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

Shortcut for \(b \approx \sqrt{A} x \) solve directly via sqrt Cauchy combined with PCG inversions. More...

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

Public Member Functions
	DirectSqrtCauchy ()
	empty object ( no memory allocation)
template<class MatrixType >
	DirectSqrtCauchy (MatrixType &A, const Container &weights, value_type epsCG, unsigned iterCauchy, std::array< value_type, 2 > EVs, int exp)
	Construct DirectSqrtCauchy.
template<class ... Params>
void	construct (Params &&...ps)
	Perfect forward parameters to one of the constructors.
unsigned	operator() (const Container &b, Container &x)
	Compute \(x \approx \sqrt{A} b \) via sqrt Cauchy integral solve.

Detailed Description

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

Shortcut for \(b \approx \sqrt{A} x \) solve directly via sqrt Cauchy combined with PCG inversions.

Member Typedef Documentation

container_type

template<class Container >

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

value_type

template<class Container >

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

Constructor & Destructor Documentation

DirectSqrtCauchy() [1/2]

template<class Container >

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

inline

empty object ( no memory allocation)

DirectSqrtCauchy() [2/2]

template<class Container >

template<class MatrixType >

dg::mat::DirectSqrtCauchy< Container >::DirectSqrtCauchy ( MatrixType & A, const Container & weights, value_type epsCG, unsigned iterCauchy, std::array< value_type, 2 > EVs, int exp )

inline

Construct DirectSqrtCauchy.

Note

The Eigenvalues can be estimated from a few lanczos iterations (which is at least more reliable than doing it semi-analytically)

dg::mat::UniversalLanczos lanczos( A.weights(), 20);
auto T = lanczos.tridiag( A, A.weights(), A.weights());
auto EVs = dg::mat::compute_extreme_EV( T);

Parameters

A	The matrix (stored by reference)
weights
epsCG
iterCauchy	maximum number of Cauchy iterations
EVs	{minimum Eigenvalue of A, maximum Eigenvalue of A}
exp	if < 0 then the inverse sqrt is computed, else the sqrt

Member Function Documentation

construct()

template<class Container >

template<class ... Params>

void dg::mat::DirectSqrtCauchy< 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

operator()()

template<class Container >

unsigned dg::mat::DirectSqrtCauchy< Container >::operator() ( const Container & b, Container & x )

inline

Compute \(x \approx \sqrt{A} b \) via sqrt Cauchy integral solve.

Parameters

b	input vector
x	output vector. Is approximating \(x \approx \sqrt{A} b \)

Returns

number of integration steps of sqrt cauchy solve

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

• sqrt_cauchy.h