Container Concepts

Vector

Description

A Vector describes common aspects of dense, packed and sparse vectors.

Refinement of

Associated types

Value type	`value_type`	The type of the vector.
Distance type	`difference_type`	A signed integral type used to represent the distance between two of the vector's iterators.
Size type	`size_type`	An unsigned integral type that can represent any nonnegative value of the vector's distance type.

Notation

`V`	A type that is a model of Vector
`v`	Objects of type `V`
`n, i`	Objects of a type convertible to `size_type`
`t`	Object of a type convertible to `value_type`
`p`	Object of a type convertible to `bool`

Definitions

Valid expressions

In addition to the expressions defined in Vector Expression the following expressions must be valid.

Name	Expression	Type requirements	Return type
Sizing constructor	`V v (n)`		`V`
Insert	`v.insert (i, t)`	`v` is mutable.	`void`
Erase	`v.erase (i)`	`v` is mutable.	`void`
Clear	`v.clear ()`	`v` is mutable.	`void`
Resize	`v.resize (n)` `v.resize (n, p)`	`v` is mutable.	`void`

Expression semantics

Semantics of an expression is defined only where it differs from, or is not defined in Vector Expression .

Name	Expression	Precondition	Semantics	Postcondition
Sizing constructor	`V v (n)`	`n >= 0`	Creates a vector of `n` elements.	`v.size () == n`.
Insert	`v.insert (i, t)`	`0 <= i < v.size ()` and `v (i)` is a copy of `value_type ()`.	A copy of `t` is inserted in `v`.	`v (i)` is a copy of `t`.
Erase	`v.erase (i)`	`0 <= i < v.size ()`	Destroys the element `v (i)` and replaces it with `value_type ()`.	`v (i)` is a copy of `value_type ()`.
Clear	`v.clear ()`		Equivalent to `for (i = 0; i < v.size (); ++ i)` `v.erase (i);`
Resize	`v.resize (n)`		Modifies the vector so that it can hold `n` elements. Erases or appends elements in order to bring the vector to the prescribed size. Appended elements are `value_type()` copies. When `p == false` then exisiting elements may no be preserved and elements will not appended as normal. That is with `p == false` the elements values after resize are undefined.	`v.size () == n`.

Complexity guarantees

The run-time complexity of the sizing constructor is linear in the vector's size.

The run-time complexity of insert and erase is specific for the vector.

The run-time complexity of resize is linear in the vector's size.

Invariants

Models

vector<T, A>
unit_vector<T>
zero_vector<T>
scalar_vector<T, A>
sparse_vector<T, A>

Matrix

Description

A Matrix describes common aspects of dense, packed and sparse matrices.

Refinement of

Matrix Expression .

Associated types

Value type	`value_type`	The type of the matrix.
Distance type	`difference_type`	A signed integral type used to represent the distance between two of the matrix's iterators.
Size type	`size_type`	An unsigned integral type that can represent any nonnegative value of the matrix's distance type.

Notation

`M`	A type that is a model of Matrix
`m`	Objects of type `M`
`n1, n2, i, j`	Objects of a type convertible to `size_type`
`t`	Object of a type convertible to `value_type`
`p`	Object of a type convertible to `bool`

Definitions

Valid expressions

In addition to the expressions defined in Matrix Expression the following expressions must be valid.

Name	Expression	Type requirements	Return type
Sizing constructor	`M m (n1, n2)`		`M`
Insert	`m.insert (i, j, t)`	`m` is mutable.	`void`
Erase	`m.erase (i, j)`	`m` is mutable.	`void`
Clear	`m.clear ()`	`m` is mutable.	`void`
Resize	`m.resize (n1, n2)` `v.resize (n1, n2, p)`	`m` is mutable.	`void`

Expression semantics

Semantics of an expression is defined only where it differs from, or is not defined in Matrix Expression .

Name	Expression	Precondition	Semantics	Postcondition
Sizing constructor	`M m (n1, n2)`	`n1 >= 0` and `n2 >= 0`	Creates a matrix of `n1` rows and `n2` columns.	`m.size1 () == n1` and `m.size2 () == n2`.
Insert	`m.insert (i, j, t)`	`0 <= i < m.size1 ()`, `0 <= j < m.size2 ()`and `m (i, j)` is a copy of `value_type ()`.	A copy of `t` is inserted in `m`.	`m (i, j)` is a copy of `t`.
Erase	`m.erase (i, j)`	`0 <= i < m.size1 ()`and `0 <= j < m.size2`	Destroys the element `m (i, j)` and replaces it with `value_type ()`.	`m (i, j)` is a copy of `value_type ()`.
Clear	`m.clear ()`		Equivalent to `for (i = 0; i < m.size1 (); ++ i)` `for (j = 0; j < m.size2 (); ++ j)` `m.erase (i, j);`
Resize	`m.resize (n1, n2)`		Modifies the matrix so that it can hold `n1` rows and `n2` columns. Erases or appends elements in order to bring the matrix to the prescribed size. Appended elements are `value_type()` copies. When `p == false` then exisiting elements may no be preserved and elements will not appended as normal. That is with `p == false` the elements values after resize are undefined.	`m.size1 () == n1` and `m.size2 () == n2`.

Complexity guarantees

The run-time complexity of the sizing constructor is quadratic in the matrix's size.

The run-time complexity of insert and erase is specific for the matrix.

The run-time complexity of resize is quadratic in the matrix's size.

Invariants

Models

matrix<T, F, A>
identity_matrix<T>
zero_matrix<T>
scalar_matrix<T>
triangular_matrix<T, F1, F2, A>
symmetric_matrix<T, F1, F2, A>
banded_matrix<T, F, A>
sparse_matrix<T, F, A>

Copyright (©) 2000-2002 Joerg Walter, Mathias Koch
Permission to copy, use, modify, sell and distribute this document is granted provided this copyright notice appears in all copies. This document is provided ``as is'' without express or implied warranty, and with no claim as to its suitability for any purpose.

Last revised: 24/06/2004