Class for interval matrices (i.e., every element of the matrix is an interval) More...

#include <IntervalMatrix.hpp>

Public Member Functions
	IntervalMatrix ()
	IntervalMatrix default constructor.

	IntervalMatrix (size_t rows, size_t cols, const std::vector< Eigen::Triplet< Interval > > &triplets)
	IntervalMatrix constructor using triplets.

	IntervalMatrix (const Eigen::Matrix< zono_float, -1, -1 > &mat_lb, const Eigen::Matrix< zono_float, -1, -1 > &mat_ub)
	IntervalMatrix constructor using dense lower and upper bound matrices.

	IntervalMatrix (const Eigen::Matrix< Interval, -1, -1 > &mat)
	IntervalMatrix constructor from Eigen matrix of intervals.

std::vector< std::vector< Interval > >	to_array () const
	Convert to a vector of vectors of Intervals (row-major)

std::tuple< int, int, std::vector< Eigen::Triplet< Interval > > >	to_triplets () const
	Convert to triplets.

Eigen::SparseMatrix< zono_float >	center () const
	Get center matrix.

Eigen::SparseMatrix< zono_float >	diam () const
	Get diameter matrix.

IntervalMatrix	radius () const
	Get radius matrix.

zono_float	width () const
	Get width of interval matrix.

IntervalMatrix	intersect (const IntervalMatrix &other) const
	Interval matrix intersection.

IntervalMatrix	interval_hull (const IntervalMatrix &other) const
	Interval matrix interval hull.

bool	contains (const Eigen::SparseMatrix< zono_float > &mat) const
	Check whether the interval matrix contains a given sparse matrix.

bool	contains_set (const IntervalMatrix &other) const
	Check whether the interval matrix contains another interval matrix.

Box	operator* (const Eigen::Vector< zono_float, -1 > &v) const
	IntervalMatrix multiplication with vector.

Box	operator* (const Box &box) const
	IntervalMatrix multiplication with Box.

IntervalMatrix	operator* (zono_float alpha) const
	IntervalMatrix scalar multiplication.

void	operator*= (zono_float alpha)
	IntervalMatrix scalar multiplication in-place.

IntervalMatrix	operator* (const Interval &interval) const
	IntervalMatrix elementwise multiplication by interval.

void	operator*= (const Interval &interval)
	IntervalMatrix elementwise multiplication by interval in-place.

IntervalMatrix	operator/ (zono_float alpha) const
	IntervalMatrix elementwise division by scalar.

void	operator/= (zono_float alpha)
	IntervalMatrix elementwise division by scalar.

IntervalMatrix	operator/ (const Interval &interval) const
	IntervalMatrix elementwise division by interval.

void	operator/= (const Interval &interval)
	IntervalMatrix elementwise division by interval in-place.

IntervalMatrix	operator* (const Eigen::SparseMatrix< zono_float, Eigen::RowMajor > &A) const
	IntervalMatrix multiplication with sparse matrix.

IntervalMatrix	operator* (const Eigen::Matrix< zono_float, -1, -1 > &A) const
	IntervalMatrix multiplication with dense matrix.

IntervalMatrix	operator* (const IntervalMatrix &other) const
	IntervalMatrix multiplication with another IntervalMatrix.

void	operator*= (const IntervalMatrix &other)
	IntervalMatrix multiplication with another IntervalMatrix in-place.

IntervalMatrix	operator+ (const IntervalMatrix &other) const
	IntervalMatrix addition.

void	operator+= (const IntervalMatrix &other)
	IntervalMatrix addition in-place.

IntervalMatrix	operator+ (const Interval &interval) const
	IntervalMatrix element-wise addition with interval.

void	operator+= (const Interval &interval)
	IntervalMatrix element-wise addition with interval in-place.

IntervalMatrix	operator+ (zono_float alpha) const
	IntervalMatrix element-wise addition with scalar.

void	operator+= (zono_float alpha)
	IntervalMatrix element-wise addition with scalar in-place.

IntervalMatrix	operator- (const IntervalMatrix &other) const
	IntervalMatrix subtraction.

void	operator-= (const IntervalMatrix &other)
	IntervalMatrix subtraction in-place.

IntervalMatrix	operator- (const Interval &interval) const
	IntervalMatrix elementwise interval subtraction.

void	operator-= (const Interval &interval)
	IntervalMatrix elementwise interval subtraction in-place.

IntervalMatrix	operator- (zono_float alpha) const
	IntervalMatrix elementwise scalar subtraction.

void	operator-= (zono_float alpha)
	IntervalMatrix elementwise scalar subtraction in-place.

IntervalMatrix	operator- () const
	IntervalMatrix negation.

IntervalMatrix	operator& (const IntervalMatrix &other) const
	Interval matrix intersection oeprator.

IntervalMatrix	operator\| (const IntervalMatrix &other) const
	Interval matrix interval hull operator.

bool	operator<= (const IntervalMatrix &other) const
	Set containment operator.

bool	operator>= (const IntervalMatrix &other) const
	Set containment operator.

bool	operator== (const IntervalMatrix &other) const
	Set equality operator.

size_t	rows () const
	Get number of rows.

size_t	cols () const
	Get number of columns.

std::string	print () const
	Print method.

Friends
IntervalMatrix	operator* (zono_float alpha, const IntervalMatrix &A)
	IntervalMatrix scalar multiplication.

IntervalMatrix	operator* (const Interval &interval, const IntervalMatrix &A)
	IntervalMatrix elementwise multiplication by interval.

IntervalMatrix	operator/ (zono_float alpha, const IntervalMatrix &A)
	IntervalMatrix elementwise scalar division.

IntervalMatrix	operator/ (const Interval &interval, const IntervalMatrix &A)
	IntervalMatrix elementwise interval division.

IntervalMatrix	operator* (const Eigen::SparseMatrix< zono_float, Eigen::RowMajor > &A, const IntervalMatrix &B)
	IntervalMatrix multiplication with sparse matrix.

IntervalMatrix	operator* (const Eigen::Matrix< zono_float, -1, -1 > &A, const IntervalMatrix &B)
	IntervalMatrix multiplication with dense matrix.

IntervalMatrix	operator+ (const Interval &interval, const IntervalMatrix &mat)
	IntervalMatrix element-wise addition with interval.

IntervalMatrix	operator+ (zono_float alpha, const IntervalMatrix &A)
	IntervalMatrix element-wise addition with scalar.

IntervalMatrix	operator- (const Interval &interval, const IntervalMatrix &mat)
	IntervalMatrix elementwise interval subtraction.

IntervalMatrix	operator- (zono_float alpha, const IntervalMatrix &A)
	IntervalMatrix elementwise scalar subtraction.

std::ostream &	operator<< (std::ostream &os, const IntervalMatrix &interval_matrix)
	print to ostream

Detailed Description

Class for interval matrices (i.e., every element of the matrix is an interval)

Constructor & Destructor Documentation

◆ IntervalMatrix() [1/4]

ZonoOpt::IntervalMatrix::IntervalMatrix ( )

inline

IntervalMatrix default constructor.

◆ IntervalMatrix() [2/4]

ZonoOpt::IntervalMatrix::IntervalMatrix	(	size_t	rows,
		size_t	cols,
		const std::vector< Eigen::Triplet< Interval > > &	triplets
	)

IntervalMatrix constructor using triplets.

Parameters

rows	number of rows
cols	number of columns
triplets	triplets for interval matrix (row, col, interval)

◆ IntervalMatrix() [3/4]

ZonoOpt::IntervalMatrix::IntervalMatrix	(	const Eigen::Matrix< zono_float, -1, -1 > &	mat_lb,
		const Eigen::Matrix< zono_float, -1, -1 > &	mat_ub
	)

IntervalMatrix constructor using dense lower and upper bound matrices.

Parameters

mat_lb	lower bound matrix
mat_ub	upper bound matrix

◆ IntervalMatrix() [4/4]

ZonoOpt::IntervalMatrix::IntervalMatrix ( const Eigen::Matrix< Interval, -1, -1 > & mat )

explicit

IntervalMatrix constructor from Eigen matrix of intervals.

Parameters

mat	matrix of intervals

Member Function Documentation

◆ center()

Eigen::SparseMatrix< zono_float > ZonoOpt::IntervalMatrix::center ( ) const

Get center matrix.

Returns: center matrix

Each element of center matrix is the center of the corresponding interval in the interval matrix

◆ cols()

size_t ZonoOpt::IntervalMatrix::cols ( ) const

inline

Get number of columns.

Returns: number of cols

◆ contains()

bool ZonoOpt::IntervalMatrix::contains ( const Eigen::SparseMatrix< zono_float > & mat ) const

Check whether the interval matrix contains a given sparse matrix.

Parameters

mat matrix

Returns: true if mat is contained in the interval matrix, false otherwise

◆ contains_set()

bool ZonoOpt::IntervalMatrix::contains_set ( const IntervalMatrix & other ) const

Check whether the interval matrix contains another interval matrix.

Parameters

other interval matrix

Returns: true if other is contained in this, false otherwise

◆ diam()

Eigen::SparseMatrix< zono_float > ZonoOpt::IntervalMatrix::diam ( ) const

Get diameter matrix.

Returns: diameter matrix

Each element of the diameter matrix is the width of the corresponding interval in the interval matrix

◆ intersect()

IntervalMatrix ZonoOpt::IntervalMatrix::intersect ( const IntervalMatrix & other ) const

Interval matrix intersection.

Parameters

other interval matrix to intersect with

Returns: IntervalMatrix

◆ interval_hull()

IntervalMatrix ZonoOpt::IntervalMatrix::interval_hull ( const IntervalMatrix & other ) const

Interval matrix interval hull.

Parameters

other interval matrix to compute hull with

Returns: IntervalMatrix

◆ operator&()

IntervalMatrix ZonoOpt::IntervalMatrix::operator& ( const IntervalMatrix & other ) const

Interval matrix intersection oeprator.

Parameters

other interval matrix to intersect with

Returns: IntervalMatrix

◆ operator*() [1/7]

Box ZonoOpt::IntervalMatrix::operator* ( const Box & box ) const

IntervalMatrix multiplication with Box.

Parameters

box rhs box

Returns: resulting box

◆ operator*() [2/7]

IntervalMatrix ZonoOpt::IntervalMatrix::operator* ( const Eigen::Matrix< zono_float, -1, -1 > & A ) const

IntervalMatrix multiplication with dense matrix.

Parameters

A	rhs matrix

Returns: resulting interval matrix

◆ operator*() [3/7]

IntervalMatrix ZonoOpt::IntervalMatrix::operator* ( const Eigen::SparseMatrix< zono_float, Eigen::RowMajor > & A ) const

IntervalMatrix multiplication with sparse matrix.

Parameters

A	rhs matrix

Returns: resulting interval matrix

◆ operator*() [4/7]

Box ZonoOpt::IntervalMatrix::operator* ( const Eigen::Vector< zono_float, -1 > & v ) const

IntervalMatrix multiplication with vector.

Parameters

v	rhs vector

Returns: resulting box

◆ operator*() [5/7]

IntervalMatrix ZonoOpt::IntervalMatrix::operator* ( const Interval & interval ) const

IntervalMatrix elementwise multiplication by interval.

Parameters

interval interval to multiply

Returns: resulting interval matrix

◆ operator*() [6/7]

IntervalMatrix ZonoOpt::IntervalMatrix::operator* ( const IntervalMatrix & other ) const

IntervalMatrix multiplication with another IntervalMatrix.

Parameters

other rhs interval matrix

Returns: resulting interval matrix

◆ operator*() [7/7]

IntervalMatrix ZonoOpt::IntervalMatrix::operator* ( zono_float alpha ) const

IntervalMatrix scalar multiplication.

Parameters

alpha scalar multiplier

Returns: resulting interval matrix

◆ operator*=() [1/3]

void ZonoOpt::IntervalMatrix::operator*= ( const Interval & interval )

IntervalMatrix elementwise multiplication by interval in-place.

Parameters

interval interval to multiply

◆ operator*=() [2/3]

void ZonoOpt::IntervalMatrix::operator*= ( const IntervalMatrix & other )

IntervalMatrix multiplication with another IntervalMatrix in-place.

Parameters

other rhs interval matrix

◆ operator*=() [3/3]

void ZonoOpt::IntervalMatrix::operator*= ( zono_float alpha )

IntervalMatrix scalar multiplication in-place.

Parameters

alpha scalar multiplier

◆ operator+() [1/3]

IntervalMatrix ZonoOpt::IntervalMatrix::operator+ ( const Interval & interval ) const

IntervalMatrix element-wise addition with interval.

Parameters

interval interval to add

Returns: resulting interval matrix

◆ operator+() [2/3]

IntervalMatrix ZonoOpt::IntervalMatrix::operator+ ( const IntervalMatrix & other ) const

IntervalMatrix addition.

Parameters

other rhs interval matrix

Returns: resulting interval matrix

◆ operator+() [3/3]

IntervalMatrix ZonoOpt::IntervalMatrix::operator+ ( zono_float alpha ) const

IntervalMatrix element-wise addition with scalar.

Parameters

alpha scalar to add

Returns: resulting interval matrix

◆ operator+=() [1/3]

void ZonoOpt::IntervalMatrix::operator+= ( const Interval & interval )

IntervalMatrix element-wise addition with interval in-place.

Parameters

interval interval to add

◆ operator+=() [2/3]

void ZonoOpt::IntervalMatrix::operator+= ( const IntervalMatrix & other )

IntervalMatrix addition in-place.

Parameters

other rhs interval matrix

◆ operator+=() [3/3]

void ZonoOpt::IntervalMatrix::operator+= ( zono_float alpha )

IntervalMatrix element-wise addition with scalar in-place.

Parameters

alpha scalar to add

◆ operator-() [1/4]

IntervalMatrix ZonoOpt::IntervalMatrix::operator- ( ) const

IntervalMatrix negation.

Returns: negated interval matrix

◆ operator-() [2/4]

IntervalMatrix ZonoOpt::IntervalMatrix::operator- ( const Interval & interval ) const

IntervalMatrix elementwise interval subtraction.

Parameters

interval interval to subtract

Returns: resulting interval matrix

◆ operator-() [3/4]

IntervalMatrix ZonoOpt::IntervalMatrix::operator- ( const IntervalMatrix & other ) const

IntervalMatrix subtraction.

Parameters

other rhs interval matrix

Returns: resulting interval matrix

◆ operator-() [4/4]

IntervalMatrix ZonoOpt::IntervalMatrix::operator- ( zono_float alpha ) const

IntervalMatrix elementwise scalar subtraction.

Parameters

alpha scalar to subtract

Returns: resulting interval matrix

◆ operator-=() [1/3]

void ZonoOpt::IntervalMatrix::operator-= ( const Interval & interval )

IntervalMatrix elementwise interval subtraction in-place.

Parameters

interval interval

◆ operator-=() [2/3]

void ZonoOpt::IntervalMatrix::operator-= ( const IntervalMatrix & other )

IntervalMatrix subtraction in-place.

Parameters

other rhs interval matrix

◆ operator-=() [3/3]

void ZonoOpt::IntervalMatrix::operator-= ( zono_float alpha )

IntervalMatrix elementwise scalar subtraction in-place.

Parameters

alpha scalar to subtract

◆ operator/() [1/2]

IntervalMatrix ZonoOpt::IntervalMatrix::operator/ ( const Interval & interval ) const

IntervalMatrix elementwise division by interval.

Parameters

interval interval to divide

Returns: resulting interval matrix (this / interval)

◆ operator/() [2/2]

IntervalMatrix ZonoOpt::IntervalMatrix::operator/ ( zono_float alpha ) const

IntervalMatrix elementwise division by scalar.

Parameters

alpha scalar to divide

Returns: resulting interval matrix (this / alpha)

◆ operator/=() [1/2]

void ZonoOpt::IntervalMatrix::operator/= ( const Interval & interval )

IntervalMatrix elementwise division by interval in-place.

Parameters

interval interval to divide

◆ operator/=() [2/2]

void ZonoOpt::IntervalMatrix::operator/= ( zono_float alpha )

IntervalMatrix elementwise division by scalar.

Parameters

alpha scalar to divide

◆ operator<=()

bool ZonoOpt::IntervalMatrix::operator<= ( const IntervalMatrix & other ) const

Set containment operator.

Parameters

other

Returns: true if this is subset of other

◆ operator==()

bool ZonoOpt::IntervalMatrix::operator== ( const IntervalMatrix & other ) const

Set equality operator.

Parameters

other

Returns: true if this and other are equal

◆ operator>=()

bool ZonoOpt::IntervalMatrix::operator>= ( const IntervalMatrix & other ) const

Set containment operator.

Parameters

other

Returns: true if this is superset of other

◆ operator|()

IntervalMatrix ZonoOpt::IntervalMatrix::operator| ( const IntervalMatrix & other ) const

Interval matrix interval hull operator.

Parameters

other interval matrix to compute hull with

Returns: IntervalMatrix

◆ print()

std::string ZonoOpt::IntervalMatrix::print ( ) const

Print method.

Returns: string display of IntervalMatrix

◆ radius()

IntervalMatrix ZonoOpt::IntervalMatrix::radius ( ) const

Get radius matrix.

Returns: radius matrix

Returns the IntervalMatrix with each interval shifted to be centered at zero

◆ rows()

size_t ZonoOpt::IntervalMatrix::rows ( ) const

inline

Get number of rows.

Returns: number of rows

◆ to_array()

std::vector< std::vector< Interval > > ZonoOpt::IntervalMatrix::to_array ( ) const

Convert to a vector of vectors of Intervals (row-major)

Returns: vector of vectors of Intervals

◆ to_triplets()

std::tuple< int, int, std::vector< Eigen::Triplet< Interval > > > ZonoOpt::IntervalMatrix::to_triplets ( ) const

Convert to triplets.

Returns: std::tuple<int, int, std::vector<Eigen::Triplet<Interval>>>

◆ width()

zono_float ZonoOpt::IntervalMatrix::width ( ) const

Get width of interval matrix.

Returns: width of interval matrix

Specifically, this returns the max width for any interval in the interval matrix

Friends And Related Symbol Documentation

◆ operator* [1/4]

IntervalMatrix operator*	(	const Eigen::Matrix< zono_float, -1, -1 > &	A,
		const IntervalMatrix &	B
	)

friend

IntervalMatrix multiplication with dense matrix.

Parameters

A	lhs matrix
B	rhs interval matrix

Returns: resulting interval matrix

◆ operator* [2/4]

IntervalMatrix operator*	(	const Eigen::SparseMatrix< zono_float, Eigen::RowMajor > &	A,
		const IntervalMatrix &	B
	)

friend

IntervalMatrix multiplication with sparse matrix.

Parameters

A	lhs matrix
B	rhs interval matrix

Returns: resulting interval matrix

◆ operator* [3/4]

IntervalMatrix operator*	(	const Interval &	interval,
		const IntervalMatrix &	A
	)

friend

IntervalMatrix elementwise multiplication by interval.

Parameters

interval	interval to multiply
A	interval matrix

Returns: resulting interval matrix

◆ operator* [4/4]

IntervalMatrix operator*	(	zono_float	alpha,
		const IntervalMatrix &	A
	)

friend

IntervalMatrix scalar multiplication.

Parameters

alpha	scalar multiplier
A	interval matrix

Returns: resulting interval matrix

◆ operator+ [1/2]

IntervalMatrix operator+	(	const Interval &	interval,
		const IntervalMatrix &	mat
	)

friend

IntervalMatrix element-wise addition with interval.

Parameters

interval	interval to add
mat	interval matrix

Returns: resulting interval matrix

◆ operator+ [2/2]

IntervalMatrix operator+	(	zono_float	alpha,
		const IntervalMatrix &	A
	)

friend

IntervalMatrix element-wise addition with scalar.

Parameters

alpha	scalar to add
A	interval matrix

Returns: resulting interval matrix

◆ operator- [1/2]

IntervalMatrix operator-	(	const Interval &	interval,
		const IntervalMatrix &	mat
	)

friend

IntervalMatrix elementwise interval subtraction.

Parameters

interval	interval
mat	interval matrix to subtract

Returns: resulting interval matrix

◆ operator- [2/2]

IntervalMatrix operator-	(	zono_float	alpha,
		const IntervalMatrix &	A
	)

friend

IntervalMatrix elementwise scalar subtraction.

Parameters

alpha	scalar
A	interval matrix to subtract

Returns: resulting interval matrix

◆ operator/ [1/2]

IntervalMatrix operator/	(	const Interval &	interval,
		const IntervalMatrix &	A
	)

friend

IntervalMatrix elementwise interval division.

Parameters

interval	interval
A	matrix to divide

Returns: resulting interval matrix (interval / this)

◆ operator/ [2/2]

IntervalMatrix operator/	(	zono_float	alpha,
		const IntervalMatrix &	A
	)

friend

IntervalMatrix elementwise scalar division.

Parameters

alpha	scalar
A	matrix to divide

Returns: resulting interval matrix (alpha / this)

◆ operator<<

std::ostream & operator<<	(	std::ostream &	os,
		const IntervalMatrix &	interval_matrix
	)

friend

print to ostream

Parameters

os	ostream
interval_matrix	reference to interval matrix

Returns: ostream

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

/home/joshr/Documents/Projects/ZonoOpt/include/zonoopt/IntervalMatrix.hpp
/home/joshr/Documents/Projects/ZonoOpt/src/IntervalMatrix.cpp

Public Member Functions

Friends

Detailed Description

Constructor & Destructor Documentation

◆ IntervalMatrix() [1/4]

◆ IntervalMatrix() [2/4]

◆ IntervalMatrix() [3/4]

◆ IntervalMatrix() [4/4]

Member Function Documentation

◆ center()

◆ cols()

◆ contains()

◆ contains_set()

◆ diam()

◆ intersect()

◆ interval_hull()

◆ operator&()

◆ operator*() [1/7]

◆ operator*() [2/7]

◆ operator*() [3/7]

◆ operator*() [4/7]

◆ operator*() [5/7]

◆ operator*() [6/7]

◆ operator*() [7/7]

◆ operator*=() [1/3]

◆ operator*=() [2/3]

◆ operator*=() [3/3]

◆ operator+() [1/3]

◆ operator+() [2/3]

◆ operator+() [3/3]

◆ operator+=() [1/3]

◆ operator+=() [2/3]

◆ operator+=() [3/3]

◆ operator-() [1/4]

◆ operator-() [2/4]

◆ operator-() [3/4]

◆ operator-() [4/4]

◆ operator-=() [1/3]

◆ operator-=() [2/3]

◆ operator-=() [3/3]

◆ operator/() [1/2]

◆ operator/() [2/2]

◆ operator/=() [1/2]

◆ operator/=() [2/2]

◆ operator<=()

◆ operator==()

◆ operator>=()

◆ operator|()

◆ print()

◆ radius()

◆ rows()

◆ to_array()

◆ to_triplets()

◆ width()

Friends And Related Symbol Documentation

◆ operator* [1/4]

◆ operator* [2/4]

◆ operator* [3/4]

◆ operator* [4/4]

◆ operator+ [1/2]

◆ operator+ [2/2]

◆ operator- [1/2]

◆ operator- [2/2]

◆ operator/ [1/2]

◆ operator/ [2/2]

◆ operator<<