# 28 Numerics library [numerics]

## 28.9 Basic linear algebra algorithms [linalg]

### 28.9.10 Transpose in-place transformation [linalg.transp]

#### 28.9.10.3 Class template layout_transpose[linalg.transp.layout.transpose]

layout_transpose is an mdspan layout mapping policy that swaps the two indices, extents, and strides of any mdspan layout mapping policy.
namespace std::linalg { template<class Layout> class layout_transpose { public: using nested_layout_type = Layout; template<class Extents> struct mapping { private: using nested-mapping-type = typename Layout::template mapping<transpose-extents-t<Extents>>; // exposition only public: using extents_type = Extents; using index_type = typename extents_type::index_type; using size_type = typename extents_type::size_type; using rank_type = typename extents_type::rank_type; using layout_type = layout_transpose; constexpr explicit mapping(const nested-mapping-type&); constexpr const extents_type& extents() const noexcept { return extents_; } constexpr index_type required_span_size() const { return nested-mapping_.required_span_size(); template<class Index0, class Index1> constexpr index_type operator()(Index0 ind0, Index1 ind1) const { return nested-mapping_(ind1, ind0); } constexpr const nested-mapping-type& nested_mapping() const noexcept { return nested-mapping_; } static constexpr bool is_always_unique() noexcept { return nested-mapping-type::is_always_unique(); } static constexpr bool is_always_exhaustive() noexcept { return nested-mapping-type::is_always_exhaustive(); } static constexpr bool is_always_strided() noexcept { return nested-mapping-type::is_always_strided(); } constexpr bool is_unique() const { return nested-mapping_.is_unique(); } constexpr bool is_exhaustive() const { return nested-mapping_.is_exhaustive(); } constexpr bool is_strided() const { return nested-mapping_.is_strided(); } constexpr index_type stride(size_t r) const; template<class OtherExtents> friend constexpr bool operator==(const mapping& x, const mapping<OtherExtents>& y); }; private: nested-mapping-type nested-mapping_; // exposition only extents_type extents_; // exposition only }; }
Layout shall meet the layout mapping policy requirements ([mdspan.layout.policy.reqmts]).
Mandates:
• Extents is a specialization of std​::​extents, and
• Extents​::​rank() equals 2.
```constexpr explicit mapping(const nested-mapping-type& map); ```
Effects:
• Initializes nested-mapping_ with map, and
• initializes extents_ with transpose-extents(map.extents()).
```constexpr index_type stride(size_t r) const; ```
Preconditions:
Returns: nested-mapping_.stride(r == 0 ? 1 : 0)
```template<class OtherExtents> friend constexpr bool operator==(const mapping& x, const mapping<OtherExtents>& y); ```
Constraints: The expression x.nested-mapping_ == y.nested-mapping_ is well-formed and its result is convertible to bool.
Returns: x.nested-mapping_ == y.nested-mapping_.