Vector and Matrix classes, and helpers. More...

Classes
struct	TooN::Matrix< Rows, Cols, Precision, Layout >
	A matrix. More...

class	TooN::DiagonalMatrix< Size, Precision, Base >
	A diagonal matrix. More...

class	TooN::Vector< Size, Precision, Base >
	A vector. More...

Functions
template<int R, int C, typename Precision , typename Base >
Precision	TooN::determinant_gaussian_elimination (const Matrix< R, C, Precision, Base > &A_)
	Compute the determinant using Gaussian elimination. More...

template<int R, int C, class P , class B >
P	TooN::determinant (const Matrix< R, C, P, B > &A)
	Compute the determinant of a matrix using an appropriate method. More...

template<int Size, class Precision , class Base >
void	TooN::Fill (Vector< Size, Precision, Base > &v, const Precision &p)

template<int Rows, int Cols, class Precision , class Base >
void	TooN::Fill (Matrix< Rows, Cols, Precision, Base > &m, const Precision &p)

template<int Size, class Precision , class Base >
Precision	TooN::norm (const Vector< Size, Precision, Base > &v)
	Compute the \(L_2\) norm of v. More...

template<int Size, class Precision , class Base >
Precision	TooN::norm_sq (const Vector< Size, Precision, Base > &v)
	Compute the \(L_2^2\) norm of v. More...

template<int Size, class Precision , class Base >
Precision	TooN::norm_1 (const Vector< Size, Precision, Base > &v)
	Compute the \(L_1\) norm of v. More...

template<int Size, class Precision , class Base >
Precision	TooN::norm_inf (const Vector< Size, Precision, Base > &v)
	Compute the \(L_\infty\) norm of v. More...

template<int Size, class Precision , class Base >
Precision	TooN::norm_2 (const Vector< Size, Precision, Base > &v)
	Compute the \(L_2\) norm of v. More...

template<int Size, class Precision , class Base >
Vector< Size, Precision >	TooN::unit (const Vector< Size, Precision, Base > &v)
	Compute a the unit vector \(\hat{v}\). More...

template<int Size, class Precision , class Base >
void	TooN::normalize (Vector< Size, Precision, Base > &&v)
	Normalize a vector in place. More...

template<int Size, typename Precision , typename Base >
Vector<(Size==Dynamic?Dynamic:Size-1)+0, Precision >	TooN::project (const Vector< Size, Precision, Base > &v)
	For a vector v of length i, return \([v_1, v_2, \cdots, v_{i-1}] / v_i \). More...

template<int Size, typename Precision , typename Base >
Vector<(Size==Dynamic?Dynamic:Size+1)+0, Precision >	TooN::unproject (const Vector< Size, Precision, Base > &v)
	For a vector v of length i, return \([v_1, v_2, \cdots, v_{i}, 1]\). More...

template<int R, int C, typename P , typename B >
P	TooN::norm_fro (const Matrix< R, C, P, B > &m)
	Frobenius (root of sum of squares) norm of input matrix m. More...

template<int R, int C, typename P , typename B >
P	TooN::norm_inf (const Matrix< R, C, P, B > &m)
	L_&#8734; (row sum) norm of input matrix m computes the maximum of the sums of absolute values over rows

template<int R, int C, typename P , typename B >
P	TooN::norm_1 (const Matrix< R, C, P, B > &m)
	L₁ (col sum) norm of input matrix m computes the maximum of the sums of absolute values over columns

template<int R, int C, typename P , typename B >
Matrix< R, C, P >	TooN::exp (const Matrix< R, C, P, B > &m)
	computes the matrix exponential of a matrix m by scaling m by 1/(powers of 2), using Taylor series and squaring again. More...

template<int R, int C, typename P , typename B >
Matrix< R, C, P >	TooN::sqrt (const Matrix< R, C, P, B > &m)
	computes a matrix square root of a matrix m by the product form of the Denman and Beavers iteration as given in Chen et al. More...

template<int R, int C, typename P , typename B >
Matrix< R, C, P >	TooN::log (const Matrix< R, C, P, B > &m)
	computes the matrix logarithm of a matrix m using the inverse scaling and squaring method. More...

template<int S, class P , class B >
bool	TooN::isfinite (const Vector< S, P, B > &v)
	Returns true if every element is finite.

template<int S, class P , class B >
bool	TooN::isnan (const Vector< S, P, B > &v)
	Returns true if any element is NaN.

template<int Rows, int Cols, typename Precision , typename Base >
void	TooN::Symmetrize (Matrix< Rows, Cols, Precision, Base > &m)
	Symmetrize a matrix. More...

template<int Rows, int Cols, typename Precision , typename Base >
Precision	TooN::trace (const Matrix< Rows, Cols, Precision, Base > &m)
	computes the trace of a square matrix

template<int Size, class P , class B >
TooN::Matrix< 3, 3, P >	TooN::cross_product_matrix (const Vector< Size, P, B > &vec)
	creates an returns a cross product matrix M from a 3 vector v, such that for all vectors w, the following holds: v ^ w = M * w More...

template<int R, int C, class Precision , class Base >
Internal::MatrixStartFill< R, C, Precision, Base >	TooN::Fill (Matrix< R, C, Precision, Base > &m)
	Set up a matrix for filling. More...

template<int Size, class Precision , class Base >
Internal::VectorStartFill< Size, Precision, Base >	TooN::Fill (Vector< Size, Precision, Base > &v)
	Set up a vector for filling. More...

template<int Rows, int Cols>
Matrix< Rows, Cols, double, Reference::RowMajor >	TooN::wrapMatrix (double *data)
	Wrap external data as a Matrix As usual, if template sizes are provided, then the run-time size is only used if the template size is not Dynamic.

template<int Rows, int Cols>
const Matrix< Rows, Cols, const double, Reference::RowMajor >	TooN::wrapMatrix (const double *data)

template<int Rows, int Cols, class Precision >
Matrix< Rows, Cols, Precision, Reference::RowMajor >	TooN::wrapMatrix (Precision *data)

template<int Rows, int Cols, class Precision >
const Matrix< Rows, Cols, const Precision, Reference::RowMajor >	TooN::wrapMatrix (const Precision *data)

template<int Rows, int Cols>
Matrix< Rows, Cols, double, Reference::RowMajor >	TooN::wrapMatrix (double *data, int rows, int cols)

template<int Rows, int Cols>
const Matrix< Rows, Cols, const double, Reference::RowMajor >	TooN::wrapMatrix (const double *data, int rows, int cols)

template<int Rows, int Cols, class Precision >
Matrix< Rows, Cols, Precision, Reference::RowMajor >	TooN::wrapMatrix (Precision *data, int rows, int cols)

template<int Rows, int Cols, class Precision >
const Matrix< Rows, Cols, const Precision, Reference::RowMajor >	TooN::wrapMatrix (const Precision *data, int rows, int cols)

template<class Precision >
Matrix< Dynamic, Dynamic, Precision, Reference::RowMajor >	TooN::wrapMatrix (Precision *data, int rows, int cols)

template<class Precision >
const Matrix< Dynamic, Dynamic, const Precision, Reference::RowMajor >	TooN::wrapMatrix (const Precision *data, int rows, int cols)

Detailed Description

Vector and Matrix classes, and helpers.

Function Documentation

◆ cross_product_matrix()

template<int Size, class P , class B >

TooN::Matrix<3, 3, P> TooN::cross_product_matrix ( const Vector< Size, P, B > & vec )

inline

creates an returns a cross product matrix M from a 3 vector v, such that for all vectors w, the following holds: v ^ w = M * w

Parameters

vec	the 3 vector input

Returns: the 3x3 matrix to set to the cross product matrix

◆ determinant()

template<int R, int C, class P , class B >

P TooN::determinant ( const Matrix< R, C, P, B > & A )

Compute the determinant of a matrix using an appropriate method.

The obvious method is used for 2x2, otherwise determinant_gaussian_elimination() or determinant_LU() is used depending on the value of TOON_DETERMINANT_LAPACK. See also Functions using LAPACK.

Parameters

A	The matrix to find the determinant of.

Returns: determinant.

◆ determinant_gaussian_elimination()

template<int R, int C, typename Precision , typename Base >

Precision TooN::determinant_gaussian_elimination ( const Matrix< R, C, Precision, Base > & A_ )

Compute the determinant using Gaussian elimination.

Parameters

A_	The matrix to find the determinant of.

Returns: determinant.

◆ exp()

template<int R, int C, typename P , typename B >

Matrix<R, C, P> TooN::exp ( const Matrix< R, C, P, B > & m )

inline

computes the matrix exponential of a matrix m by scaling m by 1/(powers of 2), using Taylor series and squaring again.

Parameters

m	input matrix, must be square

Returns: result matrix of the same size/type as input

◆ Fill() [1/4]

template<int Size, class Precision , class Base >

void TooN::Fill	(	Vector< Size, Precision, Base > &	v,
		const Precision &	p
	)

Deprecated:

◆ Fill() [2/4]

template<int Rows, int Cols, class Precision , class Base >

void TooN::Fill	(	Matrix< Rows, Cols, Precision, Base > &	m,
		const Precision &	p
	)

Deprecated:

◆ Fill() [3/4]

template<int R, int C, class Precision , class Base >

Internal::MatrixStartFill<R, C, Precision, Base> TooN::Fill ( Matrix< R, C, Precision, Base > & m )

Set up a matrix for filling.

Uses the following syntax:

Matrix<2,2> m;
Fill(m) = 1, 2,
          3, 4;

Overfill is detected at compile time if possible, underfill is detected at run-time. The checks can not be optimized out for dynamic matrices, so define TOON_NDEBUG_FILL to prevent the checks from being used.

Parameters

m	Matrix to fill

◆ Fill() [4/4]

template<int Size, class Precision , class Base >

Internal::VectorStartFill<Size, Precision, Base> TooN::Fill ( Vector< Size, Precision, Base > & v )

Set up a vector for filling.

Uses the following syntax:

Vector<2> v;

Fill(v) = 1, 2;

Overfill is detected at compile time if possible, underfill is detected at run-time. The checks can not be optimized out for dynamic vectors, so define TOON_NDEBUG_FILL to prevent the checks from being used.

Parameters

v	Vector to fill

◆ log()

template<int R, int C, typename P , typename B >

Matrix<R, C, P> TooN::log ( const Matrix< R, C, P, B > & m )

inline

computes the matrix logarithm of a matrix m using the inverse scaling and squaring method.

The overall approach is described in Chen et al. 'Approximating the logarithm of a matrix to specified accuracy', J. Matrix Anal Appl, 2001, but this implementation only uses a simple taylor series after the repeated square root operation.

Parameters

m	input matrix, must be square

Returns: the log of m of the same size/type as input

◆ norm()

template<int Size, class Precision , class Base >

Precision TooN::norm ( const Vector< Size, Precision, Base > & v )

inline

Compute the \(L_2\) norm of v.

Parameters

v v

◆ norm_1()

template<int Size, class Precision , class Base >

Precision TooN::norm_1 ( const Vector< Size, Precision, Base > & v )

inline

Compute the \(L_1\) norm of v.

Parameters

v v

◆ norm_2()

template<int Size, class Precision , class Base >

Precision TooN::norm_2 ( const Vector< Size, Precision, Base > & v )

inline

Compute the \(L_2\) norm of v.

Synonym for norm()

Parameters

v v

◆ norm_fro()

template<int R, int C, typename P , typename B >

P TooN::norm_fro ( const Matrix< R, C, P, B > & m )

inline

Frobenius (root of sum of squares) norm of input matrix m.

Parameters

m m

◆ norm_inf()

template<int Size, class Precision , class Base >

Precision TooN::norm_inf ( const Vector< Size, Precision, Base > & v )

inline

Compute the \(L_\infty\) norm of v.

Parameters

v v

◆ norm_sq()

template<int Size, class Precision , class Base >

Precision TooN::norm_sq ( const Vector< Size, Precision, Base > & v )

inline

Compute the \(L_2^2\) norm of v.

Parameters

v v

◆ normalize()

template<int Size, class Precision , class Base >

void TooN::normalize ( Vector< Size, Precision, Base > && v )

inline

Normalize a vector in place.

Parameters

v	Vector to normalize

◆ project()

template<int Size, typename Precision , typename Base >

Vector<(Size==Dynamic?Dynamic:Size-1)+0, Precision> TooN::project ( const Vector< Size, Precision, Base > & v )

inline

For a vector v of length i, return \([v_1, v_2, \cdots, v_{i-1}] / v_i \).

Parameters

v v

◆ sqrt()

template<int R, int C, typename P , typename B >

Matrix<R, C, P> TooN::sqrt ( const Matrix< R, C, P, B > & m )

inline

computes a matrix square root of a matrix m by the product form of the Denman and Beavers iteration as given in Chen et al.

'Approximating the logarithm of a matrix to specified accuracy', J. Matrix Anal Appl, 2001. This is used for the matrix logarithm function, but is useable by on its own.

Parameters

m	input matrix, must be square

Returns: a square root of m of the same size/type as input

◆ Symmetrize()

template<int Rows, int Cols, typename Precision , typename Base >

void TooN::Symmetrize ( Matrix< Rows, Cols, Precision, Base > & m )

Symmetrize a matrix.

Parameters

m m

Returns: \( \frac{m + m^{\mathsf T}}{2} \)

◆ unit()

template<int Size, class Precision , class Base >

Vector<Size, Precision> TooN::unit ( const Vector< Size, Precision, Base > & v )

inline

Compute a the unit vector \(\hat{v}\).

Parameters

v v

◆ unproject()

template<int Size, typename Precision , typename Base >

Vector<(Size==Dynamic?Dynamic:Size+1)+0, Precision> TooN::unproject ( const Vector< Size, Precision, Base > & v )

inline

For a vector v of length i, return \([v_1, v_2, \cdots, v_{i}, 1]\).

Parameters

v v

Classes

Functions

Detailed Description

Function Documentation

◆ cross_product_matrix()

◆ determinant()

◆ determinant_gaussian_elimination()

◆ exp()

◆ Fill() [1/4]

◆ Fill() [2/4]

◆ Fill() [3/4]

◆ Fill() [4/4]

◆ log()

◆ norm()

◆ norm_1()

◆ norm_2()

◆ norm_fro()

◆ norm_inf()

◆ norm_sq()

◆ normalize()

◆ project()

◆ sqrt()

◆ Symmetrize()

◆ unit()

◆ unproject()