Definition of Matrix types. More...

#include <type_traits>
#include <sstream>
#include "plumbing/defs.h"
#include "datatypes/cmplx.h"
#include "datatypes/array.h"
#include "datatypes/diagonal_matrix.h"
#include "datatypes/matrix_linalg.h"

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Classes
struct	eigen_result< M >
	type to store the return value of eigen_hermitean(): {E, U} where E is nxn DiagonalMatrix containing eigenvalues and U nxn unitary matrix, with eigenvector columns More...

class	Matrix< n, m, T >
	\( n \times m \) Matrix class which defines matrix operations. More...

class	Matrix_t< n, m, T, Mtype >
	The main \( n \times m \) matrix type template Matrix_t. This is a base class type for "useful" types which are derived from this. More...

struct	svd_result< M >
	type to store the return combo of svd: {U, D, V} where U and V are nxn unitary / orthogonal, and D is real diagonal singular value matrices. More...

Namespaces
namespace	hila
	Invert diagonal + const. matrix using Sherman-Morrison formula.

Typedefs
template<int n, typename T >
using	RowVector = Matrix< 1, n, T >
	RowVector is a 1-row Matrix.

template<int n, typename T >
using	SquareMatrix = Matrix< n, n, T >
	Square matrix is defined as alias with special case of Matrix<n,n,T>

template<int n, typename T >
using	Vector = Matrix< n, 1, T >
	Vector is defined as 1-column Matrix.

Functions
template<typename Mtype , std::enable_if_t< Mtype::is_matrix(), int > = 0>
auto	abs (const Mtype &arg)
	Return absolute value Matrix or Vector.

template<typename Mtype , std::enable_if_t< Mtype::is_matrix(), int > = 0>
auto	adjoint (const Mtype &arg)
	Return adjoint Matrix.

template<typename Mtype , std::enable_if_t< Mtype::is_matrix(), int > = 0>
auto	conj (const Mtype &arg)
	Return conjugate Matrix or Vector.

template<typename Mtype , std::enable_if_t< Mtype::is_matrix(), int > = 0>
auto	dagger (const Mtype &arg)
	Return dagger of Matrix.

template<typename Mtype , std::enable_if_t< Mtype::is_matrix(), int > = 0>
auto	imag (const Mtype &arg)
	Return imaginary of Matrix or Vector.

template<typename Mtype1 , typename Mtype2 , std::enable_if_t< Mtype1::is_matrix() &&Mtype2::is_matrix(), int > = 0>
auto	mul_trace (const Mtype1 &a, const Mtype2 &b)
	Returns trace of product of two matrices.

template<typename Mt , std::enable_if_t< Mt::is_matrix(), int > = 0>
auto	norm (const Mt &rhs)
	Returns vector norm of Matrix.

template<typename Mt , std::enable_if_t< Mt::is_matrix() &&Mt::rows()==Mt::columns(), int > = 0>
Mt	operator* (const Mt &a, const Mt &b)
	Multiplication operator Square Matrix * Square Matrix.

template<typename Mtype1 , typename Mtype2 , std::enable_if_t< Mtype1::is_matrix() &&Mtype2::is_matrix(), int > = 0, typename Rtype = hila::mat_x_mat_type<Mtype1, Mtype2>, std::enable_if_t< std::is_same< Mtype1, Rtype >::value, int > = 0>
Rtype	operator+ (Mtype1 a, const Mtype2 &b)
	Real micro-optimization Matrix + Matrix - no extra creation of variable and copy.

template<int n, int m, typename T , typename MT >
std::string	hila::prettyprint (const Matrix_t< n, m, T, MT > &A, int prec=8)
	Formats Matrix_t object in a human readable way.

template<typename Mtype , std::enable_if_t< Mtype::is_matrix(), int > = 0>
auto	real (const Mtype &arg)
	Return real of Matrix or Vector.

template<typename Mt , std::enable_if_t< Mt::is_matrix(), int > = 0>
auto	squarenorm (const Mt &rhs)
	Returns square norm of Matrix.

template<int n, int m, typename T , typename MT >
std::string	hila::to_string (const Matrix_t< n, m, T, MT > &A, int prec=8, char separator=' ')
	Converts Matrix_t object to string.

template<typename Mtype , std::enable_if_t< Mtype::is_matrix(), int > = 0>
auto	trace (const Mtype &arg)
	Return trace of square Matrix.

template<typename Mtype , std::enable_if_t< Mtype::is_matrix(), int > = 0>
auto	transpose (const Mtype &arg)
	Return transposed Matrix or Vector.

Detailed Description

Definition of Matrix types.

This file contains base matrix type Matrix_t which defines all general matrix type operations Matrix types are Matrix, Vector, RowVector, SquareMatrix of which Matrix is defined as a class and the rest are special cases of the Matrix class.

Definition in file matrix.h.

Function Documentation

◆ abs()

template<typename Mtype , std::enable_if_t< Mtype::is_matrix(), int > = 0>

auto abs ( const Mtype & arg )

inline

Return absolute value Matrix or Vector.

Wrapper around Matrix::abs

Can be called as:

Matrix<n,m,MyType> M,M_abs;

M_abs = abs(M);

Matrix

Matrix class which defines matrix operations.

Definition matrix.h:1679

abs

T abs(const Complex< T > &a)

Return absolute value of Complex number.

Definition cmplx.h:1322

Template Parameters

Mtype Matrix type

Parameters

arg	Object to compute absolute value of

Returns: auto Mtype absolute value Matrix or Vector

Definition at line 1960 of file matrix.h.

◆ adjoint()

template<typename Mtype , std::enable_if_t< Mtype::is_matrix(), int > = 0>

auto adjoint ( const Mtype & arg )

inline

Return adjoint Matrix.

Wrapper around Matrix::adjoint

Can be called as:

Matrix<n,m,MyType> M,M_adjoint;

M_conjugate = adjoint(M);

Template Parameters

Mtype Matrix type

Parameters

arg	Object to compute adjoint of

Returns: auto Mtype adjoint matrix

Definition at line 1924 of file matrix.h.

◆ conj()

template<typename Mtype , std::enable_if_t< Mtype::is_matrix(), int > = 0>

auto conj ( const Mtype & arg )

inline

Return conjugate Matrix or Vector.

Wrapper around Matrix::conj

Can be called as:

Matrix<n,m,MyType> M,M_conjugate;

M_conjugate = conj(M);

conj

Array< n, m, T > conj(const Array< n, m, T > &arg)

Return conjugate Array.

Definition array.h:648

Template Parameters

Mtype Matrix type

Parameters

arg	Object to be conjugated

Returns: auto Mtype conjugated matrix

Definition at line 1904 of file matrix.h.

◆ dagger()

template<typename Mtype , std::enable_if_t< Mtype::is_matrix(), int > = 0>

auto dagger ( const Mtype & arg )

inline

Return dagger of Matrix.

Wrapper around Matrix::adjoint

Same as adjoint

Template Parameters

Mtype Matrix type

Parameters

arg	Object to compute dagger of

Returns: auto Mtype dagger matrix

Definition at line 1940 of file matrix.h.

◆ imag()

template<typename Mtype , std::enable_if_t< Mtype::is_matrix(), int > = 0>

auto imag ( const Mtype & arg )

inline

Return imaginary of Matrix or Vector.

Wrapper around Matrix::imag

Can be called as:

Matrix<n,m,MyType> M,M_imag;

M_imag = imag(M);

imag

Array< n, m, hila::arithmetic_type< T > > imag(const Array< n, m, T > &arg)

Return imaginary part of Array.

Definition array.h:676

Template Parameters

Mtype Matrix type

Parameters

arg	Object to compute imag part of

Returns: auto Mtype imag part of arg

Definition at line 2021 of file matrix.h.

◆ mul_trace()

template<typename Mtype1 , typename Mtype2 , std::enable_if_t< Mtype1::is_matrix() &&Mtype2::is_matrix(), int > = 0>

auto mul_trace	(	const Mtype1 &	a,
		const Mtype2 &	b
	)

inline

Returns trace of product of two matrices.

Wrapper around Matrix::mul_trace in the form

mul_trace(a,b) // -> a.mul_trace(b)

mul_trace

auto mul_trace(const Mtype1 &a, const Mtype2 &b)

Returns trace of product of two matrices.

Definition matrix.h:2528

Template Parameters

Mtype1	Matrix type for a
Mtype2	Matrix type for b

Parameters

a	Left Matrix
b	Right Matrix

Returns: auto Resulting trace

Definition at line 2528 of file matrix.h.

◆ norm()

template<typename Mt , std::enable_if_t< Mt::is_matrix(), int > = 0>

auto norm ( const Mt & rhs )

inline

Returns vector norm of Matrix.

Wrapper around Matrix::norm - sqrt of sum of squared elements

Template Parameters

Mt	Matrix type

Parameters

rhs	Matrix to compute norm of

Returns: auto

Definition at line 2692 of file matrix.h.

◆ real()

template<typename Mtype , std::enable_if_t< Mtype::is_matrix(), int > = 0>

auto real ( const Mtype & arg )

inline

Return real of Matrix or Vector.

Wrapper around Matrix::real

Can be called as:

Matrix<n,m,MyType> M,M_real;

M_real = real(M);

real

Array< n, m, hila::arithmetic_type< T > > real(const Array< n, m, T > &arg)

Return real part of Array.

Definition array.h:662

Template Parameters

Mtype Matrix type

Parameters

arg	Object to compute real part of

Returns: auto Mtype real part of arg

Definition at line 2001 of file matrix.h.

◆ squarenorm()

template<typename Mt , std::enable_if_t< Mt::is_matrix(), int > = 0>

auto squarenorm ( const Mt & rhs )

inline

Returns square norm of Matrix.

Wrapper around Matrix::squarenorm - sum of squared elements

Can be called as:

Matrix<n,m,MyType> M;

auto a = squarenorm(M);

squarenorm

hila::arithmetic_type< T > squarenorm(const Array< n, m, T > &rhs)

Return square norm of Array.

Definition array.h:957

Template Parameters

Mt	Matrix type

Parameters

rhs	Matrix to compute square norm of

Returns: auto

Definition at line 2678 of file matrix.h.

◆ trace()

template<typename Mtype , std::enable_if_t< Mtype::is_matrix(), int > = 0>

auto trace ( const Mtype & arg )

inline

Return trace of square Matrix.

Wrapper around Matrix::trace

Can be called as:

Matrix<n,m,MyType> M;
MyType T;
T = trace(M);

Template Parameters

Mtype Matrix type

Parameters

arg	Object to compute trace of

Returns: auto Trace of Matrix

Definition at line 1981 of file matrix.h.

◆ transpose()

template<typename Mtype , std::enable_if_t< Mtype::is_matrix(), int > = 0>

auto transpose ( const Mtype & arg )

inline

Return transposed Matrix or Vector.

Wrapper around Matrix::transpose

Can be called as:

Matrix<n,m,MyType> M,M_transposed;

M_transposed = transpose(M);

Template Parameters

Mtype Matrix type

Parameters

arg	Object to be transposed

Returns: auto Mtype transposed matrix

Definition at line 1884 of file matrix.h.

Classes

Namespaces

Typedefs

Functions

Detailed Description

Function Documentation

◆ abs()

◆ adjoint()

◆ conj()

◆ dagger()

◆ imag()

◆ mul_trace()

◆ norm()

◆ real()

◆ squarenorm()

◆ trace()

◆ transpose()