28 Numerics library [numerics]

28.9 Basic linear algebra algorithms [linalg]

28.9.10 Transpose in-place transformation [linalg.transp] 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:
  • layout_right if Layout is layout_left;
  • otherwise, layout_left if Layout is layout_right;
  • otherwise, layout_stride if Layout is layout_stride;
  • otherwise, layout_blas_packed<OppositeTriangle, OppositeStorageOrder>, if Layout is
    layout_blas_packed<Triangle, StorageOrder> for some Triangle and StorageOrder, where
    • OppositeTriangle is conditional_t<is_same_v<Triangle, upper_triangle_t>, lower_triangle_t, upper_triangle_t> and
    • OppositeStorageOrder is conditional_t<is_same_v<StorageOrder, column_major_t>, row_major_t, column_major_t>
  • otherwise, NestedLayout if Layout is layout_transpose<NestedLayout> for some NestedLayout;
  • otherwise, layout_transpose<Layout>.
Returns: With ReturnMapping being the type typename ReturnLayout​::​template mapping<ReturnExtents>:
  • 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())
  • 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())
  • otherwise, if Layout is a specialization of layout_transpose, R(a.data_handle(), a.mapping().nested_mapping(), a.accessor())
  • 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]