A class implementing complex numbers for ARTS. More...

#include <complex>
#include "lapack.h"
#include "matpackI.h"

Classes
class	ComplexIterator1D
	The iterator class for sub vectors. More...

class	ConstComplexIterator1D
	The constant iterator class for sub vectors. More...

class	ConstComplexVectorView
	A constant view of a ComplexVector. More...

class	ComplexVectorView
	The ComplexVectorView class. More...

class	ComplexIterator2D
	The row iterator class for sub matrices. More...

class	ConstComplexIterator2D
	The const row iterator class for sub matrices. More...

class	ComplexVector
	The ComplexVector class. More...

class	ConstComplexMatrixView
	A constant view of a ComplexMatrix. More...

class	ComplexMatrixView
	The ComplexMatrixView class. More...

class	ComplexMatrix
	The ComplexMatrix class. More...

Macros
#define	a1 c.real()

#define	b1 c.imag()

#define	a2 z.real()

#define	b2 z.imag()

#define	_complex_operations_(T)

Typedefs
typedef std::complex< Numeric >	Complex

typedef Eigen::Matrix< Complex, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor >	ComplexMatrixType

typedef Eigen::Stride< Eigen::Dynamic, Eigen::Dynamic >	ComplexStrideType

typedef Eigen::Map< ComplexMatrixType, 0, ComplexStrideType >	ComplexMatrixViewMap

typedef Eigen::Map< const ComplexMatrixType, 0, ComplexStrideType >	ComplexConstMatrixViewMap

typedef Array< ComplexVector >	ArrayOfComplexVector

typedef Array< ComplexMatrix >	ArrayOfComplexMatrix

Functions
std::complex< float >	operator+ (const double &d, const std::complex< float > &c)

std::complex< float >	operator* (const double &d, const std::complex< float > &c)

std::complex< float >	operator+ (const std::complex< float > &c, const double &d)

std::complex< float >	operator* (const std::complex< float > &c, const double &d)

constexpr Numeric	abs2 (Complex c)
	squared magnitude of c More...

constexpr Complex	conj (Complex c)
	the conjugate of c More...

constexpr Complex	operator+ (Complex c, Numeric n)

constexpr Complex	operator- (Complex c, Numeric n)

constexpr Complex	operator* (Complex c, Numeric n)

constexpr Complex	operator/ (Complex c, Numeric n)

constexpr Complex	operator+ (Numeric n, Complex c)

constexpr Complex	operator- (Numeric n, Complex c)

constexpr Complex	operator* (Numeric n, Complex c)

constexpr Complex	operator/ (Numeric n, Complex c)

constexpr Complex	operator+ (Complex c, Complex z)

constexpr Complex	operator- (Complex c, Complex z)

constexpr Complex	operator* (Complex c, Complex z)

constexpr Complex	operator/ (Complex c, Complex z)

	_complex_operations_ (int) _complex_operations_(float) _complex_operations_(Index) extern const Joker joker

ConstComplexMatrixView	transpose (ConstComplexMatrixView m)
	Const version of transpose. More...

ComplexMatrixView	transpose (ComplexMatrixView m)
	Returns the transpose. More...

void	copy (ConstComplexIterator1D origin, const ConstComplexIterator1D &end, ComplexIterator1D target)
	Copy data between begin and end to target. More...

void	copy (Complex x, ComplexIterator1D target, const ComplexIterator1D &end)
	Copy a scalar to all elements. More...

void	copy (ConstComplexIterator2D origin, const ConstComplexIterator2D &end, ComplexIterator2D target)
	Copy data between begin and end to target. More...

void	copy (Complex x, ComplexIterator2D target, const ComplexIterator2D &end)
	Copy a scalar to all elements. More...

void	mult (ComplexVectorView y, const ConstComplexMatrixView &M, const ConstComplexVectorView &x)
	Matrix-Vector Multiplication. More...

void	mult (ComplexMatrixView A, const ConstComplexMatrixView &B, const ConstComplexMatrixView &C)
	Matrix-Matrix Multiplication. More...

void	mult (ComplexMatrixView A, const ConstMatrixView &B, const ConstComplexMatrixView &C)

void	mult (ComplexMatrixView A, const ConstComplexMatrixView &B, const ConstMatrixView &C)

void	mult (ComplexMatrixView A, const ConstMatrixView &B, const ConstMatrixView &C)

Complex	operator* (const ConstComplexVectorView &a, const ConstComplexVectorView &b)
	Scalar product. More...

std::ostream &	operator<< (std::ostream &os, const ConstComplexVectorView &v)
	Output operator. More...

std::ostream &	operator<< (std::ostream &os, const ConstComplexMatrixView &v)
	Output operator. More...

ComplexConstMatrixViewMap	MapToEigen (const ConstComplexMatrixView &A)

ComplexConstMatrixViewMap	MapToEigen (const ConstComplexVectorView &A)

ComplexConstMatrixViewMap	MapToEigenRow (const ConstComplexVectorView &A)

ComplexConstMatrixViewMap	MapToEigenCol (const ConstComplexVectorView &A)

ComplexMatrixViewMap	MapToEigen (ComplexMatrixView &A)

ComplexMatrixViewMap	MapToEigen (ComplexVectorView &A)

ComplexMatrixViewMap	MapToEigenRow (ComplexVectorView &A)

ComplexMatrixViewMap	MapToEigenCol (ComplexVectorView &A)

Detailed Description

A class implementing complex numbers for ARTS.

Author: Oliver Lemke olemk.nosp@m.e@co.nosp@m.re-du.nosp@m.mp.i.nosp@m.nfo

Date: 2002-12-19

Definition in file complex.h.

Macro Definition Documentation

◆ _complex_operations_

#define _complex_operations_ ( T )

Value:

  constexpr Complex operator+(Complex c, T x) {   \
    return operator+(c, static_cast<Numeric>(x)); \
  }                                               \
  constexpr Complex operator-(Complex c, T x) {   \
    return operator-(c, static_cast<Numeric>(x)); \
  }                                               \
  constexpr Complex operator*(Complex c, T x) {   \
    return operator*(c, static_cast<Numeric>(x)); \
  }                                               \
  constexpr Complex operator/(Complex c, T x) {   \
    return operator/(c, static_cast<Numeric>(x)); \
  }                                               \
                                                  \
  constexpr Complex operator+(T x, Complex c) {   \
    return operator+(static_cast<Numeric>(x), c); \
  }                                               \
  constexpr Complex operator-(T x, Complex c) {   \
    return operator-(static_cast<Numeric>(x), c); \
  }                                               \
  constexpr Complex operator*(T x, Complex c) {   \
    return operator*(static_cast<Numeric>(x), c); \
  }                                               \
  constexpr Complex operator/(T x, Complex c) {   \
    return operator/(static_cast<Numeric>(x), c); \
  }

Definition at line 118 of file complex.h.

◆ a1

#define a1 c.real()

Definition at line 56 of file complex.h.

◆ a2

#define a2 z.real()

Definition at line 58 of file complex.h.

◆ b1

#define b1 c.imag()

Definition at line 57 of file complex.h.

◆ b2

#define b2 z.imag()

Definition at line 59 of file complex.h.

Typedef Documentation

◆ ArrayOfComplexMatrix

typedef Array<ComplexMatrix> ArrayOfComplexMatrix

Definition at line 949 of file complex.h.

◆ ArrayOfComplexVector

typedef Array<ComplexVector> ArrayOfComplexVector

Definition at line 948 of file complex.h.

◆ Complex

typedef std::complex<Numeric> Complex

Definition at line 33 of file complex.h.

◆ ComplexConstMatrixViewMap

typedef Eigen::Map<const ComplexMatrixType, 0, ComplexStrideType> ComplexConstMatrixViewMap

Definition at line 172 of file complex.h.

◆ ComplexMatrixType

typedef Eigen::Matrix<Complex, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor> ComplexMatrixType

Definition at line 167 of file complex.h.

◆ ComplexMatrixViewMap

typedef Eigen::Map<ComplexMatrixType, 0, ComplexStrideType> ComplexMatrixViewMap

Definition at line 170 of file complex.h.

◆ ComplexStrideType

typedef Eigen::Stride<Eigen::Dynamic, Eigen::Dynamic> ComplexStrideType

Definition at line 168 of file complex.h.

Function Documentation

◆ _complex_operations_()

_complex_operations_ ( int ) const

◆ abs2()

constexpr Numeric abs2 ( Complex c )

constexpr

squared magnitude of c

Definition at line 62 of file complex.h.

◆ conj()

constexpr Complex conj ( Complex c )

constexpr

the conjugate of c

Definition at line 65 of file complex.h.

Referenced by ampmat_to_phamat(), Linefunctions::apply_linemixing_scaling_and_mirroring(), pCqSDHC_to_arts(), and surface_specular_R_and_b().

◆ copy() [1/4]

void copy	(	Complex	x,
		ComplexIterator1D	target,
		const ComplexIterator1D &	end
	)

Copy a scalar to all elements.

Definition at line 490 of file complex.cc.

References Zeeman::end(), and ARTS::Var::x().

◆ copy() [2/4]

void copy	(	Complex	x,
		ComplexIterator2D	target,
		const ComplexIterator2D &	end
	)

Copy a scalar to all elements.

Definition at line 1328 of file complex.cc.

References ComplexVectorView::begin(), and Zeeman::end().

◆ copy() [3/4]

void copy	(	ConstComplexIterator1D	origin,
		const ConstComplexIterator1D &	end,
		ComplexIterator1D	target
	)

Copy data between begin and end to target.

Target must be a valid area of memory. Note that the strides in the iterators can be different, so that we can for example copy data between different kinds of subvectors.

Definition at line 205 of file complex.cc.

References Zeeman::end(), ComplexIterator1D::mstride, ConstComplexIterator1D::mstride, ComplexIterator1D::mx, and ConstComplexIterator1D::mx.

Referenced by ComplexMatrix::ComplexMatrix(), ComplexVector::ComplexVector(), ComplexMatrix::operator=(), Array< base >::operator=(), ComplexMatrixView::operator=(), ComplexVectorView::operator=(), and InteractiveWorkspace::resize().

◆ copy() [4/4]

void copy	(	ConstComplexIterator2D	origin,
		const ConstComplexIterator2D &	end,
		ComplexIterator2D	target
	)

Copy data between begin and end to target.

Target must be a valid area of memory. Note that the strides in the iterators can be different, so that we can for example copy data between different kinds of subvectors.

Origin, end, and target are 2D iterators, marking rows in a matrix. For each row the 1D iterator is obtained and used to copy the elements.

Definition at line 1316 of file complex.cc.

References ConstComplexVectorView::begin(), and Zeeman::end().

◆ MapToEigen() [1/4]

ComplexMatrixViewMap MapToEigen ( ComplexMatrixView & A )

Definition at line 700 of file complex.cc.

References Range::get_start(), Range::get_stride(), ConstComplexMatrixView::mcr, ConstComplexMatrixView::mdata, ConstComplexMatrixView::mrr, ConstComplexMatrixView::ncols(), ConstComplexMatrixView::nrows(), ComplexVectorView::operator=(), and ARTS::Var::x().

◆ MapToEigen() [2/4]

ComplexMatrixViewMap MapToEigen ( ComplexVectorView & A )

Definition at line 336 of file complex.cc.

References Range::get_start(), Range::get_stride(), ConstComplexVectorView::mdata, ConstComplexVectorView::mrange, and ConstComplexVectorView::nelem().

◆ MapToEigen() [3/4]

ComplexConstMatrixViewMap MapToEigen ( const ConstComplexMatrixView & A )

Definition at line 699 of file complex.cc.

References Range::get_start(), Range::get_stride(), ConstComplexMatrixView::mcr, ConstComplexMatrixView::mdata, ConstComplexMatrixView::mrr, ConstComplexMatrixView::ncols(), and ConstComplexMatrixView::nrows().

Referenced by MapToEigenRow(), mult(), Linefunctions::set_cross_section_of_band(), test03(), xsec_species(), and zeeman_on_the_fly().

◆ MapToEigen() [4/4]

ComplexConstMatrixViewMap MapToEigen ( const ConstComplexVectorView & A )

Definition at line 334 of file complex.cc.

References Range::get_start(), Range::get_stride(), ConstComplexVectorView::mdata, ConstComplexVectorView::mrange, and ConstComplexVectorView::nelem().

◆ MapToEigenCol() [1/2]

ComplexMatrixViewMap MapToEigenCol ( ComplexVectorView & A )

Definition at line 337 of file complex.cc.

References Range::get_start(), Range::get_stride(), ConstComplexVectorView::mdata, ConstComplexVectorView::mrange, and ConstComplexVectorView::nelem().

◆ MapToEigenCol() [2/2]

ComplexConstMatrixViewMap MapToEigenCol ( const ConstComplexVectorView & A )

Definition at line 335 of file complex.cc.

References Range::get_start(), Range::get_stride(), ConstComplexVectorView::mdata, ConstComplexVectorView::mrange, and ConstComplexVectorView::nelem().

◆ MapToEigenRow() [1/2]

ComplexMatrixViewMap MapToEigenRow ( ComplexVectorView & A )

Definition at line 1702 of file complex.cc.

References MapToEigen().

◆ MapToEigenRow() [2/2]

ComplexConstMatrixViewMap MapToEigenRow ( const ConstComplexVectorView & A )

Definition at line 1672 of file complex.cc.

References MapToEigen().

Referenced by mult().

◆ mult() [1/5]

void mult	(	ComplexMatrixView	A,
		const ConstComplexMatrixView &	B,
		const ConstComplexMatrixView &	C
	)

Matrix-Matrix Multiplication.

Uses the Eigen library. Be carful to test the size of your input beforehand. Note that to keep speed, the inputs should be different variables. There is memory duplication if this is not the case. Note that it is mdata that is checked, so even if the matrices are at different parts of a tensor, there is still a slowdown

Parameters

[in,out]	A	The matrix A, that will hold the result of the multiplication.
[in]	B	The matrix B
[in]	C	The matrix C

Definition at line 688 of file complex.cc.

References MapToEigen(), ConstComplexMatrixView::mdata, ConstComplexMatrixView::ncols(), and ConstComplexMatrixView::nrows().

◆ mult() [2/5]

void mult	(	ComplexMatrixView	A,
		const ConstComplexMatrixView &	B,
		const ConstMatrixView &	C
	)

Definition at line 694 of file complex.cc.

References MapToEigen(), ConstComplexMatrixView::mdata, ConstComplexMatrixView::ncols(), ConstMatrixView::ncols(), ConstComplexMatrixView::nrows(), and ConstMatrixView::nrows().

◆ mult() [3/5]

void mult	(	ComplexMatrixView	A,
		const ConstMatrixView &	B,
		const ConstComplexMatrixView &	C
	)

Definition at line 691 of file complex.cc.

References MapToEigen(), ConstComplexMatrixView::mdata, ConstComplexMatrixView::ncols(), ConstMatrixView::ncols(), ConstComplexMatrixView::nrows(), and ConstMatrixView::nrows().

◆ mult() [4/5]

void mult	(	ComplexMatrixView	A,
		const ConstMatrixView &	B,
		const ConstMatrixView &	C
	)

Definition at line 1643 of file complex.cc.

References MapToEigen(), ConstComplexMatrixView::ncols(), ConstMatrixView::ncols(), ConstComplexMatrixView::nrows(), and ConstMatrixView::nrows().

◆ mult() [5/5]

void mult	(	ComplexVectorView	y,
		const ConstComplexMatrixView &	M,
		const ConstComplexVectorView &	x
	)

Matrix-Vector Multiplication.

Uses the Eigen library. Be carful to test the size of your input beforehand.

For left-hand multiplication, please use pure matrix-mult.

Parameters

[out]	y	The length-m ComplexVectorView where the result is stored.
[in]	M	Reference to the m-times-n Const{Complex,}MatrixView holding the matrix M.
[in]	x	Reference to the length-n Const{Complex,}VectorView holding the vector x.

Definition at line 330 of file complex.cc.

References M, MapToEigen(), MapToEigenRow(), ARTS::Var::x(), and ARTS::Var::y().

Referenced by benchmark_mult(), benchmark_oem_linear(), cloud_RT_surface(), MCAntenna::draw_los(), LinearModel::evaluate(), QuadraticModel::evaluate(), generate_test_data(), get_diydx(), get_ppath_transmat(), get_stepwise_effective_source(), get_stepwise_transmission_matrix(), iy_transmission_mult(), iyHybrid(), iySurfaceFastem(), QuadraticModel::Jacobian(), jacobianCalcFreqShift(), jacobianCalcFreqStretch(), jacobianCalcPointingZaInterp(), jacobianCalcPointingZaRecalc(), lsf(), main(), matrix_vector_mult(), MatrixMatrixMultiply(), MatrixVectorMultiply(), MCGeneral(), mcPathTraceRadar(), MCRadar(), met_mm_polarisation_hmatrix(), random_fill_matrix_pos_def(), random_fill_matrix_pos_semi_def(), MCAntenna::return_los(), rte_step_doit_replacement(), rtmethods_jacobian_finalisation(), sensor_responseAntenna(), sensor_responseBackend(), sensor_responseFrequencySwitching(), sensor_responseMetMM(), sensor_responseMixer(), sensor_responseMixerBackendPrecalcWeights(), sensor_responsePolarisation(), sensor_responseStokesRotation(), sensor_responseWMRF(), SparseSparseMultiply(), surface_calc(), test4(), test5(), test_complex_diagonalize(), test_dense_sparse_multiplication(), test_inv(), test_lusolve4D(), test_real_diagonalize(), test_solve_linear_system(), test_sparse_arithmetic(), test_sparse_dense_multiplication(), transform_x(), transform_x_back(), VectorMatrixMultiply(), yActive(), yCalc(), yCalc_mblock_loop_body(), and ySimpleSpectrometer().

◆ operator*() [1/6]

constexpr Complex operator*	(	Complex	c,
		Complex	z
	)

constexpr

Definition at line 102 of file complex.h.

◆ operator*() [2/6]

constexpr Complex operator*	(	Complex	c,
		Numeric	n
	)

constexpr

Definition at line 76 of file complex.h.

◆ operator*() [3/6]

Complex operator*	(	const ConstComplexVectorView &	a,
		const ConstComplexVectorView &	b
	)

Scalar product.

The two vectors may be identical.

Definition at line 313 of file complex.cc.

References ConstComplexVectorView::begin(), ConstComplexVectorView::end(), and ConstComplexVectorView::nelem().

◆ operator*() [4/6]

std::complex<float> operator*	(	const double &	d,
		const std::complex< float > &	c
	)

inline

Definition at line 39 of file complex.h.

◆ operator*() [5/6]

std::complex<float> operator*	(	const std::complex< float > &	c,
		const double &	d
	)

inline

Definition at line 48 of file complex.h.

◆ operator*() [6/6]

constexpr Complex operator*	(	Numeric	n,
		Complex	c
	)

constexpr

Definition at line 89 of file complex.h.

◆ operator+() [1/5]

constexpr Complex operator+	(	Complex	c,
		Complex	z
	)

constexpr

Definition at line 96 of file complex.h.

◆ operator+() [2/5]

constexpr Complex operator+	(	Complex	c,
		Numeric	n
	)

constexpr

Definition at line 70 of file complex.h.

◆ operator+() [3/5]

std::complex<float> operator+	(	const double &	d,
		const std::complex< float > &	c
	)

inline

Definition at line 35 of file complex.h.

◆ operator+() [4/5]

std::complex<float> operator+	(	const std::complex< float > &	c,
		const double &	d
	)

inline

Definition at line 44 of file complex.h.

◆ operator+() [5/5]

constexpr Complex operator+	(	Numeric	n,
		Complex	c
	)

constexpr

Definition at line 83 of file complex.h.

◆ operator-() [1/3]

constexpr Complex operator-	(	Complex	c,
		Complex	z
	)

constexpr

Definition at line 99 of file complex.h.

◆ operator-() [2/3]

constexpr Complex operator-	(	Complex	c,
		Numeric	n
	)

constexpr

Definition at line 73 of file complex.h.

◆ operator-() [3/3]

constexpr Complex operator-	(	Numeric	n,
		Complex	c
	)

constexpr

Definition at line 86 of file complex.h.

◆ operator/() [1/3]

constexpr Complex operator/	(	Complex	c,
		Complex	z
	)

constexpr

Definition at line 105 of file complex.h.

◆ operator/() [2/3]

constexpr Complex operator/	(	Complex	c,
		Numeric	n
	)

constexpr

Definition at line 79 of file complex.h.

◆ operator/() [3/3]

constexpr Complex operator/	(	Numeric	n,
		Complex	c
	)

constexpr

Definition at line 92 of file complex.h.

◆ operator<<() [1/2]

std::ostream& operator<<	(	std::ostream &	os,
		const ConstComplexMatrixView &	v
	)

Output operator.

This demonstrates how iterators can be used to traverse the matrix. The iterators know which part of the matrix is ‘active’, and also the strides in both directions. This function is a bit more complicated than necessary to illustrate the concept, because the formating should look nice. This means that the first row, and the first element in each row, have to be treated individually.

Definition at line 866 of file complex.cc.

References ConstComplexVectorView::begin(), ConstComplexMatrixView::begin(), ConstComplexVectorView::end(), and ConstComplexMatrixView::end().

◆ operator<<() [2/2]

std::ostream& operator<<	(	std::ostream &	os,
		const ConstComplexVectorView &	v
	)

Output operator.

This demonstrates how iterators can be used to traverse the vector. The iterators know which part of the vector is ‘active’, and also the stride.

Definition at line 134 of file complex.cc.

References ConstComplexVectorView::begin(), ConstComplexVectorView::end(), and Zeeman::end().

◆ transpose() [1/2]

ComplexMatrixView transpose ( ComplexMatrixView m )

Returns the transpose.

This creates a special MatrixView for the transpose. The original is not changed!

Definition at line 837 of file complex.cc.

References ConstComplexMatrixView::mcr, ConstComplexMatrixView::mdata, and ConstComplexMatrixView::mrr.

◆ transpose() [2/2]

ConstComplexMatrixView transpose ( ConstComplexMatrixView m )

Const version of transpose.

Definition at line 684 of file complex.cc.

References ConstComplexMatrixView::mcr, ConstComplexMatrixView::mdata, and ConstComplexMatrixView::mrr.

Referenced by Append(), generate_test_data(), jacobianSetAffineTransformation(), lsf(), ludcmp(), matrix_vector_mult(), MCRadar(), mult(), operator+=(), random_fill_matrix_pos_def(), random_fill_matrix_pos_semi_def(), random_fill_matrix_symmetric(), rtmethods_jacobian_finalisation(), test03(), test1(), test33(), test5(), test_dense_sparse_multiplication(), test_diagonal(), test_sparse_dense_multiplication(), transform_x(), transpose(), and WMRFSelectChannels().

Classes

Macros

Typedefs

Functions

Detailed Description

Macro Definition Documentation

◆ _complex_operations_

◆ a1

◆ a2

◆ b1

◆ b2

Typedef Documentation

◆ ArrayOfComplexMatrix

◆ ArrayOfComplexVector

◆ Complex

◆ ComplexConstMatrixViewMap

◆ ComplexMatrixType

◆ ComplexMatrixViewMap

◆ ComplexStrideType

Function Documentation

◆ _complex_operations_()

◆ abs2()

◆ conj()

◆ copy() [1/4]

◆ copy() [2/4]

◆ copy() [3/4]

◆ copy() [4/4]

◆ MapToEigen() [1/4]

◆ MapToEigen() [2/4]

◆ MapToEigen() [3/4]

◆ MapToEigen() [4/4]

◆ MapToEigenCol() [1/2]

◆ MapToEigenCol() [2/2]

◆ MapToEigenRow() [1/2]

◆ MapToEigenRow() [2/2]

◆ mult() [1/5]

◆ mult() [2/5]

◆ mult() [3/5]

◆ mult() [4/5]

◆ mult() [5/5]

◆ operator*() [1/6]

◆ operator*() [2/6]

◆ operator*() [3/6]

◆ operator*() [4/6]

◆ operator*() [5/6]

◆ operator*() [6/6]

◆ operator+() [1/5]

◆ operator+() [2/5]

◆ operator+() [3/5]

◆ operator+() [4/5]

◆ operator+() [5/5]

◆ operator-() [1/3]

◆ operator-() [2/3]

◆ operator-() [3/3]

◆ operator/() [1/3]

◆ operator/() [2/3]

◆ operator/() [3/3]

◆ operator<<() [1/2]

◆ operator<<() [2/2]

◆ transpose() [1/2]

◆ transpose() [2/2]