teetool.basis.Basis Class Reference

Basis class supports the evaluation of a basis function. More...

Inheritance diagram for teetool.basis.Basis:

Public Member Functions
def	__init__ (self, basisType, nbasis, ndim)
	The constructor of Basis. More...
def	get (self, x)
	obtain basis functions at specific points, block-diagonal More...

Private Member Functions
def	_get_1d (self, x)
	obtain basis functions at specific points More...
def	_getBasisRbf (self, x_vec, nbasis)
	evaluates the rbf basis function More...
def	_getBasisRbfVector (self, x_sca, nbasis)
	evaluates the rbf basis function for a single x More...
def	_funcRbf (self, x, mu1, sig1)
	evaluates a single rbf basis function for a single x More...
def	_getBasisBernstein (self, x_vec, nbasis)
	evaluates the Bernstein basis function in [0, 1] using the formula More...
def	_getBasisBernsteinVector (self, x_sca, nbasis)
	evaluates the Bernstein basis function in [0, 1] using the formula for a single x More...

Private Attributes
	_basisType
	'rbf' or 'bernstein' basis type More...
	_nbasis
	number of basis functions More...
	_ndim
	number of dimensions More...
	_range
	defines range of basis function More...

Detailed Description

Basis class supports the evaluation of a basis function.

These Basis functions function on the domain [0,1], however produce these on multiple dimensions by returning a block-diagonal matrix. Hence an identical basis function gets returned on each dimension.

Constructor & Destructor Documentation

__init__()

def teetool.basis.Basis.__init__	(		self,
			basisType,
			nbasis,
			ndim
	)

The constructor of Basis.

Parameters

self	object pointer
basisType	'rbf' or 'bernstein' basis-type where 'rbf' = uniformly distributed basis functions and 'bernstein' = Bernstein polynomials
nbasis	number of basis functions used
ndim	number of dimensions trajectories

Member Function Documentation

_funcRbf()

def teetool.basis.Basis._funcRbf (   self,   x,   mu1,   sig1  )

private

evaluates a single rbf basis function for a single x

Parameters

self	The object pointer.
x	point to evaluate [1 x 1]
mu1	centre of rbf
sig1	standard deviation of rbf

Returns

values of rbf basis functions [1 x nbasis]

_get_1d()

def teetool.basis.Basis._get_1d (   self,   x  )

private

obtain basis functions at specific points

Parameters

self	The object pointer.
x	points to evaluate [npoints x 1]

Returns

values of basis functions [npoints x nbasis]

_getBasisBernstein()

def teetool.basis.Basis._getBasisBernstein (   self,   x_vec,   nbasis  )

private

evaluates the Bernstein basis function in [0, 1] using the formula

Parameters

self	The object pointer.
x_vec	points to evaluate [npoints x 1]
nbasis	number of basis functions (= polynomial degree + 1)

Returns

values of Bernstein basis functions [npoints x nbasis]

_getBasisBernsteinVector()

def teetool.basis.Basis._getBasisBernsteinVector (   self,   x_sca,   nbasis  )

private

evaluates the Bernstein basis function in [0, 1] using the formula for a single x

Parameters

self	The object pointer.
x_sca	point to evaluate [1 x 1]
nbasis	number of basis functions (= polynomial degree + 1)

Returns

values of Bernstein basis functions [npoints x nbasis]

_getBasisRbf()

def teetool.basis.Basis._getBasisRbf (   self,   x_vec,   nbasis  )

private

evaluates the rbf basis function

Parameters

self	The object pointer.
x_vec	points to evaluate [npoints x 1]
nbasis	number of basis functions

Returns

values of rbf basis functions [npoints x nbasis]

_getBasisRbfVector()

def teetool.basis.Basis._getBasisRbfVector (   self,   x_sca,   nbasis  )

private

evaluates the rbf basis function for a single x

Parameters

self	The object pointer.
x_sca	point to evaluate [1 x 1]
nbasis	number of basis functions

Returns

values of rbf basis functions [1 x nbasis]

get()

def teetool.basis.Basis.get	(		self,
			x
	)

obtain basis functions at specific points, block-diagonal

Parameters

self	The object pointer.
x	points to evaluate [npoints x 1]

Returns

values of basis functions [ndim*npoints x ndim*nbasis]

Member Data Documentation

_basisType

teetool.basis.Basis._basisType

private

'rbf' or 'bernstein' basis type

_nbasis

teetool.basis.Basis._nbasis

private

number of basis functions

_ndim

teetool.basis.Basis._ndim

private

number of dimensions

_range

teetool.basis.Basis._range

private

defines range of basis function

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The documentation for this class was generated from the following file:

• teetool/basis.py