Package org.robwork.sdurw_math

Class LinearAlgebra

java.lang.Object

org.robwork.sdurw_math.LinearAlgebra

public class LinearAlgebra
extends java.lang.Object

Collection of Linear Algebra functions

Constructor Summary

Constructors

Constructor	Description
LinearAlgebra()
LinearAlgebra(long cPtr, boolean cMemoryOwn)

Method Summary

Modifier and Type	Method	Description
static boolean	checkPenroseConditions(EigenMatrixXd A, EigenMatrixXd X, double prec)	Checks the penrose conditions
void	delete()
static pairEigenMatrixXComplex_d_EigenVectorXComplex_d	eigenDecomposition(SWIGTYPE_p_Eigen__MatrixT_double_Eigen__Dynamic_Eigen__Dynamic_t Am1)	Eigen decomposition of a matrix.
static pairEigenMatrixX_d_EigenVectorX_d	eigenDecompositionSymmetric(SWIGTYPE_p_Eigen__MatrixT_double_Eigen__Dynamic_Eigen__Dynamic_t Am1)	Decomposition for a symmetric matrix.
static long	getCPtr(LinearAlgebra obj)
static boolean	isSO(EigenMatrix3d var)
static EigenMatrixXd	pseudoInverse(EigenMatrixXd am)	Calculates the moore-penrose (pseudo) inverse of a matrix \mathbf{M}^+
static EigenMatrixXd	pseudoInverse(EigenMatrixXd am, double precision)	Calculates the moore-penrose (pseudo) inverse of a matrix \mathbf{M}^+
static void	svd(EigenMatrixXd M, EigenMatrixXd U, EigenVectorXd sigma, EigenMatrixXd V)	Performs a singular value decomposition (SVD) The SVD computes the decomposition \mathbf{M}=\mathbf{U}*\mathbf{DiagonalMatrix(\sigma)}*\mathbf{V}^T .

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

LinearAlgebra

public LinearAlgebra(long cPtr,
                     boolean cMemoryOwn)

LinearAlgebra

public LinearAlgebra()

Method Detail

getCPtr

public static long getCPtr(LinearAlgebra obj)

delete

public void delete()

svd

public static void svd(EigenMatrixXd M,
                       EigenMatrixXd U,
                       EigenVectorXd sigma,
                       EigenMatrixXd V)

Performs a singular value decomposition (SVD)

The SVD computes the decomposition
\mathbf{M}=\mathbf{U}*\mathbf{DiagonalMatrix(\sigma)}*\mathbf{V}^T .

Parameters:

M - [in] the matrix to decomposite

U - [out] Result matrix \mathbf{U}

sigma - [out] The \mathbf{sigma} vector with diagonal elements

V - [out] Result matrix \mathbf{V}

pseudoInverse

public static EigenMatrixXd pseudoInverse(EigenMatrixXd am,
                                          double precision)

Calculates the moore-penrose (pseudo) inverse of a matrix
\mathbf{M}^+

Parameters:

am - [in] the matrix \mathbf{M} to be inverted

precision - [in] the precision to use, values below this
treshold are considered singular

Returns:

the pseudo-inverse \mathbf{M}^+ of \mathbf{M}

\mathbf{M}^+=\mathbf{V}\mathbf{\Sigma} ^+\mathbf{U}^T where
\mathbf{V} , \mathbf{\Sigma} and \mathbf{U}
are optained using Singular Value Decomposition (SVD)

pseudoInverse

public static EigenMatrixXd pseudoInverse(EigenMatrixXd am)

Calculates the moore-penrose (pseudo) inverse of a matrix
\mathbf{M}^+

Parameters:

am - [in] the matrix \mathbf{M} to be inverted

Returns:

the pseudo-inverse \mathbf{M}^+ of \mathbf{M}

\mathbf{M}^+=\mathbf{V}\mathbf{\Sigma} ^+\mathbf{U}^T where
\mathbf{V} , \mathbf{\Sigma} and \mathbf{U}
are optained using Singular Value Decomposition (SVD)

checkPenroseConditions

public static boolean checkPenroseConditions(EigenMatrixXd A,
                                             EigenMatrixXd X,
                                             double prec)

Checks the penrose conditions

Parameters:

A - [in] a matrix

X - [in] a pseudoinverse of A

prec - [in] the tolerance

Returns:

true if the pseudoinverse X of A fullfills the penrose
conditions, false otherwise

Checks the penrose conditions:

AXA = A

XAX = X

(AX)^T = AX

(XA)^T = XA

eigenDecompositionSymmetric

public static pairEigenMatrixX_d_EigenVectorX_d eigenDecompositionSymmetric(SWIGTYPE_p_Eigen__MatrixT_double_Eigen__Dynamic_Eigen__Dynamic_t Am1)

Decomposition for a symmetric matrix.

Parameters:

Am1 - [in] a symmetric matrix.

Returns:

the decomposition as a pair with eigenvectors and eigenvalues.

eigenDecomposition

public static pairEigenMatrixXComplex_d_EigenVectorXComplex_d eigenDecomposition(SWIGTYPE_p_Eigen__MatrixT_double_Eigen__Dynamic_Eigen__Dynamic_t Am1)

Eigen decomposition of a matrix.

Parameters:

Am1 - [in] the matrix.

Returns:

the decomposition as a pair with eigenvectors and eigenvalues.

isSO

public static boolean isSO(EigenMatrix3d var)