Matrix

Classes
class	ug::MathMatrix< N, M, T >
	A class for fixed size, dense matrices. More...
class	ug::MathMatrix< 0, 0, T >
class	ug::MathMatrix< 0, N, T >
class	ug::MathMatrix< N, 0, T >
class	ug::MathSymmetricMatrix< N, T >
	A class for fixed size, dense matrices. More...

Typedefs
typedef std::size_t	ug::MathSymmetricMatrix< N, T >::size_type
typedef T	ug::MathSymmetricMatrix< N, T >::value_type

Functions
void	ug::MathSymmetricMatrix< N, T >::assign (const MathSymmetricMatrix &v)
value_type &	ug::MathSymmetricMatrix< N, T >::entry (std::size_t row, std::size_t col)
const value_type &	ug::MathSymmetricMatrix< N, T >::entry (std::size_t row, std::size_t col) const
value_type	ug::MathSymmetricMatrix< N, T >::fnorm ()
template<typename matrix_t >
void	ug::MatAdd (matrix_t &mOut, const matrix_t &m, typename matrix_t::value_type s)
	Add a scalar to a matrix (componentwise) More...
template<typename matrix_t >
void	ug::MatAdd (matrix_t &mOut, const matrix_t &m1, const matrix_t &m2)
	adds two matrices and stores the result in a third one More...
template<typename matrix_t >
matrix_t::value_type	ug::MatContraction (const matrix_t &m1, const matrix_t &m2)
template<typename matrix_t >
matrix_t::value_type	ug::MatDeviatorTrace (const matrix_t &m, matrix_t &dev)
template<typename matrix_t >
void	ug::MatDiagSet (matrix_t &mInOut, typename matrix_t::value_type s)
	Set diagonal entries of a matrix to a scalar (other entries are not changed) More...
template<typename matrix_t >
void	ug::MatDivide (matrix_t &mOut, const matrix_t &m, typename matrix_t::value_type s)
	Devide a matrix by a scalar (componentwise) More...
template<typename matrix_t >
matrix_t::value_type	ug::MatFrobeniusNorm (matrix_t &m)
template<typename matrix_t >
matrix_t::value_type	ug::MatFrobeniusNormSq (matrix_t &m)
template<typename matrix_t , typename vector_t >
void	ug::MatHouseholder (matrix_t &mOut, const vector_t &orthoVec)
	ug::MathSymmetricMatrix< N, T >::MathSymmetricMatrix ()
	ug::MathSymmetricMatrix< N, T >::MathSymmetricMatrix (const MathSymmetricMatrix &v)
template<typename matrix_t >
void	ug::MatIdentity (matrix_t &mOut)
	Fills the matrix with the identity matrix. More...
template<typename matrix_t >
matrix_t::value_type	ug::MatInftyNorm (matrix_t &m)
template<typename matrix_t >
matrix_t::value_type	ug::MatMaxNorm (matrix_t &m)
template<size_t N, size_t M, size_t L, typename T >
void	ug::MatMultiply (MathMatrix< N, M, T > &mOut, const MathMatrix< N, L, T > &m1, const MathMatrix< L, M, T > &m2)
	multiply two matrices and stores the result in a third one More...
template<size_t N, size_t M, size_t L, size_t P, typename T >
void	ug::MatMultiply (MathMatrix< N, M, T > &mOut, const MathMatrix< N, L, T > &m1, const MathMatrix< L, P, T > &m2, const MathMatrix< P, M, T > &m3)
	multiply three matrices and stores the result in a fourth one More...
template<typename matrix_t >
void	ug::MatMultiply (matrix_t &mOut, const matrix_t &m, typename matrix_t::value_type s)
	Multiply a matrix by a scalar (componentwise) More...
template<size_t N, size_t M, typename T >
void	ug::MatMultiplyMBMT (MathMatrix< N, N, T > &mOut, const MathMatrix< N, M, T > &m1, const MathMatrix< M, M, T > &m2)
template<size_t N, size_t M, size_t L, typename T >
void	ug::MatMultiplyMBT (MathMatrix< N, M, T > &mOut, const MathMatrix< N, L, T > &m1, const MathMatrix< M, L, T > &m2)
	multiply a matrix with the transposed of a second one and stores the result in mOut More...
template<size_t N, size_t M, typename T >
void	ug::MatMultiplyMMT (MathMatrix< M, M, T > &mOut, const MathMatrix< M, N, T > &m)
	multiply a matrix with its transposed and stores the result in a second one More...
template<size_t N, size_t M, size_t L, typename T >
void	ug::MatMultiplyMTB (MathMatrix< N, M, T > &mOut, const MathMatrix< L, N, T > &m1, const MathMatrix< L, M, T > &m2)
	multiply the transposed of a matrix with a matrix and stores the result in mOut More...
template<size_t N, size_t M, typename T >
void	ug::MatMultiplyMTBM (MathMatrix< N, N, T > &mOut, const MathMatrix< M, N, T > &m1, const MathMatrix< M, M, T > &m2)
template<size_t N, size_t M, typename T >
void	ug::MatMultiplyMTM (MathMatrix< N, N, T > &mOut, const MathMatrix< M, N, T > &m)
	multiply a transposed matrix with itself and stores the result in a second one More...
template<size_t N, size_t M, size_t L, typename T >
void	ug::MatMultiplyTransposed (MathMatrix< N, M, T > &mOut, const MathMatrix< L, N, T > &m1, const MathMatrix< M, L, T > &m2)
	multiply two transposed matrices and stores the result in a third one More...
template<typename matrix_t >
matrix_t::value_type	ug::MatOneNorm (matrix_t &m)
template<typename matrix_t >
void	ug::MatRotationX (matrix_t &mOut, typename matrix_t::value_type rads)
	Fills the matrix with a matrix that rotates around the x-axis in 3 dimensions. More...
template<typename matrix_t >
void	ug::MatRotationY (matrix_t &mOut, typename matrix_t::value_type rads)
	Fills the matrix with a matrix that rotates around the y-axis in 3 dimensions. More...
template<typename matrix_t >
void	ug::MatRotationYawPitchRoll (matrix_t &mOut, typename matrix_t::value_type yaw, typename matrix_t::value_type pitch, typename matrix_t::value_type roll)
	Creates a rotation matrix given yaw, pitch and roll in radiants. More...
template<typename matrix_t >
void	ug::MatRotationZ (matrix_t &mOut, typename matrix_t::value_type rads)
	Fills the matrix with a matrix that rotates around the y-axis in 2 or 3 dimensions. More...
template<typename matrix_t >
void	ug::MatScale (matrix_t &mOut, typename matrix_t::value_type s, const matrix_t &m)
	scales a matrix_t More...
template<typename matrix_t >
void	ug::MatScaleAppend (matrix_t &mOut, typename matrix_t::value_type s, const matrix_t &m)
	scales a matrix_t and adds to result to a second matrix More...
template<typename matrix_t >
void	ug::MatSet (matrix_t &mInOut, typename matrix_t::value_type s)
	Set each matrix entry to a scalar (componentwise) More...
template<typename matrix_t >
void	ug::MatSubtract (matrix_t &mOut, const matrix_t &m, typename matrix_t::value_type s)
	Subtract a scalar from a matrix (componentwise) More...
template<typename matrix_t >
void	ug::MatSubtract (matrix_t &mOut, const matrix_t &m1, const matrix_t &m2)
	subtracts m2 from m1 and stores the result in a mOut More...
template<size_t N, size_t M, typename T >
MathMatrix< N, M, T >::value_type	ug::MaxAbsEigenvalue (const MathMatrix< M, N, T > &m)
	Computes maximum eigenvalue of a (symmetric) matrix. More...
template<size_t N, size_t M, typename T >
MathMatrix< N, M, T >::value_type	ug::MinAbsEigenvalue (const MathMatrix< M, N, T > &m)
	Computes minimum eigenvalue of a (symmetric) matrix. More...
std::size_t	ug::MathSymmetricMatrix< N, T >::num_cols () const
std::size_t	ug::MathSymmetricMatrix< N, T >::num_rows () const
value_type &	ug::MathSymmetricMatrix< N, T >::operator() (std::size_t row, std::size_t col)
const value_type &	ug::MathSymmetricMatrix< N, T >::operator() (std::size_t row, std::size_t col) const
value_type	ug::MathSymmetricMatrix< N, T >::operator* (const MathSymmetricMatrix &v) const
	Multiplies the matrix element-wise with another matrix and sums up the entries. More...
MathSymmetricMatrix &	ug::MathSymmetricMatrix< N, T >::operator*= (const value_type &val)
	Multiplies all elements of the matrix with the given value. More...
MathSymmetricMatrix &	ug::MathSymmetricMatrix< N, T >::operator+= (const MathSymmetricMatrix &B)
	Adds a matrix to 'this' one: \( A_{this} \leftarrow A_{this} + B\). More...
MathSymmetricMatrix &	ug::MathSymmetricMatrix< N, T >::operator+= (const value_type &val)
	Adds the given value to all elements of the matrix. More...
MathSymmetricMatrix &	ug::MathSymmetricMatrix< N, T >::operator-= (const MathSymmetricMatrix &B)
	Subtracts a matrix from 'this' one: \( A_{this} \leftarrow A_{this} - B\). More...
MathSymmetricMatrix &	ug::MathSymmetricMatrix< N, T >::operator-= (const value_type &val)
	Subtracts the given value from all elements of the matrix. More...
MathSymmetricMatrix &	ug::MathSymmetricMatrix< N, T >::operator/= (const value_type &val)
	Divides all elements of the matrix by the given value. More...
std::ostream &	ug::operator<< (std::ostream &outStream, const ug::MathMatrix< 2, 2 > &m)
std::ostream &	ug::operator<< (std::ostream &outStream, const ug::MathMatrix< 2, 3 > &m)
std::ostream &	ug::operator<< (std::ostream &outStream, const ug::MathMatrix< 3, 2 > &m)
std::ostream &	ug::operator<< (std::ostream &outStream, const ug::MathMatrix< 3, 3 > &m)
template<std::size_t N, std::size_t M>
std::ostream &	ug::operator<< (std::ostream &outStream, const ug::MathMatrix< N, M > &m)
	Print MathMatrix<N,M> to standard output. More...
std::ostream &	ug::operator<< (std::ostream &outStream, const ug::MathSymmetricMatrix< 2 > &m)
std::ostream &	ug::operator<< (std::ostream &outStream, const ug::MathSymmetricMatrix< 3 > &m)
template<std::size_t N>
std::ostream &	ug::operator<< (std::ostream &outStream, const ug::MathSymmetricMatrix< N > &m)
	Print MathSymmetricMatrix<N> to standard output. More...
MathSymmetricMatrix &	ug::MathSymmetricMatrix< N, T >::operator= (const MathSymmetricMatrix &v)
	Assigns the elements of the given matrix to this one. More...
MathSymmetricMatrix &	ug::MathSymmetricMatrix< N, T >::operator= (const value_type &val)
	Assigns the given value to all elements of the matrix. More...
value_type &	ug::MathSymmetricMatrix< N, T >::operator[] (std::size_t index)
const value_type &	ug::MathSymmetricMatrix< N, T >::operator[] (std::size_t index) const
void	ug::MathSymmetricMatrix< N, T >::scale_by_fnorm ()
template<size_t N, size_t M, typename T >
void	ug::Transpose (MathMatrix< N, M, T > &mOut, const MathMatrix< M, N, T > &m)
	transpose a matrix More...
template<typename matrix_t >
void	ug::Transpose (matrix_t &m)
	transpose a matrix_t, override original matrix_t More...

Variables
static const std::size_t	ug::MathSymmetricMatrix< N, T >::ColSize = N
value_type	ug::MathSymmetricMatrix< N, T >::m_data [m_size]
static const size_t	ug::MathSymmetricMatrix< N, T >::m_size = (size_t)((N*N+N)/2)
static const std::size_t	ug::MathSymmetricMatrix< N, T >::RowSize = N
template<size_t N, typename T >
MathMatrix< N, N, T >::value_type	ug::Determinant (const MathMatrix< N, N, T > &m)
	Determinant of a matrix. More...
template<typename T >
MathMatrix< 1, 1, T >::value_type	ug::Determinant (const MathMatrix< 1, 1, T > &m)
	Determinant of a matrix. More...
template<typename T >
MathMatrix< 2, 2, T >::value_type	ug::Determinant (const MathMatrix< 2, 2, T > &m)
	Determinant of a matrix. More...
template<typename T >
MathMatrix< 3, 3, T >::value_type	ug::Determinant (const MathMatrix< 3, 3, T > &m)
	Determinant of a matrix. More...
template<size_t N, size_t M, typename T >
MathMatrix< N, M, T >::value_type	ug::GramDeterminant (const MathMatrix< N, M, T > &m)
	Gram Determinant of a matrix. More...
template<typename T >
MathMatrix< 1, 1, T >::value_type	ug::GramDeterminant (const MathMatrix< 1, 1, T > &m)
	Gram Determinant of a matrix. More...
template<typename T >
MathMatrix< 2, 2, T >::value_type	ug::GramDeterminant (const MathMatrix< 2, 2, T > &m)
	Gram Determinant of a matrix. More...
template<typename T >
MathMatrix< 3, 3, T >::value_type	ug::GramDeterminant (const MathMatrix< 3, 3, T > &m)
	Gram Determinant of a matrix. More...
template<size_t N, size_t M, typename T >
MathMatrix< N, M, T >::value_type	ug::SqrtGramDeterminant (const MathMatrix< N, M, T > &m)
	Square root of Gram Determinant of a matrix. More...
template<typename T >
MathMatrix< 1, 1, T >::value_type	ug::SqrtGramDeterminant (const MathMatrix< 1, 1, T > &m)
	Square root of Gram Determinant of a matrix. More...
template<typename T >
MathMatrix< 2, 2, T >::value_type	ug::SqrtGramDeterminant (const MathMatrix< 2, 2, T > &m)
	Square root of Gram Determinant of a matrix. More...
template<typename T >
MathMatrix< 3, 3, T >::value_type	ug::SqrtGramDeterminant (const MathMatrix< 3, 3, T > &m)
	Square root of Gram Determinant of a matrix. More...
template<size_t N, size_t M, typename T >
MathMatrix< N, M, T >::value_type	ug::Inverse (MathMatrix< N, M, T > &mOut, const MathMatrix< M, N, T > &m)
	Inverse of a matrix. More...
template<typename T >
MathMatrix< 1, 1, T >::value_type	ug::Inverse (MathMatrix< 1, 1, T > &mOut, const MathMatrix< 1, 1, T > &m)
	Inverse of a matrix. More...
template<typename T >
MathMatrix< 2, 2, T >::value_type	ug::Inverse (MathMatrix< 2, 2, T > &mOut, const MathMatrix< 2, 2, T > &m)
	Inverse of a matrix. More...
template<typename T >
MathMatrix< 3, 3, T >::value_type	ug::Inverse (MathMatrix< 3, 3, T > &mOut, const MathMatrix< 3, 3, T > &m)
	Inverse of a matrix. More...
template<size_t N, size_t M, typename T >
MathMatrix< N, M, T >::value_type	ug::InverseTransposed (MathMatrix< N, M, T > &mOut, const MathMatrix< M, N, T > &m)
	Transposed-Inverse of a Matrix (= Inverse-Transposed of a Matrix) More...
template<typename T >
MathMatrix< 1, 1, T >::value_type	ug::InverseTransposed (MathMatrix< 1, 1, T > &mOut, const MathMatrix< 1, 1, T > &m)
	Transposed-Inverse of a Matrix (= Inverse-Transposed of a Matrix) More...
template<typename T >
MathMatrix< 2, 2, T >::value_type	ug::InverseTransposed (MathMatrix< 2, 2, T > &mOut, const MathMatrix< 2, 2, T > &m)
	Transposed-Inverse of a Matrix (= Inverse-Transposed of a Matrix) More...
template<typename T >
MathMatrix< 3, 3, T >::value_type	ug::InverseTransposed (MathMatrix< 3, 3, T > &mOut, const MathMatrix< 3, 3, T > &m)
	Transposed-Inverse of a Matrix (= Inverse-Transposed of a Matrix) More...
template<size_t N, size_t M, typename T >
MathMatrix< N, M, T >::value_type	ug::RightInverse (MathMatrix< N, M, T > &mOut, const MathMatrix< M, N, T > &m)
	Right-Inverse of a Matrix. More...
template<typename T >
MathMatrix< 1, 1, T >::value_type	ug::RightInverse (MathMatrix< 1, 1 > &mOut, const MathMatrix< 1, 1 > &m)
	Right-Inverse of a Matrix. More...
template<typename T >
MathMatrix< 2, 2, T >::value_type	ug::RightInverse (MathMatrix< 2, 2 > &mOut, const MathMatrix< 2, 2 > &m)
	Right-Inverse of a Matrix. More...
template<typename T >
MathMatrix< 3, 3, T >::value_type	ug::RightInverse (MathMatrix< 3, 3 > &mOut, const MathMatrix< 3, 3 > &m)
	Right-Inverse of a Matrix. More...
template<size_t N, size_t M, typename T >
MathMatrix< N, M, T >::value_type	ug::LeftInverse (MathMatrix< N, M, T > &mOut, const MathMatrix< M, N, T > &m)
	Left-Inverse of a Matrix. More...
template<typename T >
MathMatrix< 1, 1, T >::value_type	ug::LeftInverse (MathMatrix< 1, 1 > &mOut, const MathMatrix< 1, 1 > &m)
	Left-Inverse of a Matrix. More...
template<typename T >
MathMatrix< 2, 2, T >::value_type	ug::LeftInverse (MathMatrix< 2, 2 > &mOut, const MathMatrix< 2, 2 > &m)
	Left-Inverse of a Matrix. More...
template<typename T >
MathMatrix< 3, 3, T >::value_type	ug::LeftInverse (MathMatrix< 3, 3 > &mOut, const MathMatrix< 3, 3 > &m)
	Left-Inverse of a Matrix. More...
template<typename T >
MathMatrix< 1, 1, T >::value_type	ug::Trace (const MathMatrix< 1, 1, T > &m)
	Trace of a Matrix. More...
template<typename T >
MathMatrix< 2, 2, T >::value_type	ug::Trace (const MathMatrix< 2, 2, T > &m)
	Trace of a Matrix. More...
template<typename T >
MathMatrix< 3, 3, T >::value_type	ug::Trace (const MathMatrix< 3, 3, T > &m)
	Trace of a Matrix. More...

Detailed Description

Typedef Documentation

size_type

template<std::size_t N, typename T = number>

typedef std::size_t ug::MathSymmetricMatrix< N, T >::size_type

value_type

template<std::size_t N, typename T = number>

typedef T ug::MathSymmetricMatrix< N, T >::value_type

Function Documentation

assign()

template<std::size_t N, typename T = number>

void ug::MathSymmetricMatrix< N, T >::assign ( const MathSymmetricMatrix< N, T > &  v )

inlineprotected

References ug::MathSymmetricMatrix< N, T >::m_data, and ug::MathSymmetricMatrix< N, T >::m_size.

Referenced by ug::MathSymmetricMatrix< N, T >::MathSymmetricMatrix(), and ug::MathSymmetricMatrix< N, T >::operator=().

Determinant() [1/4]

template<typename T >

MathMatrix< 1, 1, T >::value_type ug::Determinant ( const MathMatrix< 1, 1, T > &  m )

inline

Determinant of a matrix.

Returns the Determinate of a matrix.

Parameters

m

Matrix

Returns

determinant of matrix

Determinant() [2/4]

template<typename T >

MathMatrix< 2, 2, T >::value_type ug::Determinant ( const MathMatrix< 2, 2, T > &  m )

inline

Determinant of a matrix.

Returns the Determinate of a matrix.

Parameters

m

Matrix

Returns

determinant of matrix

Determinant() [3/4]

template<typename T >

MathMatrix< 3, 3, T >::value_type ug::Determinant ( const MathMatrix< 3, 3, T > &  m )

inline

Determinant of a matrix.

Returns the Determinate of a matrix.

Parameters

m

Matrix

Returns

determinant of matrix

Determinant() [4/4]

template<size_t N, typename T >

MathMatrix< N, N, T >::value_type ug::Determinant ( const MathMatrix< N, N, T > &  m )

inline

Determinant of a matrix.

Returns the Determinate of a matrix.

Parameters

m

Matrix

Returns

determinant of matrix

References UG_THROW.

Referenced by ug::GramDeterminant(), ug::Inverse(), ug::InverseTransposed(), ug::RayRayIntersection2d(), and ug::SqrtGramDeterminant().

entry() [1/2]

template<std::size_t N, typename T = number>

value_type& ug::MathSymmetricMatrix< N, T >::entry ( std::size_t  row, std::size_t  col  )

inline

References ug::MathSymmetricMatrix< N, T >::m_data, and UG_ASSERT.

Referenced by ug::MathSymmetricMatrix< N, T >::operator*(), and ug::operator<<().

entry() [2/2]

template<std::size_t N, typename T = number>

const value_type& ug::MathSymmetricMatrix< N, T >::entry ( std::size_t  row, std::size_t  col  ) const

inline

References ug::MathSymmetricMatrix< N, T >::m_data, and UG_ASSERT.

fnorm()

template<std::size_t N, typename T = number>

value_type ug::MathSymmetricMatrix< N, T >::fnorm ( )

inline

References ug::MathSymmetricMatrix< N, T >::m_data, and ug::MathSymmetricMatrix< N, T >::m_size.

Referenced by ug::MathSymmetricMatrix< N, T >::scale_by_fnorm().

GramDeterminant() [1/4]

template<typename T >

MathMatrix< 1, 1, T >::value_type ug::GramDeterminant ( const MathMatrix< 1, 1, T > &  m )

inline

Gram Determinant of a matrix.

Returns Gram Determinant of a matrix, i.e. \( \det(M M^T) \).

Parameters

m

Matrix

Returns

gram determinant of matrix

References ug::Determinant().

GramDeterminant() [2/4]

template<typename T >

MathMatrix< 2, 2, T >::value_type ug::GramDeterminant ( const MathMatrix< 2, 2, T > &  m )

inline

Gram Determinant of a matrix.

Returns Gram Determinant of a matrix, i.e. \( \det(M M^T) \).

Parameters

m

Matrix

Returns

gram determinant of matrix

References ug::Determinant().

GramDeterminant() [3/4]

template<typename T >

MathMatrix< 3, 3, T >::value_type ug::GramDeterminant ( const MathMatrix< 3, 3, T > &  m )

inline

Gram Determinant of a matrix.

Returns Gram Determinant of a matrix, i.e. \( \det(M M^T) \).

Parameters

m

Matrix

Returns

gram determinant of matrix

References ug::Determinant().

GramDeterminant() [4/4]

template<size_t N, size_t M, typename T >

MathMatrix< N, M, T >::value_type ug::GramDeterminant ( const MathMatrix< N, M, T > &  m )

inline

Gram Determinant of a matrix.

Returns Gram Determinant of a matrix, i.e. \( \det(M M^T) \).

Parameters

m

Matrix

Returns

gram determinant of matrix

References ug::Determinant(), ug::MatMultiplyMMT(), and ug::MatMultiplyMTM().

Referenced by ug::SqrtGramDeterminant().

Inverse() [1/4]

template<typename T >

MathMatrix< 1, 1, T >::value_type ug::Inverse ( MathMatrix< 1, 1, T > &  mOut, const MathMatrix< 1, 1, T > &  m  )

inline

Inverse of a matrix.

Computes the inverse of a matrix and returns the determinante.

Parameters

mOut	Inverse of Matrix
m	Matrix

Returns

Determinate of Matrix

References UG_ASSERT.

Inverse() [2/4]

template<typename T >

MathMatrix< 2, 2, T >::value_type ug::Inverse ( MathMatrix< 2, 2, T > &  mOut, const MathMatrix< 2, 2, T > &  m  )

inline

Inverse of a matrix.

Computes the inverse of a matrix and returns the determinante.

Parameters

mOut	Inverse of Matrix
m	Matrix

Returns

Determinate of Matrix

References ug::Determinant(), and UG_ASSERT.

Inverse() [3/4]

template<typename T >

MathMatrix< 3, 3, T >::value_type ug::Inverse ( MathMatrix< 3, 3, T > &  mOut, const MathMatrix< 3, 3, T > &  m  )

inline

Inverse of a matrix.

Computes the inverse of a matrix and returns the determinante.

Parameters

mOut	Inverse of Matrix
m	Matrix

Returns

Determinate of Matrix

References ug::Determinant(), and UG_ASSERT.

Inverse() [4/4]

template<size_t N, size_t M, typename T >

MathMatrix< N, M, T >::value_type ug::Inverse ( MathMatrix< N, M, T > &  mOut, const MathMatrix< M, N, T > &  m  )

inline

Inverse of a matrix.

Computes the inverse of a matrix and returns the determinante.

Parameters

mOut	Inverse of Matrix
m	Matrix

Returns

Determinate of Matrix

References UG_THROW.

Referenced by ug::GradientDataExport< dim >::eval_and_deriv(), ug::ExplicitGridFunctionGradient< TGridFunction >::evaluate(), ug::H1SemiDistIntegrand< TGridFunction >::evaluate(), ug::H1EnergyDistIntegrand< TGridFunction >::evaluate(), ug::H1ErrorIntegrand< TGridFunction >::evaluate(), ug::H1SemiIntegrand< TGridFunction >::evaluate(), ug::H1EnergyIntegrand< TGridFunction >::evaluate(), ug::IntegralNormalComponentOnManifoldUsingFV1Geom(), ug::InverseTransposed(), ug::LeftInverse(), ug::MinAbsEigenvalue(), ug::RayRayIntersection2d(), and ug::RightInverse().

InverseTransposed() [1/4]

template<typename T >

MathMatrix< 1, 1, T >::value_type ug::InverseTransposed ( MathMatrix< 1, 1, T > &  mOut, const MathMatrix< 1, 1, T > &  m  )

inline

Transposed-Inverse of a Matrix (= Inverse-Transposed of a Matrix)

Computes the Inverse-Transposed of a Matrix and returns the Determinant.

Parameters

mOut	Inverse-Transposed of Matrix
m	Matrix

Returns

Determinant of Matrix

References ug::Inverse().

InverseTransposed() [2/4]

template<typename T >

MathMatrix< 2, 2, T >::value_type ug::InverseTransposed ( MathMatrix< 2, 2, T > &  mOut, const MathMatrix< 2, 2, T > &  m  )

inline

Transposed-Inverse of a Matrix (= Inverse-Transposed of a Matrix)

Computes the Inverse-Transposed of a Matrix and returns the Determinant.

Parameters

mOut	Inverse-Transposed of Matrix
m	Matrix

Returns

Determinant of Matrix

References ug::Determinant(), and UG_ASSERT.

InverseTransposed() [3/4]

template<typename T >

MathMatrix< 3, 3, T >::value_type ug::InverseTransposed ( MathMatrix< 3, 3, T > &  mOut, const MathMatrix< 3, 3, T > &  m  )

inline

Transposed-Inverse of a Matrix (= Inverse-Transposed of a Matrix)

Computes the Inverse-Transposed of a Matrix and returns the Determinant.

Parameters

mOut	Inverse-Transposed of Matrix
m	Matrix

Returns

Determinant of Matrix

References ug::Determinant(), and UG_ASSERT.

InverseTransposed() [4/4]

template<size_t N, size_t M, typename T >

MathMatrix< N, M, T >::value_type ug::InverseTransposed ( MathMatrix< N, M, T > &  mOut, const MathMatrix< M, N, T > &  m  )

inline

Transposed-Inverse of a Matrix (= Inverse-Transposed of a Matrix)

Computes the Inverse-Transposed of a Matrix and returns the Determinant.

Parameters

mOut	Inverse-Transposed of Matrix
m	Matrix

Returns

Determinant of Matrix

References UG_THROW.

LeftInverse() [1/4]

template<typename T >

MathMatrix< 1, 1, T >::value_type ug::LeftInverse ( MathMatrix< 1, 1 > &  mOut, const MathMatrix< 1, 1 > &  m  )

inline

Left-Inverse of a Matrix.

Computes the Left-Inverse of a Matrix and returns the square root of the gram determinate. For any \( A \in \mathbb{R}^{M \times N} \) (with \( M \geq N \)) the Left-Inverse is defined as

\[ A^{-1}_{left} := (A^T A)^{-1} A^T, \]

such that \( A^{-1}_{left} A = 1 \). The gram determinate is defined as \( \det{A^T A} \).

Please note, that in case of a square matrix (i.e. \( N = M \)), the Left- Inverse is identical to the Inverse and the square root of the gram determinante simplifies to the norm of the usual determinate.

Parameters

mOut	Left-Inverse of Matrix
m	Matrix

Returns

Square root of gram determinate of Matrix

References ug::Inverse().

LeftInverse() [2/4]

template<typename T >

MathMatrix< 2, 2, T >::value_type ug::LeftInverse ( MathMatrix< 2, 2 > &  mOut, const MathMatrix< 2, 2 > &  m  )

inline

Left-Inverse of a Matrix.

Computes the Left-Inverse of a Matrix and returns the square root of the gram determinate. For any \( A \in \mathbb{R}^{M \times N} \) (with \( M \geq N \)) the Left-Inverse is defined as

\[ A^{-1}_{left} := (A^T A)^{-1} A^T, \]

such that \( A^{-1}_{left} A = 1 \). The gram determinate is defined as \( \det{A^T A} \).

Please note, that in case of a square matrix (i.e. \( N = M \)), the Left- Inverse is identical to the Inverse and the square root of the gram determinante simplifies to the norm of the usual determinate.

Parameters

mOut	Left-Inverse of Matrix
m	Matrix

Returns

Square root of gram determinate of Matrix

References ug::Inverse().

LeftInverse() [3/4]

template<typename T >

MathMatrix< 3, 3, T >::value_type ug::LeftInverse ( MathMatrix< 3, 3 > &  mOut, const MathMatrix< 3, 3 > &  m  )

inline

Left-Inverse of a Matrix.

Computes the Left-Inverse of a Matrix and returns the square root of the gram determinate. For any \( A \in \mathbb{R}^{M \times N} \) (with \( M \geq N \)) the Left-Inverse is defined as

\[ A^{-1}_{left} := (A^T A)^{-1} A^T, \]

such that \( A^{-1}_{left} A = 1 \). The gram determinate is defined as \( \det{A^T A} \).

Please note, that in case of a square matrix (i.e. \( N = M \)), the Left- Inverse is identical to the Inverse and the square root of the gram determinante simplifies to the norm of the usual determinate.

Parameters

mOut	Left-Inverse of Matrix
m	Matrix

Returns

Square root of gram determinate of Matrix

References ug::Inverse().

LeftInverse() [4/4]

template<size_t N, size_t M, typename T >

MathMatrix< N, M, T >::value_type ug::LeftInverse ( MathMatrix< N, M, T > &  mOut, const MathMatrix< M, N, T > &  m  )

inline

Left-Inverse of a Matrix.

Computes the Left-Inverse of a Matrix and returns the square root of the gram determinate. For any \( A \in \mathbb{R}^{M \times N} \) (with \( M \geq N \)) the Left-Inverse is defined as

\[ A^{-1}_{left} := (A^T A)^{-1} A^T, \]

such that \( A^{-1}_{left} A = 1 \). The gram determinate is defined as \( \det{A^T A} \).

Please note, that in case of a square matrix (i.e. \( N = M \)), the Left- Inverse is identical to the Inverse and the square root of the gram determinante simplifies to the norm of the usual determinate.

Parameters

mOut	Left-Inverse of Matrix
m	Matrix

Returns

Square root of gram determinate of Matrix

References ug::Inverse(), ug::MatMultiplyMTM(), ug::MatMultiplyTransposed(), and UG_THROW.

Referenced by ug::BaseReferenceMapping< dim, worldDim, isLinear, TImpl >::global_to_local().

MatAdd() [1/2]

template<typename matrix_t >

void ug::MatAdd ( matrix_t &  mOut, const matrix_t &  m, typename matrix_t::value_type  s  )

inline

Add a scalar to a matrix (componentwise)

References s.

MatAdd() [2/2]

template<typename matrix_t >

void ug::MatAdd ( matrix_t &  mOut, const matrix_t &  m1, const matrix_t &  m2  )

inline

adds two matrices and stores the result in a third one

Referenced by ug::MatAdd().

MatContraction()

template<typename matrix_t >

matrix_t::value_type ug::MatContraction ( const matrix_t &  m1, const matrix_t &  m2  )

inline

MatDeviatorTrace()

template<typename matrix_t >

matrix_t::value_type ug::MatDeviatorTrace ( const matrix_t &  m, matrix_t &  dev  )

inline

References ug::Trace().

MatDiagSet()

template<typename matrix_t >

void ug::MatDiagSet ( matrix_t &  mInOut, typename matrix_t::value_type  s  )

inline

Set diagonal entries of a matrix to a scalar (other entries are not changed)

References s.

Referenced by ug::MatIdentity().

MatDivide()

template<typename matrix_t >

void ug::MatDivide ( matrix_t &  mOut, const matrix_t &  m, typename matrix_t::value_type  s  )

inline

Devide a matrix by a scalar (componentwise)

References s.

MatFrobeniusNorm()

template<typename matrix_t >

matrix_t::value_type ug::MatFrobeniusNorm ( matrix_t &  m )

inline

References ug::MatFrobeniusNormSq().

MatFrobeniusNormSq()

template<typename matrix_t >

matrix_t::value_type ug::MatFrobeniusNormSq ( matrix_t &  m )

inline

Referenced by ug::MatFrobeniusNorm().

MatHouseholder()

template<typename matrix_t , typename vector_t >

void ug::MatHouseholder ( matrix_t &  mOut, const vector_t &  orthoVec  )

inline

Creates a householder matrix given the orthogonal vector to the householder-hypersphere through the origin.

References ug::VecDot().

Referenced by ug::ObstacleInNormalDir< TDomain, TAlgebra >::transform_eulerian_coord_sys().

MathSymmetricMatrix() [1/2]

template<std::size_t N, typename T = number>

ug::MathSymmetricMatrix< N, T >::MathSymmetricMatrix ( )

inline

MathSymmetricMatrix() [2/2]

template<std::size_t N, typename T = number>

ug::MathSymmetricMatrix< N, T >::MathSymmetricMatrix ( const MathSymmetricMatrix< N, T > &  v )

inline

References ug::MathSymmetricMatrix< N, T >::assign().

MatIdentity()

template<typename matrix_t >

void ug::MatIdentity ( matrix_t &  mOut )

inline

Fills the matrix with the identity matrix.

References ug::MatDiagSet(), and ug::MatSet().

Referenced by ug::MatRotationX(), ug::MatRotationY(), and ug::MatRotationZ().

MatInftyNorm()

template<typename matrix_t >

matrix_t::value_type ug::MatInftyNorm ( matrix_t &  m )

inline

MatMaxNorm()

template<typename matrix_t >

matrix_t::value_type ug::MatMaxNorm ( matrix_t &  m )

inline

MatMultiply() [1/3]

template<size_t N, size_t M, size_t L, typename T >

void ug::MatMultiply ( MathMatrix< N, M, T > &  mOut, const MathMatrix< N, L, T > &  m1, const MathMatrix< L, M, T > &  m2  )

inline

multiply two matrices and stores the result in a third one

Referenced by ug::MatRotationYawPitchRoll().

MatMultiply() [2/3]

template<size_t N, size_t M, size_t L, size_t P, typename T >

void ug::MatMultiply ( MathMatrix< N, M, T > &  mOut, const MathMatrix< N, L, T > &  m1, const MathMatrix< L, P, T > &  m2, const MathMatrix< P, M, T > &  m3  )

inline

multiply three matrices and stores the result in a fourth one

MatMultiply() [3/3]

template<typename matrix_t >

void ug::MatMultiply ( matrix_t &  mOut, const matrix_t &  m, typename matrix_t::value_type  s  )

inline

Multiply a matrix by a scalar (componentwise)

References s.

MatMultiplyMBMT()

template<size_t N, size_t M, typename T >

void ug::MatMultiplyMBMT ( MathMatrix< N, N, T > &  mOut, const MathMatrix< N, M, T > &  m1, const MathMatrix< M, M, T > &  m2  )

inline

multiply a matrix m2 with a matrix m1 from left and its transpose m1^T from right and stores the result in mOut

MatMultiplyMBT()

template<size_t N, size_t M, size_t L, typename T >

void ug::MatMultiplyMBT ( MathMatrix< N, M, T > &  mOut, const MathMatrix< N, L, T > &  m1, const MathMatrix< M, L, T > &  m2  )

inline

multiply a matrix with the transposed of a second one and stores the result in mOut

MatMultiplyMMT()

template<size_t N, size_t M, typename T >

void ug::MatMultiplyMMT ( MathMatrix< M, M, T > &  mOut, const MathMatrix< M, N, T > &  m  )

inline

multiply a matrix with its transposed and stores the result in a second one

Referenced by ug::GramDeterminant(), and ug::RightInverse().

MatMultiplyMTB()

template<size_t N, size_t M, size_t L, typename T >

void ug::MatMultiplyMTB ( MathMatrix< N, M, T > &  mOut, const MathMatrix< L, N, T > &  m1, const MathMatrix< L, M, T > &  m2  )

inline

multiply the transposed of a matrix with a matrix and stores the result in mOut

MatMultiplyMTBM()

template<size_t N, size_t M, typename T >

void ug::MatMultiplyMTBM ( MathMatrix< N, N, T > &  mOut, const MathMatrix< M, N, T > &  m1, const MathMatrix< M, M, T > &  m2  )

inline

multiply a matrix m2 with a matrix m1 from right and its transpose m1^T from left and stores the result in mOut

MatMultiplyMTM()

template<size_t N, size_t M, typename T >

void ug::MatMultiplyMTM ( MathMatrix< N, N, T > &  mOut, const MathMatrix< M, N, T > &  m  )

inline

multiply a transposed matrix with itself and stores the result in a second one

Referenced by ug::GramDeterminant(), and ug::LeftInverse().

MatMultiplyTransposed()

template<size_t N, size_t M, size_t L, typename T >

void ug::MatMultiplyTransposed ( MathMatrix< N, M, T > &  mOut, const MathMatrix< L, N, T > &  m1, const MathMatrix< M, L, T > &  m2  )

inline

multiply two transposed matrices and stores the result in a third one

Referenced by ug::LeftInverse(), and ug::RightInverse().

MatOneNorm()

template<typename matrix_t >

matrix_t::value_type ug::MatOneNorm ( matrix_t &  m )

inline

MatRotationX()

template<typename matrix_t >

void ug::MatRotationX ( matrix_t &  mOut, typename matrix_t::value_type  rads  )

inline

Fills the matrix with a matrix that rotates around the x-axis in 3 dimensions.

matrix_t has to have at least 3 rows and 3 columns. Rotation is specified in radiants.

References ug::MatIdentity(), and s.

Referenced by ug::MatRotationYawPitchRoll().

MatRotationY()

template<typename matrix_t >

void ug::MatRotationY ( matrix_t &  mOut, typename matrix_t::value_type  rads  )

inline

Fills the matrix with a matrix that rotates around the y-axis in 3 dimensions.

matrix_t has to have at least 3 rows and 3 columns. Rotation is specified in radiants.

References ug::MatIdentity(), and s.

Referenced by ug::MatRotationYawPitchRoll().

MatRotationYawPitchRoll()

template<typename matrix_t >

void ug::MatRotationYawPitchRoll ( matrix_t &  mOut, typename matrix_t::value_type  yaw, typename matrix_t::value_type  pitch, typename matrix_t::value_type  roll  )

inline

Creates a rotation matrix given yaw, pitch and roll in radiants.

References ug::MatMultiply(), ug::MatRotationX(), ug::MatRotationY(), and ug::MatRotationZ().

MatRotationZ()

template<typename matrix_t >

void ug::MatRotationZ ( matrix_t &  mOut, typename matrix_t::value_type  rads  )

inline

Fills the matrix with a matrix that rotates around the y-axis in 2 or 3 dimensions.

matrix_t has to have at least 2 rows and 2 columns. Rotation is specified in radiants.

References ug::MatIdentity(), and s.

Referenced by ug::MatRotationYawPitchRoll().

MatScale()

template<typename matrix_t >

void ug::MatScale ( matrix_t &  mOut, typename matrix_t::value_type  s, const matrix_t &  m  )

inline

scales a matrix_t

References s.

Referenced by ug::DarcyVelocityLinker< dim >::eval_and_deriv().

MatScaleAppend()

template<typename matrix_t >

void ug::MatScaleAppend ( matrix_t &  mOut, typename matrix_t::value_type  s, const matrix_t &  m  )

inline

scales a matrix_t and adds to result to a second matrix

References s.

Referenced by ug::linker_traits< MathMatrix< dim, dim >, number >::mult_add(), and ug::LocalMatrix::scale_append().

MatSet()

template<typename matrix_t >

void ug::MatSet ( matrix_t &  mInOut, typename matrix_t::value_type  s  )

inline

Set each matrix entry to a scalar (componentwise)

References s.

Referenced by ug::MatIdentity(), and ug::ConvectionShapesPartialUpwind< TDim >::update().

MatSubtract() [1/2]

template<typename matrix_t >

void ug::MatSubtract ( matrix_t &  mOut, const matrix_t &  m, typename matrix_t::value_type  s  )

inline

Subtract a scalar from a matrix (componentwise)

References s.

MatSubtract() [2/2]

template<typename matrix_t >

void ug::MatSubtract ( matrix_t &  mOut, const matrix_t &  m1, const matrix_t &  m2  )

inline

subtracts m2 from m1 and stores the result in a mOut

MaxAbsEigenvalue()

template<size_t N, size_t M, typename T >

MathMatrix< N, M, T >::value_type ug::MaxAbsEigenvalue ( const MathMatrix< M, N, T > &  m )

inline

Computes maximum eigenvalue of a (symmetric) matrix.

References UG_THROW.

Referenced by ug::MinAbsEigenvalue().

MinAbsEigenvalue()

template<size_t N, size_t M, typename T >

MathMatrix<N,M,T>::value_type ug::MinAbsEigenvalue ( const MathMatrix< M, N, T > &  m )

inline

Computes minimum eigenvalue of a (symmetric) matrix.

num_cols()

template<std::size_t N, typename T = number>

std::size_t ug::MathSymmetricMatrix< N, T >::num_cols ( ) const

inline

num_rows()

template<std::size_t N, typename T = number>

std::size_t ug::MathSymmetricMatrix< N, T >::num_rows ( ) const

inline

operator()() [1/2]

template<std::size_t N, typename T = number>

value_type& ug::MathSymmetricMatrix< N, T >::operator() ( std::size_t  row, std::size_t  col  )

inline

References ug::MathSymmetricMatrix< N, T >::m_data, and UG_ASSERT.

operator()() [2/2]

template<std::size_t N, typename T = number>

const value_type& ug::MathSymmetricMatrix< N, T >::operator() ( std::size_t  row, std::size_t  col  ) const

inline

References ug::MathSymmetricMatrix< N, T >::m_data, and UG_ASSERT.

operator*()

template<std::size_t N, typename T = number>

value_type ug::MathSymmetricMatrix< N, T >::operator* ( const MathSymmetricMatrix< N, T > &  v ) const

inline

Multiplies the matrix element-wise with another matrix and sums up the entries.

Parameters

v	The Matrix.

Returns

A scalar value of the element-wise summed up products

References ug::MathSymmetricMatrix< N, T >::entry().

operator*=()

template<std::size_t N, typename T = number>

MathSymmetricMatrix& ug::MathSymmetricMatrix< N, T >::operator*= ( const value_type &  val )

inline

Multiplies all elements of the matrix with the given value.

Parameters

val	The factor.

Returns

A reference to this matrix.

References ug::MathSymmetricMatrix< N, T >::m_data, and ug::MathSymmetricMatrix< N, T >::m_size.

operator+=() [1/2]

template<std::size_t N, typename T = number>

MathSymmetricMatrix& ug::MathSymmetricMatrix< N, T >::operator+= ( const MathSymmetricMatrix< N, T > &  B )

inline

Adds a matrix to 'this' one: \( A_{this} \leftarrow A_{this} + B\).

Parameters

B	The matrix to be added.

Returns

A reference to this matrix.

References ug::MathSymmetricMatrix< N, T >::m_data, and ug::MathSymmetricMatrix< N, T >::m_size.

operator+=() [2/2]

template<std::size_t N, typename T = number>

MathSymmetricMatrix& ug::MathSymmetricMatrix< N, T >::operator+= ( const value_type &  val )

inline

Adds the given value to all elements of the matrix.

Parameters

val	The value to be added.

Returns

A reference to this matrix.

References ug::MathSymmetricMatrix< N, T >::m_data, and ug::MathSymmetricMatrix< N, T >::m_size.

operator-=() [1/2]

template<std::size_t N, typename T = number>

MathSymmetricMatrix& ug::MathSymmetricMatrix< N, T >::operator-= ( const MathSymmetricMatrix< N, T > &  B )

inline

Subtracts a matrix from 'this' one: \( A_{this} \leftarrow A_{this} - B\).

Parameters

B	The matrix to be subtracted.

Returns

A reference to this matrix.

References ug::MathSymmetricMatrix< N, T >::m_data, and ug::MathSymmetricMatrix< N, T >::m_size.

operator-=() [2/2]

template<std::size_t N, typename T = number>

MathSymmetricMatrix& ug::MathSymmetricMatrix< N, T >::operator-= ( const value_type &  val )

inline

Subtracts the given value from all elements of the matrix.

Parameters

val	The value to be subtracted.

Returns

A reference to this matrix.

References ug::MathSymmetricMatrix< N, T >::m_data, and ug::MathSymmetricMatrix< N, T >::m_size.

operator/=()

template<std::size_t N, typename T = number>

MathSymmetricMatrix& ug::MathSymmetricMatrix< N, T >::operator/= ( const value_type &  val )

inline

Divides all elements of the matrix by the given value.

Parameters

val	The divisor.

Returns

A reference to this matrix.

References ug::MathSymmetricMatrix< N, T >::m_data, and ug::MathSymmetricMatrix< N, T >::m_size.

operator<<() [1/8]

std::ostream & ug::operator<<	(	std::ostream &	outStream,
		const ug::MathMatrix< 2, 2 > &	m
	)

References ug::MathMatrix< N, M, T >::entry().

operator<<() [2/8]

std::ostream & ug::operator<<	(	std::ostream &	outStream,
		const ug::MathMatrix< 2, 3 > &	m
	)

References ug::MathMatrix< N, M, T >::entry().

operator<<() [3/8]

std::ostream & ug::operator<<	(	std::ostream &	outStream,
		const ug::MathMatrix< 3, 2 > &	m
	)

References ug::MathMatrix< N, M, T >::entry().

operator<<() [4/8]

std::ostream & ug::operator<<	(	std::ostream &	outStream,
		const ug::MathMatrix< 3, 3 > &	m
	)

References ug::MathMatrix< N, M, T >::entry().

operator<<() [5/8]

template<std::size_t N, std::size_t M>

std::ostream& ug::operator<<	(	std::ostream &	outStream,
		const ug::MathMatrix< N, M > &	m
	)

Print MathMatrix<N,M> to standard output.

References ug::MathMatrix< N, M, T >::entry().

operator<<() [6/8]

std::ostream& ug::operator<<	(	std::ostream &	outStream,
		const ug::MathSymmetricMatrix< 2 > &	m
	)

operator<<() [7/8]

std::ostream& ug::operator<<	(	std::ostream &	outStream,
		const ug::MathSymmetricMatrix< 3 > &	m
	)

operator<<() [8/8]

template<std::size_t N>

std::ostream& ug::operator<<	(	std::ostream &	outStream,
		const ug::MathSymmetricMatrix< N > &	m
	)

Print MathSymmetricMatrix<N> to standard output.

References ug::MathSymmetricMatrix< N, T >::entry().

operator=() [1/2]

template<std::size_t N, typename T = number>

MathSymmetricMatrix& ug::MathSymmetricMatrix< N, T >::operator= ( const MathSymmetricMatrix< N, T > &  v )

inline

Assigns the elements of the given matrix to this one.

Parameters

v	The matrix to be assigned.

Returns

A reference to this matrix.

References ug::MathSymmetricMatrix< N, T >::assign().

operator=() [2/2]

template<std::size_t N, typename T = number>

MathSymmetricMatrix& ug::MathSymmetricMatrix< N, T >::operator= ( const value_type &  val )

inline

Assigns the given value to all elements of the matrix.

Parameters

val	The value to be assigned to the matrix.

Returns

A reference to this matrix.

References ug::MathSymmetricMatrix< N, T >::m_data, and ug::MathSymmetricMatrix< N, T >::m_size.

operator[]() [1/2]

template<std::size_t N, typename T = number>

value_type& ug::MathSymmetricMatrix< N, T >::operator[] ( std::size_t  index )

inline

References ug::MathSymmetricMatrix< N, T >::m_data, ug::MathSymmetricMatrix< N, T >::m_size, and UG_ASSERT.

operator[]() [2/2]

template<std::size_t N, typename T = number>

const value_type& ug::MathSymmetricMatrix< N, T >::operator[] ( std::size_t  index ) const

inline

References ug::MathSymmetricMatrix< N, T >::m_data, ug::MathSymmetricMatrix< N, T >::m_size, and UG_ASSERT.

RightInverse() [1/4]

template<typename T >

MathMatrix< 1, 1, T >::value_type ug::RightInverse ( MathMatrix< 1, 1 > &  mOut, const MathMatrix< 1, 1 > &  m  )

inline

Right-Inverse of a Matrix.

Computes the Right-Inverse of a Matrix and returns the square root of the gram determinate. For any \( A \in \mathbb{R}^{M \times N} \) (with \( M \leq N \)) the Right-Inverse is defined as

\[ A^{-1}_{right} := A^T (A A^T)^{-1}, \]

such that \( A A^{-1}_{right} = 1 \). The gram determinate is defined as \( \det{A A^T} \).

Please note, that in case of a square matrix (i.e. \( N = M \)), the Right- Inverse is identical to the Inverse and the square root of the gram determinante simplifies to the norm of the usual determinate.

Parameters

mOut	Right-Inverse of Matrix
m	Matrix

Returns

Square root of gram determinate of Matrix

References ug::Inverse().

RightInverse() [2/4]

template<typename T >

MathMatrix< 2, 2, T >::value_type ug::RightInverse ( MathMatrix< 2, 2 > &  mOut, const MathMatrix< 2, 2 > &  m  )

inline

Right-Inverse of a Matrix.

Computes the Right-Inverse of a Matrix and returns the square root of the gram determinate. For any \( A \in \mathbb{R}^{M \times N} \) (with \( M \leq N \)) the Right-Inverse is defined as

\[ A^{-1}_{right} := A^T (A A^T)^{-1}, \]

such that \( A A^{-1}_{right} = 1 \). The gram determinate is defined as \( \det{A A^T} \).

Please note, that in case of a square matrix (i.e. \( N = M \)), the Right- Inverse is identical to the Inverse and the square root of the gram determinante simplifies to the norm of the usual determinate.

Parameters

mOut	Right-Inverse of Matrix
m	Matrix

Returns

Square root of gram determinate of Matrix

References ug::Inverse().

RightInverse() [3/4]

template<typename T >

MathMatrix< 3, 3, T >::value_type ug::RightInverse ( MathMatrix< 3, 3 > &  mOut, const MathMatrix< 3, 3 > &  m  )

inline

Right-Inverse of a Matrix.

Computes the Right-Inverse of a Matrix and returns the square root of the gram determinate. For any \( A \in \mathbb{R}^{M \times N} \) (with \( M \leq N \)) the Right-Inverse is defined as

\[ A^{-1}_{right} := A^T (A A^T)^{-1}, \]

such that \( A A^{-1}_{right} = 1 \). The gram determinate is defined as \( \det{A A^T} \).

Please note, that in case of a square matrix (i.e. \( N = M \)), the Right- Inverse is identical to the Inverse and the square root of the gram determinante simplifies to the norm of the usual determinate.

Parameters

mOut	Right-Inverse of Matrix
m	Matrix

Returns

Square root of gram determinate of Matrix

References ug::Inverse().

RightInverse() [4/4]

template<size_t N, size_t M, typename T >

MathMatrix< N, M, T >::value_type ug::RightInverse ( MathMatrix< N, M, T > &  mOut, const MathMatrix< M, N, T > &  m  )

inline

Right-Inverse of a Matrix.

Computes the Right-Inverse of a Matrix and returns the square root of the gram determinate. For any \( A \in \mathbb{R}^{M \times N} \) (with \( M \leq N \)) the Right-Inverse is defined as

\[ A^{-1}_{right} := A^T (A A^T)^{-1}, \]

such that \( A A^{-1}_{right} = 1 \). The gram determinate is defined as \( \det{A A^T} \).

Please note, that in case of a square matrix (i.e. \( N = M \)), the Right- Inverse is identical to the Inverse and the square root of the gram determinante simplifies to the norm of the usual determinate.

Parameters

mOut	Right-Inverse of Matrix
m	Matrix

Returns

Square root of gram determinate of Matrix

References ug::Inverse(), ug::MatMultiplyMMT(), ug::MatMultiplyTransposed(), and UG_THROW.

Referenced by ug::GridFunctionGradientData< TGridFunction >::eval_and_deriv(), ug::GridFunctionGradientComponentData< TGridFunction >::eval_and_deriv(), ug::GlobalGridFunctionGradientData< TGridFunction >::evaluate(), ug::H1DistIntegrand< TGridFunction >::evaluate(), ug::H1NormIntegrand< TGridFunction >::evaluate(), and ug::BaseReferenceMapping< dim, worldDim, isLinear, TImpl >::jacobian_transposed_inverse().

scale_by_fnorm()

template<std::size_t N, typename T = number>

void ug::MathSymmetricMatrix< N, T >::scale_by_fnorm ( )

inline

References ug::MathSymmetricMatrix< N, T >::fnorm(), ug::MathSymmetricMatrix< N, T >::m_data, and ug::MathSymmetricMatrix< N, T >::m_size.

SqrtGramDeterminant() [1/4]

template<typename T >

MathMatrix< 1, 1, T >::value_type ug::SqrtGramDeterminant ( const MathMatrix< 1, 1, T > &  m )

inline

Square root of Gram Determinant of a matrix.

Returns Square root of Gram Determinant of a matrix, i.e. \( \sqrt{\det(M M^T)} \).

Parameters

m

Matrix

Returns

square root of gram determinant of matrix

References ug::Determinant().

SqrtGramDeterminant() [2/4]

template<typename T >

MathMatrix< 2, 2, T >::value_type ug::SqrtGramDeterminant ( const MathMatrix< 2, 2, T > &  m )

inline

Square root of Gram Determinant of a matrix.

Returns Square root of Gram Determinant of a matrix, i.e. \( \sqrt{\det(M M^T)} \).

Parameters

m

Matrix

Returns

square root of gram determinant of matrix

References ug::Determinant().

SqrtGramDeterminant() [3/4]

template<typename T >

MathMatrix< 3, 3, T >::value_type ug::SqrtGramDeterminant ( const MathMatrix< 3, 3, T > &  m )

inline

Square root of Gram Determinant of a matrix.

Returns Square root of Gram Determinant of a matrix, i.e. \( \sqrt{\det(M M^T)} \).

Parameters

m

Matrix

Returns

square root of gram determinant of matrix

References ug::Determinant().

SqrtGramDeterminant() [4/4]

template<size_t N, size_t M, typename T >

MathMatrix< N, M, T >::value_type ug::SqrtGramDeterminant ( const MathMatrix< N, M, T > &  m )

inline

Square root of Gram Determinant of a matrix.

Returns Square root of Gram Determinant of a matrix, i.e. \( \sqrt{\det(M M^T)} \).

Parameters

m

Matrix

Returns

square root of gram determinant of matrix

References ug::GramDeterminant().

Referenced by ug::IntegralNormalComponentOnManifoldGeneral(), ug::Integrate(), and ug::BaseReferenceMapping< dim, worldDim, isLinear, TImpl >::sqrt_gram_det().

Trace() [1/3]

template<typename T >

MathMatrix< 1, 1, T >::value_type ug::Trace ( const MathMatrix< 1, 1, T > &  m )

inline

Trace of a Matrix.

Returns the Trace of a Matrix.

Referenced by ug::MatDeviatorTrace().

Trace() [2/3]

template<typename T >

MathMatrix< 2, 2, T >::value_type ug::Trace ( const MathMatrix< 2, 2, T > &  m )

inline

Trace of a Matrix.

Returns the Trace of a Matrix.

Trace() [3/3]

template<typename T >

MathMatrix< 3, 3, T >::value_type ug::Trace ( const MathMatrix< 3, 3, T > &  m )

inline

Trace of a Matrix.

Returns the Trace of a Matrix.

Transpose() [1/2]

template<size_t N, size_t M, typename T >

void ug::Transpose ( MathMatrix< N, M, T > &  mOut, const MathMatrix< M, N, T > &  m  )

inline

transpose a matrix

References ug::MathMatrix< N, M, T >::num_cols(), and ug::MathMatrix< N, M, T >::num_rows().

Referenced by ug::BaseReferenceMapping< dim, worldDim, isLinear, TImpl >::jacobian().

Transpose() [2/2]

template<typename matrix_t >

void ug::Transpose ( matrix_t &  m )

inline

transpose a matrix_t, override original matrix_t

References UG_ASSERT.

Variable Documentation

ColSize

template<std::size_t N, typename T = number>

const std::size_t ug::MathSymmetricMatrix< N, T >::ColSize = N

static

m_data

template<std::size_t N, typename T = number>

value_type ug::MathSymmetricMatrix< N, T >::m_data[m_size]

protected

Referenced by ug::MathSymmetricMatrix< N, T >::assign(), ug::MathSymmetricMatrix< N, T >::entry(), ug::MathSymmetricMatrix< N, T >::fnorm(), ug::MathSymmetricMatrix< N, T >::operator()(), ug::MathSymmetricMatrix< N, T >::operator*=(), ug::MathSymmetricMatrix< N, T >::operator+=(), ug::MathSymmetricMatrix< N, T >::operator-=(), ug::MathSymmetricMatrix< N, T >::operator/=(), ug::MathSymmetricMatrix< N, T >::operator=(), ug::MathSymmetricMatrix< N, T >::operator[](), and ug::MathSymmetricMatrix< N, T >::scale_by_fnorm().

m_size

template<std::size_t N, typename T = number>

const size_t ug::MathSymmetricMatrix< N, T >::m_size = (size_t)((N*N+N)/2)

staticprotected

Referenced by ug::MathSymmetricMatrix< N, T >::assign(), ug::MathSymmetricMatrix< N, T >::fnorm(), ug::MathSymmetricMatrix< N, T >::operator*=(), ug::MathSymmetricMatrix< N, T >::operator+=(), ug::MathSymmetricMatrix< N, T >::operator-=(), ug::MathSymmetricMatrix< N, T >::operator/=(), ug::MathSymmetricMatrix< N, T >::operator=(), ug::MathSymmetricMatrix< N, T >::operator[](), and ug::MathSymmetricMatrix< N, T >::scale_by_fnorm().

RowSize

template<std::size_t N, typename T = number>

const std::size_t ug::MathSymmetricMatrix< N, T >::RowSize = N

static