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linalg : hermitian_matrix_rank_2k_updateを追加 (#1233)
Signed-off-by: Yuya Asano <64895419+sukeya@users.noreply.github.com>
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# hermitian_matrix_rank_2k_update | ||
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* [mathjax enable] | ||
* linalg[meta header] | ||
* function template[meta id-type] | ||
* std::linalg[meta namespace] | ||
* cpp26[meta cpp] | ||
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```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) | ||
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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] | ||
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### 出力 | ||
``` | ||
(1) | ||
(4,0) (6,4) | ||
(6,-4) (13,0) | ||
(2) | ||
(4,0) (6,4) | ||
(6,-4) (13,0) | ||
``` | ||
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## バージョン | ||
### 言語 | ||
- C++26 | ||
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### 処理系 | ||
- [Clang](/implementation.md#clang): ?? | ||
- [GCC](/implementation.md#gcc): ?? | ||
- [ICC](/implementation.md#icc): ?? | ||
- [Visual C++](/implementation.md#visual_cpp): ?? | ||
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## 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) | ||
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## 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) | ||
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