Static Eigen-based linear-algebra helpers used across MATHLIB and the inverse solvers. More...

#include <linalg.h>

Public Types
typedef std::pair< int, int >	IdxIntValue

Public Member Functions
	~Linalg ()=default

Static Public Member Functions
static Eigen::VectorXd	combine_xyz (const Eigen::VectorXd &vec)
static double	getConditionNumber (const Eigen::MatrixXd &A, Eigen::VectorXd &s)
static double	getConditionSlope (const Eigen::MatrixXd &A, Eigen::VectorXd &s)
static void	get_whitener (Eigen::MatrixXd &A, bool pca, QString ch_type, Eigen::VectorXd &eig, Eigen::MatrixXd &eigvec)
static void	get_whitener (Eigen::MatrixXd &A, bool pca, const std::string &ch_type, Eigen::VectorXd &eig, Eigen::MatrixXd &eigvec)
static Eigen::VectorXi	intersect (const Eigen::VectorXi &v1, const Eigen::VectorXi &v2, Eigen::VectorXi &idx_sel)
static Eigen::SparseMatrix< double >	make_block_diag (const Eigen::MatrixXd &A, qint32 n)
template<typename T>
static Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic >	pinv (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &a)
static qint32	rank (const Eigen::MatrixXd &A, double tol=1e-8)
template<typename T>
static Eigen::VectorXi	sort (Eigen::Matrix< T, Eigen::Dynamic, 1 > &v, bool desc=true)
template<typename T>
static Eigen::VectorXi	sort (Eigen::Matrix< T, Eigen::Dynamic, 1 > &v_prime, Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &mat, bool desc=true)
template<typename T>
static std::vector< Eigen::Triplet< T > >	sortrows (const std::vector< Eigen::Triplet< T > > &A, qint32 column=0)
template<typename T>
static bool	compareIdxValuePairBiggerThan (const std::pair< int, T > &lhs, const std::pair< int, T > &rhs)
template<typename T>
static bool	compareIdxValuePairSmallerThan (const std::pair< int, T > &lhs, const std::pair< int, T > &rhs)
template<typename T>
static bool	compareTripletFirstEntry (const Eigen::Triplet< T > &lhs, const Eigen::Triplet< T > &rhs)
template<typename T>
static bool	compareTripletSecondEntry (const Eigen::Triplet< T > &lhs, const Eigen::Triplet< T > &rhs)

Detailed Description

Static Eigen-based linear-algebra helpers used across MATHLIB and the inverse solvers.

Static linear-algebra utilities (condition numbers, block-diagonal sparse assembly, xyz reductions, stable index sort) layered on top of Eigen for use across MATHLIB, FWDLIB and INVERSELIB.

Definition at line 72 of file linalg.h.

Member Typedef Documentation

◆ IdxIntValue

typedef std::pair<int, int> UTILSLIB::Linalg::IdxIntValue

Typedef of a pair of ints.

Definition at line 75 of file linalg.h.

Constructor & Destructor Documentation

◆ ~Linalg()

UTILSLIB::Linalg::~Linalg ( )

default

Destroys the Linalg object.

Member Function Documentation

◆ combine_xyz()

VectorXd Linalg::combine_xyz ( const Eigen::VectorXd & vec )

static

Compute the three Cartesian components of a vector together.

Parameters

[in] vec Input row vector [ x1 y1 z1 ... x_n y_n z_n ].

Returns: Output vector [x1^2+y1^2+z1^2 ... x_n^2+y_n^2+z_n^2 ].

Definition at line 57 of file linalg.cpp.

◆ compareIdxValuePairBiggerThan()

template<typename T>

bool UTILSLIB::Linalg::compareIdxValuePairBiggerThan	(	const std::pair< int, T > &	lhs,
		const std::pair< int, T > &	rhs )

inlinestatic

Compares two index-value-pairs (greater-than).

Parameters

[in]	lhs	Left index-value pair.
[in]	rhs	Right index-value pair.

Returns: True if the value of lhs is greater than the value of rhs.

Definition at line 363 of file linalg.h.

◆ compareIdxValuePairSmallerThan()

template<typename T>

bool UTILSLIB::Linalg::compareIdxValuePairSmallerThan	(	const std::pair< int, T > &	lhs,
		const std::pair< int, T > &	rhs )

inlinestatic

Compares two index-value-pairs (less-than).

Parameters

[in]	lhs	Left index-value pair.
[in]	rhs	Right index-value pair.

Returns: True if the value of lhs is less than the value of rhs.

Definition at line 372 of file linalg.h.

◆ compareTripletFirstEntry()

template<typename T>

bool UTILSLIB::Linalg::compareTripletFirstEntry	(	const Eigen::Triplet< T > &	lhs,
		const Eigen::Triplet< T > &	rhs )

inlinestatic

Compares triplet first entry (row).

Parameters

[in]	lhs	Left triplet.
[in]	rhs	Right triplet.

Returns: True if the row index of lhs is less than that of rhs.

Definition at line 381 of file linalg.h.

◆ compareTripletSecondEntry()

template<typename T>

bool UTILSLIB::Linalg::compareTripletSecondEntry	(	const Eigen::Triplet< T > &	lhs,
		const Eigen::Triplet< T > &	rhs )

inlinestatic

Compares triplet second entry (column).

Parameters

[in]	lhs	Left triplet.
[in]	rhs	Right triplet.

Returns: True if the column index of lhs is less than that of rhs.

Definition at line 390 of file linalg.h.

◆ get_whitener() [1/2]

void UTILSLIB::Linalg::get_whitener	(	Eigen::MatrixXd &	A,
		bool	pca,
		const std::string &	ch_type,
		Eigen::VectorXd &	eig,
		Eigen::MatrixXd &	eigvec )

static

Returns the whitener of a given matrix.

Parameters

[in]	A	Matrix to compute the whitener from.
[in]	pca	Perform a PCA.
[in]	ch_type	Channel type string.
[out]	eig	Eigenvalues.
[out]	eigvec	Eigenvectors (transposed).

◆ get_whitener() [2/2]

void UTILSLIB::Linalg::get_whitener	(	Eigen::MatrixXd &	A,
		bool	pca,
		QString	ch_type,
		Eigen::VectorXd &	eig,
		Eigen::MatrixXd &	eigvec )

static

Returns the whitener of a given matrix.

Parameters

[in]	A	Matrix to compute the whitener from.
[in]	pca	Perform a PCA.
[in]	ch_type	Channel type string.
[out]	eig	Eigenvalues.
[out]	eigvec	Eigenvectors (transposed).

◆ getConditionNumber()

double Linalg::getConditionNumber	(	const Eigen::MatrixXd &	A,
		Eigen::VectorXd &	s )

static

Returns the condition number of a given matrix.

Parameters

[in]	A	Matrix to compute the condition number from.
[out]	s	Singular values of A.

Returns: the condition number.

Definition at line 78 of file linalg.cpp.

◆ getConditionSlope()

double Linalg::getConditionSlope	(	const Eigen::MatrixXd &	A,
		Eigen::VectorXd &	s )

static

Returns the condition slope of a given matrix.

Parameters

[in]	A	Matrix to compute the condition number from.
[out]	s	Singular values of A.

Returns: the condition slope.

Definition at line 91 of file linalg.cpp.

◆ intersect()

VectorXi Linalg::intersect	(	const Eigen::VectorXi &	v1,
		const Eigen::VectorXi &	v2,
		Eigen::VectorXi &	idx_sel )

static

Find the intersection of two vectors.

Parameters

[in]	v1	Input vector 1.
[in]	v2	Input vector 2.
[out]	idx_sel	Index of intersection based on v1.

Returns: the sorted, unique values that are in both of the input arrays.

Definition at line 160 of file linalg.cpp.

◆ make_block_diag()

SparseMatrix< double > Linalg::make_block_diag	(	const Eigen::MatrixXd &	A,
		qint32	n )

static

Make a sparse block diagonal matrix.

Returns a sparse block diagonal, diagonalized from the elements in "A". "A" is ma x na, comprising bdn=(na/"n") blocks of submatrices. Each submatrix is ma x "n", and these submatrices are placed down the diagonal of the matrix.

Parameters

[in]	A	Matrix which should be diagonalized.
[in]	n	Columns of the submatrices.

Returns: A sparse block diagonal, diagonalized from the elements in "A".

Definition at line 193 of file linalg.cpp.

◆ pinv()

template<typename T>

Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > UTILSLIB::Linalg::pinv ( const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > & a )

static

Creates the pseudo inverse of a matrix.

Parameters

[in] a Matrix to compute the pseudo inverse of.

Returns: the pseudo inverse of a.

Definition at line 399 of file linalg.h.

◆ rank()

qint32 Linalg::rank	(	const Eigen::MatrixXd &	A,
		double	tol = 1e-8 )

static

Returns the rank of a matrix A.

Parameters

[in]	A	Matrix to get the rank from.
[in]	tol	Relative threshold: biggest singular value multiplied with tol is smallest singular value considered non-zero.

Returns: rank of matrix A.

Definition at line 226 of file linalg.cpp.

◆ sort() [1/2]

template<typename T>

Eigen::VectorXi UTILSLIB::Linalg::sort	(	Eigen::Matrix< T, Eigen::Dynamic, 1 > &	v,
		bool	desc = true )

static

Sorts a vector (ascending order) in place and returns the track of the original indices.

Parameters

[in,out]	v	Vector to sort; it's sorted in place.
[in]	desc	If true its sorted in a descending order, otherwise ascending (default = true).

Returns: Vector of the original indices in the new order.

Definition at line 298 of file linalg.h.

◆ sort() [2/2]

template<typename T>

Eigen::VectorXi UTILSLIB::Linalg::sort	(	Eigen::Matrix< T, Eigen::Dynamic, 1 > &	v_prime,
		Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &	mat,
		bool	desc = true )

static

Sorts a vector and a corresponding matrix in place and returns the track of the original indices. The matrix is sorted along the columns using the vector values for comparison.

Parameters

[in,out]	v_prime	Vector to sort (sorted in place).
[in,out]	mat	Matrix to sort (sorted in place).
[in]	desc	If true its sorted in a descending order, otherwise ascending (default = true).

Returns: Vector of the original indices in the new order.

Definition at line 325 of file linalg.h.

◆ sortrows()

template<typename T>

std::vector< Eigen::Triplet< T > > UTILSLIB::Linalg::sortrows	(	const std::vector< Eigen::Triplet< T > > &	A,
		qint32	column = 0 )

static

Sort rows in ascending order.

Parameters

[in]	A	Triplet vector to sort.
[in]	column	Sorts the triplet vector based on the column specified.

Returns: Sorted copy of the triplet vector.

Definition at line 344 of file linalg.h.

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

src/libraries/math/linalg.h
src/libraries/math/linalg.cpp

Public Types

Public Member Functions

Static Public Member Functions

Detailed Description

Member Typedef Documentation

◆ IdxIntValue

Constructor & Destructor Documentation

◆ ~Linalg()

Member Function Documentation

◆ combine_xyz()

◆ compareIdxValuePairBiggerThan()

◆ compareIdxValuePairSmallerThan()

◆ compareTripletFirstEntry()

◆ compareTripletSecondEntry()

◆ get_whitener() [1/2]

◆ get_whitener() [2/2]

◆ getConditionNumber()

◆ getConditionSlope()

◆ intersect()

◆ make_block_diag()

◆ pinv()

◆ rank()

◆ sort() [1/2]

◆ sort() [2/2]

◆ sortrows()