[linalg.transp.transposed]

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

## 29.9 Basic linear algebra algorithms [[linalg]](linalg#transp.transposed)

### 29.9.10 Transpose in-place transformation [[linalg.transp]](linalg.transp#transposed)

#### 29.9.10.4 Function template transposed [linalg.transp.transposed]

[1](#1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L13119)

The transposed function
takes a rank-2 mdspan representing a matrix, and
returns a new mdspan representing the input matrix's transpose[.](#1.sentence-1)

The input matrix's data are not modified, and
the returned mdspan accesses the input matrix's data in place[.](#1.sentence-2)

[🔗](#lib:transposed)

`  template<class ElementType, class Extents, class Layout, class Accessor>
    constexpr auto transposed(mdspan<ElementType, Extents, Layout, Accessor> a);
`

[2](#2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L13132)

*Mandates*: Extents​::​rank() == 2 is true[.](#2.sentence-1)

[3](#3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L13136)

Let ReturnExtents be*transpose-extents-t*<Extents>[.](#3.sentence-1)

Let R bemdspan<ElementType, ReturnExtents, ReturnLayout, Accessor>,
where ReturnLayout is:

- [(3.1)](#3.1)

layout_right if Layout is layout_left;

- [(3.2)](#3.2)

otherwise, layout_left if Layout is layout_right;

- [(3.3)](#3.3)

otherwise, layout_right_padded<PaddingValue> if Layout is  
layout_left_padded<PaddingValue> for some size_t value PaddingValue;

- [(3.4)](#3.4)

otherwise, layout_left_padded<PaddingValue> if Layout is  
layout_right_padded<PaddingValue> for some size_t value PaddingValue;

- [(3.5)](#3.5)

otherwise, layout_stride if Layout is layout_stride;

- [(3.6)](#3.6)

otherwise,layout_blas_packed<OppositeTriangle, OppositeStorageOrder>,
if Layout is  
layout_blas_packed<Triangle, StorageOrder> for some Triangle and StorageOrder, where
  * [(3.6.1)](#3.6.1)

OppositeTriangle isconditional_t<is_same_v<Triangle, upper_triangle_t>,
 lower_triangle_t, upper_triangle_t> and

  * [(3.6.2)](#3.6.2)

OppositeStorageOrder isconditional_t<is_same_v<StorageOrder, column_major_t>, row_major_t, column_major_t>

- [(3.7)](#3.7)

otherwise, NestedLayout if Layout is layout_transpose<NestedLayout> for some NestedLayout;

- [(3.8)](#3.8)

otherwise, layout_transpose<Layout>[.](#3.sentence-2)

[4](#4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L13185)

*Returns*: With ReturnMapping being
the type typename ReturnLayout​::​template mapping<ReturnExtents>:

- [(4.1)](#4.1)

if Layout is layout_left, layout_right, or
a specialization of layout_blas_packed,R(a.data_handle(), ReturnMapping(*transpose-extents*(a.mapping().extents())),
 a.accessor())

- [(4.2)](#4.2)

otherwise,R(a.data_handle(), ReturnMapping(*transpose-extents*(a.mapping().extents()),
 a.mapping().stride(1)), a.accessor()) if Layout is layout_left_padded<PaddingValue> for some size_t value PaddingValue;

- [(4.3)](#4.3)

otherwise,R(a.data_handle(), ReturnMapping(*transpose-extents*(a.mapping().extents()),
 a.mapping().stride(0)), a.accessor()) if Layout is layout_right_padded<PaddingValue> for some size_t value PaddingValue;

- [(4.4)](#4.4)

otherwise, if Layout is layout_stride,R(a.data_handle(), ReturnMapping(*transpose-extents*(a.mapping().extents()),
 array{a.mapping().stride(1), a.mapping().stride(0)}), a.accessor())

- [(4.5)](#4.5)

otherwise, if Layout is a specialization of layout_transpose,R(a.data_handle(), a.mapping().nested_mapping(), a.accessor())

- [(4.6)](#4.6)

otherwise,R(a.data_handle(), ReturnMapping(a.mapping()), a.accessor())

[5](#5)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L13232)

[*Example [1](#example-1)*: void test_transposed(mdspan<double, extents<size_t, 3, 4>> a) {const auto num_rows = a.extent(0); const auto num_cols = a.extent(1); auto a_t = transposed(a);
 assert(num_rows == a_t.extent(1));
 assert(num_cols == a_t.extent(0));
 assert(a.stride(0) == a_t.stride(1));
 assert(a.stride(1) == a_t.stride(0)); for (size_t row = 0; row < num_rows; ++row) {for (size_t col = 0; col < num_rows; ++col) { assert(a[row, col] == a_t[col, row]); }}auto a_t_t = transposed(a_t);
 assert(num_rows == a_t_t.extent(0));
 assert(num_cols == a_t_t.extent(1));
 assert(a.stride(0) == a_t_t.stride(0));
 assert(a.stride(1) == a_t_t.stride(1)); for (size_t row = 0; row < num_rows; ++row) {for (size_t col = 0; col < num_rows; ++col) { assert(a[row, col] == a_t_t[row, col]); }}} — *end example*]