#include <Matrix.h>

Inherited by Vector.

Public Member Functions
	Matrix ()

	Matrix (int rows, int columns)

	Matrix (const Matrix &original)

	~Matrix ()

double	get (int r, int c) const

double	get (int i) const

Matrix	getColumn (int c) const

int	getColumns () const

int	getRows () const

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

double &	operator() (int i)

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

Matrix &	operator= (const Matrix &other)

Protected Member Functions
void	allocateMemory (int rows, int columns)

void	deallocateMemory ()

void	setValues (double value)

void	setValues (const Matrix &other)

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 (double a)

double	det (const Matrix &A)

double	dot (const Matrix &A, const Matrix &B)

Matrix	identity (int size)

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

Matrix	operator\| (const Matrix &A, const Matrix &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)

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 ( )

Default Constructor (constructs a 2x2 Matrix).

◆ Matrix() [2/3]

Matrix::Matrix	(	int	rows,
		int	columns
	)

Explicit Value Constructor.

Parameters

rows	The number of rows
columns	The number of columns

◆ Matrix() [3/3]

Matrix::Matrix ( const Matrix & original )

A copy constructor.

Note: A copy constructor is critical because without on 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()

Matrix::~Matrix ( )

Destructor

Member Function Documentation

◆ allocateMemory()

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

protected

Allocate memory for this Matrix.

Parameters

rows	The number of rows
columns	The number of columns

◆ deallocateMemory()

void Matrix::deallocateMemory ( )

protected

Deallocate the memory used by this Matrix

◆ get() [1/2]

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

◆ get() [2/2]

double Matrix::get ( int i ) const

Get a particular element of this Matrix if it contains a single row or single column.

Parameters

i The index

Exceptions

out_of_range	if i is out of bounds
length_error	if this is neither a single row nor single column

Returns: The value of the element

◆ getColumn()

Matrix Matrix::getColumn ( int c ) const

Get a column of this Matrix.

Note: This is not an efficient method, and it would be much better to use rows rather than columns (since we are using row-major ordering). However, this is more consistent with the mathematical treatment in most books.

Parameters

c	The index of the column (0-based)

Exceptions

out_of_range if c is out of bounds

Returns: The column at the given index

◆ 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()() [1/2]

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()() [2/2]

double & Matrix::operator() ( int i )

Access a particular element of this Matrix using the function call operator if it contains a single row or single column.

Parameters

i The index

Exceptions

out_of_range	if i is out of bounds
length_error	if this is neither a single row nor single column

Returns: The 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 the list is 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 don't conform

Returns: The Matrix referred to by this

◆ setValues() [1/4]

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() [2/4]

void Matrix::setValues ( const Matrix & other )

protected

Set the value of all elements in this Matrix to the value of the corresponding elements in another Matrix.

Parameters

other The other Matrix

◆ setValues() [3/4]

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() [4/4]

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 [1/2]

double det ( double a )

friend

Calculate the determinant of a scalar.

Parameters

a	The value of the scalar

Returns: The determinant of a (which is just a)

◆ det [2/2]

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 or isn't square

Returns: The value of the determinant

◆ dot

double dot	(	const Matrix &	A,
		const Matrix &	B
	)

friend

Calculate the dot product (more commonly known as the scalar product) of two Matrixes.

Note: While the steps in this calculation are the same as in matrix multiplication (of a 1xn and nx1 Matrix), the result is a scalar, not a Matrix. Hence, the need for this method.

We could return (trans(A)*B).get(0,0) but this would create two matrices needlessly.

This function is in the Matrix class, rather than the Vector class, because it is sometimes used with Matrixes

Parameters

A	The left-side Matrix
B	The right-side Matrix

Exceptions

length_error if the sizes don't conform

Returns: The dot product

◆ 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: An identity Matrix

◆ mminor

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

friend

Calculate the minor (i.e., the determinant of the submatrix formed by deleting a row and column).

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 is out of bounds
length_error	if A isn't square

Returns: The minor

◆ operator!=

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

friend

Compare two matrices to see if they have different elements.

Parameters

A	The first matrix
B	The second matrix

Exceptions

length_error if the shapes of A and B do not conform

Returns: true if they have any different elements; false otherwise

◆ operator* [1/3]

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: \( \mathbf{A} \mathbf{B} \) [which is (m x s)]

◆ operator* [2/3]

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* [3/3]

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 another Matrix from this matrix (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

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|

Matrix operator\|	(	const Matrix &	A,
		const Matrix &	B
	)

friend

Concatenate the columns of Matrix A and the columns Matrix B.

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

Parameters

A	The left Matrix
B	The right Matrix

Exceptions

length_error if the shapes of A and B do not conform

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

◆ submatrix

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

friend

Remove a row and column from a matrix.

Parameters

A	The matrix
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 rows in this Matrix.

◆ rows

int Matrix::rows

protected

The number of columnd 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() [1/2]

◆ get() [2/2]

◆ getColumn()

◆ getColumns()

◆ getRows()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ setValues() [1/4]

◆ setValues() [2/4]

◆ setValues() [3/4]

◆ setValues() [4/4]

Friends And Related Function Documentation

◆ cof

◆ det [1/2]

◆ det [2/2]

◆ dot

◆ identity

◆ mminor

◆ operator!=

◆ operator* [1/3]

◆ operator* [2/3]

◆ operator* [3/3]

◆ operator+

◆ operator-

◆ operator==

◆ operator|

◆ submatrix

◆ trans

Member Data Documentation

◆ columns

◆ rows

◆ values