matrix of complex double values dimensions (rows x cols) More...

#include <linalg.h>

Inheritance diagram for ComplexMatrix:

Public Member Functions
	ComplexMatrix (int r, int c)
	Default constructor: full of zeroes.

	ComplexMatrix (const DoubleMatrix &m)
	Constructor sets matrix equal to m.

	ComplexMatrix (const ComplexVector &v)
	Constructor sets square matrix's diagonal values equal to elements of v.

template<class E >
ComplexMatrix &	operator= (const MatXpr< Complex, E > &x)
	this is the only required operator to make this class work with ETs

ComplexMatrix &	operator= (const ComplexMatrix &other)

template<typename E >
	ComplexMatrix (const MatXpr< Complex, E > &m)

Complex &	operator() (int i, int j)
	Returns ijth element.

Complex	operator() (int i, int j) const

Complex	display (int i, int j) const
	returns ijth element

int	displayRows () const

int	displayCols () const

const ComplexMatrix &	display () const

std::size_t	size () const
	returns whole matrix

const ComplexMatrix &	operator= (const Complex &v)
	Sets diagonal entries equal to v, rest are 0.

Complex	min (int &k, int &l) const

void	swaprows (int i, int j)
	Obvious elementary row/column operations. More...

void	swapcols (int i, int j)
	Swaps column i with column j.

void	setCols (int)
	change number of columns (Warning: can be slow because it internally copys a std::valarray<double>)

void	setRows (int)
	change number of rows (Warning: can be slow because it internally copys a std::valarray<double>)

void	resize (int, int)
	resize matrix (Warning: can be slow because it internally copys a std::valarray<double>)

Complex	trace () const

ComplexMatrix	transpose () const

ComplexMatrix	hermitianConjugate () const

ComplexMatrix	complexConjugate () const

DoubleMatrix	real () const
	Real part of matrix.

DoubleMatrix	imag () const
	Imaginary part of matrix.

double	nonHermiticity () const
	Measures how far from Hermitian your matrix is.

void	symmetrise ()
	Fills in lower bottom half of a square matrix copying the top right.

double	compare (const ComplexMatrix &a) const
	Returns the sum of the modulus of the difference of each element.

DoubleMatrix	makeHermitianRealForDiag () const
	This should only be applied to Hermitian matrices. More...

double	diagonaliseHerm (ComplexMatrix &v, DoubleVector &w) const
	Again, only for Hermitian matrices. More...

double	takagi (ComplexMatrix &v, ComplexVector &w) const

double	diagonaliseSym2by2 (ComplexMatrix &v, ComplexVector &w) const

double	diagonalise (ComplexMatrix &u, ComplexMatrix &v, DoubleVector &w) const
	Now for any Complex matrix. More...

ComplexMatrix	apply (Complex(*fn)(Complex)) const
	Applies fn to every element.

Public Member Functions inherited from MatIndexable< Complex, ComplexMatrix >
Complex	operator() (int m, int n) const

int	displayRows () const

int	displayCols () const

ComplexMatrix &	assign_from (const MatXpr< Complex, E > &x)

ComplexMatrix	copy_from (const MatXpr< Complex, E > &x)

MatIndexable &	operator+= (const MatXpr< Complex, E > &x)

MatIndexable &	*operator=** (Complex x)

Friends
class	DoubleMatrix

Detailed Description

matrix of complex double values dimensions (rows x cols)

Member Function Documentation

◆ diagonalise()

double ComplexMatrix::diagonalise	(	ComplexMatrix &	u,
		ComplexMatrix &	v,
		DoubleVector &	w
	)		const

Now for any Complex matrix.

For general non-singular complex matrices \( W = U A V^\dag \), where \( W \) is a matrix of diagonal values. The double output is an estimate of how accurate the diagonalisation is.

Multiply \( i^{th} \) column of V by exp(i theta) in order to end up with real eigenvalues

◆ diagonaliseHerm()

double ComplexMatrix::diagonaliseHerm	(	ComplexMatrix &	v,
		DoubleVector &	w
	)		const

Again, only for Hermitian matrices.

For HERMITIAN MATRICES ONLY! \( A = V W V^\dag \) where W is a matrix of the eigenvalues therefore \( W = V^\dag A V \). The double output is an estimate of how accurate the diagonalisation is.

Store every other eigenvalue in w (they are repeated when realified)

◆ diagonaliseSym2by2()

double ComplexMatrix::diagonaliseSym2by2	(	ComplexMatrix &	v,
		ComplexVector &	w
	)		const

For Complex Symmetric matrices only. Performs eigenvalue factorisation, ie \( U A U^T = diag(\sigma_1, \sigma_2) \) for the 2 by 2 case. w has eigenvalues and the double return is numerical error. The matrices CANNOT be singular. From physics/0607103

◆ makeHermitianRealForDiag()

DoubleMatrix ComplexMatrix::makeHermitianRealForDiag ( ) const

This should only be applied to Hermitian matrices.

This should only be applied to Hermitian matrices: makes a 2n x 2n real matrix out of [ A -B ] ready for diagonalisation. It's especially not [ B A ] efficient for large matrices.

◆ min()

Complex ComplexMatrix::min	(	int &	k,
		int &	l
	)		const

smallest absolute element

◆ swaprows()

void ComplexMatrix::swaprows	(	int	i,
		int	j
	)

Obvious elementary row/column operations.

Swaps row i with row j

◆ takagi()

double ComplexMatrix::takagi	(	ComplexMatrix &	v,
		ComplexVector &	w
	)		const

For Complex Symmetric matrices only. Performs Takagi factorisation, ie \( U^* A U^\dag = diag(\sigma_1, \sigma_2) \) for the 2 by 2 case. w has eigenvalues and the double return is numerical error. The matrices can be singular.

Choice of sign for numerical round-off

The documentation for this class was generated from the following files:

src/linalg.h
src/linalg.cpp

Public Member Functions

Friends