linalg::StandardInnerProduct< Vec > Struct Template Reference

Canonical inner product on a fixed-size vector over a scalar field. More...

#include <inner_product.hpp>

Public Types
using	domain_type = remove_cvref_t< Vec >
	Unqualified vector type accepted by both arguments.
using	scalar_type = vector_element_t< domain_type >
	Real or complex scalar field of the vector domain.
using	codomain_type = scalar_type
	Scalar result type; equal to scalar_type.

Public Member Functions
constexpr codomain_type	operator() (const domain_type &lhs, const domain_type &rhs) const
	Pair two vectors from the same domain.

Detailed Description

template<FieldVector Vec>
struct linalg::StandardInnerProduct< Vec >

Canonical inner product on a fixed-size vector over a scalar field.

For a real vector, evaluation computes sum_i(lhs(i) * rhs(i)). For a complex vector, it computes the Hermitian inner product sum_i(conj(lhs(i)) * rhs(i)): the first argument is conjugate-linear and the second is linear. This convention makes <x, x> real and nonnegative mathematically, although its C++ return type remains the vector's scalar type (including std::complex<T>).

The vector dimension is known at compile time, the accumulation begins from the scalar's value-initialized zero, and evaluation is constexpr whenever the scalar operations are constant-evaluable.

Template Parameters

Vec	Field-vector domain. cv/ref qualification is normalized in the associated types.

Definition at line 34 of file inner_product.hpp.

Member Typedef Documentation

codomain_type

template<FieldVector Vec>

using linalg::StandardInnerProduct< Vec >::codomain_type = scalar_type

Scalar result type; equal to scalar_type.

Definition at line 40 of file inner_product.hpp.

domain_type

template<FieldVector Vec>

using linalg::StandardInnerProduct< Vec >::domain_type = remove_cvref_t<Vec>

Unqualified vector type accepted by both arguments.

Definition at line 36 of file inner_product.hpp.

scalar_type

template<FieldVector Vec>

using linalg::StandardInnerProduct< Vec >::scalar_type = vector_element_t<domain_type>

Real or complex scalar field of the vector domain.

Definition at line 38 of file inner_product.hpp.

Member Function Documentation

operator()()

template<FieldVector Vec>

constexpr codomain_type linalg::StandardInnerProduct< Vec >::operator() ( const domain_type &  lhs, const domain_type &  rhs  ) const

inlineconstexpr

Pair two vectors from the same domain.

Parameters

lhs	First argument; conjugated element-wise for a complex field.
rhs	Second argument; never conjugated.

Returns

Scalar inner-product value.

Definition at line 48 of file inner_product.hpp.

References linalg::mat_rows_v.

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The documentation for this struct was generated from the following file:

• include/akreon/linalg/operator/inner_product.hpp