Namespaces
	impl

Classes
class	FrameTransform

class	NormRand
	A static class grouping function for normal random number generator. More...

class	Quaternion

class	Rand
	A static class grouping function for uniform random number generator. More...

class	RandnScalar
	A random number generator, normal distribution. More...

class	RandScalar
	A random number generator, uniform in the range 0-1. More...

class	Vec2D

Functions
yarp::sig::Matrix	pile (const yarp::sig::Matrix &m1, const yarp::sig::Matrix &m2)
	Matrix-Matrix concatenation by column (defined in Math.h). More...

yarp::sig::Matrix	pile (const yarp::sig::Vector &v, const yarp::sig::Matrix &m)
	Vector-Matrix concatenation (defined in Math.h). More...

yarp::sig::Matrix	pile (const yarp::sig::Matrix &m, const yarp::sig::Vector &v)
	Matrix-Vector concatenation (defined in Math.h). More...

yarp::sig::Matrix	pile (const yarp::sig::Vector &v1, const yarp::sig::Vector &v2)
	Vector-Vector concatenation (defined in Math.h). More...

yarp::sig::Matrix	cat (const yarp::sig::Matrix &m1, const yarp::sig::Matrix &m2)
	Matrix-Matrix concatenation by row (defined in Math.h). More...

yarp::sig::Matrix	cat (const yarp::sig::Matrix &m, const yarp::sig::Vector &v)
	Matrix-Vector concatenation (defined in Math.h). More...

yarp::sig::Matrix	cat (const yarp::sig::Vector &v, const yarp::sig::Matrix &m)
	Vector-Matrix concatenation (defined in Math.h). More...

yarp::sig::Vector	cat (const yarp::sig::Vector &v1, const yarp::sig::Vector &v2)
	Vector-Vector concatenation (defined in Math.h). More...

yarp::sig::Vector	cat (const yarp::sig::Vector &v, double s)
	Vector-scalar concatenation (defined in Math.h). More...

yarp::sig::Vector	cat (double s, const yarp::sig::Vector &v)
	Scalar-vector concatenation (defined in Math.h). More...

yarp::sig::Vector	cat (double s1, double s2)
	Scalar-scalar concatenation (defined in Math.h). More...

yarp::sig::Vector	cat (double s1, double s2, double s3)

yarp::sig::Vector	cat (double s1, double s2, double s3, double s4)

yarp::sig::Vector	cat (double s1, double s2, double s3, double s4, double s5)

double	dot (const yarp::sig::Vector &a, const yarp::sig::Vector &b)
	Scalar product between vectors (defined in Math.h). More...

yarp::sig::Matrix	outerProduct (const yarp::sig::Vector &a, const yarp::sig::Vector &b)
	Outer product between vectors (defined in Math.h). More...

yarp::sig::Vector	cross (const yarp::sig::Vector &a, const yarp::sig::Vector &b)
	Compute the cross product between two vectors (defined in Math.h). More...

yarp::sig::Matrix	crossProductMatrix (const yarp::sig::Vector &v)
	Compute the cross product matrix, that is a 3-by-3 skew-symmetric matrix (defined in Math.h). More...

bool	crossProductMatrix (const yarp::sig::Vector &v, yarp::sig::Matrix &res)
	Compute the cross product matrix, that is a 3-by-3 skew-symmetric matrix (defined in Math.h). More...

double	norm (const yarp::sig::Vector &v)
	Returns the Euclidean norm of the vector (defined in Math.h). More...

double	norm2 (const yarp::sig::Vector &v)
	Returns the Euclidean squared norm of the vector (defined in Math.h). More...

double	findMax (const yarp::sig::Vector &v)
	Returns the maximum of the elements of a real vector (defined in Math.h). More...

double	findMin (const yarp::sig::Vector &v)
	Returns the minimum of the elements of a real vector (defined in Math.h). More...

yarp::sig::Vector	zeros (int s)
	Creates a vector of zeros (defined in Math.h). More...

yarp::sig::Vector	ones (int s)
	Creates a vector of ones (defined in Math.h). More...

yarp::sig::Matrix	eye (int r, int c)
	Build an identity matrix (defined in Math.h). More...

yarp::sig::Matrix	eye (int n)
	Build a square identity matrix (defined in Math.h). More...

yarp::sig::Matrix	zeros (int r, int c)
	Build a matrix of zeros (defined in Math.h). More...

double	det (const yarp::sig::Matrix &in)
	Computes the determinant of a matrix (defined in Math.h). More...

yarp::sig::Matrix	luinv (const yarp::sig::Matrix &in)
	Invert a square matrix using LU-decomposition (defined in Math.h). More...

bool	eigenValues (const yarp::sig::Matrix &in, yarp::sig::Vector &real, yarp::sig::Vector &img)
	Computes eigenvalues of the n-by-n real nonsymmetric matrix (defined in Math.h). More...

double	sign (const double &v)
	Invert a symmetric and positive definite matrix using Cholesky decomposition (defined in Math.h). More...

yarp::sig::Vector	sign (const yarp::sig::Vector &v)
	Returns the sign vector of a real vector, that is a vector with 1 if the value is positive, -1 if negative, 0 if equal to zero (defined in Math.h). More...

yarp::sig::Vector	dcm2axis (const yarp::sig::Matrix &R)
	Converts a dcm (direction cosine matrix) rotation matrix R to axis/angle representation (defined in Math.h). More...

yarp::sig::Matrix	axis2dcm (const yarp::sig::Vector &v)
	Returns a dcm (direction cosine matrix) rotation matrix R from axis/angle representation (defined in Math.h). More...

yarp::sig::Vector	dcm2euler (const yarp::sig::Matrix &R)
	Converts a dcm (direction cosine matrix) rotation matrix to euler angles (ZYZ) (defined in Math.h). More...

yarp::sig::Matrix	euler2dcm (const yarp::sig::Vector &euler)
	Converts euler angles (ZYZ) vector in the corresponding dcm (direction cosine matrix) rotation matrix (defined in Math.h). More...

yarp::sig::Vector	dcm2rpy (const yarp::sig::Matrix &R)
	Converts a dcm (direction cosine matrix) rotation matrix to roll-pitch-yaw angles (defined in Math.h). More...

yarp::sig::Matrix	rpy2dcm (const yarp::sig::Vector &rpy)
	Converts roll-pitch-yaw angles in the corresponding dcm (direction cosine matrix) rotation matrix (defined in Math.h). More...

yarp::sig::Vector	dcm2ypr (const yarp::sig::Matrix &R)
	Converts a dcm (direction cosine matrix) rotation matrix to yaw-roll-pitch angles (defined in Math.h). More...

yarp::sig::Matrix	ypr2dcm (const yarp::sig::Vector &ypr)
	Converts yaw-pitch-roll angles in the corresponding dcm (direction cosine matrix) rotation matrix (defined in Math.h). More...

yarp::sig::Matrix	SE3inv (const yarp::sig::Matrix &H)
	Returns the inverse of a 4 by 4 rototranslational matrix (defined in Math.h). More...

yarp::sig::Matrix	adjoint (const yarp::sig::Matrix &H)
	Returns the adjoint matrix of a given roto-translational matrix (defined in Math.h). More...

yarp::sig::Matrix	adjointInv (const yarp::sig::Matrix &H)
	Returns the inverse of the adjoint matrix of a given roto-translational matrix (defined in Math.h). More...

void	SVD (const yarp::sig::Matrix &in, yarp::sig::Matrix &U, yarp::sig::Vector &S, yarp::sig::Matrix &V)
	Factorize the M-by-N matrix 'in' into the singular value decomposition in = U S V^T (defined in SVD.h). More...

void	SVDMod (const yarp::sig::Matrix &in, yarp::sig::Matrix &U, yarp::sig::Vector &S, yarp::sig::Matrix &V)
	Perform SVD decomposition on a MxN matrix (for M >= N) (defined in SVD.h). More...

void	SVDJacobi (const yarp::sig::Matrix &in, yarp::sig::Matrix &U, yarp::sig::Vector &S, yarp::sig::Matrix &V)
	Perform SVD decomposition on a matrix using the Jacobi method (defined in SVD.h). More...

yarp::sig::Matrix	pinv (const yarp::sig::Matrix &in, double tol=0.0)
	Perform the moore-penrose pseudo-inverse of a matrix (defined in SVD.h). More...

void	pinv (const yarp::sig::Matrix &in, yarp::sig::Matrix &out, double tol=0.0)
	Perform the moore-penrose pseudo-inverse of a matrix (defined in SVD.h). More...

yarp::sig::Matrix	pinv (const yarp::sig::Matrix &in, yarp::sig::Vector &sv, double tol=0.0)
	Perform the moore-penrose pseudo-inverse of a matrix (defined in SVD.h). More...

void	pinv (const yarp::sig::Matrix &in, yarp::sig::Matrix &out, yarp::sig::Vector &sv, double tol=0.0)
	Perform the moore-penrose pseudo-inverse of a matrix (defined in SVD.h). More...

yarp::sig::Matrix	pinvDamped (const yarp::sig::Matrix &in, yarp::sig::Vector &sv, double damp)
	Perform the damped pseudo-inverse of a matrix (defined in SVD.h). More...

yarp::sig::Matrix	pinvDamped (const yarp::sig::Matrix &in, double damp)
	Perform the damped pseudo-inverse of a matrix (defined in SVD.h). More...

void	pinvDamped (const yarp::sig::Matrix &in, yarp::sig::Matrix &out, double damp)
	Perform the damped pseudo-inverse of a matrix (defined in SVD.h). More...

void	pinvDamped (const yarp::sig::Matrix &in, yarp::sig::Matrix &out, yarp::sig::Vector &sv, double damp)
	Perform the damped pseudo-inverse of a matrix (defined in SVD.h). More...

yarp::sig::Matrix	projectionMatrix (const yarp::sig::Matrix &A, double tol=0.0)
	Compute the projection matrix of A, that is defined as A times its pseudoinverse: A*pinv(A) (defined in SVD.h). More...

void	projectionMatrix (const yarp::sig::Matrix &A, yarp::sig::Matrix &out, double tol=0.0)
	Compute the projection matrix of A, that is defined as A times its pseudoinverse: A*pinv(A) (defined in SVD.h). More...

yarp::sig::Matrix	nullspaceProjection (const yarp::sig::Matrix &A, double tol=0.0)
	Compute the nullspace projection matrix of A, that is defined as the difference between the identity matrix and the pseudoinverse of A times A: (I - pinv(A)*A) (defined in SVD.h). More...

void	nullspaceProjection (const yarp::sig::Matrix &A, yarp::sig::Matrix &out, double tol=0.0)
	Compute the nullspace projection matrix of A, that is defined as the difference between the identity matrix and the pseudoinverse of A times A: (I - pinv(A)*A) (defined in SVD.h). More...

Function Documentation

◆ adjoint()

Matrix yarp::math::adjoint ( const yarp::sig::Matrix & H )

Returns the adjoint matrix of a given roto-translational matrix (defined in Math.h).

The adjoint is a (6x6) matrix: [R , S(r)*R; 0, R] where R is the rotational part of H, and r the translational part.

Parameters

H	is the 4 by 4 rototranslational matrix.

Returns: the adjoint matrix

Definition at line 904 of file math.cpp.

◆ adjointInv()

Matrix yarp::math::adjointInv ( const yarp::sig::Matrix & H )

Returns the inverse of the adjoint matrix of a given roto-translational matrix (defined in Math.h).

The inverse of an adjoint is a (6x6) matrix: [R^T , -S(R^T*r)*R^T; 0 , R^T] where R is the rotational part of H, and r the translational part.

Parameters

H	is the 4 by 4 rototranslational matrix.

Returns: the inverse of the adjoint matrix

Definition at line 930 of file math.cpp.

◆ axis2dcm()

Matrix yarp::math::axis2dcm ( const yarp::sig::Vector & v )

Returns a dcm (direction cosine matrix) rotation matrix R from axis/angle representation (defined in Math.h).

Parameters

v	is the axis/angle vector.

Returns: 4 by 4 homogeneous matrix with the rotation components in the top left 3 by 3 submatrix.

Definition at line 689 of file math.cpp.

◆ cat() [1/10]

Matrix yarp::math::cat	(	const yarp::sig::Matrix &	m,
		const yarp::sig::Vector &	v
	)

Matrix-Vector concatenation (defined in Math.h).

Add a column at the end of a matrix.

Parameters

m	a matrix nXm
v	a vector n

Returns: a matrix nX(m+1)

Definition at line 363 of file math.cpp.

◆ cat() [2/10]

Matrix yarp::math::cat	(	const yarp::sig::Matrix &	m1,
		const yarp::sig::Matrix &	m2
	)

Matrix-Matrix concatenation by row (defined in Math.h).

Parameters

m1	a matrix nXm
m2	a matrix nXr

Returns: a matrix nX(m+r)

Definition at line 349 of file math.cpp.

◆ cat() [3/10]

Matrix yarp::math::cat	(	const yarp::sig::Vector &	v,
		const yarp::sig::Matrix &	m
	)

Vector-Matrix concatenation (defined in Math.h).

Add a column at the beginning of a matrix.

Parameters

m	a matrix nXm
v	a vector n

Returns: a matrix nX(m+1)

Definition at line 376 of file math.cpp.

◆ cat() [4/10]

Vector yarp::math::cat	(	const yarp::sig::Vector &	v,
		double	s
	)

Vector-scalar concatenation (defined in Math.h).

Create a vector by putting the scalar at the end of the vector.

Parameters

v	an n-vector
s	a scalar

Returns: a (n+1)-vector

Definition at line 401 of file math.cpp.

◆ cat() [5/10]

Vector yarp::math::cat	(	const yarp::sig::Vector &	v1,
		const yarp::sig::Vector &	v2
	)

Vector-Vector concatenation (defined in Math.h).

Create a vector by putting two vectors side by side.

Parameters

v1	an n-vector
v2	an m-vector

Returns: a (n+m)-vector

Definition at line 389 of file math.cpp.

◆ cat() [6/10]

Vector yarp::math::cat	(	double	s,
		const yarp::sig::Vector &	v
	)

Scalar-vector concatenation (defined in Math.h).

Create a vector by putting the scalar at the beginning of the vector.

Parameters

s	a scalar
v	an n-vector

Returns: a (n+1)-vector

Definition at line 412 of file math.cpp.

◆ cat() [7/10]

Vector yarp::math::cat	(	double	s1,
		double	s2
	)

Scalar-scalar concatenation (defined in Math.h).

Create a vector containing the two specified scalar values.

Parameters

s1	a scalar
s2	a scalar

Returns: a 2-vector

Definition at line 423 of file math.cpp.

◆ cat() [8/10]

Vector yarp::math::cat	(	double	s1,
		double	s2,
		double	s3
	)

Definition at line 431 of file math.cpp.

◆ cat() [9/10]

Vector yarp::math::cat	(	double	s1,
		double	s2,
		double	s3,
		double	s4
	)

Definition at line 440 of file math.cpp.

◆ cat() [10/10]

Vector yarp::math::cat	(	double	s1,
		double	s2,
		double	s3,
		double	s4,
		double	s5
	)

Definition at line 450 of file math.cpp.

◆ cross()

Vector yarp::math::cross	(	const yarp::sig::Vector &	a,
		const yarp::sig::Vector &	b
	)

Compute the cross product between two vectors (defined in Math.h).

Parameters

a	first input vector
b	second input vector

Returns: axb

Definition at line 480 of file math.cpp.

◆ crossProductMatrix() [1/2]

Matrix yarp::math::crossProductMatrix ( const yarp::sig::Vector & v )

Compute the cross product matrix, that is a 3-by-3 skew-symmetric matrix (defined in Math.h).

Parameters

v	the vector

Returns: the cross product matrix

Definition at line 491 of file math.cpp.

◆ crossProductMatrix() [2/2]

bool yarp::math::crossProductMatrix	(	const yarp::sig::Vector &	v,
		yarp::sig::Matrix &	res
	)

Compute the cross product matrix, that is a 3-by-3 skew-symmetric matrix (defined in Math.h).

Parameters

v	the vector
res	the cross product matrix

Returns: true if operation succeeded, false otherwise

Definition at line 504 of file math.cpp.

◆ dcm2axis()

Vector yarp::math::dcm2axis ( const yarp::sig::Matrix & R )

Converts a dcm (direction cosine matrix) rotation matrix R to axis/angle representation (defined in Math.h).

Parameters

R	is the input matrix.

Returns: 4 by 1 vector for the axis/angle representation.

Definition at line 647 of file math.cpp.

◆ dcm2euler()

Vector yarp::math::dcm2euler ( const yarp::sig::Matrix & R )

Converts a dcm (direction cosine matrix) rotation matrix to euler angles (ZYZ) (defined in Math.h).

Three angles are returned in a vector with the following format:

$\mathbf{v} = [\alpha, \beta, \gamma ]$

such that the returned matrix satisfies the following:

$R = R_z(\alpha) R_y(\beta) R_z(\gamma)$

Parameters

R	is the input ZYZ rotation matrix.

Returns: 3 by 1 vector for the Euler angles representation.

Definition at line 726 of file math.cpp.

◆ dcm2rpy()

Vector yarp::math::dcm2rpy ( const yarp::sig::Matrix & R )

Converts a dcm (direction cosine matrix) rotation matrix to roll-pitch-yaw angles (defined in Math.h).

Three angles are returned in a vector with the following format:

$\mathbf{v} = [\psi, \theta, \phi ]$

such that the returned matrix satisfies the following:

$R = R_z(\phi) R_y(\theta) R_x(\psi)$

Parameters

R	is the input ZYX rotation matrix.

Returns: 3 by 1 vector for the roll pitch-yaw-angles representation.

Definition at line 780 of file math.cpp.

◆ dcm2ypr()

Vector yarp::math::dcm2ypr ( const yarp::sig::Matrix & R )

Converts a dcm (direction cosine matrix) rotation matrix to yaw-roll-pitch angles (defined in Math.h).

Three angles are returned in a vector with the following format:

$\mathbf{v} = [\phi, \theta, \psi ]$

such that the returned matrix satisfies the following:

$R = R_x(\psi) R_y(\theta) R_z(\phi)$

Parameters

R	is the input XYZ rotation matrix.

Returns: 3 by 1 vector for the yaw-pitch-roll angles representation.

Definition at line 834 of file math.cpp.

◆ det()

double yarp::math::det ( const yarp::sig::Matrix & in )

Computes the determinant of a matrix (defined in Math.h).

Parameters

in	the matrix

Definition at line 583 of file math.cpp.

◆ dot()

double yarp::math::dot	(	const yarp::sig::Vector &	a,
		const yarp::sig::Vector &	b
	)

Scalar product between vectors (defined in Math.h).

Returns: a^T*b, where a and b are column vectors

Definition at line 461 of file math.cpp.

◆ eigenValues()

bool yarp::math::eigenValues	(	const yarp::sig::Matrix &	in,
		yarp::sig::Vector &	real,
		yarp::sig::Vector &	img
	)

Computes eigenvalues of the n-by-n real nonsymmetric matrix (defined in Math.h).

Parameters

in	nonsymmetric n-by-n matrix
real	the real part of eigen values
img	the imaginary part of eigen values

Returns: the real and imaginary part of the eigen values in separate matrices

Definition at line 600 of file math.cpp.

◆ euler2dcm()

Matrix yarp::math::euler2dcm ( const yarp::sig::Vector & euler )

Converts euler angles (ZYZ) vector in the corresponding dcm (direction cosine matrix) rotation matrix (defined in Math.h).

The three euler angles are specified in a vector with the following structure:

$\mathbf{v} = [\alpha, \beta, \gamma ]$

and the returned matrix is:

$R = R_z(\alpha) R_y(\beta) R_z(\gamma)$

Parameters

euler is the input vector (alpha=z-rotation, beta=y-rotation, gamma=z-rotation).

Returns: 4 by 4 homogeneous matrix representing the ZYZ rotation with the rotation components in the top left 3 by 3 submatrix.

Definition at line 764 of file math.cpp.

◆ eye() [1/2]

Matrix yarp::math::eye ( int n )

Build a square identity matrix (defined in Math.h).

Parameters

n	number of rows and columns

Returns: the new matrix

Definition at line 570 of file math.cpp.

◆ eye() [2/2]

Matrix yarp::math::eye	(	int	r,
		int	c
	)

Build an identity matrix (defined in Math.h).

Parameters

r	number of rows
c	number of columns

Returns: the new matrix

Definition at line 562 of file math.cpp.

◆ findMax()

double yarp::math::findMax ( const yarp::sig::Vector & v )

Returns the maximum of the elements of a real vector (defined in Math.h).

Parameters

v	is the input vector.

Returns: max(v).

Definition at line 530 of file math.cpp.

◆ findMin()

double yarp::math::findMin ( const yarp::sig::Vector & v )

Returns the minimum of the elements of a real vector (defined in Math.h).

Parameters

v	is the input vector.

Returns: min(v).

Definition at line 541 of file math.cpp.

◆ luinv()

Matrix yarp::math::luinv ( const yarp::sig::Matrix & in )

Invert a square matrix using LU-decomposition (defined in Math.h).

Parameters

in	square matrix

Returns: the inverse of the matrix

Definition at line 588 of file math.cpp.

◆ norm()

double yarp::math::norm ( const yarp::sig::Vector & v )

Returns the Euclidean norm of the vector (defined in Math.h).

Parameters

v	is the input vector.

Returns: ||v||.

Definition at line 520 of file math.cpp.

◆ norm2()

double yarp::math::norm2 ( const yarp::sig::Vector & v )

Returns the Euclidean squared norm of the vector (defined in Math.h).

Parameters

v	is the input vector.

Returns: ||v||^2.

Definition at line 525 of file math.cpp.

◆ nullspaceProjection() [1/2]

Matrix yarp::math::nullspaceProjection	(	const yarp::sig::Matrix &	A,
		double	tol = `0.0`
	)

Compute the nullspace projection matrix of A, that is defined as the difference between the identity matrix and the pseudoinverse of A times A: (I - pinv(A)*A) (defined in SVD.h).

Multiplying this null projection matrix times a vector projects the vector in the nullspace of A.

Parameters

A	input matrix
tol	singular values less than tol are set to zero

Returns: The projection matrix associated with the nullspace of A

Definition at line 178 of file SVD.cpp.

◆ nullspaceProjection() [2/2]

void yarp::math::nullspaceProjection	(	const yarp::sig::Matrix &	A,
		yarp::sig::Matrix &	out,
		double	tol = `0.0`
	)

Compute the nullspace projection matrix of A, that is defined as the difference between the identity matrix and the pseudoinverse of A times A: (I - pinv(A)*A) (defined in SVD.h).

Multiplying this projection matrix times a vector projects the vector in the range of A.

Parameters

A	input matrix
out	the projection matrix associated with the nullspace of A
tol	singular values less than tol are set to zero

Definition at line 185 of file SVD.cpp.

◆ ones()

Vector yarp::math::ones ( int s )

Creates a vector of ones (defined in Math.h).

Parameters

s	the size of the new vector

Returns: a copy of the new vector

Definition at line 557 of file math.cpp.

◆ outerProduct()

Matrix yarp::math::outerProduct	(	const yarp::sig::Vector &	a,
		const yarp::sig::Vector &	b
	)

Outer product between vectors (defined in Math.h).

Returns: a*b^T, where a and b are column vectors

Definition at line 469 of file math.cpp.

◆ pile() [1/4]

Matrix yarp::math::pile	(	const yarp::sig::Matrix &	m,
		const yarp::sig::Vector &	v
	)

Matrix-Vector concatenation (defined in Math.h).

Add a row at the end of a matrix.

Parameters

m	a matrix nXm
v	a vector m

Returns: a matrix (n+1)Xm

Definition at line 311 of file math.cpp.

◆ pile() [2/4]

Matrix yarp::math::pile	(	const yarp::sig::Matrix &	m1,
		const yarp::sig::Matrix &	m2
	)

Matrix-Matrix concatenation by column (defined in Math.h).

Parameters

m1	a matrix nXm
m2	a matrix rXm

Returns: a matrix (n+r)Xm

Definition at line 297 of file math.cpp.

◆ pile() [3/4]

Matrix yarp::math::pile	(	const yarp::sig::Vector &	v,
		const yarp::sig::Matrix &	m
	)

Vector-Matrix concatenation (defined in Math.h).

Add a row at the beginning of a matrix.

Parameters

m	a matrix nXm
v	a vector m

Returns: a matrix (n+1)Xm

Definition at line 324 of file math.cpp.

◆ pile() [4/4]

Matrix yarp::math::pile	(	const yarp::sig::Vector &	v1,
		const yarp::sig::Vector &	v2
	)

Vector-Vector concatenation (defined in Math.h).

Create a two row matrix by stacking two vectors.

Parameters

v1	an n-vector
v2	an n-vector

Returns: a matrix 2Xn

Definition at line 337 of file math.cpp.

◆ pinv() [1/4]

Matrix yarp::math::pinv	(	const yarp::sig::Matrix &	in,
		double	tol = `0.0`
	)

Perform the moore-penrose pseudo-inverse of a matrix (defined in SVD.h).

Parameters

in	input matrix
tol	singular values less than tol are set to zero

Returns: pseudo-inverse of the matrix 'in'

Definition at line 49 of file SVD.cpp.

◆ pinv() [2/4]

void yarp::math::pinv	(	const yarp::sig::Matrix &	in,
		yarp::sig::Matrix &	out,
		double	tol = `0.0`
	)

Perform the moore-penrose pseudo-inverse of a matrix (defined in SVD.h).

Parameters

in	input matrix
out	pseudo-inverse of the matrix 'in'
tol	singular values less than tol are set to zero

Definition at line 64 of file SVD.cpp.

◆ pinv() [3/4]

void yarp::math::pinv	(	const yarp::sig::Matrix &	in,
		yarp::sig::Matrix &	out,
		yarp::sig::Vector &	sv,
		double	tol = `0.0`
	)

Perform the moore-penrose pseudo-inverse of a matrix (defined in SVD.h).

Parameters

in	input matrix
out	pseudo-inverse of the matrix 'in'
sv	vector containing the singular values of the input matrix
tol	singular values less than tol are set to zero

Definition at line 96 of file SVD.cpp.

◆ pinv() [4/4]

Matrix yarp::math::pinv	(	const yarp::sig::Matrix &	in,
		yarp::sig::Vector &	sv,
		double	tol = `0.0`
	)

Perform the moore-penrose pseudo-inverse of a matrix (defined in SVD.h).

Parameters

in	input matrix
sv	vector containing the singular values of the input matrix
tol	singular values less than tol are set to zero

Returns: pseudo-inverse of the matrix 'in'

Definition at line 79 of file SVD.cpp.

◆ pinvDamped() [1/4]

Matrix yarp::math::pinvDamped	(	const yarp::sig::Matrix &	in,
		double	damp
	)

Perform the damped pseudo-inverse of a matrix (defined in SVD.h).

Parameters

in	input matrix
damp	damping factor

Definition at line 120 of file SVD.cpp.

◆ pinvDamped() [2/4]

void yarp::math::pinvDamped	(	const yarp::sig::Matrix &	in,
		yarp::sig::Matrix &	out,
		double	damp
	)

Perform the damped pseudo-inverse of a matrix (defined in SVD.h).

Parameters

in	input matrix
out	damped pseudo-inverse of the matrix 'in'
damp	damping factor

Definition at line 129 of file SVD.cpp.

◆ pinvDamped() [3/4]

void yarp::math::pinvDamped	(	const yarp::sig::Matrix &	in,
		yarp::sig::Matrix &	out,
		yarp::sig::Vector &	sv,
		double	damp
	)

Perform the damped pseudo-inverse of a matrix (defined in SVD.h).

Parameters

in	input matrix
out	damped pseudo-inverse of the matrix 'in'
sv	vector containing the singular values of the input matrix
damp	damping factor

Definition at line 136 of file SVD.cpp.

◆ pinvDamped() [4/4]

Matrix yarp::math::pinvDamped	(	const yarp::sig::Matrix &	in,
		yarp::sig::Vector &	sv,
		double	damp
	)

Perform the damped pseudo-inverse of a matrix (defined in SVD.h).

Parameters

in	input matrix
sv	vector containing the singular values of the input matrix
damp	damping factor

Definition at line 113 of file SVD.cpp.

◆ projectionMatrix() [1/2]

Matrix yarp::math::projectionMatrix	(	const yarp::sig::Matrix &	A,
		double	tol = `0.0`
	)

Compute the projection matrix of A, that is defined as A times its pseudoinverse: A*pinv(A) (defined in SVD.h).

Multiplying this projection matrix times a vector projects the vector in the range of A.

Parameters

A	input matrix
tol	singular values less than tol are set to zero

Returns: The projection matrix associated with the range of A

Definition at line 153 of file SVD.cpp.

◆ projectionMatrix() [2/2]

void yarp::math::projectionMatrix	(	const yarp::sig::Matrix &	A,
		yarp::sig::Matrix &	out,
		double	tol = `0.0`
	)

Compute the projection matrix of A, that is defined as A times its pseudoinverse: A*pinv(A) (defined in SVD.h).

Multiplying this projection matrix times a vector projects the vector in the range of A.

Parameters

A	input matrix
out	the projection matrix associated with the range of A
tol	singular values less than tol are set to zero

Definition at line 160 of file SVD.cpp.

◆ rpy2dcm()

Matrix yarp::math::rpy2dcm ( const yarp::sig::Vector & rpy )

Converts roll-pitch-yaw angles in the corresponding dcm (direction cosine matrix) rotation matrix (defined in Math.h).

The three angles are specified in a vector with the following structure:

$\mathbf{v} = [\psi, \theta, \phi ]$

and the returned matrix is:

$R = R_z(\phi) R_y(\theta) R_x(\psi)$

Parameters

rpy	is the input vector (\psi=roll x-rotation,\theta=pitch y-rotation, \phi=yaw z-rotation).

Returns: 4 by 4 homogeneous matrix representing the ZYX rotation with the rotation components in the top left 3 by 3 submatrix.

Definition at line 818 of file math.cpp.

◆ SE3inv()

Matrix yarp::math::SE3inv ( const yarp::sig::Matrix & H )

Returns the inverse of a 4 by 4 rototranslational matrix (defined in Math.h).

Parameters

H	is the 4 by 4 rototranslational matrix.

Returns: inverse of 4 by 4 rototranslational matrix.

Note: about 5 times faster than pinv()

Definition at line 883 of file math.cpp.

◆ sign() [1/2]

double yarp::math::sign ( const double & v )

Invert a symmetric and positive definite matrix using Cholesky decomposition (defined in Math.h).

Parameters

in	symmetric and positive definite matrix

Returns: the inverse of the matrix Returns the sign of a real number: 1 if positive, -1 if negative, 0 if equal to zero (defined in Math.h)

Parameters

v	is a real number.

Returns: sign(v).

Definition at line 632 of file math.cpp.

◆ sign() [2/2]

Vector yarp::math::sign ( const yarp::sig::Vector & v )

Returns the sign vector of a real vector, that is a vector with 1 if the value is positive, -1 if negative, 0 if equal to zero (defined in Math.h).

Parameters

v	is the input vector.

Returns: sign(v).

Definition at line 638 of file math.cpp.

◆ SVD()

void yarp::math::SVD	(	const yarp::sig::Matrix &	in,
		yarp::sig::Matrix &	U,
		yarp::sig::Vector &	S,
		yarp::sig::Matrix &	V
	)

Factorize the M-by-N matrix 'in' into the singular value decomposition in = U S V^T (defined in SVD.h).

The diagonal elements of the singular value matrix S are stored in the vector S. The singular values are non-negative and form a non-increasing sequence from S_1 to S_N. The matrix V contains the elements of V in untransposed form. To form the product U S V^T it is necessary to take the transpose of V. Defining K as min(M, N) the the input matrices are:

Parameters

in	input M-by-N matrix to decompose
U	output M-by-K orthogonal matrix
S	output K-dimensional vector containing the diagonal entries of the diagonal matrix S
V	output N-by-K orthogonal matrix

Note: If U, S, V do not have the expected sizes they are resized automatically.; The routine computes the thin version of the SVD. Mathematically, the full SVD is defined with U and V as square orthogonal matrices and S as an M-by-N diagonal matrix.; This function uses the Jacobi SVD algorithm.

Definition at line 25 of file SVD.cpp.

◆ SVDJacobi()

void yarp::math::SVDJacobi	(	const yarp::sig::Matrix &	in,
		yarp::sig::Matrix &	U,
		yarp::sig::Vector &	S,
		yarp::sig::Matrix &	V
	)

Perform SVD decomposition on a matrix using the Jacobi method (defined in SVD.h).

The Jacobi method can compute singular values to higher relative accuracy than Golub-Reinsch algorithms.

Note: If U, S, V do not have the expected sizes they are resized automatically.; This function uses the Jacobi SVD algorithm.

Definition at line 35 of file SVD.cpp.

◆ SVDMod()

void yarp::math::SVDMod	(	const yarp::sig::Matrix &	in,
		yarp::sig::Matrix &	U,
		yarp::sig::Vector &	S,
		yarp::sig::Matrix &	V
	)

Perform SVD decomposition on a MxN matrix (for M >= N) (defined in SVD.h).

Note: If U, S, V do not have the expected sizes they are resized automatically.; This function uses the Jacobi SVD algorithm.

Definition at line 30 of file SVD.cpp.

◆ ypr2dcm()

Matrix yarp::math::ypr2dcm ( const yarp::sig::Vector & ypr )

Converts yaw-pitch-roll angles in the corresponding dcm (direction cosine matrix) rotation matrix (defined in Math.h).

The three angles are specified in a vector with the following structure:

$\mathbf{v} = [\phi, \theta, \psi ]$

and the returned matrix is:

$R = R_x(\psi) R_y(\theta) R_z(\phi)$

Parameters

ypr	is the input vector (\phi=yaw z-rotation, \theta=pitch y-rotation, \psi=roll x-rotation).

Returns: 4 by 4 homogeneous matrix representing the XYZ rotation with the rotation components in the top left 3 by 3 submatrix.

Definition at line 867 of file math.cpp.

◆ zeros() [1/2]

Matrix yarp::math::zeros	(	int	r,
		int	c
	)

Build a matrix of zeros (defined in Math.h).

Parameters

r	number of rows
c	number of columns

Definition at line 575 of file math.cpp.

◆ zeros() [2/2]

Vector yarp::math::zeros ( int s )

Creates a vector of zeros (defined in Math.h).

Parameters

s	the size of the new vector

Returns: a copy of the new vector

Definition at line 552 of file math.cpp.

Namespaces

Classes

Functions

Function Documentation

◆ adjoint()

◆ adjointInv()

◆ axis2dcm()

◆ cat() [1/10]

◆ cat() [2/10]

◆ cat() [3/10]

◆ cat() [4/10]

◆ cat() [5/10]

◆ cat() [6/10]

◆ cat() [7/10]

◆ cat() [8/10]

◆ cat() [9/10]

◆ cat() [10/10]

◆ cross()

◆ crossProductMatrix() [1/2]

◆ crossProductMatrix() [2/2]

◆ dcm2axis()

◆ dcm2euler()

◆ dcm2rpy()

◆ dcm2ypr()

◆ det()

◆ dot()

◆ eigenValues()

◆ euler2dcm()

◆ eye() [1/2]

◆ eye() [2/2]

◆ findMax()

◆ findMin()

◆ luinv()

◆ norm()

◆ norm2()

◆ nullspaceProjection() [1/2]

◆ nullspaceProjection() [2/2]

◆ ones()

◆ outerProduct()

◆ pile() [1/4]

◆ pile() [2/4]

◆ pile() [3/4]

◆ pile() [4/4]

◆ pinv() [1/4]

◆ pinv() [2/4]

◆ pinv() [3/4]

◆ pinv() [4/4]

◆ pinvDamped() [1/4]

◆ pinvDamped() [2/4]

◆ pinvDamped() [3/4]

◆ pinvDamped() [4/4]

◆ projectionMatrix() [1/2]

◆ projectionMatrix() [2/2]

◆ rpy2dcm()

◆ SE3inv()

◆ sign() [1/2]

◆ sign() [2/2]

◆ SVD()

◆ SVDJacobi()

◆ SVDMod()

◆ ypr2dcm()

◆ zeros() [1/2]

◆ zeros() [2/2]