BandMatrix Class Reference

A class for banded matrices, involving matrix inversion processes. More...

#include <BandMatrix.h>

Inheritance diagram for BandMatrix:

Collaboration diagram for BandMatrix:

Public Member Functions
	BandMatrix ()
	Base Constructor. More...
	BandMatrix (size_t n, size_t kl, size_t ku, doublereal v=0.0)
	Creates a banded matrix and sets all elements to zero. More...
	BandMatrix (const BandMatrix &y)
	Copy constructor. More...
BandMatrix &	operator= (const BandMatrix &y)
	assignment operator More...
void	resize (size_t n, size_t kl, size_t ku, doublereal v=0.0)
	Resize the matrix problem. More...
void	bfill (doublereal v=0.0)
	Fill or zero the matrix. More...
doublereal &	operator() (size_t i, size_t j)
	Index into the (i,j) element. More...
doublereal	operator() (size_t i, size_t j) const
	Constant Index into the (i,j) element. More...
doublereal &	value (size_t i, size_t j)
	Return a changeable reference to element (i,j). More...
doublereal	value (size_t i, size_t j) const
	Return the value of element (i,j). More...
size_t	index (size_t i, size_t j) const
	Returns the location in the internal 1D array corresponding to the (i,j) element in the banded array. More...
doublereal	_value (size_t i, size_t j) const
	Return the value of the (i,j) element for (i,j) within the bandwidth. More...
virtual size_t	nRows () const
	Return the number of rows in the matrix. More...
virtual size_t	nRowsAndStruct (size_t *const iStruct=0) const
	Return the size and structure of the matrix. More...
size_t	nColumns () const
	Number of columns. More...
size_t	nSubDiagonals () const
	Number of subdiagonals. More...
size_t	nSuperDiagonals () const
	Number of superdiagonals. More...
size_t	ldim () const
	Return the number of rows of storage needed for the band storage. More...
vector_int &	ipiv ()
	Return a reference to the pivot vector. More...
virtual void	mult (const doublereal *b, doublereal *prod) const
	Multiply A*b and write result to prod. More...
virtual void	leftMult (const doublereal *const b, doublereal *const prod) const
	Multiply b*A and write result to prod. More...
int	factor ()
	Perform an LU decomposition, the LAPACK routine DGBTRF is used. More...
int	solve (const doublereal *const b, doublereal *const x)
	Solve the matrix problem Ax = b. More...
int	solve (doublereal *b, size_t nrhs=1, size_t ldb=0)
	Solve the matrix problem Ax = b. More...
virtual vector_fp::iterator	begin ()
	Returns an iterator for the start of the band storage data. More...
vector_fp::iterator	end ()
	Returns an iterator for the end of the band storage data. More...
vector_fp::const_iterator	begin () const
	Returns a const iterator for the start of the band storage data. More...
vector_fp::const_iterator	end () const
	Returns a const iterator for the end of the band storage data. More...
virtual void	zero ()
	Zero the matrix elements. More...
virtual doublereal	rcond (doublereal a1norm)
	Returns an estimate of the inverse of the condition number for the matrix. More...
virtual int	factorAlgorithm () const
	Returns the factor algorithm used. More...
virtual doublereal	oneNorm () const
	Returns the one norm of the matrix. More...
virtual GeneralMatrix *	duplMyselfAsGeneralMatrix () const
	Duplicator member function. More...
virtual doublereal *	ptrColumn (size_t j)
	Return a pointer to the top of column j, column values are assumed to be contiguous in memory. More...
virtual doublereal *const *	colPts ()
	Return a vector of const pointers to the columns. More...
virtual void	copyData (const GeneralMatrix &y)
	Copy the data from one array into another without doing any checking. More...
virtual size_t	checkRows (doublereal &valueSmall) const
	Check to see if we have any zero rows in the Jacobian. More...
virtual size_t	checkColumns (doublereal &valueSmall) const
	Check to see if we have any zero columns in the Jacobian. More...
virtual void	useFactorAlgorithm (int fAlgorithm)
	Change the way the matrix is factored. More...
Public Member Functions inherited from GeneralMatrix
	GeneralMatrix (int matType)
	Base Constructor. More...
	GeneralMatrix (const GeneralMatrix &right)
	Copy Constructor. More...
GeneralMatrix &	operator= (const GeneralMatrix &right)
	Assignment operator. More...
virtual	~GeneralMatrix ()
	Destructor. Does nothing. More...
virtual int	factorQR ()
	Factors the A matrix using the QR algorithm, overwriting A. More...
virtual doublereal	rcondQR ()
	Returns an estimate of the inverse of the condition number for the matrix. More...
virtual void	clearFactorFlag ()
	clear the factored flag More...
virtual bool	factored () const
	true if the current factorization is up to date with the matrix More...

Protected Attributes
vector_fp	data
	Matrix data. More...
vector_fp	ludata
	Factorized data. More...
size_t	m_n
	Number of rows and columns of the matrix. More...
size_t	m_kl
	Number of subdiagonals of the matrix. More...
size_t	m_ku
	Number of super diagonals of the matrix. More...
doublereal	m_zero
	value of zero More...
vector_int	m_ipiv
	Pivot vector. More...
std::vector< doublereal * >	m_colPtrs
	Vector of column pointers. More...
vector_int	iwork_
	Extra work array needed - size = n. More...
vector_fp	work_
	Extra dp work array needed - size = 3n. More...
Protected Attributes inherited from GeneralMatrix
int	m_factored
	Indicates whether the matrix is factored. More...

Additional Inherited Members
Public Attributes inherited from GeneralMatrix
int	matrixType_
	Matrix type. More...

Detailed Description

A class for banded matrices, involving matrix inversion processes.

The class is based upon the LAPACK banded storage matrix format.

An important issue with this class is that it stores both the original data and the LU factorization of the data. This means that the banded matrix typically will take up twice the room that it is expected to take.

QR factorizations of banded matrices are not included in the original LAPACK work. Add-ons are available. However, they are not included here. Instead we just use the stock LU decompositions.

This class is a derived class of the base class GeneralMatrix. However, within the oneD directory, the class is used as is, without reference to the GeneralMatrix base type.

Definition at line 33 of file BandMatrix.h.

Constructor & Destructor Documentation

BandMatrix

(

)

Base Constructor.

• Create an 0 by 0 matrix, and initialize all elements to 0.

Definition at line 22 of file BandMatrix.cpp.

Referenced by BandMatrix::duplMyselfAsGeneralMatrix().

BandMatrix	(	size_t	n,
		size_t	kl,
		size_t	ku,
		doublereal	v = 0.0
	)

Creates a banded matrix and sets all elements to zero.

Create an n by n banded matrix, and initialize all elements to v.

Parameters

n	size of the square matrix
kl	band size on the lower portion of the matrix
ku	band size on the upper portion of the matrix
v	initial value of all matrix components.

Definition at line 31 of file BandMatrix.cpp.

References BandMatrix::data, BandMatrix::ludata, BandMatrix::m_colPtrs, BandMatrix::m_ipiv, and BandMatrix::m_n.

BandMatrix

(

const BandMatrix &

y

)

Copy constructor.

Parameters

y	Matrix to be copied

Definition at line 50 of file BandMatrix.cpp.

References BandMatrix::data, BandMatrix::ludata, BandMatrix::m_colPtrs, BandMatrix::m_ipiv, BandMatrix::m_kl, BandMatrix::m_ku, and BandMatrix::m_n.

Member Function Documentation

BandMatrix & operator=

(

const BandMatrix &

y

)

assignment operator

Parameters

y	reference to the matrix to be copied

Definition at line 70 of file BandMatrix.cpp.

References BandMatrix::data, BandMatrix::ludata, BandMatrix::m_colPtrs, BandMatrix::m_ipiv, BandMatrix::m_kl, BandMatrix::m_ku, BandMatrix::m_n, and GeneralMatrix::operator=().

void resize	(	size_t	n,
		size_t	kl,
		size_t	ku,
		doublereal	v = 0.0
	)

Resize the matrix problem.

All data is lost

Parameters

n	size of the square matrix
kl	band size on the lower portion of the matrix
ku	band size on the upper portion of the matrix
v	initial value of all matrix components.

Definition at line 90 of file BandMatrix.cpp.

References BandMatrix::data, BandMatrix::ludata, BandMatrix::m_colPtrs, GeneralMatrix::m_factored, BandMatrix::m_ipiv, BandMatrix::m_kl, BandMatrix::m_ku, and BandMatrix::m_n.

void bfill

(

doublereal

v = 0.0

)

Fill or zero the matrix.

Parameters

v	Fill value, defaults to zero.

Definition at line 107 of file BandMatrix.cpp.

References BandMatrix::data, and GeneralMatrix::m_factored.

Referenced by MultiJac::eval().

doublereal & operator() ( size_t  i, size_t  j  )

virtual

Index into the (i,j) element.

Parameters

i	row
j	column

Returns a changeable reference to the matrix entry

Implements GeneralMatrix.

Definition at line 119 of file BandMatrix.cpp.

References BandMatrix::value().

doublereal operator() ( size_t  i, size_t  j  ) const

virtual

Constant Index into the (i,j) element.

Parameters

i	row
j	column

Returns an unchangeable reference to the matrix entry

Implements GeneralMatrix.

Definition at line 124 of file BandMatrix.cpp.

References BandMatrix::value().

doublereal & value	(	size_t	i,
		size_t	j
	)

Return a changeable reference to element (i,j).

Since this method may alter the element value, it may need to be refactored, so the flag m_factored is set to false.

Parameters

i	row
j	column

Returns

Returns a reference to the value of the matrix entry

Definition at line 129 of file BandMatrix.cpp.

References BandMatrix::data, BandMatrix::index(), GeneralMatrix::m_factored, BandMatrix::m_kl, and BandMatrix::m_zero.

Referenced by BandMatrix::checkColumns(), BandMatrix::checkRows(), MultiJac::eval(), BandMatrix::oneNorm(), and BandMatrix::operator()().

doublereal value	(	size_t	i,
		size_t	j
	)		const

Return the value of element (i,j).

This method does not alter the array.

Parameters

i	row
j	column

Returns

Returns the value of the matrix entry

Definition at line 138 of file BandMatrix.cpp.

References BandMatrix::data, BandMatrix::index(), and BandMatrix::m_kl.

size_t index	(	size_t	i,
		size_t	j
	)		const

Returns the location in the internal 1D array corresponding to the (i,j) element in the banded array.

Parameters

i	row
j	column

Returns

Returns the index of the matrix entry

Definition at line 146 of file BandMatrix.cpp.

References BandMatrix::m_kl, and BandMatrix::m_ku.

Referenced by BandMatrix::_value(), and BandMatrix::value().

doublereal _value	(	size_t	i,
		size_t	j
	)		const

Return the value of the (i,j) element for (i,j) within the bandwidth.

For efficiency, this method does not check that (i,j) are within the bandwidth; it is up to the calling program to insure that this is true.

Parameters

i	row
j	column

Returns

Returns the value of the matrix entry

Definition at line 154 of file BandMatrix.cpp.

References BandMatrix::data, and BandMatrix::index().

Referenced by BandMatrix::leftMult(), and BandMatrix::mult().

size_t nRows ( ) const

virtual

Return the number of rows in the matrix.

Implements GeneralMatrix.

Definition at line 159 of file BandMatrix.cpp.

References BandMatrix::m_n.

Referenced by BandMatrix::factor(), BandMatrix::mult(), and Cantera::operator<<().

size_t nRowsAndStruct ( size_t *const  iStruct = 0 ) const

virtual

Return the size and structure of the matrix.

Parameters

iStruct

OUTPUT Pointer to a vector of ints that describe the structure of the matrix. istruct[0] = kl istruct[1] = ku

Returns

returns the number of rows and columns in the matrix.

Implements GeneralMatrix.

Definition at line 164 of file BandMatrix.cpp.

References BandMatrix::m_kl, BandMatrix::m_ku, and BandMatrix::m_n.

size_t nColumns

(

)

const

Number of columns.

Definition at line 173 of file BandMatrix.cpp.

References BandMatrix::m_n.

Referenced by BandMatrix::factor(), BandMatrix::leftMult(), Cantera::operator<<(), and BandMatrix::solve().

size_t nSubDiagonals

(

)

const

Number of subdiagonals.

Definition at line 178 of file BandMatrix.cpp.

References BandMatrix::m_kl.

Referenced by BandMatrix::factor(), and BandMatrix::solve().

size_t nSuperDiagonals

(

)

const

Number of superdiagonals.

Definition at line 183 of file BandMatrix.cpp.

References BandMatrix::m_ku.

Referenced by BandMatrix::factor(), and BandMatrix::solve().

size_t ldim

(

)

const

Return the number of rows of storage needed for the band storage.

Definition at line 188 of file BandMatrix.cpp.

References BandMatrix::m_kl, and BandMatrix::m_ku.

Referenced by BandMatrix::factor(), and BandMatrix::solve().

vector_int & ipiv

(

)

Return a reference to the pivot vector.

Definition at line 193 of file BandMatrix.cpp.

References BandMatrix::m_ipiv.

Referenced by BandMatrix::factor(), and BandMatrix::solve().

void mult ( const doublereal *  b, doublereal *  prod  ) const

virtual

Multiply A*b and write result to prod.

Implements GeneralMatrix.

Definition at line 198 of file BandMatrix.cpp.

References BandMatrix::_value(), BandMatrix::m_kl, BandMatrix::m_ku, BandMatrix::m_n, and BandMatrix::nRows().

void leftMult ( const doublereal *const  b, doublereal *const  prod  ) const

virtual

Multiply b*A and write result to prod.

Parameters

b	Vector to do the lh multiplication
prod	OUTPUT vector to receive the result

Implements GeneralMatrix.

Definition at line 215 of file BandMatrix.cpp.

References BandMatrix::_value(), BandMatrix::m_kl, BandMatrix::m_ku, BandMatrix::m_n, and BandMatrix::nColumns().

int factor ( )

virtual

Perform an LU decomposition, the LAPACK routine DGBTRF is used.

The factorization is saved in ludata.

Returns

Return a success flag. 0 indicates a success ~0 Some error occurred, see the LAPACK documentation

Implements GeneralMatrix.

Definition at line 233 of file BandMatrix.cpp.

References BandMatrix::data, DATA_PTR, BandMatrix::ipiv(), BandMatrix::ldim(), BandMatrix::ludata, GeneralMatrix::m_factored, BandMatrix::nColumns(), BandMatrix::nRows(), BandMatrix::nSubDiagonals(), and BandMatrix::nSuperDiagonals().

Referenced by BandMatrix::solve().

int solve	(	const doublereal *const	b,
		doublereal *const	x
	)

Solve the matrix problem Ax = b.

Parameters

b	INPUT RHS of the problem
x	OUTPUT solution to the problem

Returns

Return a success flag 0 indicates a success ~0 Some error occurred, see the LAPACK documentation

Definition at line 252 of file BandMatrix.cpp.

References BandMatrix::m_n.

Referenced by MultiNewton::step().

int solve ( doublereal *  b, size_t  nrhs = 1, size_t  ldb = 0  )

virtual

Solve the matrix problem Ax = b.

Parameters

b	INPUT RHS of the problem OUTPUT solution to the problem
nrhs	Number of right hand sides to solve
ldb	Leading dimension of b. Default is nColumns()

Returns

Return a success flag 0 indicates a success ~0 Some error occurred, see the LAPACK documentation

Implements GeneralMatrix.

Definition at line 258 of file BandMatrix.cpp.

References DATA_PTR, BandMatrix::factor(), BandMatrix::ipiv(), BandMatrix::ldim(), BandMatrix::ludata, GeneralMatrix::m_factored, BandMatrix::nColumns(), BandMatrix::nSubDiagonals(), and BandMatrix::nSuperDiagonals().

vector_fp::iterator begin ( )

virtual

Returns an iterator for the start of the band storage data.

Iterator points to the beginning of the data, and it is changeable.

Implements GeneralMatrix.

Definition at line 281 of file BandMatrix.cpp.

References BandMatrix::data, and GeneralMatrix::m_factored.

vector_fp::iterator end

(

)

Returns an iterator for the end of the band storage data.

Iterator points to the end of the data, and it is changeable.

Definition at line 287 of file BandMatrix.cpp.

References BandMatrix::data, and GeneralMatrix::m_factored.

vector_fp::const_iterator begin ( ) const

virtual

Returns a const iterator for the start of the band storage data.

Iterator points to the beginning of the data, and it is not changeable.

Implements GeneralMatrix.

Definition at line 293 of file BandMatrix.cpp.

References BandMatrix::data.

vector_fp::const_iterator end

(

)

const

Returns a const iterator for the end of the band storage data.

Iterator points to the end of the data, and it is not changeable.

Definition at line 298 of file BandMatrix.cpp.

References BandMatrix::data.

void zero ( )

virtual

Zero the matrix elements.

Implements GeneralMatrix.

Definition at line 113 of file BandMatrix.cpp.

References BandMatrix::data, and GeneralMatrix::m_factored.

doublereal rcond ( doublereal  a1norm )

virtual

Returns an estimate of the inverse of the condition number for the matrix.

The matrix must have been previously factored using the LU algorithm

Parameters

a1norm

Norm of the matrix

Returns

returns the inverse of the condition number

Implements GeneralMatrix.

Definition at line 316 of file BandMatrix.cpp.

References DATA_PTR, Cantera::int2str(), BandMatrix::iwork_, BandMatrix::ludata, GeneralMatrix::m_factored, BandMatrix::m_ipiv, BandMatrix::m_kl, BandMatrix::m_ku, BandMatrix::m_n, BandMatrix::work_, and Cantera::writelogf().

int factorAlgorithm ( ) const

virtual

Returns the factor algorithm used.

This method will always return 0 (LU) for band matrices.

Implements GeneralMatrix.

Definition at line 346 of file BandMatrix.cpp.

doublereal oneNorm ( ) const

virtual

Returns the one norm of the matrix.

Implements GeneralMatrix.

Definition at line 351 of file BandMatrix.cpp.

References BandMatrix::m_colPtrs, BandMatrix::m_kl, BandMatrix::m_ku, BandMatrix::m_n, and BandMatrix::value().

GeneralMatrix * duplMyselfAsGeneralMatrix ( ) const

virtual

Duplicator member function.

This function will duplicate the matrix given a generic GeneralMatrix

Returns

Returns a pointer to the malloced object

Implements GeneralMatrix.

Definition at line 411 of file BandMatrix.cpp.

References BandMatrix::BandMatrix().

doublereal * ptrColumn ( size_t  j )

virtual

Return a pointer to the top of column j, column values are assumed to be contiguous in memory.

The LAPACK bandstructure has column values which are contiguous in memory:

On entry, the matrix A in band storage, in rows KL+1 to 2*KL+KU+1; rows 1 to KL of the array need not be set. The j-th column of A is stored in the j-th column of the array AB as follows: AB(KL + KU + 1 + i - j,j) = A(i,j) for max(1, j - KU) <= i <= min(m, j + KL)

This routine returns the position of AB(1,j) (fortran-1 indexing) in the above format

So to address the (i,j) position, you use the following indexing:

double *colP_j = matrix.ptrColumn(j); double a_i_j = colP_j[kl + ku + i - j];

Parameters

j	Value of the column

Returns

Returns a pointer to the top of the column

Implements GeneralMatrix.

Definition at line 416 of file BandMatrix.cpp.

References BandMatrix::m_colPtrs.

doublereal *const * colPts ( )

virtual

Return a vector of const pointers to the columns.

Note the value of the pointers are protected by their being const. However, the value of the matrix is open to being changed.

Returns

returns a vector of pointers to the top of the columns of the matrices.

Implements GeneralMatrix.

Definition at line 421 of file BandMatrix.cpp.

References BandMatrix::m_colPtrs.

void copyData ( const GeneralMatrix &  y )

virtual

Copy the data from one array into another without doing any checking.

This differs from the assignment operator as no resizing is done and memcpy() is used.

Parameters

y	Array to be copied

Deprecated:

To be removed after Cantera 2.2.

Implements GeneralMatrix.

Definition at line 426 of file BandMatrix.cpp.

References BandMatrix::data, DATA_PTR, GeneralMatrix::m_factored, BandMatrix::m_kl, BandMatrix::m_ku, BandMatrix::m_n, GeneralMatrix::ptrColumn(), and Cantera::warn_deprecated().

size_t checkRows ( doublereal &  valueSmall ) const

virtual

Check to see if we have any zero rows in the Jacobian.

This utility routine checks to see if any rows are zero. The smallest row is returned along with the largest coefficient in that row

Parameters

valueSmall

OUTPUT value of the largest coefficient in the smallest row

Returns

index of the row that is most nearly zero

Implements GeneralMatrix.

Definition at line 367 of file BandMatrix.cpp.

References BandMatrix::m_kl, BandMatrix::m_ku, BandMatrix::m_n, Cantera::npos, and BandMatrix::value().

size_t checkColumns ( doublereal &  valueSmall ) const

virtual

Check to see if we have any zero columns in the Jacobian.

This utility routine checks to see if any columns are zero. The smallest column is returned along with the largest coefficient in that column

Parameters

valueSmall

OUTPUT value of the largest coefficient in the smallest column

Returns

index of the column that is most nearly zero

Implements GeneralMatrix.

Definition at line 389 of file BandMatrix.cpp.

References BandMatrix::m_kl, BandMatrix::m_ku, BandMatrix::m_n, Cantera::npos, and BandMatrix::value().

void useFactorAlgorithm ( int  fAlgorithm )

virtual

Change the way the matrix is factored.

Parameters

fAlgorithm

integer 0 LU factorization 1 QR factorization

Reimplemented from GeneralMatrix.

Definition at line 435 of file BandMatrix.cpp.

Member Data Documentation

vector_fp data

protected

Matrix data.

Definition at line 315 of file BandMatrix.h.

Referenced by BandMatrix::_value(), BandMatrix::BandMatrix(), BandMatrix::begin(), BandMatrix::bfill(), BandMatrix::copyData(), BandMatrix::end(), BandMatrix::factor(), BandMatrix::operator=(), BandMatrix::resize(), BandMatrix::value(), and BandMatrix::zero().

vector_fp ludata

protected

Factorized data.

Definition at line 318 of file BandMatrix.h.

Referenced by BandMatrix::BandMatrix(), BandMatrix::factor(), BandMatrix::operator=(), BandMatrix::rcond(), BandMatrix::resize(), and BandMatrix::solve().

size_t m_n

protected

Number of rows and columns of the matrix.

Definition at line 321 of file BandMatrix.h.

Referenced by BandMatrix::BandMatrix(), BandMatrix::checkColumns(), BandMatrix::checkRows(), BandMatrix::copyData(), BandMatrix::leftMult(), BandMatrix::mult(), BandMatrix::nColumns(), BandMatrix::nRows(), BandMatrix::nRowsAndStruct(), BandMatrix::oneNorm(), BandMatrix::operator=(), BandMatrix::rcond(), BandMatrix::resize(), and BandMatrix::solve().

size_t m_kl

protected

Number of subdiagonals of the matrix.

Definition at line 324 of file BandMatrix.h.

Referenced by BandMatrix::BandMatrix(), BandMatrix::checkColumns(), BandMatrix::checkRows(), BandMatrix::copyData(), BandMatrix::index(), BandMatrix::ldim(), BandMatrix::leftMult(), BandMatrix::mult(), BandMatrix::nRowsAndStruct(), BandMatrix::nSubDiagonals(), BandMatrix::oneNorm(), BandMatrix::operator=(), BandMatrix::rcond(), BandMatrix::resize(), and BandMatrix::value().

size_t m_ku

protected

Number of super diagonals of the matrix.

Definition at line 327 of file BandMatrix.h.

Referenced by BandMatrix::BandMatrix(), BandMatrix::checkColumns(), BandMatrix::checkRows(), BandMatrix::copyData(), BandMatrix::index(), BandMatrix::ldim(), BandMatrix::leftMult(), BandMatrix::mult(), BandMatrix::nRowsAndStruct(), BandMatrix::nSuperDiagonals(), BandMatrix::oneNorm(), BandMatrix::operator=(), BandMatrix::rcond(), and BandMatrix::resize().

doublereal m_zero

protected

value of zero

Definition at line 330 of file BandMatrix.h.

Referenced by BandMatrix::value().

vector_int m_ipiv

protected

Pivot vector.

Definition at line 333 of file BandMatrix.h.

Referenced by BandMatrix::BandMatrix(), BandMatrix::ipiv(), BandMatrix::operator=(), BandMatrix::rcond(), and BandMatrix::resize().

std::vector<doublereal*> m_colPtrs

protected

Vector of column pointers.

Definition at line 336 of file BandMatrix.h.

Referenced by BandMatrix::BandMatrix(), BandMatrix::colPts(), BandMatrix::oneNorm(), BandMatrix::operator=(), BandMatrix::ptrColumn(), and BandMatrix::resize().

vector_int iwork_

protected

Extra work array needed - size = n.

Definition at line 339 of file BandMatrix.h.

Referenced by BandMatrix::rcond().

vector_fp work_

protected

Extra dp work array needed - size = 3n.

Definition at line 342 of file BandMatrix.h.

Referenced by BandMatrix::rcond().

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

• BandMatrix.h
• BandMatrix.cpp