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 tagsstruct column_major_t;inlineconstexpr column_major_t column_major;struct row_major_t;inlineconstexpr row_major_t row_major; // triangle tagsstruct upper_triangle_t;inlineconstexpr upper_triangle_t upper_triangle;struct lower_triangle_t;inlineconstexpr lower_triangle_t lower_triangle; // diagonal tagsstruct implicit_unit_diagonal_t;inlineconstexpr implicit_unit_diagonal_t implicit_unit_diagonal;struct explicit_diagonal_t;inlineconstexpr explicit_diagonal_t explicit_diagonal; // class template layout_blas_packedtemplate<class Triangle, class StorageOrder>class layout_blas_packed; // exposition-only concepts and traitstemplate<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 transformationtemplate<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); // conjugated in-place transformationtemplate<class Accessor>class conjugated_accessor; template<class ElementType, class Extents, class Layout, class Accessor>constexprauto conjugated(mdspan<ElementType, Extents, Layout, Accessor> a); // transposed in-place transformationtemplate<class Layout>class layout_transpose; template<class ElementType, class Extents, class Layout, class Accessor>constexprauto transposed(mdspan<ElementType, Extents, Layout, Accessor> a); // conjugated transposed in-place transformationtemplate<class ElementType, class Extents, class Layout, class Accessor>constexprauto 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 rotationtemplate<__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 elementstemplate<__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 scalartemplate<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 elementstemplate<__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 elementwisetemplate<__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 vectorstemplate<__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 vectorstemplate<__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 elementstemplate<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 vectortemplate<__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 elementstemplate<__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 elementstemplate<__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 matrixtemplate<__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 matrixtemplate<__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 matrixtemplate<__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 producttemplate<__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 producttemplate<__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 producttemplate<__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 producttemplate<__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 producttemplate<__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 producttemplate<__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 placetemplate<__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 placetemplate<__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 updatetemplate<__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 updatetemplate<__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 updatetemplate<__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 updatetemplate<__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 updatetemplate<__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 updatetemplate<__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 producttemplate<__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 producttemplate<__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 producttemplate<__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 producttemplate<__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 producttemplate<__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 producttemplate<__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 producttemplate<__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 producttemplate<__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 producttemplate<__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 producttemplate<__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 producttemplate<__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 producttemplate<__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 producttemplate<__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 updatetemplate<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 updatetemplate<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 updatetemplate<__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 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); // solve multiple triangular linear systems// with triangular matrix on the lefttemplate<__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 righttemplate<__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;};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 ={};}
[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>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; };};}
[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)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;// 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; constexprtypename offset_policy::data_handle_type offset(data_handle_type p, size_t i)const; constexprconst NestedAccessor& nested_accessor()constnoexcept{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; 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);};};}
[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();}
