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 $$m × n matrix with the columns as specified by $$S. 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 $$A.

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: $$0 i n - 1.
NT&	M ( int i, int j)	returns $$Mi,j. Precondition: $$0 i m-1 and $$0 j n-1.
void	M.swap_rows ( int i, int j)
		swaps rows $$i and $$j. Precondition: $$0 i m-1 and $$0 j m-1.
void	M.swap_columns ( int i, int j)
		swaps columns $$i and $$j. 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 $$M.
terator	M.end ()	an iterator pointing beyond the last entry of $$M.

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.