[linalg.conj]

# 29 Numerics library [[numerics]](./#numerics)

## 29.9 Basic linear algebra algorithms [[linalg]](linalg#conj)

### 29.9.9 Conjugated in-place transformation [linalg.conj]

#### [29.9.9.1](#intro) Introduction [[linalg.conj.intro]](linalg.conj.intro)

[1](#intro-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L12756)

The conjugated function takes an mdspan x,
and returns a new read-only mdspan y with the same domain as x,
whose elements are the complex conjugates
of the corresponding elements of x[.](#intro-1.sentence-1)

#### [29.9.9.2](#conjugatedaccessor) Class template conjugated_accessor [[linalg.conj.conjugatedaccessor]](linalg.conj.conjugatedaccessor)

[1](#conjugatedaccessor-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L12765)

The class template conjugated_accessor is an mdspan accessor policy
which upon access produces conjugate elements[.](#conjugatedaccessor-1.sentence-1)

It is part of the implementation ofconjugated ([[linalg.conj.conjugated]](#conjugated "29.9.9.3 Function template conjugated"))[.](#conjugatedaccessor-1.sentence-2)

namespace std::linalg {template<class NestedAccessor>class [conjugated_accessor](#lib:conjugated_accessor "29.9.9.2 Class template conjugated_­accessor [linalg.conj.conjugatedaccessor]") {public:using element_type = add_const_t<decltype(*conj-if-needed*(declval<NestedAccessor::element_type>()))>; using reference = remove_const_t<element_type>; using data_handle_type = typename NestedAccessor::data_handle_type; using offset_policy = conjugated_accessor<NestedAccessor::offset_policy>; constexpr conjugated_accessor() = default; template<class OtherNestedAccessor>explicit(!is_convertible_v<OtherNestedAccessor, NestedAccessor>>)constexpr conjugated_accessor(const conjugated_accessor<OtherNestedAccessor>& other); constexpr reference access(data_handle_type p, size_t i) const; constexpr typename offset_policy::data_handle_type
 offset(data_handle_type p, size_t i) const; constexpr const NestedAccessor& nested_accessor() const noexcept { return *nested-accessor_*; }private: NestedAccessor *nested-accessor_*{}; // *exposition only*};}

[2](#conjugatedaccessor-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L12801)

*Mandates*: 

- [(2.1)](#conjugatedaccessor-2.1)

element_type is valid and denotes a type,

- [(2.2)](#conjugatedaccessor-2.2)

is_copy_constructible_v<reference> is true,

- [(2.3)](#conjugatedaccessor-2.3)

is_reference_v<element_type> is false, and

- [(2.4)](#conjugatedaccessor-2.4)

NestedAccessor meets the accessor policy requirements ([[mdspan.accessor.reqmts]](mdspan.accessor.reqmts "23.7.3.5.2 Requirements"))[.](#conjugatedaccessor-2.sentence-1)

[ð](#lib:conjugated_accessor,constructor)

`constexpr conjugated_accessor(const NestedAccessor& acc);
`

[3](#conjugatedaccessor-3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L12820)

*Effects*: Direct-non-list-initializes*nested-accessor_* with acc[.](#conjugatedaccessor-3.sentence-1)

[ð](#lib:conjugated_accessor,constructor_)

`template<class OtherNestedAccessor>
  explicit(!is_convertible_v<OtherNestedAccessor, NestedAccessor>>)
    constexpr conjugated_accessor(const conjugated_accessor<OtherNestedAccessor>& other);
`

[4](#conjugatedaccessor-4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L12834)

*Constraints*: is_constructible_v<NestedAccessor, const OtherNestedAccessor&> is true[.](#conjugatedaccessor-4.sentence-1)

[5](#conjugatedaccessor-5)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L12839)

*Effects*: Direct-non-list-initializes *nested-accessor_* with other.nested_accessor()[.](#conjugatedaccessor-5.sentence-1)

[ð](#lib:conjugated_accessor,access)

`constexpr reference access(data_handle_type p, size_t i) const;
`

[6](#conjugatedaccessor-6)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L12851)

*Returns*: *conj-if-needed*(NestedAccessor​::​element_type(*nested-accessor_*.access(p, i)))

[ð](#lib:conjugated_accessor,offset)

`constexpr typename offset_policy::data_handle_type offset(data_handle_type p, size_t i) const;
`

[7](#conjugatedaccessor-7)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L12862)

*Returns*: *nested-accessor_*.offset(p, i)

#### [29.9.9.3](#conjugated) Function template conjugated [[linalg.conj.conjugated]](linalg.conj.conjugated)

[ð](#conjugated-itemdecl:1)

`  template<class ElementType, class Extents, class Layout, class Accessor>
    constexpr auto [conjugated](#lib:conjugated "29.9.9.3 Function template conjugated [linalg.conj.conjugated]")(mdspan<ElementType, Extents, Layout, Accessor> a);
`

[1](#conjugated-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L12875)

Let A be

- [(1.1)](#conjugated-1.1)

remove_cvref_t<decltype(a.accessor().nested_accessor())> if Accessor is a specialization of conjugated_accessor;

- [(1.2)](#conjugated-1.2)

otherwise,Accessor if remove_cvref_t<ElementType> is an arithmetic type;

- [(1.3)](#conjugated-1.3)

otherwise,conjugated_accessor<Accessor> if the expression conj(E) is valid for any subexpression E whose type is remove_cvref_t<ElementType> with overload resolution performed in a context that includes the declarationtemplate<class U> U conj(const U&) = delete;;

- [(1.4)](#conjugated-1.4)

otherwise,Accessor[.](#conjugated-1.sentence-1)

[2](#conjugated-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L12896)

*Returns*: Let MD be mdspan<typename A​::​element_type, Extents, Layout, A>[.](#conjugated-2.sentence-1)

- [(2.1)](#conjugated-2.1)

MD(a.data_handle(), a.mapping(), a.accessor().nested_accessor()) if Accessor is a  
specialization of conjugated_accessor;

- [(2.2)](#conjugated-2.2)

otherwise,a, if is_same_v<A, Accessor> is true;

- [(2.3)](#conjugated-2.3)

otherwise,MD(a.data_handle(), a.mapping(), conjugated_accessor(a.accessor())).

[3](#conjugated-3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L12912)

[*Example [1](#conjugated-example-1)*: void test_conjugated_complex(mdspan<complex<double>, extents<int, 10>> a) {auto a_conj = conjugated(a); for (int i = 0; i < a.extent(0); ++i) { assert(a_conj[i] == conj(a[i]); }auto a_conj_conj = conjugated(a_conj); for (int i = 0; i < a.extent(0); ++i) { assert(a_conj_conj[i] == a[i]); }}void test_conjugated_real(mdspan<double, extents<int, 10>> a) {auto a_conj = conjugated(a); for (int i = 0; i < a.extent(0); ++i) { assert(a_conj[i] == a[i]); }auto a_conj_conj = conjugated(a_conj); for (int i = 0; i < a.extent(0); ++i) { assert(a_conj_conj[i] == a[i]); }} â *end example*]
