linalg_ops.hpp File Reference

#include "operator/inner_product.hpp"
#include "operator/operator_traits.hpp"
#include "vector/vector.hpp"

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Namespaces
namespace	linalg

Functions
template<VectorContainer Vec>
constexpr auto	linalg::add (const Vec &A, const Vec &B)
	add two vectors together to get a third
template<VectorContainer Vec>
constexpr auto	linalg::operator+ (const Vec &A, const Vec &B)
	operator overload for add
template<MatrixContainer Mat>
constexpr auto	linalg::add (const Mat &A, const Mat &B)
	Add two shape-compatible matrices element by element.
template<MatrixContainer Mat>
constexpr auto	linalg::operator+ (const Mat &A, const Mat &B)
	Matrix addition operator delegating to add.
template<VectorContainer Vec, Field Alpha>
constexpr auto	linalg::scalar_multiplication (const Alpha &alpha, const Vec &A)
	multiply a vector A with a scalar alpha
template<VectorContainer Vec, Field Alpha>
constexpr auto	linalg::operator* (const Alpha &alpha, const Vec &A)
	operator overload for scalar multiplication
template<MatrixContainer Mat, Field Alpha>
constexpr auto	linalg::scalar_multiplication (const Alpha &alpha, const Mat &A)
	Multiply every matrix entry by a field scalar.
template<MatrixContainer Mat, Field Alpha>
constexpr auto	linalg::operator* (const Alpha &alpha, const Mat &A)
	Left scalar-matrix multiplication operator.
template<VectorContainer Vec>
constexpr auto	linalg::operator- (const Vec &A, const Vec &B)
	operator overload for subtraction
template<MatrixContainer Mat>
constexpr auto	linalg::operator- (const Mat &A, const Mat &B)
	Subtract two matrices as A + (-1) * B.
template<FieldVector Vec>
constexpr auto	linalg::transpose (const Vec &x)
	tranpose of a vector
template<ComplexVector Vec>
constexpr auto	linalg::conjugate (const Vec &x)
	conjugate a vector
template<FieldVector Vec> requires (vector_dim_v<Vec> == 3)
constexpr auto	linalg::cross (const Vec &x, const Vec &y)
	cross product between x x y = Z
template<FieldVector Vec> requires (vector_dim_v<Vec> > 0)
constexpr bool	linalg::all_zero (const Vec &x)
	simple function that checks if a vector contains only zeros (hence spans nullspace)
template<std::size_t idx, FieldVector Vec> requires (vector_dim_v<Vec> > 0 && idx < vector_dim_v<Vec>)
constexpr auto	linalg::splice (const Vec &x)
	splice operator
template<MatrixContainer MatA, MatrixContainer MatB> requires (MatMulCompatible<MatA, MatB>)
constexpr auto	linalg::outer_product (const MatA &A, const MatB &B)
	Multiply matrix-shaped column and row operands as an outer product.
template<MatrixContainer Mat>
constexpr auto	linalg::transpose (const Mat &A)
	transpose of a matrix
template<SquareMatrix Mat> requires (mat_rows_v<Mat> > 0)
constexpr auto	linalg::trace (const Mat &A)
	trace of a matrix
template<MatrixContainer Mat> requires (Complex<matrix_scalar_t<Mat>>)
constexpr auto	linalg::conjugate_transpose (const Mat &A)
	conjugate transpose of a matrix
template<MatrixContainer MatA, MatrixContainer MatB> requires (MatMulCompatible<MatA, MatB>)
constexpr auto	linalg::operator* (const MatA &A, const MatB &B)
	Multiply compatible matrices with the standard row-column product.
template<MatrixContainer Mat, VectorContainer Vec> requires (MatVecCompatible<Mat, Vec>)
constexpr auto	linalg::operator* (const Mat &A, const Vec &X)
	Apply a compatible matrix to a vector.
template<VectorContainer Vec> requires (vector_dim_v<Vec> > 0)
constexpr auto	linalg::min (const Vec &x)
	min element
template<VectorContainer Vec> requires (vector_dim_v<Vec> > 0)
constexpr auto	linalg::max (const Vec &x)
	max element
template<VectorContainer Vec> requires (vector_dim_v<Vec> > 0)
constexpr std::size_t	linalg::arg_min (const Vec &x)
	min element
template<VectorContainer Vec> requires (vector_dim_v<Vec> > 0)
constexpr std::size_t	linalg::arg_max (const Vec &x)
	max element