openvdb::OPENVDB_VERSION_NAME::math::pcg Namespace Reference

Namespaces
	internal

Classes
class	Vector
	Lightweight, variable-length vector. More...
class	SparseStencilMatrix
	Sparse, square matrix representing a 3D stencil operator of size STENCIL_SIZE. More...
class	Preconditioner
	Base class for conjugate gradient preconditioners. More...
class	JacobiPreconditioner
	Diagonal preconditioner. More...
class	IncompleteCholeskyPreconditioner
	Preconditioner using incomplete Cholesky factorization. More...
struct	State
	Information about the state of a conjugate gradient solution. More...

Typedefs
using	SizeType = Index32
using	SizeRange = tbb::blocked_range< SizeType >
using	VectorS = Vector< float >
using	VectorD = Vector< double >

Functions
template<typename ValueType >
State	terminationDefaults ()
	Return default termination conditions for a conjugate gradient solver. More...
template<typename PositiveDefMatrix >
State	solve (const PositiveDefMatrix &A, const Vector< typename PositiveDefMatrix::ValueType > &b, Vector< typename PositiveDefMatrix::ValueType > &x, Preconditioner< typename PositiveDefMatrix::ValueType > &preconditioner, const State &termination=terminationDefaults< typename PositiveDefMatrix::ValueType >())
	Solve Ax = b via the preconditioned conjugate gradient method. More...
template<typename PositiveDefMatrix , typename Interrupter >
State	solve (const PositiveDefMatrix &A, const Vector< typename PositiveDefMatrix::ValueType > &b, Vector< typename PositiveDefMatrix::ValueType > &x, Preconditioner< typename PositiveDefMatrix::ValueType > &preconditioner, Interrupter &interrupter, const State &termination=terminationDefaults< typename PositiveDefMatrix::ValueType >())
	Solve Ax = b via the preconditioned conjugate gradient method. More...
std::ostream &	operator<< (std::ostream &os, const State &state)

Typedef Documentation

using openvdb::OPENVDB_VERSION_NAME::math::pcg::SizeRange = typedef tbb::blocked_range<SizeType>

Definition at line 35 of file ConjGradient.h.

using openvdb::OPENVDB_VERSION_NAME::math::pcg::SizeType = typedef Index32

Definition at line 33 of file ConjGradient.h.

using openvdb::OPENVDB_VERSION_NAME::math::pcg::VectorD = typedef Vector<double>

Definition at line 228 of file ConjGradient.h.

using openvdb::OPENVDB_VERSION_NAME::math::pcg::VectorS = typedef Vector<float>

Definition at line 227 of file ConjGradient.h.

Function Documentation

std::ostream& openvdb::OPENVDB_VERSION_NAME::math::pcg::operator<< ( std::ostream &  os, const State &  state  )

inline

Definition at line 545 of file ConjGradient.h.

template<typename PositiveDefMatrix >

State openvdb::OPENVDB_VERSION_NAME::math::pcg::solve ( const PositiveDefMatrix &  A, const Vector< typename PositiveDefMatrix::ValueType > &  b, Vector< typename PositiveDefMatrix::ValueType > &  x, Preconditioner< typename PositiveDefMatrix::ValueType > &  preconditioner, const State &  termination = terminationDefaults<typename PositiveDefMatrix::ValueType>()  )

inline

Solve Ax = b via the preconditioned conjugate gradient method.

Parameters

A	a symmetric, positive-definite, N x N matrix
b	a vector of size N
x	a vector of size N
preconditioner	a Preconditioner matrix
termination	termination conditions given as a State object with the following fields: success ignored iterations the maximum number of iterations, with or without convergence relativeError the relative error ||b − Ax|| / ||b|| that denotes convergence absoluteError the absolute error ||b − Ax|| that denotes convergence

Exceptions

ArithmeticError

if either x or b is not of the appropriate size.

Definition at line 1608 of file ConjGradient.h.

template<typename PositiveDefMatrix , typename Interrupter >

State openvdb::OPENVDB_VERSION_NAME::math::pcg::solve ( const PositiveDefMatrix &  A, const Vector< typename PositiveDefMatrix::ValueType > &  b, Vector< typename PositiveDefMatrix::ValueType > &  x, Preconditioner< typename PositiveDefMatrix::ValueType > &  preconditioner, Interrupter &  interrupter, const State &  termination = terminationDefaults<typename PositiveDefMatrix::ValueType>()  )

inline

Solve Ax = b via the preconditioned conjugate gradient method.

Parameters

A	a symmetric, positive-definite, N x N matrix
b	a vector of size N
x	a vector of size N
preconditioner	a Preconditioner matrix
termination	termination conditions given as a State object with the following fields: success ignored iterations the maximum number of iterations, with or without convergence relativeError the relative error ||b − Ax|| / ||b|| that denotes convergence absoluteError the absolute error ||b − Ax|| that denotes convergence
interrupter	an object adhering to the util::NullInterrupter interface with which computation can be interrupted

Exceptions

ArithmeticError	if either x or b is not of the appropriate size.
RuntimeError	if the computation is interrupted.

Definition at line 1622 of file ConjGradient.h.

template<typename ValueType >

State openvdb::OPENVDB_VERSION_NAME::math::pcg::terminationDefaults ( )

inline

Return default termination conditions for a conjugate gradient solver.

Definition at line 57 of file ConjGradient.h.