linalg : hermitian_matrix_rank_2k_updateを追加 (#1233)

Signed-off-by: Yuya Asano <64895419+sukeya@users.noreply.github.com>

Author: sukeya

reference/linalg.md

@@ -107,7 +107,7 @@ BLAS 1, 2, 3のアルゴリズムでテンプレートパラメータが特に
 | [`symmetric_matrix_rank_k_update`](linalg/symmetric_matrix_rank_k_update.md) | xSYRK: 対称行列のRank-k更新 (function template) | C++26 |
 | [`hermitian_matrix_rank_k_update`](linalg/hermitian_matrix_rank_k_update.md) | xHERK: ハミルトニアン行列のRank-k更新 (function template) | C++26 |
 | [`symmetric_matrix_rank_2k_update`](linalg/symmetric_matrix_rank_2k_update.md) | xSYR2K: 対称行列のRank-2k更新 (function template) | C++26 |
-| `hermitian_matrix_rank_2k_update` | xHER2K: ハミルトニアン行列のRank-2k更新 (function template) | C++26 |
+| [`hermitian_matrix_rank_2k_update`](linalg/hermitian_matrix_rank_2k_update.md) | xHER2K: ハミルトニアン行列のRank-2k更新 (function template) | C++26 |
 | `triangular_matrix_matrix_left_solve` | xTRSM: 三角行列の連立一次方程式を解く (function template) | C++26 |
 | `triangular_matrix_matrix_right_solve` | xTRSM: 三角行列の連立一次方程式を解く (function template) | C++26 |
 

reference/linalg/hermitian_matrix_rank_2k_update.md

@@ -0,0 +1,207 @@
+# hermitian_matrix_rank_2k_update
+
+
+* [mathjax enable]
+* linalg[meta header]
+* function template[meta id-type]
+* std::linalg[meta namespace]
+* cpp26[meta cpp]
+
+
+```cpp
+namespace std::linalg {
+  template<in-matrix InMat1,
+           in-matrix InMat2,
+           possibly-packed-inout-matrix InOutMat,
+           class Triangle>
+  void hermitian_matrix_rank_2k_update(
+    InMat1 A,
+    InMat2 B,
+    InOutMat C,
+    Triangle t); // (1)
+
+  template<class ExecutionPolicy,
+           in-matrix InMat1,
+           in-matrix InMat2,
+           possibly-packed-inout-matrix InOutMat,
+           class Triangle>
+  void hermitian_matrix_rank_2k_update(
+    ExecutionPolicy&& exec,
+    InMat1 A,
+    InMat2 B,
+    InOutMat C,
+    Triangle t); // (2)
+}
+```
+
+
+## 概要
+エルミートな(対称かつ共役を取る)rank-2k updateを対称行列に行う。
+引数`t`は対称行列の成分が上三角にあるのか、それとも下三角にあるのかを示す。
+
+- (1): $C \leftarrow C + AB^* + BA^*$
+- (2): (1)を指定された実行ポリシーで実行する。
+
+
+## 適格要件
+- 共通:
+    + `Triangle`は[`upper_triangle_t`](upper_triangle_t.md)または[`lower_triangle_t`](lower_triangle_t.md)
+    + `InMat`が[`layout_blas_packed`](layout_blas_packed.md)を持つなら、レイアウトの`Triangle`テンプレート引数とこの関数の`Triangle`テンプレート引数が同じ型
+    + [`possibly-addable`](possibly-addable.md)`<decltype(A), decltype(B), decltype(C)>()`が`true`
+    + [`compatible-static-extents`](compatible-static-extents.md)`<decltype(A), decltype(A)>(0, 1)`が`true` (つまり`A`が正方行列であること)
+- (2): [`is_execution_policy`](/reference/execution/is_execution_policy.md)`<ExecutionPolicy>::value`が`true`
+
+
+## 事前条件
+- `A.extent(0) == A.extent(1)`
+- [`addable`](addable.md)`(A, B, C)`が`true`
+
+
+## 効果
+$C \leftarrow C + AB^* + BA^*$
+
+
+## 戻り値
+なし
+
+
+## 計算量
+$O(\verb|A.extent(0)| \times \verb|A.extent(1)| \times \verb|C.extent(0)|)$
+
+
+## 例
+**[注意] 処理系にあるコンパイラで確認していないため、間違っているかもしれません。**
+
+```cpp example
+#include <array>
+#include <iostream>
+#include <linalg>
+#include <mdspan>
+#include <vector>
+
+template <class Matrix>
+void print_mat(const Matrix& A) {
+  for(int i = 0; i < A.extent(0); ++i) {
+    for(int j = 0; j < i; ++j) {
+      std::cout << A[j, i] << ' ';
+    }
+    for(int j = i; j < A.extent(1) - 1; ++j) {
+      std::cout << A[i, j] << ' ';
+    }
+    std::cout << A[i, A.extent(1) - 1] << '\n';
+  }
+}
+
+template <class Matrix>
+void init_mat(Matrix& A, double geta = 0.0) {
+  for(int i = 0; i < A.extent(0); ++i) {
+    for(int j = 0; j < A.extent(1); ++j) {
+      A[i,j] = std::complex<double>(i + geta, j + geta);
+    }
+  }
+}
+
+template <class Matrix>
+void init_herm_mat(Matrix& A) {
+  for(int i = 0; i < A.extent(0); ++i) {
+    A[i, i] = std::complex<double>(i, 0);
+    for(int j = i + 1; j < A.extent(1); ++j) {
+      A[i, j] = std::complex<double>(i, j);
+    }
+  }
+}
+
+int main()
+{
+  constexpr size_t N = 2;
+
+  using Scalar = std::complex<double>;
+  using Vector = std::vector<Scalar>;
+  using HermitianMatrix = std::mdspan<
+      Scalar,
+      std::extents<size_t, N, N>,
+      std::linalg::layout_blas_packed<
+        std::linalg::upper_triangle_t,
+        std::linalg::row_major_t>
+    >;
+
+  Vector A_vec(N * N);
+  Vector B_vec(N * N);
+  Vector C_vec(N * N);
+
+  std::mdspan A(A_vec.data());
+  std::mdspan B(B_vec.data());
+  HermitianMatrix C(C_vec.data());
+
+  init_mat(A);
+  init_mat(B, 1);
+  init_herm_mat(C);
+
+  // (1)
+  std::cout << "(1)\n";
+  std::linalg::hermitian_matrix_rank_2k_update(
+    A,
+    B,
+    C,
+    std::linalg::upper_triangle);
+  print_mat(C);
+
+  // (2)
+  init_herm_mat(C);
+  std::cout << "(2)\n";
+  std::linalg::hermitian_matrix_rank_2k_update(
+    std::execution::par,
+    A,
+    B,
+    C,
+    std::linalg::upper_triangle);
+  print_mat(C);
+
+  return 0;
+}
+```
+* A.extent[link /reference/mdspan/extents/extent.md]
+* std::complex[link /reference/complex/complex.md]
+* std::mdspan[link /reference/mdspan/mdspan.md]
+* std::extents[link /reference/mdspan/extents.md]
+* std::linalg::layout_blas_packed[link /reference/linalg/layout_blas_packed.md]
+* std::linalg::upper_triangle_t[link /reference/linalg/upper_triangle_t.md]
+* std::linalg::row_major_t[link /reference/linalg/row_major_t.md]
+* std::linalg::upper_triangle[link /reference/linalg/upper_triangle_t.md]
+* std::execution::par[link /reference/execution/execution/execution_policy.md]
+* std::linalg::hermitian_matrix_rank_2k_update[color ff0000]
+
+
+### 出力
+```
+(1)
+(4,0) (6,4)
+(6,-4) (13,0)
+(2)
+(4,0) (6,4)
+(6,-4) (13,0)
+```
+
+
+## バージョン
+### 言語
+- C++26
+
+### 処理系
+- [Clang](/implementation.md#clang): ??
+- [GCC](/implementation.md#gcc): ??
+- [ICC](/implementation.md#icc): ??
+- [Visual C++](/implementation.md#visual_cpp): ??
+
+
+## 関連項目
+- [`execution`](/reference/execution.md)
+- [`mdspan`](/reference/mdspan.md)
+- [`upper_triangle_t`](upper_triangle_t.md)
+- [`lower_triangle_t`](lower_triangle_t.md)
+
+
+## 参照
+- [P1673R13 A free function linear algebra interface based on the BLAS](https://www.open-std.org/jtc1/sc22/wg21/docs/papers/2023/p1673r13.html)
+- [LAPACK: {he,sy}r2k: Hermitian/symmetric rank-2k update](https://netlib.org/lapack/explore-html/d8/d94/group__her2k.html)
+