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icl::math::PolynomialRegression< T > Class Template Reference

Generic Implementation of the Polynomial Regression algorithm. More...

#include <PolynomialRegression.h>

Classes

class  Result
 result type More...
 

Public Member Functions

 PolynomialRegression (const std::string &function)
 create instance with given function generator More...
 
const Resultapply (const Matrix &xs, const Matrix &ys, bool useSVD=false)
 computes the polynomial regression parameters More...
 
std::string getFunctionString () const
 returns the interpreted function string More...
 

Protected Attributes

Matrix m_buf
 internal buffer More...
 
Result m_result
 internal result buffer (always returned as const-reference) More...
 

Private Types

typedef DynMatrix< T > Matrix
 internally used matrxi type More...
 
typedef
PolynomialRegressionAttrib< T > 
Attrib
 internally used type More...
 

Detailed Description

template<class T>
class icl::math::PolynomialRegression< T >

Generic Implementation of the Polynomial Regression algorithm.

Polynomial regression applies least square regression based on a polynomial that is computed on the input variables. It minimized p(x) a = y, for a given polynomial function p(x). x can be a scalar of a vector. The same is true for y. Each entry of x and y resp. is assued to be one row of the input matrices xs and ys.

Results

The resulting PolynomialRegression::Result instance can be used to compute the output of the a given set of input variables simultaneously. It contains the optimal solution of a, which is used to compute y = p(x) a.

The Polynomial Function definition

The PolynomialRegression class uses a rather very simple but intuitive syntax for the definition of the used polynomial. Here is an example that contains all allowed parts: "1 + x0 + x1 + x0*x1 + x1^2 + x2^2" White spaces are ignored; tokens are defined by the "+"-delimiter. Tokens can be of form

Member Typedef Documentation

template<class T >
typedef PolynomialRegressionAttrib<T> icl::math::PolynomialRegression< T >::Attrib
private

internally used type

template<class T >
typedef DynMatrix<T> icl::math::PolynomialRegression< T >::Matrix
private

internally used matrxi type

Constructor & Destructor Documentation

template<class T >
icl::math::PolynomialRegression< T >::PolynomialRegression ( const std::string &  function)

create instance with given function generator

Member Function Documentation

template<class T >
const Result& icl::math::PolynomialRegression< T >::apply ( const Matrix xs,
const Matrix ys,
bool  useSVD = false 
)

computes the polynomial regression parameters

The input matrices xs and ys must have the same number of rows, and xs needs to have at least m_attribMaxIndex+1 columns. The input dimension is given by the number of columns in xs, the output dimension is defined by the number of columns in ys. Each row of xs and ys resp. defines a single input/output pair that is used for the internal least-square based optimization

Optionally, the internally computed pseudo inverse that solves p(xs) a = ys, which is p(xs).pinv() can be computed using an SVD-based approach. This is usually slower, but more stable and less prone to singular-matrix-exceptions.

template<class T >
std::string icl::math::PolynomialRegression< T >::getFunctionString ( ) const

returns the interpreted function string

Member Data Documentation

template<class T >
Matrix icl::math::PolynomialRegression< T >::m_buf
mutableprotected

internal buffer

template<class T >
Result icl::math::PolynomialRegression< T >::m_result
protected

internal result buffer (always returned as const-reference)


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