Classes
class	vcg::ndim::Matrix< TYPE >
class	vcg::ndim::MatrixDiag< N, S >
class	vcg::ndim::MatrixDiagBase
Typedefs
typedef vcg::ndim::Matrix< double >	vcg::ndim::MatrixMNd
typedef vcg::ndim::Matrix< float >	vcg::ndim::MatrixMNf
Enumerations
enum	vcg::SortingStrategy { vcg::LeaveUnsorted = 0, vcg::SortAscending = 1, vcg::SortDescending = 2 }
Functions
template<typename MATRIX_TYPE , typename POINT_TYPE >
static void	vcg::Jacobi (MATRIX_TYPE &w, POINT_TYPE &d, MATRIX_TYPE &v, int &nrot)
template<typename MATRIX_TYPE >
static void	vcg::JacobiRotate (MATRIX_TYPE &A, typename MATRIX_TYPE::ScalarType s, typename MATRIX_TYPE::ScalarType tau, int i, int j, int k, int l)
template<typename TYPE >
static TYPE	vcg::pythagora (TYPE a, TYPE b)
template<class S >
void	vcg::RotationalPartByPolarDecomposition (const vcg::Matrix33< S > &m, vcg::Matrix33< S > &r)
template<typename TYPE >
static TYPE	vcg::sign (TYPE a, TYPE b)
template<typename MATRIX_TYPE >
static void	vcg::SingularValueBacksubstitution (const MATRIX_TYPE &U, const typename MATRIX_TYPE::ScalarType W, const MATRIX_TYPE &V, typename MATRIX_TYPE::ScalarType x, const typename MATRIX_TYPE::ScalarType *b)
template<typename MATRIX_TYPE >
static bool	vcg::SingularValueDecomposition (MATRIX_TYPE &A, typename MATRIX_TYPE::ScalarType *W, MATRIX_TYPE &V, const SortingStrategy sorting=LeaveUnsorted, const int max_iters=30)
template<typename MATRIX_TYPE >
void	vcg::Sort (MATRIX_TYPE &U, typename MATRIX_TYPE::ScalarType W[], MATRIX_TYPE &V, const SortingStrategy sorting)
template<typename MATRIX_TYPE , typename POINT_TYPE >
void	vcg::SortEigenvaluesAndEigenvectors (POINT_TYPE &eigenvalues, MATRIX_TYPE &eigenvectors, bool absComparison=false)
template<typename TYPE >
static TYPE	vcg::sqr (TYPE a)

Typedef Documentation

typedef vcg::ndim::Matrix<double> vcg::ndim::MatrixMNd

Definition at line 761 of file old_deprecated_matrix.h.

typedef vcg::ndim::Matrix<float> vcg::ndim::MatrixMNf

Definition at line 762 of file old_deprecated_matrix.h.

Enumeration Type Documentation

enum vcg::SortingStrategy

Enumerator:

LeaveUnsorted
SortAscending
SortDescending

Definition at line 251 of file old_lin_algebra.h.

Function Documentation

template<typename MATRIX_TYPE , typename POINT_TYPE >

static void vcg::Jacobi	(	MATRIX_TYPE &	w,
		POINT_TYPE &	d,
		MATRIX_TYPE &	v,
		int &	nrot
	)		`[static]`

Computes all eigenvalues and eigenvectors of a real symmetric matrix . On output, elements of the input matrix above the diagonal are destroyed.

Parameters:

d	returns the eigenvalues of a.
v	is a matrix whose columns contain, the normalized eigenvectors
nrot	returns the number of Jacobi rotations that were required.

Definition at line 83 of file old_lin_algebra.h.

template<typename MATRIX_TYPE >

static void vcg::JacobiRotate	(	MATRIX_TYPE &	A,
		typename MATRIX_TYPE::ScalarType	s,
		typename MATRIX_TYPE::ScalarType	tau,
		int	i,
		int	j,
		int	k,
		int	l
	)		`[static]`

Definition at line 67 of file old_lin_algebra.h.

template<typename TYPE >

static TYPE vcg::pythagora	(	TYPE	a,
		TYPE	b
	)		`[inline, static]`

Definition at line 232 of file old_lin_algebra.h.

template<class S >

void vcg::RotationalPartByPolarDecomposition	(	const vcg::Matrix33< S > &	m,
		vcg::Matrix33< S > &	r
	)

Extract the rotational part of a matrix by polar decomposition m = R*S. Polar decomposition is computed by taking r = m * sqrt(m^t*m)^{-1}

Definition at line 39 of file polar_decomposition.h.

template<typename TYPE >

static TYPE vcg::sign	(	TYPE	a,
		TYPE	b
	)		`[inline, static]`

Definition at line 243 of file old_lin_algebra.h.

template<typename MATRIX_TYPE >

static void vcg::SingularValueBacksubstitution	(	const MATRIX_TYPE &	U,
		const typename MATRIX_TYPE::ScalarType *	W,
		const MATRIX_TYPE &	V,
		typename MATRIX_TYPE::ScalarType *	x,
		const typename MATRIX_TYPE::ScalarType *	b
	)		`[static]`

Solves AxX = B for a vector X, where A is specified by the matrices U_mxn, W_nx1 and V_nxn as returned by SingularValueDecomposition. No input quantities are destroyed, so the routine may be called sequentially with different bxs.

Parameters:

x	is the output solution vector (x_nx1)
b	is the input right-hand side (b_nx1)

Definition at line 624 of file old_lin_algebra.h.

template<typename MATRIX_TYPE >

static bool vcg::SingularValueDecomposition	(	MATRIX_TYPE &	A,
		typename MATRIX_TYPE::ScalarType *	W,
		MATRIX_TYPE &	V,
		const SortingStrategy	sorting = `LeaveUnsorted`,
		const int	max_iters = `30`
	)		`[static]`

Given a matrix A_mxn, this routine computes its singular value decomposition, i.e. A=UxWxV^T. The matrix A will be destroyed! (This is the implementation described in Numerical Recipies).

Parameters:

A	the matrix to be decomposed
W	the diagonal matrix of singular values W, stored as a vector W[1...N]
V	the matrix V (not the transpose V^T)
max_iters	max iteration number (default = 30).

Returns:

Definition at line 267 of file old_lin_algebra.h.

template<typename MATRIX_TYPE >

void vcg::Sort	(	MATRIX_TYPE &	U,
		typename MATRIX_TYPE::ScalarType	W[],
		MATRIX_TYPE &	V,
		const SortingStrategy	sorting
	)

Sort the singular values computed by the SingularValueDecomposition procedure and modify the matrices U and V accordingly.

Definition at line 524 of file old_lin_algebra.h.

template<typename MATRIX_TYPE , typename POINT_TYPE >

void vcg::SortEigenvaluesAndEigenvectors	(	POINT_TYPE &	eigenvalues,
		MATRIX_TYPE &	eigenvectors,
		bool	absComparison = `false`
	)

Given the eigenvectors and the eigenvalues as output from JacobiRotate, sorts the eigenvalues into descending order, and rearranges the columns of v correspondinlgy.

Parameters:

eigenvalues
eigenvector	(in columns)
absComparison	sort according to the absolute values of the eigenvalues.

Definition at line 180 of file old_lin_algebra.h.

template<typename TYPE >

static TYPE vcg::sqr ( TYPE a ) [inline, static]

Definition at line 224 of file old_lin_algebra.h.

Classes

Typedefs

Enumerations

Functions

Typedef Documentation

Enumeration Type Documentation

Function Documentation