#include <matrix.h>

Inheritance diagram for Matrix:

Collaboration diagram for Matrix:

Public Member Functions
	Matrix ()
	default constructor: zero matrix (0x0) More...

	Matrix (I _m, I _n, const D *_data=0)
	constucts a matrix with the given size. More...

	Matrix (I _m, I _n, D def)
	constucts a matrix with the given size and fills it with the default value More...

	Matrix (const Matrix &c)
	constucts a instance on the base of a deep copy of the given matrix More...

	Matrix (Matrix &&c)
	copy move constructor More...

	~Matrix ()

I	getM () const

I	getN () const

I	size () const

D	val (I i, I j) const

D &	val (I i, I j)

D	valDef0 (I i, I j) const

void	set (I _m, I _n, const D *_data=0)
	sets the size of the matrix and maybe the data if given (row-wise). More...

void	set (const D *_data)
	sets the data (row-wise). More...

Matrix	row (I index) const

Matrix	rows (I startindex, I endindex) const

Matrix	column (I index) const

Matrix	columns (I startindex, I endindex) const

int	convertToBuffer (D *buffer, I len) const
	stores the content of the matrix (row-wise) in the given buffer More...

std::list< D >	convertToList () const

const D *	unsafeGetData () const
	returns a pointer to the data. UNSAFE!!! More...

bool	store (FILE *f) const
	stores the Matrix into the given file stream (same as write) More...

bool	restore (FILE *f)
	reads a Matrix from the given file stream uses read (or old binary format) More...

bool	write (FILE *f) const
	writes the Matrix into the given file stream (ascii) More...

bool	read (FILE *f, bool skipIdentifier=false)
	reads a Matrix from the given file stream (ascii) More...

void	add (const Matrix &a, const Matrix &b)
	addition: this = a + b More...

void	add (const Matrix &a, const D &summand)

void	sub (const Matrix &a, const Matrix &b)
	add scalar to each element More...

void	mult (const Matrix &a, const Matrix &b)
	multiplication: this = a * b More...

void	mult (const Matrix &a, const D &fac)
	scaling: this = a * fac More...

void	exp (const Matrix &a, int exponent)
	exponent, this = a^i, More...

bool	isNulltimesNull () const
	returns true if matrix is a 0x0 matrix More...

bool	isVector () const
	returns true if matrix is a vector More...

bool	equals (const Matrix &a) const
	bytewise comparison (compares data buffer bytewise, which implies that n1m1 == n2m2 but not necessarily n1==n2) More...

bool	hasSameSizeAs (const Matrix &a) const

Matrix	pseudoInverse (const D &lambda=1e-8) const
	calculates the pseudoinverse, depending on the shape of the matrix the left or right pseudoinverse is used. More...

Matrix	secureInverse () const
	calculates the secure inverse of a square matrix. More...

bool	hasNormalEntries () const
	returns true if all entries are normal floating point numbers, otherwise false (e.g. More...

Matrix	map (D(*fun)(D)) const
	maps the matrix to a new matrix with all elements mapped with the given function More...

Matrix	mapP (D param, D(*fun)(D, D)) const
	like map but with additional double parameter for the mapping function (first argument of fun is parameter, the second is the value) More...

Matrix	mapP (void param, D(fun)(void *, D)) const
	like map but with additional arbitrary parameter for the mapping function More...

Matrix	multrowwise (const Matrix &factors) const
	row-wise multiplication More...

Matrix	multcolwise (const Matrix &factors) const
	column-wise multiplication More...

Matrix	multMT () const
	optimised multiplication of Matrix with its transposed: M * M^T More...

Matrix	multTM () const
	optimised multiplication of transpsoed of Matrix with itself: M^T * M More...

D	elementProduct () const
	returns the product of all elements ( $\Pi_{ij} m_{ij}$ ) More...

D	elementSum () const
	returns the sum of all elements ( $\sum_{ij} m_{ij}$ ) More...

D	norm_sqr () const
	returns the sum of all squares of all elements ( $\sum_{ij} m_{ij}^2$ ) this is also known as the square of the Frobenius norm. More...

Matrix	above (const Matrix &a) const
	returns a matrix that consists of this matrix above A (number of rows is getM + a.getM()) More...

Matrix	beside (const Matrix &a) const
	returns a matrix that consists of this left beside A (number of columns is getN + a.getN()) More...

Matrix &	operator= (const Matrix &c)
	deep copy More...

Matrix &	operator= (Matrix &&c)
	deep copy move operator More...

Matrix	operator+ (const Matrix &sum) const
	sum of two matrices More...

Matrix	operator- (const Matrix &sum) const
	difference of two matrices More...

Matrix	operator* (const Matrix &fac) const
	matrix product More...

Matrix	operator* (const D &fac) const
	product with scalar (D) (only right side) More...

Matrix	operator^ (int exponent) const
	special matrix potence: More...

Matrix	operator& (const Matrix &b) const
	row-wise multiplication More...

Matrix &	operator+= (const Matrix &c)
	combined assigment operator (higher performance) More...

Matrix &	operator-= (const Matrix &c)
	combined assigment operator (higher performance) More...

Matrix &	operator*= (const Matrix &c)
	combined assigment operator (higher performance) More...

Matrix &	operator*= (const D &fac)
	combined assigment operator (higher performance) More...

Matrix &	operator&= (const Matrix &c)
	combined assigment operator (higher performance) More...

bool	operator== (const Matrix &c) const
	comparison operator (compares elements with tolerance distance of COMPARE_EPS) More...

void	copy (const Matrix &c)
	performs a deep copy of the given matrix More...

Matrix &	toTranspose ()
	inplace transpose More...

Matrix &	toZero ()
	inplace converts matrix to zero matrix More...

Matrix &	toId ()
	inplace converts matrix to identity (use ^0 to get a copy version of it) More...

Matrix &	toSum (const Matrix &a)
	inplace addition: this = this + a More...

Matrix &	toSum (const D &sum)
	inplace addition: this = this + a, where a is a scalar More...

Matrix &	toDiff (const Matrix &a)
	inplace subtraction: this = this - a More...

Matrix &	toMult (const Matrix &a)
	inplace multiplication: this = this * a More...

Matrix &	toMult (const D &fac)
	inplace multiplication with scalar: this = this*fac More...

Matrix &	toExp (int exponent)
	special inplace matrix power: More...

Matrix &	toMap (D(*fun)(D))
	inplace mapping of matrix elements (element-wise application) More...

Matrix &	toMapP (D param, D(*fun)(D, D))
	like toMap, but with an extra double parameter for the mapping function. More...

Matrix &	toMapP (void param, D(fun)(void *, D))
	like toMap, but with an extra arbitrary parameter for the mapping function. More...

Matrix &	toMap2 (D(*fun)(D, D), const Matrix &b)
	like toMap, but with using 2 matrices More...

Matrix &	toMap2P (D param, D(*fun)(D, D, D), const Matrix &b)
	like toMap2, but with additional parameter More...

Matrix &	toMap2P (void param, D(fun)(void *, D, D), const Matrix &b)
	like toMap2P, but with arbitrary parameter More...

Matrix &	toMultrowwise (const Matrix &factors)
	Inplace row-wise multiplication. More...

Matrix &	toMultcolwise (const Matrix &factors)
	Inplace column-wise multiplication. More...

Matrix &	toAbove (const Matrix &a)
	sets the matrix a below this matrix More...

Matrix &	toBeside (const Matrix &a)
	sets the matrix a right beside this matrix More...

Matrix &	toSort ()
	sorts the matrix (rowwise) More...

Matrix &	reshape (I m, I n)
	reshapes the matrix without destroying the data. More...

Matrix &	pluslambdaI (double lambda=1e-8)
	adds the given value to the diagonal More...

Matrix &	addRows (I numberRows, const D *_data=0)
	adds one or more rows to the existing matrix and fills it with the given data More...

Matrix &	addRows (I numberRows, const Matrix &dataMatrix)
	same as toAbove(dataMatrix) More...

Matrix &	addColumns (I numberColumns, const D *_data=0)
	adds one or more columns to the existing matrix same as toBeside(Matrix(getM, numberColumns, _data)) More...

Matrix &	addColumns (I numberColumns, const Matrix &dataMatrix)
	same as toBeside(dataMatrix) More...

Matrix &	removeRows (I numberRows)
	removes one or more rows from the end if an existing matrix (inplace!), same as reshape(getM()-numberRows, getN()); More...

Matrix &	removeColumns (I numberColumns)
	removes one or more columns from the end of the existing matrix (inplace!) resets the size of the matrix and deletes the appropiate data. More...

Public Member Functions inherited from Storeable
virtual	~Storeable ()

bool	storeToFile (const char *filename) const
	Provided for convenience. More...

bool	restoreFromFile (const char *filename)
	Provided for convenience. More...

Static Public Member Functions
static Matrix	map2 (D(*fun)(D, D), const Matrix &a, const Matrix &b)
	binary map operator for matrices. More...

static Matrix	map2P (D param, D(*fun)(D, D, D), const Matrix &a, const Matrix &b)
	like map2 but with additional parameter. More...

static Matrix	map2P (void param, D(fun)(void *, D, D), const Matrix &a, const Matrix &b)
	like map2P but with arbitrary paramters (void*) instead of double More...

Friends
std::ostream &	operator<< (std::ostream &, const Matrix &)
	printing operator: output format: mxn ( row0 ..rown ) where rowX is tab seperated list of values More...

Detailed Description

Matrix type.

Type D is datatype of matrix elements, which is fixed to double. Type I is the indextype of matrix elements, which is fixed to unsigned int. There are basicly two different types of operation: Inplace operations and copy operations. Please use the latter ones unless you know what you are doing. Just in case of critical performance optimisation use the inplace operations. The most convinient way is to use the overloaded operators (like + * ...). All constructed matrices are initialized with zero elements (unless data is given). All functions perform range checks if in debug mode (i.e. if NDEBUG is not defined). Please use debug version (default) for testing

See Also: examples/matrix/matrixexample.cpp

Author: Georg Martius

Examples:: integration/main.cpp, and matrix/matrixexample.cpp.

Constructor & Destructor Documentation

Matrix ( )

inline

default constructor: zero matrix (0x0)

Matrix	(	I	_m,
		I	_n,
		const D *	_data = `0`
	)

constucts a matrix with the given size.

If _data is null then the matrix is filled with zeros. otherwise matrix will be filled with _data in a row-wise manner. In this case _data must be at least _m*_n elements long

Matrix	(	I	_m,
		I	_n,
		D	def
	)

constucts a matrix with the given size and fills it with the default value

Matrix ( const Matrix & c )

constucts a instance on the base of a deep copy of the given matrix

Matrix ( Matrix && c )

copy move constructor

~Matrix ( )

inline

Member Function Documentation

Matrix above ( const Matrix & a ) const

returns a matrix that consists of this matrix above A (number of rows is getM + a.getM())

returns a matrix that consists of b below this

void add	(	const Matrix &	a,
		const Matrix &	b
	)

addition: this = a + b

void add	(	const Matrix &	a,
		const D &	summand
	)

Matrix & addColumns	(	I	numberColumns,
		const D *	_data = `0`
	)

adds one or more columns to the existing matrix same as toBeside(Matrix(getM, numberColumns, _data))

See Also: toBeside()

Parameters

numberColumns	number of columns to add (this extends n)
_data	data to add

Returns: the address of the matrix itself

Matrix & addColumns	(	I	numberColumns,
		const Matrix &	dataMatrix
	)

same as toBeside(dataMatrix)

See Also: toBeside()

Parameters

numberColumns	number of columns to add (unused)
dataMatrix	matrix which contains the data of the new rows

Returns: the address of the matrix itself

Matrix & addRows	(	I	numberRows,
		const D *	_data = `0`
	)

adds one or more rows to the existing matrix and fills it with the given data

same as toAbove(Matrix(numberRows,getN(),data))

Parameters

numberRows	number of rows to add (this extends m)
_data	data to add

Returns: the address of the matrix itself

Matrix & addRows	(	I	numberRows,
		const Matrix &	dataMatrix
	)

same as toAbove(dataMatrix)

Parameters

numberRows	number of rows to add (unused)
dataMatrix	matrix which contains the data of the new rows

Returns: the address of the matrix itself

Matrix beside ( const Matrix & a ) const

returns a matrix that consists of this left beside A (number of columns is getN + a.getN())

returns a matrix that consists of b right beside this

Matrix column ( I index ) const

Returns: column-vector(as Mx1 matrix) containing the index'th column

Examples:: matrix/matrixexample.cpp.

Matrix columns	(	I	startindex,
		I	endindex
	)		const

Returns: submatrix (as MxK matrix) containing column from startindex to endindex inclusively (K=endindex-startindex) indices can be out of bounds, they are clipped in any case

int convertToBuffer	(	D *	buffer,
		I	len
	)		const

stores the content of the matrix (row-wise) in the given buffer

Parameters

buffer	Buffer for storing the elements (should have the length given by len)
len	Length of the provided buffer. In any case only min(len, getM()*getN()) elements are copied.

Returns: number of actually written elements

std::list< D > convertToList ( ) const

Returns: a list of the content of the matrix (row-wise)

void copy ( const Matrix & c )

inline

performs a deep copy of the given matrix

D elementProduct ( ) const

returns the product of all elements ( $\Pi_{ij} m_{ij}$ )

returns the product of all elements

D elementSum ( ) const

returns the sum of all elements ( $\sum_{ij} m_{ij}$ )

returns the sum of all elements

bool equals ( const Matrix & a ) const

bytewise comparison (compares data buffer bytewise, which implies that n1*m1 == n2*m2 but not necessarily n1==n2)

void exp	(	const Matrix &	a,
		int	exponent
	)

exponent, this = a^i,

See Also: toExp

I getM ( ) const

inline

Returns: number of rows

I getN ( ) const

inline

Returns: number of columns

bool hasNormalEntries ( ) const

returns true if all entries are normal floating point numbers, otherwise false (e.g.

for nan and inf)

bool hasSameSizeAs ( const Matrix & a ) const

inline

Returns: true of a and this have the same size

bool isNulltimesNull ( ) const

returns true if matrix is a 0x0 matrix

ACCESSORS ///////////////////////////////////////////////////////////////.

returns true if matrix is a 0x0 matrix

bool isVector ( ) const

returns true if matrix is a vector

Matrix map ( D(*)(D) fun ) const

maps the matrix to a new matrix with all elements mapped with the given function

Examples:: matrix/matrixexample.cpp.

Matrix map2	(	D(*)(D, D)	fun,
		const Matrix &	a,
		const Matrix &	b
	)

static

binary map operator for matrices.

The resulting matrix consists of the function values applied to the elements of a and b. In haskell this would something like: map (uncurry . fun) $ zip a b

Matrix map2P	(	D	param,
		D(*)(D, D, D)	fun,
		const Matrix &	a,
		const Matrix &	b
	)

static

like map2 but with additional parameter.

The first argument of fun is the parameter and the second and third comes from the matrix elements. In haskell this would something like: map (uncurry . (fun p)) $ zip a b

Matrix map2P	(	void *	param,
		D()(void , D, D)	fun,
		const Matrix &	a,
		const Matrix &	b
	)

static

like map2P but with arbitrary paramters (void*) instead of double

Matrix mapP	(	D	param,
		D(*)(D, D)	fun
	)		const

like map but with additional double parameter for the mapping function (first argument of fun is parameter, the second is the value)

Matrix mapP	(	void *	param,
		D()(void , D)	fun
	)		const

like map but with additional arbitrary parameter for the mapping function

void mult	(	const Matrix &	a,
		const Matrix &	b
	)

multiplication: this = a * b

void mult	(	const Matrix &	a,
		const D &	fac
	)

scaling: this = a * fac

Matrix multcolwise ( const Matrix & factors ) const

column-wise multiplication

Parameters

factors column vector (Mx1) of factors, one for each column

Matrix multMT ( ) const

optimised multiplication of Matrix with its transposed: M * M^T

Matrix multrowwise ( const Matrix & factors ) const

row-wise multiplication

Parameters

factors column vector (Mx1) of factors, one for each row

Matrix multTM ( ) const

optimised multiplication of transpsoed of Matrix with itself: M^T * M

D norm_sqr ( ) const

returns the sum of all squares of all elements ( $\sum_{ij} m_{ij}^2$ ) this is also known as the square of the Frobenius norm.

returns the sum of all elements

Matrix operator& ( const Matrix & b ) const

row-wise multiplication

Matrix& operator&= ( const Matrix & c )

inline

combined assigment operator (higher performance)

Matrix operator* ( const Matrix & fac ) const

matrix product

Matrix operator* ( const D & fac ) const

product with scalar (D) (only right side)

product with scalar (double)

Matrix& operator*= ( const Matrix & c )

inline

combined assigment operator (higher performance)

Matrix& operator*= ( const D & fac )

inline

combined assigment operator (higher performance)

Matrix operator+ ( const Matrix & sum ) const

sum of two matrices

Matrix& operator+= ( const Matrix & c )

inline

combined assigment operator (higher performance)

Matrix operator- ( const Matrix & sum ) const

difference of two matrices

Matrix& operator-= ( const Matrix & c )

inline

combined assigment operator (higher performance)

Matrix& operator= ( const Matrix & c )

inline

deep copy

Matrix & operator= ( Matrix && c )

deep copy move operator

bool operator== ( const Matrix & c ) const

comparison operator (compares elements with tolerance distance of COMPARE_EPS)

Matrix operator^ ( int exponent ) const

special matrix potence:

Parameters

exponent	-1 -> inverse; 0 -> Identity Matrix; 1 -> itself; T -> Transpose
exp	-1 -> inverse; 0 -> Identity Matrix; 1 -> itself; 2-> Matrix*Matrix^T T -> Transpose

Matrix & pluslambdaI ( double lambda = 1e-8 )

adds the given value to the diagonal

Matrix pseudoInverse ( const D & lambda = 1e-8 ) const

calculates the pseudoinverse, depending on the shape of the matrix the left or right pseudoinverse is used.

If the matrix has more columns than rows then we use

$A^{+} = (A^T A + \lambda \mathbb I)^{-1}A^T$

otherwise

$A^{+} = A^T(A A^T + \lambda \mathbb I)^{-1}$

bool read	(	FILE *	f,
		bool	skipIdentifier = `false`
	)

reads a Matrix from the given file stream (ascii)

Matrix & removeColumns ( I numberColumns )

removes one or more columns from the end of the existing matrix (inplace!) resets the size of the matrix and deletes the appropiate data.

Parameters

numberColumns number of columns to remove (this reduces n)

Returns: the address of the matrix itself

Matrix & removeRows ( I numberRows )

removes one or more rows from the end if an existing matrix (inplace!), same as reshape(getM()-numberRows, getN());

Parameters

numberRows number of rows to remove (from the end) (this reduces m)

Returns: the address of the matrix itself

Matrix & reshape	(	I	m,
		I	n
	)

reshapes the matrix without destroying the data.

Remember: The data is stored rowwise.

Only shrinking is allowed i.e. m*n must be lower or equal to getM()*getN()

bool restore ( FILE * f )

virtual

reads a Matrix from the given file stream uses read (or old binary format)

reads a Matrix from the given file stream ASCII (can load old binary format)

Implements Storeable.

Matrix row ( I index ) const

Returns: row-vector(as 1xN matrix) containing the index'th row

Examples:: matrix/matrixexample.cpp.

Matrix rows	(	I	startindex,
		I	endindex
	)		const

Returns: submatrix (as KxN matrix) containing row from startindex to endindex inclusively (K=stopindex-endindex) indices can be out of bounds, they are clipped in any case

Matrix secureInverse ( ) const

calculates the secure inverse of a square matrix.

If singular then the pseudoinverse is used.

void set	(	I	_m,
		I	_n,
		const D *	_data = `0`
	)

sets the size of the matrix and maybe the data if given (row-wise).

If data=null then the matrix is set to zero

See Also: toZero(); constructor Matrix(m,n,data)

Examples:: matrix/matrixexample.cpp.

void set ( const D * _data )

sets the data (row-wise).

Parameters

_data if null then matrix elements are set to zero otherwise the field MUST have the length should be getM()*getN()

I size ( ) const

inline

Returns: number number elements in the matrix (getM()*getN())

bool store ( FILE * f ) const

virtual

stores the Matrix into the given file stream (same as write)

stores the Matrix into the given file stream ASCII

Implements Storeable.

void sub	(	const Matrix &	a,
		const Matrix &	b
	)

add scalar to each element

subtraction: this = a - b

Matrix & toAbove ( const Matrix & a )

sets the matrix a below this matrix

Matrix & toBeside ( const Matrix & a )

sets the matrix a right beside this matrix

Matrix & toDiff ( const Matrix & a )

inplace subtraction: this = this - a

Matrix & toExp ( int exponent )

special inplace matrix power:

Parameters

exponent -1 -> inverse; (matrix MUST be SQUARE and NONZERO) 0 -> Identity Matrix; 1 -> itself; n -> n-th power; T -> Transpose

Matrix & toId ( )

inplace converts matrix to identity (use ^0 to get a copy version of it)

Examples:: integration/main.cpp.

Matrix & toMap ( D(*)(D) fun )

inplace mapping of matrix elements (element-wise application)

Matrix & toMap2	(	D(*)(D, D)	fun,
		const Matrix &	b
	)

like toMap, but with using 2 matrices

Matrix & toMap2P	(	D	param,
		D(*)(D, D, D)	fun,
		const Matrix &	b
	)

like toMap2, but with additional parameter

Matrix & toMap2P	(	void *	param,
		D()(void , D, D)	fun,
		const Matrix &	b
	)

like toMap2P, but with arbitrary parameter

Matrix & toMapP	(	D	param,
		D(*)(D, D)	fun
	)

like toMap, but with an extra double parameter for the mapping function.

Matrix & toMapP	(	void *	param,
		D()(void , D)	fun
	)

like toMap, but with an extra arbitrary parameter for the mapping function.

Matrix & toMult ( const Matrix & a )

inplace multiplication: this = this * a

Matrix & toMult ( const D & fac )

inplace multiplication with scalar: this = this*fac

Matrix & toMultcolwise ( const Matrix & factors )

Inplace column-wise multiplication.

Parameters

factors column vector of factors, one for each column

Matrix & toMultrowwise ( const Matrix & factors )

Inplace row-wise multiplication.

Parameters

factors column vector of factors, one for each row

Matrix & toSort ( )

sorts the matrix (rowwise)

Matrix & toSum ( const Matrix & a )

inplace addition: this = this + a

Matrix & toSum ( const D & sum )

inplace addition: this = this + a, where a is a scalar

Matrix & toTranspose ( )

inplace transpose

Matrix & toZero ( )

inplace converts matrix to zero matrix

const D* unsafeGetData ( ) const

inline

returns a pointer to the data. UNSAFE!!!

D val	(	I	i,
		I	j
	)		const

inline

Returns: element at position i,j (row, column index)

Examples:: matrix/matrixexample.cpp.

D& val	(	I	i,
		I	j
	)

inline

Returns: reference to element at position i,j (can be used as left side value)

D valDef0	(	I	i,
		I	j
	)		const

inline

Returns: element at position i,j (row, column index) and 0 if out of bounds

bool write ( FILE * f ) const

writes the Matrix into the given file stream (ascii)

Friends And Related Function Documentation

std::ostream& operator<<	(	std::ostream &	str,
		const Matrix &	mat
	)

friend

printing operator: output format: mxn (
row0
..rown
) where rowX is tab seperated list of values

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

Public Member Functions

Static Public Member Functions

Friends

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation