dg::mat::InvSqrtODE< Container > Struct Template Reference

Right hand side of the square root ODE. More...

Public Types
using	container_type = Container
using	value_type = dg::get_value_type< Container >

Public Member Functions
	InvSqrtODE ()
template<class MatrixType >
	InvSqrtODE (MatrixType &A, const Container &copyable)
	Construct SqrtOde operator. More...
template<class ... Params>
void	construct (Params &&...ps)
	Perfect forward parameters to one of the constructors. More...
const value_type &	time () const
auto	make_operator () const
template<class MatrixType >
void	set_inverse_operator (const MatrixType &OpInv)
void	operator() (value_type t, const Container &y, Container &yp)
	Compute rhs term. More...

Detailed Description

template<class Container>
struct dg::mat::InvSqrtODE< Container >

Right hand side of the square root ODE.

\[ \dot{y}= \left[(1-t) A +t I\right]^{-1} (I - A)/2 y \]

where \( A\) is the matrix

This class is based on the approach of the paper Numerical approximation of the product of the square root of a matrix with a vector by E. J. Allen et al

Note

Solution of ODE: \( y(1) = \frac{1}{\sqrt{A}} y(0)\) If \( y(0) = A b \) then we get \( y(1) = \sqrt{A} b\)

Member Typedef Documentation

container_type

template<class Container >

using dg::mat::InvSqrtODE< Container >::container_type = Container

value_type

template<class Container >

using dg::mat::InvSqrtODE< Container >::value_type = dg::get_value_type<Container>

Constructor & Destructor Documentation

InvSqrtODE() [1/2]

template<class Container >

dg::mat::InvSqrtODE< Container >::InvSqrtODE ( )

inline

InvSqrtODE() [2/2]

template<class Container >

template<class MatrixType >

dg::mat::InvSqrtODE< Container >::InvSqrtODE ( MatrixType &  A, const Container &  copyable  )

inline

Construct SqrtOde operator.

Parameters

A	matrix (stored by reference so needs to live)
copyable	copyable container

Member Function Documentation

construct()

template<class Container >

template<class ... Params>

void dg::mat::InvSqrtODE< Container >::construct ( Params &&...  ps )

inline

Perfect forward parameters to one of the constructors.

Template Parameters

Params

deduced by the compiler

Parameters

ps	parameters forwarded to constructors

make_operator()

template<class Container >

auto dg::mat::InvSqrtODE< Container >::make_operator ( ) const

inline

operator()()

template<class Container >

void dg::mat::InvSqrtODE< Container >::operator() ( value_type  t, const Container &  y, Container &  yp  )

inline

Compute rhs term.

i.e.

\[ yp= (tI + (1-t) A)^{-1} (I - A)/2 y \]

Parameters

t	is time
y	is \( y\)
yp	is \( \dot{y}\)

Note

Solution of ODE: \( y(1) = 1/\sqrt{A} y(0)\)

set_inverse_operator()

template<class Container >

template<class MatrixType >

void dg::mat::InvSqrtODE< Container >::set_inverse_operator ( const MatrixType &  OpInv )

inline

time()

template<class Container >

const value_type & dg::mat::InvSqrtODE< Container >::time ( ) const

inline

---

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

• sqrt_ode.h