Dense matrix formats

Collaboration diagram for Dense matrix formats:

Classes
class	dg::Operator< T >
	A square nxn matrix. More...

Functions
template<class ContainerType >
auto	dg::asDenseMatrix (const std::vector< const ContainerType * > &in)
	Lightweight DenseMatrix for dg::blas2::gemv. More...
template<class ContainerType >
auto	dg::asDenseMatrix (const std::vector< const ContainerType * > &in, unsigned size)
	Lightweight DenseMatrix for dg::blas2::gemv. More...
template<class ContainerType >
std::vector< const ContainerType * >	dg::asPointers (const std::vector< ContainerType > &in)
	Convert a vector of vectors to a vector of pointers. More...
template<class T >
T	dg::create::lu_pivot (dg::Operator< T > &m, std::vector< unsigned > &p)
	LU Decomposition with partial pivoting. More...
template<class T >
void	dg::create::lu_solve (const dg::Operator< T > &lu, const std::vector< unsigned > &p, std::vector< T > &b)
	Solve the linear system with the LU decomposition. More...
template<class T >
dg::Operator< T >	dg::create::inverse (const dg::Operator< T > &in)
	Compute the inverse of a square matrix. More...
template<class T >
dg::Operator< T >	dg::invert (const dg::Operator< T > &in)
	Alias for dg::create::inverse. Compute inverse of square matrix. More...

Detailed Description

Function Documentation

asDenseMatrix() [1/2]

template<class ContainerType >

auto dg::asDenseMatrix

(

const std::vector< const ContainerType * > &

in

)

Lightweight DenseMatrix for dg::blas2::gemv.

The philosophy is that a column matrix is represented by a std::vector of pointers and can be multiplied with a coefficient vector

\[ \vec y = V \vec c = \sum_i c_i \vec v_{i} \]

where \( v_i\) are the columns of \( V\)

std::vector<Container> matrix( 10, x);
std::vector<const Container*> matrix_ptrs = dg::asPointers(matrix);
std::vector<value_type> coeffs( 10, 0.5);
dg::blas2::gemv( 1., dg::asDenseMatrix(matrix_ptrs), coeffs, 0.,  x);

Note

the implemented summation algorithm is a pairwise summation algorithm optimized for small sized number of columns ( <= 64)

Parameters

in	a collection of pointers that form the columns of the dense matrix

Returns

an opaque type that internally adds a Tag that tells the compiler that the std::vector is to be interpreted as a dense matrix and call the correct implementation.

Template Parameters

ContainerType

Any class for which a specialization of TensorTraits exists and which fulfills the requirements of the there defined data and execution policies derived from AnyVectorTag and AnyPolicyTag. Among others dg::HVec (serial), dg::DVec (cuda / omp), dg::MHVec (mpi + serial) or dg::MDVec (mpi + cuda / omp) std::vector<dg::DVec> (vector of shared device vectors), std::array<double, 4> (array of 4 doubles) or std::map < std::string, dg::DVec> ( a map of named vectors) double (scalar) and other primitive types ... If there are several ContainerTypes in the argument list, then TensorTraits must exist for all of them

See also

See The dg dispatch system for a detailed explanation of our type dispatch system

asDenseMatrix() [2/2]

template<class ContainerType >

auto dg::asDenseMatrix	(	const std::vector< const ContainerType * > &	in,
		unsigned	size
	)

Lightweight DenseMatrix for dg::blas2::gemv.

The philosophy is that a column matrix is represented by a std::vector of pointers and can be multiplied with a coefficient vector

\[ \vec y = V \vec c = \sum_i c_i \vec v_{i} \]

where \( v_i\) are the columns of \( V\)

std::vector<Container> matrix( 10, x);
std::vector<const Container*> matrix_ptrs = dg::asPointers(matrix);
std::vector<value_type> coeffs( 10, 0.5);
dg::blas2::gemv( 1., dg::asDenseMatrix(matrix_ptrs), coeffs, 0.,  x);

Note

the implemented summation algorithm is a pairwise summation algorithm optimized for small sized number of columns ( <= 64)

Parameters

in	a collection of pointers that form the columns of the dense matrix

Returns

an opaque type that internally adds a Tag that tells the compiler that the std::vector is to be interpreted as a dense matrix and call the correct implementation.

Template Parameters

ContainerType

Any class for which a specialization of TensorTraits exists and which fulfills the requirements of the there defined data and execution policies derived from AnyVectorTag and AnyPolicyTag. Among others dg::HVec (serial), dg::DVec (cuda / omp), dg::MHVec (mpi + serial) or dg::MDVec (mpi + cuda / omp) std::vector<dg::DVec> (vector of shared device vectors), std::array<double, 4> (array of 4 doubles) or std::map < std::string, dg::DVec> ( a map of named vectors) double (scalar) and other primitive types ... If there are several ContainerTypes in the argument list, then TensorTraits must exist for all of them

See also

See The dg dispatch system for a detailed explanation of our type dispatch system

Parameters

size	only the first size pointers are used in the matrix (i.e. the number of columns is size)

asPointers()

template<class ContainerType >

std::vector< const ContainerType * > dg::asPointers

(

const std::vector< ContainerType > &

in

)

Convert a vector of vectors to a vector of pointers.

A convenience function that can be used in combination with asDenseMatrix

std::vector<Container> matrix( 10, x);
std::vector<const Container*> matrix_ptrs = dg::asPointers(matrix);
std::vector<value_type> coeffs( 10, 0.5);
dg::blas2::gemv( 1., dg::asDenseMatrix(matrix_ptrs), coeffs, 0.,  x);

Parameters

in	a collection of vectors that form the columns of the dense matrix

Returns

a vector of pointers with ptrs[i] = &in[i]

Attention

DO NOT HOLD POINTERS AS PRIVATE DATA MEMBERS IN A CLASS unless you also plan to overload the copy and assignment operators

Template Parameters

ContainerType

Any class for which a specialization of TensorTraits exists and which fulfills the requirements of the there defined data and execution policies derived from AnyVectorTag and AnyPolicyTag. Among others dg::HVec (serial), dg::DVec (cuda / omp), dg::MHVec (mpi + serial) or dg::MDVec (mpi + cuda / omp) std::vector<dg::DVec> (vector of shared device vectors), std::array<double, 4> (array of 4 doubles) or std::map < std::string, dg::DVec> ( a map of named vectors) double (scalar) and other primitive types ... If there are several ContainerTypes in the argument list, then TensorTraits must exist for all of them

See also

See The dg dispatch system for a detailed explanation of our type dispatch system

inverse()

template<class T >

dg::Operator< T > dg::create::inverse

(

const dg::Operator< T > &

in

)

Compute the inverse of a square matrix.

using lu decomposition in combination with our accurate scalar products

Template Parameters

T	value type

Parameters

in	input matrix

Returns

the inverse of in if it exists

Exceptions

std::runtime_error

if in is singular

invert()

template<class T >

dg::Operator< T > dg::invert

(

const dg::Operator< T > &

in

)

Alias for dg::create::inverse. Compute inverse of square matrix.

using lu decomposition in combination with our accurate scalar products

Template Parameters

T	value type

Parameters

in	input matrix

Returns

the inverse of in if it exists

Exceptions

std::runtime_error

if in is singular

lu_pivot()

template<class T >

T dg::create::lu_pivot	(	dg::Operator< T > &	m,
		std::vector< unsigned > &	p
	)

LU Decomposition with partial pivoting.

Template Parameters

T	value type

Exceptions

std::runtime_error

if the matrix is singular

Parameters

m	contains lu decomposition of input on output (inplace transformation)
p	contains the pivot elements on output

Returns

determinant of m

Note

uses extended accuracy of dg::exblas which makes it quite robust against almost singular matrices

See also

dg::create::lu_solve

lu_solve()

template<class T >

void dg::create::lu_solve	(	const dg::Operator< T > &	lu,
		const std::vector< unsigned > &	p,
		std::vector< T > &	b
	)

Solve the linear system with the LU decomposition.

Template Parameters

T	value type

Parameters

lu	result of dg::create::lu_pivot
p	pivot vector from dg::create::lu_pivot
b	right hand side (contains solution on output)