dg::mat::MCGFuncEigen< Container > Class Template Reference

EXPERIMENTAL Shortcut for \(x \approx f(A) b \) solve via exploiting first a Krylov projection achieved by the M-CG method and a matrix function computation via Eigen-decomposition. More...

Public Types
using	value_type = dg::get_value_type< Container >
using	HDiaMatrix = cusp::dia_matrix< int, value_type, cusp::host_memory >
using	HCooMatrix = cusp::coo_matrix< int, value_type, cusp::host_memory >
using	HArray2d = cusp::array2d< value_type, cusp::host_memory >
using	HArray1d = cusp::array1d< value_type, cusp::host_memory >
using	HVec = dg::HVec

Public Member Functions
	MCGFuncEigen ()
	Allocate nothing, Call construct method before usage. More...
	MCGFuncEigen (const Container &copyable, unsigned max_iterations)
	Construct MCGFuncEigen. More...
template<class ... Params>
void	construct (Params &&...ps)
	Perfect forward parameters to one of the constructors. More...
template<class MatrixType , class ContainerType0 , class ContainerType1 , class ContainerType2 , class UnaryOp >
unsigned	operator() (ContainerType0 &x, UnaryOp f, MatrixType &&A, const ContainerType1 &b, const ContainerType2 &weights, value_type eps, value_type nrmb_correction, value_type res_fac)
	Compute \(x \approx f(A)*b \) via M-CG method and Eigen decomposition. More...

Detailed Description

template<class Container>
class dg::mat::MCGFuncEigen< Container >

EXPERIMENTAL Shortcut for \(x \approx f(A) b \) solve via exploiting first a Krylov projection achieved by the M-CG method and a matrix function computation via Eigen-decomposition.

Attention

This class has the exact same result as the corresponding UniversalLanczos class. Its use is for mere experimental purposes.

A is self-adjoint in the weights \( W\)

The approximation relies on Projection \(x = f(A) b \approx R f(\tilde T)^{-1} e_1\), where \(\tilde T\) and \(R\) are the tridiagonal and orthogonal matrix of the M-CG solve and \(e_1\) is the normalized unit vector. The vector \(f(\tilde T) e_1\) is computed via the Eigen decomposition and similarity transform of \( \tilde T\).

Note

Since MCG and Lanczos are equivalent the result of this class is the same within round-off errors as a Lanczos solve with the "residual" error norm

Member Typedef Documentation

HArray1d

template<class Container >

using dg::mat::MCGFuncEigen< Container >::HArray1d = cusp::array1d< value_type, cusp::host_memory>

HArray2d

template<class Container >

using dg::mat::MCGFuncEigen< Container >::HArray2d = cusp::array2d< value_type, cusp::host_memory>

HCooMatrix

template<class Container >

using dg::mat::MCGFuncEigen< Container >::HCooMatrix = cusp::coo_matrix<int, value_type, cusp::host_memory>

HDiaMatrix

template<class Container >

using dg::mat::MCGFuncEigen< Container >::HDiaMatrix = cusp::dia_matrix<int, value_type, cusp::host_memory>

HVec

template<class Container >

using dg::mat::MCGFuncEigen< Container >::HVec = dg::HVec

value_type

template<class Container >

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

Constructor & Destructor Documentation

MCGFuncEigen() [1/2]

template<class Container >

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

inline

Allocate nothing, Call construct method before usage.

MCGFuncEigen() [2/2]

template<class Container >

dg::mat::MCGFuncEigen< Container >::MCGFuncEigen ( const Container &  copyable, unsigned  max_iterations  )

inline

Construct MCGFuncEigen.

Parameters

copyable	a copyable container
max_iterations	Max iterations of Lanczos method

Member Function Documentation

construct()

template<class Container >

template<class ... Params>

void dg::mat::MCGFuncEigen< 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 >

template<class MatrixType , class ContainerType0 , class ContainerType1 , class ContainerType2 , class UnaryOp >

unsigned dg::mat::MCGFuncEigen< Container >::operator() ( ContainerType0 &  x, UnaryOp  f, MatrixType &&  A, const ContainerType1 &  b, const ContainerType2 &  weights, value_type  eps, value_type  nrmb_correction, value_type  res_fac  )

inline

Compute \(x \approx f(A)*b \) via M-CG method and Eigen decomposition.

Parameters

b	input vector
x	output vector
f	the matrix function (e.g. dg::SQRT<double> or dg::EXP<double>)
A	self-adjoint and semi-positive definit matrix
weights	weights
eps	relative accuracy of M-CG method
nrmb_correction	the absolute error C in units of eps to be respected
res_fac	residual factor for stopping criterium of M-CG method

Returns

number of iterations of M-CG routine

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

• mcg.h