STK::MultiLeastSquare< ArrayB, ArrayA > Class Template Reference

The class MultiLeastSQquare solve the least square problem when the response b is multidimensional. More...

#include <STK_MultiLeastSquare.h>

Inheritance diagram for STK::MultiLeastSquare< ArrayB, ArrayA >:

Public Types
typedef ILeastSquare< MultiLeastSquare< ArrayB, ArrayA > >	Base

Public Member Functions
	MultiLeastSquare (ArrayB const &b, ArrayA const &a, bool isBref=false, bool isAref=false)
	constructor
virtual	~MultiLeastSquare ()
	Destructor.
bool	runImpl ()
	compute the multidimensional regression
template<class Weights >
bool	runImpl (Weights const &weights)
	compute the weighted multidimensional regression
Public Member Functions inherited from STK::ILeastSquare< MultiLeastSquare< ArrayB, ArrayA > >
virtual	~ILeastSquare ()
	Destructor.
Integer const &	rank () const
ArrayA const &	a () const
ArrayB const &	b () const
ArrayB const &	x () const
virtual bool	run ()
	Compute the Least-Square solution.
bool	run (VecWeights const &weights)
	Compute the weighted Least-Square solution.
bool	run (Weights const &weights)
Public Member Functions inherited from STK::IRunnerBase
String const &	error () const
	get the last error message.
Public Member Functions inherited from STK::IRecursiveTemplate< Derived >
Derived &	asDerived ()
	static cast : return a reference of this with a cast to the derived class.
Derived const &	asDerived () const
	static cast : return a const reference of this with a cast to the derived class.
Derived *	asPtrDerived ()
	static cast : return a ptr on a Derived of this with a cast to the derived class.
Derived const *	asPtrDerived () const
	static cast : return a ptr on a constant Derived of this with a cast to the derived class.
Derived *	clone () const
	create a leaf using the copy constructor of the Derived class.
Derived *	clone (bool isRef) const
	create a leaf using the copy constructor of the Derived class and a flag determining if the clone is a reference or not.

Additional Inherited Members
Protected Types inherited from STK::ILeastSquare< MultiLeastSquare< ArrayB, ArrayA > >
typedef hidden::AlgebraTraits< MultiLeastSquare< ArrayB, ArrayA > >::ArrayB	ArrayB
typedef hidden::AlgebraTraits< MultiLeastSquare< ArrayB, ArrayA > >::ArrayA	ArrayA
Protected Member Functions inherited from STK::ILeastSquare< MultiLeastSquare< ArrayB, ArrayA > >
	ILeastSquare (ArrayB const &b, ArrayA const &a, bool isBref=false, bool isAref=false)
	Default constructor.
	ILeastSquare (ExprBase< OtherArrayB > const &b, ExprBase< OtherArrayA > const &a)
	template constructor
Protected Member Functions inherited from STK::IRunnerBase
	IRunnerBase ()
	default constructor
	IRunnerBase (IRunnerBase const &runner)
	copy constructor
virtual	~IRunnerBase ()
	destructor
virtual void	update ()
	update the runner.
Protected Member Functions inherited from STK::IRecursiveTemplate< Derived >
	IRecursiveTemplate ()
	constructor.
	~IRecursiveTemplate ()
	destructor.
Protected Attributes inherited from STK::ILeastSquare< MultiLeastSquare< ArrayB, ArrayA > >
ArrayB	b_
	Array or vector of the left hand side.
ArrayA	a_
	Array of the right hand side.
ArrayB	x_
	Array of the solution (a vector if b is a vector, a matrix otherwise)
Integer	rank_
	rank of matrix A
Protected Attributes inherited from STK::IRunnerBase
String	msg_error_
	String with the last error message.
bool	hasRun_
	true if run has been used, false otherwise

Detailed Description

template<class ArrayB, class ArrayA>
class STK::MultiLeastSquare< ArrayB, ArrayA >

The class MultiLeastSQquare solve the least square problem when the response b is multidimensional.

The class MultiLeastSquare allows to solve the least-square problem

• A is an m-by-n matrix which may be rank-deficient.
• B can be a vector or a Matrix.

It computes the minimum-norm solution to a real linear least squares problem: minimize 2-norm(| b - A*x |) using the singular value decomposition (SVD) of A. A is an M-by-N matrix which may be rank-deficient.

See also

ILeastSquare, lapack::MultiLeastSquare

Definition at line 80 of file STK_MultiLeastSquare.h.

Member Typedef Documentation

Base

template<class ArrayB , class ArrayA >

typedef ILeastSquare<MultiLeastSquare<ArrayB, ArrayA> > STK::MultiLeastSquare< ArrayB, ArrayA >::Base

Definition at line 83 of file STK_MultiLeastSquare.h.

Constructor & Destructor Documentation

MultiLeastSquare()

template<class ArrayB , class ArrayA >

STK::MultiLeastSquare< ArrayB, ArrayA >::MultiLeastSquare ( ArrayB const &  b, ArrayA const &  a, bool  isBref = false, bool  isAref = false  )

inline

constructor

Parameters

b,a	the left hand side and the right hand side of the least square problem.
isBref,isAref	are the left hand side and the right hand side references ?

Definition at line 92 of file STK_MultiLeastSquare.h.

                          : Base(b, a, isBref, isAref) {}

~MultiLeastSquare()

template<class ArrayB , class ArrayA >

virtual STK::MultiLeastSquare< ArrayB, ArrayA >::~MultiLeastSquare ( )

inlinevirtual

Destructor.

Definition at line 95 of file STK_MultiLeastSquare.h.

{};

Member Function Documentation

runImpl() [1/2]

template<class ArrayB , class ArrayA >

bool STK::MultiLeastSquare< ArrayB, ArrayA >::runImpl

(

)

compute the multidimensional regression

Definition at line 104 of file STK_MultiLeastSquare.h.

{
  // compute a'a
  ArraySquareX prod = a_.transpose() * a_;
  // compute (a'a)^{-1}
  SymEigen<ArraySquareX> decomp(prod);
  decomp.run();
  rank_ = decomp.rank();
  // compute (a'a)^{-1}b'a
  if (a_.sizeRows() < b_.sizeCols())
  { x_ = (decomp.ginv(prod) * a_.transpose()) * b_;}
  else
  { x_ = decomp.ginv(prod) * (a_.transpose() * b_);}
  return true;
}

References STK::IRegression< YArray, XArray, Weights >::run(), and STK::ArrayBase< Derived >::transpose().

runImpl() [2/2]

template<class ArrayB , class ArrayA >

template<class Weights >

bool STK::MultiLeastSquare< ArrayB, ArrayA >::runImpl

(

Weights const &

weights

)

compute the weighted multidimensional regression

Definition at line 123 of file STK_MultiLeastSquare.h.

{
  STK_STATIC_ASSERT_ONE_DIMENSION_ONLY(Weights);
  // compute a'a
  CSquareX prod = a_.transpose() * weights.diagonalize() * a_;
  // compute (a'a)^{-1}
  SymEigen<CSquareX> decomp(prod);
  decomp.run();
  rank_ = decomp.rank();
  // compute (a'a)^{-1}b'a
  if (a_.sizeRows() < b_.sizeCols())
  { x_ = (decomp.ginv(prod) * a_.transpose())  * weights.diagonalize() * b_;}
  else
  { x_ = decomp.ginv(prod) * (a_.transpose() * weights.diagonalize() * b_);}
  return true;
}

References STK::IRegression< YArray, XArray, Weights >::run(), STK_STATIC_ASSERT_ONE_DIMENSION_ONLY, and STK::ArrayBase< Derived >::transpose().

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

• STK_MultiLeastSquare.h