29 Numerics library [numerics]

29.9 Basic linear algebra algorithms [linalg]

29.9.10 Transpose in-place transformation [linalg.transp]

29.9.10.4 Function template transposed [linalg.transp.transposed]

The transposed function takes a rank-2 mdspan representing a matrix, and returns a new mdspan representing the input matrix's transpose.

The input matrix's data are not modified, and the returned mdspan accesses the input matrix's data in place.

🔗

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

Mandates: Extents::rank() == 2 is true.

Let ReturnExtents be transpose-extents-t<Extents>.

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

(3.1)
layout_right if Layout is layout_left;
(3.2)
otherwise, layout_left if Layout is layout_right;
(3.3)
otherwise, layout_right_padded<PaddingValue> if Layout is
layout_left_padded<PaddingValue> for some size_t value PaddingValue;
(3.4)
otherwise, layout_left_padded<PaddingValue> if Layout is
layout_right_padded<PaddingValue> for some size_t value PaddingValue;
(3.5)
otherwise, layout_stride if Layout is layout_stride;
(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)
  OppositeTriangle is conditional_t<is_same_v<Triangle, upper_triangle_t>, lower_triangle_t, upper_triangle_t> and
- (3.6.2)
  OppositeStorageOrder is conditional_t<is_same_v<StorageOrder, column_major_t>, row_major_t, column_major_t>
(3.7)
otherwise, NestedLayout if Layout is layout_transpose<NestedLayout> for some NestedLayout;
(3.8)
otherwise, layout_transpose<Layout>.

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

(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)
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)
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)
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)
otherwise, if Layout is a specialization of layout_transpose, R(a.data_handle(), a.mapping().nested_mapping(), a.accessor())
(4.6)
otherwise, R(a.data_handle(), ReturnMapping(a.mapping()), a.accessor())

[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]