28.9 Basic linear algebra algorithms [linalg]
namespace std::linalg {
struct column_major_t;
inline constexpr column_major_t column_major;
struct row_major_t;
inline constexpr row_major_t row_major;
struct upper_triangle_t;
inline constexpr upper_triangle_t upper_triangle;
struct lower_triangle_t;
inline constexpr lower_triangle_t lower_triangle;
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;
template<class Triangle, class StorageOrder>
class layout_blas_packed;
template<class T>
constexpr bool is-mdspan = see below;
template<class T>
concept in-vector = see below;
template<class T>
concept out-vector = see below;
template<class T>
concept inout-vector = see below;
template<class T>
concept in-matrix = see below;
template<class T>
concept out-matrix = see below;
template<class T>
concept inout-matrix = see below;
template<class T>
concept possibly-packed-inout-matrix = see below;
template<class T>
concept in-object = see below;
template<class T>
concept out-object = see below;
template<class T>
concept inout-object = see below;
template<class ScalingFactor, class NestedAccessor>
class scaled_accessor;
template<class ScalingFactor,
class ElementType, class Extents, class Layout, class Accessor>
constexpr auto scaled(ScalingFactor alpha, mdspan<ElementType, Extents, Layout, Accessor> x);
template<class NestedAccessor>
class conjugated_accessor;
template<class ElementType, class Extents, class Layout, class Accessor>
constexpr auto conjugated(mdspan<ElementType, Extents, Layout, Accessor> a);
template<class Layout>
class layout_transpose;
template<class ElementType, class Extents, class Layout, class Accessor>
constexpr auto transposed(mdspan<ElementType, Extents, Layout, Accessor> a);
template<class ElementType, class Extents, class Layout, class Accessor>
constexpr auto conjugate_transposed(mdspan<ElementType, Extents, Layout, Accessor> a);
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;
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);
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);
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);
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);
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);
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);
template<class ExecutionPolicy, in-vector InVec1, in-vector InVec2>
auto dot(ExecutionPolicy&& exec,
InVec1 v1, InVec2 v2);
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);
template<class ExecutionPolicy, in-vector InVec1, in-vector InVec2>
auto dotc(ExecutionPolicy&& exec,
InVec1 v1, InVec2 v2);
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);
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);
template<class ExecutionPolicy, in-vector InVec>
auto vector_two_norm(ExecutionPolicy&& exec, InVec v);
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);
template<class ExecutionPolicy, in-vector InVec>
auto vector_abs_sum(ExecutionPolicy&& exec, InVec v);
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);
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);
template<class ExecutionPolicy, in-matrix InMat>
auto matrix_frob_norm(ExecutionPolicy&& exec, InMat A);
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);
template<class ExecutionPolicy, in-matrix InMat>
auto matrix_one_norm(ExecutionPolicy&& exec, InMat A);
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);
template<class ExecutionPolicy, in-matrix InMat>
auto matrix_inf_norm(ExecutionPolicy&& exec, InMat A);
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);
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);
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);
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);
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);
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);
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);
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);
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);
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);
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);
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 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);
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<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);
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);
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);
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);
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);
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, in-matrix InMat2, class Triangle, out-matrix OutMat>
void symmetric_matrix_product(InMat1 A, InMat2 B, 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 A, InMat2 B, Triangle t, OutMat C);
template<in-matrix InMat1, in-matrix InMat2, class Triangle, out-matrix OutMat>
void hermitian_matrix_product(InMat1 A, InMat2 B, 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 A, InMat2 B, Triangle t, OutMat C);
template<in-matrix InMat1, in-matrix InMat2, class Triangle, class DiagonalStorage,
out-matrix OutMat>
void triangular_matrix_product(InMat1 A, InMat2 B, 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 A, InMat2 B, Triangle t, DiagonalStorage d, OutMat C);
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);
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);
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);
template<in-matrix InMat1, in-matrix InMat2, class Triangle, in-matrix InMat3,
out-matrix OutMat>
void symmetric_matrix_product(InMat1 A, InMat2 B, 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 A, InMat2 B, Triangle t, InMat3 E, OutMat C);
template<in-matrix InMat1, in-matrix InMat2, class Triangle, in-matrix InMat3,
out-matrix OutMat>
void hermitian_matrix_product(InMat1 A, InMat2 B, 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 A, InMat2 B, Triangle t, InMat3 E, OutMat C);
template<in-matrix InMat1, in-matrix InMat2, class Triangle, class DiagonalStorage,
in-matrix InMat3, out-matrix OutMat>
void triangular_matrix_product(InMat1 A, InMat2 B, 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 A, InMat2 B, Triangle t, DiagonalStorage d, InMat3 E,
OutMat C);
template<in-matrix InMat, class Triangle, class DiagonalStorage, inout-matrix InOutMat>
void triangular_matrix_left_product(InMat A, Triangle t, DiagonalStorage d, InOutMat C);
template<class ExecutionPolicy,
in-matrix InMat, class Triangle, class DiagonalStorage, inout-matrix InOutMat>
void triangular_matrix_left_product(ExecutionPolicy&& exec,
InMat A, Triangle t, DiagonalStorage d, InOutMat C);
template<in-matrix InMat, class Triangle, class DiagonalStorage, inout-matrix InOutMat>
void triangular_matrix_right_product(InMat A, Triangle t, DiagonalStorage d, InOutMat C);
template<class ExecutionPolicy,
in-matrix InMat, class Triangle, class DiagonalStorage, inout-matrix InOutMat>
void triangular_matrix_right_product(ExecutionPolicy&& exec,
InMat A, Triangle t, DiagonalStorage d, InOutMat C);
template<class Scalar, in-matrix InMat, possibly-packed-inout-matrix InOutMat, class Triangle>
void symmetric_matrix_rank_k_update(Scalar alpha, InMat A, InOutMat C, Triangle t);
template<class ExecutionPolicy, class Scalar,
in-matrix InMat, possibly-packed-inout-matrix InOutMat, class Triangle>
void symmetric_matrix_rank_k_update(ExecutionPolicy&& exec,
Scalar alpha, InMat A, InOutMat C, Triangle t);
template<in-matrix InMat, possibly-packed-inout-matrix InOutMat, class Triangle>
void symmetric_matrix_rank_k_update(InMat A, InOutMat C, Triangle t);
template<class ExecutionPolicy,
in-matrix InMat, possibly-packed-inout-matrix InOutMat, class Triangle>
void symmetric_matrix_rank_k_update(ExecutionPolicy&& exec,
InMat A, InOutMat C, Triangle t);
template<class Scalar, in-matrix InMat, possibly-packed-inout-matrix InOutMat, class Triangle>
void hermitian_matrix_rank_k_update(Scalar alpha, InMat A, InOutMat C, Triangle t);
template<class ExecutionPolicy,
class Scalar, in-matrix InMat, possibly-packed-inout-matrix InOutMat, class Triangle>
void hermitian_matrix_rank_k_update(ExecutionPolicy&& exec,
Scalar alpha, InMat A, InOutMat C, Triangle t);
template<in-matrix InMat, possibly-packed-inout-matrix InOutMat, class Triangle>
void hermitian_matrix_rank_k_update(InMat A, InOutMat C, Triangle t);
template<class ExecutionPolicy,
in-matrix InMat, possibly-packed-inout-matrix InOutMat, class Triangle>
void hermitian_matrix_rank_k_update(ExecutionPolicy&& exec,
InMat A, InOutMat C, Triangle t);
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);
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);
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,
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,
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,
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 InMat, class Triangle, class DiagonalStorage,
inout-matrix InOutMat, class BinaryDivideOp>
void triangular_matrix_matrix_left_solve(InMat A, Triangle t, DiagonalStorage d,
InOutMat B, BinaryDivideOp divide);
template<class ExecutionPolicy,
in-matrix InMat, class Triangle, class DiagonalStorage,
inout-matrix InOutMat, class BinaryDivideOp>
void triangular_matrix_matrix_left_solve(ExecutionPolicy&& exec,
InMat A, Triangle t, DiagonalStorage d,
InOutMat B, BinaryDivideOp divide);
template<in-matrix InMat, class Triangle, class DiagonalStorage, inout-matrix InOutMat>
void triangular_matrix_matrix_left_solve(InMat A, Triangle t, DiagonalStorage d,
InOutMat B);
template<class ExecutionPolicy,
in-matrix InMat, class Triangle, class DiagonalStorage, inout-matrix InOutMat>
void triangular_matrix_matrix_left_solve(ExecutionPolicy&& exec,
InMat A, Triangle t, DiagonalStorage d,
InOutMat B);
template<in-matrix InMat, class Triangle, class DiagonalStorage,
inout-matrix InOutMat, class BinaryDivideOp>
void triangular_matrix_matrix_right_solve(InMat A, Triangle t, DiagonalStorage d,
InOutMat B, BinaryDivideOp divide);
template<class ExecutionPolicy,
in-matrix InMat, class Triangle, class DiagonalStorage,
inout-matrix InOutMat, class BinaryDivideOp>
void triangular_matrix_matrix_right_solve(ExecutionPolicy&& exec,
InMat A, Triangle t, DiagonalStorage d,
InOutMat B, BinaryDivideOp divide);
template<in-matrix InMat, class Triangle, class DiagonalStorage, inout-matrix InOutMat>
void triangular_matrix_matrix_right_solve(InMat A, Triangle t, DiagonalStorage d,
InOutMat B);
template<class ExecutionPolicy,
in-matrix InMat, class Triangle, class DiagonalStorage, inout-matrix InOutMat>
void triangular_matrix_matrix_right_solve(ExecutionPolicy&& exec,
InMat A, Triangle t, DiagonalStorage d,
InOutMat B);
}