dg::mat::MatrixSqrt< ContainerType > Struct Template Reference

Fast computation of \( \vec x = A^{\pm 1/2}\vec b\) for self-adjoint positive definite \(A\). More...

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

Public Member Functions
	MatrixSqrt ()=default
	Construct empty.
template<class MatrixType >
	MatrixSqrt (MatrixType &A, int exp, const ContainerType &weights, value_type eps_rel, value_type nrmb_correction=1., unsigned max_iter=500, unsigned cauchy_steps=40)
	Construct from matrix.
template<class ... Params>
void	construct (Params &&...ps)
	Perfect forward parameters to one of the constructors.
unsigned	get_iter () const
	Get the number of Lanczos iterations in latest call to operator()
void	set_benchmark (bool benchmark, std::string message="SQRT")
	Set or unset performance timings during iterations.
template<class ContainerType0 , class ContainerType1 >
void	operator() (const ContainerType0 b, ContainerType1 &x)
	Apply matrix sqrt.

Detailed Description

template<class ContainerType>
struct dg::mat::MatrixSqrt< ContainerType >

Fast computation of \( \vec x = A^{\pm 1/2}\vec b\) for self-adjoint positive definite \(A\).

Convenience wrapper that uses dg::mat::UniversalLanczos combined with dg::mat::make_SqrtCauchyEigen_Te1 in its "universal" stopping criterion

Note

This is the fastest method to compute matrix square roots vector multiplications that we found to date

Attention

Just as in the Lanczos or PCG methods the matrix \( A\) needs to be positive-definite (i.e. it won't work for negative definite)

Member Typedef Documentation

container_type

template<class ContainerType >

using dg::mat::MatrixSqrt< ContainerType >::container_type = ContainerType

value_type

template<class ContainerType >

using dg::mat::MatrixSqrt< ContainerType >::value_type = dg::get_value_type<ContainerType>

Constructor & Destructor Documentation

MatrixSqrt() [1/2]

template<class ContainerType >

dg::mat::MatrixSqrt< ContainerType >::MatrixSqrt ( )

default

Construct empty.

MatrixSqrt() [2/2]

template<class ContainerType >

template<class MatrixType >

dg::mat::MatrixSqrt< ContainerType >::MatrixSqrt ( MatrixType & A, int exp, const ContainerType & weights, value_type eps_rel, value_type nrmb_correction = 1., unsigned max_iter = 500, unsigned cauchy_steps = 40 )

inline

Construct from matrix.

Template Parameters

MatrixType

Parameters

A	self-adjoint matrix; is stored by reference
exp	exponent, if < 0 then 1/sqrt(A) is computed, else sqrt(A)
weights	the weights in which A is self-adjoint
eps_rel	relative accuracy of solution
nrmb_correction	absolute accuracy in units of eps_rel
max_iter	Maximum number of iterations in Lanczos tridiagonalization
cauchy_steps	number of cells in the Cauchy integral

Member Function Documentation

construct()

template<class ContainerType >

template<class ... Params>

void dg::mat::MatrixSqrt< ContainerType >::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

get_iter()

template<class ContainerType >

unsigned dg::mat::MatrixSqrt< ContainerType >::get_iter ( ) const

inline

Get the number of Lanczos iterations in latest call to operator()

operator()()

template<class ContainerType >

template<class ContainerType0 , class ContainerType1 >

void dg::mat::MatrixSqrt< ContainerType >::operator() ( const ContainerType0 b, ContainerType1 & x )

inline

Apply matrix sqrt.

Parameters

b	input vector
x	output vector, contains \( x = A^{\pm 1/2} \vec b\)

set_benchmark()

template<class ContainerType >

void dg::mat::MatrixSqrt< ContainerType >::set_benchmark ( bool benchmark, std::string message = "SQRT" )

inline

Set or unset performance timings during iterations.

Parameters

benchmark	If true, additional output will be written to std::cout during solution
message	An optional identifier that is printed together with the benchmark (intended use is to distinguish different messages in the output)

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

• matrixsqrt.h