Compute the Singular Value Decomposition of an array. More...

#include <STK_ISvd.h>

Inheritance diagram for STK::ISvd< Derived >:

Public Member Functions
Type	det () const

Type	trace () const

Type	norm () const

int	rank () const

ArrayU const &	U () const

ArrayV const &	V () const

ArrayD const &	D () const

virtual bool	run ()
	implement the run method

template<class OtherArray >
void	setData (OtherArray const &A, bool withU=true, bool withV=true)
	Set a new data set to ISvd class.

template<class OtherArray >
OtherArray &	ginv (OtherArray &res) const
	Compute the generalized inverse of the matrix and put the result in res.

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.

Protected Types
typedef hidden::AlgebraTraits< Derived >::ArrayU	ArrayU

typedef hidden::AlgebraTraits< Derived >::ArrayD	ArrayD

typedef hidden::AlgebraTraits< Derived >::ArrayV	ArrayV

typedef ArrayU::Type	Type

Protected Member Functions
	ISvd (ArrayU const &A, bool ref, bool withU=true, bool withV=true)
	Default constructor.

template<class OtherDerived >
	ISvd (ArrayBase< OtherDerived > const &A, bool withU=true, bool withV=true)
	constructor with other kind of array/expression

	ISvd (ISvd const &S)
	Copy Constructor.

virtual	~ISvd ()
	destructor.

ISvd &	operator= (const ISvd &S)
	Operator = : overwrite the ISvd with S.

virtual void	finalize ()
	Finalize any operations that have to be done after the computation of the decomposition.

int	nrowU () const

int	ncolU () const

int	nrowD () const

int	ncolD () const

int	nrowV () const

int	ncolV () const

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
ArrayU	U_
	U_ matrix.

ArrayV	V_
	V_ matrix.

ArrayD	D_
	Diagonal array of the singular values.

bool	withU_
	Compute U_ ?

bool	withV_
	Compute V_ ?

Type	norm_
	trace norm

int	rank_
	rank

Type	trace_
	trace norm

Type	det_
	determinant

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 Derived>
class STK::ISvd< Derived >

Compute the Singular Value Decomposition of an array.

The method take as:

input: A matrix A(nrow,ncol)
output:
1. U Array (nrow,ncolU).
2. D Vector (ncol)
3. V Array (ncol,ncol). and perform the decomposition:
A = UDV' U can have more columns than A, and it is possible to compute some (all) vectors of Ker(A).

Definition at line 60 of file STK_ISvd.h.

Member Typedef Documentation

◆ ArrayD

template<class Derived >

typedef hidden::AlgebraTraits<Derived>::ArrayD STK::ISvd< Derived >::ArrayD

protected

Definition at line 64 of file STK_ISvd.h.

◆ ArrayU

template<class Derived >

typedef hidden::AlgebraTraits<Derived>::ArrayU STK::ISvd< Derived >::ArrayU

protected

Definition at line 63 of file STK_ISvd.h.

◆ ArrayV

template<class Derived >

typedef hidden::AlgebraTraits<Derived>::ArrayV STK::ISvd< Derived >::ArrayV

protected

Definition at line 65 of file STK_ISvd.h.

◆ Type

template<class Derived >

typedef ArrayU::Type STK::ISvd< Derived >::Type

protected

Definition at line 66 of file STK_ISvd.h.

Constructor & Destructor Documentation

◆ ISvd() [1/3]

template<class Derived >

STK::ISvd< Derived >::ISvd	(	ArrayU const &	A,
		bool	ref,
		bool	withU = `true`,
		bool	withV = `true`
	)

inlineprotected

Default constructor.

Parameters

A	the matrix to decompose.
ref	if true, U_ is a reference of A.
withU	if `true` save the left Householder transforms in `U_`.
withV	if `true` save the right Householder transforms in `V_`.

Definition at line 74 of file STK_ISvd.h.

               : U_(A, ref), V_(), D_()
               , withU_(withU), withV_(withV), norm_(0), rank_(0), trace_(0), det_(0)
    {}

◆ ISvd() [2/3]

template<class Derived >

template<class OtherDerived >

STK::ISvd< Derived >::ISvd	(	ArrayBase< OtherDerived > const &	A,
		bool	withU = `true`,
		bool	withV = `true`
	)

inlineprotected

constructor with other kind of array/expression

Parameters

A	the matrix/expression to decompose.
withU	if `true` save the left Householder transforms in `U_`.
withV	if `true` save the right Householder transforms in `V_`.

Definition at line 84 of file STK_ISvd.h.

               : U_(A), V_(), D_()
               , withU_(withU), withV_(withV), norm_(0), rank_(0), trace_(0), det_(0)
    {}

◆ ISvd() [3/3]

template<class Derived >

STK::ISvd< Derived >::ISvd ( ISvd< Derived > const & S )

inlineprotected

Copy Constructor.

Parameters

S	the Svd to copy

Definition at line 91 of file STK_ISvd.h.

               : U_(S.U_, S.U_.isRef()), V_(S.V_), D_(S.D_)
               , withU_(S.withU_), withV_(S.withV_)
               , norm_(S.norm_), rank_(S.rank_), trace_(S.trace_), det_(S.det_)
    {}

◆ ~ISvd()

template<class Derived >

virtual STK::ISvd< Derived >::~ISvd ( )

inlineprotectedvirtual

destructor.

Definition at line 97 of file STK_ISvd.h.

97{}

Member Function Documentation

◆ D()

template<class Derived >

ArrayD const & STK::ISvd< Derived >::D ( ) const

inline

Returns: D

Definition at line 152 of file STK_ISvd.h.

152{ return D_;}

References STK::ISvd< Derived >::D_.

Referenced by main().

◆ det()

template<class Derived >

Type STK::ISvd< Derived >::det ( ) const

inline

Returns: the product of the singular values

Definition at line 140 of file STK_ISvd.h.

140{ return det_;}

References STK::ISvd< Derived >::det_.

Referenced by STK::hidden::InvertMatrixImpl< Matrix, Size_ >::invertMatrixXX().

◆ finalize()

template<class Derived >

virtual void STK::ISvd< Derived >::finalize ( )

inlineprotectedvirtual

Finalize any operations that have to be done after the computation of the decomposition.

Definition at line 111 of file STK_ISvd.h.

    {
      // compute sign and trace
      trace_ = 0.;
      int s = 1;
      for (int i=D_.begin(); i< D_.end(); ++i )
      {
        Type value = D_[i];
        s *= sign(value);
        trace_ += value;
      }
 
      // compute norm_ (2-norm) and determinant
      norm_ = D_.maxElt();
      det_  = 0;
      if (D_.abs().minElt() > 0)
      { det_ = s * std::exp(D_.abs().log().sum());}
 
      // compute norm_ rank_
      rank_ = D_.size(); // full rank
      Type tol = norm_ * Arithmetic<Type>::epsilon();
      for (int i=D_.begin(); i< D_.end(); ++i )
      { if (std::abs(D_[i]) < tol) { rank_--;}}
 
    }

References STK::ISvd< Derived >::D_, STK::ISvd< Derived >::det_, STK::ISvd< Derived >::norm_, STK::ISvd< Derived >::rank_, STK::sign(), and STK::ISvd< Derived >::trace_.

Referenced by STK::ISvd< Derived >::run().

◆ ginv()

template<class Derived >

template<class OtherArray >

OtherArray & STK::ISvd< Derived >::ginv ( OtherArray & res ) const

Compute the generalized inverse of the matrix and put the result in res.

Parameters

res	array with the result

Returns: the result

Definition at line 227 of file STK_ISvd.h.

{
  Type tol = Arithmetic<Type>::epsilon() * norm_;
  if(tol==0) { tol = Arithmetic<Type>::epsilon();}
  // compute D
  if (U_.cols() != D_.range())
  {
    Array2DDiagonal<Real> diag(U_.cols(), 0.0);
    for (int i= D_.begin(); i< D_.end(); ++i) { diag[i]=D_[i];}
    res = V_ * diag.safeInverse(tol) * U_.transpose();
  }
  else
  {
    res = V_ * D_.diagonalize().safeInverse(tol) * U_.transpose();
  }
  // compute and return UD^{-1}V'
  return (res);
}

Referenced by STK::hidden::InvertMatrixImpl< Matrix, Size_ >::invertMatrixXX().

◆ ncolD()

template<class Derived >

int STK::ISvd< Derived >::ncolD ( ) const

inlineprotected

Returns: the number of columns of D_

Definition at line 214 of file STK_ISvd.h.

214{ return D_.sizeCols();}

References STK::ISvd< Derived >::D_.

◆ ncolU()

template<class Derived >

int STK::ISvd< Derived >::ncolU ( ) const

inlineprotected

Returns: the number of columns of U_

Definition at line 210 of file STK_ISvd.h.

210{ return U_.sizeCols();}

References STK::ISvd< Derived >::U_.

◆ ncolV()

template<class Derived >

int STK::ISvd< Derived >::ncolV ( ) const

inlineprotected

Returns: the number of columns of V_

Definition at line 218 of file STK_ISvd.h.

218{ return V_.sizeCols();}

References STK::ISvd< Derived >::V_.

◆ norm()

template<class Derived >

Type STK::ISvd< Derived >::norm ( ) const

inline

Returns: the norm of the matrix

Definition at line 144 of file STK_ISvd.h.

144{ return norm_;}

References STK::ISvd< Derived >::norm_.

◆ nrowD()

template<class Derived >

int STK::ISvd< Derived >::nrowD ( ) const

inlineprotected

Returns: the number of columns of D_

Definition at line 212 of file STK_ISvd.h.

212{ return D_.sizeRows();}

References STK::ISvd< Derived >::D_.

◆ nrowU()

template<class Derived >

int STK::ISvd< Derived >::nrowU ( ) const

inlineprotected

Returns: the number of rows of U_

Definition at line 208 of file STK_ISvd.h.

208{ return U_.sizeRows();}

References STK::ISvd< Derived >::U_.

◆ nrowV()

template<class Derived >

int STK::ISvd< Derived >::nrowV ( ) const

inlineprotected

Returns: the number of rows of V_

Definition at line 216 of file STK_ISvd.h.

216{ return V_.sizeRows();}

References STK::ISvd< Derived >::V_.

◆ operator=()

template<class Derived >

ISvd & STK::ISvd< Derived >::operator= ( const ISvd< Derived > & S )

inlineprotected

Operator = : overwrite the ISvd with S.

Parameters

S	the Svd to copy

Definition at line 101 of file STK_ISvd.h.

    {
      U_ = S.U_; V_ = S.V_;  D_ = S.D_;
      withU_ =  S.withU_; withV_ = S.withV_;
      norm_ = S.norm_; rank_ = S.rank_; trace_ = S.trace_; det_ = S.det_;
      return *this;
    }

References STK::ISvd< Derived >::D_, STK::ISvd< Derived >::det_, STK::ISvd< Derived >::norm_, STK::ISvd< Derived >::rank_, STK::ISvd< Derived >::trace_, STK::ISvd< Derived >::U_, STK::ISvd< Derived >::V_, STK::ISvd< Derived >::withU_, and STK::ISvd< Derived >::withV_.

◆ rank()

template<class Derived >

int STK::ISvd< Derived >::rank ( ) const

inline

Returns: the rank of the matrix

Definition at line 146 of file STK_ISvd.h.

146{ return rank_;}

References STK::ISvd< Derived >::rank_.

◆ run()

template<class Derived >

virtual bool STK::ISvd< Derived >::run ( )

inlinevirtual

implement the run method

Implements STK::IRunnerBase.

Reimplemented in STK::WeightedSvd< Array, WRows, WCols >.

Definition at line 155 of file STK_ISvd.h.

    {
      if (U_.empty()) { return true;}
      // compute Svd decomposition
      if (!this->asDerived().runImpl()) return false;
      finalize();
      return true;
    }

References STK::IRecursiveTemplate< Derived >::asDerived(), STK::ISvd< Derived >::finalize(), and STK::ISvd< Derived >::U_.

Referenced by STK::hidden::InvertMatrixImpl< Matrix, Size_ >::invertMatrixXX(), main(), and STK::WeightedSvd< Array, WRows, WCols >::run().

◆ setData()

template<class Derived >

template<class OtherArray >

void STK::ISvd< Derived >::setData	(	OtherArray const &	A,
		bool	withU = `true`,
		bool	withV = `true`
	)

inline

Set a new data set to ISvd class.

Note: Take care that if U_ was previously a reference, it cannot be modified.

Warning: A^{-1}A give identity matrix if m<=n, and AA^{-1} give identity matrix if n<=m

Parameters

A	is the matrix to decompose.
withU	if `true`, we save the left Housolder transforms in U_.
withV	if `true`, we save the right Housolder transforms in V_.

Definition at line 173 of file STK_ISvd.h.

    {
      U_ = A;           // Copy A in U_
      withU_ = withU;   // copy withU_ value
      withV_ = withV;   // copy withV_ value
      V_.resize(0,0), D_.resize(0);
    }

References STK::ISvd< Derived >::D_, STK::ISvd< Derived >::U_, STK::ISvd< Derived >::V_, STK::ISvd< Derived >::withU_, and STK::ISvd< Derived >::withV_.

◆ trace()

template<class Derived >

Type STK::ISvd< Derived >::trace ( ) const

inline

Returns: the sum of the singular values

Definition at line 142 of file STK_ISvd.h.

142{ return trace_;}

References STK::ISvd< Derived >::trace_.

◆ U()

template<class Derived >

ArrayU const & STK::ISvd< Derived >::U ( ) const

inline

Returns: U

Definition at line 148 of file STK_ISvd.h.

148{ return U_;}

References STK::ISvd< Derived >::U_.

Referenced by main().

◆ V()

template<class Derived >

ArrayV const & STK::ISvd< Derived >::V ( ) const

inline

Returns: V

Definition at line 150 of file STK_ISvd.h.

150{ return V_;}

References STK::ISvd< Derived >::V_.

Referenced by main().

Member Data Documentation

◆ D_

template<class Derived >

ArrayD STK::ISvd< Derived >::D_

protected

Diagonal array of the singular values.

Definition at line 193 of file STK_ISvd.h.

Referenced by STK::ISvd< Derived >::D(), STK::ISvd< Derived >::finalize(), STK::ISvd< Derived >::ncolD(), STK::ISvd< Derived >::nrowD(), STK::ISvd< Derived >::operator=(), and STK::ISvd< Derived >::setData().

◆ det_

template<class Derived >

Type STK::ISvd< Derived >::det_

protected

determinant

Definition at line 205 of file STK_ISvd.h.

Referenced by STK::ISvd< Derived >::det(), STK::ISvd< Derived >::finalize(), and STK::ISvd< Derived >::operator=().

◆ norm_

template<class Derived >

Type STK::ISvd< Derived >::norm_

protected

trace norm

Definition at line 199 of file STK_ISvd.h.

Referenced by STK::ISvd< Derived >::finalize(), STK::ISvd< Derived >::norm(), and STK::ISvd< Derived >::operator=().

◆ rank_

template<class Derived >

int STK::ISvd< Derived >::rank_

protected

rank

Definition at line 201 of file STK_ISvd.h.

Referenced by STK::ISvd< Derived >::finalize(), STK::ISvd< Derived >::operator=(), and STK::ISvd< Derived >::rank().

◆ trace_

template<class Derived >

Type STK::ISvd< Derived >::trace_

protected

trace norm

Definition at line 203 of file STK_ISvd.h.

Referenced by STK::ISvd< Derived >::finalize(), STK::ISvd< Derived >::operator=(), and STK::ISvd< Derived >::trace().

◆ U_

template<class Derived >

ArrayU STK::ISvd< Derived >::U_

protected

U_ matrix.

Definition at line 189 of file STK_ISvd.h.

Referenced by STK::ISvd< Derived >::ncolU(), STK::ISvd< Derived >::nrowU(), STK::ISvd< Derived >::operator=(), STK::ISvd< Derived >::run(), STK::ISvd< Derived >::setData(), and STK::ISvd< Derived >::U().

◆ V_

template<class Derived >

ArrayV STK::ISvd< Derived >::V_

protected

V_ matrix.

Definition at line 191 of file STK_ISvd.h.

Referenced by STK::ISvd< Derived >::ncolV(), STK::ISvd< Derived >::nrowV(), STK::ISvd< Derived >::operator=(), STK::ISvd< Derived >::setData(), and STK::ISvd< Derived >::V().

◆ withU_

template<class Derived >

bool STK::ISvd< Derived >::withU_

protected

Compute U_ ?

Definition at line 195 of file STK_ISvd.h.

Referenced by STK::ISvd< Derived >::operator=(), and STK::ISvd< Derived >::setData().

◆ withV_

template<class Derived >

bool STK::ISvd< Derived >::withV_

protected

Compute V_ ?

Definition at line 197 of file STK_ISvd.h.

Referenced by STK::ISvd< Derived >::operator=(), and STK::ISvd< Derived >::setData().

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

STK_ISvd.h

Public Member Functions

Protected Types

Protected Member Functions

Protected Attributes

Detailed Description

Member Typedef Documentation

◆ ArrayD

◆ ArrayU

◆ ArrayV

◆ Type

Constructor & Destructor Documentation

◆ ISvd() [1/3]

◆ ISvd() [2/3]

◆ ISvd() [3/3]

◆ ~ISvd()

Member Function Documentation

◆ D()

◆ det()

◆ finalize()

◆ ginv()

◆ ncolD()

◆ ncolU()

◆ ncolV()

◆ norm()

◆ nrowD()

◆ nrowU()

◆ nrowV()

◆ operator=()

◆ rank()

◆ run()

◆ setData()

◆ trace()

◆ U()

◆ V()

Member Data Documentation

◆ D_

◆ det_

◆ norm_

◆ rank_

◆ trace_

◆ U_

◆ V_

◆ withU_

◆ withV_