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MatBand(Type) Class Reference

dense banded matrix. More...

#include <MatBand_Type.h>

Inheritance diagram for MatBand(Type)::

Public Methods
	MatBand(Type) ()
	MatBand(Type) (int n, int bandwidth, bool symm_storage=false, bool pivot_allowed=false)
	MatBand(Type) (int nrows, int ncolumns, int bandwidth, bool symm_storage=false, bool pivot_allowed=false)
	MatBand(Type) (const MatBand(Type) &X)
	MatBand(Type) (const Matrix(prm_Type) &pm)
virtual	~MatBand(Type) ()
virtual int	getNoColumns () const
virtual int	getNoNonzeroes () const
virtual void	size (int &m, int &n) const
void	setBandwidth (int bandwidth, bool symm_storage=false, bool pivot_allowed=false)
int	getBandwidth () const
int	getLowerBandwidth () const
int	getUpperBandwidth () const
bool	insideBand (const int i, const int j) const
virtual bool	makeItSimilar (Handle(Matrix(Type)) &M) const
virtual bool	redim (const Matrix(prm_Type) &pm)
bool	redim (int n, int bandwidth_, bool symm_storage_, bool pivot_allowed_)
bool	redim (int nrows, int ncolumns, int bandwidth, bool symm_storage, bool pivot_allowed)
virtual bool	redim (const VecSimple(int) &ivec, const VecSimple(int) &jvec, int new_nrows, int new_ncolumns)
virtual void	getIndexSet (VecSimple(int) &ivec, VecSimple(int) &jvec) const
virtual bool	validIndexSet (const VecSimple(int) &ivec, const VecSimple(int) &jvec, const int new_nrows, const int new_ncolumns)
virtual Type&	elm (int i, int j)
bool	denseIndex2bandIndex (int i, int j, int &ib, int &jb)
virtual void	fill (const Matrix(Type) &X)
virtual void	fill (Type a)
MatBand(Type)&	operator= (const MatBand(Type) &X)
MatBand(Type)&	operator= (const Type &a)
virtual void	assemble (const Mat(Type) &em, const VecSimple(int) &idx_row_trans, const VecSimple(int) &idx_col_trans, int elm_no)
virtual void	add (Matrix(Type) &bb, Matrix(Type) &cb)
virtual void	add (Matrix(Type) &bb, char s, Matrix(Type) &cb)
virtual void	add (Matrix(Type) &bb, Type b, Matrix(Type) &cb)
virtual void	add (Type a, Matrix(Type) &bm, Type b, Matrix(Type) &cb)
void	add (MatBand(Type) &y, int power)
void	add (Type value)
virtual void	mult (Type value)
virtual void	prod (const Vector(Type) &xb, Vector(Type) &yb, TransposeMode tpmode=NOT_TRANSPOSED, bool add_to_yb=false) const
virtual void	transpose ()
virtual void	conjTranspose ()
virtual void	colManip (LinEqConstraint &constraint_eq, Vec(Type) &vc, VecSimple(bool) &essential_dof)
virtual void	rowManip (LinEqConstraint &constraint_eq, Vec(Type) &vc, VecSimple(bool) &essential_dof)
virtual bool	factSVD (Vec(Type) &, Mat(Type) &, real=1.0e-6)
virtual void	forwBackSVD (const Vec(Type) &, const Mat(Type) &, const Vec(Type) &, Vec(Type) &)
virtual bool	factChol (bool=true)
virtual void	forwBackChol (Vec(Type) &, Vec(Type) &)
virtual bool	factLU ()
virtual void	forwBackLU (Vec(Type) &b, Vec(Type) &x)
virtual bool	factLU (VecSimple(int) &perm, Vec(Type) &scratch)
virtual bool	factLU (VecSimple(int) &perm)
virtual void	forwBackLU (Vec(Type) &b, Vec(Type) &x, const VecSimple(int) &perm)
virtual bool	factorize (const FactStrategy &fstrategy)
virtual void	forwBack (Vector(Type) &bb, Vector(Type) &xb)
virtual void	inverse (Mat(Type) &inv)
virtual void	inverse (Mat(Type) &inv, Vec(Type) &scratch)
virtual void	inverse (Mat(Type) &inv, VecSimple(int) &perm, Vec(Type)&scratch)
virtual Type	det ()
virtual void	SSOR1it (Vector(Type) &xnew, const Vector(Type) &xold, const Vector(Type) &b, real omega, TransposeMode tpmode=NOT_TRANSPOSED) const
virtual void	SSORsolve (Vector(Type) &y, const Vector(Type) &c, real omega, TransposeMode tpmode=NOT_TRANSPOSED) const
virtual void	SOR1it (Vector(Type) &xnew, const Vector(Type) &xold, const Vector(Type) &b, real omega, TransposeMode tpmode=NOT_TRANSPOSED) const
virtual void	SORsolve (Vector(Type) &y, const Vector(Type) &c, real omega, TransposeMode tpmode=NOT_TRANSPOSED) const
virtual void	Jacobi1it (Vector(Type) &xnew, const Vector(Type) &xold, const Vector(Type) &b, TransposeMode tpmode=NOT_TRANSPOSED) const
virtual void	Jacobisolve (Vector(Type) &y, const Vector(Type) &c, TransposeMode tpmode=NOT_TRANSPOSED) const
virtual void	print (Os os, const char *header=NULL, int nentries_per_line=3) const
void	printAscii (Os os, const char *header=NULL) const
virtual void	scan (Is is)
virtual void	save (const char filename, const char name="X") const
virtual void	load (const char filename, const char name="X")
CLASS_INFO	VIRTUAL_CAST (MatBand(Type)) private
virtual void	prod (const Matrix(Type) &, const Matrix(Type) &, TransposeMode=NOT_TRANSPOSED, TransposeMode=NOT_TRANSPOSED)
void	prod (const Matrix(Type) &, const Matrix(Type) &, bool, TransposeMode=NOT_TRANSPOSED, TransposeMode=NOT_TRANSPOSED)
Protected Methods
int	actual_bandwidth (int bandwidth_, bool symm_storage_, bool pivot_allowed_) const
bool	validAttributes (int bandwidth, bool &symm_storage, bool &pivot_allowed) const
bool	factLU_symm ()
void	forwBackLU_symm (Vec(Type) &b, Vec(Type) &x)
bool	factLU_nonsymm ()
void	forwBackLU_nonsymm (Vec(Type) &b, Vec(Type) &x)
void	prod_symm (const Vec(Type) &x, Vec(Type) &y, transposeFP(Type) transform, bool transposed, bool add_to_yb=false) const
void	prod_nonsymm (const Vec(Type) &x, Vec(Type) &y, transposeFP(Type) transform, bool transposed, bool add_to_yb=false) const
virtual void	copy_matrix_attributes (const Matrix(Type) &X)
virtual void	copy_matrix_attributes (const Mat(Type) &X)
virtual void	copy_matrix_attributes (const MatBand(Type) &X)
virtual void	reset ()
bool	redim (int n)
bool	redim (int nrows_, int ncolumns_)
Protected Attributes
int	full_ncols
int	bandwidth
int&	ndiags
Type	zero_entry
Friends
Os&	operator<< (Os &os, const MatBand(Type) &X)
Is&	operator>> (Is &is, MatBand(Type) &X)

Detailed Description

dense banded matrix.

NAME: MatBand(Type) - dense banded matrix

DESCRIPTION:

The class is a specialization of class "MatDense(Type)" and implements a standard banded matrix format. The class allows both symmetric and nonsymmetric storage schemes.

Constructor & Destructor Documentation

MatBand(Type)::MatBand_Type ( ) [inline]

MatBand(Type)::MatBand_Type ( int n,

int bandwidth,

bool symm_storage = false,

bool pivot_allowed = false )

See documentation of one of the overloaded constructor.

MatBand(Type)::MatBand_Type ( int nrows,

int ncolumns,

int bandwidth,

bool symm_storage = false,

bool pivot_allowed = false )

See documentation of one of the overloaded constructor.

MatBand(Type)::MatBand_Type ( const MatBand(Type) & X )

See documentation of one of the overloaded constructor.

MatBand(Type)::MatBand_Type ( const Matrix(prm_Type) & pm )

See documentation of one of the overloaded constructor.

MatBand(Type)::~MatBand(Type) ( ) [virtual]

Member Function Documentation

void MatBand(Type)::Jacobi1it ( Vector(Type) & xnew,

const Vector(Type) & xold,

const Vector(Type) & b,

TransposeMode tpmode = NOT_TRANSPOSED ) const [virtual]

void MatBand(Type)::Jacobisolve ( Vector(Type) & y,

const Vector(Type) & c,

TransposeMode tpmode = NOT_TRANSPOSED ) const [virtual]

void MatBand(Type)::SOR1it ( Vector(Type) & xnew,

const Vector(Type) & xold,

const Vector(Type) & b,

real omega,

TransposeMode tpmode = NOT_TRANSPOSED ) const [virtual]

void MatBand(Type)::SORsolve ( Vector(Type) & y,

const Vector(Type) & c,

real omega,

TransposeMode tpmode = NOT_TRANSPOSED ) const [virtual]

void MatBand(Type)::SSOR1it ( Vector(Type) & xnew,

const Vector(Type) & xold,

const Vector(Type) & b,

real omega,

TransposeMode tpmode = NOT_TRANSPOSED ) const [virtual]

void MatBand(Type)::SSORsolve ( Vector(Type) & y,

const Vector(Type) & c,

real omega,

TransposeMode tpmode = NOT_TRANSPOSED ) const [virtual]

CLASS_INFO MatBand(Type)::VIRTUAL_CAST ( MatBand(Type) ) [inline]

int MatBand(Type)::actual_bandwidth ( int bandwidth_,

bool symm_storage_,

bool pivot_allowed_ ) const [inline, protected]

void MatBand(Type)::add ( Type value )

void MatBand(Type)::add ( MatBand(Type) & y,

int power )

void MatBand(Type)::add ( Type a,

Matrix(Type) & bm,

Type b,

Matrix(Type) & cb ) [virtual]

void MatBand(Type)::add ( Matrix(Type) & bb,

Type b,

Matrix(Type) & cb ) [virtual]

void MatBand(Type)::add ( Matrix(Type) & bb,

char s,

Matrix(Type) & cb ) [virtual]

void MatBand(Type)::add ( Matrix(Type) & bb,

Matrix(Type) & cb ) [virtual]

void MatBand(Type)::assemble ( const Mat(Type) & em,

const VecSimple(int) & idx_row_trans,

const VecSimple(int) & idx_col_trans,

int elm_no ) [virtual]

void MatBand(Type)::colManip ( LinEqConstraint & constraint_eq,

Vec(Type) & vc,

VecSimple(bool) & essential_dof ) [virtual]

void MatBand(Type)::conjTranspose ( ) [inline, virtual]

void MatBand(Type)::copy_matrix_attributes ( const MatBand(Type) & X ) [protected, virtual]

void MatBand(Type)::copy_matrix_attributes ( const Mat(Type) & X ) [protected, virtual]

void MatBand(Type)::copy_matrix_attributes ( const Matrix(Type) & X ) [protected, virtual]

bool MatBand(Type)::denseIndex2bandIndex ( int i,

int j,

int & ib,

int & jb )

given an index "(i,j)" in a dense matrix ("Mat" or "MatDense"), the function computes the corresponding index "(ib,jb)" in the "MatBand" storage. Internal parameters such as the bandwidth and whether the banded matrix is symmetric or not, influence the index computation. The function returns a true value if the given index was inside the band, otherwise it returns a false value, indicating that the "(ib,jb)" is not inside the band (this implies that the matrix entry corresponding to "(i,j") is zero). The "denseIndex2bandIndex" function makes it easy to code the "elm" function, or in other words, index a band matrix is if it were a dense matrix.

Type MatBand(Type)::det ( ) [virtual]

Type & MatBand(Type)::elm ( int i,

int j ) [virtual]

This function returns entry "(i,j)" of the current matrix as if it was represented as a full "m" by "n" matrix, i.e., the arguments "i" and "j" can run from one to "m" and "n", respectively. This indexing functionality can be used both for assignments and extractions of matrix entries. However, assignments to an entry that is outside the allocated band is neglected since such positions is regarded as zeros by definition.

bool MatBand(Type)::factChol ( bool = true ) [inline, virtual]

bool MatBand(Type)::factLU ( VecSimple(int) & perm ) [virtual]

See documentation of one of the overloaded functions.

bool MatBand(Type)::factLU ( VecSimple(int) & perm,

Vec(Type) & scratch ) [virtual]

See documentation of one of the overloaded functions.

bool MatBand(Type)::factLU ( ) [virtual]

As for other matrix formats, this functions finds the LU decomposition of the matrix by Gaussian elimination. However, in case of symmetric storage of the banded matrix, this function actually computes D and L in an "LDL^T" factorization. Since this is compensated for in calls to "forwBackLU", the user does usually not have to worry about this behaviour.
Please note that pivoting is allowed only for the nonsymmetric storage format.

bool MatBand(Type)::factLU_nonsymm ( ) [protected]

bool MatBand(Type)::factLU_symm ( ) [protected]

bool MatBand(Type)::factSVD ( Vec(Type) &,

Mat(Type) &,

real = 1.0e-6 ) [inline, virtual]

bool MatBand(Type)::factorize ( const FactStrategy & fstrategy ) [virtual]

void MatBand(Type)::fill ( Type a ) [inline, virtual]

void MatBand(Type)::fill ( const Matrix(Type) & X ) [virtual]

void MatBand(Type)::forwBack ( Vector(Type) & bb,

Vector(Type) & xb ) [virtual]

void MatBand(Type)::forwBackChol ( Vec(Type) &,

Vec(Type) & ) [inline, virtual]

void MatBand(Type)::forwBackLU ( Vec(Type) & b,

Vec(Type) & x,

const VecSimple(int) & perm ) [virtual]

void MatBand(Type)::forwBackLU ( Vec(Type) & b,

Vec(Type) & x ) [virtual]

void MatBand(Type)::forwBackLU_nonsymm ( Vec(Type) & b,

Vec(Type) & x ) [protected]

void MatBand(Type)::forwBackLU_symm ( Vec(Type) & b,

Vec(Type) & x ) [protected]

void MatBand(Type)::forwBackSVD ( const Vec(Type) &,

const Mat(Type) &,

const Vec(Type) &,

Vec(Type) & ) [inline, virtual]

int MatBand(Type)::getBandwidth ( ) const [inline]

returns the value of "bandwidth", i.e. the requested band width including the main diagonal. The specialized versions "getLowerBandwidth" and "getUpperBandwidth" return the lower and upper bandwidths excluding the main diagonal. The upper bandwidth takes into account storage space allocated for pivoting. The reported values refers to the matrix in a logical sense, i.e. both functions report a nonzero number even for the symmetric storage format.

void MatBand(Type)::getIndexSet ( VecSimple(int) & ivec,

VecSimple(int) & jvec ) const [virtual]

int MatBand(Type)::getLowerBandwidth ( ) const

int MatBand(Type)::getNoColumns ( ) const [inline, virtual]

int MatBand(Type)::getNoNonzeroes ( ) const [virtual]

int MatBand(Type)::getUpperBandwidth ( ) const

bool MatBand(Type)::insideBand ( const int i,

const int j ) const

void MatBand(Type)::inverse ( Mat(Type) & inv,

VecSimple(int) & perm,

Vec(Type)& scratch ) [virtual]

void MatBand(Type)::inverse ( Mat(Type) & inv,

Vec(Type) & scratch ) [virtual]

void MatBand(Type)::inverse ( Mat(Type) & inv ) [virtual]

void MatBand(Type)::load ( const char * filename,

const char * name = "X" ) [virtual]

bool MatBand(Type)::makeItSimilar ( Handle(Matrix(Type)) & M ) const [virtual]

void MatBand(Type)::mult ( Type value ) [virtual]

MatBand(Type) & MatBand(Type)::operator= ( const Type & a ) [inline]

MatBand(Type) & MatBand(Type)::operator= ( const MatBand(Type) & X )

void MatBand(Type)::print ( Os os,

const char * header = NULL,

int nentries_per_line = 3 ) const [virtual]

The "print" function is very similar to "MatSimple print", but since the storage of a band matrix is different, the index information related to each entry is a bit special. We print the index as

(16, 3 / 13)=4.25439
which means that this entry is located in row 16, with column number 3 in the band matrix storage structure, but with column number 13 if the matrix were a standard dense matrix. Note that the row numbers in a banded storage and a standard dense matrix coincide, but the column numbers do not. If the special index with an asterix,

(1, 3 / *)=0.00000
is encountered, it means that the storage location (1,3) in a banded matrix has no associated entry in a standard dense matrix (hence the values of such artificial entries in the banded storage structure are always zero).

void MatBand(Type)::printAscii ( Os os,

const char * header = NULL ) const

void MatBand(Type)::prod ( const Matrix(Type) &,

const Matrix(Type) &,

bool,

TransposeMode = NOT_TRANSPOSED,

TransposeMode = NOT_TRANSPOSED ) [inline]

void MatBand(Type)::prod ( const Matrix(Type) &,

const Matrix(Type) &,

TransposeMode = NOT_TRANSPOSED,

TransposeMode = NOT_TRANSPOSED ) [inline, virtual]

void MatBand(Type)::prod ( const Vector(Type) & xb,

Vector(Type) & yb,

TransposeMode tpmode = NOT_TRANSPOSED,

bool add_to_yb = false ) const [virtual]

void MatBand(Type)::prod_nonsymm ( const Vec(Type) & x,

Vec(Type) & y,

transposeFP(Type) transform,

bool transposed,

bool add_to_yb = false ) const [protected]

void MatBand(Type)::prod_symm ( const Vec(Type) & x,

Vec(Type) & y,

transposeFP(Type) transform,

bool transposed,

bool add_to_yb = false ) const [protected]

bool MatBand(Type)::redim ( const VecSimple(int) & ivec,

const VecSimple(int) & jvec,

int new_nrows,

int new_ncolumns ) [virtual]

See documentation of one of the overloaded functions.

bool MatBand(Type)::redim ( int nrows,

int ncolumns,

int bandwidth,

bool symm_storage,

bool pivot_allowed )

See documentation of one of the overloaded functions.

bool MatBand(Type)::redim ( int n,

int bandwidth_,

bool symm_storage_,

bool pivot_allowed_ ) [inline]

See documentation of one of the overloaded functions.

bool MatBand(Type)::redim ( const Matrix(prm_Type) & pm ) [virtual]

See documentation of one of the overloaded functions.

bool MatBand(Type)::redim ( int nrows_,

int ncolumns_ ) [inline, protected]

See documentation of one of the overloaded functions.

bool MatBand(Type)::redim ( int n ) [inline, protected]

In addition to the "redim" accepting a "Matrix_prm(Type)" type argument, there are versions of this function that accept the argument sequences of the "MatBand" specific constructors. The matrix is then redimensioned according to the given parameter values.

void MatBand(Type)::reset ( ) [protected, virtual]

void MatBand(Type)::rowManip ( LinEqConstraint & constraint_eq,

Vec(Type) & vc,

VecSimple(bool) & essential_dof ) [virtual]

void MatBand(Type)::save ( const char * filename,

const char * name = "X" ) const [virtual]

void MatBand(Type)::scan ( Is is ) [virtual]

void MatBand(Type)::setBandwidth ( int bandwidth,

bool symm_storage = false,

bool pivot_allowed = false )

If the matrix is instanciated by one of the general-purpose constructors, this function may be used for setting a new bandwidth. In addition, it is possible to specify the flags for symmetric storage and/or pivoting. The latter option only refers to allocation of space to hold row permutations caused by pivoting. To actually force pivoting in a matrix decomposition, one has to call the correct member function for this operation. Alternatively, this can be achieved by setting the appropriate flag for a direct solver in the "LinEqSolver" hierarchy.
When calling "setBandwidth", the matrix is implicitly redimensioned according to the supplied argument values.

void MatBand(Type)::size ( int & m,

int & n ) const [inline, virtual]

void MatBand(Type)::transpose ( ) [inline, virtual]

bool MatBand(Type)::validAttributes ( int bandwidth,

bool & symm_storage,

bool & pivot_allowed ) const [protected]

bool MatBand(Type)::validIndexSet ( const VecSimple(int) & ivec,

const VecSimple(int) & jvec,

const int new_nrows,

const int new_ncolumns ) [virtual]

Friends And Related Function Documentation

Os & operator<< ( Os & os,

const MatBand(Type) & X ) [friend]

Is & operator>> ( Is & is,

MatBand(Type) & X ) [friend]

Member Data Documentation

int MatBand(Type)::bandwidth [protected]

int MatBand(Type)::full_ncols [protected]

int & MatBand(Type)::ndiags [protected]

Type MatBand(Type)::zero_entry [protected]

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

MatBand_Type.h

Diffpack Documentation

MatBand(Type) Class Reference

Public Methods

Protected Methods

Protected Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation