MatrixStructure Class Reference
[Matrix Characteristics]

Matrix "structure" refers to an inherent mathematical (or at least algorithmic) characteristic of the matrix rather than a storage strategy. More...

#include <MatrixCharacteristics.h>

List of all members.

Classes
struct	Mask
Public Types
enum	Structure { NoStructure = 0x00000000, Matrix1d = 0x00000001, Zero = 0x00000002, Identity = 0x00000004, Permutation = 0x00000008, RepeatedDiagonal = 0x00000010, Diagonal = 0x00000020, BiDiagonal = 0x00000040, TriDiagonal = 0x00000080, BandedSymmetric = 0x00000100, BandedHermitian = 0x00000200, Banded = 0x00000400, Triangular = 0x00000800, QuasiTriangular = 0x00001000, Hessenberg = 0x00002000, Symmetric = 0x00004000, Hermitian = 0x00008000, SkewSymmetric = 0x00010000, SkewHermitian = 0x00020000, Full = 0x00040000 }
enum	Position { NoPosition = 0x0000, Lower = 0x0001, Upper = 0x0002 }
	For triangular matrices, we have to know which triangle we're talking about. More...
enum	DiagValue { NoDiagValue = 0x0000, StoredDiag = 0x0001, ZeroDiag = 0x0002, UnitDiag = 0x0004 }
	For triangular, symmetric, and hermitian matrices the diagonal elements may have a single, assumed value rather than being stored in memory. More...
typedef unsigned int	StructureMask
typedef unsigned short	PositionMask
typedef unsigned short	DiagValueMask
Public Member Functions
MatrixStructure &	setMissingAttributes ()
std::string	name () const
	MatrixStructure ()
	MatrixStructure (Structure s, Position p=NoPosition, DiagValue d=NoDiagValue)
	This constructor is also an implicit conversion from the Structure enum to a MatrixStructure object which does not specify Position or DiagValue.
Mask	mask () const
	Given a Structure commitment, which more-restrictive Structures will still satisfy this commitment? Returned value is a mask with a bit set for every Structure that is satisfactory.
Structure	getStructure () const
Position	getPosition () const
DiagValue	getDiagValue () const
MatrixStructure &	setStructure (Structure s)
MatrixStructure &	setPosition (Position p)
MatrixStructure &	setDiagValue (DiagValue d)
MatrixStructure &	set (Structure s, Position p, DiagValue d)
MatrixStructure &	setToNone ()
Static Public Member Functions
static const char *	name (Structure)
static StructureMask	calcStructureMask (Structure)
static const char *	name (Position)
static PositionMask	calcPositionMask (Structure)
static const char *	name (DiagValue)
static DiagValueMask	calcDiagValueMask (Structure)
Static Public Attributes
static const StructureMask	AnyStructure = 0x0007ffffU
static const StructureMask	UncommittedStructure = 0xffffffffU
static const PositionMask	AnyPosition = 0x0003U
static const PositionMask	UncommittedPosition = 0xffffU
static const DiagValueMask	AnyDiagValue = 0x0003U
static const DiagValueMask	UncommittedDiagValue = 0xffffU

Detailed Description

Matrix "structure" refers to an inherent mathematical (or at least algorithmic) characteristic of the matrix rather than a storage strategy.

Symmetry is the clearest example of this; it is far more significant mathematically than just a way to save storage and reduce operation count.

Member Typedef Documentation

typedef unsigned short DiagValueMask

typedef unsigned short PositionMask

typedef unsigned int StructureMask

Member Enumeration Documentation

enum DiagValue

For triangular, symmetric, and hermitian matrices the diagonal elements may have a single, assumed value rather than being stored in memory.

This specifies the value. Don't confuse this with the similar MatrixStorage type which simply says whether there is a known value rather than stored values, *not* what that value is.

Enumerator:

NoDiagValue
StoredDiag
ZeroDiag
UnitDiag

enum Position

For triangular matrices, we have to know which triangle we're talking about.

Don't confuse this with MatrixStorage::Placement which has to do with where we put it in memory, *not* what matrix is being represented.

Enumerator:

NoPosition
Lower
Upper

enum Structure

Enumerator:

NoStructure	unspecified structure
Matrix1d	a 1-d matrix (could be row or column)
Zero	a matrix of all zeroes
Identity	diagonal matrix with repeated 1's
Permutation	permutation of an identity matrix
RepeatedDiagonal	diagonal matrix with repeated element
Diagonal	diagonal matrix with arbitrary elements
BiDiagonal	diagonal plus one upper or lower band
TriDiagonal	diagonal plus one upper and one lower band
BandedSymmetric	diagonal plus adjacent symmetric bands
BandedHermitian	diagonal plus adjacent conjugate bands
Banded	diagonal plus upper and lower bands
Triangular	diagonal plus all upper or all lower bands
QuasiTriangular	triangular but with 2x2 blocks on the diagonal
Hessenberg	triangular plus one band above/below diagonal
Symmetric	symmetric: elt(i,j)==elt(j,i)
Hermitian	hermitian: elt(i,j)==conjugate(elt(j,i))
SkewSymmetric	skew symmetric: elt(i,j) == -elt(j,i)
SkewHermitian	skew hermitian: elt(i,j) == -conjugate(elt(j,i))
Full	full mxn matrix, all elements distinct

Constructor & Destructor Documentation

MatrixStructure ( ) [inline]

MatrixStructure	(	Structure	s,
		Position	p = `NoPosition`,
		DiagValue	d = `NoDiagValue`
	)			`[inline]`

This constructor is also an implicit conversion from the Structure enum to a MatrixStructure object which does not specify Position or DiagValue.

Member Function Documentation

static DiagValueMask calcDiagValueMask ( Structure ) [static]

static PositionMask calcPositionMask ( Structure ) [static]

static StructureMask calcStructureMask ( Structure ) [static]

DiagValue getDiagValue ( ) const [inline]

Referenced by Mask::isSatisfiedBy().

Position getPosition ( ) const [inline]

Referenced by Mask::isSatisfiedBy().

Structure getStructure ( ) const [inline]

Referenced by Mask::isSatisfiedBy().

Mask mask ( ) const

Given a Structure commitment, which more-restrictive Structures will still satisfy this commitment? Returned value is a mask with a bit set for every Structure that is satisfactory.

For example, if the commitment is "Banded", "Diagonal" is also acceptable.

Referenced by MatrixCommitment::commitStructure(), and MatrixCommitment::MatrixCommitment().

std::string name ( ) const [inline]

static const char* name ( DiagValue ) [static]