algebra Namespace Reference

Classes
class	iteration
class	w_sparseMat
	Write-mode sparse matrix. More...
class	r_sparseMat
	Read-mode square sparse matrix. More...

Typedefs
using	MatrixShape = std::vector< std::set< int > >

Enumerations
enum	algoStatus { UNDEFINED = -1 , CONVERGED = 0 , ITER_OVERFLOW = 1 , CANNOT_CONVERGE = 2 }

Functions
template<typename T >
T	sq (const T x)
template<typename T >
void	scaled (const T alpha, std::vector< T > &Y)
template<typename T >
void	p_direct (const std::vector< T > &X, const std::vector< T > &Y, std::vector< T > &Z)
template<typename T >
void	add (const std::vector< T > &X, std::vector< T > &Y)
template<typename T >
void	sub (const std::vector< T > &X, std::vector< T > &Y)
template<typename T >
void	scaled_add (const std::vector< T > &X, const T alpha, std::vector< T > &Y)
template<typename T >
void	mult (r_sparseMat &A, std::vector< T > const &X, std::vector< T > &Y)
template<typename T >
void	applyMask (const std::vector< int > &mask, std::vector< T > &X)
std::ostream &	operator<< (std::ostream &flux, r_sparseMat const &m)
template<typename T >
bool	check (std::vector< T > &v)
template<typename T >
T	dot (const std::vector< T > &X, const std::vector< T > &Y)
template<typename T >
T	norm (std::vector< T > &X)
template<typename T >
void	bicg (iteration< T > &iter, r_sparseMat &A, std::vector< T > &x, const std::vector< T > &rhs)
template<typename T >
void	bicg_dir (iteration< T > &iter, r_sparseMat &A, std::vector< T > &x, const std::vector< T > &rhs, const std::vector< T > &xd, const std::vector< int > &ld)
template<typename T >
T	bicg_dir (iteration< T > &iter, r_sparseMat &A, std::vector< T > &x, const std::vector< T > &rhs, const std::vector< int > &ld)
template<typename T >
void	cg (iteration< T > &iter, r_sparseMat &A, std::vector< T > &x, const std::vector< T > &rhs)
template<typename T >
void	cg_dir (iteration< T > &iter, r_sparseMat &A, std::vector< T > &x, const std::vector< T > &rhs, const std::vector< T > &xd, const std::vector< int > &ld)

Detailed Description

grab altogether sparse matrix, vector and dedicated functions, and various gradient conjugate algorithms

Typedef Documentation

MatrixShape

using algebra::MatrixShape = typedef std::vector<std::set<int> >

The shape of a sparse matrix is the set of valid indices. Specifically, the shape element at index i is the set of j indices such that (i, j) is a valid index pair for the matrix.

Enumeration Type Documentation

algoStatus

enum algebra::algoStatus

status of iterative algorithm UNDEFINED means no iteration done CONVERGED means algo succeeded after some iterations < MAXITER to achieve residu<TOL ITER_OVERFLOW means number of iterations has exceeded MAXITER CANNOT_CONVERGE means an algebric operation leads to nan (might happen while computing beta in bicg inner loop)

Function Documentation

add()

template<typename T >

void algebra::add	(	const std::vector< T > &	X,
		std::vector< T > &	Y
	)

Y += X

applyMask()

template<typename T >

void algebra::applyMask	(	const std::vector< int > &	mask,
		std::vector< T > &	X
	)

apply a mask to vector X : all coefficients in vector mask are zeroed in X

bicg()

template<typename T >

void algebra::bicg	(	iteration< T > &	iter,
		r_sparseMat &	A,
		std::vector< T > &	x,
		const std::vector< T > &	rhs
	)

solve A x = rhs. Algo is stabilized biconjugate gradient with diagonal preconditioner, vectors x and rhs must have the same size. The status of the convergence is returned in iter.status as well as total number of iterations and error

bicg_dir() [1/2]

template<typename T >

T algebra::bicg_dir	(	iteration< T > &	iter,
		r_sparseMat &	A,
		std::vector< T > &	x,
		const std::vector< T > &	rhs,
		const std::vector< int > &	ld
	)

directional stabilized biconjugate gradient (mask is ld) with diagonal preconditioner, returns residu iter is an iteration object the linear system to solve is A x = rhs ld is a mask: a list of indices that will be zeroed when using applyMask(ld, vector)

bicg_dir() [2/2]

template<typename T >

void algebra::bicg_dir	(	iteration< T > &	iter,
		r_sparseMat &	A,
		std::vector< T > &	x,
		const std::vector< T > &	rhs,
		const std::vector< T > &	xd,
		const std::vector< int > &	ld
	)

directional stabilized biconjugate gradient (mask) with diagonal preconditioner with Dirichlet conditions, returns residu iter is an iteration object the linear system to solve is A x = rhs ld is a mask: a list of indices that will be zeroed when using applyMask(ld, vector) xd is a vector containing some values on the nodes where Dirichlet applies

cg()

template<typename T >

void algebra::cg	(	iteration< T > &	iter,
		r_sparseMat &	A,
		std::vector< T > &	x,
		const std::vector< T > &	rhs
	)

solver for A x = rhs. Algo is conjugate gradient with diagonal preconditioner. vectors x and rhs must have the same size. The status of the convergence is returned in iter.status as well as total number of iterations and error

cg_dir()

template<typename T >

void algebra::cg_dir	(	iteration< T > &	iter,
		r_sparseMat &	A,
		std::vector< T > &	x,
		const std::vector< T > &	rhs,
		const std::vector< T > &	xd,
		const std::vector< int > &	ld
	)

solver for A x = rhs. Algo is conjugate gradient with diagonal preconditioner with Dirichlet conditions (through masking technique) vectors x and rhs must have the same size. ld is a vector of indices where to apply zeros, xd the corresponding values. The status of the convergence is returned in iter.status as well as total number of iterations and error

check()

template<typename T >

bool algebra::check

(

std::vector< T > &

v

)

return true if the given vector is free of NaNs

dot()

template<typename T >

T algebra::dot	(	const std::vector< T > &	X,
		const std::vector< T > &	Y
	)

returns scalar product X.Y

mult()

template<typename T >

void algebra::mult	(	r_sparseMat &	A,
		std::vector< T > const &	X,
		std::vector< T > &	Y
	)

Y = A*X with r_sparseMat A

norm()

template<typename T >

T algebra::norm

(

std::vector< T > &

X

)

euclidian norm of vector X

operator<<()

std::ostream& algebra::operator<< ( std::ostream &  flux, r_sparseMat const &  m  )

inline

operator<< for r_sparseMat

p_direct()

template<typename T >

void algebra::p_direct	(	const std::vector< T > &	X,
		const std::vector< T > &	Y,
		std::vector< T > &	Z
	)

direct product (component to component or Hadamard product)

scaled()

template<typename T >

void algebra::scaled	(	const T	alpha,
		std::vector< T > &	Y
	)

Y *= alpha

scaled_add()

template<typename T >

void algebra::scaled_add	(	const std::vector< T > &	X,
		const T	alpha,
		std::vector< T > &	Y
	)

Y += alpha*X

sq()

template<typename T >

T algebra::sq

(

const T

x

)

returns x²

sub()

template<typename T >

void algebra::sub	(	const std::vector< T > &	X,
		std::vector< T > &	Y
	)

Y -= X