Matrix

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Matrix

Definition

An instance of data type Matrix is a matrix of variables of number type NT. The types Matrix and Vector together realize many functions of basic linear algebra.

Types

Matrix::NT
	the ring type of the components.

Matrix::iterator
	bidirectional iterator for accessing all components row-wise.

Matrix::row_iterator
	random access iterator for accessing row entries.

Matrix::column_iterator
	random access iterator for accessing column entries.

There also constant versions of the above iterators: const_iterator, row_const_iterator, and column_const_iterator.

Matrix::Identity
	a tag class for identity initialization

Matrix::Vector
	the vector type used.

Creation

Matrix M;

creates an instance M of type Matrix.

Matrix M ( int n);

creates an instance M of type Matrix of dimension

n × n initialized to the zero matrix.

Matrix M ( int m, int n);

creates an instance M of type Matrix of dimension

m × n initialized to the zero matrix.

Matrix M ( std::pair<int,int> p);

creates an instance M of type Matrix of dimension p.first

× p.second initialized to the zero matrix.

Matrix M ( int n, Identity, NT x = NT(1));

creates an instance M of type Matrix of dimension

n × n initialized to the identity matrix (times x).

Matrix M ( int m, int n, NT x);

creates an instance M of type Matrix of dimension

m × n initialized to the matrix with x entries.

template <class Forward_iterator>

Matrix M ( Forward_iterator first, Forward_iterator last);

creates an instance M of type Matrix. Let

S be the ordered set of

n column-vectors of common dimension

m as given by the iterator range [first,last). M is initialized to an

m × n matrix with the columns as specified by

Precondition:

Forward_iterator has a value type V from which we require to provide a iterator type V::const_iterator, to have V::value_type == NT.
Note that Vector or std::vector<NT> fulfill these requirements.

Matrix M ( std::vector< Vector > A);

creates an instance M of type Matrix. Let

A be an array of

n column-vectors of common dimension

m. M is initialized to an

m × n matrix with the columns as specified by

Operations

int

M.row_dimension ()

returns

n, the number of rows of M.

int

M.column_dimension ()

returns

m, the number of columns of M.

std::pair<int,int>

M.dimension ()

returns

(m,n), the dimension pair of M.

Vector

M.row ( int i)

returns the

i-th row of M (an

m - vector).

Precondition:

0 i m - 1.

Vector

M.column ( int i)

returns the

i-th column of M (an

n - vector).

Precondition:

0 i n - 1.

NT&

M ( int i , int j )

returns

M_i,j.

Precondition:

0 i m-1 and

0 j n-1.

void

M.swap_rows ( int i, int j)

swaps rows

i and

Precondition:

0 i m-1 and

0 j m-1.

void

M.swap_columns ( int i, int j)

swaps columns

i and

Precondition:

0 i n-1 and

0 j n-1.

row_iterator

M.row_begin ( int i)

an iterator pointing to the first entry of the

ith row.

Precondition:

0 i m-1.

row_iterator

M.row_end ( int i)

an iterator pointing beyond the last entry of the

ith row.

Precondition:

0 i m-1.

column_iterator

M.column_begin ( int i)

an iterator pointing to the first entry of the

ith column.

Precondition:

0 i n-1.

column_iterator

M.column_end ( int i)

an iterator pointing beyond the last entry of the

ith column.

Precondition:

0 i n-1.

iterator

M.begin ()

an iterator pointing to the first entry of

terator

M.end ()

an iterator pointing beyond the last entry of

The same operations exist for row_const_iterator, column_const_iterator and const_iterator.

bool	M == M1	Test for equality.

bool	M != M1	Test for inequality.

Arithmetic Operators

Matrix

M + M1

Addition.

Precondition:

M.row_dimension() == M1.row_dimension() and
M.column_dimension() == M1.column_dimension().

Matrix

M - M1

Subtraction.

Precondition:

M.row_dimension() == M1.row_dimension() and
M.column_dimension() == M1.column_dimension().

Matrix

- M

Negation.

Matrix

M * M1

Multiplication.

Precondition:

M.column_dimension() = M1.row_dimension().

Vector

M * Vector vec

Multiplication with vector.

Precondition:

M.column_dimension() = vec.dimension().

Matrix

NT x * M

Multiplication of every entry with x.

Matrix

M * NT x

Multiplication of every entry with x.

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CGAL Open Source Project. Release 3.3.1. 25 August 2007.