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cppdraft/linalg/conj.md
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cppdraft/linalg/conj.md
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[linalg.conj]
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# 29 Numerics library [[numerics]](./#numerics)
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## 29.9 Basic linear algebra algorithms [[linalg]](linalg#conj)
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### 29.9.9 Conjugated in-place transformation [linalg.conj]
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#### [29.9.9.1](#intro) Introduction [[linalg.conj.intro]](linalg.conj.intro)
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[1](#intro-1)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L12756)
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The conjugated function takes an mdspan x,
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and returns a new read-only mdspan y with the same domain as x,
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whose elements are the complex conjugates
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of the corresponding elements of x[.](#intro-1.sentence-1)
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#### [29.9.9.2](#conjugatedaccessor) Class template conjugated_accessor [[linalg.conj.conjugatedaccessor]](linalg.conj.conjugatedaccessor)
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[1](#conjugatedaccessor-1)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L12765)
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The class template conjugated_accessor is an mdspan accessor policy
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which upon access produces conjugate elements[.](#conjugatedaccessor-1.sentence-1)
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It is part of the implementation ofconjugated ([[linalg.conj.conjugated]](#conjugated "29.9.9.3 Function template conjugated"))[.](#conjugatedaccessor-1.sentence-2)
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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
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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*};}
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[2](#conjugatedaccessor-2)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L12801)
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*Mandates*:
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- [(2.1)](#conjugatedaccessor-2.1)
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element_type is valid and denotes a type,
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- [(2.2)](#conjugatedaccessor-2.2)
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is_copy_constructible_v<reference> is true,
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- [(2.3)](#conjugatedaccessor-2.3)
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is_reference_v<element_type> is false, and
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- [(2.4)](#conjugatedaccessor-2.4)
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NestedAccessor meets the accessor policy requirements ([[mdspan.accessor.reqmts]](mdspan.accessor.reqmts "23.7.3.5.2 Requirements"))[.](#conjugatedaccessor-2.sentence-1)
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[ð](#lib:conjugated_accessor,constructor)
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`constexpr conjugated_accessor(const NestedAccessor& acc);
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`
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[3](#conjugatedaccessor-3)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L12820)
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*Effects*: Direct-non-list-initializes*nested-accessor_* with acc[.](#conjugatedaccessor-3.sentence-1)
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[ð](#lib:conjugated_accessor,constructor_)
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`template<class OtherNestedAccessor>
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explicit(!is_convertible_v<OtherNestedAccessor, NestedAccessor>>)
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constexpr conjugated_accessor(const conjugated_accessor<OtherNestedAccessor>& other);
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`
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[4](#conjugatedaccessor-4)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L12834)
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*Constraints*: is_constructible_v<NestedAccessor, const OtherNestedAccessor&> is true[.](#conjugatedaccessor-4.sentence-1)
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[5](#conjugatedaccessor-5)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L12839)
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*Effects*: Direct-non-list-initializes *nested-accessor_* with other.nested_accessor()[.](#conjugatedaccessor-5.sentence-1)
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[ð](#lib:conjugated_accessor,access)
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`constexpr reference access(data_handle_type p, size_t i) const;
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`
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[6](#conjugatedaccessor-6)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L12851)
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*Returns*: *conj-if-needed*(NestedAccessor::element_type(*nested-accessor_*.access(p, i)))
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[ð](#lib:conjugated_accessor,offset)
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`constexpr typename offset_policy::data_handle_type offset(data_handle_type p, size_t i) const;
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`
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[7](#conjugatedaccessor-7)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L12862)
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*Returns*: *nested-accessor_*.offset(p, i)
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#### [29.9.9.3](#conjugated) Function template conjugated [[linalg.conj.conjugated]](linalg.conj.conjugated)
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[ð](#conjugated-itemdecl:1)
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` template<class ElementType, class Extents, class Layout, class Accessor>
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constexpr auto [conjugated](#lib:conjugated "29.9.9.3 Function template conjugated [linalg.conj.conjugated]")(mdspan<ElementType, Extents, Layout, Accessor> a);
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`
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[1](#conjugated-1)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L12875)
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Let A be
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- [(1.1)](#conjugated-1.1)
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remove_cvref_t<decltype(a.accessor().nested_accessor())> if Accessor is a specialization of conjugated_accessor;
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- [(1.2)](#conjugated-1.2)
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otherwise,Accessor if remove_cvref_t<ElementType> is an arithmetic type;
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- [(1.3)](#conjugated-1.3)
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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;;
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- [(1.4)](#conjugated-1.4)
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otherwise,Accessor[.](#conjugated-1.sentence-1)
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[2](#conjugated-2)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L12896)
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*Returns*: Let MD be mdspan<typename A::element_type, Extents, Layout, A>[.](#conjugated-2.sentence-1)
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- [(2.1)](#conjugated-2.1)
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MD(a.data_handle(), a.mapping(), a.accessor().nested_accessor()) if Accessor is a
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specialization of conjugated_accessor;
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- [(2.2)](#conjugated-2.2)
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otherwise,a, if is_same_v<A, Accessor> is true;
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- [(2.3)](#conjugated-2.3)
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otherwise,MD(a.data_handle(), a.mapping(), conjugated_accessor(a.accessor())).
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[3](#conjugated-3)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L12912)
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[*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*]
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