Tiny Matrix class template. More...

#include <tiny_algebra.hpp>

Public Types
typedef Intern::DataTypeExtractor< ValueType >::MyDataType	DataType
	The basic data type buried in the lowest level of the vector. More...

typedef Vector< T_, n_, sn_ >	RowType
	the type of a single matrix row More...

typedef T_	ValueType
	the data type of the matrix More...

Public Member Functions
CUDA_HOST_DEVICE	Matrix ()
	default constructor More...

template<typename T2_ , int sma_, int sna_>
CUDA_HOST_DEVICE	Matrix (const Matrix< T2_, m_, n_, sma_, sna_ > &a)
	copy constructor More...

template<typename Tx_ >
CUDA_HOST_DEVICE	Matrix (const std::initializer_list< std::initializer_list< Tx_ > > &x)
	Initializer list constructor. More...

template<typename Tx_ >
CUDA_HOST_DEVICE	Matrix (const std::initializer_list< Tx_ > &x)
	Initializer list of Tiny::Vector constructor. More...

CUDA_HOST_DEVICE	Matrix (DataType value)
	value-assignment constructor More...

template<int k_, int l_, int sma_, int sna_, int smb_, int snb_, int smd_, int snd_>
CUDA_HOST_DEVICE Matrix &	add_double_mat_mult (const Matrix< T_, k_, l_, sma_, sna_ > &a, const Matrix< T_, k_, m_, smb_, snb_ > &b, const Matrix< T_, l_, n_, smd_, snd_ > &d, DataType alpha=DataType(1))
	Adds the algebraic matrix double-product of three other matrices onto this matrix. More...

template<int la_, int lb_, int sma_, int sna_, int smb_, int snb_>
CUDA_HOST_DEVICE Matrix &	add_mat_mat_mult (const Matrix< T_, m_, la_, sma_, sna_ > &a, const Matrix< T_, lb_, n_, smb_, snb_ > &b, DataType alpha=DataType(1))
	Adds the algebraic matrix-product of two other matrices onto this matrix. More...

template<int snx_, int sny_>
CUDA_HOST_DEVICE Matrix &	add_outer_product (const Vector< T_, m_, snx_ > &x, const Vector< T_, n_, sny_ > &y, const DataType alpha=DataType(1))
	Adds the outer product of two vectors onto the matrix. More...

CUDA_HOST_DEVICE Matrix &	add_scalar_main_diag (DataType alpha)
	Adds a value onto the matrix's main diagonal. More...

template<int l_, int snv_, int slt_, int smt_, int snt_>
CUDA_HOST_DEVICE Matrix &	add_vec_tensor_mult (const Vector< T_, l_, snv_ > &x, const Tensor3< T_, l_, m_, n_, slt_, smt_, snt_ > &t, DataType alpha=DataType(1))
	Adds the result of a vector-tensor left-product onto this matrix. More...

template<int sma_, int sna_>
CUDA_HOST_DEVICE Matrix &	axpy (DataType alpha, const Matrix< T_, m_, n_, sma_, sna_ > &a)
	Adds another scaled matrix onto this matrix. More...

template<typename Tx_ , int sma_, int sna_>
CUDA_HOST_DEVICE void	convert (const Matrix< Tx_, m_, n_, sma_, sna_ > &a)
	conversion operator More...

template<int sma_, int sna_>
CUDA_HOST_DEVICE void	copy (const Matrix< T_, m_, n_, sma_, sna_ > &a)
	Copies a matrix. More...

template<int mm_, int nn_, int ma_, int na_, int sma_, int sna_>
CUDA_HOST_DEVICE void	copy_n (const Matrix< T_, ma_, na_, sma_, sna_ > &a)
	Copies the upper left mm_ x nn_ entries of a matrix. More...

CUDA_HOST_DEVICE DataType	det () const
	Returns the determinant of the matrix. More...

CUDA_HOST_DEVICE void	format (DataType alpha=DataType(0))
	Formats the matrix. More...

CUDA_HOST_DEVICE DataType	norm_frobenius () const
	Returns the Frobenius norm of the matrix. More...

CUDA_HOST_DEVICE DataType	norm_frobenius_sqr () const
	Returns the Frobenius norm squared of the matrix. More...

CUDA_HOST_DEVICE DataType	norm_hessian_sqr () const
	Returns the Hessian norm square. More...

CUDA_HOST_DEVICE DataType	norm_sub_id_frobenius () const
	Returns the Frobenius norm of the difference of this matrix and the identity matrix. More...

CUDA_HOST_DEVICE T_ &	operator() (int i, int j)
	Access operator. More...

CUDA_HOST_DEVICE const T_ &	operator() (int i, int j) const
	Access operator. More...

CUDA_HOST_DEVICE Matrix &	operator*= (DataType alpha)
	scalar-right-multiply-by operator More...

template<int sma_, int sna_>
CUDA_HOST_DEVICE Matrix &	operator+= (const Matrix< T_, m_, n_, sma_, sna_ > &a)
	matrix component-wise addition operator More...

template<int sma_, int sna_>
CUDA_HOST_DEVICE Matrix &	operator-= (const Matrix< T_, m_, n_, sma_, sna_ > &a)
	matrix component-wise subtraction operator More...

template<int sma_, int sna_>
CUDA_HOST_DEVICE Matrix &	operator= (const Matrix< T_, m_, n_, sma_, sna_ > &a)
	assignment operator More...

template<typename Tx_ >
CUDA_HOST_DEVICE Matrix &	operator= (const std::initializer_list< std::initializer_list< Tx_ > > &x)
	Initializer list assignment operator. More...

template<typename Tx_ >
CUDA_HOST_DEVICE Matrix &	operator= (const std::initializer_list< Tx_ > &x)
	Initializer list assignment operator. More...

CUDA_HOST_DEVICE Matrix &	operator= (DataType value)
	value-assignment operator More...

CUDA_HOST_DEVICE RowType &	operator[] (int i)
	Row-Access operator. More...

CUDA_HOST_DEVICE const RowType &	operator[] (int i) const
	Row-Access operator. More...

template<int snx_, int sny_>
CUDA_HOST_DEVICE DataType	scalar_product (const Vector< T_, m_, snx_ > &x, const Vector< T_, n_, sny_ > &y) const
	Computes the scalar product of two vectors with this matrix. More...

template<int sma_, int sna_>
CUDA_HOST_DEVICE Matrix &	set_cofactor (const Matrix< T_, m_, n_, sma_, sna_ > &a)
	Sets this matrix to the cofactor matrix of another matrix. More...

template<int k_, int l_, int sma_, int sna_, int smb_, int snb_, int smd_, int snd_>
CUDA_HOST_DEVICE Matrix &	set_double_mat_mult (const Matrix< T_, k_, l_, sma_, sna_ > &a, const Matrix< T_, k_, m_, smb_, snb_ > &b, const Matrix< T_, l_, n_, smd_, snd_ > &d, T_ alpha=T_(1))
	Sets this matrix to the algebraic matrix double-product of three other matrices. More...

template<int l_, int sla_, int sna_>
CUDA_HOST_DEVICE Matrix &	set_gram (const Matrix< T_, l_, n_, sla_, sna_ > &a)
	Sets this matrix to the Gram matrix of another matrix. More...

CUDA_HOST_DEVICE Matrix &	set_identity ()
	Sets this matrix to the identity matrix. More...

template<int sma_, int sna_>
CUDA_HOST_DEVICE Matrix &	set_inverse (const Matrix< T_, m_, n_, sma_, sna_ > &a)
	Sets this matrix to the inverse of another matrix. More...

template<int la_, int lb_, int sma_, int sna_, int smb_, int snb_>
CUDA_HOST_DEVICE Matrix &	set_mat_mat_mult (const Matrix< T_, m_, la_, sma_, sna_ > &a, const Matrix< T_, lb_, n_, smb_, snb_ > &b)
	Sets this matrix to the algebraic matrix-product of two other matrices. More...

template<int snx_, int sny_>
CUDA_HOST_DEVICE Matrix &	set_outer_product (const Vector< T_, m_, snx_ > &x, const Vector< T_, n_, sny_ > &y)
	Sets this matrix to the outer product of two vectors. More...

CUDA_HOST_DEVICE Matrix &	set_rotation_2d (T_ angle)
	Sets this matrix to a 2D rotation matrix. More...

CUDA_HOST_DEVICE Matrix &	set_rotation_3d (T_ yaw, T_ pitch, T_ roll)
	Sets this matrix to a 3D yaw-pitch-roll rotation matrix. More...

template<int sma_, int sna_>
CUDA_HOST_DEVICE Matrix &	set_transpose (const Matrix< T_, n_, m_, sma_, sna_ > &a)
	Sets this matrix to the transpose of another matrix. More...

template<int l_, int snv_, int slt_, int smt_, int snt_>
CUDA_HOST_DEVICE Matrix &	set_vec_tensor_mult (const Vector< T_, l_, snv_ > &x, const Tensor3< T_, l_, m_, n_, slt_, smt_, snt_ > &t, DataType alpha=DataType(1))
	Sets this matrix to the result of a vector-tensor left-product. More...

CUDA_HOST_DEVICE DataType	trace () const
	Returns the trace of the matrix. More...

CUDA_HOST_DEVICE DataType	vol () const
	Returns the volume of the matrix. More...

Static Public Member Functions
static CUDA_HOST_DEVICE Matrix	null ()
	Returns a null-matrix. More...

Public Attributes
RowType	v [sm_]
	actual matrix data; that's an array of vectors More...

Static Public Attributes
static constexpr int	m = m_
	the row count of the matrix More...

static constexpr int	n = n_
	the column count of the matrix More...

static constexpr int	sm = sm_
	the row stride of the matrix More...

static constexpr int	sn = sn_
	the column stride of the matrix More...

Friends
CUDA_HOST friend std::ostream &	operator<< (std::ostream &lhs, const Matrix &A)
	Tiny::Matrix streaming operator. More...

CUDA_HOST friend std::istream &	operator>> (std::istream &in, Matrix &A)
	Tiny::Matrix streaming operator. More...

Detailed Description

template<typename T_, int m_, int n_, int sm_ = m_, int sn_ = n_>
class FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >

Tiny Matrix class template.

This class template implements a matrix whose value type and size is given at compile-time. The value type can be a primitive type, or some other object like a Vector.

Template Parameters

T_	The datatype that the vector shall contain.
m_,n_	The number rows and columns of the matrix. Must be > 0.
sm_	The row stride of the matrix. Must be >= `m_`.
sn_	The column stride of the matrix. Must be >= `n_`.

Author: Peter Zajac

Definition at line 84 of file tiny_algebra.hpp.

Member Typedef Documentation

◆ DataType

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

typedef Intern::DataTypeExtractor<ValueType>::MyDataType FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::DataType

The basic data type buried in the lowest level of the vector.

Definition at line 1368 of file tiny_algebra.hpp.

◆ RowType

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

typedef Vector<T_, n_, sn_> FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::RowType

the type of a single matrix row

Definition at line 1371 of file tiny_algebra.hpp.

◆ ValueType

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

typedef T_ FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::ValueType

the data type of the matrix

Definition at line 1366 of file tiny_algebra.hpp.

Constructor & Destructor Documentation

◆ Matrix() [1/5]

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

CUDA_HOST_DEVICE FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::Matrix ( )

inline

default constructor

Definition at line 1376 of file tiny_algebra.hpp.

◆ Matrix() [2/5]

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

CUDA_HOST_DEVICE FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::Matrix ( DataType value )

inlineexplicit

value-assignment constructor

Definition at line 1381 of file tiny_algebra.hpp.

References FEAT::value.

◆ Matrix() [3/5]

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

template<typename T2_ , int sma_, int sna_>

CUDA_HOST_DEVICE FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::Matrix ( const Matrix< T2_, m_, n_, sma_, sna_ > & a )

inline

copy constructor

Definition at line 1391 of file tiny_algebra.hpp.

References FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::v.

◆ Matrix() [4/5]

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

template<typename Tx_ >

CUDA_HOST_DEVICE FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::Matrix ( const std::initializer_list< Tx_ > & x )

inlineexplicit

Initializer list of Tiny::Vector constructor.

Tiny::Vector<double, 2> v{...}, w{...};

Tiny::Matrix<double, 2, 2> m{v, w};

FEAT::Tiny::Matrix

Tiny Matrix class template.

Definition: tiny_algebra.hpp:84

FEAT::Tiny::Matrix::m

static constexpr int m

the row count of the matrix

Definition: tiny_algebra.hpp:1357

FEAT::Tiny::Matrix::v

RowType v[sm_]

actual matrix data; that's an array of vectors

Definition: tiny_algebra.hpp:1373

FEAT::Tiny::Vector

Tiny Vector class template.

Definition: tiny_algebra.hpp:56

Parameters

[in] x The initializer list whose elements are to be assigned.

Definition at line 1414 of file tiny_algebra.hpp.

References XASSERTM.

◆ Matrix() [5/5]

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

template<typename Tx_ >

CUDA_HOST_DEVICE FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::Matrix ( const std::initializer_list< std::initializer_list< Tx_ > > & x )

inlineexplicit

Initializer list constructor.

Note: This overload seems to be necessary, because the example code below does not compile otherwise for some reason that I do not understand...

Tiny::Matrix<double, 2, 2> v{{0.0, 1.0}, {2.0, 3.0}};

Parameters

[in] x The initializer list whose elements are to be assigned.

Definition at line 1436 of file tiny_algebra.hpp.

References XASSERTM.

Member Function Documentation

◆ add_double_mat_mult()

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

template<int k_, int l_, int sma_, int sna_, int smb_, int snb_, int smd_, int snd_>

CUDA_HOST_DEVICE Matrix & FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::add_double_mat_mult	(	const Matrix< T_, k_, l_, sma_, sna_ > &	a,
		const Matrix< T_, k_, m_, smb_, snb_ > &	b,
		const Matrix< T_, l_, n_, smd_, snd_ > &	d,
		DataType	alpha = `DataType(1)`
	)

inline

Adds the algebraic matrix double-product of three other matrices onto this matrix.

Let C denote this m-by-n matrix, B the left k-by-m input matrix, D the right l-by-n input matrix and A the inner k-by-l input matrix, then this operation computes:

\[ C \leftarrow C + \alpha B^\top\cdot A\cdot D\]

Parameters

[in]	a	The inner k-by-l multiplicand matrix.
[in]	b	The left k-by-m multiplicand matrix.
[in]	d	The right l-by-n multiplicand matrix.
[in]	alpha	A scaling factor for the product.

Returns: *this

Definition at line 2145 of file tiny_algebra.hpp.

References ASSERTM.

◆ add_mat_mat_mult()

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

template<int la_, int lb_, int sma_, int sna_, int smb_, int snb_>

CUDA_HOST_DEVICE Matrix & FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::add_mat_mat_mult	(	const Matrix< T_, m_, la_, sma_, sna_ > &	a,
		const Matrix< T_, lb_, n_, smb_, snb_ > &	b,
		DataType	alpha = `DataType(1)`
	)

inline

Adds the algebraic matrix-product of two other matrices onto this matrix.

Let C denote this matrix, and let A denote the left m-by-l matrix and B the right l-by-n matrix, then this function computes:

\[ C\leftarrow C + \alpha A\cdot B \]

Parameters

[in]	a	The left m-by-l multiplicand matrix.
[in]	b	The right l-by-n multiplicand matrix.
[in]	alpha	A scaling factor for the product.

Returns: *this

Definition at line 2071 of file tiny_algebra.hpp.

References ASSERTM.

◆ add_outer_product()

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

template<int snx_, int sny_>

CUDA_HOST_DEVICE Matrix & FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::add_outer_product	(	const Vector< T_, m_, snx_ > &	x,
		const Vector< T_, n_, sny_ > &	y,
		const DataType	alpha = `DataType(1)`
	)

inline

Adds the outer product of two vectors onto the matrix.

This function performs:

\[ a_{ij} \leftarrow a_{ij} + \alpha x_i y_j \]

Parameters

[in]	x	The left multiplicand vector of size `m_`.
[in]	y	The right multiplicand vector of size `n_`.
[in]	alpha	The scaling factor for the outer product.

Returns: *this

Definition at line 1971 of file tiny_algebra.hpp.

Referenced by FEAT::Assembly::BurgersBlockedAssemblyTaskBase< Job_, DataType_, block_size_ >::assemble_burgers_point(), FEAT::Assembly::BurgersCarreauBlockedAssemblyTaskBase< Job_, DataType_, block_size_ >::assemble_burgers_point(), FEAT::Assembly::BurgersAssembler< DataType_, IndexType_, dim_ >::assemble_matrix(), FEAT::Assembly::OldroydAssembler::assemble_matrix(), FEAT::Assembly::BurgersAssemblerCarreau< DataType_, IndexType_, dim_ >::assemble_vector(), FEAT::Assembly::VelocityAnalyser::compute(), FEAT::Assembly::DiscreteEvaluator::eval_fe_gradient(), FEAT::Assembly::BurgersAssemblyTaskBase< Job_, DataType_ >::prepare_point(), and FEAT::Assembly::BurgersCarreauAssemblyTaskBase< Job_, DataType_ >::prepare_point().

◆ add_scalar_main_diag()

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

CUDA_HOST_DEVICE Matrix & FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::add_scalar_main_diag ( DataType alpha )

inline

Adds a value onto the matrix's main diagonal.

Parameters

[in] alpha The value that is to be added onto the main diagonal.

Definition at line 2045 of file tiny_algebra.hpp.

Referenced by FEAT::Assembly::BurgersBlockedAssemblyTaskBase< Job_, DataType_, block_size_ >::assemble_burgers_point(), FEAT::Assembly::BurgersCarreauBlockedAssemblyTaskBase< Job_, DataType_, block_size_ >::assemble_burgers_point(), FEAT::Assembly::OldroydAssembler::assemble_matrix(), FEAT::Assembly::BurgersBlockedAssemblyTaskBase< Job_, DataType_, block_size_ >::assemble_streamline_diffusion(), FEAT::Assembly::BurgersCarreauBlockedAssemblyTaskBase< Job_, DataType_, block_size_ >::assemble_streamline_diffusion(), FEAT::Assembly::Common::LaplaceOperatorBlocked< dimension_ >::Evaluator< AsmTraits_ >::eval(), FEAT::Assembly::Common::IdentityOperatorBlocked< dimension_ >::Evaluator< AsmTraits_ >::eval(), and FEAT::Assembly::Common::DuDvOperatorBlocked< dimension_ >::Evaluator< AsmTraits_ >::eval().

◆ add_vec_tensor_mult()

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

template<int l_, int snv_, int slt_, int smt_, int snt_>

CUDA_HOST_DEVICE Matrix & FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::add_vec_tensor_mult	(	const Vector< T_, l_, snv_ > &	x,
		const Tensor3< T_, l_, m_, n_, slt_, smt_, snt_ > &	t,
		DataType	alpha = `DataType(1)`
	)

inline

Adds the result of a vector-tensor left-product onto this matrix.

Let A denote this m-by-n matrix, v the l-size input vector and T the l-by-m-by-b input tensor, then this operation computes:

\[ \forall i\in\{0,...,m-1\},j\in\{0,...,n-1\}:~ A_{ij} \leftarrow A_{ij} + \alpha \sum_{k=0}^{l-1} v_k\cdot T_{kij}\]

Note: This function is used for the computation of second-order derivatives by the chain rule.

Parameters

[in]	x	The l-size vector that serves as a left multiplicand.
[in]	t	The l-by-m-by-n tensor that serves as a right multiplicand.
[in]	alpha	A scaling factor for the product.

Returns: *this

Definition at line 2234 of file tiny_algebra.hpp.

◆ axpy()

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

template<int sma_, int sna_>

CUDA_HOST_DEVICE Matrix & FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::axpy	(	DataType	alpha,
		const Matrix< T_, m_, n_, sma_, sna_ > &	a
	)

inline

Adds another scaled matrix onto this matrix.

Parameters

[in]	alpha	The scaling parameter for the axpy.
[in]	a	The matrix to be added onto this matrix.

Returns: *this

Definition at line 2027 of file tiny_algebra.hpp.

References FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::v.

Referenced by FEAT::Assembly::BurgersBlockedAssemblyTaskBase< Job_, DataType_, block_size_ >::assemble_burgers_point(), FEAT::Assembly::BurgersCarreauBlockedAssemblyTaskBase< Job_, DataType_, block_size_ >::assemble_burgers_point(), FEAT::Assembly::BurgersAssemblerCarreau< DataType_, IndexType_, dim_ >::assemble_vector(), and FEAT::Assembly::BurgersCarreauAssemblyTaskBase< Job_, DataType_ >::prepare_point().

◆ convert()

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

template<typename Tx_ , int sma_, int sna_>

CUDA_HOST_DEVICE void FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::convert ( const Matrix< Tx_, m_, n_, sma_, sna_ > & a )

inline

conversion operator

Definition at line 1510 of file tiny_algebra.hpp.

References FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::v.

◆ copy()

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

template<int sma_, int sna_>

CUDA_HOST_DEVICE void FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::copy ( const Matrix< T_, m_, n_, sma_, sna_ > & a )

inline

Copies a matrix.

Parameters

[in] a The source matrix to copy

Definition at line 1601 of file tiny_algebra.hpp.

References FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::v.

◆ copy_n()

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

template<int mm_, int nn_, int ma_, int na_, int sma_, int sna_>

CUDA_HOST_DEVICE void FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::copy_n ( const Matrix< T_, ma_, na_, sma_, sna_ > & a )

inline

Copies the upper left mm_ x nn_ entries of a matrix.

Template Parameters

mm_	The number of matrix rows to copy; must be mm_ <= min(m_, ma_)
nn_	The number of matrix columns to copy; must be nn_ <= min(n_, na_)

Parameters

[in] x The source vector to copy the elements from

Definition at line 1621 of file tiny_algebra.hpp.

References FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::v.

◆ det()

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

CUDA_HOST_DEVICE DataType FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::det ( ) const

inline

Returns the determinant of the matrix.

Warning: This function only works for m_ = n_ and will intentionally fail to compile in any other case.

Returns: The determinant of the matrix.

Definition at line 1778 of file tiny_algebra.hpp.

◆ format()

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

CUDA_HOST_DEVICE void FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::format ( DataType alpha = DataType(0) )

inline

Formats the matrix.

Parameters

[in] alpha The value that the matrix is to be set to.

Definition at line 1638 of file tiny_algebra.hpp.

References FEAT::Tiny::Vector< T_, n_, s_ >::format().

◆ norm_frobenius()

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

CUDA_HOST_DEVICE DataType FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::norm_frobenius ( ) const

inline

Returns the Frobenius norm of the matrix.

This function computes and returns

\[ \Big(\sum_{i=0}^{m-1}\sum_{j=0}^{n-1} (A_{ij})^2\Big)^{\frac{1}{2}} \]

Returns: The Frobenius norm of the matrix.

Definition at line 1687 of file tiny_algebra.hpp.

References FEAT::Math::sqrt().

Referenced by FEAT::Assembly::GridTransfer::assemble_prolongation(), FEAT::Assembly::SpaceTransfer::assemble_transfer(), FEAT::Assembly::GridTransfer::assemble_truncation(), FEAT::Assembly::BurgersAssemblerCarreau< DataType_, IndexType_, dim_ >::assemble_vector(), FEAT::Assembly::BurgersCarreauAssemblyTaskBase< Job_, DataType_ >::prepare_point(), FEAT::Assembly::GridTransfer::prolongate_vector(), and FEAT::Assembly::SpaceTransfer::transfer_vector().

◆ norm_frobenius_sqr()

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

CUDA_HOST_DEVICE DataType FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::norm_frobenius_sqr ( ) const

inline

Returns the Frobenius norm squared of the matrix.

This function computes and returns

\[ \sum_{i=0}^{m-1}\sum_{j=0}^{n-1} (A_{ij})^2\]

Returns: The Frobenius norm of the matrix.

Definition at line 1704 of file tiny_algebra.hpp.

References FEAT::Math::sqr().

◆ norm_hessian_sqr()

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

CUDA_HOST_DEVICE DataType FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::norm_hessian_sqr ( ) const

inline

Returns the Hessian norm square.

This function computes and returns

\[ \sum_{i=0}^{m-1}\sum_{j=0}^{n-1} K_{ij}\cdot (A_{ij})^2 \]

where K_ij is 1 for i=j and 1/2 otherwise.

Note: This function is used for the computation of the H^2 semi-norm of a function.

Returns: The Hessian norm square of the matrix.

Definition at line 1657 of file tiny_algebra.hpp.

References FEAT::Math::sqr().

Referenced by FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::add_hess().

◆ norm_sub_id_frobenius()

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

CUDA_HOST_DEVICE DataType FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::norm_sub_id_frobenius ( ) const

inline

Returns the Frobenius norm of the difference of this matrix and the identity matrix.

Returns: The Frobenius norm of the difference of this matrix and the identity matrix.

Definition at line 1726 of file tiny_algebra.hpp.

References FEAT::Math::sqr(), and FEAT::Math::sqrt().

Referenced by FEAT::Geometry::Atlas::Extrude< Mesh_, SubChart_ >::write().

◆ null()

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

static CUDA_HOST_DEVICE Matrix FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::null ( )

inlinestatic

Returns a null-matrix.

Definition at line 2365 of file tiny_algebra.hpp.

◆ operator()() [1/2]

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

CUDA_HOST_DEVICE T_ & FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::operator()	(	int	i,
		int	j
	)

inline

Access operator.

Parameters

[in] i,j The indices of the matrix entry that is to be returned.

Returns: A (const) reference to the matrix entry at position (i,j).

Definition at line 1525 of file tiny_algebra.hpp.

References ASSERTM.

◆ operator()() [2/2]

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

CUDA_HOST_DEVICE const T_ & FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::operator()	(	int	i,
		int	j
	)		const

inline

Access operator.

Parameters

[in] i,j The indices of the matrix entry that is to be returned.

Returns: A (const) reference to the matrix entry at position (i,j).

Definition at line 1533 of file tiny_algebra.hpp.

References ASSERTM.

◆ operator*=()

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

CUDA_HOST_DEVICE Matrix & FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::operator*= ( DataType alpha )

inline

scalar-right-multiply-by operator

Definition at line 1563 of file tiny_algebra.hpp.

◆ operator+=()

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

template<int sma_, int sna_>

CUDA_HOST_DEVICE Matrix & FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::operator+= ( const Matrix< T_, m_, n_, sma_, sna_ > & a )

inline

matrix component-wise addition operator

Definition at line 1574 of file tiny_algebra.hpp.

References FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::v.

◆ operator-=()

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

template<int sma_, int sna_>

CUDA_HOST_DEVICE Matrix & FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::operator-= ( const Matrix< T_, m_, n_, sma_, sna_ > & a )

inline

matrix component-wise subtraction operator

Definition at line 1585 of file tiny_algebra.hpp.

References FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::v.

◆ operator=() [1/4]

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

template<int sma_, int sna_>

CUDA_HOST_DEVICE Matrix & FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::operator= ( const Matrix< T_, m_, n_, sma_, sna_ > & a )

inline

assignment operator

Definition at line 1456 of file tiny_algebra.hpp.

References FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::v.

◆ operator=() [2/4]

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

template<typename Tx_ >

CUDA_HOST_DEVICE Matrix & FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::operator= ( const std::initializer_list< std::initializer_list< Tx_ > > & x )

inline

Initializer list assignment operator.

Tiny::Matrix<double, 2, 2> m;

m = {{0.0, 1.0}, {2.0, 3.0}};

Parameters

[in] x The initializer list whose elements are to be assigned.

Definition at line 1499 of file tiny_algebra.hpp.

References XASSERTM.

◆ operator=() [3/4]

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

template<typename Tx_ >

CUDA_HOST_DEVICE Matrix & FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::operator= ( const std::initializer_list< Tx_ > & x )

inline

Initializer list assignment operator.

Tiny::Vector<double, 2> v{1.0, 2.0}, w{3.0, 4.0};
Tiny::Matrix<double, 2, 2> m;
m = {v, w};

Parameters

[in] x The initializer list whose elements are to be assigned.

Definition at line 1478 of file tiny_algebra.hpp.

References XASSERTM.

◆ operator=() [4/4]

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

CUDA_HOST_DEVICE Matrix & FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::operator= ( DataType value )

inline

value-assignment operator

Definition at line 1445 of file tiny_algebra.hpp.

References FEAT::value.

◆ operator[]() [1/2]

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

CUDA_HOST_DEVICE RowType & FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::operator[] ( int i )

inline

Row-Access operator.

Parameters

[in] i The index of the row that is to be returned.

Returns: A (const) reference to the i-th row of the matrix.S

Definition at line 1549 of file tiny_algebra.hpp.

References ASSERTM.

◆ operator[]() [2/2]

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

CUDA_HOST_DEVICE const RowType & FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::operator[] ( int i ) const

inline

Row-Access operator.

Parameters

[in] i The index of the row that is to be returned.

Returns: A (const) reference to the i-th row of the matrix.S

Definition at line 1556 of file tiny_algebra.hpp.

References ASSERTM.

◆ scalar_product()

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

template<int snx_, int sny_>

CUDA_HOST_DEVICE DataType FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::scalar_product	(	const Vector< T_, m_, snx_ > &	x,
		const Vector< T_, n_, sny_ > &	y
	)		const

inline

Computes the scalar product of two vectors with this matrix.

This function returns

\[ x^\top\cdot A\cdot y = \sum_{i=0}^{m-1}\sum_{j=0}^{n-1} x_i\cdot A_{ij}\cdot y_j\]

Parameters

[in]	x	The left muliplicant vector of size `m_`.
[in]	y	The right multiplicand vector of size `n_`.

Returns: The scalar product of x and y with this matrix.

Definition at line 1943 of file tiny_algebra.hpp.

References FEAT::Tiny::dot().

Referenced by FEAT::Assembly::Common::LaplaceBeltramiOperator::Evaluator< AsmTraits_ >::eval().

◆ set_cofactor()

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

template<int sma_, int sna_>

CUDA_HOST_DEVICE Matrix & FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::set_cofactor ( const Matrix< T_, m_, n_, sma_, sna_ > & a )

inline

Sets this matrix to the cofactor matrix of another matrix.

\( \mathrm{Cof}(A) \) is the cofactor matrix of \( A \). If \(A \in \mathbb{R}^{n \times n}\), define \(A^{(i,j)} \in \mathbb{R}^{n-1 \times n-1}\) as the matrix obtained by deleting the \( i \)th column and \( j \)th row of \( A \). Then

\[ \mathrm{Cof}(A)_{i,j} = (-1)^{i+j} \det(A^{(i,j)}) \]

and if \( A \in \mathrm{GL}_n\), \( \mathrm{Cof}(A) = \det(A) A^{-T} \).

Warning: This function only works for m_ = n_ and will intentionally fail to compile in any other case.

Parameters

[in] a The matrix whose cofactor matrix is to be stored in this matrix.

Returns: *this

Definition at line 1862 of file tiny_algebra.hpp.

References ASSERTM.

◆ set_double_mat_mult()

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

template<int k_, int l_, int sma_, int sna_, int smb_, int snb_, int smd_, int snd_>

CUDA_HOST_DEVICE Matrix & FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::set_double_mat_mult	(	const Matrix< T_, k_, l_, sma_, sna_ > &	a,
		const Matrix< T_, k_, m_, smb_, snb_ > &	b,
		const Matrix< T_, l_, n_, smd_, snd_ > &	d,
		T_	alpha = `T_(1)`
	)

inline

Sets this matrix to the algebraic matrix double-product of three other matrices.

Let C denote this m-by-n matrix, B the left k-by-m input matrix, D the right l-by-n input matrix and A the inner k-by-l input matrix, then this operation computes:

\[ C \leftarrow B^\top\cdot A\cdot D\]

Parameters

[in]	a	The inner k-by-l multiplicand matrix.
[in]	b	The left k-by-m multiplicand matrix.
[in]	d	The right l-by-n multiplicand matrix.
[in]	alpha	A scaling factor for the product.

Returns: *this

Definition at line 2198 of file tiny_algebra.hpp.

References ASSERTM.

◆ set_gram()

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

template<int l_, int sla_, int sna_>

CUDA_HOST_DEVICE Matrix & FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::set_gram ( const Matrix< T_, l_, n_, sla_, sna_ > & a )

inline

Sets this matrix to the Gram matrix of another matrix.

Let C denote this n-by-n matrix, and let A denote the l-by-n input matrix, then this function computes:

\[ C\leftarrow A^\top\cdot A \]

Parameters

[in] a The matrix whose Gram matrix is to be stored in this matrix.

Returns: *this

Definition at line 1907 of file tiny_algebra.hpp.

References FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::v.

◆ set_identity()

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

CUDA_HOST_DEVICE Matrix & FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::set_identity ( )

inline

Sets this matrix to the identity matrix.

Returns: *this

Definition at line 2289 of file tiny_algebra.hpp.

Referenced by FEAT::Geometry::Intern::AdaptiveMeshStorage< MeshShape_, TemplateSet_, VertexType_ >::_aux_rot_mat().

◆ set_inverse()

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

template<int sma_, int sna_>

CUDA_HOST_DEVICE Matrix & FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::set_inverse ( const Matrix< T_, m_, n_, sma_, sna_ > & a )

inline

Sets this matrix to the inverse of another matrix.

Warning: This function only works for m_ = n_ and will intentionally fail to compile in any other case.

Parameters

[in] a The matrix whose inverse is to be stored in this matrix.

Returns: *this

Definition at line 1810 of file tiny_algebra.hpp.

References ASSERTM.

Referenced by FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Quadrilateral >::_build_coeff_matrix(), FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Hexahedron >::_build_coeff_matrix(), FEAT::Space::Q1TBNP::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Quadrilateral >::_build_coeff_matrix(), FEAT::Space::Q1TBNP::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Hexahedron >::_build_coeff_matrix(), FEAT::Trafo::Standard::inverse_mapping(), and FEAT::Space::Argyris::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Simplex< 2 > >::prepare().

◆ set_mat_mat_mult()

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

template<int la_, int lb_, int sma_, int sna_, int smb_, int snb_>

CUDA_HOST_DEVICE Matrix & FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::set_mat_mat_mult	(	const Matrix< T_, m_, la_, sma_, sna_ > &	a,
		const Matrix< T_, lb_, n_, smb_, snb_ > &	b
	)

inline

Sets this matrix to the algebraic matrix-product of two other matrices.

Let C denote this matrix, and let A denote the left m-by-l matrix and B the right l-by-n matrix, then this function computes:

\[ C\leftarrow A\cdot B \]

Parameters

[in]	a	The left m-by-l multiplicand matrix.
[in]	b	The right l-by-n multiplicand matrix.

Returns: *this

Definition at line 2112 of file tiny_algebra.hpp.

References ASSERTM.

Referenced by FEAT::LAFEM::SparseMatrixBCSR< DT_, IT_, BlockHeight_, BlockWidth_ >::add_double_mat_product(), FEAT::Assembly::GridTransfer::assemble_prolongation(), FEAT::Assembly::SpaceTransfer::assemble_transfer(), FEAT::Assembly::GridTransfer::assemble_truncation(), FEAT::Tiny::operator*(), FEAT::Assembly::GridTransfer::prolongate_vector(), and FEAT::Assembly::SpaceTransfer::transfer_vector().

◆ set_outer_product()

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

template<int snx_, int sny_>

CUDA_HOST_DEVICE Matrix & FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::set_outer_product	(	const Vector< T_, m_, snx_ > &	x,
		const Vector< T_, n_, sny_ > &	y
	)

inline

Sets this matrix to the outer product of two vectors.

This function performs:

\[ a_{ij} \leftarrow x_i y_j \]

Parameters

[in]	x	The left multiplicand vector of size `m_`.
[in]	y	The right multiplicand vector of size `n_`.

Returns: *this

Definition at line 2001 of file tiny_algebra.hpp.

Referenced by FEAT::Assembly::Common::DuDvOperatorBlocked< dimension_ >::Evaluator< AsmTraits_ >::eval().

◆ set_rotation_2d()

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

CUDA_HOST_DEVICE Matrix & FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::set_rotation_2d ( T_ angle )

inline

Sets this matrix to a 2D rotation matrix.

Parameters

[in] angle Specifies the rotation angle in radians

Returns: *this

Definition at line 2305 of file tiny_algebra.hpp.

References FEAT::Math::cos(), and FEAT::Math::sin().

Referenced by FEAT::Analytic::PolarCoordinate< Function_, pos_range_ >::PolarCoordinate(), FEAT::Geometry::Intern::AdaptiveMeshStorage< MeshShape_, TemplateSet_, VertexType_ >::_aux_rot_mat(), FEAT::Geometry::Atlas::Bezier< Mesh_ >::transform(), and FEAT::Geometry::Atlas::Circle< Mesh_ >::transform().

◆ set_rotation_3d()

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

CUDA_HOST_DEVICE Matrix & FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::set_rotation_3d	(	T_	yaw,
		T_	pitch,
		T_	roll
	)

inline

Sets this matrix to a 3D yaw-pitch-roll rotation matrix.

This function sets a 3D rotation matrix by specifying the yaw, pitch and roll angles.

The convention for the rotation is Z-Y'-X'', also known as nautical angles.

See also

Returns: *this

Definition at line 2332 of file tiny_algebra.hpp.

References FEAT::Math::cos(), and FEAT::Math::sin().

Referenced by FEAT::Geometry::Intern::AdaptiveMeshStorage< MeshShape_, TemplateSet_, VertexType_ >::_aux_rot_mat(), FEAT::Geometry::MeshExtruder< ConformalMesh< Shape::Hypercube< 2 >, 2, Coord_ > >::extrude_vertex_set(), FEAT::Geometry::Atlas::Sphere< Mesh_ >::transform(), and FEAT::Geometry::Atlas::SurfaceMesh< Mesh_ >::transform().

◆ set_transpose()

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

template<int sma_, int sna_>

CUDA_HOST_DEVICE Matrix & FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::set_transpose ( const Matrix< T_, n_, m_, sma_, sna_ > & a )

inline

Sets this matrix to the transpose of another matrix.

Parameters

[in] a The matrix whose transpose is to be stored in this matrix.

Returns: *this

Definition at line 1879 of file tiny_algebra.hpp.

References ASSERTM, and FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::v.

Referenced by FEAT::Assembly::BurgersAssemblerCarreau< DataType_, IndexType_, dim_ >::assemble_vector(), FEAT::Assembly::BurgersCarreauAssemblyTaskBase< Job_, DataType_ >::prepare_point(), and FEAT::LAFEM::SparseMatrixBCSR< DT_, IT_, BlockHeight_, BlockWidth_ >::transpose().

◆ set_vec_tensor_mult()

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

template<int l_, int snv_, int slt_, int smt_, int snt_>

CUDA_HOST_DEVICE Matrix & FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::set_vec_tensor_mult	(	const Vector< T_, l_, snv_ > &	x,
		const Tensor3< T_, l_, m_, n_, slt_, smt_, snt_ > &	t,
		DataType	alpha = `DataType(1)`
	)

inline

Sets this matrix to the result of a vector-tensor left-product.

Let A denote this m-by-n matrix, v the l-size input vector and T the l-by-m-by-b input tensor, then this operation computes:

\[ \forall i\in\{0,...,m-1\},j\in\{0,...,n-1\}:~ A_{ij} \leftarrow \alpha \sum_{k=0}^{l-1} v_k\cdot T_{kij}\]

Note: This function is used for the computation of second-order derivatives by the chain rule.

Parameters

[in]	x	The l-size vector that serves as a left multiplicand.
[in]	t	The l-by-m-by-n tensor that serves as a right multiplicand.
[in]	alpha	A scaling factor for the product.

Returns: *this

Definition at line 2275 of file tiny_algebra.hpp.

◆ trace()

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

CUDA_HOST_DEVICE DataType FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::trace ( ) const

inline

Returns the trace of the matrix.

This function computes and returns

\[ \sum_{i=0}^{\min(m,n)} A_{ii}\]

i.e. the sum of all main diagonal elements.

Returns: The trace of the matrix.

Definition at line 1756 of file tiny_algebra.hpp.

References FEAT::Math::min().

Referenced by FEAT::Assembly::FunctionIntegralInfo< DataType_, ValueType_, GradientType_, HessianType_ >::add_grad(), and FEAT::Assembly::VelocityAnalyser::compute().

◆ vol()

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

CUDA_HOST_DEVICE DataType FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::vol ( ) const

inline

Returns the volume of the matrix.

The volume of a matrix A is defined as:

\[ \textnormal{vol}(A) := \sqrt{\textnormal{det}(A^\top\cdot A)} \]

Note: For m_ = n_, the volume of the matrix equals the absolute of its determinant.; For m_ < n_, the volume of the matrix is always zero.

Returns: The volume of the matrix.

Definition at line 1794 of file tiny_algebra.hpp.

Friends And Related Function Documentation

◆ operator<<

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

CUDA_HOST friend std::ostream & operator<<	(	std::ostream &	lhs,
		const Matrix< T_, m_, n_, sm_, sn_ > &	A
	)

friend

Tiny::Matrix streaming operator.

Parameters

[in]	lhs	The target stream.
[in]	A	The matrix to be streamed.

Definition at line 2376 of file tiny_algebra.hpp.

◆ operator>>

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

CUDA_HOST friend std::istream & operator>>	(	std::istream &	in,
		Matrix< T_, m_, n_, sm_, sn_ > &	A
	)

friend

Tiny::Matrix streaming operator.

Parameters

[in]	in	The input stream.
[in]	A	The matrix to fill.

Definition at line 2393 of file tiny_algebra.hpp.

Member Data Documentation

◆ m

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

constexpr int FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::m = m_

staticconstexpr

the row count of the matrix

Definition at line 1357 of file tiny_algebra.hpp.

Referenced by FEAT::Geometry::Atlas::SurfaceMesh< Mesh_ >::get_normal_on_tria().

◆ n

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

constexpr int FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::n = n_

staticconstexpr

the column count of the matrix

Definition at line 1359 of file tiny_algebra.hpp.

Referenced by FEAT::Geometry::Atlas::SurfaceMesh< Mesh_ >::get_normal_on_tria().

◆ sm

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

constexpr int FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::sm = sm_

staticconstexpr

the row stride of the matrix

Definition at line 1361 of file tiny_algebra.hpp.

◆ sn

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

constexpr int FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::sn = sn_

staticconstexpr

the column stride of the matrix

Definition at line 1363 of file tiny_algebra.hpp.

Referenced by FEAT::Assembly::GridTransfer::assemble_prolongation(), FEAT::Assembly::SpaceTransfer::assemble_transfer(), FEAT::Assembly::GridTransfer::assemble_truncation(), FEAT::Assembly::GridTransfer::prolongate_vector(), and FEAT::Assembly::SpaceTransfer::transfer_vector().

◆ v

template<typename T_ , int m_, int n_, int sm_ = m_, int sn_ = n_>

RowType FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::v[sm_]

actual matrix data; that's an array of vectors

Definition at line 1373 of file tiny_algebra.hpp.

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

kernel/util/tiny_algebra.hpp

Public Types

Public Member Functions

Static Public Member Functions

Public Attributes

Static Public Attributes

Friends

Detailed Description

Member Typedef Documentation

◆ DataType

◆ RowType

◆ ValueType

Constructor & Destructor Documentation

◆ Matrix() [1/5]

◆ Matrix() [2/5]

◆ Matrix() [3/5]

◆ Matrix() [4/5]

◆ Matrix() [5/5]

Member Function Documentation

◆ add_double_mat_mult()

◆ add_mat_mat_mult()

◆ add_outer_product()

◆ add_scalar_main_diag()

◆ add_vec_tensor_mult()

◆ axpy()

◆ convert()

◆ copy()

◆ copy_n()

◆ det()

◆ format()

◆ norm_frobenius()

◆ norm_frobenius_sqr()

◆ norm_hessian_sqr()

◆ norm_sub_id_frobenius()

◆ null()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator*=()

◆ operator+=()

◆ operator-=()

◆ operator=() [1/4]

◆ operator=() [2/4]

◆ operator=() [3/4]

◆ operator=() [4/4]

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ scalar_product()

◆ set_cofactor()

◆ set_double_mat_mult()

◆ set_gram()

◆ set_identity()

◆ set_inverse()

◆ set_mat_mat_mult()

◆ set_outer_product()

◆ set_rotation_2d()

◆ set_rotation_3d()

◆ set_transpose()

◆ set_vec_tensor_mult()

◆ trace()

◆ vol()

Friends And Related Function Documentation

◆ operator<<

◆ operator>>

Member Data Documentation

◆ m

◆ n

◆ sm

◆ sn

◆ v