matrix Class Reference

Representation of a two-dimensional matrix. More...

#include "matrix.h"

List of all members.

Public Member Functions
	matrix ()
	Constructs an empty matrix.
	matrix (int numberRows, int numberColumns, double value=0)
	Constructs a matrix with given number of rows and columns.
int	numColumns () const
	Returns the current number of columns for the matrix.
int	numRows () const
	Returns the current number of rows for the matrix.
matrix	size () const
	Returns a row-vector whose entries designate the current dimensions of the matrix.
void	reshape (int r, int c)
	Reshapes the matrix to the new number of rows and columns.
matrix	diag () const
	Converts between two-dimensional matrixes and one-dimensional diagonals.
matrix	transpose () const
	Generates a matrix that is the transpose form of the current one.
bool	operator== (const matrix &other) const
	Tests if two matrices have identical dimension and content.
bool	operator!= (const matrix &other) const
	The converse of the equivalence test.
double	operator() (int r, int c) const
	Provides read-only access to a specific matrix element.
double &	operator() (int r, int c)
	Provides a live reference to a specific matrix element.
double	operator() (int k) const
	Provides read-only access to a matrix element specified with a linear index.
double &	operator() (int k)
	Provides a live reference to a matrix element specified with a linear index.
matrix	operator- () const
	Generates a matrix that is the negated form of the current one.
matrix	operator+ (const matrix &other) const
	Generates a matrix that is the element-by-element sum of two matrices.
matrix &	operator+= (const matrix &other)
	Mutates a matrix by doing an element-by-element addition with another matrix.
matrix	operator+ (double scalar) const
	Generates a matrix by adding a scalar constant to each element of another matrix.
matrix &	operator+= (double scalar)
	Mutates a matrix by adding a scalar constant to each element.
matrix	operator- (const matrix &other) const
	Generates a matrix that is the element-by-element difference of two matrices.
matrix &	operator-= (const matrix &other)
	Mutates a matrix by doing an element-by-element addition with another matrix.
matrix	operator- (double scalar) const
	Generates a matrix by subtracting a scalar constant from each element of another matrix.
matrix &	operator-= (double scalar)
	Mutates a matrix by subtracting a scalar constant from each element.
matrix	operator* (const matrix &other) const
	Generates a matrix that is the product of two matrices.
matrix &	operator*= (const matrix &other)
	Mutates a matrix by multiplying it with another.
matrix	operator* (double scalar) const
	Generates a matrix by multiplying each element of another matrix by a scalar constant.
matrix &	operator*= (double scalar)
	Mutates a matrix by multiplying each element by a scalar constant.

---

Detailed Description

Representation of a two-dimensional matrix.

This represents a two-dimensional matrix of double precision floating-point numbers. It may be that the span of one or both of the dimensions is one, in which case this represents a row vector or column vector. One or both of the dimensions might be zero, in which case it represents an empty matrix.

When linearized, the matrix is stored in column-major order.

---

Constructor & Destructor Documentation

matrix

(

)

Constructs an empty matrix.

Technically, this matrix is 0x0 dimensional.

matrix	(	int	numberRows,
		int	numberColumns,
		double	value = 0
	)

Constructs a matrix with given number of rows and columns.

By default, all matrix entries are zero, but they can be set to any indicated scalar value.

Parameters:

	numberRows	the initial number of rows
	numberColumns	the initial number of columns
	value	the initial value for all entries (0 by default)

---

Member Function Documentation

int numColumns

(

)

const

Returns the current number of columns for the matrix.

int numRows

(

)

const

Returns the current number of rows for the matrix.

matrix size

(

)

const

Returns a row-vector whose entries designate the current dimensions of the matrix.

As an example, if a matrix currently had contents:

 5 15  3  8
20  2 14  3

a call to size would return the result

2 4

as there are two rows and four columns.

void reshape	(	int	r,
		int	c
	)

Reshapes the matrix to the new number of rows and columns.

Parameters:

	r	desired number of rows
	c	desired number of columns

Exceptions:

invalid_argument

if total number of elements does not remain the same

matrix diag

(

)

const

Converts between two-dimensional matrixes and one-dimensional diagonals.

Specifically, if the given matrix is one-dimensional, then this constructs a new square matrix that has the given entries along the diagonal, and zeros elsewhere.

Alternatively, if the given matrix is two-dimensional, this returns a new matrix that represents a row-vector describing the diagonal of the given matrix.

As an example, given a matrix m with contents:

 5 15  3

a call to m.diag() would return the result

 5  0  0
 0 15  0
 0  0  3

Conversely, given a matrix m with contents

 5 15  3  8
20  2 25  3
 0  0 23  9
 0  0 50  0

a call to m.diag() would return the result

 5  2 23  9

Note that if the original matrix is not square, the diagonal has length that is the shorter of the number of rows or number of columns. For example, givne a matrix m with contents

 5 15  3  8
20  2 25  3

a call to m.diag() would return the result

 5  2

matrix transpose

(

)

const

Generates a matrix that is the transpose form of the current one.

As a simple example, assume that matrix m has contents:

 5 15  3  8
20  2 14  3

Then the expression

m.transpose()

will result in a new matrix

 5 20
15  2
 3 14
 8  3

Note that the contents of the original matrix m remain unchanged.

bool operator==

(

const matrix &

other

)

const

Tests if two matrices have identical dimension and content.

Parameters:

other

the second matrix in an expression (m == other)

bool operator!=

(

const matrix &

other

)

const

The converse of the equivalence test.

Parameters:

other

the second matrix in an expression (m != other)

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

Provides read-only access to a specific matrix element.

As a simple example, assume that matrix m has contents:

 5 15  3  8
20  2 14  3

This method is invoked when using the syntax

double v = m(1,2);

in which case the value 14 results (as that is row 1, column 2).

Parameters:

	r	the indicated row (with 0 designating the top row)
	c	the indicated column (with 0 designating the leftmost column)

Exceptions:

out_of_range

if either index is invalid for the current dimensions

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

Provides a live reference to a specific matrix element.

The caller may use the reference to directly mutate the content of the cell. As a simple example, assume that matrix m has contents:

 5 15  3  8
20  2 14  3

This method is invoked when using the syntax

m(1,2) = 25;

in which case the matrix now has contents

 5 15  3  8
20  2 25  3

Note that if a row or column is indicated beyond the current extent of the matrix, the matrix is automatically reized to make room for the new entry, with other new cells getting value 0. For example the syntax This method is invoked when using the syntax

m(3,2) = 50;

causes the above matrix to be reconfigured as

 5 15  3  8
20  2 25  3
 0  0  0  0
 0  0 50  0

Parameters:

	r	the indicated row (with 0 designating the top row)
	c	the indicated column (with 0 designating the leftmost column)

Exceptions:

out_of_range

if either index is negative

double operator()

(

int

k

)

const

Provides read-only access to a matrix element specified with a linear index.

Matrices are linearized using the column-major convention. As a simple example, assume that matrix m has contents:

 5 15  3  8
20  2 14  3

This method is invoked when using the syntax

double v = m(5);

in which case the value 14 results (as that has index 5 in column-major order).

Parameters:

k

the zero-indexed location in column-major order

Exceptions:

out_of_range

if index is invalid

double& operator()

(

int

k

)

Provides a live reference to a matrix element specified with a linear index.

Matrices are linearized using the column-major convention. As a simple example, assume that matrix m has contents:

 5 15  3  8
20  2 14  3

This method is invoked when using the syntax

m(5) = 25

in which case the matrix now has contents

 5 15  3  8
20  2 25  3

Note: unlike the (row,column) form of this assignment, a matrix cannot be resized using the linearized index unless it is either a row vector or column vector.

Parameters:

k

the zero-indexed location in column-major order

Exceptions:

	out_of_range	if index is negative
	out_of_range	if index is beyond the extent of a two-dimensional matrix

matrix operator-

(

)

const

Generates a matrix that is the negated form of the current one.

As a simple example, assume that matrix m has contents:

 5 15  3  8
20  2 14  3

Then the expression

-m

will result in a new matrix

 -5 -15  -3  -8
-20  -2 -14  -3

Note that the contents of the original matrix m remain unchanged.

matrix operator+

(

const matrix &

other

)

const

Generates a matrix that is the element-by-element sum of two matrices.

As a simple example, assume that matrix A has contents:

 5 15  3  8
20  2 14  3

and matrix B has contents:

 2 14 23 10
11 12  5  9

Then the syntax

C = A + B

will result in a new matrix C with contents

 7 29 26 18
31 14 19 12

Note that the contents of both A and B remain unchanged, although one could be reassigned using a syntax such as

A = A + B;

See also operator+= below.

Exceptions:

invalid_argument

if matrix dimensions do not agree

matrix& operator+=

(

const matrix &

other

)

Mutates a matrix by doing an element-by-element addition with another matrix.

As a simple example, assume that matrix A has contents:

 5 15  3  8
20  2 14  3

and matrix B has contents:

 2 14 23 10
11 12  5  9

Then the command

A += B

will cause the contents of A to be set to

 7 29 26 18
31 14 19 12

while leaving the contents of B unchanged.

Exceptions:

invalid_argument

if matrix dimensions do not agree

matrix operator+

(

double

scalar

)

const

Generates a matrix by adding a scalar constant to each element of another matrix.

As a simple example, assume that matrix A has contents:

 5 15  3  8
20  2 14  3

Then the syntax

B = A + 5;

will result in a new matrix B with contents

10 20  8 13
25  7 19  8

while leaving the contents of A unchanged.

matrix& operator+=

(

double

scalar

)

Mutates a matrix by adding a scalar constant to each element.

As a simple example, assume that matrix A has contents:

 5 15  3  8
20  2 14  3

Then the syntax

A += 5

causes the contents of A to be set to

10 20  8 13
25  7 19  8

matrix operator-

(

const matrix &

other

)

const

Generates a matrix that is the element-by-element difference of two matrices.

As a simple example, assume that matrix A has contents:

 5 15  3  8
20  2 14  3

and matrix B has contents:

 2 14 23 10
11 12  5  9

Then the syntax

C = A - B

will result in a new matrix C with contents

  3   1 -20  -2
  9 -10   9  -6

Note that the contents of both A and B remain unchanged, although one could be reassigned using a syntax such as

A = A - B;

See also operator-= below.

Exceptions:

invalid_argument

if matrix dimensions do not agree

matrix& operator-=

(

const matrix &

other

)

Mutates a matrix by doing an element-by-element addition with another matrix.

As a simple example, assume that matrix A has contents:

 5 15  3  8
20  2 14  3

and matrix B has contents:

 2 14 23 10
11 12  5  9

Then the command

A -= B

will cause the contents of A to be set to

  3   1 -20  -2
  9 -10   9  -6

while leaving the contents of B unchanged.

Exceptions:

invalid_argument

if matrix dimensions do not agree

matrix operator-

(

double

scalar

)

const

Generates a matrix by subtracting a scalar constant from each element of another matrix.

As a simple example, assume that matrix A has contents:

 5 15  3  8
20  2 14  3

Then the syntax

B = A - 5;

will result in a new matrix B with contents

 0 10 -2  3
15 -3  9 -2

while leaving the contents of A unchanged.

matrix& operator-=

(

double

scalar

)

Mutates a matrix by subtracting a scalar constant from each element.

As a simple example, assume that matrix A has contents:

 5 15  3  8
20  2 14  3

Then the syntax

A -= 5

causes the contents of A to be set to

 0 10 -2  3
15 -3  9 -2

matrix operator*

(

const matrix &

other

)

const

Generates a matrix that is the product of two matrices.

As a simple example, assume that matrix A has contents:

 5 15  3  8
20  2 14  3

and matrix B has contents:

 3
10
 2
14

Then the syntax

C = A * B

will result in a new matrix C with contents

283
150

Note that the contents of both A and B remain unchanged.

Exceptions:

invalid_argument

if the inner matrix dimensions do not agree. That is, when computing A*B, the number of columns in A must match the number of rows in B.

matrix& operator*=

(

const matrix &

other

)

Mutates a matrix by multiplying it with another.

As a simple example, assume that matrix A has contents:

 5 15  3  8
20  2 14  3

and matrix B has contents:

 3
10
 2
14

Then the syntax

A *= B

will cause the contents of A to be reset to

283
150

while leaving the contents of B unchanged.

Note: the inner dimensions of the product must agree or else a runtime error occurs. That is the number of columns in A must match the number of rows in B when computing A*B. The resulting product has the same number of rows as A and the same number of columns as B.

matrix operator*

(

double

scalar

)

const

Generates a matrix by multiplying each element of another matrix by a scalar constant.

As a simple example, assume that matrix A has contents:

 5 15  3  8
20  2 14  3

Then the syntax

B = A * 2;

will result in a new matrix B with contents

10 30  6 16
40  4 28  6

while leaving the contents of A unchanged.

matrix& operator*=

(

double

scalar

)

Mutates a matrix by multiplying each element by a scalar constant.

As a simple example, assume that matrix A has contents:

 5 15  3  8
20  2 14  3

Then the syntax

A *= 2

causes the contents of A to be set to

10 30  6 16
40  4 28  6

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

• matrix.h