#include <itkFEMLinearSystemWrapper.h>

Inheritance diagram for itk::fem::LinearSystemWrapper:

Collaboration diagram for itk::fem::LinearSystemWrapper:

Public Types
typedef std::vector< unsigned int >	ColumnArray
typedef const Self *	ConstPointer
typedef Self *	Pointer
typedef LinearSystemWrapper	Self
typedef Solution	Superclass
Public Types inherited from itk::fem::Solution
typedef double	Float

Public Member Functions
virtual void	AddMatrixMatrix (unsigned int matrixIndex1, unsigned int matrixIndex2)
virtual void	AddMatrixValue (unsigned int i, unsigned int j, Float value, unsigned int matrixIndex=0)=0
virtual void	AddSolutionValue (unsigned int i, Float value, unsigned int solutionIndex=0)=0
virtual void	AddVectorValue (unsigned int i, Float value, unsigned int vectorIndex=0)=0
virtual void	AddVectorVector (unsigned int vectorIndex1, unsigned int vectorIndex2)
virtual void	Clean (void)
virtual void	CopyMatrix (unsigned int matrixIndex1, unsigned int matrixIndex2)
virtual void	CopySolution2Vector (unsigned int solutionIndex, unsigned int vectorIndex)=0
virtual void	CopyVector (unsigned int vectorSource, unsigned int vectorDestination)
virtual void	CopyVector2Solution (unsigned int vectorIndex, unsigned int solutionIndex)=0
virtual void	DestroyMatrix (unsigned int matrixIndex=0)=0
virtual void	DestroySolution (unsigned int solutionIndex=0)=0
virtual void	DestroyVector (unsigned int vectorIndex=0)=0
virtual void	GetColumnsOfNonZeroMatrixElementsInRow (unsigned int row, ColumnArray &cols, unsigned int matrixIndex=0)
virtual Float	GetMatrixValue (unsigned int i, unsigned int j, unsigned int matrixIndex=0) const =0
unsigned int	GetNumberOfMatrices () const
unsigned int	GetNumberOfSolutions () const
unsigned int	GetNumberOfVectors () const
unsigned int	GetSystemOrder () const
virtual Float	GetVectorValue (unsigned int i, unsigned int vectorIndex=0) const =0
virtual void	InitializeMatrix (unsigned int matrixIndex=0)=0
virtual void	InitializeSolution (unsigned int solutionIndex=0)=0
virtual void	InitializeVector (unsigned int vectorIndex=0)=0
virtual bool	IsMatrixInitialized (unsigned int matrixIndex=0)=0
virtual bool	IsSolutionInitialized (unsigned int solutionIndex=0)=0
virtual bool	IsVectorInitialized (unsigned int vectorIndex=0)=0
virtual void	MultiplyMatrixMatrix (unsigned int resultMatrixIndex, unsigned int leftMatrixIndex, unsigned int rightMatrixIndex)=0
virtual void	MultiplyMatrixSolution (unsigned int resultVectorIndex, unsigned int matrixIndex, unsigned int solutionIndex)
virtual void	MultiplyMatrixVector (unsigned int resultVectorIndex, unsigned int matrixIndex, unsigned int vectorIndex)
virtual void	OptimizeMatrixStorage (unsigned int matrixIndex, unsigned int tempMatrixIndex)
virtual void	ReverseCuthillMckeeOrdering (ColumnArray &newNumbering, unsigned int matrixIndex=0)
virtual void	ScaleMatrix (Float scale, unsigned int matrixIndex=0)
void	ScaleSolution (Float scale, unsigned int solutionIndex=0)
void	ScaleVector (Float scale, unsigned int vectorIndex=0)
virtual void	SetMatrixValue (unsigned int i, unsigned int j, Float value, unsigned int matrixIndex=0)=0
void	SetNumberOfMatrices (unsigned int nMatrices)
void	SetNumberOfSolutions (unsigned int nSolutions)
void	SetNumberOfVectors (unsigned int nVectors)
virtual void	SetSolutionValue (unsigned int i, Float value, unsigned int solutionIndex=0)=0
void	SetSystemOrder (unsigned int N)
virtual void	SetVectorValue (unsigned int i, Float value, unsigned int vectorIndex=0)=0
virtual void	Solve (void)=0
virtual void	SwapMatrices (unsigned int matrixIndex1, unsigned int matrixIndex2)=0
virtual void	SwapSolutions (unsigned int solutionIndex1, unsigned int solutionIndex2)=0
virtual void	SwapVectors (unsigned int vectorIndex1, unsigned int vectorIndex2)=0
virtual	~LinearSystemWrapper ()

	LinearSystemWrapper ()
Public Member Functions inherited from itk::fem::Solution
virtual Float	GetSolutionValue (unsigned int i, unsigned int solutionIndex=0) const =0
virtual	~Solution ()

Protected Attributes
unsigned int	m_NumberOfMatrices
unsigned int	m_NumberOfSolutions
unsigned int	m_NumberOfVectors
unsigned int	m_Order

Private Member Functions
void	CuthillMckeeOrdering (ColumnArray &newNumbering, int startingRow, unsigned int matrixIndex=0)
void	FollowConnectionsCuthillMckeeOrdering (unsigned int rowNumber, ColumnArray &rowDegree, ColumnArray &newNumbering, unsigned int nextRowNumber, unsigned int matrixIndex=0)
	LinearSystemWrapper (const LinearSystemWrapper &)
const LinearSystemWrapper &	operator= (const LinearSystemWrapper &)

Detailed Description

Defines all functions required by Solver class to allocate, assemble and solve a linear system of equation.

Linear system is defined as A*x=B, where A is a square matrix and F is a vector. Member functions are provided to access a specific element within A and B. Objects of derived classes should make appropriate calls to the numeric library in implementation of virtual functions to assemble and solve the linear system.

See comments for each virtual member for more information about how to derive a new LinearSystemWrapper class. An example derived class LinearSystemWrapperVNL is defined to use VNL sparse matrix representation and solver.

See also:: Solver::SetLinearSystemWrapper

Definition at line 53 of file itkFEMLinearSystemWrapper.h.

Member Typedef Documentation

typedef std::vector<unsigned int> itk::fem::LinearSystemWrapper::ColumnArray

Definition at line 61 of file itkFEMLinearSystemWrapper.h.

typedef const Self* itk::fem::LinearSystemWrapper::ConstPointer

Const pointer to an object.

Reimplemented from itk::fem::Solution.

Definition at line 59 of file itkFEMLinearSystemWrapper.h.

typedef Self* itk::fem::LinearSystemWrapper::Pointer

Pointer to an object.

Reimplemented from itk::fem::Solution.

Definition at line 58 of file itkFEMLinearSystemWrapper.h.

typedef LinearSystemWrapper itk::fem::LinearSystemWrapper::Self

Standard "Self" typedef.

Reimplemented from itk::fem::Solution.

Reimplemented in itk::fem::LinearSystemWrapperItpack.

Definition at line 56 of file itkFEMLinearSystemWrapper.h.

typedef Solution itk::fem::LinearSystemWrapper::Superclass

Standard "Superclass" typedef.

Reimplemented from itk::fem::Solution.

Reimplemented in itk::fem::LinearSystemWrapperItpack.

Definition at line 57 of file itkFEMLinearSystemWrapper.h.

Constructor & Destructor Documentation

itk::fem::LinearSystemWrapper::LinearSystemWrapper ( )

inline

Constructor for linear system, should perform any initialization that is required by derived class.

Definition at line 67 of file itkFEMLinearSystemWrapper.h.

virtual itk::fem::LinearSystemWrapper::~LinearSystemWrapper ( )

inlinevirtual

Virtual destructor should properly destroy the object and clean up any memory allocated for matrix and vector storage.

Definition at line 79 of file itkFEMLinearSystemWrapper.h.

itk::fem::LinearSystemWrapper::LinearSystemWrapper ( const LinearSystemWrapper & )

private

Copy constructor is not allowed.

Member Function Documentation

virtual void itk::fem::LinearSystemWrapper::AddMatrixMatrix	(	unsigned int	matrixIndex1,
		unsigned int	matrixIndex2
	)

virtual

Adds two matrices storing the result in the first matrix.

Parameters:

matrixIndex1	index of a matrix to add the other matrix to
matrixIndex2	index of matrix to add

virtual void itk::fem::LinearSystemWrapper::AddMatrixValue	(	unsigned int	i,
		unsigned int	j,
		Float	value,
		unsigned int	matrixIndex = `0`
	)

pure virtual

Virtual function to add a value to a specific element of the A matrix.

Parameters:

i	row of the element
j	column of the element
value	value to add to the existing element
matrixIndex	index of matrix to add value to

Implemented in itk::fem::LinearSystemWrapperItpack, itk::fem::LinearSystemWrapperVNL, and itk::fem::LinearSystemWrapperDenseVNL.

virtual void itk::fem::LinearSystemWrapper::AddSolutionValue	(	unsigned int	i,
		Float	value,
		unsigned int	solutionIndex = `0`
	)

pure virtual

Virtual function to add a value of specific element of the solution vector.

Parameters:

i	element Index in solution vector
value	new value of the element
solutionIndex	index of solution vector to add value to

Implemented in itk::fem::LinearSystemWrapperItpack, itk::fem::LinearSystemWrapperVNL, and itk::fem::LinearSystemWrapperDenseVNL.

virtual void itk::fem::LinearSystemWrapper::AddVectorValue	(	unsigned int	i,
		Float	value,
		unsigned int	vectorIndex = `0`
	)

pure virtual

Virtual function to add a value to a specific element of the B vector.

Parameters:

i	row of the element
value	value to add to the existing element
vectorIndex	index of vector to add value to

Implemented in itk::fem::LinearSystemWrapperItpack, itk::fem::LinearSystemWrapperVNL, and itk::fem::LinearSystemWrapperDenseVNL.

virtual void itk::fem::LinearSystemWrapper::AddVectorVector	(	unsigned int	vectorIndex1,
		unsigned int	vectorIndex2
	)

virtual

Adds two vectors storing the result in the first vector.

Parameters:

vectorIndex1	index of a vector to add the other vector to
vectorIndex2	index of vector to add

virtual void itk::fem::LinearSystemWrapper::Clean ( void )

virtual

Clear all the data (matrices) inside the system, so that the system is ready to solve another problem from scratch.

virtual void itk::fem::LinearSystemWrapper::CopyMatrix	(	unsigned int	matrixIndex1,
		unsigned int	matrixIndex2
	)

virtual

Copies the content of source matrix to destination matrix. Any existing data in destination matrix is overwritten.

Parameters:

matrixIndex1	index of a matrix that will be copied
matrixIndex2	index of matrix to copy to

virtual void itk::fem::LinearSystemWrapper::CopySolution2Vector	(	unsigned int	solutionIndex,
		unsigned int	vectorIndex
	)

pure virtual

Copy a solution vector to a vector

Parameters:

solutionIndex	index of solution vector to copy
vectorIndex	index of vector to copy solution to

virtual void itk::fem::LinearSystemWrapper::CopyVector	(	unsigned int	vectorSource,
		unsigned int	vectorDestination
	)

virtual

Copy a vector

Parameters:

vectorSource	index of a vector to copy
vectorDestination	index to copy the vector to

virtual void itk::fem::LinearSystemWrapper::CopyVector2Solution	(	unsigned int	vectorIndex,
		unsigned int	solutionIndex
	)

pure virtual

Copy a vector to a solution vector

Parameters:

vectorIndex	index of a vector to copy
solutionIndex	index of a solution to copy the solution to

Implemented in itk::fem::LinearSystemWrapperItpack, itk::fem::LinearSystemWrapperDenseVNL, and itk::fem::LinearSystemWrapperVNL.

void itk::fem::LinearSystemWrapper::CuthillMckeeOrdering	(	ColumnArray &	newNumbering,
		int	startingRow,
		unsigned int	matrixIndex = `0`
	)

private

matrix reordering utility

virtual void itk::fem::LinearSystemWrapper::DestroyMatrix ( unsigned int matrixIndex = 0 )

pure virtual

Free the memory from a matrix

Parameters:

matrixIndex index of matrix to destroy

Implemented in itk::fem::LinearSystemWrapperItpack, itk::fem::LinearSystemWrapperVNL, and itk::fem::LinearSystemWrapperDenseVNL.

virtual void itk::fem::LinearSystemWrapper::DestroySolution ( unsigned int solutionIndex = 0 )

pure virtual

Free the memory from a solution vector

Parameters:

solutionIndex index of solution vector to destroy

Implemented in itk::fem::LinearSystemWrapperItpack, itk::fem::LinearSystemWrapperVNL, and itk::fem::LinearSystemWrapperDenseVNL.

virtual void itk::fem::LinearSystemWrapper::DestroyVector ( unsigned int vectorIndex = 0 )

pure virtual

Free the memory from a vector

Parameters:

vectorIndex index of vector to destroy

Implemented in itk::fem::LinearSystemWrapperItpack, itk::fem::LinearSystemWrapperVNL, and itk::fem::LinearSystemWrapperDenseVNL.

void itk::fem::LinearSystemWrapper::FollowConnectionsCuthillMckeeOrdering	(	unsigned int	rowNumber,
		ColumnArray &	rowDegree,
		ColumnArray &	newNumbering,
		unsigned int	nextRowNumber,
		unsigned int	matrixIndex = `0`
	)

private

virtual void itk::fem::LinearSystemWrapper::GetColumnsOfNonZeroMatrixElementsInRow	(	unsigned int	row,
		ColumnArray &	cols,
		unsigned int	matrixIndex = `0`
	)

virtual

Returns the column index (zero based) of the i-th non zero (non allocated)element in a given row of A matrix. This function is useful for optimizations when sparse matrices are used. Note that the value of an element with returned column index may actually be equal zero.

Parameters:

row	Row number
cols	Which element in that row. Can range from 0 to number of elements allocated in a row. If this is out of range, the function returns -1.
matrixIndex	Index of matrix (defaults to 0)

Reimplemented in itk::fem::LinearSystemWrapperItpack.

virtual Float itk::fem::LinearSystemWrapper::GetMatrixValue	(	unsigned int	i,
		unsigned int	j,
		unsigned int	matrixIndex = `0`
	)		const

pure virtual

Virtual function to get a value of a specific element of a matrix.

Parameters:

i	row of the element
j	column of the element
matrixIndex	index of matrix to get value from

Implemented in itk::fem::LinearSystemWrapperItpack, itk::fem::LinearSystemWrapperVNL, and itk::fem::LinearSystemWrapperDenseVNL.

unsigned int itk::fem::LinearSystemWrapper::GetNumberOfMatrices ( ) const

inline

Get Index of matrices used by system

Definition at line 129 of file itkFEMLinearSystemWrapper.h.

References m_NumberOfMatrices.

unsigned int itk::fem::LinearSystemWrapper::GetNumberOfSolutions ( ) const

inline

Get Index of solutions used by system

Definition at line 163 of file itkFEMLinearSystemWrapper.h.

References m_NumberOfSolutions.

unsigned int itk::fem::LinearSystemWrapper::GetNumberOfVectors ( ) const

inline

Get Index of vectors used by system

Definition at line 146 of file itkFEMLinearSystemWrapper.h.

References m_NumberOfVectors.

unsigned int itk::fem::LinearSystemWrapper::GetSystemOrder ( ) const

inline

Get the order of the system

Definition at line 102 of file itkFEMLinearSystemWrapper.h.

References m_Order.

virtual Float itk::fem::LinearSystemWrapper::GetVectorValue	(	unsigned int	i,
		unsigned int	vectorIndex = `0`
	)		const

pure virtual

Virtual function to get a value of a specific element of the B vector.

Parameters:

i	row of the element
vectorIndex	index of vector to get value from

Implemented in itk::fem::LinearSystemWrapperItpack, itk::fem::LinearSystemWrapperVNL, and itk::fem::LinearSystemWrapperDenseVNL.

virtual void itk::fem::LinearSystemWrapper::InitializeMatrix ( unsigned int matrixIndex = 0 )

pure virtual

Initialization of the A matrix. First any existing data for matrix A must be be destroyed, and then a new matrix is created in the memory. All elements in A must be set to zero.

Parameters:

matrixIndex index of matrix to initialize

Implemented in itk::fem::LinearSystemWrapperItpack, itk::fem::LinearSystemWrapperVNL, and itk::fem::LinearSystemWrapperDenseVNL.

virtual void itk::fem::LinearSystemWrapper::InitializeSolution ( unsigned int solutionIndex = 0 )

pure virtual

Initialization of a solution vector. Existing memory must be destroyed and the new solution vector is created in memory. All values should be set to zero.

Parameters:

solutionIndex index of solution vector to initialize

Implemented in itk::fem::LinearSystemWrapperItpack, itk::fem::LinearSystemWrapperVNL, and itk::fem::LinearSystemWrapperDenseVNL.

virtual void itk::fem::LinearSystemWrapper::InitializeVector ( unsigned int vectorIndex = 0 )

pure virtual

Initialization of the a vector. First any existing data for vector B must be destroyed, then new vector is created in the memory. All elements in B must be set to zero.

Implemented in itk::fem::LinearSystemWrapperItpack, itk::fem::LinearSystemWrapperVNL, and itk::fem::LinearSystemWrapperDenseVNL.

virtual bool itk::fem::LinearSystemWrapper::IsMatrixInitialized ( unsigned int matrixIndex = 0 )

pure virtual

Check to see if matrix is initialized

Parameters:

matrixIndex index of matrix to examine

Implemented in itk::fem::LinearSystemWrapperItpack, itk::fem::LinearSystemWrapperVNL, and itk::fem::LinearSystemWrapperDenseVNL.

virtual bool itk::fem::LinearSystemWrapper::IsSolutionInitialized ( unsigned int solutionIndex = 0 )

pure virtual

Check to see if solution vector is initialized

Parameters:

solutionIndex index of solution vector to examine

Implemented in itk::fem::LinearSystemWrapperItpack, itk::fem::LinearSystemWrapperVNL, and itk::fem::LinearSystemWrapperDenseVNL.

virtual bool itk::fem::LinearSystemWrapper::IsVectorInitialized ( unsigned int vectorIndex = 0 )

pure virtual

Check to see if vector is initialized

Parameters:

vectorIndex vector of index to examine

Implemented in itk::fem::LinearSystemWrapperItpack, itk::fem::LinearSystemWrapperVNL, and itk::fem::LinearSystemWrapperDenseVNL.

virtual void itk::fem::LinearSystemWrapper::MultiplyMatrixMatrix	(	unsigned int	resultMatrixIndex,
		unsigned int	leftMatrixIndex,
		unsigned int	rightMatrixIndex
	)

pure virtual

Perform a matrix*matrix operation and store the result in the linear system

Parameters:

leftMatrixIndex	index of left matrix
rightMatrixIndex	index of right matrix
resultMatrixIndex	index of matrix where solution is stored

Implemented in itk::fem::LinearSystemWrapperItpack, itk::fem::LinearSystemWrapperDenseVNL, and itk::fem::LinearSystemWrapperVNL.

virtual void itk::fem::LinearSystemWrapper::MultiplyMatrixSolution	(	unsigned int	resultVectorIndex,
		unsigned int	matrixIndex,
		unsigned int	solutionIndex
	)

virtual

Perform a matrix*solution operation and store the result in the linear system

Parameters:

matrixIndex	index of matrix to multiply
solutionIndex	index of solution to multiply
resultVectorIndex	index of vector where result is store

Reimplemented in itk::fem::LinearSystemWrapperItpack.

virtual void itk::fem::LinearSystemWrapper::MultiplyMatrixVector	(	unsigned int	resultVectorIndex,
		unsigned int	matrixIndex,
		unsigned int	vectorIndex
	)

virtual

Perform a matrix*vector operation and store the result in the linear system

Parameters:

matrixIndex	index of matrix to multiply
vectorIndex	index of vector to multiply
resultVectorIndex	index of vector where result is store

Reimplemented in itk::fem::LinearSystemWrapperItpack, itk::fem::LinearSystemWrapperDenseVNL, and itk::fem::LinearSystemWrapperVNL.

const LinearSystemWrapper& itk::fem::LinearSystemWrapper::operator= ( const LinearSystemWrapper & )

private

Asignment operator is not allowed.

virtual void itk::fem::LinearSystemWrapper::OptimizeMatrixStorage	(	unsigned int	matrixIndex,
		unsigned int	tempMatrixIndex
	)

virtual

Remove all zeros from a matrix

Parameters:

matrixIndex	index of matrix to remove zeros from
tempMatrixIndex	index of matrix to use for temp storage space

Note:: an extra matrix must be allocated by the solver in order to use this method

virtual void itk::fem::LinearSystemWrapper::ReverseCuthillMckeeOrdering	(	ColumnArray &	newNumbering,
		unsigned int	matrixIndex = `0`
	)

virtual

Reorder the Degrees of Freedom in order to reduce bandwidth of matrix

Parameters:

matrixIndex	index of matrix to examine
newNumbering	vector of new degree of freedom ordering

virtual void itk::fem::LinearSystemWrapper::ScaleMatrix	(	Float	scale,
		unsigned int	matrixIndex = `0`
	)

virtual

Multiplies all elements of a matrix by a scalar

Parameters:

scale	scalar to multiply all matrix values by
matrixIndex	index of matrix to modify

Reimplemented in itk::fem::LinearSystemWrapperItpack, itk::fem::LinearSystemWrapperVNL, and itk::fem::LinearSystemWrapperDenseVNL.

void itk::fem::LinearSystemWrapper::ScaleSolution	(	Float	scale,
		unsigned int	solutionIndex = `0`
	)

Multiplies all elements of a solution by a scalar

Parameters:

scale	scalar to multiply all solution values by
solutionIndex	index of solution to modify

Reimplemented in itk::fem::LinearSystemWrapperDenseVNL.

void itk::fem::LinearSystemWrapper::ScaleVector	(	Float	scale,
		unsigned int	vectorIndex = `0`
	)

Multiplies all elements of a vector by a scalar

Parameters:

scale	scalar to multiply all vector values by
vectorIndex	index of vector to modify

Reimplemented in itk::fem::LinearSystemWrapperDenseVNL.

virtual void itk::fem::LinearSystemWrapper::SetMatrixValue	(	unsigned int	i,
		unsigned int	j,
		Float	value,
		unsigned int	matrixIndex = `0`
	)

pure virtual

Virtual function to set a value of a specific element of the A matrix.

Parameters:

i	row of the element
j	column of the element
value	new value of the element
matrixIndex	index of matrix to set value in

Implemented in itk::fem::LinearSystemWrapperItpack, itk::fem::LinearSystemWrapperVNL, and itk::fem::LinearSystemWrapperDenseVNL.

void itk::fem::LinearSystemWrapper::SetNumberOfMatrices ( unsigned int nMatrices )

inline

Set Index of matrices used by the system

Parameters:

nMatrices Index of matrices used by system

Definition at line 111 of file itkFEMLinearSystemWrapper.h.

References m_NumberOfMatrices.

void itk::fem::LinearSystemWrapper::SetNumberOfSolutions ( unsigned int nSolutions )

inline

Set Index of solutions used by the system

Parameters:

nSolutions Index of solutions used by system

Definition at line 155 of file itkFEMLinearSystemWrapper.h.

References m_NumberOfSolutions.

void itk::fem::LinearSystemWrapper::SetNumberOfVectors ( unsigned int nVectors )

inline

Set Index of vectors used by the system

Parameters:

nVectors Index of vectors used by system

Definition at line 138 of file itkFEMLinearSystemWrapper.h.

References m_NumberOfVectors.

virtual void itk::fem::LinearSystemWrapper::SetSolutionValue	(	unsigned int	i,
		Float	value,
		unsigned int	solutionIndex = `0`
	)

pure virtual

Virtual function to set a value of specific element of the solution vector.

Parameters:

i	element Index in solution vector
value	new value of the element
solutionIndex	index of solution vector to set value in

Implemented in itk::fem::LinearSystemWrapperItpack, itk::fem::LinearSystemWrapperVNL, and itk::fem::LinearSystemWrapperDenseVNL.

void itk::fem::LinearSystemWrapper::SetSystemOrder ( unsigned int N )

inline

Set the order of the system. All matrices will be of size NxN and all vectors will be of size N

Parameters:

N	order of the linear system

Definition at line 94 of file itkFEMLinearSystemWrapper.h.

References m_Order.

virtual void itk::fem::LinearSystemWrapper::SetVectorValue	(	unsigned int	i,
		Float	value,
		unsigned int	vectorIndex = `0`
	)

pure virtual

Virtual function to set a value of a specific element of the B vector.

Parameters:

i	row of the element
value	new value of the element
vectorIndex	index of vector to set value in

Implemented in itk::fem::LinearSystemWrapperItpack, itk::fem::LinearSystemWrapperVNL, and itk::fem::LinearSystemWrapperDenseVNL.

virtual void itk::fem::LinearSystemWrapper::Solve ( void )

pure virtual

Solves the linear system and creates the solution vector, which can later be accessed via GetSolutionValue(i,SolutionIndex) member function. Here all the major processing is done with calls to external numeric library.