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) | ||
[edit] 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); }
[edit] 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 = { }; }
[edit] 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; }; }; }
[edit] 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 }; }
[edit] 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; } }; }
[edit] 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); }; }; }
[edit] 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(); }
