Generic fixed-size dense matrix class using a row-major storage format. More...

#include <mitsuba/core/matrix.h>

Public Member Functions
	Matrix ()
	Construct a new MxN matrix without initializing it. More...

	Matrix (T value)
	Initialize the matrix with constant entries. More...

	Matrix (const T _m[M][N])
	Initialize the matrix from a given MxN array. More...

	Matrix (const T _m[M *N])
	Initialize the matrix from a given (flat) MxN array in row-major order. More...

	Matrix (Stream *stream)
	Unserialize a matrix from a stream. More...

	Matrix (const Matrix &mtx)
	Copy constructor. More...

void	setIdentity ()
	Initialize with the identity matrix. More...

void	setZero ()
	Initialize with zeroes. More...

T &	operator() (int i, int j)
	Indexing operator. More...

const T &	operator() (int i, int j) const
	Indexing operator (const verions) More...

bool	operator== (const Matrix &mat) const
	Equality operator. More...

bool	operator!= (const Matrix &mat) const
	Inequality operator. More...

Matrix &	operator= (const Matrix &mat)
	Assignment operator. More...

Matrix	operator+ (const Matrix &mat) const
	Matrix addition (returns a temporary) More...

Matrix	operator+ (T value) const
	Matrix-scalar addition (returns a temporary) More...

const Matrix &	operator+= (const Matrix &mat)
	Matrix addition. More...

const Matrix &	operator+= (T value)
	Matrix-scalar addition. More...

Matrix	operator- (const Matrix &mat) const
	Matrix subtraction (returns a temporary) More...

Matrix	operator- (T value) const
	Matrix-scalar subtraction (returns a temporary) More...

const Matrix &	operator-= (const Matrix &mat)
	Matrix subtraction. More...

const Matrix &	operator- (T value)
	Matrix-scalar subtraction. More...

const Matrix &	operator-= (T value)
	Matrix-scalar addition. More...

Matrix	operator- () const
	Component-wise negation. More...

Matrix	operator* (T value) const
	Scalar multiplication (creates a temporary) More...

const Matrix &	operator*= (T value)
	Scalar multiplication. More...

Matrix	operator/ (T value) const
	Scalar division (creates a temporary) More...

const Matrix &	operator/= (T value)
	Scalar division. More...

const Matrix &	operator*= (const Matrix &mat)
	Matrix multiplication (for square matrices) More...

Float	trace () const
	Compute the trace of a square matrix. More...

Float	frob () const
	Compute the Frobenius norm. More...

bool	lu (Matrix &LU, int piv[M], int &pivsign) const
	Compute the LU decomposition of a matrix. More...

bool	chol (Matrix &L) const

template<int K>
void	cholSolve (const Matrix< M, K, T > &B, Matrix< M, K, T > &X) const

template<int K>
void	luSolve (const Matrix< M, K, T > &B, Matrix< M, K, T > &X, int piv[M]) const

T	luDet (int pivsign) const
	Compute the determinant of a decomposed matrix created by lu() More...

T	cholDet () const
	Compute the determinant of a decomposed matrix created by chol() More...

bool	isZero () const
	Check if the matrix is identically zero. More...

bool	isIdentity () const
	Test if this is the identity matrix. More...

T	det () const
	Compute the determinant of a square matrix (internally creates a LU decomposition) More...

bool	invert (Matrix &target) const
	Compute the inverse of a square matrix using the Gauss-Jordan algorithm. More...

void	symEig (Matrix &Q, T d[M]) const
	Perform a symmetric eigendecomposition of a square matrix into Q and D. More...

void	transpose (Matrix< N, M, T > &target) const
	Compute the transpose of this matrix. More...

void	serialize (Stream *stream) const
	Serialize the matrix to a stream. More...

std::string	toString () const
	Return a string representation. More...

template<int K>
void	cholSolve (const Matrix< M, K, T > &B, Matrix< M, K, T > &X) const

template<int K>
void	luSolve (const Matrix< M, K, T > &B, Matrix< M, K, T > &X, int piv[M]) const

Public Attributes
T	m [M][N]

Static Protected Member Functions
static void	tred2 (T V[M][N], T d[N], T e[N])
	Symmetric Householder reduction to tridiagonal form. More...

static void	tql2 (T V[M][N], T d[N], T e[N])
	Symmetric tridiagonal QL algorithm. More...

Detailed Description

template<int M, int N, typename T>
struct mitsuba::Matrix< M, N, T >

Generic fixed-size dense matrix class using a row-major storage format.

Constructor & Destructor Documentation

template<int M, int N, typename T>

mitsuba::Matrix< M, N, T >::Matrix ( )

inline

Construct a new MxN matrix without initializing it.

This constructor is useful when the matrix will either not be used at all (it might be part of a larger data structure) or initialized at a later point in time. Always make sure that one of the two is the case! Otherwise your program will do computations involving uninitialized memory, which will probably lead to a difficult-to-find bug.

template<int M, int N, typename T>

mitsuba::Matrix< M, N, T >::Matrix ( T value )

inlineexplicit

Initialize the matrix with constant entries.

template<int M, int N, typename T>

mitsuba::Matrix< M, N, T >::Matrix ( const T _m[M][N] )

inlineexplicit

Initialize the matrix from a given MxN array.

template<int M, int N, typename T>

mitsuba::Matrix< M, N, T >::Matrix ( const T _m[M *N] )

inlineexplicit

Initialize the matrix from a given (flat) MxN array in row-major order.

template<int M, int N, typename T>

mitsuba::Matrix< M, N, T >::Matrix ( Stream * stream )

inlineexplicit

Unserialize a matrix from a stream.

template<int M, int N, typename T>

mitsuba::Matrix< M, N, T >::Matrix ( const Matrix< M, N, T > & mtx )

inline

Copy constructor.

Member Function Documentation

template<int M, int N, typename T>

MTS_NAMESPACE_BEGIN bool Matrix< M, N, T >::chol ( Matrix< M, N, T > & L ) const

Compute the Cholesky decomposition of a symmetric positive definite matrix

Parameters

L	Target matrix (a lower triangular matrix such that A=L*L')

Returns: false If the matrix is not symmetric positive definite. Based on the implementation in JAMA.

template<int M, int N, typename T>

T Matrix< M, N, T >::cholDet ( ) const

Compute the determinant of a decomposed matrix created by chol()

template<int M, int N, typename T>

template<int K>

void mitsuba::Matrix< M, N, T >::cholSolve	(	const Matrix< M, K, T > &	B,
		Matrix< M, K, T > &	X
	)		const

template<int M, int N, typename T>

template<int K>

void mitsuba::Matrix< M, N, T >::cholSolve	(	const Matrix< M, K, T > &	B,
		Matrix< M, K, T > &	X
	)		const

Solve A*X==B, where this is a Cholesky decomposition of A created by chol()

Parameters

B	A matrix with as many rows as A and any number of columns
X	A matrix such that LL'X == B

Based on the implementation in JAMA.

template<int M, int N, typename T>

T mitsuba::Matrix< M, N, T >::det ( ) const

inline

Compute the determinant of a square matrix (internally creates a LU decomposition)

template<int M, int N, typename T>

Float mitsuba::Matrix< M, N, T >::frob ( ) const

inline

Compute the Frobenius norm.

template<int M, int N, typename T>

bool Matrix< M, N, T >::invert ( Matrix< M, N, T > & target ) const

Compute the inverse of a square matrix using the Gauss-Jordan algorithm.

template<int M, int N, typename T>

bool mitsuba::Matrix< M, N, T >::isIdentity ( ) const

inline

Test if this is the identity matrix.

template<int M, int N, typename T>

bool mitsuba::Matrix< M, N, T >::isZero ( ) const

inline

Check if the matrix is identically zero.

template<int M, int N, typename T>

bool Matrix< M, N, T >::lu	(	Matrix< M, N, T > &	LU,
		int	piv[M],
		int &	pivsign
	)		const

Compute the LU decomposition of a matrix.

For an m-by-n matrix A with m >= n, the LU decomposition is an m-by-n unit lower triangular matrix L, an n-by-n upper triangular matrix U,

and a permutation vector piv of length m so that A(piv,:) = L*U. If m < n, then L is m-by-m and U is m-by-n.

The LU decomposition with pivoting always exists, even if the matrix is singular, so the constructor will never fail. The primary use of the

LU decomposition is in the solution of square systems of simultaneous linear equations.

Parameters

Target	matrix (the L and U parts will be stored together in a packed format)
piv	Storage for the permutation created by the pivoting
pivsign	Sign of the permutation

Returns: true if the matrix was nonsingular.

Based on the implementation in JAMA.

template<int M, int N, typename T>

T Matrix< M, N, T >::luDet ( int pivsign ) const

Compute the determinant of a decomposed matrix created by lu()

Parameters

pivsign The sign of the pivoting permutation returned by lu()

Based on the implementation in JAMA.

template<int M, int N, typename T>

template<int K>

void mitsuba::Matrix< M, N, T >::luSolve	(	const Matrix< M, K, T > &	B,
		Matrix< M, K, T > &	X,
		int	piv[M]
	)		const

template<int M, int N, typename T>

template<int K>

void mitsuba::Matrix< M, N, T >::luSolve	(	const Matrix< M, K, T > &	B,
		Matrix< M, K, T > &	X,
		int	piv[M]
	)		const

Solve A*X==B, where this is a LU decomposition of A created by lu()

Parameters

B	A matrix with as many rows as A and any number of columns
X	A matrix such that LUX == B(piv, :)
piv	Pivot vector returned by lu()

Based on the implementation in JAMA.

template<int M, int N, typename T>

bool mitsuba::Matrix< M, N, T >::operator!= ( const Matrix< M, N, T > & mat ) const

inline

Inequality operator.

template<int M, int N, typename T>

T& mitsuba::Matrix< M, N, T >::operator()	(	int	i,
		int	j
	)

inline

Indexing operator.

template<int M, int N, typename T>

const T& mitsuba::Matrix< M, N, T >::operator()	(	int	i,
		int	j
	)		const

inline

Indexing operator (const verions)

template<int M, int N, typename T>

Matrix mitsuba::Matrix< M, N, T >::operator* ( T value ) const

inline

Scalar multiplication (creates a temporary)

template<int M, int N, typename T>

const Matrix& mitsuba::Matrix< M, N, T >::operator*= ( T value )

inline

Scalar multiplication.

template<int M, int N, typename T>

const Matrix& mitsuba::Matrix< M, N, T >::operator*= ( const Matrix< M, N, T > & mat )

inline

Matrix multiplication (for square matrices)

template<int M, int N, typename T>

Matrix mitsuba::Matrix< M, N, T >::operator+ ( const Matrix< M, N, T > & mat ) const

inline

Matrix addition (returns a temporary)

template<int M, int N, typename T>

Matrix mitsuba::Matrix< M, N, T >::operator+ ( T value ) const

inline

Matrix-scalar addition (returns a temporary)

template<int M, int N, typename T>

const Matrix& mitsuba::Matrix< M, N, T >::operator+= ( const Matrix< M, N, T > & mat )

inline

Matrix addition.

template<int M, int N, typename T>

const Matrix& mitsuba::Matrix< M, N, T >::operator+= ( T value )

inline

Matrix-scalar addition.

template<int M, int N, typename T>

Matrix mitsuba::Matrix< M, N, T >::operator- ( const Matrix< M, N, T > & mat ) const

inline

Matrix subtraction (returns a temporary)

template<int M, int N, typename T>

Matrix mitsuba::Matrix< M, N, T >::operator- ( T value ) const

inline

Matrix-scalar subtraction (returns a temporary)

template<int M, int N, typename T>

const Matrix& mitsuba::Matrix< M, N, T >::operator- ( T value )

inline

Matrix-scalar subtraction.

template<int M, int N, typename T>

Matrix mitsuba::Matrix< M, N, T >::operator- ( ) const

inline

Component-wise negation.

template<int M, int N, typename T>

const Matrix& mitsuba::Matrix< M, N, T >::operator-= ( const Matrix< M, N, T > & mat )

inline

Matrix subtraction.

template<int M, int N, typename T>

const Matrix& mitsuba::Matrix< M, N, T >::operator-= ( T value )

inline

Matrix-scalar addition.

template<int M, int N, typename T>

Matrix mitsuba::Matrix< M, N, T >::operator/ ( T value ) const

inline

Scalar division (creates a temporary)

template<int M, int N, typename T>

const Matrix& mitsuba::Matrix< M, N, T >::operator/= ( T value )

inline

Scalar division.

template<int M, int N, typename T>

Matrix& mitsuba::Matrix< M, N, T >::operator= ( const Matrix< M, N, T > & mat )

inline

Assignment operator.

template<int M, int N, typename T>

bool mitsuba::Matrix< M, N, T >::operator== ( const Matrix< M, N, T > & mat ) const

inline

Equality operator.

template<int M, int N, typename T>

void mitsuba::Matrix< M, N, T >::serialize ( Stream * stream ) const

inline

Serialize the matrix to a stream.

template<int M, int N, typename T>

void mitsuba::Matrix< M, N, T >::setIdentity ( )

inline

Initialize with the identity matrix.

template<int M, int N, typename T>

void mitsuba::Matrix< M, N, T >::setZero ( )

inline

Initialize with zeroes.

template<int M, int N, typename T>

void mitsuba::Matrix< M, N, T >::symEig	(	Matrix< M, N, T > &	Q,
		T	d[M]
	)		const

inline

Perform a symmetric eigendecomposition of a square matrix into Q and D.

Based on the implementation in JAMA.

template<int M, int N, typename T>

std::string mitsuba::Matrix< M, N, T >::toString ( ) const

inline

Return a string representation.

template<int M, int N, typename T>

void Matrix< M, N, T >::tql2	(	T	V[M][N],
		T	d[N],
		T	e[N]
	)

staticprotected

Symmetric tridiagonal QL algorithm.

template<int M, int N, typename T>

Float mitsuba::Matrix< M, N, T >::trace ( ) const

inline

Compute the trace of a square matrix.

template<int M, int N, typename T>

void mitsuba::Matrix< M, N, T >::transpose ( Matrix< N, M, T > & target ) const

inline

Compute the transpose of this matrix.

template<int M, int N, typename T>

void Matrix< M, N, T >::tred2	(	T	V[M][N],
		T	d[N],
		T	e[N]
	)

staticprotected

Symmetric Householder reduction to tridiagonal form.

Member Data Documentation

template<int M, int N, typename T>

T mitsuba::Matrix< M, N, T >::m[M][N]

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

include/mitsuba/core/matrix.h
include/mitsuba/core/matrix.inl

Public Member Functions

Public Attributes

Static Protected Member Functions

Detailed Description

template<int M, int N, typename T> struct mitsuba::Matrix< M, N, T >

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<int M, int N, typename T>
struct mitsuba::Matrix< M, N, T >