Matrix Class Reference

#include <matrix.h>

Collaboration diagram for Matrix:

Public Member Functions
	Matrix (int rowDim=0, int colDim=0)
	Matrix::Matrix Default constructor - creates a Matrix of given dimension (0x0) Use resize(m,n) or zeromatrix(m,n) to resize it.
	Matrix (const Matrix &b)
	Matrix::Matrix Copy constructor. Creates a Matrix identical to Matrix b Allows Matrix a=b declaration Every MatrixRow object holds max_int=32762.
	~Matrix ()
	Matrix::~Matrix Destructor.
void	clear ()
	Clears data.
void	resize (const int m, const int n)
	Resizes this matrix to m x n Called before every operation on new matrices. Every MatrixRow object holds max_int=32762.
qreal	item (int r, int c)
	Returns the (r,c) matrix element.
void	setItem (const int r, const int c, const qreal elem)
	Sets the (r,c) matrix element calling the setColumn method.
qreal	operator() (const int r, const int c)
MatrixRow &	operator[] (const int &r)
void	clearItem (int r, int c)
	Clears the (r,c) matrix element.
int	cols ()
int	rows ()
int	size ()
void	findMinMaxValues (qreal &min, qreal &max, bool &hasRealNumbers)
	finds Min-Max values in current Matrix
void	NeighboursNearestFarthest (qreal &min, qreal &max, int &imin, int &jmin, int &imax, int &jmax)
	Like Matrix::findMinMaxValues only it skips r==c.
void	deleteRowColumn (int i)
	Deletes row and column and shifts rows and cols accordingly.
void	identityMatrix (int dim)
	Makes this square matrix the identity square matrix I.
void	zeroMatrix (const int m, const int n)
	Makes this matrix the zero matrix of size mxn.
void	fillMatrix (qreal value)
	Fills a matrix with a given value.
Matrix &	subtractFromI ()
	Subtracts this matrix from I and returns.
Matrix &	operator= (Matrix &a)
	Matrix equality/assignment , operator = Allows copying a matrix onto another using b=a where b,a matrices Equals two matrices.
void	sum (Matrix &a, Matrix &b)
	Matrix addition Takes two (nxn) matrices and returns their sum as a reference to this Same algorithm as operator +, just different interface. In this case, you use something like: c.sum(a,b)
void	operator+= (Matrix &b)
	Matrix::operator += Matrix add another matrix: += Adds to this matrix another matrix B of the same dim and returns to this Allows A+=B.
Matrix &	operator+ (Matrix &b)
	Matrix addition, operator + Adds this matrix and B of the same dim and returns the sum S Allows S = A+B.
Matrix &	operator- (Matrix &b)
	Matrix subtraction, operator - Subtract this matrix - B of the same dim and returns the result S Allows S = A-B.
Matrix &	operator* (Matrix &b)
	Matrix multiplication, operator * Multiplies (right) this matrix with given matrix b. Allows P = A * B where A,B of same dimension and returns product as a reference to the calling object.
void	operator*= (Matrix &b)
	Multiplies (right) this m x n matrix with given n x p matrix b and returns the product in the calling matrix which becomes an m x p matrix. This convenience operator *= allows A *= B.
void	product (Matrix &A, Matrix &B, bool symmetry=false)
	Matrix Multiplication. Given two matrices A (mxn) and B (nxp) computes their product and stores it to the calling matrix which becomes an m x p matrix Allows P.product(A, B)
Matrix &	productSym (Matrix &a, Matrix &b)
	Takes two ( N x N ) matrices (symmetric) and outputs an upper triangular matrix.
void	swapRows (int rowA, int rowB)
	Swaps row A with row B of this matrix.
void	multiplyScalar (const qreal &f)
	Scalar Multiplication. Multiplies this by qreal f and returns the product matrix of the same dim Allows to use P.multiplyScalar(f)
void	multiplyRow (int row, qreal value)
	Multiply every element of row by value.
void	productByVector (qreal in[], qreal out[], const bool &leftMultiply=false)
	Calculates the matrix-by-vector product Ax of this matrix Default product: Ax if leftMultiply=true then it returns the left product xA.
Matrix &	pow (int n, bool symmetry=false)
	Returns the n-nth power of this matrix.
Matrix &	expBySquaring2 (Matrix &Y, Matrix &X, int n, bool symmetry=false)
	Recursive algorithm implementing "Exponentiation by squaring". Also known as Fast Modulo Multiplication, this algorithm allows fast computation of a large power n of square matrix X.
qreal	distanceManhattan (qreal x[], qreal y[], int n)
	Helper function, takes to vectors and returns their Manhattan distance (also known as l1 norm, Taxicab or L1 distance) which is the sum of the absolute differences of their coordinates.
qreal	distanceEuclidean (qreal x[], int n)
	Helper function, computes the Euclideian length (also known as L2 distance) of a vector: if x = (x1 x2 ... xn), then ||x|| = square_root(x1*x1 + x2*x2 + ... + xn*xn)
void	powerIteration (qreal x[], qreal &xsum, qreal &xmax, int &xmaxi, qreal &xmin, int &xmini, const qreal eps, const int &maxIter)
	Implementation of the Power method which computes the leading eigenvector x of this matrix, that is the eigenvector corresponding to the largest positive eigenvalue. In the process, it also computes min and max values. Used by Eigenvector Centrality (EVC). We use C arrays instead of std::vectors or anything else, as we know from start the size (n) of vectors x and tmp This approach is faster than using std::vector when n > 1000.
Matrix &	degreeMatrix ()
	Returns the Degree Matrix of this matrix. The Degree Matrix is diagonal matrix which contains information about the degree of each graph vertex (row of the adjacency matrix) Allows S = A.degreeMatrix()
Matrix &	laplacianMatrix ()
	Returns the Laplacian of this matrix. The Laplacian is a NxN matrix L = D - A where D is the degree matrix of A Allows S = A.laplacianMatrix()
Matrix &	transpose ()
	Returns the Transpose of this matrix Allows T = A.transpose()
Matrix &	cocitationMatrix ()
	Returns the Cocitation Matrix of this matrix (C = A * A^T) Allows T = A.cocitationMatrix()
Matrix &	inverseByGaussJordanElimination (Matrix &a)
	Inverts given matrix A by Gauss Jordan elimination Input: matrix A Output: matrix A becomes unit matrix this becomes the invert of A and is returned back.
Matrix &	inverse (Matrix &a)
	Computes and returns the inverse of given matrix a Allows b.inverse(a)
bool	solve (qreal b[])
	Computes and returns the solution of the set of n linear equations A·x = b Allows A.solve(b)
bool	ludcmp (Matrix &a, const int &n, int indx[], qreal &d)
	Given matrix a, it replaces a by the LU decomposition of a rowwise permutation of itself. Used in combination with lubksb to solve linear equations or invert a matrix.
void	lubksb (Matrix &a, const int &n, int indx[], qreal b[])
	Solves the set of n linear equations A·X = b, where A nxn matrix decomposed as L·U (L lower triangular and U upper triangular) by forward substitution and backsubstitution.
Matrix &	distancesMatrix (const int &metric, const QString varLocation, const bool &diagonal, const bool &considerWeights)
	Computes the dissimilarities matrix of the variables (rows, columns, both) of this matrix using the user defined metric.
Matrix &	similarityMatrix (Matrix &AM, const int &measure, const QString varLocation="Rows", const bool &diagonal=false, const bool &considerWeights=true)
	Computes the pair-wise matching score of the rows, columns or both of the given matrix AM, based on the given matching measure and returns the similarity matrix.
Matrix &	pearsonCorrelationCoefficients (Matrix &AM, const QString &varLocation="Rows", const bool &diagonal=false)
	Computes the Pearson Correlation Coefficient of the rows or the columns of the given matrix AM.
bool	printHTMLTable (QTextStream &os, const bool markDiag=false, const bool &plain=false, const bool &printInfinity=true)
	Prints this matrix as HTML table This has the problem that the real actorNumber != elementLabel i.e. when we have deleted a node/vertex.
bool	printMatrixConsole (bool debug=true)
	Prints this matrix to stderr or stdout.
bool	illDefined ()
	Checks if matrix is ill-defined (contains at least an inf element)

Private Attributes
MatrixRow *	row
int	m_rows
int	m_cols

Friends
QTextStream &	operator<< (QTextStream &os, Matrix &m)
	Prints matrix m to given textstream.

Constructor & Destructor Documentation

Matrix() [1/2]

Matrix::Matrix	(	int	rowDim = 0,
		int	colDim = 0
	)

Matrix::Matrix Default constructor - creates a Matrix of given dimension (0x0) Use resize(m,n) or zeromatrix(m,n) to resize it.

default constructor - default rows = cols = 0

Parameters

Actors

Matrix() [2/2]

Matrix::Matrix

(

const Matrix &

b

)

Matrix::Matrix Copy constructor. Creates a Matrix identical to Matrix b Allows Matrix a=b declaration Every MatrixRow object holds max_int=32762.

Parameters

b

~Matrix()

Matrix::~Matrix

(

)

Matrix::~Matrix Destructor.

Member Function Documentation

clear()

void Matrix::clear

(

)

Clears data.

clearItem()

void Matrix::clearItem	(	int	r,
		int	c
	)

Clears the (r,c) matrix element.

Parameters

r
c

cocitationMatrix()

Matrix & Matrix::cocitationMatrix

(

)

Returns the Cocitation Matrix of this matrix (C = A * A^T) Allows T = A.cocitationMatrix()

Parameters

b

Returns

Matrix T

cols()

int Matrix::cols ( )

inline

degreeMatrix()

Matrix & Matrix::degreeMatrix

(

)

Returns the Degree Matrix of this matrix. The Degree Matrix is diagonal matrix which contains information about the degree of each graph vertex (row of the adjacency matrix) Allows S = A.degreeMatrix()

Parameters

b

Returns

Matrix S

deleteRowColumn()

void Matrix::deleteRowColumn

(

int

erased

)

Deletes row and column and shifts rows and cols accordingly.

Parameters

erased

row/col to delete

distanceEuclidean()

qreal Matrix::distanceEuclidean	(	qreal	x[],
		int	n
	)

Helper function, computes the Euclideian length (also known as L2 distance) of a vector: if x = (x1 x2 ... xn), then ||x|| = square_root(x1*x1 + x2*x2 + ... + xn*xn)

Parameters

x
n

Returns

distanceManhattan()

qreal Matrix::distanceManhattan	(	qreal	x[],
		qreal	y[],
		int	n
	)

Helper function, takes to vectors and returns their Manhattan distance (also known as l1 norm, Taxicab or L1 distance) which is the sum of the absolute differences of their coordinates.

Parameters

x
y

Returns

distancesMatrix()

Matrix & Matrix::distancesMatrix	(	const int &	metric,
		const QString	varLocation,
		const bool &	diagonal,
		const bool &	considerWeights
	)

Computes the dissimilarities matrix of the variables (rows, columns, both) of this matrix using the user defined metric.

Parameters

metric
varLocation
diagonal
considerWeights

Returns

expBySquaring2()

Matrix & Matrix::expBySquaring2	(	Matrix &	Y,
		Matrix &	X,
		int	n,
		bool	symmetry = false
	)

Recursive algorithm implementing "Exponentiation by squaring". Also known as Fast Modulo Multiplication, this algorithm allows fast computation of a large power n of square matrix X.

Parameters

Y	must be the Identity matrix on first call
X	the matrix to be powered
n	the power
symmetry

Returns

Matrix&

On first call, parameters must be: Y=I, X the orginal matrix to power and n the power. Returns the power of matrix X to this object. For n > 4 it is more efficient than naively multiplying the base with itself repeatedly.

fillMatrix()

void Matrix::fillMatrix

(

qreal

value

)

Fills a matrix with a given value.

Parameters

value

findMinMaxValues()

void Matrix::findMinMaxValues	(	qreal &	min,
		qreal &	max,
		bool &	hasRealNumbers
	)

finds Min-Max values in current Matrix

Parameters

min	value in the matrix
max	value Complexity: O(n^2)

identityMatrix()

void Matrix::identityMatrix

(

int

dim

)

Makes this square matrix the identity square matrix I.

Parameters

dim

illDefined()

bool Matrix::illDefined

(

)

Checks if matrix is ill-defined (contains at least an inf element)

Returns

inverse()

Matrix & Matrix::inverse

(

Matrix &

a

)

Computes and returns the inverse of given matrix a Allows b.inverse(a)

Parameters

a

Returns

inverseByGaussJordanElimination()

Matrix & Matrix::inverseByGaussJordanElimination

(

Matrix &

A

)

Inverts given matrix A by Gauss Jordan elimination Input: matrix A Output: matrix A becomes unit matrix this becomes the invert of A and is returned back.

Parameters

A

Returns

inverse matrix of A

item()

qreal Matrix::item	(	int	r,
		int	c
	)

Returns the (r,c) matrix element.

Parameters

r
c

Returns

laplacianMatrix()

Matrix & Matrix::laplacianMatrix

(

)

Returns the Laplacian of this matrix. The Laplacian is a NxN matrix L = D - A where D is the degree matrix of A Allows S = A.laplacianMatrix()

Parameters

b

Returns

Matrix S

lubksb()

void Matrix::lubksb	(	Matrix &	a,
		const int &	n,
		int	indx[],
		qreal	b[]
	)

Solves the set of n linear equations A·X = b, where A nxn matrix decomposed as L·U (L lower triangular and U upper triangular) by forward substitution and backsubstitution.

Given A = L·U we have A · x = (L · U) · x = L · (U · x) = b So, this routine first solves L · y = b for the vector y by forward substitution and then solves U · x = y for the vector x using backsubstitution

Parameters

a	input matrix a as the LU decomposition of A, returned by the routine ludcmp
n	input size of matrix
indx	input vector, records the row permutation, returned by the routine ludcmp
b	input array as the right-hand side vector B, and output with the solution vector X

Returns

:

a, n, and indx are not modified by this routine and can be left in place for successive calls with different right-hand sides b. This routine takes into account the possibility that b will begin with many zero elements, so it is efficient for use in matrix inversion.

Code adapted from Knuth's Numerical Recipes in C, pp 47

ludcmp()

bool Matrix::ludcmp	(	Matrix &	a,
		const int &	n,
		int	indx[],
		qreal &	d
	)

Given matrix a, it replaces a by the LU decomposition of a rowwise permutation of itself. Used in combination with lubksb to solve linear equations or invert a matrix.

Parameters

a	input matrix n x n and output arranged as in Knuth's equation (2.3.14)
n	input size of matrix
indx	output vector, records the row permutation effected by the partial pivoting
d	output as ±1 depending on whether the number of row interchanges was even or odd

Returns

:

Code adapted from Knuth's Numerical Recipes in C, pp 46

multiplyRow()

void Matrix::multiplyRow	(	int	row,
		qreal	value
	)

Multiply every element of row by value.

Parameters

row
value

multiplyScalar()

void Matrix::multiplyScalar

(

const qreal &

f

)

Scalar Multiplication. Multiplies this by qreal f and returns the product matrix of the same dim Allows to use P.multiplyScalar(f)

Parameters

f

NeighboursNearestFarthest()

void Matrix::NeighboursNearestFarthest	(	qreal &	min,
		qreal &	max,
		int &	imin,
		int &	jmin,
		int &	imax,
		int &	jmax
	)

Like Matrix::findMinMaxValues only it skips r==c.

Parameters

min	value. If (r,c) = minimum, it mean that neighbors r and c are the nearest in the matrix/network
max	value Complexity: O(n^2)

operator()()

qreal Matrix::operator() ( const int  r, const int  c  )

inline

operator*()

Matrix & Matrix::operator*

(

Matrix &

b

)

Matrix multiplication, operator * Multiplies (right) this matrix with given matrix b. Allows P = A * B where A,B of same dimension and returns product as a reference to the calling object.

Parameters

b
symmetry

Returns

operator*=()

void Matrix::operator*=

(

Matrix &

b

)

Multiplies (right) this m x n matrix with given n x p matrix b and returns the product in the calling matrix which becomes an m x p matrix. This convenience operator *= allows A *= B.

Parameters

b
symmetry

Returns

operator+()

Matrix & Matrix::operator+

(

Matrix &

b

)

Matrix addition, operator + Adds this matrix and B of the same dim and returns the sum S Allows S = A+B.

Parameters

b

Returns

Matrix S

operator+=()

void Matrix::operator+=

(

Matrix &

b

)

Matrix::operator += Matrix add another matrix: += Adds to this matrix another matrix B of the same dim and returns to this Allows A+=B.

Parameters

b

Returns

this

operator-()

Matrix & Matrix::operator-

(

Matrix &

b

)

Matrix subtraction, operator - Subtract this matrix - B of the same dim and returns the result S Allows S = A-B.

Parameters

b

Returns

Matrix S

operator=()

Matrix & Matrix::operator=

(

Matrix &

a

)

Matrix equality/assignment , operator = Allows copying a matrix onto another using b=a where b,a matrices Equals two matrices.

Parameters

a

Returns

operator[]()

MatrixRow & Matrix::operator[] ( const int &  r )

inline

pearsonCorrelationCoefficients()

Matrix & Matrix::pearsonCorrelationCoefficients	(	Matrix &	AM,
		const QString &	varLocation = "Rows",
		const bool &	diagonal = false
	)

Computes the Pearson Correlation Coefficient of the rows or the columns of the given matrix AM.

Parameters

AM

Matrix

Returns

Matrix nxn with PPC values for every pair of rows/columns of AM

pow()

Matrix & Matrix::pow	(	int	n,
		bool	symmetry = false
	)

Returns the n-nth power of this matrix.

Parameters

n
symmetry

Returns

Matrix

powerIteration()

void Matrix::powerIteration	(	qreal	x[],
		qreal &	xsum,
		qreal &	xmax,
		int &	xmaxi,
		qreal &	xmin,
		int &	xmini,
		const qreal	eps,
		const int &	maxIter
	)

Implementation of the Power method which computes the leading eigenvector x of this matrix, that is the eigenvector corresponding to the largest positive eigenvalue. In the process, it also computes min and max values. Used by Eigenvector Centrality (EVC). We use C arrays instead of std::vectors or anything else, as we know from start the size (n) of vectors x and tmp This approach is faster than using std::vector when n > 1000.

Parameters

x
xsum
xmax
xmaxi
xmin
xmini
eps
maxIter

printHTMLTable()

bool Matrix::printHTMLTable	(	QTextStream &	os,
		const bool	markDiag = false,
		const bool &	plain = false,
		const bool &	printInfinity = true
	)

Prints this matrix as HTML table This has the problem that the real actorNumber != elementLabel i.e. when we have deleted a node/vertex.

Parameters

os
debug

Returns

printMatrixConsole()

bool Matrix::printMatrixConsole

(

bool

debug = true

)

Prints this matrix to stderr or stdout.

Returns

product()

void Matrix::product	(	Matrix &	A,
		Matrix &	B,
		bool	symmetry = false
	)

Matrix Multiplication. Given two matrices A (mxn) and B (nxp) computes their product and stores it to the calling matrix which becomes an m x p matrix Allows P.product(A, B)

Parameters

A
B
symmetry

Returns

i x k matrix

productByVector()

void Matrix::productByVector	(	qreal	in[],
		qreal	out[],
		const bool &	leftMultiply = false
	)

Calculates the matrix-by-vector product Ax of this matrix Default product: Ax if leftMultiply=true then it returns the left product xA.

Parameters

in	input array/vector
out	output array
leftMultiply

productSym()

Matrix & Matrix::productSym	(	Matrix &	a,
		Matrix &	b
	)

Takes two ( N x N ) matrices (symmetric) and outputs an upper triangular matrix.

Parameters

a
b

Returns

resize()

void Matrix::resize	(	const int	m,
		const int	n
	)

Resizes this matrix to m x n Called before every operation on new matrices. Every MatrixRow object holds max_int=32762.

Parameters

Actors

rows()

int Matrix::rows ( )

inline

setItem()

void Matrix::setItem	(	const int	r,
		const int	c,
		const qreal	elem
	)

Sets the (r,c) matrix element calling the setColumn method.

Parameters

r
c
elem

similarityMatrix()

Matrix & Matrix::similarityMatrix	(	Matrix &	AM,
		const int &	measure,
		const QString	varLocation = "Rows",
		const bool &	diagonal = false,
		const bool &	considerWeights = true
	)

Computes the pair-wise matching score of the rows, columns or both of the given matrix AM, based on the given matching measure and returns the similarity matrix.

Parameters

AM

Matrix

Returns

Matrix nxn with matching scores for every pair of rows/columns of AM

size()

int Matrix::size ( )

inline

solve()

bool Matrix::solve

(

qreal

b[]

)

Computes and returns the solution of the set of n linear equations A·x = b Allows A.solve(b)

Parameters

b

vector

Returns

subtractFromI()

Matrix & Matrix::subtractFromI

(

)

Subtracts this matrix from I and returns.

Returns

I-this to this matrix

sum()

void Matrix::sum	(	Matrix &	a,
		Matrix &	b
	)

Matrix addition Takes two (nxn) matrices and returns their sum as a reference to this Same algorithm as operator +, just different interface. In this case, you use something like: c.sum(a,b)

Parameters

a
b

Returns

swapRows()

void Matrix::swapRows	(	int	rowA,
		int	rowB
	)

Swaps row A with row B of this matrix.

Parameters

rowA
rowB

transpose()

Matrix & Matrix::transpose

(

)

Returns the Transpose of this matrix Allows T = A.transpose()

Parameters

b

Returns

Matrix T

zeroMatrix()

void Matrix::zeroMatrix	(	const int	m,
		const int	n
	)

Makes this matrix the zero matrix of size mxn.

Parameters

m
n

Friends And Related Symbol Documentation

operator<<

QTextStream & operator<< ( QTextStream &  os, Matrix &  m  )

friend

Prints matrix m to given textstream.

Parameters

os
m

Returns

Field Documentation

m_cols

int Matrix::m_cols

private

m_rows

int Matrix::m_rows

private

row

MatrixRow* Matrix::row

private

---

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

• /home/dimitris/socnetv/app/src/matrix.h
• /home/dimitris/socnetv/app/src/matrix.cpp