Standard library header <linalg> (C++26)
From cppreference.com
This header is part of the numeric library.
Classes | |
Defined in namespace
std::linalg | |
(C++26) |
std::mdspan layout mapping policy that represents a square matrix that stores only the entries in one triangle, in a packed contiguous format (class template) |
(C++26) |
std::mdspan accessor policy whose reference represents the product of a scaling factor that is fixed and its nested std::mdspan accessor's reference (class template) |
(C++26) |
std::mdspan accessor policy whose reference represents the complex conjugate of its nested std::mdspan accessor's reference (class template) |
(C++26) |
std::mdspan layout mapping policy that swaps the rightmost two indices, extents, and strides of any unique layout mapping policy (class template) |
Tags | |
Defined in namespace
std::linalg | |
| describe the order of elements in an std::mdspan with linalg::layout_blas_packed layout (tag) | |
| specify whether algorithms and other users of a matrix should access the upper triangle or lower triangle of the matrix (tag) | |
| specify whether algorithms should access diagonal entries of the matrix (tag) | |
Functions | |
Defined in namespace
std::linalg | |
In-place transformations | |
(C++26) |
returns a new read-only std::mdspan computed by the elementwise product of the scaling factor and the corresponding elements of the given std::mdspan (function template) |
(C++26) |
returns a new read-only std::mdspan whose elements are the complex conjugates of the corresponding elements of the given std::mdspan (function template) |
(C++26) |
returns a new std::mdspan representing the transpose of the input matrix by the given std::mdspan (function template) |
(C++26) |
returns a conjugate transpose view of an object (function template) |
BLAS 1 functions | |
(C++26) |
generates plane rotation (function template) |
(C++26) |
applies plane rotation to vectors (function template) |
(C++26) |
swaps all corresponding elements of matrix or vector (function template) |
(C++26) |
overwrites matrix or vector with the result of computing the elementwise multiplication by a scalar (function template) |
(C++26) |
copies elements of one matrix or vector into another (function template) |
(C++26) |
adds vectors or matrices elementwise (function template) |
(C++26) |
returns nonconjugated dot product of two vectors (function template) |
(C++26) |
returns conjugated dot product of two vectors (function template) |
(C++26) |
returns scaled sum of squares of the vector elements (function template) |
(C++26) |
returns Euclidean norm of a vector (function template) |
(C++26) |
returns sum of absolute values of the vector elements (function template) |
(C++26) |
returns index of maximum absolute value of vector elements (function template) |
(C++26) |
returns Frobenius norm of a matrix (function template) |
(C++26) |
returns one norm of a matrix (function template) |
(C++26) |
returns infinity norm of a matrix (function template) |
BLAS 2 functions | |
(C++26) |
computes matrix-vector product (function template) |
| computes symmetric matrix-vector product (function template) | |
| computes Hermitian matrix-vector product (function template) | |
| computes triangular matrix-vector product (function template) | |
| solves a triangular linear system (function template) | |
(C++26) |
performs nonsymmetric nonconjugated rank-1 update of a matrix (function template) |
(C++26) |
performs nonsymmetric conjugated rank-1 update of a matrix (function template) |
| performs rank-1 update of a symmetric matrix (function template) | |
| performs rank-1 update of a Hermitian matrix (function template) | |
| performs rank-2 update of a symmetric matrix (function template) | |
| performs rank-2 update of a Hermitian matrix (function template) | |
BLAS 3 functions | |
(C++26) |
computes matrix-matrix product (function template) |
(C++26) |
computes symmetric matrix-matrix product (function template) |
(C++26) |
computes Hermitian matrix-matrix product (function template) |
| computes triangular matrix-matrix product (function template) | |
| performs rank-k update of a symmetric matrix (function template) | |
| performs rank-k update of a Hermitian matrix (function template) | |
| performs rank-2k update of a symmetric matrix (function template) | |
| performs rank-2k update of a Hermitian matrix (function template) | |
| solves multiple triangular linear systems (function template) | |
Synopsis
namespace std::linalg {
// storage order tags
struct column_major_t;
inline constexpr column_major_t column_major;
struct row_major_t;
inline constexpr row_major_t row_major;
// triangle tags
struct upper_triangle_t;
inline constexpr upper_triangle_t upper_triangle;
struct lower_triangle_t;
inline constexpr lower_triangle_t lower_triangle;
// diagonal tags
struct implicit_unit_diagonal_t;
inline constexpr implicit_unit_diagonal_t implicit_unit_diagonal;
struct explicit_diagonal_t;
inline constexpr explicit_diagonal_t explicit_diagonal;
// class template layout_blas_packed
template<class Triangle, class StorageOrder>
class layout_blas_packed;
// exposition-only concepts and traits
template<class T>
struct __is_mdspan; // exposition only
template<class T>
concept __in_vector = /* see description */; // exposition only
template<class T>
concept __out_vector = /* see description */; // exposition only
template<class T>
concept __inout_vector = /* see description */; // exposition only
template<class T>
concept __in_matrix = /* see description */; // exposition only
template<class T>
concept __out_matrix = /* see description */; // exposition only
template<class T>
concept __inout_matrix = /* see description */; // exposition only
template<class T>
concept __possibly_packed_inout_matrix = /* see description */; // exposition only
template<class T>
concept __in_object = /* see description */; // exposition only
template<class T>
concept __out_object = /* see description */; // exposition only
template<class T>
concept __inout_object = /* see description */; // exposition only
// scaled in-place transformation
template<class ScalingFactor, class Accessor>
class scaled_accessor;
template<class ScalingFactor,
class ElementType, class Extents, class Layout, class Accessor>
constexpr auto scaled(ScalingFactor scaling_factor,
mdspan<ElementType, Extents, Layout, Accessor> x);
// conjugated in-place transformation
template<class Accessor>
class conjugated_accessor;
template<class ElementType, class Extents, class Layout, class Accessor>
constexpr auto conjugated(mdspan<ElementType, Extents, Layout, Accessor> a);
// transposed in-place transformation
template<class Layout>
class layout_transpose;
template<class ElementType, class Extents, class Layout, class Accessor>
constexpr auto transposed(mdspan<ElementType, Extents, Layout, Accessor> a);
// conjugated transposed in-place transformation
template<class ElementType, class Extents, class Layout, class Accessor>
constexpr auto conjugate_transposed(mdspan<ElementType, Extents, Layout, Accessor> a);
// algorithms
// compute Givens rotation
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;
// apply computed Givens rotation
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);
// swap elements
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);
// multiply elements by scalar
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);
// copy elements
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);
// add elementwise
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);
// nonconjugated dot product of two vectors
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) -> /* see description */;
template<class ExecutionPolicy, __in_vector InVec1, __in_vector InVec2>
auto dot(ExecutionPolicy&& exec, InVec1 v1, InVec2 v2) -> /* see description */;
// conjugated dot product of two vectors
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) -> /* see description */;
template<class ExecutionPolicy, __in_vector InVec1, __in_vector InVec2>
auto dotc(ExecutionPolicy&& exec, InVec1 v1, InVec2 v2) -> /* see description */;
// Scaled sum of squares of a vector's elements
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);
// Euclidean norm of a vector
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) -> /* see description */;
template<class ExecutionPolicy, __in_vector InVec>
auto vector_two_norm(ExecutionPolicy&& exec, InVec v) -> /* see description */;
// sum of absolute values of vector elements
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) -> /* see description */;
template<class ExecutionPolicy, __in_vector InVec>
auto vector_abs_sum(ExecutionPolicy&& exec, InVec v) -> /* see description */;
// index of maximum absolute value of vector elements
template<__in_vector InVec>
typename InVec::extents_type vector_idx_abs_max(InVec v);
template<class ExecutionPolicy, __in_vector InVec>
typename InVec::extents_type vector_idx_abs_max(ExecutionPolicy&& exec, InVec v);
// Frobenius norm of a matrix
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) -> /* see description */;
template<class ExecutionPolicy, __in_matrix InMat>
auto matrix_frob_norm(ExecutionPolicy&& exec, InMat A) -> /* see description */;
// One norm of a matrix
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) -> /* see description */;
template<class ExecutionPolicy, __in_matrix InMat>
auto matrix_one_norm(ExecutionPolicy&& exec, InMat A) -> /* see description */;
// Infinity norm of a matrix
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) -> /* see description */;
template<class ExecutionPolicy, __in_matrix InMat>
auto matrix_inf_norm(ExecutionPolicy&& exec, InMat A) -> /* see description */;
// general matrix-vector product
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);
// symmetric matrix-vector product
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);
// Hermitian matrix-vector product
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);
// Triangular matrix-vector product
// Overwriting triangular matrix-vector product
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);
// In-place triangular matrix-vector product
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);
// Updating triangular matrix-vector product
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);
// Solve a triangular linear system, not in place
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);
// Solve a triangular linear system, in place
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);
// nonconjugated rank-1 matrix update
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);
// conjugated rank-1 matrix update
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);
// symmetric rank-1 matrix update
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);
// Hermitian rank-1 matrix update
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);
// symmetric rank-2 matrix update
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);
// Hermitian rank-2 matrix update
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);
// general matrix-matrix product
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);
// symmetric matrix-matrix product
// overwriting symmetric matrix-matrix left product
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);
// overwriting symmetric matrix-matrix right product
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);
// updating symmetric matrix-matrix left product
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);
// updating symmetric matrix-matrix right product
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);
// Hermitian matrix-matrix product
// overwriting Hermitian matrix-matrix left product
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);
// overwriting Hermitian matrix-matrix right product
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);
// updating Hermitian matrix-matrix left product
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);
// updating Hermitian matrix-matrix right product
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);
// triangular matrix-matrix product
// overwriting triangular matrix-matrix left product
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);
// overwriting triangular matrix-matrix right product
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);
// updating triangular matrix-matrix left product
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);
// updating triangular matrix-matrix right product
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);
// rank-k symmetric matrix update
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);
// rank-k Hermitian matrix update
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);
// rank-2k symmetric matrix update
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);
// rank-2k Hermitian matrix update
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);
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);
// solve multiple triangular linear systems
// with triangular matrix on the left
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);
// solve multiple triangular linear systems
// with triangular matrix on the right
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);
}
Tags
namespace std::linalg {
struct column_major_t {
explicit column_major_t() = default;
};
inline constexpr column_major_t column_major = { };
struct row_major_t {
explicit row_major_t() = default;
};
inline constexpr row_major_t row_major = { };
struct upper_triangle_t {
explicit upper_triangle_t() = default;
};
inline constexpr upper_triangle_t upper_triangle = { };
struct lower_triangle_t {
explicit lower_triangle_t() = default;
};
inline constexpr lower_triangle_t lower_triangle = { };
struct implicit_unit_diagonal_t {
explicit implicit_unit_diagonal_t() = default;
};
inline constexpr implicit_unit_diagonal_t implicit_unit_diagonal = { };
struct explicit_diagonal_t {
explicit explicit_diagonal_t() = default;
};
inline constexpr explicit_diagonal_t explicit_diagonal = { };
}
Class template std::linalg::layout_blas_packed
namespace std::linalg {
template<class Triangle, class StorageOrder>
class layout_blas_packed {
public:
using triangle_type = Triangle;
using storage_order_type = StorageOrder;
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{}; // exposition only
public:
constexpr mapping() noexcept = default;
constexpr mapping(const mapping&) noexcept = default;
constexpr mapping(const extents_type& e) noexcept;
template<class OtherExtents>
constexpr explicit(!is_convertible_v<OtherExtents, extents_type>)
mapping(const mapping<OtherExtents>& other) noexcept;
constexpr mapping& operator=(const mapping&) noexcept = default;
constexpr extents_type extents() const noexcept { return __the_extents; }
constexpr size_type required_span_size() const noexcept;
template<class Index0, class Index1>
constexpr index_type operator() (Index0 ind0, Index1 ind1) const noexcept;
static constexpr bool 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);
}
static constexpr bool is_always_exhaustive() { return true; }
static constexpr bool is_always_strided() {
return is_always_unique();
}
constexpr bool is_unique() const noexcept {
return __the_extents.extent(0) < 2;
}
constexpr bool is_exhaustive() const noexcept { return true; }
constexpr bool is_strided() const noexcept {
return __the_extents.extent(0) < 2;
}
constexpr index_type stride(rank_type) const noexcept;
template<class OtherExtents>
friend constexpr bool
operator==(const mapping&, const mapping<OtherExtents>&) noexcept;
};
};
}
Class template 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) const noexcept;
constexpr
offset_policy::data_handle_type offset(data_handle_type p, size_t i) const noexcept;
constexpr const ScalingFactor& scaling_factor() const noexcept
{ return __scaling_factor; }
constexpr const NestedAccessor& nested_accessor() const noexcept
{ return __nested_accessor; }
private:
ScalingFactor __scaling_factor; // exposition only
NestedAccessor __nested_accessor; // exposition only
};
}
Class template std::linalg::conjugated_accessor
namespace std::linalg {
template<class NestedAccessor>
class conjugated_accessor {
private:
NestedAccessor __nested_accessor; // exposition only
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;
constexpr typename offset_policy::data_handle_type
offset(data_handle_type p, size_t i) const;
constexpr const NestedAccessor& nested_accessor() const noexcept
{ return __nested_accessor; }
};
}
Class template std::linalg::layout_transpose
namespace std::linalg {
template<class InputExtents>
using __transpose_extents_t = /* see description */; // exposition only
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>>; // exposition only
__nested_mapping_type __nested_mapping; // exposition only
extents_type __extents; // exposition only
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;
constexpr explicit mapping(const __nested_mapping_type& map);
constexpr const extents_type& extents() const noexcept { 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); }
constexpr const __nested_mapping_type& nested_mapping() const noexcept
{ return __nested_mapping; }
static constexpr bool is_always_unique() noexcept
{ return __nested_mapping_type::is_always_unique(); }
static constexpr bool is_always_exhaustive() noexcept
{ return __nested_mapping_type::is_always_exhaustive(); }
static constexpr bool is_always_strided() noexcept
{ return __nested_mapping_type::is_always_strided(); }
constexpr bool is_unique() const
{ return __nested_mapping.is_unique(); }
constexpr bool is_exhaustive() const
{ return __nested_mapping.is_exhaustive(); }
constexpr bool is_strided() const
{ return __nested_mapping.is_strided(); }
constexpr index_type stride(size_t r) const;
template<class OtherExtents>
friend constexpr bool
operator==(const mapping& x, const mapping<OtherExtents>& y);
};
};
}
Helper concepts and traits
namespace std::linalg {
template<class T>
struct __is_mdspan : false_type {}; // exposition only
template<class ElementType, class Extents, class Layout, class Accessor>
struct __is_mdspan<mdspan<ElementType, Extents, Layout, Accessor>>
: true_type {}; // exposition only
template<class T>
concept __in_vector = // exposition only
__is_mdspan<T>::value &&
T::rank() == 1;
template<class T>
concept __out_vector = // exposition only
__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 = // exposition only
__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 = // exposition only
__is_mdspan<T>::value &&
T::rank() == 2;
template<class T>
concept __out_matrix = // exposition only
__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 = // exposition only
__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 = // exposition only
__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 = // exposition only
__is_mdspan<T>::value &&
(T::rank() == 1 || T::rank() == 2);
template<class T>
concept __out_object = // exposition only
__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 = // exposition only
__is_mdspan<T>::value &&
(T::rank() == 1 || T::rank() == 2) &&
is_assignable_v<typename T::reference, typename T::element_type> &&
T::is_always_unique();
}