This class holds all static methods to perform linear algebra operations on vectors and matrices. More...

#include <LinearAlgebra.h>

Collaboration diagram for Isis::LinearAlgebra:

Public Types
typedef boost::numeric::ublas::matrix< double >	Matrix
	Definition for an Isis::LinearAlgebra::Matrix of doubles. More...

typedef boost::numeric::ublas::symmetric_matrix< double, boost::numeric::ublas::upper >	SymmetricMatrix
	Definition for an Isis::LinearAlgebra::SymmetrixMatrix of doubles with an upper configuration. More...

typedef boost::numeric::ublas::vector< double >	Vector
	Definition for an Isis::LinearAlgebra::Vector of doubles. More...

typedef QPair< Vector, Angle >	AxisAngle
	Definition for an Axis-Angle pair. More...

typedef QPair< Angle, int >	EulerAngle
	Definition for an EulerAngle pair. More...

Static Public Member Functions
static bool	isIdentity (const Matrix &matrix)
	Determines whether the given matrix is the identity. More...

static bool	isOrthogonal (const Matrix &matrix)
	Determines whether the given matrix is orthogonal by verifying that the matrix and its tranpose are inverses. More...

static bool	isRotationMatrix (const Matrix &matrix)
	Determines whether the given matrix is a rotation matrix. More...

static bool	isZero (const Matrix &matrix)
	Determines whether the given matrix is filled with zereos. More...

static bool	isZero (const Vector &vector)
	Determines whether the given vector is filled with zereos. More...

static bool	isEmpty (const Vector &vector)
	Determines whether the given vector is empty (i.e. More...

static bool	isUnit (const Vector &vector)
	Determines whether the given vector is a unit vector. More...

static Matrix	identity (int size)
	Returns the identity matrix of size NxN. More...

static Matrix	transpose (const Matrix &matrix)
	Returns the transpose of the given matrix. More...

static Matrix	inverse (const Matrix &matrix)
	Returns the inverse of a 2x2 or 3x3 matrix. More...

static Matrix	zeroMatrix (int rows, int columns)
	Returns a matrix with given dimensions that is filled with zeroes. More...

static Vector	zeroVector (int size)
	Returns a vector of given length that is filled with zeroes. More...

static double	determinant (const Matrix &matrix)
	Returns the determinant of the given 3x3 matrix. More...

static Vector	normalize (const Vector &vector)
	Returns a unit vector that is codirectional with the given vector by dividing each component of the vector by the vector magnitude. More...

static double	magnitude (const Vector &vector)
	Computes the magnitude (i.e., the length) of the given vector using the Euclidean norm (L2 norm). More...

static double	absoluteMaximum (const Vector &vector)
	Returns the maximum norm (L-infinity norm) for the given vector. More...

static Matrix	multiply (const Matrix &matrix1, const Matrix &matrix2)
	Returns the product of two matrices. More...

static Vector	multiply (const Matrix &matrix, const Vector &vector)
	Computes the product of the given matrix and vector. More...

static Vector	multiply (double scalar, const Vector &vector)
	Multiplies the given scalar and vector. More...

static Matrix	multiply (double scalar, const Matrix &matrix)
	Multiplies the given scalar and matrix. More...

static Vector	add (const Vector &vector1, const Vector &vector2)
	Adds the two given vectors. More...

static Vector	subtract (const Vector &vector1, const Vector &vector2)
	Subtracts the right vector from the left vector. More...

static Vector	crossProduct (const Vector &vector1, const Vector &vector2)
	Returns the cross product of two vectors. More...

static Vector	normalizedCrossProduct (const Vector &vector1, const Vector &vector2)
	Divides each vector by its corresponding absolute maximum, computes the cross product of the new vectors, and normalizes the resultant vector from the cross product. More...

static Matrix	outerProduct (const Vector &vector1, const Vector &vector2)
	Computes the outer product of the given vectors. More...

static double	dotProduct (const Vector &vector1, const Vector &vector2)
	Computes the dot product of the given vectors. More...

static double	innerProduct (const Vector &vector1, const Vector &vector2)
	Computes the inner product of the given vectors. More...

static Vector	project (const Vector &vector1, const Vector &vector2)
	Compute the vector projection of vector1 onto vector2. More...

static Vector	rotate (const Vector &vector, const Vector &axis, Angle angle)
	Rotates a vector about an axis vector given a specified angle. More...

static Vector	perpendicular (const Vector &vector1, const Vector &vector2)
	Finds the unique vector P such that A = V + P, V is parallel to B and P is perpendicular to B, where A is the first vector (vector1) and B is the second vector (vector2) passed in by the user. More...

static AxisAngle	toAxisAngle (const Matrix &rotationMatrix)
	Converts a rotation's representation from a matrix to a axis of rotation and its corresponding rotation angle. More...

static Matrix	toMatrix (const AxisAngle &axisAngle)
	Converts a rotation's representation from an axis of rotation and its corresponding rotation angle to a 3x3 matrix. More...

static Matrix	toMatrix (const Vector &axis, Angle angle)
	Converts a rotation's representation from an axis of rotation and its corresponding rotation angle to a 3x3 matrix. More...

static QList< EulerAngle >	toEulerAngles (const Matrix &rotationMatrix, const QList< int > axes)
	Converts a rotation's representation from a matrix to a set of Euler angles with corresponding axes. More...

static Matrix	toMatrix (const QList< EulerAngle > &eulerAngles)
	Converts a rotation's representation from a list of Euler angles (3 angles, each with a corresponding axis) to a 3x3 matrix. More...

static Matrix	toMatrix (const EulerAngle &angle3, const EulerAngle &angle2, const EulerAngle &angle1)
	Converts a rotation's representation from a set of Euler angles (3 angles, each with a corresponding axis) to a 3x3 matrix. More...

static Vector	toQuaternion (const Matrix &rotationMatrix)
	Converts a rotation's representation from a matrix to a unit quaternion. More...

static Matrix	toMatrix (const Vector &quaternion)
	Converts a rotation's representation from a quaternion to a 3x3 matrix. More...

static void	setRow (Matrix &matrix, const Vector &vector, int rowIndex)
	Sets the row of the given matrix to the values of the given vector. More...

static void	setColumn (Matrix &matrix, const Vector &vector, int columnIndex)
	Sets the column of the given matrix to the values of the given vector. More...

static Vector	row (const Matrix &matrix, int rowIndex)
	Returns a vector whose components match those of the given matrix row. More...

static Vector	column (const Matrix &matrix, int columnIndex)
	Returns a vector whose components match those of the given matrix column. More...

static void	setVec3 (Vector *v, double v0, double v1, double v2)
	Fills the first three elements of the given vector with the given values. More...

static void	setVec4 (Vector *v, double v0, double v1, double v2, double v3)
	Fills the first four elements of the given vector with the given values. More...

static Vector	vector (double v0, double v1, double v2)
	Constructs a 3 dimensional vector with the given component values. More...

static Vector	vector (double v0, double v1, double v2, double v3)
	Constructs a 4 dimensional vector with the given component values. More...

static Vector	subVector (const Vector &v, int start, int size)
	Constructs a vector of given size using the given vector and starting index. More...

Protected Member Functions
	LinearAlgebra ()
	Default constructor for a LinearAlgebra object. More...

	~LinearAlgebra ()
	Destructor for a LinearAlgebra object. More...

Detailed Description

This class holds all static methods to perform linear algebra operations on vectors and matrices.

This class has 4 representations of a 3 dimensional rotation

A 3 X 3 rotation matrix
An angle/axis pair - This pair is made up of a vector (axis) and angle of rotation about that axis.
A quaternion - This is saved as a 4-valued unit vector of the form q = (q0, q1, q2, q3) where for the angle/axis pair of the form (A, (ux, uy, uz)), we have q0 = cos(A/2), q1 = ux*sin(A/2), q2 = uy*sin(A/2), q3 = uz*sin(A/2).
A set of Euler angles - This is a set of three angles and their corresponding axis of rotation. In this case, each axis must be one of the x, y, or z axes for the coordinate system.

Author: 2013-06-01 Jeannie Backer

History:

2013-06-01 Jeannie Backer - Original version.

2013-08-07 Kimberly Oyama - Updated documentation.

2016-07-25 Jeannie Backer - Updated documentation and test.

2016-08-05 Jeannie Backer - Replace std abs() function with qAbs() from QtGlobal.

2016-08-16 Jesse Mapel - Added BOOST_UBLAS_NO_STD_CERR definition to prevent Boost from outputing debug information to standard out when throwing exceptions. Fixes #2302.

2017-12-12 Jeannie Backer - Added SymmetricMatrix typedef.

Todo:

document methods (a) add naif routine names to documentation where appropriate, (b) clean up comments within methods, (3) use naif documentation where appropriate

add links to naif documentation web pages???

add proper scopes

implement norm2 (L2 norm)?

implement trace?

common validate errors - vector size match, 3x3 matrix, 3D vector

what is more expensive - unitize vector and compare to 1 or isOrthogonal?

rename local variables m2q and q2m

implement qdq2av (Quaternion and quaternion derivative to angular velocity)?

implement qxq (Quaternion times quaternion)?

implement qderiv (Quadratic derivative)?

When converting quaternion, axis-angle, Euler angle to rot matrix, should we verify that the matrix is valid (is a rotation matrix)???

isQuaternion???

should we throw error in q2m if q = 0???

q2m - why check if sharpen when q is not unit if it is required to be a unit? throw an error?

axisar - throw error if axis is origin? If we rotate about about origin, then we get a zero matrix - not a rotation... except maybe trivially... (or do we get identity??? indicating no rotation)

double check all indexing on code copied from NAIF - indices should reverse col/row order and subtract 1

Definition at line 104 of file LinearAlgebra.h.

Member Typedef Documentation

◆ AxisAngle

typedef QPair<Vector, Angle> Isis::LinearAlgebra::AxisAngle

Definition for an Axis-Angle pair.

This is a three dimensional rotation represented as an axis of rotation and a corresponding rotation angle. AxisAngle is a typedef for a QPair of an Isis::LinearAlgebra::Vector and an Isis::Angle.

Definition at line 144 of file LinearAlgebra.h.

◆ EulerAngle

typedef QPair<Angle, int> Isis::LinearAlgebra::EulerAngle

Definition for an EulerAngle pair.

This is a three dimensional rotation represented as an Euler angle and the number corresponding to its rotation axis. EulerAngle is a typedef for a QPair of an Isis::Angle and an integer (1, 2, or 3).

Definition at line 151 of file LinearAlgebra.h.

◆ Matrix

typedef boost::numeric::ublas::matrix<double> Isis::LinearAlgebra::Matrix

Definition for an Isis::LinearAlgebra::Matrix of doubles.

This is a typedef for a boost matrix.

Note: This typedef is used so that we can add functionality to an existing matrix type and/or change which third party library's matrix we are using without changing all references to this type in the ISIS API.

Definition at line 115 of file LinearAlgebra.h.

◆ SymmetricMatrix

typedef boost::numeric::ublas::symmetric_matrix<double, boost::numeric::ublas::upper> Isis::LinearAlgebra::SymmetricMatrix

Definition for an Isis::LinearAlgebra::SymmetrixMatrix of doubles with an upper configuration.

This is a typedef for a boost symmetric_matrix.

Note: This typedef is used so that we can add functionality to an existing matrix type and/or change which third party library's matrix we are using without changing all references to this type in the ISIS API.

Definition at line 125 of file LinearAlgebra.h.

◆ Vector

typedef boost::numeric::ublas::vector<double> Isis::LinearAlgebra::Vector

Definition for an Isis::LinearAlgebra::Vector of doubles.

This is a typedef for a boost vector.

Note: This typedef is used so that we can add functionality to an existing vector type and/or change which third party library's vector we are using without changing all references to this type in the ISIS API.

Definition at line 135 of file LinearAlgebra.h.

Constructor & Destructor Documentation

◆ LinearAlgebra()

Isis::LinearAlgebra::LinearAlgebra ( )

protected

Default constructor for a LinearAlgebra object.

This is protected so it can never be constructed. The static methods and typedefs in this class are meant to be used without a LinearAlgebra object.

Definition at line 52 of file LinearAlgebra.cpp.

◆ ~LinearAlgebra()

Isis::LinearAlgebra::~LinearAlgebra ( )

protected

Destructor for a LinearAlgebra object.

Definition at line 59 of file LinearAlgebra.cpp.

Member Function Documentation

◆ absoluteMaximum()

double Isis::LinearAlgebra::absoluteMaximum ( const Vector & vector )

static

Returns the maximum norm (L-infinity norm) for the given vector.

The maximum norm is defined by the absolute values of the vector components:

\( \| v \|_\infty = \max_{i=1}^n \{ \mid v_i \mid \} \)

Parameters

vector The vector whose absolute maximum will be returned.

Returns: double The maximum of the absolute values of the vector components.

Definition at line 514 of file LinearAlgebra.cpp.

References vector().

Referenced by magnitude(), normalizedCrossProduct(), and perpendicular().

◆ add()

LinearAlgebra::Vector Isis::LinearAlgebra::add	(	const Vector &	vector1,
		const Vector &	vector2
	)

static

Adds the two given vectors.

Parameters

vector1	The first vector.
vector2	The second vector.

Returns: LinearAlgebra::Vector The sum of the vectors.

Exceptions

IException::Programmer "Unable to add vectors with mismatched sizes."

Definition at line 617 of file LinearAlgebra.cpp.

References _FILEINFO_, Isis::IException::Programmer, and Isis::toString().

◆ column()

LinearAlgebra::Vector Isis::LinearAlgebra::column	(	const Matrix &	matrix,
		int	columnIndex
	)

static

Returns a vector whose components match those of the given matrix column.

Parameters

matrix	The matrix to pull values from.
columnIndex	The index of the matrix column to grab.

Returns: LinearAlgebra::Vector A vector whose values match the given column of the given matrix.

Exceptions

IException::Programmer "Unable to get the matrix column to the given vector. Column index is out of bounds."

Definition at line 1676 of file LinearAlgebra.cpp.

References _FILEINFO_, Isis::IException::Programmer, and Isis::toString().

Referenced by isRotationMatrix(), toEulerAngles(), and toMatrix().

◆ crossProduct()

LinearAlgebra::Vector Isis::LinearAlgebra::crossProduct	(	const Vector &	vector1,
		const Vector &	vector2
	)

static

Returns the cross product of two vectors.

Note: the cross-product requires the vectors to have exactly three components each.

Parameters

vector1	The vector to the left of the cross product operator.
vector2	The vector to the right of the cross product operator.

Returns: LinearAlgebra::Vector The cross product of the given vectors (i.e. vector1 x vector2).

Exceptions

IException::Programmer "Unable to calculate the cross product on vectors that are not size 3. "

Definition at line 671 of file LinearAlgebra.cpp.

References _FILEINFO_, Isis::IException::Programmer, and Isis::toString().

Referenced by normalizedCrossProduct(), and rotate().

◆ determinant()

double Isis::LinearAlgebra::determinant ( const Matrix & matrix )

static

Returns the determinant of the given 3x3 matrix.

Parameters

LinearAlgebra::Matrix The 3x3 matrix whose determinant will be calculated.

Returns: double The determinant of the given matrix.

Exceptions

IException::Programmer "Unable to calculate the determinant for the given matrix. This method only calculates the determinant for 2x2 or 3x3 matrices."

Definition at line 423 of file LinearAlgebra.cpp.

References _FILEINFO_, Isis::IException::Programmer, and Isis::toString().

Referenced by inverse(), and isRotationMatrix().

◆ dotProduct()

double Isis::LinearAlgebra::dotProduct	(	const Vector &	vector1,
		const Vector &	vector2
	)

static

Computes the dot product of the given vectors.

For Euclidean space, this is the same as the inner product, so these methods are interchangeable.

See also: innerProduct()

Parameters

vector1	The first vector.
vector2	The second vector.

Returns: double The dot product of the vectors.

Definition at line 764 of file LinearAlgebra.cpp.

References innerProduct().

Referenced by isUnit(), project(), Isis::RosettaOsirisCameraDistortionMap::SetFocalPlane(), and Isis::RosettaOsirisCameraDistortionMap::SetUndistortedFocalPlane().

◆ identity()

LinearAlgebra::Matrix Isis::LinearAlgebra::identity ( int size )

static

Returns the identity matrix of size NxN.

Parameters

int	The size of the square matrix.

Returns: LinearAlgebra::Matrix The NxN square matrix.

Exceptions

IException::Programmer "Can not create identity matrix of negative size."

Definition at line 367 of file LinearAlgebra.cpp.

References _FILEINFO_, Isis::IException::Programmer, and Isis::toString().

Referenced by inverse(), and toMatrix().

◆ innerProduct()

double Isis::LinearAlgebra::innerProduct	(	const Vector &	vector1,
		const Vector &	vector2
	)

static

Computes the inner product of the given vectors.

For Euclidean space, this is the same as the dot product, so these methods are interchangeable.

See also: dotProduct()

Parameters

vector1	The first vector.
vector2	The second vector.

Returns: double The inner product of the vectors.

Exceptions

IException::Programmer "Unable to compute the dot product for vectors with mismatched sizes."

Definition at line 784 of file LinearAlgebra.cpp.

References _FILEINFO_, Isis::IException::Programmer, and Isis::toString().

Referenced by dotProduct().

◆ inverse()

LinearAlgebra::Matrix Isis::LinearAlgebra::inverse ( const Matrix & matrix )

static

Returns the inverse of a 2x2 or 3x3 matrix.

Throws an error if the given matrix is not invertible.

Parameters

matrix The matrix to inverse.

Returns: LinearAlgebra::Matrix The inverse matrix.

Exceptions

IException::Programmer	"The given matrix is not invertible. The determinant is 0.0."
IException::Programmer	"Unable to invert the given matrix."

Definition at line 295 of file LinearAlgebra.cpp.

References _FILEINFO_, determinant(), identity(), isOrthogonal(), Isis::IException::Programmer, and transpose().

◆ isEmpty()

bool Isis::LinearAlgebra::isEmpty ( const Vector & vector )

static

Determines whether the given vector is empty (i.e.

size 0).

Parameters

vector The vector to check.

Returns: bool Returns true if the size of the given vector is zero.

Definition at line 263 of file LinearAlgebra.cpp.

References vector().

◆ isIdentity()

bool Isis::LinearAlgebra::isIdentity ( const Matrix & matrix )

static

Determines whether the given matrix is the identity.

Non-square matrices always return false. A qfuzzycompare is used when checking the zeroes and ones.

Parameters

matrix The matrix to check. Automatically returns false if not square.

Returns: bool Returns true if the matrix is a square identity matrix (i.e. there are ones down the diagonal and zeroes elsewhere).

Definition at line 74 of file LinearAlgebra.cpp.

References row().

Referenced by isOrthogonal().

◆ isOrthogonal()

bool Isis::LinearAlgebra::isOrthogonal ( const Matrix & matrix )

static

Determines whether the given matrix is orthogonal by verifying that the matrix and its tranpose are inverses.

Parameters

matrix The matrix to check. Automatically returns false if not square.

Returns: bool Returns true if the matrix is orthogonal.

Definition at line 102 of file LinearAlgebra.cpp.

References isIdentity(), multiply(), and transpose().

Referenced by inverse().

◆ isRotationMatrix()

bool Isis::LinearAlgebra::isRotationMatrix ( const Matrix & matrix )

static

Determines whether the given matrix is a rotation matrix.

Parameters

matrix The matrix to check. Automatically returns false if not 2x2 or 3x3.

Returns: bool Returns true if the given matrix represents a rotation.

Exceptions

IException::Programmer "Unable to determine whether the given matrix is a rotation matrix."

Definition at line 126 of file LinearAlgebra.cpp.

References _FILEINFO_, column(), determinant(), magnitude(), Isis::IException::Programmer, and setColumn().

Referenced by toAxisAngle(), toEulerAngles(), and toQuaternion().

◆ isUnit()

bool Isis::LinearAlgebra::isUnit ( const Vector & vector )

static

Determines whether the given vector is a unit vector.

Parameters

vector The vector to check.

Returns: bool Returns true if the vector is a unit vector.

Definition at line 275 of file LinearAlgebra.cpp.

References dotProduct(), and vector().

Referenced by toMatrix(), and toQuaternion().

◆ isZero() [1/2]

bool Isis::LinearAlgebra::isZero ( const Matrix & matrix )

static

Determines whether the given matrix is filled with zereos.

Parameters

vector The matrix to check.

Returns: bool Returns true if the matrix is all zereos.

Definition at line 224 of file LinearAlgebra.cpp.

Referenced by magnitude(), normalize(), perpendicular(), project(), rotate(), toAxisAngle(), and toMatrix().

◆ isZero() [2/2]

bool Isis::LinearAlgebra::isZero ( const Vector & vector )

static

Determines whether the given vector is filled with zereos.

Parameters

vector The vector to check.

Returns: bool Returns true if the vector is all zereos.

Definition at line 244 of file LinearAlgebra.cpp.

References vector().

◆ magnitude()

double Isis::LinearAlgebra::magnitude ( const Vector & vector )

static

Computes the magnitude (i.e., the length) of the given vector using the Euclidean norm (L2 norm).

The maximum norm (L-infinity) is also used to stabilize the solution in order to avoid overflow. This method uses the computation

\( \| v \| = \| v \|_\infty \| \frac{v}{\| v \|_\infty} \|_2 \) where \( \| u \|_\infty = \max_{i=1}^n \{ \mid u_i \mid \} \) is the maximum norm and \( \| u \|_2 = \sqrt{\sum_{i=1}^n u_1^2} \) is the Euclidean norm.

See also: absoluteMaximum()

Parameters

vector The vector whose magnitude will be computed.

Returns: double The magnitude (length) of the given vector.

Definition at line 487 of file LinearAlgebra.cpp.

References absoluteMaximum(), isZero(), and vector().

Referenced by Isis::EmbreeShapeModel::intersectSurface(), isRotationMatrix(), Isis::EmbreeShapeModel::isVisibleFrom(), Isis::EmbreeShapeModel::localRadius(), Isis::EmbreeTargetShape::maximumSceneDistance(), normalize(), Isis::RosettaOsirisCameraDistortionMap::SetUndistortedFocalPlane(), Isis::EmbreeShapeModel::sortHits(), and toAxisAngle().

◆ multiply() [1/4]

LinearAlgebra::Matrix Isis::LinearAlgebra::multiply	(	const Matrix &	matrix1,
		const Matrix &	matrix2
	)

static

Returns the product of two matrices.

Will throw an error if the matrices are not properly sized (the number of columns of the first matrix must match the number or rows of the second matrix).

Parameters

matrix1	The left matrix.
matrix2	The right matrix.

Returns: LinearAlgebra::Matrix The resultant matrix product.

Exceptions

IException::Programmer "Unable to multiply matrices with mismatched dimensions."

Definition at line 532 of file LinearAlgebra.cpp.

References _FILEINFO_, Isis::IException::Programmer, and Isis::toString().

Referenced by isOrthogonal(), Isis::RosettaOsirisCameraDistortionMap::SetFocalPlane(), Isis::RosettaOsirisCameraDistortionMap::SetUndistortedFocalPlane(), and toEulerAngles().

◆ multiply() [2/4]

LinearAlgebra::Vector Isis::LinearAlgebra::multiply	(	const Matrix &	matrix,
		const Vector &	vector
	)

static

Computes the product of the given matrix and vector.

The vector will be multiplied on the right side of the given matrix. Will throw an error if the two are not properly sized (matrix columns not equal to vector size).

Parameters

matrix	The matrix to be multiplied.
vector	The column vector to be multiplied on the right side of the matrix.

Returns: LinearAlgebra::Vector The resultant vector.

Exceptions

IException::Programmer "Unable to multiply matrix and vector with mismatched dimensions."

Definition at line 563 of file LinearAlgebra.cpp.

References _FILEINFO_, Isis::IException::Programmer, Isis::toString(), and vector().

◆ multiply() [3/4]

LinearAlgebra::Vector Isis::LinearAlgebra::multiply	(	double	scalar,
		const Vector &	vector
	)

static

Multiplies the given scalar and vector.

Parameters

scalar	The scalar to be multiplied by each component of the vector.
vector	The vector to be scaled.

Returns: LinearAlgebra::Vector The resultant scaled vector.

Definition at line 586 of file LinearAlgebra.cpp.

References vector().

◆ multiply() [4/4]

LinearAlgebra::Matrix Isis::LinearAlgebra::multiply	(	double	scalar,
		const Matrix &	matrix
	)

static

Multiplies the given scalar and matrix.

Parameters

scalar	The scalar to be multiplied by each element of the matrix.
matrix	The matrix to be scaled.

Returns: LinearAlgebra::Matrix The resultant scaled matrix.

Definition at line 600 of file LinearAlgebra.cpp.

◆ normalize()

LinearAlgebra::Vector Isis::LinearAlgebra::normalize ( const Vector & vector )

static

Returns a unit vector that is codirectional with the given vector by dividing each component of the vector by the vector magnitude.

\( \hat{v} = \frac{v}{\| v \|} \) where \( \| u \|_ \) is the magnitude of u.

See also: magnitude()

Parameters

vector The vector to be normalized.

Returns: LinearAlgebra::Vector A unit vector from the given vector.

Exceptions

IException::Programmer "Unable to normalize the zero vector."

Definition at line 460 of file LinearAlgebra.cpp.

References _FILEINFO_, isZero(), magnitude(), Isis::IException::Unknown, and vector().

Referenced by Isis::EmbreeTargetShape::getHitInformation(), Isis::EmbreeShapeModel::intersectSurface(), normalizedCrossProduct(), Isis::EmbreeShapeModel::pointToRay(), rotate(), toAxisAngle(), toEulerAngles(), toMatrix(), and toQuaternion().

◆ normalizedCrossProduct()

LinearAlgebra::Vector Isis::LinearAlgebra::normalizedCrossProduct	(	const Vector &	vector1,
		const Vector &	vector2
	)

static

Divides each vector by its corresponding absolute maximum, computes the cross product of the new vectors, and normalizes the resultant vector from the cross product.

Note: the cross-product requires the vectors to have exactly three components each.

Parameters

vector1	The vector to the left of the cross product operator.
vector2	The vector to the right of the cross product operator.

Returns: LinearAlgebra::Vector The normalized cross product of the given vectors (i.e. normalize(vector1/absoluteMaximum(vector1) x vector2/absoluteMaximum(vector2))).

Definition at line 704 of file LinearAlgebra.cpp.

References absoluteMaximum(), crossProduct(), and normalize().

◆ outerProduct()

LinearAlgebra::Matrix Isis::LinearAlgebra::outerProduct	(	const Vector &	vector1,
		const Vector &	vector2
	)

static

Computes the outer product of the given vectors.

The outer product operation is defined as the cross product of vector1 and the conjugate transpose of vector2.

Parameters

vector1	The vector to the left side of the outer product operator.
vector2	The vector to the right side of the outer product operator.

Returns: LinearAlgebra::Matrix The outer product matrix of the given vectors.

Exceptions

IException::Programmer "Unable to compute the outer product for vectors with mismatched sizes."

Definition at line 740 of file LinearAlgebra.cpp.

References _FILEINFO_, Isis::IException::Programmer, and Isis::toString().

◆ perpendicular()

LinearAlgebra::Vector Isis::LinearAlgebra::perpendicular	(	const Vector &	vector1,
		const Vector &	vector2
	)

static

Finds the unique vector P such that A = V + P, V is parallel to B and P is perpendicular to B, where A is the first vector (vector1) and B is the second vector (vector2) passed in by the user.

For all vectors A and B, there exists unique vectors V and P such that 1) A = V + P 2) V is parallel to B
3) P is perpendicular to B

Parameters

vector1	The first vector, denoted A in the description.
vector2	The second vector, denoted B in the description.

Returns: LinearAlgebra::Vector A vector perpendicular to vector2 and equal to vector1-parallel2 (where parallel2 is some vector that is parallel to vector2).

Definition at line 915 of file LinearAlgebra.cpp.

References absoluteMaximum(), isZero(), and project().

◆ project()

LinearAlgebra::Vector Isis::LinearAlgebra::project	(	const Vector &	vector1,
		const Vector &	vector2
	)

static

Compute the vector projection of vector1 onto vector2.

This is the orthogonal projection of vector1 onto a line that is parallel to vector2.

It is defined by \( proj_{v_2} v_1 = \frac{v_1 \cdot v_2}{\| v_2 \|^2}v_2 \) where \( \| u \|_ \) is the magnitude of u.

Parameters

vector1	The vector to the left of the project operator.
vector2	The vector to the right of the project operator.

Returns: LinearAlgebra::Vector The resultant vector that is the orthogonal projection of vector1 onto vector2.

Exceptions

IException::Programmer "Unable to project vector1 onto vector2 with mismatched sizes."

Definition at line 816 of file LinearAlgebra.cpp.

References _FILEINFO_, dotProduct(), isZero(), Isis::IException::Programmer, and Isis::toString().

Referenced by perpendicular(), and rotate().

◆ rotate()

LinearAlgebra::Vector Isis::LinearAlgebra::rotate	(	const Vector &	vector,
		const Vector &	axis,
		Angle	angle
	)

static

Rotates a vector about an axis vector given a specified angle.

Note: this method only rotates a vector with three components since the cross product calculation requires this.

Parameters

vector	The vector to rotate, which must have three components.
axis	A vector defining the axis, which must also have three components.
angle	The angle to rotate.

Returns: LinearAlgebra::Vector The rotated vector.

Exceptions

IException::Programmer "Unable to rotate vector about the given axis and angle. Vectors must be of size 3 to perform rotation. "

Definition at line 855 of file LinearAlgebra.cpp.

References _FILEINFO_, crossProduct(), isZero(), normalize(), Isis::IException::Programmer, project(), Isis::Angle::radians(), Isis::toString(), and vector().

Referenced by toMatrix().

◆ row()

LinearAlgebra::Vector Isis::LinearAlgebra::row	(	const Matrix &	matrix,
		int	rowIndex
	)

static

Returns a vector whose components match those of the given matrix row.

Parameters

matrix	The matrix to pull values from.
rowIndex	The index of the matrix row to grab.

Returns: LinearAlgebra::Vector A vector whose values match the given row of the given matrix.

Exceptions

IException::Programmer "Unable to get the matrix row to the given vector. Row index is out of bounds."

Definition at line 1653 of file LinearAlgebra.cpp.

References _FILEINFO_, Isis::IException::Programmer, and Isis::toString().

Referenced by isIdentity().

◆ setColumn()

void Isis::LinearAlgebra::setColumn	(	Matrix &	matrix,
		const Vector &	vector,
		int	columnIndex
	)

static

Sets the column of the given matrix to the values of the given vector.

Parameters

matrix	The address of the matrix to be altered.
vector	The vector with the new values.
columnIndex	The index of the column to be altered.

Exceptions

IException::Programmer "Unable to set the matrix column to the given vector. Column index is out of bounds."

Definition at line 1630 of file LinearAlgebra.cpp.

References _FILEINFO_, Isis::IException::Programmer, Isis::toString(), and vector().

Referenced by isRotationMatrix(), toEulerAngles(), and toMatrix().

◆ setRow()

void Isis::LinearAlgebra::setRow	(	Matrix &	matrix,
		const Vector &	vector,
		int	rowIndex
	)

static

Sets the row of the given matrix to the values of the given vector.

Parameters

matrix	The address of the matrix to be altered.
vector	The vector with the new values.
rowIndex	The index of the row to be altered.

Exceptions

IException::Programmer "Unable to set the matrix row to the given vector. Row index is out of bounds."

Definition at line 1609 of file LinearAlgebra.cpp.

References _FILEINFO_, Isis::IException::Programmer, Isis::toString(), and vector().

◆ setVec3()

void Isis::LinearAlgebra::setVec3	(	Vector *	v,
		double	v0,
		double	v1,
		double	v2
	)

static

Fills the first three elements of the given vector with the given values.

Parameters

v	A pointer to a 3-dimensional vector to be filled.
v0	The first component of the vector.
v1	The second component of the vector.
v2	The third component of the vector.

Definition at line 1735 of file LinearAlgebra.cpp.

◆ setVec4()

void Isis::LinearAlgebra::setVec4	(	Vector *	v,
		double	v0,
		double	v1,
		double	v2,
		double	v3
	)

static

Fills the first four elements of the given vector with the given values.

Parameters

v	A pointer to a 4-dimensional vector to be filled.
v0	The first component of the vector.
v1	The second component of the vector.
v2	The third component of the vector.
v3	The fourth component of the vector.

Definition at line 1751 of file LinearAlgebra.cpp.

◆ subtract()

LinearAlgebra::Vector Isis::LinearAlgebra::subtract	(	const Vector &	vector1,
		const Vector &	vector2
	)

static

Subtracts the right vector from the left vector.

Parameters

vector1	The vector to the left of the subtraction operator.
vector2	The vector to the right of the subtraction operator.

Returns: LinearAlgebra::Vector The difference of the vectors (i.e. vector1 - vector2).

Exceptions

IException::Programmer "Unable to subtract vectors with mismatched sizes."

Definition at line 643 of file LinearAlgebra.cpp.

References _FILEINFO_, Isis::IException::Programmer, and Isis::toString().

◆ subVector()

LinearAlgebra::Vector Isis::LinearAlgebra::subVector	(	const Vector &	v,
		int	startIndex,
		int	size
	)

static

Constructs a vector of given size using the given vector and starting index.

Parameters

v	The original vector to get values from.
startIndex	The index of the original vector, used to indicate the first value that will be copied to the new vector.
size	The number of elements from the original vector to copy to the new vector.

Returns: LinearAlgebra::Vector A sub-vector containing values from the original vector.

Definition at line 1772 of file LinearAlgebra.cpp.

◆ toAxisAngle()

LinearAlgebra::AxisAngle Isis::LinearAlgebra::toAxisAngle ( const Matrix & rotationMatrix )

static

Converts a rotation's representation from a matrix to a axis of rotation and its corresponding rotation angle.

Parameters

rotationMatrix A matrix representing a rotation.

Returns: LinearAlgebra::AxisAngle The axis-angle pair representing the rotation.

Exceptions

IException::Programmer "Unable to convert the given matrix to an axis of rotation and a rotation angle. A 3x3 matrix is required." @throw IException::Programmer "Unable to convert the given matrix to an axis of rotation and a rotation angle. The given matrix is not a rotation matrix."

Definition at line 956 of file LinearAlgebra.cpp.

References _FILEINFO_, isRotationMatrix(), isZero(), magnitude(), normalize(), Isis::PI, Isis::IException::Programmer, Isis::Angle::setRadians(), toQuaternion(), and Isis::toString().

◆ toEulerAngles()

QList< LinearAlgebra::EulerAngle > Isis::LinearAlgebra::toEulerAngles	(	const Matrix &	rotationMatrix,
		const QList< int >	axes
	)

static

Converts a rotation's representation from a matrix to a set of Euler angles with corresponding axes.

Parameters

rotationMatrix	A matrix representing a rotation.
axes	A list containing the order of axes.

Returns: QList< LinearAlgebra::EulerAngle> The list of 3 Euler angles with their axes representing the rotation.

Exceptions

IException::Programmer	"Unable to convert the given matrix to Euler angles. Exactly 3 axis codes are required."
IException::Programmer	"Unable to convert the given matrix to Euler angles using the given axis codes. Axis codes must be 1, 2, or 3."
IException::Programmer	"Unable to convert the given matrix to Euler angles using the given axis codes. The middle axis code must differ from its neighbors." @throw IException::Programmer "Unable to convert the given matrix to Euler angles. A 3x3 matrix is required." @throw IException::Programmer "Unable to convert the given matrix to Euler angles. The given matrix is not a rotation matrix."

Definition at line 1034 of file LinearAlgebra.cpp.

References _FILEINFO_, column(), isRotationMatrix(), multiply(), normalize(), Isis::IException::Programmer, setColumn(), Isis::Angle::setRadians(), Isis::toString(), transpose(), and zeroMatrix().

◆ toMatrix() [1/5]

LinearAlgebra::Matrix Isis::LinearAlgebra::toMatrix ( const AxisAngle & axisAngle )

static

Converts a rotation's representation from an axis of rotation and its corresponding rotation angle to a 3x3 matrix.

Parameters

axisAngle The axis-angle pair representation of a rotation

Returns: LinearAlgebra::Matrix The matrix representation of the rotation.

Definition at line 1425 of file LinearAlgebra.cpp.

Referenced by toMatrix().

◆ toMatrix() [2/5]

LinearAlgebra::Matrix Isis::LinearAlgebra::toMatrix	(	const Vector &	axis,
		Angle	angle
	)

static

Converts a rotation's representation from an axis of rotation and its corresponding rotation angle to a 3x3 matrix.

Parameters

axis	The axis of rotation for a rotation.
angle	The rotation angle.

Returns: LinearAlgebra::Matrix The matrix representing the rotation.

Exceptions

IException::Programmer "Unable to convert the given vector and angle to a rotation matrix. The given vector is not a 3D axis vector."

Definition at line 1388 of file LinearAlgebra.cpp.

References _FILEINFO_, column(), identity(), Isis::IException::Programmer, rotate(), setColumn(), and Isis::toString().

◆ toMatrix() [3/5]

LinearAlgebra::Matrix Isis::LinearAlgebra::toMatrix ( const QList< EulerAngle > & eulerAngles )

static

Converts a rotation's representation from a list of Euler angles (3 angles, each with a corresponding axis) to a 3x3 matrix.

Parameters

eulerAngles The Euler angle representation of a rotation.

Returns: LinearAlgebra::Matrix The matrix representation of the rotation.

Exceptions

IException::Programmer "Unable to convert the given Euler angles to a matrix. Exactly 3 Euler angles are required."

Definition at line 1528 of file LinearAlgebra.cpp.

References _FILEINFO_, Isis::IException::Programmer, toMatrix(), and Isis::toString().

◆ toMatrix() [4/5]

LinearAlgebra::Matrix Isis::LinearAlgebra::toMatrix	(	const EulerAngle &	angle3,
		const EulerAngle &	angle2,
		const EulerAngle &	angle1
	)

static

Converts a rotation's representation from a set of Euler angles (3 angles, each with a corresponding axis) to a 3x3 matrix.

Parameters

angle3	The third angle and its axis.
angle2	The second angle and its axis.
angle1	The first angle and its axis.

Returns: LinearAlgebra::Matrix The matrix representation of the rotation.

Exceptions

IException::Programmer "Unable to convert the given Euler angles to a matrix using the given axis codes. Axis codes must be 1, 2, or 3."

Definition at line 1445 of file LinearAlgebra.cpp.

References _FILEINFO_, Isis::IException::Programmer, and Isis::toString().

◆ toMatrix() [5/5]

LinearAlgebra::Matrix Isis::LinearAlgebra::toMatrix ( const Vector & quaternion )

static

Converts a rotation's representation from a quaternion to a 3x3 matrix.

Note, if the given vector is not a unit vector or the zero vector, this method will normalize it before computing the corresponding matrix.

Parameters

quaternion A unit quaternion representation of a rotation.

Returns: LinearAlgebra::Matrix The matrix representation of the rotation.

Exceptions

IException::Programmer "Unable to convert the given vector to a rotation matrix. The given vector is not a quaternion."

Definition at line 1555 of file LinearAlgebra.cpp.

References _FILEINFO_, isUnit(), isZero(), normalize(), Isis::IException::Programmer, and Isis::toString().

◆ toQuaternion()

LinearAlgebra::Vector Isis::LinearAlgebra::toQuaternion ( const Matrix & rotationMatrix )

static

Converts a rotation's representation from a matrix to a unit quaternion.

Parameters

rotationMatrix A matrix representing a rotation.

Returns: LinearAlgebra::Vector A unit quaternion representing the rotation.

Exceptions

IException::Programmer	"Unable to convert the given matrix to a quaternion. A 3x3 matrix is required.
IException::Programmer	"Unable to convert the given matrix to an axis of rotation and a rotation angle. The given matrix is not a rotation matrix."

Definition at line 1194 of file LinearAlgebra.cpp.

References _FILEINFO_, isRotationMatrix(), isUnit(), normalize(), Isis::IException::Programmer, and Isis::toString().

Referenced by toAxisAngle().

◆ transpose()

LinearAlgebra::Matrix Isis::LinearAlgebra::transpose ( const Matrix & matrix )

static

Returns the transpose of the given matrix.

Parameters

matrix The matrix to transpose.

Returns: LinearAlgebra::Matrix The transposed matrix.

Definition at line 352 of file LinearAlgebra.cpp.

Referenced by inverse(), isOrthogonal(), and toEulerAngles().

◆ vector() [1/2]

LinearAlgebra::Vector Isis::LinearAlgebra::vector	(	double	v0,
		double	v1,
		double	v2
	)

static

Constructs a 3 dimensional vector with the given component values.

Parameters

v0	The first component of the vector.
v1	The second component of the vector.
v2	The third component of the vector.

Returns: LinearAlgebra::Vector A vector containing the given values.

Definition at line 1697 of file LinearAlgebra.cpp.

Referenced by absoluteMaximum(), Isis::EmbreeShapeModel::intersectSurface(), isEmpty(), isUnit(), Isis::EmbreeShapeModel::isVisibleFrom(), isZero(), magnitude(), multiply(), normalize(), Isis::EmbreeShapeModel::pointToRay(), Isis::RayHitInformation::RayHitInformation(), rotate(), setColumn(), and setRow().

◆ vector() [2/2]

LinearAlgebra::Vector Isis::LinearAlgebra::vector	(	double	v0,
		double	v1,
		double	v2,
		double	v3
	)

static

Constructs a 4 dimensional vector with the given component values.

Parameters

v0	The first component of the vector.
v1	The second component of the vector.
v2	The third component of the vector.
v3	The fourth component of the vector.

Returns: LinearAlgebra::Vector A vector containing the given values.

Definition at line 1717 of file LinearAlgebra.cpp.

◆ zeroMatrix()

LinearAlgebra::Matrix Isis::LinearAlgebra::zeroMatrix	(	int	rows,
		int	columns
	)

static

Returns a matrix with given dimensions that is filled with zeroes.

Parameters

rows	The number of rows in the returned matrix.
columns	The number of colums in the returned matrix.

Returns: LinearAlgebra::Matrix A zero-filled matrix.

Definition at line 391 of file LinearAlgebra.cpp.

Referenced by Isis::RosettaOsirisCamera::initDistortion(), Isis::RosettaOsirisCameraDistortionMap::RosettaOsirisCameraDistortionMap(), Isis::RosettaOsirisCameraDistortionMap::SetUndistortedFocalPlane(), and toEulerAngles().

◆ zeroVector()

LinearAlgebra::Vector Isis::LinearAlgebra::zeroVector ( int size )

static

Returns a vector of given length that is filled with zeroes.

Parameters

size	Size of the vector.

Returns: LinearAlgebra::Vector A zero-filled vector.

Definition at line 404 of file LinearAlgebra.cpp.

Referenced by Isis::RosettaOsirisCameraDistortionMap::SetFocalPlane(), and Isis::RosettaOsirisCameraDistortionMap::SetUndistortedFocalPlane().

The documentation for this class was generated from the following files:

src/base/objs/LinearAlgebra/LinearAlgebra.h
src/base/objs/LinearAlgebra/LinearAlgebra.cpp

Public Types

Static Public Member Functions

Protected Member Functions

Detailed Description

Member Typedef Documentation

◆ AxisAngle

◆ EulerAngle

◆ Matrix

◆ SymmetricMatrix

◆ Vector

Constructor & Destructor Documentation

◆ LinearAlgebra()

◆ ~LinearAlgebra()

Member Function Documentation

◆ absoluteMaximum()

◆ add()

◆ column()

◆ crossProduct()

◆ determinant()

◆ dotProduct()

◆ identity()

◆ innerProduct()

◆ inverse()

◆ isEmpty()

◆ isIdentity()

◆ isOrthogonal()

◆ isRotationMatrix()

◆ isUnit()

◆ isZero() [1/2]

◆ isZero() [2/2]

◆ magnitude()

◆ multiply() [1/4]

◆ multiply() [2/4]

◆ multiply() [3/4]

◆ multiply() [4/4]

◆ normalize()

◆ normalizedCrossProduct()

◆ outerProduct()

◆ perpendicular()

◆ project()

◆ rotate()

◆ row()

◆ setColumn()

◆ setRow()

◆ setVec3()

◆ setVec4()

◆ subtract()

◆ subVector()

◆ toAxisAngle()

◆ toEulerAngles()

◆ toMatrix() [1/5]

◆ toMatrix() [2/5]

◆ toMatrix() [3/5]

◆ toMatrix() [4/5]

◆ toMatrix() [5/5]

◆ toQuaternion()

◆ transpose()

◆ vector() [1/2]

◆ vector() [2/2]

◆ zeroMatrix()

◆ zeroVector()