Basic class for matrices. More...

#include <Matrix.h>

Inheritance diagram for Matrix:

Public Member Functions
	Matrix (size_t size=1)
	Square Matrix constructor. More...

	Matrix (size_t rows, size_t cols)
	General Matrix constructor. More...

	Matrix (const Matrix &mat)
	Matrix copy constructor. More...

virtual	~Matrix ()
	Matrix destructor. More...

Matrix &	operator= (const Matrix &mat)
	Matrix assignment operator. More...

double &	operator() (size_t row, size_t col)
	Matrix element access. More...

const double &	operator() (size_t row, size_t col) const
	Matrix element access (`const` version). More...

size_t	numRows () const
	Number of rows in a Matrix. More...

size_t	numCols () const
	Number of columns in a Matrix. More...

size_t	numElements () const
	Number of elements in a Matrix. More...

Matrix	operator- () const
	Unary minus. More...

Matrix &	operator+= (const Matrix &mat)
	Matrix addition-assignment operator. More...

Matrix &	operator-= (const Matrix &mat)
	Matrix subtraction-assignment operator. More...

Matrix &	operator*= (double s)
	Matrix-scalar multiplication-assignment operator. More...

Matrix &	operator/= (double s)
	Matrix-scalar multiplication-assignment operator. More...

Matrix	transpose () const
	Matrix transpose. More...

Static Public Member Functions
static Matrix	identity (size_t rows, size_t cols)
	Factory method for Identity Matrices. More...

static Matrix	zero (size_t rows, size_t cols)
	Factory method for Zero Matrices. More...

Protected Attributes
size_t	rows_
	Number of rows in the Matrix. More...

size_t	cols_
	Number of columns in the Matrix. More...

std::vector< double >	data_
	Storage for Matrix data elements. More...

Related Functions
(Note that these are not member functions.)
Matrix	operator* (const Matrix &lhs, const Matrix &rhs)
	Matrix-Matrix multiplication operator. More...

Matrix	operator+ (const Matrix &lhs, const Matrix &rhs)
	Matrix addition operator. More...

Matrix	operator- (const Matrix &lhs, const Matrix &rhs)
	Matrix subtraction operator. More...

Matrix	operator* (double s, const Matrix &mat)
	scalar-Matrix multiplication operator. More...

Matrix	operator* (const Matrix &mat, double s)
	Matrix-scalar multiplication operator. More...

Matrix	operator/ (const Matrix &mat, double s)
	Matrix-scalar division operator. More...

std::ostream &	operator<< (std::ostream &outputStream, const Matrix &mat)
	Stream insertion operator. More...

std::istream &	operator>> (std::istream &inputStream, Matrix &mat)
	Stream extraction operator. More...

Detailed Description

Basic class for matrices.

This class provides basic matrix operatations (addition, subtraction, multiplication, etc.) as overloaded operators. This is sufficient for COSC432 and the Ray Tracer assignment, but does not include more advanced operations like inverse, or matrix decompositions.

The class is designed to be simple and easy to understand rather than optimal or hyper-efficient. For production code a more professional library (such as Eigen) is recommended.

Constructor & Destructor Documentation

◆ Matrix() [1/3]

Matrix::Matrix ( size_t size = 1 )

Square Matrix constructor.

This constructor creates a square (size x size) matrix. If no size is provided, it creates a 1 x 1 matrix, and so also provides a default constructor.

Parameters

size	The size of the resulting Matrix.

◆ Matrix() [2/3]

Matrix::Matrix	(	size_t	rows,
		size_t	cols
	)

General Matrix constructor.

This constructor creates a matrix of the specified size. The number of rows and columns is specified and must be postivie integers.

Parameters

rows	The number of rows in the resulting Matrix.
cols	The number of columns in the resulting Matrix.

◆ Matrix() [3/3]

Matrix::Matrix ( const Matrix & mat )

Matrix copy constructor.

This constructor creates a new Matrix which is a copy of an existing one. The new Matrix has independent storage etc.

Parameters

mat	The Matrix to copy.

◆ ~Matrix()

Matrix::~Matrix ( )

virtual

Matrix destructor.

The Matrices are based on std::vector, so there's not much to do here, but it is provided for completeness. Note that this is virtual, since other classes (like Vector) may inherit from Matrix.

Member Function Documentation

◆ identity()

Matrix Matrix::identity	(	size_t	rows,
		size_t	cols
	)

static

Factory method for Identity Matrices.

This returns an Identity Matrix of a given size. Identity Matrices have ones on the main diagonal, and zeros off the diagonal. For non-square Matrices, any 'extra' rows or columns are all zero.

Parameters

rows	The number of rows in the resulting Matrix.
cols	The number of columns in the resulting Matrix.

Returns: A rows x cols Identity matrix

◆ numCols()

size_t Matrix::numCols ( ) const

Number of columns in a Matrix.

Returns: The number of columns in the given Matrix.

◆ numElements()

size_t Matrix::numElements ( ) const

Number of elements in a Matrix.

Returns: The number of elements in the given Matrix.

◆ numRows()

size_t Matrix::numRows ( ) const

Number of rows in a Matrix.

Returns: The number of rows in the given Matrix.

◆ operator()() [1/2]

double & Matrix::operator()	(	size_t	row,
		size_t	col
	)

Matrix element access.

This method provides access to the elements of a Matrix using the syntax A(i,j). This notation is equivalent to A.operator()(i,j). Since a reference is returned, this can be used for assignment, eg: A(1,2)=3.1415; The values of row and column must be less than the size of the Matrix.

Parameters

row	The row of the Matrix to access.
col	The column of the Matrix to access.

Returns: A reference to the requested element of the Matrix.

◆ operator()() [2/2]

const double & Matrix::operator()	(	size_t	row,
		size_t	col
	)		const

Matrix element access (const version).

This method provides access to the elements of a const Matrix using the syntax A(i,j). Since a const reference is returned, this cannot be used for assignment, but it can be applied to const Matrices. The values of row and column must be less than the size of the Matrix.

Parameters

row	The row of the Matrix to access.
col	The column of the Matrix to access.

Returns: A const reference to the requested element of the Matrix.

◆ operator*=()

Matrix & Matrix::operator*= ( double s )

Matrix-scalar multiplication-assignment operator.

This scales a Matrix in place. Note that there is no *= operator defined between two Matrices. This is because Matrix multiplication is not commutative, so A*B != B*A in general. That makes A*=B a little confusing. Following C++ convention, this should mean A=A*B, but we'll often be multiplying vectors by matrices, and a*=B would intuitively mean a=B*a. This is easily avoided by not having *= for two Matrices.

Parameters

s	The scalar multiplier to apply to `this`.

Returns: A reference to the updated this, to allow chaining of assignment.

◆ operator+=()

Matrix & Matrix::operator+= ( const Matrix & mat )

Matrix addition-assignment operator.

This adds a Matrix to an existing one in place. The two Matrices must have the same size.

Parameters

mat	The Matrix to add to `this`.

Returns: A reference to the updated this, to allow chaining of assignment.

◆ operator-()

Matrix Matrix::operator- ( ) const

Unary minus.

This provides the ability to negate a Matrix. -A is equivalent to A.operator-()

Returns: A negated version of the Matrix.

◆ operator-=()

Matrix & Matrix::operator-= ( const Matrix & mat )

Matrix subtraction-assignment operator.

This subtracts a Matrix from an existing one in place. The two Matrices must have the same size.

Parameters

mat	The Matrix to subtract from `this`.

Returns: A reference to the updated this, to allow chaining of assignment.

◆ operator/=()

Matrix & Matrix::operator/= ( double s )

Matrix-scalar multiplication-assignment operator.

This divides a Matrix in place.

Parameters

s	The scalar multiplier to divide `this` by.

Returns: A reference to the updated this, to allow chaining of assignment.

◆ operator=()

Matrix & Matrix::operator= ( const Matrix & mat )

Matrix assignment operator.

This allows expressions like A = B; where A and B are Matrices. It also allows chained assignment, like A = B = C;

Parameters

mat	The Matrix on the right hand side of the assignment.

Returns: a reference to this, to allow chaining of assignment.

◆ transpose()

Matrix Matrix::transpose ( ) const

Matrix transpose.

This creates the transpose of a Matrix, which is a new Matrix with the original rows and columns interchanged.

Returns: A transposed copy of this.

◆ zero()

Matrix Matrix::zero	(	size_t	rows,
		size_t	cols
	)

static

Factory method for Zero Matrices.

This returns a Zero Matrix of a given size. Zero matrices have all entries set to Zero (unsurprisingly).

Parameters

rows	The number of rows in the resulting Matrix.
cols	The number of columns in the resulting Matrix.

Returns: A rows x cols Zero Matrix

Friends And Related Function Documentation

◆ operator* [1/3]

Matrix operator*	(	const Matrix &	lhs,
		const Matrix &	rhs
	)

friend

Matrix-Matrix multiplication operator.

This creates the product of two Matrices. The first Matrix must have the same number of columns as the second Matrix has rows.

Note that multiplication is declared as a friend. It could be declared as a normal method Matrix operator*(const Matrix& rhs);. The friend form provides a more symmetric view of the two Matrices being multiplied. It could also be defined in terms of a *= operator, but it is not clear whether A *= B; means A = A*B or A = B*A. So this is omitted to avoid confusion.

Parameters

lhs	The Matrix on the left hand side of the *.
rhs	The Matrix on the right hand side of the *.

Returns: The Matrix formed by lhs * rhs.

◆ operator*() [2/3]

Matrix operator*	(	const Matrix &	mat,
		double	s
	)

This creates the product of a Matrix and a scalar.

Parameters

mat	The Matrix to be scaled.
s	The scalar value to multiply the Matrix by.

Returns: The Matrix formed by mat*s.

◆ operator*() [3/3]

Matrix operator*	(	double	s,
		const Matrix &	mat
	)

This creates the product of a scalar and a Matrix.

Parameters

s	The scalar value to multiply the Matrix by.
mat	The Matrix to be scaled.

Returns: The Matrix formed by s*mat.

◆ operator+()

Matrix operator+	(	const Matrix &	lhs,
		const Matrix &	rhs
	)

This performs addition of two Matrices. The two Matrices must have the same size

Parameters

lhs	The Matrix on the left hand side of the +.
rhs	The Matrix on the right hand side of the +.

Returns: The Matrix formed by lhs + rhs.

◆ operator-()

Matrix operator-	(	const Matrix &	lhs,
		const Matrix &	rhs
	)

This performs subtraction of two Matrices. The two Matrices must have the same size

Parameters

lhs	The Matrix on the left hand side of the -.
rhs	The Matrix on the right hand side of the -.

Returns: The Matrix formed by lhs - rhs.

◆ operator/()

Matrix operator/	(	const Matrix &	mat,
		double	s
	)

This creates the result of a Matrix divided by a scalar. Division by a scalar, s, is essentially the same as multiplcation (or scaling) by 1/s. Division by numbers close to 0 will result in NaN and Inf values and wildly unstable results as normal.

Parameters

mat	The Matrix to be scaled.
s	The scalar value to divide the Matrix by.

Returns: The Matrix formed by mat/s.

◆ operator<<()

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

Provides the ability to output Matrices to C++ streams, including std::cout and filestreams.

Parameters

outputStream	the stream to send the Matrix to.
mat	the matrix to send to the stream.

Returns: The updated output stream.

◆ operator>>()

std::istream & operator>>	(	std::istream &	inputStream,
		Matrix &	mat
	)

Provides the ability to read Matrices from C++ streams, including std::cin and filestreams. The size of the Matrix determines how much data is read from the stream.

Parameters

inputStream	the stream to read the Matrix from.
mat	the matrix to read from the stream.

Returns: The updated input stream.

Member Data Documentation

◆ cols_

size_t Matrix::cols_

protected

Number of columns in the Matrix.

◆ data_

std::vector<double> Matrix::data_

protected

Storage for Matrix data elements.

◆ rows_

size_t Matrix::rows_

protected

Number of rows in the Matrix.

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

Public Member Functions

Static Public Member Functions

Protected Attributes

Related Functions

Detailed Description

Constructor & Destructor Documentation

◆ Matrix() [1/3]

◆ Matrix() [2/3]

◆ Matrix() [3/3]

◆ ~Matrix()

Member Function Documentation

◆ identity()

◆ numCols()

◆ numElements()

◆ numRows()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator*=()

◆ operator+=()

◆ operator-()

◆ operator-=()

◆ operator/=()

◆ operator=()

◆ transpose()

◆ zero()

Friends And Related Function Documentation

◆ operator* [1/3]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ operator+()

◆ operator-()

◆ operator/()

◆ operator<<()

◆ operator>>()

Member Data Documentation

◆ cols_

◆ data_

◆ rows_