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

Computation of \( \vec x = f(A)\vec b\) for self-adjoint positive definite \( A\). More...

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

Public Member Functions
	MatrixFunction ()=default
	Construct empty. More...
template<class MatrixType >
	MatrixFunction (MatrixType &A, const ContainerType &weights, value_type eps_rel, value_type nrmb_correction=1., unsigned max_iter=500, std::function< value_type(value_type)> f_inner=[](value_type x){return x;})
	Construct from matrix. More...
template<class ... Params>
void	construct (Params &&...ps)
	Perfect forward parameters to one of the constructors. More...
unsigned	get_iter () const
	Get the number of Lanczos iterations in latest call to operator() More...
void	set_benchmark (bool benchmark, std::string message="Function")
	Set or unset performance timings during iterations. More...
template<class UnaryOp , class ContainerType0 , class ContainerType1 >
void	operator() (UnaryOp f_outer, const ContainerType0 b, ContainerType1 &x)
	Apply matrix function. More...

Detailed Description

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

Computation of \( \vec x = f(A)\vec b\) for self-adjoint positive definite \( A\).

where \( f(x) = f_{outer}(f_{inner}(x))\) is composed of an inner pre-factor function \(f_{inner}(x)\) and an outer \( f_{outer}(x)\) function. The rational for this design choice is maintain flexibility when using this class in one of our exponential integrators where the outer function is set by the time integrator itself while \( f_{inner}\) can be set by the user. Outside the exponential time integrator \( f_{inner}\) has no use and left as the default identity.

The class is a convenience wrapper that uses dg::mat::UniversalLanczos combined with dg::mat::make_FuncEigen_Te1( f) in its "universal" stopping criterion

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::MatrixFunction< ContainerType >::container_type = ContainerType

value_type

template<class ContainerType >

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

Constructor & Destructor Documentation

MatrixFunction() [1/2]

template<class ContainerType >

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

default

Construct empty.

MatrixFunction() [2/2]

template<class ContainerType >

template<class MatrixType >

dg::mat::MatrixFunction< ContainerType >::MatrixFunction ( MatrixType &  A, const ContainerType &  weights, value_type  eps_rel, value_type  nrmb_correction = 1., unsigned  max_iter = 500, std::function< value_type(value_type)>  f_inner = [](value_type x){return x;}  )

inline

Construct from matrix.

Template Parameters

MatrixType

Parameters

A	self-adjoint matrix; is stored by reference
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
f_inner	the inner "pre-factor" function (useful only in connection with a exponential integrator where f_outer is set by the integrator)

Member Function Documentation

construct()

template<class ContainerType >

template<class ... Params>

void dg::mat::MatrixFunction< 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::MatrixFunction< ContainerType >::get_iter ( ) const

inline

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

operator()()

template<class ContainerType >

template<class UnaryOp , class ContainerType0 , class ContainerType1 >

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

inline

Apply matrix function.

Parameters

f_outer	Matrix function to apply together with f_inner from constructor
b	input vector
x	output vector, contains \( x = f(A) \vec b\)

set_benchmark()

template<class ContainerType >

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

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