#include <Matrix.h>

Public Member Functions
	Matrix (int rows, int columns)

	Matrix (const Matrix &original)

	Matrix (const Vector &v)

	~Matrix ()

double	get (int r, int c) const

int	getColumns () const

int	getRows () const

double &	operator() (int r, int c)

Matrix &	operator= (std::initializer_list< double > values)

Matrix &	operator= (const Matrix &other)

Protected Member Functions
void	allocateMemory ()

void	deallocateMemory ()

void	setSize (int rows, int columns)

void	setValues (double value)

void	setValues (const double *values)

void	setValues (double **values)

Protected Attributes
double **	values

int	columns

int	rows

Friends
double	cof (const Matrix &A, int i, int j)

double	det (const Matrix &A)

Matrix	identity (int size)

double	mminor (const Matrix &A, int i, int j)

Matrix	multiply (const Vector &a, const Vector &b)

Matrix	operator+ (const Matrix &A, const Matrix &B)

Matrix	operator- (const Matrix &A, const Matrix &B)

Matrix	operator* (const Matrix &A, const Matrix &B)

Vector	operator* (const Vector &v, const Matrix &M)

Vector	operator* (const Matrix &M, const Vector &v)

Matrix	operator* (double k, const Matrix &A)

Matrix	operator* (const Matrix &A, double k)

bool	operator== (const Matrix &A, const Matrix &B)

bool	operator!= (const Matrix &A, const Matrix &B)

Matrix	submatrix (const Matrix &A, int i, int j)

Matrix	trans (const Matrix &A)

Detailed Description

An encapsulation of a Matrix.

Constructor & Destructor Documentation

◆ Matrix() [1/3]

Matrix::Matrix	(	int	rows,
		int	columns
	)

A constructor that does not allow for initial values (i.e., that initializes all elements to 0.0). The Matrix must be initialized with the assignment operator.

Example of use:

Matrix y(3,3);

Parameters

rows	The number of rows
columns	The number of columns

◆ Matrix() [2/3]

Matrix::Matrix ( const Matrix & original )

A copy constructor.

Note: A copy constructor is critical because without one we can't pass a Matrix by value (which requires that it be possible to make a copy).

Parameters

original The Matrix to copy

◆ Matrix() [3/3]

Matrix::Matrix ( const Vector & v )

explicit

Construct a Matrix from a Vector.

The resulting Matrix will be eithe nx1 or 1xn depending on the orientation of the Vector

Parameters

v	The Vector to "copy"

◆ ~Matrix()

Matrix::~Matrix ( )

Destructor.

Member Function Documentation

◆ allocateMemory()

void Matrix::allocateMemory ( )

protected

Allocate memory for this Matrix.

◆ deallocateMemory()

void Matrix::deallocateMemory ( )

protected

Deallocate the memory used by this Matrix.

◆ get()

double Matrix::get	(	int	r,
		int	c
	)		const

Get a particular element of this Matrix.

Parameters

r	The row index
c	The column index

Exceptions

out_of_range if r or c are out of bounds

Returns: The value of the element

◆ getColumns()

int Matrix::getColumns ( ) const

Get the number of columns in this Matrix.

Returns: The number of columns

◆ getRows()

int Matrix::getRows ( ) const

Get the number of rows in this Matrix.

Returns: The number of rows

◆ operator()()

double & Matrix::operator()	(	int	r,
		int	c
	)

Access an element of this Matrix using the function-call operator.

Note: This method returns by reference so that this operator can be used on the left side of the assignment operator. Though this can be dangerous in general (since the value being referred to may not always exist), in this case it shouldn't cause any problems.

Examples of use:

d = y(1,1);

y(2,3) = 5.0;

Parameters

r	The row index
c	The column index

Exceptions

out_of_range if r or c are out of bounds

Returns: The value of the element

◆ operator=() [1/2]

Matrix & Matrix::operator= ( std::initializer_list< double > values )

Assign an initializer_list to this Matrix.

Example of use:

y = {1, 2, 3,
     4, 5, 6,
     7, 8, 9};

Note: This method is not void so that one can write x = y = {1, 2} (which first assigns {1, 2} to y and then assigns the result of that assignment to x). It returns the result by reference because there is no concern that this will not refer to something.

Parameters

values The initializer_list containing the values

Exceptions

length_error if values is of the wrong size

Returns: The Matrix referred to by this

◆ operator=() [2/2]

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

Assign another Matrix to this Matrix.

Note: This method is not void so that one can write x = y = z (which first assigns z to y and then assigns the result of that assignment to x). It returns the result by reference because there is no concern that this will not refer to something.

Parameters

other The Matrix to copy

Exceptions

length_error if the shapes do not conform

Returns: The Matrix referred to by this

◆ setSize()

void Matrix::setSize	(	int	rows,
		int	columns
	)

protected

Set the size of this Matrix. Note: This method should only be called by constructors.

Parameters

rows	The number of rows
columns	The number of columns

◆ setValues() [1/3]

void Matrix::setValues ( double value )

protected

Set the value of all elements in this Matrix to the given value.

Parameters

value The value to assign to every element

◆ setValues() [2/3]

void Matrix::setValues ( const double * values )

protected

Set the value of each element in this Matrix to the value of the corresponding element in a row-major array.

Parameters

values A pointer to the row-major array

◆ setValues() [3/3]

void Matrix::setValues ( double ** values )

protected

Set the value of each element in this Matrix to the value of the corresponding element in a "two-dimensional" array.

Parameters

values A pointer to the "two-dimensional" array

Friends And Related Function Documentation

◆ cof

double cof	(	const Matrix &	A,
		int	i,
		int	j
	)

friend

Calculate the cofactor of a square matrix (i.e., the signed determinate of the matrix with row i and column j removed).

Parameters

A	The matrix (which must be square)
i	The index of the row to exclude
j	The index of the column to exclude

Exceptions

length_error	if the Matrix isn't square
out_of_range	if i or j are out of bounds

Returns: The cofactor

◆ det

double det ( const Matrix & A )

friend

Calculate the determinant of a square matrix.

Note: This implementation is not efficient since it explicitly creates each of the minors. However, it is easy to understand.

Parameters

A	The matrix (which must be square)

Exceptions

length_error	if the Matrix is smaller than 2x2
length_error	if the Matrix isn't square

Returns: \(|A|\)

◆ identity

Matrix identity ( int size )

friend

Create and return an identity matrix.

Note: This function must return by value because the result Matrix is a local variable.

Parameters

size	The number of rows == columns in the (square) matrix

Returns: \( I \)

◆ mminor

double mminor	(	const Matrix &	A,
		int	i,
		int	j
	)

friend

Calculate a particular minor for a square matrix (i.e., the determinant of the matrix with row i and column j removed).

Parameters

A	The matrix (which must be square)
i	The index of the row to exclude
j	The index of the column to exclude

Exceptions

out_of_range if i or j are out of bounds

Returns: The minor

◆ multiply

Matrix multiply	(	const Vector &	a,
		const Vector &	b
	)

friend

Multiply a column Vector and a row Vector.

Note: We can't overload the * operator for this purpose because it is already overloaded in the Vector class for the dot/inner product

Parameters

a	The column Vector
b	The row Vector

Exceptions

length_error if the shapes of a and b do not conform

Returns: \( \mathbf{a} \mathbf{b} \)

◆ operator!=

bool operator!=	(	const Matrix &	A,
		const Matrix &	B
	)

friend

Compare two matrices to see if they have different elements (beyond a given TOLERANCE).

Parameters

A	The first matrix
B	The second matrix

Exceptions

length_error if the shapes of A and B do not conform

Returns: true or false

◆ operator* [1/5]

Matrix operator*	(	const Matrix &	A,
		const Matrix &	B
	)

friend

Multiply two matrices.

Note: This method must return by value because the result Matrix is a local variable.

Parameters

A	The first matrix (m x n)
B	The second matrix (n x s)

Exceptions

length_error if the shapes of A and B do not conform

Returns: \( \mathbf{A} \mathbf{B} \) (m x s)

◆ operator* [2/5]

Vector operator*	(	const Vector &	v,
		const Matrix &	M
	)

friend

Multiply a row Vector and a Matrix.

Note: This method must return by value because the result Vector is a local variable.

It is worth noting that, if this method returned a Matrix rather than a Vector, it could be implemented as return (Matrix(v) * M);

Parameters

v	The row Vector
M	The Matrix

Exceptions

length_error if the shapes of v and M do not conform

Returns: The row Vector \( \mathbf{v} \mathbf{M} \)

◆ operator* [3/5]

Vector operator*	(	const Matrix &	M,
		const Vector &	v
	)

friend

Multiply a Matrix and a column Vector.

Note: This method must return by value because the result Matrix is a local variable.

It is worth noting that, if this method returned a Matrix rather than a Vector, it could be implemented as return return (M * Matrix(v));

Parameters

M	The Matrix
v	The column Vector

Returns: column Vector \( \mathbf{M} \mathbf{v} \)

◆ operator* [4/5]

Matrix operator*	(	double	k,
		const Matrix &	A
	)

friend

Multiply a scalar and a matrix.

Note: This method must return by value because the result Matrix is a local variable.

Parameters

k	The scalar
A	The matrix

Returns: \( k \mathbf{A} \)

◆ operator* [5/5]

Matrix operator*	(	const Matrix &	A,
		double	k
	)

friend

Multiply a matrix and a scalar.

Note: This method must return by value because the result Matrix is a local variable.

Parameters

A	The matrix
k	The scalar

Returns: \( \mathbf{A} k \)

◆ operator+

Matrix operator+	(	const Matrix &	A,
		const Matrix &	B
	)

friend

Add the Matrix A and the Matrix B.

Note: This method must return by value because the result Matrix is a local variable.

Parameters

A	One Matrix
B	The other Matrix

Exceptions

length_error if the shapes of A and B do not conform

Returns: \( \mathbf{A} + \mathbf{B} \)

◆ operator-

Matrix operator-	(	const Matrix &	A,
		const Matrix &	B
	)

friend

Subtract the Matrix B from the Matrix A (component by component).

Note: This method must return by value because the result Matrix is a local variable.

Parameters

A	One Matrix
B	The other Matrix

Exceptions

length_error if the shapes of A and B do not conform

Returns: \( \mathbf{A} - \mathbf{B} \)

◆ operator==

bool operator==	(	const Matrix &	A,
		const Matrix &	B
	)

friend

Compare two matrices to see if they have identical elements (within a given TOLERANCE for each element).

Parameters

A	The first matrix
B	The second matrix

Exceptions

length_error if the shapes of A and B do not conform

Returns: true or false

◆ submatrix

Matrix submatrix	(	const Matrix &	A,
		int	i,
		int	j
	)

friend

Remove a row and column from a matrix

Parameters

A	The matrix (which must be square)
i	The index of the row to exclude
j	The index of the col to exclude

Exceptions

length_error	the Matrix is smaller than 2x2
out_of_range	if i or j are out of bounds

Returns: The submatrix (i.e., A with row i and column j excluded)

◆ trans

Matrix trans ( const Matrix & A )

friend

Create and return a transposed version of a given matrix.

Note: This function must return by value because the result Matrix is a local variable.

Parameters

A	The original Matrix

Returns: \( \mathbf{A}^T \)

Member Data Documentation

◆ columns

int Matrix::columns

protected

The number of columns in this Matrix.

◆ rows

int Matrix::rows

protected

The number of rows in this Matrix.

◆ values

double** Matrix::values

protected

The elements of this Matrix.

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

Matrix.h
Matrix.cpp

Public Member Functions

Protected Member Functions

Protected Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Matrix() [1/3]

◆ Matrix() [2/3]

◆ Matrix() [3/3]

◆ ~Matrix()

Member Function Documentation

◆ allocateMemory()

◆ deallocateMemory()

◆ get()

◆ getColumns()

◆ getRows()

◆ operator()()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ setSize()

◆ setValues() [1/3]

◆ setValues() [2/3]

◆ setValues() [3/3]

Friends And Related Function Documentation

◆ cof

◆ det

◆ identity

◆ mminor

◆ multiply

◆ operator!=

◆ operator* [1/5]

◆ operator* [2/5]

◆ operator* [3/5]

◆ operator* [4/5]

◆ operator* [5/5]

◆ operator+

◆ operator-

◆ operator==

◆ submatrix

◆ trans

Member Data Documentation

◆ columns

◆ rows

◆ values