openvdb::v12_1::math::pcg Namespace Reference

Namespaces
namespace	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.
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.
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.
std::ostream &	operator<< (std::ostream &os, const State &state)

Typedef Documentation

SizeRange

using SizeRange = tbb::blocked_range<SizeType>

SizeType

using SizeType = Index32

VectorD

using VectorD = Vector<double>

VectorS

using VectorS = Vector<float>

Function Documentation

operator<<()

std::ostream & operator<< ( std::ostream & os, const State & state )

inline

solve() [1/2]

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>() )

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.

solve() [2/2]

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>() )

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.

terminationDefaults()

template<typename ValueType>

State terminationDefaults ( )

inline

Return default termination conditions for a conjugate gradient solver.