SVD Class Reference

#include <svd.h>

List of all members.

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Detailed Description

The SVD class performs singular value decomposition on TNT matricies.

It can also solve systems of linear equations using the SVD method. In doing so it eliminates small singular values to improve matrix conditioning.

Todo:

Perhaps the SVD class could keep a local copy of the decomposition for the last matrix decomposed and repeatedly use it in a solver function which only passes the vector to be solved for.

Definition at line 40 of file svd.h.

Public Member Functions
	SVD (int l=CONVERGE_LIMIT)
	Constructor.
bool	compute (TNT::Matrix< double > &A, TNT::Vector< double > &W, TNT::Matrix< double > &V)
	Computes SVD using TNT Matrices.
void	solve (TNT::Matrix< double > &U, TNT::Vector< double > &W, TNT::Matrix< double > &V, TNT::Vector< double > b, TNT::Vector< double > &x)
	Solves a system of equations using SVD components.
bool	solve (TNT::Matrix< double > A, TNT::Vector< double > &x, TNT::Vector< double > b)
	Solves a system of equations.
Private Member Functions
double	pythag (double a, double b)
	Computes sqrt(a^2 + b^2 ).
void	condition (TNT::Vector< double > &w)
	Fixes ill-conditioning by removing small singular values.
Private Attributes
int	limit
	Maximum number of iterations for convergance.

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Constructor & Destructor Documentation

SVD::SVD (  int  l = CONVERGE_LIMIT  )  [inline]

Constructor. Parameters: l  Iteration limit for convergance. Definition at line 58 of file svd.h. References limit.

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Member Function Documentation

bool SVD::compute (  TNT::Matrix< double > &  a, TNT::Vector< double > &  w, TNT::Matrix< double > &  v )

Computes SVD using TNT Matrices. Parameters: a  Matrix to decompose (replaced by orthogonal matrix U). w  Vector of singular values (actually a diagonal matrix). v  Orthogonal matrix V. Note: Orthogonal matrix U is returned in a! Returns: False if convergance fails. Definition at line 93 of file svd.cpp. References FMAX, IMIN, limit, pythag(), and SIGN. Referenced by solve().

void SVD::condition (  TNT::Vector< double > &  w  )  [private]

Fixes ill-conditioning by removing small singular values. Parameters: w  Singular value vector to be conditioned. Definition at line 33 of file svd.cpp. Referenced by solve().

double SVD::pythag (  double  a, double  b )  [private]

Computes sqrt(a^2 + b^2 ). No destructive underflow or overflow. Definition at line 16 of file svd.cpp. References SQR. Referenced by compute().

bool SVD::solve (  TNT::Matrix< double >  A, TNT::Vector< double > &  x, TNT::Vector< double >  b )

Solves a system of equations. Parameters: A  Matrix of coefficients. x  Vector of variables. b  Solution vector. Returns: False if SVD did not converge, true otherwise Definition at line 323 of file svd.cpp. References compute(), condition(), and solve().

void SVD::solve (  TNT::Matrix< double > &  u, TNT::Vector< double > &  w, TNT::Matrix< double > &  v, TNT::Vector< double >  b, TNT::Vector< double > &  x )

Solves a system of equations using SVD components. Parameters: u  Orthogonal SVD matrix U. w  Singular value vector W. v  Orthogonal SVD matrix V. b  Solution vector. x  Variable vector. Definition at line 287 of file svd.cpp. Referenced by SurfacePropagation::applyConstraint(), Implicit::interpolate(), and solve().

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Member Data Documentation

int SVD::limit [private]

Maximum number of iterations for convergance. Definition at line 44 of file svd.h. Referenced by compute(), and SVD().

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

• svd.h
• svd.cpp

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