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cppdraft/linalg/conjtransposed.md

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+[linalg.conjtransposed]
+
+# 29 Numerics library [[numerics]](./#numerics)
+
+## 29.9 Basic linear algebra algorithms [[linalg]](linalg#conjtransposed)
+
+### 29.9.11 Conjugate transpose in-place transform [linalg.conjtransposed]
+
+[1](#1)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L13268)
+
+The conjugate_transposed function
+returns a conjugate transpose view of an object[.](#1.sentence-1)
+
+This combines the effects of transposed and conjugated[.](#1.sentence-2)
+
+[🔗](#lib:conjugate_transposed)
+
+`  template<class ElementType, class Extents, class Layout, class Accessor>
+    constexpr auto conjugate_transposed(mdspan<ElementType, Extents, Layout, Accessor> a);
+`
+
+[2](#2)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L13279)
+
+*Effects*: Equivalent to: return conjugated(transposed(a));
+
+[3](#3)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L13284)
+
+[*Example [1](#example-1)*: void test_conjugate_transposed(mdspan<complex<double>, extents<size_t, 3, 4>> a) {const auto num_rows = a.extent(0); const auto num_cols = a.extent(1); auto a_ct = conjugate_transposed(a);
+ assert(num_rows == a_ct.extent(1));
+ assert(num_cols == a_ct.extent(0));
+ assert(a.stride(0) == a_ct.stride(1));
+ assert(a.stride(1) == a_ct.stride(0)); for (size_t row = 0; row < num_rows; ++row) {for (size_t col = 0; col < num_rows; ++col) { assert(a[row, col] == conj(a_ct[col, row])); }}auto a_ct_ct = conjugate_transposed(a_ct);
+ assert(num_rows == a_ct_ct.extent(0));
+ assert(num_cols == a_ct_ct.extent(1));
+ assert(a.stride(0) == a_ct_ct.stride(0));
+ assert(a.stride(1) == a_ct_ct.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_ct_ct[row, col]);
+ assert(conj(a_ct[col, row]) == a_ct_ct[row, col]); }}} — *end example*]