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Container Concepts

Vector

Description

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

Associated types

In addition to the types defined by Vector Expression

 Public base vector_container V must be derived from this public base type. Storage array V::array_type Dense Vector ONLY. The type of underlying storage array used to store the elements. The array_type must model the Storage concept.

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

Valid expressions

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

Name Expression Type requirements Return type
Sizing constructor V v (n)   V
Insert v.insert_element (i, t) v is mutable. void
Erase v.erase_element (i) v is mutable. void
Clear v.clear () v is mutable. void
Resize v.resize (n)
v.resize (n, p)
v is mutable. void
Storage v.data() v is mutable and Dense. array_type& if v is mutable, const array_type& otherwise

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 Allocates a vector ofn elements. v.size () == n.
Element access [2] v[n] 0<n>v.size() returns the n-th element in v
Insert v.insert_element (i, t) 0 <= i < v.size (). Inserts an element at v (i) with value t. The storage requirement of the Vector may be increased. v (i) is equal to t.
Erase v.erase_element (i) 0 <= i < v.size () Destroys the element as v (i) and replaces it with the default value_type (). The storage requirement of the Vector may be decreased. v (i) is equal to value_type ().
Clear v.clear ()   Equivalent to
for (i = 0; i < v.size (); ++ i)
v.erase_element (i);

Resize v.resize (n) v.resize (n, p)   Reallocates 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 copies of value_type().
When p == false then existing elements are not preserved and elements will not appended as normal. Instead the vector is in the same state as that after an equivalent sizing constructor.
v.size () == n.
Storage v.data() Returns a reference to the underlying dense storage.

Complexity guarantees

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

The run-time complexity of insert_element and erase_element is specific for the Vector model and it depends on increases/decreases in storage requirements.

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

Models

• vector, bounded_vector, c_vector
• unit_vector, zero_vector, scalar_vector
• mapped_vector;, compressed_vector, coordinate_vector

Notes

[1] As a user you need not care about Vector being a refinement of the VectorExpression. Being a refinement of the VectorExpression is only important for the template-expression engine but not the user.

[2] The operator[] is added purely for convenience and compatibility with the std::vector. In uBLAS however, generally operator() is used for indexing because this can be used for both vectors and matrices.

Matrix

Description

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

Associated types

In addition to the types defined by Matrix Expression

 Public base matrix_container M must be derived from this public base type. Storage array M::array_type Dense Matrix ONLY. The type of underlying storage array used to store the elements. The array_type must model the Storage concept.

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

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_element (i, j, t) m is mutable. void
Erase m.erase_element (i, j) m is mutable. void
Clear m.clear () m is mutable. void
Resize m.resize (n1, n2)
m.resize (n1, n2, p)
m is mutable. void
Storage m.data() m is mutable and Dense. array_type& if m is mutable, const array_type& otherwise

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 Allocates a matrix of n1 rows and n2 columns. m.size1 () == n1 and m.size2 () == n2.
Insert m.insert_element (i, j, t) 0 <= i < m.size1 (),
0 <= j < m.size2 ().
Inserts an element at m (i, j) with value t. The storage requirement of the Matrix may be increased. m (i, j) is equal to t.
Erase m.erase_element (i, j) 0 <= i < m.size1 ()and  0 <= j < m.size2 Destroys the element as m (i, j) and replaces it with the default value_type (). The storage requirement of the Matrix may be decreased. m (i, j) is equal to value_type ().
Clear m.clear ()   Equivalent to
for (i = 0; i < m.size1 (); ++ i)
for (j = 0; j < m.size2 (); ++ j)
m.erase_element (i, j);

Resize m.resize (n1, n2) m.resize (n1, n2, p)    Reallocate 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 existing elements are not preserved and elements will not appended as normal. Instead the matrix is in the same state as that after an equivalent sizing constructor.
m.size1 () == n1 and m.size2 () == n2.
Storage m.data() Returns a reference to the underlying dense storage.

Complexity guarantees

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

The run-time complexity of insert_element and erase_element is specific for the Matrix model and it depends on increases/decreases in storage requirements.

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

Models

• matrix, bounded_matrix, c_matrix
• identity_matrix , zero_matrix , scalar_matrix
• triangular_matrix , symmetric_matrix , banded_matrix
• mapped_matrix , compressed_matrix , coordinate_matrix

Notes

[1] As a user you need not care about Matrix being a refinement of the MatrixExpression. Being a refinement of the MatrixExpression is only important for the template-expression engine but not the user.

Tensor

Description

A Tensor describes common aspects of dense multidimensional arrays.

Associated types

In addition to the types defined by Tensor Expression

 Public base tensor_container tensor_t must be derived from this public base type. Storage array tensor_t::array_type Dense tensor ONLY. The type of underlying storage array used to store the elements. The array_type must model the Storage concept.

Notation

 tensor_t A type that is a model of Tensor t Objects of type tensor_t n1, n2, np, m1, m2, mq  Dimension objects of a type convertible to size_type i1, i2, ip, j, k  Index objects of a type convertible to size_type v Object of a type convertible to value_type

Valid expressions

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

Name Expression Type requirements Return type
Sizing constructor T t(n1, n2, ..., np)   T
Write t.at(i1, i2, ..., ip) t is mutable. void
Read t.at(i1, i2, ..., ip) t is mutable. v
Clear t.clear () t is mutable. void
Resize t.resize(m1, m2, ... , mq) t is mutable. void
Storage t.data() t is mutable and dense. pointer if t is mutable, const_pointer otherwise

Expression semantics

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

Name Expression Precondition Semantics Postcondition
Sizing constructor T t(n1, n2, ..., np) $n_r \geq 1$ for $1\leq 1 \leq p$ Allocates a p-order tensor with dimension extents $n_1,n_2,\dots,n_p$. t.size(r)==nr for $1\leq r \leq p$.
Write t.at(i1,i2,...,ip)=v $0 \leq i_r < n_r$ for $1 \leq r \leq p$. Writes an element at multi-index position $i_1,i_2,\dots,i_p$ with value v. t(i1,i2,...,ip) is equal to v.
Read v=t.at(i1,i2,...,ip) $0 \leq i_r < n_r$ for $1 \leq r \leq p$. Reads the element at multi-index position $(i_1,i2_,\dots,i_p)$ and returns a value v. t(i1,i2,...,ip) is equal to v.
Clear t.clear()   Removes all elements from the container.
Resize t.resize(m1, m2, ..., mq) $m_r \geq 1$ for $1\leq 1 \leq q$ Reallocate the matrix so that it can hold $m_1\times m_2\times \cdots \times m_q$ elements.
Erases or appends elements in order to bring the matrix to the prescribed size. Appended elements are value_type() copies.
t.size(r) == mr for $1\leq r \leq q$.
Storage m.data() Returns a reference to the underlying dense storage.

Complexity guarantees

The run-time complexity of contructor is linear in the tensor's size $n_1 \times n_2 \times \cdots \times n_p$.

The run-time complexity of write() and read() is linear in the order of the tensor.

The run-time complexity of resize is at most linear in the tensor's size $m_1 \times m_2 \times \cdots \times n_q$.

Models

• tensor

Notes

[1] As a user you need not care about Tensor being a refinement of the TensorExpression. Being a refinement of the TensorExpression is only important for the template-expression engine but not the user.