MathLin_SVD.hxx File Reference

#include <MathUtils_Types.hxx>
#include <MathUtils_Config.hxx>
#include <math_Recipes.hxx>
#include <MathUtils_Core.hxx>
#include <cmath>
#include <algorithm>

Data Structures
struct	MathLin::SVDResult
	Result for SVD decomposition. More...

Namespaces
namespace	MathLin

Functions
SVDResult	MathLin::SVD (const math_Matrix &theA, double theTolerance=1.0e-15)
	Singular Value Decomposition: A = U * diag(S) * V^T.
LinearResult	MathLin::SolveSVD (const math_Matrix &theA, const math_Vector &theB, double theTolerance=1.0e-6)
	Solve linear system Ax = b using SVD decomposition. This is particularly useful for ill-conditioned or singular systems.
InverseResult	MathLin::PseudoInverse (const math_Matrix &theA, double theTolerance=1.0e-6)
	Compute pseudo-inverse (Moore-Penrose inverse) of matrix A. A^+ = V * diag(1/w) * U^T where singular values below threshold are set to 0.
double	MathLin::ConditionNumber (const math_Matrix &theA)
	Compute condition number of matrix using SVD. Condition number = sigma_max / sigma_min (ratio of largest to smallest singular value).
int	MathLin::NumericalRank (const math_Matrix &theA, double theTolerance=1.0e-15)
	Compute numerical rank of matrix using SVD. Rank is the number of singular values above the threshold.