NumModelPolynomialC - Model for fitting n-dimensional polynomials.

Developer Documentation

Centre for Vision, Speech & Signal Processing

Comments:
It provides a class implementation fitting functions of the form Y=f(X) where each element of Y is an k'th polynomial of the elements of X.

For example, when a second order polynomial is selected and X and Y have 2 and 3 elements respectively and A is the matrix of model weights then:

 Y[0] = A[0][0] + A[0][1]X[0] + A[0][2]X[0]^2 + A[0][3]X[1] + A[0][4]X[1]^2
 Y[1] = A[1][0] + A[1][1]X[0] + A[1][2]X[0]^2 + A[1][3]X[1] + A[1][4]X[1]^2
 Y[2] = A[2][0] + A[2][1]X[0] + A[2][2]X[0]^2 + A[2][3]X[1] + A[2][4]X[1]^2

Note that in this model there are no cross parameter terms regardless of the model order selected, ie each term is only a power of an individual element of X.

Parent Classes:

NumModelC

Methods:

NumModelPolynomialC(UIntT order)

Constructor

order	the order of the polynomial for each term of X

#include "amma/Num/NumModel.hh"

NumModelBC & Body()

Access body.

const NumModelBC & Body() const

Access body.

NumModelC Copy() const

Makes a deep copy

void Initialise(const NumVVDataSetC & train)

Initialises model to an untrained state

train	data set provided to give model example of data

Must be overloaded in derived class that train incrementally and provides a mechanism for restarting training from scratch. Default behaviour is to do nothing.

void Fit(const NumVVDataSetC & train)

Used to train the model using set of input/output vectors
It should be assumed that the same sort of data will be provided for fitting as was presented to the Initialise function previously. ie same preprocessing should be applied as was appropriate for the initialisation sample set.

#include "amma/Num/NumFunc.hh"

BooleanT IsA(const DPEntityC & pb): Check if an object is a NumFuncC.
NumFuncC Copy() const: Makes a deep copy
NumFuncC & operator=(const NumFuncC & oth): Assignment operator
VectorC Evaluate(const VectorC & X) const: Evaluates function Y=f(X)
DListC<VectorC> Evaluate(const DListC<VectorC> & listX) const: Evaluates function Y=f(X) for a list of X
VectorC operator()(const VectorC & X) const: Evaluates function Y=f(X)
MatrixC Jacobian(const VectorC & X) const: Evaluates Jacobian df(X)/dX
Note that this is not const=0 since the base class will calculate a numerical estimate of the Jacobian using differences if the member function is not overloaded in derived classes to provide an analytical solution.
const StringC GetInfo() const: Gets string describing object
const StringC GetName() const: Gets type name of the object
UIntT SizeX() const: Input vector dimension
UIntT SizeY() const: Output vector dimension
BooleanT Save(ostream & out) const: Writes object to stream, cna be loaded using constructor
NumFuncBC & Body(): Access body.
const NumFuncBC & Body() const: Access body.

#include "amma/DP/Process.hh"

DPProcessBodyC<VectorC,VectorC> & Body(): Access body.
const DPProcessBodyC<VectorC,VectorC> & Body() const: Access body.
VectorC Apply(const VectorC & dat): Apply operation.
NB. This may become constant in the future, but the situation isn't clear at the moment.
IntT ApplyArray(const SArray1dC<VectorC> & in,SArray1dC<VectorC> & out): Streaming version.
const DPProcessC<VectorC,VectorC> operator=(const DPProcessC<VectorC,VectorC> & in): Assignment operator
const DPProcessC<VectorC,VectorC> Copy() const: Make a copy of this process. Some type defs.
DPProcessBaseBodyC & Body(): Access body.
const DPProcessBaseBodyC & Body() const: Access body.
const type_info & InputType() const: Get input type.
const type_info & OutputType() const: Get input type.
BooleanT IsStateless() const: Is operation stateless ?
DPProcessBaseBodyC::ProcTypeT OpType() const: Operation type lossy/lossless.
const DPProcessBaseC & operator=(const DPProcessBaseC & oth): Assignment operator.

#include "amma/DP/Entity.hh"

const DPEntityC & operator=(const DPEntityC & dat): Assignment.
DPEntityBodyC & Body(): Access body.
const DPEntityBodyC & Body() const: Access body.
BooleanT Save(ostream & out) const

#include "amma/RCHandleA.hh"

RCAbstractC Abstract(): Create an abstract handle to this object.
BooleanT IsHandleType(const DT &) const: Is handle of given type ?
void CheckHandleType(const DT & dummy) const: Check handle type. Throw an expception if not.
BooleanT Save(ostream & out) const: Save to ostream.
RCHandleAC<DPEntityBodyC> Copy() const: Creat a deep copy of this object.
protected:

#include "amma/RCHandle.hh"

BooleanT IsValid() const: Check its a valid handle.
BooleanT IsValidObject() const: Check its a valid handle, and that the object is pointed to is also valid.
RCHandleC<DPEntityBodyC> & operator=(const RCHandleC<DPEntityBodyC> & oth): Assignment.
BooleanT operator==(const RCHandleC<DPEntityBodyC> & oth) const: Comparison operator.
BooleanT operator!=(const RCHandleC<DPEntityBodyC> & oth) const: Comparison operator.
UIntT Hash() const: Hash function.x
BooleanT IsConst() const: Is object constant ?
BooleanT IsNotConst() const: Is object not constant ?
void SetConst(void) const: Lock the object.
This is const as a convience though it actual modified the object, often object you wish to ensure are constant already have const set. protected:
void Invalidate(): Turn this into an invalid handle.
DPEntityBodyC & Body(): Direct access to body.
const DPEntityBodyC & Body() const: Constant access to body.

Programmer:Robert Crida, Documentation by CxxDoc: Tue Mar 20 10:49:27 2001

NumModelPolynomialC

Model for fitting n-dimensional polynomials.

include	"amma/Num/NumModelPolynomial.hh"
User Level:	Default
Library:	NumModelBasicModels
Example:	testNumModel.cc
Section:	Numerical Methods.Multidimensional Models.Implementation
In Scope:	std