标准库标头 <linalg> (C++26)
来自cppreference.com
此头文件是数值库的一部分。
类 | ||
在命名空间 std::linalg 定义 | ||
(C++26) | std::mdspan 布局映射策略，表示仅存储一个三角形中的各项的方阵，以打包连续格式存储 (类模板) | |
(C++26) | std::mdspan 访问器策略，其引用表示一个固定缩放因数和其嵌套 std::mdspan 访问器的引用的乘积 (类模板) | |
(C++26) | std::mdspan 访问器策略，其引用代表的是其嵌套 std::mdspan 访问器的引用的复共轭 (类模板) | |
(C++26) | std::mdspan 布局映射策略，交换任意唯一布局映射策略的最右侧两套索引、尺度和步长 (类模板) | |
标签 | ||
在命名空间 std::linalg 定义 | ||
| 描述具有 linalg::layout_blas_packed 布局的 std::mdspan 的元素顺序 (标签) | ||
| 指定算法和矩阵的其他使用方应当访问矩阵的上三角还是下三角 (标签) | ||
| 指定算法是否应当访问矩阵的对角线项 (标签) | ||
函数 | ||
在命名空间 std::linalg 定义 | ||
原位变换 | ||
(C++26) | 返回新的只读 std::mdspan，逐元素计算缩放因子和给定 std::mdspan 的相应元素的乘积 (函数模板) | |
(C++26) | 返回新的只读 std::mdspan，其各元素为给定 std::mdspan 对象的对应元素的复共轭 (函数模板) | |
(C++26) | 返回表示给定 std::mdspan 的输入矩阵的转置的新 std::mdspan (函数模板) | |
(C++26) | 返回对象的共轭转置视图 (函数模板) | |
BLAS 1 函数 | ||
(C++26) | 产生平面旋转 (函数模板) | |
(C++26) | 应用平面旋转到向量 (函数模板) | |
(C++26) | 交换矩阵或向量的全部对应元素 (函数模板) | |
(C++26) | 以计算矩阵或向量和一个标量的逐元素相乘的结果对它覆写 (函数模板) | |
(C++26) | 复制矩阵或向量的各元素给另一个 (函数模板) | |
(C++26) | 按元素添加向量或矩阵 (函数模板) | |
(C++26) | 返回两个向量的非共轭点积 (函数模板) | |
(C++26) | 返回两个向量的共轭点积 (函数模板) | |
(C++26) | 返回缩放的向量各元素平方和 (函数模板) | |
(C++26) | 返回向量的欧氏范数 (函数模板) | |
(C++26) | 返回向量各元素绝对值的和 (函数模板) | |
(C++26) | 返回向量各元素最大绝对值的索引 (函数模板) | |
(C++26) | 返回矩阵的弗罗贝尼乌斯范数 (函数模板) | |
(C++26) | 返回矩阵的 1-范数 (函数模板) | |
(C++26) | 返回矩阵的 ∞-范数 (函数模板) | |
BLAS 2 函数 | ||
(C++26) | 计算矩阵-向量乘积 (函数模板) | |
| 计算对称矩阵-向量乘积 (函数模板) | ||
| 计算厄米特矩阵-向量乘积 (函数模板) | ||
| 计算三角矩阵-向量乘积 (函数模板) | ||
| 求解三角线性系统 (函数模板) | ||
(C++26) | 实施矩阵的非对称非共轭秩-1 更新 (函数模板) | |
(C++26) | 实施矩阵的非对称共轭秩-1 更新 (函数模板) | |
| 实施对称矩阵的秩-1 更新 (函数模板) | ||
| 实施厄米特矩阵的秩-1 更新 (函数模板) | ||
| 实施对称矩阵的秩-2 更新 (函数模板) | ||
| 实施厄米特矩阵的秩-2 更新 (函数模板) | ||
BLAS 3 函数 | ||
(C++26) | 计算矩阵-矩阵乘积 (函数模板) | |
(C++26) | 计算对称矩阵-矩阵乘积 (函数模板) | |
(C++26) | 计算厄米特矩阵-矩阵乘积 (函数模板) | |
| 计算三角矩阵-矩阵乘积 (函数模板) | ||
| 实施对称矩阵的秩-k 更新 (函数模板) | ||
| 实施厄米特矩阵的秩-k 更新 (函数模板) | ||
| 实施对称矩阵的秩-2k 更新 (函数模板) | ||
| 实施厄米特矩阵的秩-2k 更新 (函数模板) | ||
| 求解多重三角线性系统 (函数模板) | ||
[编辑]概要
namespace std::linalg{ // 存储顺序标签struct column_major_t;inlineconstexpr column_major_t column_major;struct row_major_t;inlineconstexpr row_major_t row_major; // 三角形标签struct upper_triangle_t;inlineconstexpr upper_triangle_t upper_triangle;struct lower_triangle_t;inlineconstexpr lower_triangle_t lower_triangle; // 对角线标签struct implicit_unit_diagonal_t;inlineconstexpr implicit_unit_diagonal_t implicit_unit_diagonal;struct explicit_diagonal_t;inlineconstexpr explicit_diagonal_t explicit_diagonal; // 类模板 layout_blas_packedtemplate<class Triangle, class StorageOrder>class layout_blas_packed; // 仅用于阐释的概念和特征template<class T>struct __is_mdspan;// 仅用于阐释 template<class T> concept __in_vector =/* 见描述 */;// 仅用于阐释 template<class T> concept __out_vector =/* 见描述 */;// 仅用于阐释 template<class T> concept __inout_vector =/* 见描述 */;// 仅用于阐释 template<class T> concept __in_matrix =/* 见描述 */;// 仅用于阐释 template<class T> concept __out_matrix =/* 见描述 */;// 仅用于阐释 template<class T> concept __inout_matrix =/* 见描述 */;// 仅用于阐释 template<class T> concept __possibly_packed_inout_matrix =/* 见描述 */;// 仅用于阐释 template<class T> concept __in_object =/* 见描述 */;// 仅用于阐释 template<class T> concept __out_object =/* 见描述 */;// 仅用于阐释 template<class T> concept __inout_object =/* 见描述 */;// 仅用于阐释 // 缩放原位变换template<class ScalingFactor, class Accessor>class scaled_accessor; template<class ScalingFactor, class ElementType, class Extents, class Layout, class Accessor>constexprauto scaled(ScalingFactor scaling_factor, mdspan<ElementType, Extents, Layout, Accessor> x); // 共轭原位变换template<class Accessor>class conjugated_accessor; template<class ElementType, class Extents, class Layout, class Accessor>constexprauto conjugated(mdspan<ElementType, Extents, Layout, Accessor> a); // 转置原位变换template<class Layout>class layout_transpose; template<class ElementType, class Extents, class Layout, class Accessor>constexprauto transposed(mdspan<ElementType, Extents, Layout, Accessor> a); // 共轭转置原位变换template<class ElementType, class Extents, class Layout, class Accessor>constexprauto conjugate_transposed(mdspan<ElementType, Extents, Layout, Accessor> a); // 算法// 计算 Givens 旋转 template<class Real>struct setup_givens_rotation_result { Real c; Real s; Real r;}; template<class Real>struct setup_givens_rotation_result<complex<Real>>{ Real c; complex<Real> s; complex<Real> r;}; template<class Real> setup_givens_rotation_result<Real> setup_givens_rotation(Real a, Real b)noexcept; template<class Real> setup_givens_rotation_result<complex<Real>> setup_givens_rotation(complex<Real> a, complex<Real> b)noexcept; // 运用计算的 Givens 旋转template<__inout_vector InOutVec1, __inout_vector InOutVec2, class Real>void apply_givens_rotation(InOutVec1 x, InOutVec2 y, Real c, Real s); template<class ExecutionPolicy, __inout_vector InOutVec1, __inout_vector InOutVec2, class Real>void apply_givens_rotation(ExecutionPolicy&& exec, InOutVec1 x, InOutVec2 y, Real c, Real s); template<__inout_vector InOutVec1, __inout_vector InOutVec2, class Real>void apply_givens_rotation(InOutVec1 x, InOutVec2 y, Real c, complex<Real> s); template<class ExecutionPolicy, __inout_vector InOutVec1, __inout_vector InOutVec2, class Real>void apply_givens_rotation(ExecutionPolicy&& exec, InOutVec1 x, InOutVec2 y, Real c, complex<Real> s); // 交换元素template<__inout_object InOutObj1, __inout_object InOutObj2>void swap_elements(InOutObj1 x, InOutObj2 y); template<class ExecutionPolicy, __inout_object InOutObj1, __inout_object InOutObj2>void swap_elements(ExecutionPolicy&& exec, InOutObj1 x, InOutObj2 y); // 各元素乘以缩放比例template<class Scalar, __inout_object InOutObj>void scale(Scalar alpha, InOutObj x); template<class ExecutionPolicy, class Scalar, __inout_object InOutObj>void scale(ExecutionPolicy&& exec, Scalar alpha, InOutObj x); // 复制元素template<__in_object InObj, __out_object OutObj>void copy(InObj x, OutObj y); template<class ExecutionPolicy, __in_object InObj, __out_object OutObj>void copy(ExecutionPolicy&& exec, InObj x, OutObj y); // 逐元素加template<__in_object InObj1, __in_object InObj2, __out_object OutObj>void add(InObj1 x, InObj2 y, OutObj z); template<class ExecutionPolicy, __in_object InObj1, __in_object InObj2, __out_object OutObj>void add(ExecutionPolicy&& exec, InObj1 x, InObj2 y, OutObj z); // 两个向量的非共轭点积template<__in_vector InVec1, __in_vector InVec2, class Scalar> Scalar dot(InVec1 v1, InVec2 v2, Scalar init); template<class ExecutionPolicy, __in_vector InVec1, __in_vector InVec2, class Scalar> Scalar dot(ExecutionPolicy&& exec, InVec1 v1, InVec2 v2, Scalar init); template<__in_vector InVec1, __in_vector InVec2>auto dot(InVec1 v1, InVec2 v2)->/* 见描述 */; template<class ExecutionPolicy, __in_vector InVec1, __in_vector InVec2>auto dot(ExecutionPolicy&& exec, InVec1 v1, InVec2 v2)->/* 见描述 */; // 两个向量的共轭点积template<__in_vector InVec1, __in_vector InVec2, class Scalar> Scalar dotc(InVec1 v1, InVec2 v2, Scalar init); template<class ExecutionPolicy, __in_vector InVec1, __in_vector InVec2, class Scalar> Scalar dotc(ExecutionPolicy&& exec, InVec1 v1, InVec2 v2, Scalar init); template<__in_vector InVec1, __in_vector InVec2>auto dotc(InVec1 v1, InVec2 v2)->/* 见描述 */; template<class ExecutionPolicy, __in_vector InVec1, __in_vector InVec2>auto dotc(ExecutionPolicy&& exec, InVec1 v1, InVec2 v2)->/* 见描述 */; // 向量各元素的缩放平方和template<class Scalar>struct sum_of_squares_result { Scalar scaling_factor; Scalar scaled_sum_of_squares;}; template<__in_vector InVec, class Scalar> sum_of_squares_result<Scalar> vector_sum_of_squares(InVec v, sum_of_squares_result<Scalar> init); template<class ExecutionPolicy, __in_vector InVec, class Scalar> sum_of_squares_result<Scalar> vector_sum_of_squares(ExecutionPolicy&& exec, InVec v, sum_of_squares_result<Scalar> init); // 向量的欧式范数template<__in_vector InVec, class Scalar> Scalar vector_two_norm(InVec v, Scalar init); template<class ExecutionPolicy, __in_vector InVec, class Scalar> Scalar vector_two_norm(ExecutionPolicy&& exec, InVec v, Scalar init); template<__in_vector InVec>auto vector_two_norm(InVec v)->/* 见描述 */; template<class ExecutionPolicy, __in_vector InVec>auto vector_two_norm(ExecutionPolicy&& exec, InVec v)->/* 见描述 */; // 向量各元素的绝对值和template<__in_vector InVec, class Scalar> Scalar vector_abs_sum(InVec v, Scalar init);template<class ExecutionPolicy, __in_vector InVec, class Scalar> Scalar vector_abs_sum(ExecutionPolicy&& exec, InVec v, Scalar init); template<__in_vector InVec>auto vector_abs_sum(InVec v)->/* 见描述 */; template<class ExecutionPolicy, __in_vector InVec>auto vector_abs_sum(ExecutionPolicy&& exec, InVec v)->/* 见描述 */; // 向量各元素最大绝对值的索引template<__in_vector InVec>typename InVec::extents_type idx_abs_max(InVec v); template<class ExecutionPolicy, __in_vector InVec>typename InVec::extents_type idx_abs_max(ExecutionPolicy&& exec, InVec v); // 矩阵的弗罗贝尼乌斯范数template<__in_matrix InMat, class Scalar> Scalar matrix_frob_norm(InMat A, Scalar init); template<class ExecutionPolicy, __in_matrix InMat, class Scalar> Scalar matrix_frob_norm(ExecutionPolicy&& exec, InMat A, Scalar init); template<__in_matrix InMat>auto matrix_frob_norm(InMat A)->/* 见描述 */; template<class ExecutionPolicy, __in_matrix InMat>auto matrix_frob_norm(ExecutionPolicy&& exec, InMat A)->/* 见描述 */; // 矩阵的 1-范数template<__in_matrix InMat, class Scalar> Scalar matrix_one_norm(InMat A, Scalar init); template<class ExecutionPolicy, __in_matrix InMat, class Scalar> Scalar matrix_one_norm(ExecutionPolicy&& exec, InMat A, Scalar init); template<__in_matrix InMat>auto matrix_one_norm(InMat A)->/* 见描述 */; template<class ExecutionPolicy, __in_matrix InMat>auto matrix_one_norm(ExecutionPolicy&& exec, InMat A)->/* 见描述 */; // 矩阵的 ∞-范数template<__in_matrix InMat, class Scalar> Scalar matrix_inf_norm(InMat A, Scalar init); template<class ExecutionPolicy, __in_matrix InMat, class Scalar> Scalar matrix_inf_norm(ExecutionPolicy&& exec, InMat A, Scalar init); template<__in_matrix InMat>auto matrix_inf_norm(InMat A)->/* 见描述 */; template<class ExecutionPolicy, __in_matrix InMat>auto matrix_inf_norm(ExecutionPolicy&& exec, InMat A)->/* 见描述 */; // 通用矩阵与向量乘积template<__in_matrix InMat, __in_vector InVec, __out_vector OutVec>void matrix_vector_product(InMat A, InVec x, OutVec y); template<class ExecutionPolicy, __in_matrix InMat, __in_vector InVec, __out_vector OutVec>void matrix_vector_product(ExecutionPolicy&& exec, InMat A, InVec x, OutVec y); template<__in_matrix InMat, __in_vector InVec1, __in_vector InVec2, __out_vector OutVec>void matrix_vector_product(InMat A, InVec1 x, InVec2 y, OutVec z); template<class ExecutionPolicy, __in_matrix InMat, __in_vector InVec1, __in_vector InVec2, __out_vector OutVec>void matrix_vector_product(ExecutionPolicy&& exec, InMat A, InVec1 x, InVec2 y, OutVec z); // 对称矩阵与向量乘积template<__in_matrix InMat, class Triangle, __in_vector InVec, __out_vector OutVec>void symmetric_matrix_vector_product(InMat A, Triangle t, InVec x, OutVec y); template<class ExecutionPolicy, __in_matrix InMat, class Triangle, __in_vector InVec, __out_vector OutVec>void symmetric_matrix_vector_product(ExecutionPolicy&& exec, InMat A, Triangle t, InVec x, OutVec y); template<__in_matrix InMat, class Triangle, __in_vector InVec1, __in_vector InVec2, __out_vector OutVec>void symmetric_matrix_vector_product(InMat A, Triangle t, InVec1 x, InVec2 y, OutVec z); template<class ExecutionPolicy, __in_matrix InMat, class Triangle, __in_vector InVec1, __in_vector InVec2, __out_vector OutVec>void symmetric_matrix_vector_product(ExecutionPolicy&& exec, InMat A, Triangle t, InVec1 x, InVec2 y, OutVec z); // 厄米特矩阵与向量乘积template<__in_matrix InMat, class Triangle, __in_vector InVec, __out_vector OutVec>void hermitian_matrix_vector_product(InMat A, Triangle t, InVec x, OutVec y); template<class ExecutionPolicy, __in_matrix InMat, class Triangle, __in_vector InVec, __out_vector OutVec>void hermitian_matrix_vector_product(ExecutionPolicy&& exec, InMat A, Triangle t, InVec x, OutVec y); template<__in_matrix InMat, class Triangle, __in_vector InVec1, __in_vector InVec2, __out_vector OutVec>void hermitian_matrix_vector_product(InMat A, Triangle t, InVec1 x, InVec2 y, OutVec z); template<class ExecutionPolicy, __in_matrix InMat, class Triangle, __in_vector InVec1, __in_vector InVec2, __out_vector OutVec>void hermitian_matrix_vector_product(ExecutionPolicy&& exec, InMat A, Triangle t, InVec1 x, InVec2 y, OutVec z); // 三角形矩阵与向量乘积// 覆写三角形矩阵与向量乘积template<__in_matrix InMat, class Triangle, class DiagonalStorage, __in_vector InVec, __out_vector OutVec>void triangular_matrix_vector_product(InMat A, Triangle t, DiagonalStorage d, InVec x, OutVec y); template<class ExecutionPolicy, __in_matrix InMat, class Triangle, class DiagonalStorage, __in_vector InVec, __out_vector OutVec>void triangular_matrix_vector_product(ExecutionPolicy&& exec, InMat A, Triangle t, DiagonalStorage d, InVec x, OutVec y); // 原位三角形矩阵与向量乘积template<__in_matrix InMat, class Triangle, class DiagonalStorage, __inout_vector InOutVec>void triangular_matrix_vector_product(InMat A, Triangle t, DiagonalStorage d, InOutVec y); template<class ExecutionPolicy, __in_matrix InMat, class Triangle, class DiagonalStorage, __inout_vector InOutVec>void triangular_matrix_vector_product(ExecutionPolicy&& exec, InMat A, Triangle t, DiagonalStorage d, InOutVec y); // 更新三角形矩阵与向量乘积template<__in_matrix InMat, class Triangle, class DiagonalStorage, __in_vector InVec1, __in_vector InVec2, __out_vector OutVec>void triangular_matrix_vector_product(InMat A, Triangle t, DiagonalStorage d, InVec1 x, InVec2 y, OutVec z); template<class ExecutionPolicy, __in_matrix InMat, class Triangle, class DiagonalStorage, __in_vector InVec1, __in_vector InVec2, __out_vector OutVec>void triangular_matrix_vector_product(ExecutionPolicy&& exec, InMat A, Triangle t, DiagonalStorage d, InVec1 x, InVec2 y, OutVec z); // 非原位，求解三角形线性系统template<__in_matrix InMat, class Triangle, class DiagonalStorage, __in_vector InVec, __out_vector OutVec, class BinaryDivideOp>void triangular_matrix_vector_solve(InMat A, Triangle t, DiagonalStorage d, InVec b, OutVec x, BinaryDivideOp divide); template<class ExecutionPolicy, __in_matrix InMat, class Triangle, class DiagonalStorage, __in_vector InVec, __out_vector OutVec, class BinaryDivideOp>void triangular_matrix_vector_solve(ExecutionPolicy&& exec, InMat A, Triangle t, DiagonalStorage d, InVec b, OutVec x, BinaryDivideOp divide); template<__in_matrix InMat, class Triangle, class DiagonalStorage, __in_vector InVec, __out_vector OutVec>void triangular_matrix_vector_solve(InMat A, Triangle t, DiagonalStorage d, InVec b, OutVec x); template<class ExecutionPolicy, __in_matrix InMat, class Triangle, class DiagonalStorage, __in_vector InVec, __out_vector OutVec>void triangular_matrix_vector_solve(ExecutionPolicy&& exec, InMat A, Triangle t, DiagonalStorage d, InVec b, OutVec x); // 原位，求解三角形线性系统template<__in_matrix InMat, class Triangle, class DiagonalStorage, __inout_vector InOutVec, class BinaryDivideOp>void triangular_matrix_vector_solve(InMat A, Triangle t, DiagonalStorage d, InOutVec b, BinaryDivideOp divide); template<class ExecutionPolicy, __in_matrix InMat, class Triangle, class DiagonalStorage, __inout_vector InOutVec, class BinaryDivideOp>void triangular_matrix_vector_solve(ExecutionPolicy&& exec, InMat A, Triangle t, DiagonalStorage d, InOutVec b, BinaryDivideOp divide); template<__in_matrix InMat, class Triangle, class DiagonalStorage, __inout_vector InOutVec>void triangular_matrix_vector_solve(InMat A, Triangle t, DiagonalStorage d, InOutVec b); template<class ExecutionPolicy, __in_matrix InMat, class Triangle, class DiagonalStorage, __inout_vector InOutVec>void triangular_matrix_vector_solve(ExecutionPolicy&& exec, InMat A, Triangle t, DiagonalStorage d, InOutVec b); // 非共轭的秩-1 矩阵更新template<__in_vector InVec1, __in_vector InVec2, __inout_matrix InOutMat>void matrix_rank_1_update(InVec1 x, InVec2 y, InOutMat A); template<class ExecutionPolicy, __in_vector InVec1, __in_vector InVec2, __inout_matrix InOutMat>void matrix_rank_1_update(ExecutionPolicy&& exec, InVec1 x, InVec2 y, InOutMat A); // 共轭的秩-1 矩阵更新template<__in_vector InVec1, __in_vector InVec2, __inout_matrix InOutMat>void matrix_rank_1_update_c(InVec1 x, InVec2 y, InOutMat A); template<class ExecutionPolicy, __in_vector InVec1, __in_vector InVec2, __inout_matrix InOutMat>void matrix_rank_1_update_c(ExecutionPolicy&& exec, InVec1 x, InVec2 y, InOutMat A); // 对称的秩-1 矩阵更新template<__in_vector InVec, __possibly_packed_inout_matrix InOutMat, class Triangle>void symmetric_matrix_rank_1_update(InVec x, InOutMat A, Triangle t); template<class ExecutionPolicy, __in_vector InVec, __possibly_packed_inout_matrix InOutMat, class Triangle>void symmetric_matrix_rank_1_update(ExecutionPolicy&& exec, InVec x, InOutMat A, Triangle t); template<class Scalar, __in_vector InVec, __possibly_packed_inout_matrix InOutMat, class Triangle>void symmetric_matrix_rank_1_update(Scalar alpha, InVec x, InOutMat A, Triangle t); template<class ExecutionPolicy, class Scalar, __in_vector InVec, __possibly_packed_inout_matrix InOutMat, class Triangle>void symmetric_matrix_rank_1_update(ExecutionPolicy&& exec, Scalar alpha, InVec x, InOutMat A, Triangle t); // 厄米特秩-1 矩阵更新template<__in_vector InVec, __possibly_packed_inout_matrix InOutMat, class Triangle>void hermitian_matrix_rank_1_update(InVec x, InOutMat A, Triangle t); template<class ExecutionPolicy, __in_vector InVec, __possibly_packed_inout_matrix InOutMat, class Triangle>void hermitian_matrix_rank_1_update(ExecutionPolicy&& exec, InVec x, InOutMat A, Triangle t); template<class Scalar, __in_vector InVec, __possibly_packed_inout_matrix InOutMat, class Triangle>void hermitian_matrix_rank_1_update(Scalar alpha, InVec x, InOutMat A, Triangle t); template<class ExecutionPolicy, class Scalar, __in_vector InVec, __possibly_packed_inout_matrix InOutMat, class Triangle>void hermitian_matrix_rank_1_update(ExecutionPolicy&& exec, Scalar alpha, InVec x, InOutMat A, Triangle t); // 对称的秩-2 矩阵更新template<__in_vector InVec1, __in_vector InVec2, __possibly_packed_inout_matrix InOutMat, class Triangle>void symmetric_matrix_rank_2_update(InVec1 x, InVec2 y, InOutMat A, Triangle t); template<class ExecutionPolicy, __in_vector InVec1, __in_vector InVec2, __possibly_packed_inout_matrix InOutMat, class Triangle>void symmetric_matrix_rank_2_update(ExecutionPolicy&& exec, InVec1 x, InVec2 y, InOutMat A, Triangle t); // 厄米特秩-2 矩阵更新template<__in_vector InVec1, __in_vector InVec2, __possibly_packed_inout_matrix InOutMat, class Triangle>void hermitian_matrix_rank_2_update(InVec1 x, InVec2 y, InOutMat A, Triangle t); template<class ExecutionPolicy, __in_vector InVec1, __in_vector InVec2, __possibly_packed_inout_matrix InOutMat, class Triangle>void hermitian_matrix_rank_2_update(ExecutionPolicy&& exec, InVec1 x, InVec2 y, InOutMat A, Triangle t); // 通用矩阵与矩阵乘积template<__in_matrix InMat1, __in_matrix InMat2, __out_matrix OutMat>void matrix_product(InMat1 A, InMat2 B, OutMat C); template<class ExecutionPolicy, __in_matrix InMat1, __in_matrix InMat2, __out_matrix OutMat>void matrix_product(ExecutionPolicy&& exec, InMat1 A, InMat2 B, OutMat C); template<__in_matrix InMat1, __in_matrix InMat2, __in_matrix InMat3, __out_matrix OutMat>void matrix_product(InMat1 A, InMat2 B, InMat3 E, OutMat C); template<class ExecutionPolicy, __in_matrix InMat1, __in_matrix InMat2, __in_matrix InMat3, __out_matrix OutMat>void matrix_product(ExecutionPolicy&& exec, InMat1 A, InMat2 B, InMat3 E, OutMat C); // 对称矩阵与矩阵乘积// 覆写对称矩阵与矩阵左乘template<__in_matrix InMat1, class Triangle, __in_matrix InMat2, __out_matrix OutMat>void symmetric_matrix_product(InMat1 A, Triangle t, InMat2 B, OutMat C); template<class ExecutionPolicy, __in_matrix InMat1, class Triangle, __in_matrix InMat2, __out_matrix OutMat>void symmetric_matrix_product(ExecutionPolicy&& exec, InMat1 A, Triangle t, InMat2 B, OutMat C); // 覆写对称矩阵与矩阵右乘template<__in_matrix InMat1, __in_matrix InMat2, class Triangle, __out_matrix OutMat>void symmetric_matrix_product(InMat1 B, InMat2 A, Triangle t, OutMat C); template<class ExecutionPolicy, __in_matrix InMat1, __in_matrix InMat2, class Triangle, __out_matrix OutMat>void symmetric_matrix_product(ExecutionPolicy&& exec, InMat1 B, InMat2 A, Triangle t, OutMat C); // 更新对称矩阵与矩阵左乘template<__in_matrix InMat1, class Triangle, __in_matrix InMat2, __in_matrix InMat3, __out_matrix OutMat>void symmetric_matrix_product(InMat1 A, Triangle t, InMat2 B, InMat3 E, OutMat C); template<class ExecutionPolicy, __in_matrix InMat1, class Triangle, __in_matrix InMat2, __in_matrix InMat3, __out_matrix OutMat>void symmetric_matrix_product(ExecutionPolicy&& exec, InMat1 A, Triangle t, InMat2 B, InMat3 E, OutMat C); // 更新对称矩阵与矩阵右乘template<__in_matrix InMat1, __in_matrix InMat2, class Triangle, __in_matrix InMat3, __out_matrix OutMat>void symmetric_matrix_product(InMat1 B, InMat2 A, Triangle t, InMat3 E, OutMat C); template<class ExecutionPolicy, __in_matrix InMat1, __in_matrix InMat2, class Triangle, __in_matrix InMat3, __out_matrix OutMat>void symmetric_matrix_product(ExecutionPolicy&& exec, InMat1 B, InMat2 A, Triangle t, InMat3 E, OutMat C); // 厄米特矩阵与矩阵乘积// 覆写厄米特矩阵与矩阵左乘template<__in_matrix InMat1, class Triangle, __in_matrix InMat2, __out_matrix OutMat>void hermitian_matrix_product(InMat1 A, Triangle t, InMat2 B, OutMat C);template<class ExecutionPolicy, __in_matrix InMat1, class Triangle, __in_matrix InMat2, __out_matrix OutMat>void hermitian_matrix_product(ExecutionPolicy&& exec, InMat1 A, Triangle t, InMat2 B, OutMat C); // 覆写厄米特矩阵与矩阵右乘template<__in_matrix InMat1, __in_matrix InMat2, class Triangle, __out_matrix OutMat>void hermitian_matrix_product(InMat1 B, InMat2 A, Triangle t, OutMat C); template<class ExecutionPolicy, __in_matrix InMat1, __in_matrix InMat2, class Triangle, __out_matrix OutMat>void hermitian_matrix_product(ExecutionPolicy&& exec, InMat1 B, InMat2 A, Triangle t, OutMat C); // 更新厄米特矩阵与矩阵左乘template<__in_matrix InMat1, class Triangle, __in_matrix InMat2, __in_matrix InMat3, __out_matrix OutMat>void hermitian_matrix_product(InMat1 A, Triangle t, InMat2 B, InMat3 E, OutMat C); template<class ExecutionPolicy, __in_matrix InMat1, class Triangle, __in_matrix InMat2, __in_matrix InMat3, __out_matrix OutMat>void hermitian_matrix_product(ExecutionPolicy&& exec, InMat1 A, Triangle t, InMat2 B, InMat3 E, OutMat C); // 更新厄米特矩阵与矩阵右乘template<__in_matrix InMat1, __in_matrix InMat2, class Triangle, __in_matrix InMat3, __out_matrix OutMat>void hermitian_matrix_product(InMat1 B, InMat2 A, Triangle t, InMat3 E, OutMat C); template<class ExecutionPolicy, __in_matrix InMat1, __in_matrix InMat2, class Triangle, __in_matrix InMat3, __out_matrix OutMat>void hermitian_matrix_product(ExecutionPolicy&& exec, InMat1 B, InMat2 A, Triangle t, InMat3 E, OutMat C); // 三角形矩阵与矩阵乘积// 覆写三角形矩阵与矩阵左乘template<__in_matrix InMat1, class Triangle, class DiagonalStorage, __in_matrix InMat2, __out_matrix OutMat>void triangular_matrix_product(InMat1 A, Triangle t, DiagonalStorage d, InMat2 B, OutMat C); template<class ExecutionPolicy, __in_matrix InMat1, class Triangle, class DiagonalStorage, __in_matrix InMat2, __out_matrix OutMat>void triangular_matrix_product(ExecutionPolicy&& exec, InMat1 A, Triangle t, DiagonalStorage d, InMat2 B, OutMat C); template<__in_matrix InMat1, class Triangle, class DiagonalStorage, __inout_matrix InOutMat>void triangular_matrix_left_product(InMat1 A, Triangle t, DiagonalStorage d, InOutMat C); template<class ExecutionPolicy, __in_matrix InMat1, class Triangle, class DiagonalStorage, __inout_matrix InOutMat>void triangular_matrix_left_product(ExecutionPolicy&& exec, InMat1 A, Triangle t, DiagonalStorage d, InOutMat C); // 覆写三角形矩阵与矩阵右乘template<__in_matrix InMat1, __in_matrix InMat2, class Triangle, class DiagonalStorage, __out_matrix OutMat>void triangular_matrix_product(InMat1 B, InMat2 A, Triangle t, DiagonalStorage d, OutMat C); template<class ExecutionPolicy, __in_matrix InMat1, __in_matrix InMat2, class Triangle, class DiagonalStorage, __out_matrix OutMat>void triangular_matrix_product(ExecutionPolicy&& exec, InMat1 B, InMat2 A, Triangle t, DiagonalStorage d, OutMat C); template<__in_matrix InMat1, class Triangle, class DiagonalStorage, __inout_matrix InOutMat>void triangular_matrix_right_product(InMat1 A, Triangle t, DiagonalStorage d, InOutMat C); template<class ExecutionPolicy, __in_matrix InMat1, class Triangle, class DiagonalStorage, __inout_matrix InOutMat>void triangular_matrix_right_product(ExecutionPolicy&& exec, InMat1 A, Triangle t, DiagonalStorage d, InOutMat C); // 更新三角形矩阵与矩阵左乘template<__in_matrix InMat1, class Triangle, class DiagonalStorage, __in_matrix InMat2, __in_matrix InMat3, __out_matrix OutMat>void triangular_matrix_product(InMat1 A, Triangle t, DiagonalStorage d, InMat2 B, InMat3 E, OutMat C); template<class ExecutionPolicy, __in_matrix InMat1, class Triangle, class DiagonalStorage, __in_matrix InMat2, __in_matrix InMat3, __out_matrix OutMat>void triangular_matrix_product(ExecutionPolicy&& exec, InMat1 A, Triangle t, DiagonalStorage d, InMat2 B, InMat3 E, OutMat C); // 更新三角形矩阵与矩阵右乘template<__in_matrix InMat1, __in_matrix InMat2, class Triangle, class DiagonalStorage, __in_matrix InMat3, __out_matrix OutMat>void triangular_matrix_product(InMat1 B, InMat2 A, Triangle t, DiagonalStorage d, InMat3 E, OutMat C); template<class ExecutionPolicy, __in_matrix InMat1, __in_matrix InMat2, class Triangle, class DiagonalStorage, __in_matrix InMat3, __out_matrix OutMat>void triangular_matrix_product(ExecutionPolicy&& exec, InMat1 B, InMat2 A, Triangle t, DiagonalStorage d, InMat3 E, OutMat C); // 秩-k 对称矩阵更新template<class Scalar, __in_matrix InMat1, __possibly_packed_inout_matrix InOutMat, class Triangle>void symmetric_matrix_rank_k_update(Scalar alpha, InMat1 A, InOutMat C, Triangle t); template<class Scalar, class ExecutionPolicy, ___in_matrix InMat1, __possibly_packed_inout_matrix InOutMat, class Triangle>void symmetric_matrix_rank_k_update(ExecutionPolicy&& exec, Scalar alpha, InMat1 A, InOutMat C, Triangle t); template<__in_matrix InMat1, __possibly_packed_inout_matrix InOutMat, class Triangle>void symmetric_matrix_rank_k_update(InMat1 A, InOutMat C, Triangle t); template<class ExecutionPolicy, __in_matrix InMat1, __possibly_packed_inout_matrix InOutMat, class Triangle>void symmetric_matrix_rank_k_update(ExecutionPolicy&& exec, InMat1 A, InOutMat C, Triangle t); // 秩-k 厄米特矩阵更新template<class Scalar, __in_matrix InMat1, __possibly_packed_inout_matrix InOutMat, class Triangle>void hermitian_matrix_rank_k_update(Scalar alpha, InMat1 A, InOutMat C, Triangle t); template<class ExecutionPolicy, class Scalar, __in_matrix InMat1, __possibly_packed_inout_matrix InOutMat, class Triangle void hermitian_matrix_rank_k_update(ExecutionPolicy&& exec, Scalar alpha, InMat1 A, InOutMat C, Triangle t); template<__in_matrix InMat1, __possibly_packed_inout_matrix InOutMat, class Triangle>void hermitian_matrix_rank_k_update(InMat1 A, InOutMat C, Triangle t); template<class ExecutionPolicy, __in_matrix InMat1, __possibly_packed_inout_matrix InOutMat, class Triangle>void hermitian_matrix_rank_k_update(ExecutionPolicy&& exec, InMat1 A, InOutMat C, Triangle t); // 秩-2k 对称矩阵更新template<__in_matrix InMat1, __in_matrix InMat2, __possibly_packed_inout_matrix InOutMat, class Triangle>void symmetric_matrix_rank_2k_update(InMat1 A, InMat2 B, InOutMat C, Triangle t); template<class ExecutionPolicy, __in_matrix InMat1, __in_matrix InMat2, __possibly_packed_inout_matrix InOutMat, class Triangle>void symmetric_matrix_rank_2k_update(ExecutionPolicy&& exec, InMat1 A, InMat2 B, InOutMat C, Triangle t); // 秩-2k 厄米特矩阵更新matrix updatetemplate<__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); 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); // 求解多个三角形的线性系统// 三角形矩阵在左侧template<__in_matrix InMat1, class Triangle, class DiagonalStorage, __in_matrix InMat2, __out_matrix OutMat, class BinaryDivideOp>void triangular_matrix_matrix_left_solve(InMat1 A, Triangle t, DiagonalStorage d, InMat2 B, OutMat X, BinaryDivideOp divide); template<class ExecutionPolicy, __in_matrix InMat1, class Triangle, class DiagonalStorage, __in_matrix InMat2, __out_matrix OutMat, class BinaryDivideOp>void triangular_matrix_matrix_left_solve(ExecutionPolicy&& exec, InMat1 A, Triangle t, DiagonalStorage d, InMat2 B, OutMat X, BinaryDivideOp divide); template<__in_matrix InMat1, class Triangle, class DiagonalStorage, __inout_matrix InOutMat, class BinaryDivideOp>void triangular_matrix_matrix_left_solve(InMat1 A, Triangle t, DiagonalStorage d, InOutMat B, BinaryDivideOp divide); template<class ExecutionPolicy, __in_matrix InMat1, class Triangle, class DiagonalStorage, __inout_matrix InOutMat, class BinaryDivideOp>void triangular_matrix_matrix_left_solve(ExecutionPolicy&& exec, InMat1 A, Triangle t, DiagonalStorage d, InOutMat B, BinaryDivideOp divide); template<__in_matrix InMat1, class Triangle, class DiagonalStorage, __in_matrix InMat2, __out_matrix OutMat>void triangular_matrix_matrix_left_solve(InMat1 A, Triangle t, DiagonalStorage d, InMat2 B, OutMat X); template<class ExecutionPolicy, __in_matrix InMat1, class Triangle, class DiagonalStorage, __in_matrix InMat2, __out_matrix OutMat>void triangular_matrix_matrix_left_solve(ExecutionPolicy&& exec, InMat1 A, Triangle t, DiagonalStorage d, InMat2 B, OutMat X); template<__in_matrix InMat1, class Triangle, class DiagonalStorage, __inout_matrix InOutMat>void triangular_matrix_matrix_left_solve(InMat1 A, Triangle t, DiagonalStorage d, InOutMat B); template<class ExecutionPolicy, __in_matrix InMat1, class Triangle, class DiagonalStorage, __inout_matrix InOutMat>void triangular_matrix_matrix_left_solve(ExecutionPolicy&& exec, InMat1 A, Triangle t, DiagonalStorage d, InOutMat B); // 求解多个三角形的线性系统// 三角形矩阵在右侧template<__in_matrix InMat1, class Triangle, class DiagonalStorage, __in_matrix InMat2, __out_matrix OutMat, class BinaryDivideOp>void triangular_matrix_matrix_right_solve(InMat1 A, Triangle t, DiagonalStorage d, InMat2 B, OutMat X, BinaryDivideOp divide); template<class ExecutionPolicy, __in_matrix InMat1, class Triangle, class DiagonalStorage, __in_matrix InMat2, __out_matrix OutMat, class BinaryDivideOp>void triangular_matrix_matrix_right_solve(ExecutionPolicy&& exec, InMat1 A, Triangle t, DiagonalStorage d, InMat2 B, OutMat X, BinaryDivideOp divide); template<__in_matrix InMat1, class Triangle, class DiagonalStorage, __inout_matrix InOutMat, class BinaryDivideOp>void triangular_matrix_matrix_right_solve(InMat1 A, Triangle t, DiagonalStorage d, InOutMat B, BinaryDivideOp divide); template<class ExecutionPolicy, __in_matrix InMat1, class Triangle, class DiagonalStorage, __inout_matrix InOutMat, class BinaryDivideOp>void triangular_matrix_matrix_right_solve(ExecutionPolicy&& exec, InMat1 A, Triangle t, DiagonalStorage d, InOutMat B, BinaryDivideOp divide)); template<__in_matrix InMat1, class Triangle, class DiagonalStorage, __in_matrix InMat2, __out_matrix OutMat>void triangular_matrix_matrix_right_solve(InMat1 A, Triangle t, DiagonalStorage d, InMat2 B, OutMat X); template<class ExecutionPolicy, __in_matrix InMat1, class Triangle, class DiagonalStorage, __in_matrix InMat2, __out_matrix OutMat>void triangular_matrix_matrix_right_solve(ExecutionPolicy&& exec, InMat1 A, Triangle t, DiagonalStorage d, InMat2 B, OutMat X); template<__in_matrix InMat1, class Triangle, class DiagonalStorage, __inout_matrix InOutMat>void triangular_matrix_matrix_right_solve(InMat1 A, Triangle t, DiagonalStorage d, InOutMat B); template<class ExecutionPolicy, __in_matrix InMat1, class Triangle, class DiagonalStorage, __inout_matrix InOutMat>void triangular_matrix_matrix_right_solve(ExecutionPolicy&& exec, InMat1 A, Triangle t, DiagonalStorage d, InOutMat B);}
[编辑]标签
namespace std::linalg{struct column_major_t {explicit column_major_t()=default;};inlineconstexpr column_major_t column_major ={}; struct row_major_t {explicit row_major_t()=default;};inlineconstexpr row_major_t row_major ={}; struct upper_triangle_t {explicit upper_triangle_t()=default;};inlineconstexpr upper_triangle_t upper_triangle ={}; struct lower_triangle_t {explicit lower_triangle_t()=default;};inlineconstexpr lower_triangle_t lower_triangle ={}; struct implicit_unit_diagonal_t {explicit implicit_unit_diagonal_t()=default;};inlineconstexpr implicit_unit_diagonal_t implicit_unit_diagonal ={}; struct explicit_diagonal_t {explicit explicit_diagonal_t()=default;};inlineconstexpr explicit_diagonal_t explicit_diagonal ={};}
[编辑]类模板 std::linalg::layout_blas_packed
namespace std::linalg{template<class Triangle, class StorageOrder>class layout_blas_packed {public:template<class Extents>struct mapping {public:using extents_type = Extents;using index_type =typename extents_type::index_type;using size_type =typename extents_type::size_type;using rank_type =typename extents_type::rank_type;using layout_type = layout_blas_packed<Triangle, StorageOrder>; private: Extents __the_extents{};// 仅用于阐释 public:constexpr mapping()noexcept=default;constexpr mapping(const mapping&)noexcept=default;constexpr mapping(const extents_type& e)noexcept;template<class OtherExtents>constexprexplicit(!is_convertible_v<OtherExtents, extents_type>) mapping(const mapping<OtherExtents>& other)noexcept; constexpr mapping& operator=(const mapping&)noexcept=default; constexpr extents_type extents()constnoexcept{return the-extents;} constexpr size_type required_span_size()constnoexcept; template<class Index0, class Index1>constexpr index_type operator()(Index0 ind0, Index1 ind1)constnoexcept; staticconstexprbool is_always_unique(){return(extents_type::static_extent(0)!= dynamic_extent && extents_type::static_extent(0)<2)||(extents_type::static_extent(1)!= dynamic_extent && extents_type::static_extent(1)<2);}staticconstexprbool is_always_exhaustive(){returntrue;}staticconstexprbool is_always_strided(){return is_always_unique();} constexprbool is_unique()constnoexcept{return __the_extents.extent(0)<2;}constexprbool is_exhaustive()constnoexcept{returntrue;}constexprbool is_strided()constnoexcept{return __the_extents.extent(0)<2;} constexpr index_type stride(rank_type)constnoexcept; template<class OtherExtents>friendconstexprbool operator==(const mapping&, const mapping<OtherExtents>&)noexcept; };};}
[编辑]类模板 std::linalg::scaled_accessor
namespace std::linalg{template<class ScalingFactor, class NestedAccessor>class scaled_accessor {public:using element_type = add_const_t<decltype(declval<ScalingFactor>()* declval<NestedAccessor::element_type>())>;using reference = remove_const_t<element_type>;using data_handle_type = NestedAccessor::data_handle_type;using offset_policy = scaled_accessor<ScalingFactor, NestedAccessor::offset_policy>; constexpr scaled_accessor()=default;template<class OtherNestedAccessor>explicit(!is_convertible_v<OtherNestedAccessor, NestedAccessor>)constexpr scaled_accessor(const scaled_accessor<ScalingFactor, OtherNestedAccessor>&);constexpr scaled_accessor(const ScalingFactor& s, const Accessor& a); constexpr reference access(data_handle_type p, size_t i)constnoexcept;constexpr offset_policy::data_handle_type offset(data_handle_type p, size_t i)constnoexcept; constexprconst ScalingFactor& scaling_factor()constnoexcept{return __scaling_factor;}constexprconst NestedAccessor& nested_accessor()constnoexcept{return __nested_accessor;} private: ScalingFactor __scaling_factor;// 仅用于阐释 NestedAccessor __nested_accessor;// 仅用于阐释};}
[编辑]类模板 std::linalg::conjugated_accessor
namespace std::linalg{template<class NestedAccessor>class conjugated_accessor {private: NestedAccessor __nested_accessor;// 仅用于阐释 public:using element_type = add_const_t<decltype(/*conj-if-needed*/(declval<NestedAccessor::element_type>()))>;using reference = remove_const_t<element_type>;using data_handle_type =typename NestedAccessor::data_handle_type;using offset_policy = conjugated_accessor<NestedAccessor::offset_policy>; constexpr conjugated_accessor()=default;template<class OtherNestedAccessor>explicit(!is_convertible_v<OtherNestedAccessor, NestedAccessor>)constexpr conjugated_accessor(const conjugated_accessor<OtherNestedAccessor>& other); constexpr reference access(data_handle_type p, size_t i)const; constexprtypename offset_policy::data_handle_type offset(data_handle_type p, size_t i)const; constexprconst NestedAccessor& nested_accessor()constnoexcept{return __nested_accessor;}};}
[编辑]类模板 std::linalg::layout_transpose
namespace std::linalg{template<class InputExtents>using __transpose_extents_t =/* 见说明 */;// 仅用于阐释 template<class Layout>class layout_transpose {public:using nested_layout_type = Layout; template<class Extents>struct mapping {private:using __nested_mapping_type =typename Layout::template mapping< __transpose_extents_t<Extents>>;// 仅用于阐释 __nested_mapping_type __nested_mapping;// 仅用于阐释 extents_type __extents;// 仅用于阐释 public:using extents_type = Extents;using index_type =typename extents_type::index_type;using size_type =typename extents_type::size_type;using rank_type =typename extents_type::rank_type;using layout_type = layout_transpose; constexprexplicit mapping(const __nested_mapping_type& map); constexprconst extents_type& extents()constnoexcept{return __extents;} constexpr index_type required_span_size()const{return __nested_mapping.required_span_size();} template<class Index0, class Index1>constexpr index_type operator()(Index0 ind0, Index1 ind1)const{return __nested_mapping(ind1, ind0);} constexprconst __nested_mapping_type& nested_mapping()constnoexcept{return __nested_mapping;} staticconstexprbool is_always_unique()noexcept{return __nested_mapping_type::is_always_unique();}staticconstexprbool is_always_exhaustive()noexcept{return __nested_mapping_type::is_always_exhaustive();}staticconstexprbool is_always_strided()noexcept{return __nested_mapping_type::is_always_strided();} constexprbool is_unique()const{return __nested_mapping.is_unique();}constexprbool is_exhaustive()const{return __nested_mapping.is_exhaustive();}constexprbool is_strided()const{return __nested_mapping.is_strided();} constexpr index_type stride(size_t r)const; template<class OtherExtents>friendconstexprbool operator==(const mapping& x, const mapping<OtherExtents>& y);};};}
[编辑]辅助概念和特征
namespace std::linalg{template<class T>struct __is_mdspan : false_type {};// 仅用于阐释 template<class ElementType, class Extents, class Layout, class Accessor>struct __is_mdspan<mdspan<ElementType, Extents, Layout, Accessor>>: true_type {};// 仅用于阐释 template<class T> concept __in_vector =// 仅用于阐释 __is_mdspan<T>::value&& T::rank()==1; template<class T> concept __out_vector =// 仅用于阐释 __is_mdspan<T>::value&& T::rank()==1&& is_assignable_v<typename T::reference, typename T::element_type>&& T::is_always_unique(); template<class T> concept __inout_vector =// 仅用于阐释 __is_mdspan<T>::value&& T::rank()==1&& is_assignable_v<typename T::reference, typename T::element_type>&& T::is_always_unique(); template<class T> concept __in_matrix =// 仅用于阐释 __is_mdspan<T>::value&& T::rank()==2; template<class T> concept __out_matrix =// 仅用于阐释 __is_mdspan<T>::value&& T::rank()==2&& is_assignable_v<typename T::reference, typename T::element_type>&& T::is_always_unique(); template<class T> concept __inout_matrix =// 仅用于阐释 __is_mdspan<T>::value&& T::rank()==2&& is_assignable_v<typename T::reference, typename T::element_type>&& T::is_always_unique(); template<class T> concept __possibly_packed_inout_matrix =// 仅用于阐释 __is_mdspan<T>::value&& T::rank()==2&& is_assignable_v<typename T::reference, typename T::element_type>&&(T::is_always_unique()|| is_same_v<typename T::layout_type, layout_blas_packed>); template<class T> concept __in_object =// 仅用于阐释 __is_mdspan<T>::value&&(T::rank()==1|| T::rank()==2); template<class T> concept __out_object =// 仅用于阐释 __is_mdspan<T>::value&&(T::rank()==1|| T::rank()==2)&& is_assignable_v<typename T::reference, typename T::element_type>&& T::is_always_unique(); template<class T> concept __inout_object =// 仅用于阐释 __is_mdspan<T>::value&&(T::rank()==1|| T::rank()==2)&& is_assignable_v<typename T::reference, typename T::element_type>&& T::is_always_unique();}
