cppdraft_translate/cppdraft/linalg/conj.md

[linalg.conj]

29 Numerics library [numerics]

29.9 Basic linear algebra algorithms [linalg]

29.9.9 Conjugated in-place transformation [linalg.conj]

29.9.9.1 Introduction [linalg.conj.intro]

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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.

29.9.9.2 Class template conjugated_accessor [linalg.conj.conjugatedaccessor]

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The class template conjugated_accessor is an mdspan accessor policy which upon access produces conjugate elements.

It is part of the implementation ofconjugated ([linalg.conj.conjugated]).

namespace std::linalg {templateclass conjugated_accessor {public:using element_type = add_const_t<decltype(conj-if-needed(declvalNestedAccessor::element_type()))>; using reference = remove_const_t<element_type>; using data_handle_type = typename NestedAccessor::data_handle_type; using offset_policy = conjugated_accessorNestedAccessor::offset_policy; constexpr conjugated_accessor() = default; templateexplicit(!is_convertible_v<OtherNestedAccessor, NestedAccessor>>)constexpr conjugated_accessor(const conjugated_accessor& 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};}

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Mandates:

• (2.1)

element_type is valid and denotes a type,

• (2.2)

is_copy_constructible_v is true,

• (2.3)

is_reference_v<element_type> is false, and

• (2.4)

NestedAccessor meets the accessor policy requirements ([mdspan.accessor.reqmts]).

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constexpr conjugated_accessor(const NestedAccessor& acc);

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Effects: Direct-non-list-initializesnested-accessor_ with acc.

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

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Constraints: is_constructible_v<NestedAccessor, const OtherNestedAccessor&> is true.

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Effects: Direct-non-list-initializes nested-accessor_ with other.nested_accessor().

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

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

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

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

29.9.9.3 Function template conjugated [linalg.conj.conjugated]

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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);

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Let A be

• (1.1)

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

• (1.2)

otherwise,Accessor if remove_cvref_t is an arithmetic type;

• (1.3)

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

• (1.4)

otherwise,Accessor.

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Returns: Let MD be mdspan<typename A​::​element_type, Extents, Layout, A>.

• (2.1)

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

• (2.2)

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

• (2.3)

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

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[Example 1: void test_conjugated_complex(mdspan<complex, 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]); }} — end example]