LSMG: LSsystem Class Reference

List of all members.


Public Member Functions
	LSsystem (boost::shared_ptr< std::vector< double > > U, boost::shared_ptr< std::vector< double > > V, boost::shared_ptr< std::vector< double > > Zvals, int noX, int noY, boost::shared_ptr< GenMatrix< UCBspl_real > > PHI, double smoothingFac=1.0)
void	setWeights (boost::shared_ptr< std::map< int, double, std::less< int > > > weights)
void	buildEqSystem (bool buildRHS=true)
void	relaxGaussSeidel (int noIterations)
void	relaxCG (int noIterations)
void	relaxCGPrecond (int noIterations)
void	relaxJacobi (int noIterations, double omega=2./3.)
void	setDomain (double umin, double vmin, double umax, double vmax)
void	getDomain (double &umin, double &vmin, double &umax, double &vmax)
int	numberOfUnknowns () const
void	setSmoothingFactor (double smoothingFac)
bool	addPoint (double u, double v, double z, double weight=1.0, bool addToRHS=true)
double	currentSolutionNorm () const
double	residual_l2 (bool scaled=false) const
double	residual_linf () const
Static Public Member Functions
static double	rowMatVecMult (int row_no, const MatSparse &A, const GenMatrix< UCBspl_real > &x)
Friends
class	MGsystem

Detailed Description

LSsystem - The class takes a set of scattered data and produces a B-spline surface that approximates the scattered data. The approximation scheme is a least square fit with a thin plate spline smoothing term. A set of iterative equation solvers can be used to produce the set of B-spline coefficients.

No stopping criteria for the equation solvers are provided - the user control is only through the given number of iterations. Thus, we call it relaxation in the documentation. But the relaxation step may be repeated many times.

Note that the format of the scattered data and the solution vector is exactly the same as in the SINTEF MBA (Multilevel B-spline Approximation) Library. Thus, a good starting vector can be found by running MBA first. This is also necessary for surfaces with large coefficient grids (and unevenly distributed data), which otherwise will converge very slow.

This class can also be (and should be) considered as a relaxation step for the multigrid methods in class MGsystem. MGsystem contains a number of multigrid schemes which produces better results than LSsystem alone.

   LSsystem lssys(xArr, yArr, zArr, noX, noY, PHI);  // initialize with scattered data and initial solution vector
   lssys.buildEqSystem(); // Build the equation system
   lssys.relaxCG(noIterations); // Run the given number of iterations with conjugate gradients

Constructor & Destructor Documentation

LSsystem::LSsystem	(	boost::shared_ptr< std::vector< double > >	U,
		boost::shared_ptr< std::vector< double > >	V,
		boost::shared_ptr< std::vector< double > >	Zvals,
		int	noX,
		int	noY,
		boost::shared_ptr< GenMatrix< UCBspl_real > >	PHI,
		double	smoothingFac = `1.0`
	)

Constructor with (standard) shared pointers to scattered data

Parameters:

	U,:	x-values
	V,:	y-values
	Z,:	z-values
	noX,noY,:	Number of coefficients in each direction of the spline surface
	PHI,:	The spline coefficients
	smoothingFac,:	Smoothing factor; a weight that determines the smoothness of the surface. See LSsystem::setSmoothingFactor.

Member Function Documentation

void LSsystem::buildEqSystem ( bool buildRHS = true )

Builds the system matrix and the right hand side (uses solution vector given by constructor)

void LSsystem::relaxGaussSeidel ( int noIterations )

Gauss-Seidel relaxation

void LSsystem::relaxCG ( int noIterations )

Conjugate Gradient relaxation

void LSsystem::relaxCGPrecond ( int noIterations )

Conjugate Gradient relaxation with multigrid preconditioning

void LSsystem::relaxJacobi	(	int	noIterations,
		double	omega = `2./3.`
	)

Jacobi relaxation

void LSsystem::setDomain	(	double	umin,
		double	vmin,
		double	umax,
		double	vmax
	)

Set the domain over which the surface is to be defined. The default is the xy-range of the scattered data. If used, this must be done before creating the surface.

Note:: This function can only be used to expand the domain beyond the xy-range of the scattered data. It is the users responsibility to check that no scattered data falls outside the domain. (use std::min_element and std::max_element to find range of data for std::vector)

See also:: MGsystem::setDomain

void LSsystem::getDomain	(	double &	umin,
		double &	vmin,
		double &	umax,
		double &	vmax
	)

Get the domain over which the surface is defined

int LSsystem::numberOfUnknowns ( ) const [inline]

Number of unknowns in the equation system, i.e. B-spline coefficients.

void LSsystem::setSmoothingFactor ( double smoothingFac )

Adjust the thin plate spline energy. By default this value is 1.0. To get a surface that is smoother (but less accurate) than the default, a value grater than 1.0 should be given and vice versa. This will typically be done after relaxation has been run and one want a a surface that is smoother, or less smooth and more accurate, than obtained in from previous relaxation. Relaxation must then be run afterwards.

See also:: MGsystem::setSmoothingFactor

bool LSsystem::addPoint	(	double	u,
		double	v,
		double	z,
		double	weight = `1.0`,
		bool	addToRHS = `true`
	)

Add a point to the data set. This can be done after relaxation has been run as in the example above, but relaxation must be run again afterwards. A weight of importance different fro 1.0 can be given.

Return values:

bool false if (u,v) is outside the domain.

double LSsystem::currentSolutionNorm ( ) const

Calculate the l2 norm of the current solution (Frobenius)

double LSsystem::residual_l2 ( bool scaled = false ) const

The discrete l_2 norm of the residual ||b-Ax||_2 possibly scaled by area of grid cell

LSsystem Class Reference

Public Member Functions

Static Public Member Functions

Friends

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation