Math.h File Reference

#include <yarp/sig/Vector.h>
#include <yarp/sig/Matrix.h>
#include <yarp/math/api.h>
#include <yarp/math/Quaternion.h>

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Namespaces
	yarp
	The main, catch-all namespace for YARP.
	yarp::math

Functions
yarp::sig::Vector	operator+ (const yarp::sig::Vector &a, const double &s)
	Mathematical operations. More...
yarp::sig::Vector	operator+ (const double &s, const yarp::sig::Vector &a)
	Addition operator between a scalar and a vector (defined in Math.h). More...
yarp::sig::Vector &	operator+= (yarp::sig::Vector &a, const double &s)
	Addition operator between a scalar and a vector (defined in Math.h). More...
yarp::sig::Vector	operator+ (const yarp::sig::Vector &a, const yarp::sig::Vector &b)
	Addition operator between vectors, returns a+b (defined in Math.h). More...
yarp::sig::Vector &	operator+= (yarp::sig::Vector &a, const yarp::sig::Vector &b)
	Addition operator between vectors, returns a+b (defined in Math.h). More...
yarp::sig::Matrix	operator+ (const yarp::sig::Matrix &a, const yarp::sig::Matrix &b)
	Addition operator between matrices, returns a+b (defined in Math.h). More...
yarp::sig::Matrix &	operator+= (yarp::sig::Matrix &a, const yarp::sig::Matrix &b)
	Addition operator between matrices, returns a+b (defined in Math.h). More...
yarp::sig::Vector	operator- (const yarp::sig::Vector &a, const double &s)
	Subtraction operator between a vector and a scalar (defined in Math.h). More...
yarp::sig::Vector	operator- (const double &s, const yarp::sig::Vector &a)
	Subtraction operator between a scalar and a vector (defined in Math.h). More...
yarp::sig::Vector &	operator-= (yarp::sig::Vector &a, const double &s)
	Subtraction operator between a vector and a scalar (defined in Math.h). More...
yarp::sig::Vector	operator- (const yarp::sig::Vector &a, const yarp::sig::Vector &b)
	Subtraction operator between vectors, returns a-b (defined in Math.h). More...
yarp::sig::Vector &	operator-= (yarp::sig::Vector &a, const yarp::sig::Vector &b)
	Subtraction operator between vectors, returns a-b (defined in Math.h). More...
yarp::sig::Matrix	operator- (const yarp::sig::Matrix &a, const yarp::sig::Matrix &b)
	Subtraction operator between matrices, returns a-b (defined in Math.h). More...
yarp::sig::Matrix &	operator-= (yarp::sig::Matrix &a, const yarp::sig::Matrix &b)
	Subtraction operator between matrices, returns a-b (defined in Math.h). More...
yarp::sig::Vector	operator* (double k, const yarp::sig::Vector &b)
	Scalar-vector product operator (defined in Math.h). More...
yarp::sig::Vector	operator* (const yarp::sig::Vector &b, double k)
	Vector-scalar product operator (defined in Math.h). More...
yarp::sig::Vector &	operator*= (yarp::sig::Vector &b, double k)
	Vector-scalar product operator (defined in Math.h). More...
yarp::sig::Vector	operator* (const yarp::sig::Vector &a, const yarp::sig::Matrix &m)
	Vector-matrix product operator (defined in Math.h). More...
yarp::sig::Vector &	operator*= (yarp::sig::Vector &a, const yarp::sig::Matrix &m)
	Vector-matrix product operator (defined in Math.h). More...
yarp::sig::Vector	operator* (const yarp::sig::Matrix &m, const yarp::sig::Vector &a)
	Matrix-vector product operator (defined in Math.h). More...
yarp::sig::Matrix	operator* (const yarp::sig::Matrix &a, const yarp::sig::Matrix &b)
	Matrix-matrix product operator (defined in Math.h). More...
yarp::sig::Matrix &	operator*= (yarp::sig::Matrix &a, const yarp::sig::Matrix &b)
	Matrix-matrix product operator (defined in Math.h). More...
yarp::sig::Matrix	operator* (const double k, const yarp::sig::Matrix &M)
	Scalar-matrix product operator (defined in Math.h). More...
yarp::sig::Matrix	operator* (const yarp::sig::Matrix &M, const double k)
	Matrix-scalar product operator (defined in Math.h). More...
yarp::sig::Matrix &	operator*= (yarp::sig::Matrix &M, const double k)
	Matrix-scalar product operator (defined in Math.h). More...
yarp::sig::Vector	operator* (const yarp::sig::Vector &a, const yarp::sig::Vector &b)
	Vector-vector element-wise product operator (defined in Math.h). More...
yarp::sig::Vector &	operator*= (yarp::sig::Vector &a, const yarp::sig::Vector &b)
	Vector-vector element-wise product operator (defined in Math.h). More...
yarp::math::Quaternion	operator* (const yarp::math::Quaternion &a, const yarp::math::Quaternion &b)
	Quaternion-quaternion hamilton product operator (defined in Math.h). More...
yarp::sig::Vector	operator/ (const yarp::sig::Vector &a, const yarp::sig::Vector &b)
	Vector-vector element-wise division operator (defined in Math.h). More...
yarp::sig::Vector &	operator/= (yarp::sig::Vector &a, const yarp::sig::Vector &b)
	Vector-vector element-wise division operator (defined in Math.h). More...
yarp::sig::Vector	operator/ (const yarp::sig::Vector &b, double k)
	Vector-scalar division operator (defined in Math.h). More...
yarp::sig::Vector &	operator/= (yarp::sig::Vector &b, double k)
	Vector-scalar division operator (defined in Math.h). More...
yarp::sig::Matrix	operator/ (const yarp::sig::Matrix &M, double k)
	Matrix-scalar division operator (defined in Math.h). More...
yarp::sig::Matrix &	operator/= (yarp::sig::Matrix &M, double k)
	Matrix-scalar division operator (defined in Math.h). More...
yarp::sig::Matrix	yarp::math::pile (const yarp::sig::Matrix &m1, const yarp::sig::Matrix &m2)
	Matrix-Matrix concatenation by column (defined in Math.h). More...
yarp::sig::Matrix	yarp::math::pile (const yarp::sig::Vector &v, const yarp::sig::Matrix &m)
	Vector-Matrix concatenation (defined in Math.h). More...
yarp::sig::Matrix	yarp::math::pile (const yarp::sig::Matrix &m, const yarp::sig::Vector &v)
	Matrix-Vector concatenation (defined in Math.h). More...
yarp::sig::Matrix	yarp::math::pile (const yarp::sig::Vector &v1, const yarp::sig::Vector &v2)
	Vector-Vector concatenation (defined in Math.h). More...
yarp::sig::Matrix	yarp::math::cat (const yarp::sig::Matrix &m1, const yarp::sig::Matrix &m2)
	Matrix-Matrix concatenation by row (defined in Math.h). More...
yarp::sig::Matrix	yarp::math::cat (const yarp::sig::Matrix &m, const yarp::sig::Vector &v)
	Matrix-Vector concatenation (defined in Math.h). More...
yarp::sig::Matrix	yarp::math::cat (const yarp::sig::Vector &v, const yarp::sig::Matrix &m)
	Vector-Matrix concatenation (defined in Math.h). More...
yarp::sig::Vector	yarp::math::cat (const yarp::sig::Vector &v1, const yarp::sig::Vector &v2)
	Vector-Vector concatenation (defined in Math.h). More...
yarp::sig::Vector	yarp::math::cat (const yarp::sig::Vector &v, double s)
	Vector-scalar concatenation (defined in Math.h). More...
yarp::sig::Vector	yarp::math::cat (double s, const yarp::sig::Vector &v)
	Scalar-vector concatenation (defined in Math.h). More...
yarp::sig::Vector	yarp::math::cat (double s1, double s2)
	Scalar-scalar concatenation (defined in Math.h). More...
yarp::sig::Vector	yarp::math::cat (double s1, double s2, double s3)
yarp::sig::Vector	yarp::math::cat (double s1, double s2, double s3, double s4)
yarp::sig::Vector	yarp::math::cat (double s1, double s2, double s3, double s4, double s5)
double	yarp::math::dot (const yarp::sig::Vector &a, const yarp::sig::Vector &b)
	Scalar product between vectors (defined in Math.h). More...
yarp::sig::Matrix	yarp::math::outerProduct (const yarp::sig::Vector &a, const yarp::sig::Vector &b)
	Outer product between vectors (defined in Math.h). More...
yarp::sig::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). More...
yarp::sig::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). More...
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). More...
double	yarp::math::norm (const yarp::sig::Vector &v)
	Returns the Euclidean norm of the vector (defined in Math.h). More...
double	yarp::math::norm2 (const yarp::sig::Vector &v)
	Returns the Euclidean squared norm of the vector (defined in Math.h). More...
double	yarp::math::findMax (const yarp::sig::Vector &v)
	Returns the maximum of the elements of a real vector (defined in Math.h). More...
double	yarp::math::findMin (const yarp::sig::Vector &v)
	Returns the minimum of the elements of a real vector (defined in Math.h). More...
yarp::sig::Vector	yarp::math::zeros (int s)
	Creates a vector of zeros (defined in Math.h). More...
yarp::sig::Vector	yarp::math::ones (int s)
	Creates a vector of ones (defined in Math.h). More...
yarp::sig::Matrix	yarp::math::eye (int r, int c)
	Build an identity matrix (defined in Math.h). More...
yarp::sig::Matrix	yarp::math::eye (int n)
	Build a square identity matrix (defined in Math.h). More...
yarp::sig::Matrix	yarp::math::zeros (int r, int c)
	Build a matrix of zeros (defined in Math.h). More...
double	yarp::math::det (const yarp::sig::Matrix &in)
	Computes the determinant of a matrix (defined in Math.h). More...
yarp::sig::Matrix	yarp::math::luinv (const yarp::sig::Matrix &in)
	Invert a square matrix using LU-decomposition (defined in Math.h). More...
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). More...
double	yarp::math::sign (const double &v)
	Invert a symmetric and positive definite matrix using Cholesky decomposition (defined in Math.h). More...
yarp::sig::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). More...
yarp::sig::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). More...
yarp::sig::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). More...
yarp::sig::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). More...
yarp::sig::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). More...
yarp::sig::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). More...
yarp::sig::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). More...
yarp::sig::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). More...
yarp::sig::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). More...
yarp::sig::Matrix	yarp::math::SE3inv (const yarp::sig::Matrix &H)
	Returns the inverse of a 4 by 4 rototranslational matrix (defined in Math.h). More...
yarp::sig::Matrix	yarp::math::adjoint (const yarp::sig::Matrix &H)
	Returns the adjoint matrix of a given roto-translational matrix (defined in Math.h). More...
yarp::sig::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). More...

Function Documentation

operator*() [1/9]

yarp::sig::Matrix operator*	(	const double	k,
		const yarp::sig::Matrix &	M
	)

Scalar-matrix product operator (defined in Math.h).

Parameters

k	a scalar
M	a matrix

Returns

k*M

Definition at line 208 of file math.cpp.

operator*() [2/9]

yarp::math::Quaternion operator*	(	const yarp::math::Quaternion &	a,
		const yarp::math::Quaternion &	b
	)

Quaternion-quaternion hamilton product operator (defined in Math.h).

reference: "Stevens, Brian L., Frank L. Lewis, Aircraft Control and Simulation, Wiley–Interscience, 2nd Edition".

Parameters

a	a quaternion
b	a quaternion

Returns

a*b

Definition at line 242 of file math.cpp.

operator*() [3/9]

yarp::sig::Matrix operator*	(	const yarp::sig::Matrix &	a,
		const yarp::sig::Matrix &	b
	)

Matrix-matrix product operator (defined in Math.h).

Parameters

a	a matrix
b	a matrix

Returns

a*b

Definition at line 187 of file math.cpp.

operator*() [4/9]

yarp::sig::Matrix operator*	(	const yarp::sig::Matrix &	M,
		const double	k
	)

Matrix-scalar product operator (defined in Math.h).

Parameters

M	a matrix
k	a scalar

Returns

M*k

Definition at line 214 of file math.cpp.

operator*() [5/9]

yarp::sig::Vector operator*	(	const yarp::sig::Matrix &	m,
		const yarp::sig::Vector &	a
	)

Matrix-vector product operator (defined in Math.h).

Parameters

a	is a vector (interpreted as a column)
m	is a matrix

Returns

m*a

Definition at line 177 of file math.cpp.

operator*() [6/9]

yarp::sig::Vector operator*	(	const yarp::sig::Vector &	a,
		const yarp::sig::Matrix &	m
	)

Vector-matrix product operator (defined in Math.h).

Parameters

a	is a vector (interpreted as a row)
m	is a matrix

Returns

a*m

Definition at line 156 of file math.cpp.

operator*() [7/9]

yarp::sig::Vector operator*	(	const yarp::sig::Vector &	a,
		const yarp::sig::Vector &	b
	)

Vector-vector element-wise product operator (defined in Math.h).

Parameters

a	a vector
b	a vector

Returns

a.*b (matlab notation)

Definition at line 227 of file math.cpp.

operator*() [8/9]

yarp::sig::Vector operator*	(	const yarp::sig::Vector &	b,
		double	k
	)

Vector-scalar product operator (defined in Math.h).

Parameters

b	a vector
k	a scalar

Returns

b*k

Definition at line 142 of file math.cpp.

operator*() [9/9]

yarp::sig::Vector operator*	(	double	k,
		const yarp::sig::Vector &	b
	)

Scalar-vector product operator (defined in Math.h).

Parameters

k	a scalar
b	vector

Returns

k*b

Definition at line 137 of file math.cpp.

operator*=() [1/5]

yarp::sig::Matrix& operator*=	(	yarp::sig::Matrix &	a,
		const yarp::sig::Matrix &	b
	)

Matrix-matrix product operator (defined in Math.h).

Parameters

a	a matrix
b	a matrix

Returns

a*b

Definition at line 197 of file math.cpp.

operator*=() [2/5]

yarp::sig::Matrix& operator*=	(	yarp::sig::Matrix &	M,
		const double	k
	)

Matrix-scalar product operator (defined in Math.h).

Parameters

M	a matrix
k	a scalar

Returns

M*k

Definition at line 219 of file math.cpp.

operator*=() [3/5]

yarp::sig::Vector& operator*=	(	yarp::sig::Vector &	a,
		const yarp::sig::Matrix &	m
	)

Vector-matrix product operator (defined in Math.h).

Parameters

a	is a vector (interpreted as a row)
m	is a matrix

Returns

a*m

Definition at line 166 of file math.cpp.

operator*=() [4/5]

yarp::sig::Vector& operator*=	(	yarp::sig::Vector &	a,
		const yarp::sig::Vector &	b
	)

Vector-vector element-wise product operator (defined in Math.h).

Parameters

a	a vector
b	a vector

Returns

a.*b (matlab notation)

Definition at line 233 of file math.cpp.

operator*=() [5/5]

yarp::sig::Vector& operator*=	(	yarp::sig::Vector &	b,
		double	k
	)

Vector-scalar product operator (defined in Math.h).

Parameters

b	a vector
k	a scalar

Returns

b*k

Definition at line 148 of file math.cpp.

operator+() [1/4]

yarp::sig::Vector operator+	(	const double &	s,
		const yarp::sig::Vector &	a
	)

Addition operator between a scalar and a vector (defined in Math.h).

Sum the scalar to all the elements of the vector.

Definition at line 36 of file math.cpp.

operator+() [2/4]

yarp::sig::Matrix operator+	(	const yarp::sig::Matrix &	a,
		const yarp::sig::Matrix &	b
	)

Addition operator between matrices, returns a+b (defined in Math.h).

Definition at line 64 of file math.cpp.

operator+() [3/4]

yarp::sig::Vector operator+	(	const yarp::sig::Vector &	a,
		const double &	s
	)

Mathematical operations.

Addition operator between a scalar and a vector (defined in Math.h). Sum the scalar to all the elements of the vector.

Definition at line 30 of file math.cpp.

operator+() [4/4]

yarp::sig::Vector operator+	(	const yarp::sig::Vector &	a,
		const yarp::sig::Vector &	b
	)

Addition operator between vectors, returns a+b (defined in Math.h).

Definition at line 49 of file math.cpp.

operator+=() [1/3]

yarp::sig::Matrix& operator+=	(	yarp::sig::Matrix &	a,
		const yarp::sig::Matrix &	b
	)

Addition operator between matrices, returns a+b (defined in Math.h).

Definition at line 70 of file math.cpp.

operator+=() [2/3]

yarp::sig::Vector& operator+=	(	yarp::sig::Vector &	a,
		const double &	s
	)

Addition operator between a scalar and a vector (defined in Math.h).

Sum the scalar to all the elements of the vector.

Definition at line 41 of file math.cpp.

operator+=() [3/3]

yarp::sig::Vector& operator+=	(	yarp::sig::Vector &	a,
		const yarp::sig::Vector &	b
	)

Addition operator between vectors, returns a+b (defined in Math.h).

Definition at line 55 of file math.cpp.

operator-() [1/4]

yarp::sig::Vector operator-	(	const double &	s,
		const yarp::sig::Vector &	a
	)

Subtraction operator between a scalar and a vector (defined in Math.h).

Multiply the vector by -1 and sum the scalar to the result.

Definition at line 87 of file math.cpp.

operator-() [2/4]

yarp::sig::Matrix operator-	(	const yarp::sig::Matrix &	a,
		const yarp::sig::Matrix &	b
	)

Subtraction operator between matrices, returns a-b (defined in Math.h).

Definition at line 119 of file math.cpp.

operator-() [3/4]

yarp::sig::Vector operator-	(	const yarp::sig::Vector &	a,
		const double &	s
	)

Subtraction operator between a vector and a scalar (defined in Math.h).

Subtract the scalar to all the elements of the vector.

Definition at line 81 of file math.cpp.

operator-() [4/4]

yarp::sig::Vector operator-	(	const yarp::sig::Vector &	a,
		const yarp::sig::Vector &	b
	)

Subtraction operator between vectors, returns a-b (defined in Math.h).

Definition at line 104 of file math.cpp.

operator-=() [1/3]

yarp::sig::Matrix& operator-=	(	yarp::sig::Matrix &	a,
		const yarp::sig::Matrix &	b
	)

Subtraction operator between matrices, returns a-b (defined in Math.h).

Definition at line 125 of file math.cpp.

operator-=() [2/3]

yarp::sig::Vector& operator-=	(	yarp::sig::Vector &	a,
		const double &	s
	)

Subtraction operator between a vector and a scalar (defined in Math.h).

Subtract the scalar to all the elements of the vector.

Definition at line 96 of file math.cpp.

operator-=() [3/3]

yarp::sig::Vector& operator-=	(	yarp::sig::Vector &	a,
		const yarp::sig::Vector &	b
	)

Subtraction operator between vectors, returns a-b (defined in Math.h).

Definition at line 110 of file math.cpp.

operator/() [1/3]

yarp::sig::Matrix operator/	(	const yarp::sig::Matrix &	M,
		double	k
	)

Matrix-scalar division operator (defined in Math.h).

Parameters

M	a matrix
k	a scalar

Returns

M./k (matlab notation)

Definition at line 280 of file math.cpp.

operator/() [2/3]

yarp::sig::Vector operator/	(	const yarp::sig::Vector &	a,
		const yarp::sig::Vector &	b
	)

Vector-vector element-wise division operator (defined in Math.h).

Parameters

a	a vector
b	a vector

Returns

a./b (matlab notation)

Definition at line 250 of file math.cpp.

operator/() [3/3]

yarp::sig::Vector operator/	(	const yarp::sig::Vector &	b,
		double	k
	)

Vector-scalar division operator (defined in Math.h).

Parameters

b	a vector
k	a scalar

Returns

b/k

Definition at line 265 of file math.cpp.

operator/=() [1/3]

yarp::sig::Matrix& operator/=	(	yarp::sig::Matrix &	M,
		double	k
	)

Matrix-scalar division operator (defined in Math.h).

Parameters

M	a matrix
k	a scalar

Returns

M./k (matlab notation)

Definition at line 286 of file math.cpp.

operator/=() [2/3]

yarp::sig::Vector& operator/=	(	yarp::sig::Vector &	a,
		const yarp::sig::Vector &	b
	)

Vector-vector element-wise division operator (defined in Math.h).

Parameters

a	a vector
b	a vector

Returns

a./b (matlab notation)

Definition at line 256 of file math.cpp.

operator/=() [3/3]

yarp::sig::Vector& operator/=	(	yarp::sig::Vector &	b,
		double	k
	)

Vector-scalar division operator (defined in Math.h).

Parameters

b	a vector
k	a scalar

Returns

b/k

Definition at line 271 of file math.cpp.