GlsMatrix< Type, DIM > Class Template Reference

#include <gls_matrix.h>

Inheritance diagram for GlsMatrix< Type, DIM >:

Public Member Functions
	GlsMatrix ()
	GlsMatrix (const CStyleMatrix m)
	GlsMatrix (const Type *m)
	GlsMatrix (const GlsMatrix< Type, DIM > &m)
virtual	~GlsMatrix ()
void	Dump () const
void	Clear ()
Type *	Data ()
const Type *	Data () const
void	MakeIdentity ()
Type	Determinant () const
GlsMatrix< Type, DIM >	Inverse () const
void	Invert ()
GlsMatrix< Type, DIM >	Transposition () const
void	Transpose ()
bool	IsDiagonal () const
bool	IsIdentity () const
bool	IsScalar () const
bool	IsSingular () const
bool	IsSymmetric () const
bool	IsSkewSymmetric () const
bool	IsLowerTriangular () const
bool	IsUpperTriangular () const

Protected Member Functions
void	Initialize ()
int	Pivot (unsigned row)
bool	closeValues (Type lv, Type rv) const

Protected Attributes
Type	_data [DIM *DIM]
Type *	_matrix [DIM]

Static Protected Attributes
static const double	PRECISION = 1e-7

Detailed Description

template<class Type, int DIM = 4>
class disti::GlsMatrix< Type, DIM >

The GlsMatrix class provides support for an n x n square matrix of any numeric type. Most basic matrix operations are supported. Internally, the matrix terms are stored contiguously in column-major order so that the matrix data can be passed to OpenGL matrix operations. However, instances of this class can be treated as row-major matrices since the API performs the conversion to column-major ordering for the user.

Constructor & Destructor Documentation

GlsMatrix

(

)

Default constructor. The new matrix will be the identity matrix.

GlsMatrix

(

const CStyleMatrix

m

)

Constructor. This will transpose m so that the matrix is stored in column-major order, but a caller can pass one in that is in row-major order, which is more intuitive.

Parameters

m	a row-major, two-dimensional array to initialize the matrix with.

GlsMatrix

(

const Type *

m

)

Constructor.

Parameters

m	a column-major, one-dimensional array containing all values to initialize the matrix with.

GlsMatrix

(

const GlsMatrix< Type, DIM > &

m

)

Copy Constructor.

Parameters

m	matrix to copy.

~GlsMatrix ( )

virtual

Destructor.

Member Function Documentation

void Clear ( )

inline

Zero out the matrix so that all terms are equal to zero.

bool closeValues ( Type  lv, Type  rv  ) const

inlineprotected

Decides if the two values are close together determined by the constant PRECISION. The formula is lv - PRECISION < rv < lv + PRECISION

Parameters

lv	left value
rv	right value

Type* Data ( )

inline

Provides access to the raw column-major matrix data as a one dimensional array in a format suitable for Open GL matrix operations.

const Type* Data ( ) const

inline

Provides access to the raw column-major matrix data as a one dimensional array in a format suitable for Open GL matrix operations.

Type Determinant

(

)

const

Calculates the determinant of the matrix.

Returns

the calculated value of the determinant.

void Dump

(

)

const

Dump the contents of the matrix to standard output.

void Initialize ( )

inlineprotected

This should be called from all constructors, as it initializes the matrix column index so that matrix elements can be addressed in two dimensions, but a multiplication is not incurred when doing so.

GlsMatrix< Type, DIM > Inverse

(

)

const

Calculates the inverse of this matrix. The inverse of matrix A is B if AB = BA = I, where I is the identity matrix. The inverse of a matrix is the notion corresponding to the reciprocal of a nonzero real number.

Returns

the inverse of this matrix.

void Invert ( )

inline

Sets this matrix equal to its inverse.

bool IsDiagonal ( ) const

inline

Determines if this is a diagonal matrix. An n x n matrix A = [Aij] is called a diagonal matrix if Aij = 0 for i != j. Thus, for a diagonal matrix, the terms off the main diagonal are all zero.

Returns

true if the matrix is a diagonal matrix, false otherwise.

bool IsIdentity ( ) const

inline

Determines if this matrix is equal to the identity matrix. The identity matrix is I = [Aij], where Aii = 1 and Aij = 0 for i != j. Thus, for the identity matrix, the terms off the main diagonal are all zero, and the terms on the main diagonal are all one.

Returns

true if the matrix is the identity matrix, false otherwise.

bool IsLowerTriangular ( ) const

inline

Determines if this matrix is lower triangular. An n x n matrix A = [Aij] is lower triangular if Aij = 0 for i < j.

Returns

true if the matrix is lower triangular, false otherwise.

bool IsScalar ( ) const

inline

Determines if this is a scalar matrix. A scalar matrix is a diagonal matrix whose diagonal terms are equal.

Returns

true if the matrix is a scalar matrix, false otherwise.

bool IsSingular ( ) const

inline

Determines if this matrix is singular, or non-invertible. A singular matrix has no inverse.

Returns

true if the matrix is singular, false otherwise.

bool IsSkewSymmetric ( ) const

inline

Determines if this matrix is skew symmetric. A matrix is skew symmetric if its transpose is equal to its negative, i.e. -A = A'.

Returns

true if the matrix is skew symmetric, false otherwise.

bool IsSymmetric ( ) const

inline

Determines if this matrix is symmetric. A matrix is symmetric if it is equal to its transpose, i.e. A = A'.

Returns

true if the matrix is symmetric, false otherwise.

bool IsUpperTriangular ( ) const

inline

Determines if this matrix is upper triangular. An n x n matrix A = [Aij] is upper triangular if Aij = 0 for i > j.

Returns

true if the matrix is upper triangular, false otherwise.

void MakeIdentity ( )

inline

Set this matrix to the identity matrix. The identity matrix is I = [Aij], where Aii = 1 and Aij = 0 for i != j. Thus, for the identity matrix, the terms off the main diagonal are all zero, and the terms on the main diagonal are all one.

int Pivot ( unsigned  row )

protected

Pivoting is used in conjunction with Gauss-Jordan reduction to find the inverse of a matrix and in Gaussian Elimination to find the determinant of a matrix. It involves the elementary row operation of interchanging rows (or columns in our column-major matrix). Only the row passed in and rows below it are considered. The row passed in will be swapped with another row below it by selecting the desired pivot element. The pivot is the largest term (in magnitude) in the column equal to row for any of the considered rows. This will always put the largest (in magnitude) term from the column on the diagonal of the matrix.

Parameters

row	is the current row to pivot about. Rows above this are not considered during pivoting, as these rows should already be in their proper form.

void Transpose ( )

inline

Sets this matrix equal to its transpose.

GlsMatrix< Type, DIM > Transposition ( ) const

inline

Calculates the transpose of this matrix. The transpose of a matrix is obtained by interchanging its rows and columns.

Returns

the transpose of this matrix.

Member Data Documentation

Type _data[DIM *DIM]

protected

This is the actual matrix data stored in column-major ordering in a one-dimensional array of the appropriate size to store all matrix terms. The data is stored in this manner so that it can be passed to OpenGL matrix operations, which expect matrices to be ordered this way.

Type* _matrix[DIM]

protected

A column index array. Each element in this array "points" to a column of the matrix within the above data. By using this index, we can address matrix terms using two dimensions, column and row, without incurring a multiplication. Eg. matrix[0] points to a column within data, which is the address of the first term in the column. We can further address into the column and access a particular row by adding another dimension, eg. matrix[0][1]. The indices must be set up at construction time.

const double PRECISION = 1e-7

staticprotected

A very tiny number, close to zero. Used to compare floats

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

• gls_matrix.h