

https://stackoverflow.com/questions/16970982/find-unique-rows-in-numpy-array