Expression Concepts

Scalar Expression

Description

A Scalar Expression is an expression convertible to a scalar type.

Refinement of

Default Constructible.

Associated types

Notation

| S | A type that is a model of Scalar Expression |

Definitions

Valid expressions

In addition to the expressions defined in Default Constructible the following expressions must be valid.

Name	Expression	Type requirements	Return type
Evaluation	`operator value_type () const`		`value_type`

Expression semantics

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

Name	Expression	Precondition	Semantics	Postcondition
Evaluation	`operator value_type () const`		Evaluates the scalar expression.

Complexity guarantees

The run-time complexity of the evaluation is specific for the evaluated scalar expression.

Invariants

Models

vector_scalar_unary
vector_scalar_binary

Vector Expression

Description

A Vector Expression is an expression evaluatable to a vector. Vector Expression provides an Indexed Bidirectional Iterator or an Indexed Random Access Iterator .

Refinement of

Default Constructible.

Associated types

Notation

| V | A type that is a model of Vector Expression | | v, v1, v2 | Object of type V | | i | Object of a type convertible to size_type | | t | Object of a type convertible to value_type |

Definitions

Valid expressions

In addition to the expressions defined in Default Constructible the following expressions must be valid.

Name	Expression	Type requirements	Return type
Beginning of range	`v.begin ()`		`const_iterator`
`v.begin ()`	`v` is mutable.	`iterator`
End of range	`v.end ()`		`const_iterator`
`v.end ()`	`v` is mutable.	`iterator`
Size	`v.size ()`		`size_type`
Swap	`v1.swap (v2)`	`v1` and `v2` are mutable.	`void`
Beginning of reverse range	`v.rbegin ()`		`const_reverse_iterator`
`v.rbegin ()`	`v` is mutable.	`reverse_iterator`
End of reverse range	`v.rend ()`		`const_reverse_iterator`
`v.rend ()`	`v` is mutable.	`reverse_iterator`
Element access	`v (i)`	`i` is convertible to `size_type`.	Convertible to `value_type`.
Assignment	`v2 = v1`	`v2` is mutable and `v1` is convertible to `V`.	`V &`
`v2.assign (v1)`	`v2` is mutable and `v1` is convertible to `V`.	`V &`
Computed assignment	`v2 += v1`	`v2` is mutable and `v1` is convertible to `V`.	`V &`
`v2.plus_assign (v1)`	`v2` is mutable and `v1` is convertible to `V`.	`V &`
`v2 -= v1`	`v2` is mutable and `v1` is convertible to `V`.	`V &`
`v2.minus_assign (v1)`	`v2` is mutable and `v1` is convertible to `V`.	`V &`
`v *= t`	`v` is mutable and `t` is convertible to `value_type`.	`V &`

Expression semantics

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

Name	Expression	Precondition	Semantics	Postcondition
Beginning of range	`v.begin ()`		Returns an iterator pointing to the first element in the vector expression.	`v.begin ()` is either dereferenceable or past-the-end. It is past-the-end if and only if `v.size () ==
0`.
End of range	`v.end ()`		Returns an iterator pointing one past the last element in the vector expression.	`v.end ()` is past-the-end.
Size	`v.size ()`		Returns the size of the vector expression, that is, its number of elements.	`v.size () >= 0`
Swap	`v1.swap (v2)`		Equivalent to `swap (v1, v2)`.
Beginning of reverse range	`v.rbegin ()`		Equivalent to `reverse_iterator (v.end ())`.	`v.rbegin ()` is either dereferenceable or past-the-end. It is past-the-end if and only if `v.size () ==
0`.
End of reverse range	`v.rend ()`		Equivalent to `reverse_iterator (v.begin ())`.	`v.rend ()` is past-the-end.
Element access	`v (i)`	`0 <= i < v.size ()`	Returns the `i`-th element of the vector expression.
Assignment	`v2 = v1`	`v1.size () == v2.size ()`	Assigns every element of the evaluated vector expression `v1` to the corresponding element of `v2` .
`v2.assign (v1)`	`v1.size () == v2.size ()`	Assigns every element of `v1` to the corresponding element of `v2`.
Computed assignment	`v2 += v1`	`v1.size () == v2.size ()`	Adds every element of the evaluated vector expression `v1` to the corresponding element of `v2`.
`v2.plus_assign (v1)`	`v1.size () == v2.size ()`	Adds every element of `v1` to the corresponding element of `v2`.
`v2 -= v1`	`v1.size () == v2.size ()`	Subtracts every element of the evaluated vector expression `v1` from the corresponding element of `v2` .
`v2.minus_assign (v1)`	`v1.size () == v2.size ()`	Subtracts every element of `v1` from the corresponding element of `v2`.
`v *= t`		Multiplies every element of `v` with `t` .

Complexity guarantees

The run-time complexity of begin () and end () is specific for the evaluated vector expression, typically amortized constant time.

The run-time complexity of size () is constant time.

The run-time complexity of swap () is specific for the evaluated vector expression, typically constant time.

The run-time complexity of rbegin () and rend () is specific for the evaluated vector expression, typically amortized constant time.

The run-time complexity of the element access is specific for the evaluated vector expression, typically amortized constant time for the dense and logarithmic for the sparse case.

The run-time complexity of the arithmetic operations is specific for the evaluated vector expressions, typically linear in the size of the expressions.

Invariants

| Valid range | For any vector expression v, [v.begin (), v.end ()) is a valid range. | | Completeness | An algorithm that iterates through the range [v.begin (), v.end ()) will pass through every element of v . | | Valid reverse range | [v.rbegin (), v.rend ()) is a valid range. | | Equivalence of ranges | The distance from v.begin () to v.end () is the same as the distance from v.rbegin () to v.rend (). |

Models

vector_range;
vector_slice
matrix_row
matrix_column
matrix_vector_range
matrix_vector_slice
vector_unary
vector_binary
vector_binary_scalar1
vector_binary_scalar2
matrix_vector_unary1
matrix_vector_unary2
matrix_vector_binary1
matrix_vector_binary2

Matrix Expression

Description

A Matrix Expression is an expression evaluatable to a matrix. Matrix Expression provides an Indexed Bidirectional Column/Row Iterator or an Indexed Random Access Column/Row Iterator .

Refinement of

Default Constructible.

Associated types

immutable types

| Public base | matrix_expression<M> | M must be derived from this public base type. | | Value type | value_type | The element type of the matrix expression. | | Const reference type | const_reference | The return type when accessing an element of a constant matrix expression.
Convertable to a value_type. | | Size type | size_type | The index type of the matrix expression. Am unsigned integral type used to represent size and index values.
Can represent any nonnegative value of difference_type. | | Distance type | difference_type | A signed integral type used to represent the distance between two of the matrix expression's iterators. | | Const iterator types | const_iterator1 | A type of column iterator that may be used to examine a matrix expression's elements. | | const_iterator2 | A type of row iterator that may be used to examine a matrix expression's elements. | | Const reverse iterator types | const_reverse_iterator1 | A Reverse Iterator adaptor whose base iterator type is the matrix expression's const column iterator type. | | const_reverse_iterator2 | A Reverse Iterator adaptor whose base iterator type is the matrix expression's const row iterator type. |

mutable types

| Reference type | reference | The return type when accessing an element of a matrix expression.
Convertable to a value_type. | | Iterator types | iterator1 | A type of column iterator that may be used to modify a matrix expression's elements. | | iterator2 | A type of row iterator that may be used to modify a matrix expression's elements. | | Reverse iterator types | reverse_iterator1 | A Reverse Iterator adaptor whose base iterator type is the matrix expression's column iterator type. | | reverse_iterator2 | A Reverse Iterator adaptor whose base iterator type is the matrix expression's row iterator type. |

Notation

| M | A type that is a model of Matrix Expression | | m, m1, m2 | Object of type M | | i, j | Objects of a type convertible to size_type | | t | Object of a type convertible to value_type |

Definitions

Valid expressions

In addition to the expressions defined in Default Constructible the following expressions must be valid.

immutable expressions

Name	Expression	Type requirements	Return type
Size	`m.size1 ()`		`size_type`
`m.size2 ()`		`size_type`

possibly mutable expressions

Name	Expression	Type requirements	Return type
Beginning of range	`m.begin1 ()`		`const_iterator1`
`m.begin2 ()`		`const_iterator2`
`m.begin1 ()`	`m` is mutable.	`iterator1`
`m.begin2 ()`	`m` is mutable.	`iterator2`
End of range	`m.end1 ()`		`const_iterator1`
`m.end2 ()`		`const_iterator2`
`m.end1 ()`	`m` is mutable.	`iterator1`
`m.end2 ()`	`m` is mutable.	`iterator2`
Swap	`m1.swap (m2)`	`m1` and `m2` are mutable.	`void`
Beginning of reverse range	`m.rbegin1 ()`		`const_reverse_iterator1`
`m.rbegin2 ()`		`const_reverse_iterator2`
`m.rbegin1 ()`	`m` is mutable.	`reverse_iterator1`
`m.rbegin2 ()`	`m` is mutable.	`reverse_iterator2`
End of reverse range	`m.rend1 ()`		`const_reverse_iterator1`
`m.rend2 ()`		`const_reverse_iterator2`
`m.rend1 ()`	`m` is mutable.	`reverse_iterator1`
`m.rend2 ()`	`m` is mutable.	`reverse_iterator2`
Element access	`m (i, j)`	`i` and `j` are convertible to `size_type` .	Convertible to `value_type`.
Assignment	`m2 = m1`	`m2` is mutable and `m1` is convertible to `M`.	`M &`
`m2.assign (m1)`	`m2` is mutable and `m1` is convertible to `M`.	`M &`
Computed assignment	`m2 += m1`	`m2` is mutable and `m1` is convertible to `M`.	`M &`
`m2.plus_assign (m1)`	`m2` is mutable and `m1` is convertible to `M`.	`M &`
`m2 -= m1`	`m2` is mutable and `m1` is convertible to `M`.	`M &`
`m2.minus_assign (m1)`	`m2` is mutable and `m1` is convertible to `M`.	`M &`
`m *= t`	`m` is mutable and `t` is convertible to `value_type`.	`M &`

Expression semantics

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

Name	Expression	Precondition	Semantics	Postcondition
Beginning of range	`m.begin1 ()`		Returns an iterator pointing to the first element in the first column of a matrix expression.	`m.begin1 ()` is either dereferenceable or past-the-end. It is past-the-end if and only if `m.size1 () ==
0`.
`m.begin2 ()`		Returns an iterator pointing to the first element in the first row of a matrix expression.	`m.begin2 ()` is either dereferenceable or past-the-end. It is past-the-end if and only if `m.size2 () ==
0`.
End of range	`m.end1 ()`		Returns an iterator pointing one past the last element in the matrix expression.	`m.end1 ()` is past-the-end.
`m.end2 ()`		Returns an iterator pointing one past the last element in the matrix expression.	`m.end2 ()` is past-the-end.
Size	`m.size1 ()`		Returns the number of rows of the matrix expression.	`m.size1 () >= 0`
`m.size2 ()`		Returns the number of columns of the matrix expression.	`m.size2 () >= 0`
Swap	`m1.swap (m2)`		Equivalent to `swap (m1, m2)`.
Beginning of reverse range	`m.rbegin1 ()`		Equivalent to `reverse_iterator1 (m.end1 ())`.	`m.rbegin1 ()` is either dereferenceable or past-the-end. It is past-the-end if and only if `m.size1 () ==
0`.
`m.rbegin2 ()`		Equivalent to `reverse_iterator2 (m.end2 ())`.	`m.rbegin2 ()` is either dereferenceable or past-the-end. It is past-the-end if and only if `m.size2 () ==
0`.
End of reverse range	`m.rend1 ()`		Equivalent to `reverse_iterator1 (m.begin1
())`.	`m.rend1 ()` is past-the-end.
`m.rend2 ()`		Equivalent to `reverse_iterator2 (m.begin2
())`.	`m.rend2 ()` is past-the-end.
Element access	`m (i, j)`	`0 <= i < m.size1 ()` and `0 <= j <
m.size2 ()`	Returns the `j`-th element of the `i`-th row of the matrix expression.
Assignment	`m2 = m1`	`m1.size1 () == m2.size1 ()` and `
m1.size2 () == m2.size2 ()`	Assigns every element of the evaluated matrix expression `m1` to the corresponding element of `m2` .
`m2.assign (m1)`	`m1.size1 () == m2.size1 ()` and `
m1.size2 () == m2.size2 ()`	Assigns every element of `m1` to the corresponding element of `m2`.
Computed assignment	`m2 += m1`	`m1.size1 () == m2.size1 ()` and `
m1.size2 () == m2.size2 ()`	Adds every element of the evaluated matrix expression `m1` to the corresponding element of `m2`.
`m2.plus_assign (m1)`	`m1.size1 () == m2.size1 ()` and `
m1.size2 () == m2.size2 ()`	Adds every element of `m1` to the corresponding element of `m2`.
`m2 -= m1`	`m1.size1 () == m2.size1 ()` and `
m1.size2 () == m2.size2 ()`	Subtracts every element of the evaluated matrix expression `m1` from the corresponding element of `m2` .
`m2.minus_assign (m1)`	`m1.size1 () == m2.size1 ()` and `
m1.size2 () == m2.size2 ()`	Subtracts every element of `m1` from the corresponding element of `m2`.
`m *= t`		Multiplies every element of `m` with `t` .

Complexity guarantees

The run-time complexity of begin1 (), begin2 () , end1 () and end2 () is specific for the evaluated matrix expression.

The run-time complexity of size1 () and size2 () is constant time.

The run-time complexity of swap () is specific for the evaluated matrix expression, typically constant time.

The run-time complexity of rbegin1 (), rbegin2 () , rend1 () and rend2 () is specific for the evaluated matrix expression.

The run-time complexity of the element access is specific for the evaluated matrix expression, typically amortized constant time for the dense and logarithmic for the sparse case.

The run-time complexity of the arithmetic operations is specific for the evaluated matrix expressions, typically quadratic in the size of the proxies.

Invariants

| Valid range | For any matrix expression m, [m.begin1 (), m.end1 ()) and [m.begin2 (), m.end2 ()) are valid ranges. | | Completeness | An algorithm that iterates through the range [m.begin1 (), m.end1 ()) will pass through every row of m , an algorithm that iterates through the range [m.begin2 (), m.end2 ()) will pass through every column of m . | | Valid reverse range | [m.rbegin1 (), m.rend1 ()) and [m.rbegin2 (), m.rend2 ()) are valid ranges. | | Equivalence of ranges | The distance from m.begin1 () to m.end1 () is the same as the distance from m.rbegin1 () to m.rend1 () and the distance from m.begin2 () to m.end2 () is the same as the distance from m.rbegin2 () to m.rend2 (). |

Models

matrix_range
matrix_slice;
triangular_adaptor
symmetric_adaptor
banded_adaptor
vector_matrix_binary
matrix_unary1
matrix_unary2
matrix_binary
matrix_binary_scalar1
matrix_binary_scalar2
matrix_matrix_binary

Copyright (©) 2000-2002 Joerg Walter, Mathias Koch
Use, modification and distribution are subject to the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt).