MultiArrayComplex.h File Reference

#include "MultiArray.h"
#include <Eigen/Dense>
#include <boost/serialization/complex.hpp>
#include <complex>

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Namespaces
namespace	boost
namespace	boost::json
namespace	cppqedutils
	Namespace alias for Boost.Hana, used for compile-time sequences and heterogeneous containers.

Concepts
concept	cppqedutils::scalar
	Concept satisfied by scalar numeric types usable as operator coefficients: any type convertible to double or dcomp.

Typedefs
typedef std::complex< double >	dcomp
	Double-precision complex number. Named to resemble a built-in type rather than a class.
using	CMatrix = Eigen::MatrixX< dcomp >
	Dense complex matrix type (Eigen dynamic-size).
using	CVector = Eigen::VectorX< dcomp >
	Dense complex vector type (Eigen dynamic-size).

Functions
bool	isNonZero (dcomp c)
	Returns true if either the real or imaginary part of c is non-zero.
bool	hasRealPart (dcomp c)
	Returns true if the real part of c is non-zero.
bool	hasImagPart (dcomp c)
	Returns true if the imaginary part of c is non-zero.
bool	absCompare (dcomp c1, dcomp c2)
	Comparator by absolute value, for use with sorting algorithms.
bool	realCompare (dcomp c1, dcomp c2)
	Comparator by real part, for use with sorting algorithms.
auto	sqr (auto &&x) noexcept(noexcept(x *x)) -> decltype(x *x)
	Generic square: x*x. Return type is deduced; noexcept and SFINAE are propagated.
double	relativeDeviation (const auto &a, const auto &b)
	Relative deviation between two values: |a-b| / (|a|+|b|). Returns 0 if both are zero.
double	sqrAbs (dcomp v)
	Squared absolute value of a complex number: |v|^2 = re^2 + im^2, computed as such (std::norm), not as the square of the rounded std::abs.
dcomp	textbookProduct (dcomp a, dcomp b)
	Complex product by the textbook formula \((a+ib)(c+id)=(ac-bd)+i(ad+bc)\), for hot loops.
template<class T >
void	boost::json::tag_invoke (value_from_tag, value &jv, const std::complex< T > &c)
	Boost.JSON serialization for std::complex<T>: emits a two-element JSON array [re, im].
template<class T >
std::complex< T >	boost::json::tag_invoke (value_to_tag< std::complex< T > >, const value &jv)
	Boost.JSON deserialization for std::complex<T>: reads from a two-element JSON array [re, im].
template<size_t RANK>
auto	cppqedutils::vectorize (MultiArray< dcomp, RANK > &ma)
	Maps a mutable MultiArray<dcomp,RANK> to an Eigen column vector (no data copy).
template<size_t RANK>
auto	cppqedutils::vectorize (const MultiArray< dcomp, RANK > &ma)
	Maps a const MultiArray<dcomp,RANK> to a const Eigen column vector (no data copy).
template<size_t TWO_TIMES_RANK> requires ( !(TWO_TIMES_RANK%2) )
Extents< TWO_TIMES_RANK/2 >	cppqedutils::halveExtents (Extents< TWO_TIMES_RANK > extents)
	Extracts the first half of a rank-2R extent array, verifying that both halves are equal.
template<size_t TWO_TIMES_RANK>
auto	cppqedutils::matricize (MultiArray< dcomp, TWO_TIMES_RANK > &ma)
	Maps a mutable rank-2R MultiArray<dcomp> to an Eigen square matrix (no data copy). The matrix dimension is prod(extents[0..R-1]); requires equal first and second half extents.
template<size_t TWO_TIMES_RANK>
auto	cppqedutils::matricize (const MultiArray< dcomp, TWO_TIMES_RANK > &ma)
	Maps a const rank-2R MultiArray<dcomp> to a const Eigen square matrix (no data copy).
template<size_t RANK1, size_t RANK2>
auto	cppqedutils::directProduct (const MultiArray< dcomp, RANK1 > &m1, const MultiArray< dcomp, RANK2 > &m2, std::function< dcomp(dcomp, dcomp)> func=std::multiplies< dcomp >{})
	Tensor (outer) product of two complex multi-arrays.
template<size_t RANK>
MultiArray< dcomp, RANK > &	cppqedutils::conj (MultiArray< dcomp, RANK > &ma)
	In-place complex conjugation of all elements of ma.
template<size_t RANK>
double	cppqedutils::frobeniusNormSqr (const MultiArray< dcomp, RANK > &ma)
	Squared Frobenius norm: \(\sum_{i}|a_i|^2\). Returns 0 for an empty array.
template<size_t RANK>
double	cppqedutils::frobeniusNorm (const MultiArray< dcomp, RANK > &ma)
	Frobenius norm: \(\sqrt{\sum_{i}|a_i|^2}\).
template<size_t TWO_TIMES_RANK>
void	cppqedutils::hermitianConjugateSelf (MultiArrayView< dcomp, TWO_TIMES_RANK > mav)
	In-place Hermitian conjugation of a rank-2R matrix view mav.
template<size_t TWO_TIMES_RANK>
void	cppqedutils::twoTimesRealPartOfSelf (MultiArrayView< dcomp, TWO_TIMES_RANK > mav)
	In-place replacement of a rank-2R matrix view mav with M + M† (twice its Hermitian part).

Typedef Documentation

CMatrix

using CMatrix = Eigen::MatrixX<dcomp>

Dense complex matrix type (Eigen dynamic-size).

CVector

using CVector = Eigen::VectorX<dcomp>

Dense complex vector type (Eigen dynamic-size).

dcomp

typedef std::complex<double> dcomp

Double-precision complex number. Named to resemble a built-in type rather than a class.

Function Documentation

absCompare()

bool absCompare ( dcomp  c1, dcomp  c2  )

inline

Comparator by absolute value, for use with sorting algorithms.

hasImagPart()

bool hasImagPart ( dcomp  c )

inline

Returns true if the imaginary part of c is non-zero.

hasRealPart()

bool hasRealPart ( dcomp  c )

inline

Returns true if the real part of c is non-zero.

isNonZero()

bool isNonZero ( dcomp  c )

inline

Returns true if either the real or imaginary part of c is non-zero.

realCompare()

bool realCompare ( dcomp  c1, dcomp  c2  )

inline

Comparator by real part, for use with sorting algorithms.

relativeDeviation()

double relativeDeviation	(	const auto &	a,
		const auto &	b
	)

Relative deviation between two values: |a-b| / (|a|+|b|). Returns 0 if both are zero.

sqr()

auto sqr ( auto &&  x ) -> decltype(x*x)

noexcept

Generic square: x*x. Return type is deduced; noexcept and SFINAE are propagated.

See also

https://stackoverflow.com/a/64849248/1171157

sqrAbs()

double sqrAbs ( dcomp  v )

inline

Squared absolute value of a complex number: |v|^2 = re^2 + im^2, computed as such (std::norm), not as the square of the rounded std::abs.

textbookProduct()

dcomp textbookProduct ( dcomp  a, dcomp  b  )

inline

Complex product by the textbook formula \((a+ib)(c+id)=(ac-bd)+i(ad+bc)\), for hot loops.

By default, GCC and Clang multiply std::complex according to C99 Annex G: when both parts of the textbook result are NaN, a library call (__muldc3) tries to recover an infinite result. That check keeps loops from vectorizing. This function omits the recovery, so its speed does not depend on -fcx-limited-range. Otherwise it evaluates the same expression as the default: the two differ only where an infinite operand makes both parts NaN.

See also

Performance of MultiDiagonal for what the check costs.