Class : HermitianMatrix
HermitianMatrix :
prototype: HermitianMatrix ()
description:default constructor
HermitianMatrix :
prototype: HermitianMatrix (int , bool zero = false )
description:constructor for an empty matrix
input parameters:
dimension = matrix dimension
zero = true if matrix has to be filled with zeros
HermitianMatrix :
prototype: HermitianMatrix (double* , double* , double* , int dimension )
description:constructor from matrix elements (without duplicating datas)
input parameters:
diagonal = pointer to diagonal element array
realOffDiagonal = pointer to real part of off-diagonal elements
imaginaryOffDiagonal = pointer to imaginary part of off-diagonal elements
dimension = matrix dimension
HermitianMatrix :
prototype: HermitianMatrix (const HermitianMatrix& M )
description:copy constructor (without duplicating datas)
input parameters:
M = matrix to copy
HermitianMatrix :
prototype: HermitianMatrix (const RealTriDiagonalSymmetricMatrix& M )
description:copy constructor from a real tridiagonal symmetric matrix (without duplicating diagonal elements)
input parameters:
M = matrix to copy
~HermitianMatrix :
prototype: ~HermitianMatrix ()
description:destructor
operator = :
prototype: HermitianMatrix& operator = (const HermitianMatrix& M )
description:assignement (without duplicating datas)
input parameters:
M = matrix to copy
return value: reference on modified matrix
operator = :
prototype: HermitianMatrix& operator = (const RealTriDiagonalSymmetricMatrix& M )
description:assignement from a real tridiagonal symmetric matrix (without duplicating datas)
input parameters:
M = matrix to copy
return value: reference on modified matrix
Clone :
prototype: Matrix* Clone ()
description:return pointer on a clone matrix (without duplicating datas)
input parameters:
retrun value = pointer on new matrix
SetMatrixElement :
prototype: void SetMatrixElement (int , int , double x )
description:set a matrix element
input parameters:
i = line position
j = column position
x = new value for matrix element
SetMatrixElement :
prototype: void SetMatrixElement (int , int , const Complex& x )
description:set a matrix element
input parameters:
i = line position
j = column position
x = new value for matrix element
AddToMatrixElement :
prototype: void AddToMatrixElement (int , int , double x )
description:add a value to a matrix element
input parameters:
i = line position
j = column position
x = value to add to matrix element
AddToMatrixElement :
prototype: void AddToMatrixElement (int , int , const Complex& x )
description:add a value a matrix element
input parameters:
i = line position
j = column position
x = value to add to matrix element
Resize :
prototype: void Resize (int , int nbrColumn )
description:Resize matrix
input parameters:
nbrRow = new number of rows
nbrColumn = new number of columns
ResizeAndClean :
prototype: void ResizeAndClean (int , int nbrColumn )
description:Resize matrix and set to zero all elements that have been added
input parameters:
nbrRow = new number of rows
nbrColumn = new number of columns
operator + :
prototype: friend HermitianMatrix operator + (const HermitianMatrix& ,
const HermitianMatrix& M2 )
description:add two matrices
input parameters:
M1 = first matrix
M2 = second matrix
return value: sum of the two matrices
operator + :
prototype: friend HermitianMatrix operator + (const RealTriDiagonalSymmetricMatrix& ,
const HermitianMatrix& M2 )
description:add two matrices where the left one is a real tridiagonal symmetric matrix
input parameters:
M1 = left matrix
M2 = right matrix
return value: sum of the two matrices
operator + :
prototype: friend HermitianMatrix operator + (const HermitianMatrix& ,
const RealTriDiagonalSymmetricMatrix& M2 )
description:add two matrices where the right one is a real tridiagonal symmetric matrix
input parameters:
M1 = left matrix
M2 = right matrix
return value: sum of the two matrices
operator - :
prototype: friend HermitianMatrix operator - (const HermitianMatrix& ,
const HermitianMatrix& M2 )
description:substract two matrices
input parameters:
M1 = first matrix
M2 = matrix to substract to M1
return value: difference of the two matrices
operator - :
prototype: friend HermitianMatrix operator - (const RealTriDiagonalSymmetricMatrix& ,
const HermitianMatrix& M2 )
description:substract two matrices where the left one is a real tridiagonal symmetric matrix
input parameters:
M1 = first matrix
M2 = matrix to substract to M1
return value: difference of the two matrices
operator - :
prototype: friend HermitianMatrix operator - (const HermitianMatrix& ,
const RealTriDiagonalSymmetricMatrix& M2 )
description:substract two matrices where the right one is a real tridiagonal symmetric matrix
input parameters:
M1 = first matrix
M2 = matrix to substract to M1
return value: difference of the two matrices
operator * :
prototype: friend HermitianMatrix operator * (const HermitianMatrix& , double x )
description:multiply a matrix by a real number (right multiplication)
input parameters:
M = source matrix
x = real number to use
return value: product result
operator * :
prototype: friend HermitianMatrix operator * (double , const HermitianMatrix& M )
description:multiply a matrix by a real number (left multiplication)
input parameters:
M = source matrix
x = real number to use
return value: product result
operator / :
prototype: friend HermitianMatrix operator / (const HermitianMatrix& , double x )
description:divide a matrix by a real number (right multiplication)
input parameters:
M = source matrix
x = real number to use
return value: division result
operator += :
prototype: HermitianMatrix& operator += (const HermitianMatrix& M )
description:add two matrices
input parameters:
M = matrix to add to current matrix
return value: reference on current matrix
operator += :
prototype: HermitianMatrix& operator += (const RealTriDiagonalSymmetricMatrix& M )
description:add two matrices where the right one is a real tridiagonal symmetric matrix
input parameters:
M = matrix to add to current matrix
return value: reference on current matrix
operator -= :
prototype: HermitianMatrix& operator -= (const HermitianMatrix& M )
description:substract two matrices
input parameters:
M = matrix to substract to current matrix
return value: reference on current matrix
operator -= :
prototype: HermitianMatrix& operator -= (const RealTriDiagonalSymmetricMatrix& M )
description:substract two matrices where the right one is a real tridiagonal symmetric matrix
input parameters:
M = matrix to substract to current matrix
return value: reference on current matrix
operator *= :
prototype: HermitianMatrix& operator *= (double x )
description:multiply a matrix by a real number
input parameters:
x = real number to use
return value: reference on current matrix
operator /= :
prototype: HermitianMatrix& operator /= (double x )
description:divide a matrix by a real number
input parameters:
x = real number to use
return value: reference on current matrix
MatrixElement :
prototype: Complex MatrixElement (ComplexVector& , ComplexVector& V2 )
description:evaluate matrix element
input parameters:
V1 = vector to left multiply with current matrix
V2 = vector to right multiply with current matrix
return value: corresponding matrix element
Conjugate :
prototype: Matrix* Conjugate (RealMatrix& UnitaryM )
description:conjugate a matrix with an unitary matrix (Ut M U)
input parameters:
UnitaryM = unitary matrix to use
return value: pointer to conjugated matrix
Conjugate :
prototype: HermitianMatrix Conjugate (ComplexMatrix& UnitaryM )
description:conjugate an hermitian matrix with an unitary matrix (Ut M U)
input parameters:
UnitaryM = unitary matrix to use
return value: conjugated matrix
InvConjugate :
prototype: HermitianMatrix InvConjugate (ComplexMatrix& UnitaryM )
description:conjugate an hermitian matrix with an hermitian transposed unitary matrix (U M Ut)
input parameters:
UnitaryM = unitary matrix to use
return value: conjugated matrix
Tr :
prototype: double Tr ()
description:evaluate matrix trace
input parameters:
return value: matrix trace
Det :
prototype: double Det ()
description:evaluate matrix determinant
input parameters:
return value: matrix determinant
Lanczos :
prototype: RealTriDiagonalSymmetricMatrix& Lanczos (int , RealTriDiagonalSymmetricMatrix& , ComplexVector& V1 )
description:Tridiagonalize an hermitian matrix using Lanczos algorithm without re-orthogonalizing base at each step
input parameters:
dimension = maximum iteration number
M = reference on complex tridiagonal hermitian matrix where result has to be stored
V1 = reference on complex vector used as first vector (will contain last produced vector at the end)
return value: reference on complex tridiagonal hermitian matrix
Lanczos :
prototype: RealTriDiagonalSymmetricMatrix& Lanczos (int , RealTriDiagonalSymmetricMatrix& , ComplexMatrix& Q )
description:Tridiagonalize an hermitian matrix using Lanczos algorithm without re-orthogonalizing base at each step
input parameters:
dimension = maximum iteration number
M = reference on real tridiagonal symmetric matrix where result has to be stored
Q = matrix where new orthonormalized base will be stored (first column is used as first vector)
return value: reference on complex tridiagonal hermitian matrix
OrthoLanczos :
prototype: RealTriDiagonalSymmetricMatrix& OrthoLanczos (int , RealTriDiagonalSymmetricMatrix& , ComplexMatrix& ,
double err = 0.00000001 )
description:Tridiagonalize an hermitian matrix using Lanczos algorithm without re-orthogonalizing base at each step, if during process a
null vector appears then new random vector is evaluated
input parameters:
dimension = maximum iteration number
M = reference on real tridiagonal symmetric matrix where result has to be stored
Q = matrix where new orthonormalized base will be stored (first column is used as first vector)
err = absolute error on vector norm
return value: reference on complex tridiagonal hermitian matrix
Householder :
prototype: RealTriDiagonalSymmetricMatrix& Householder (RealTriDiagonalSymmetricMatrix& , double , ComplexMatrix& Q )
description:Tridiagonalize a hermitian matrix using Householder algorithm and evaluate transformation matrix
input parameters:
M = reference on real tridiagonal symmetric matrix where result has to be stored
err = absolute error on matrix element
Q = matrix where transformation matrix has to be stored
return value: reference on real tridiagonal symmetric matrix
ConvertToSymmetricMatrix :
prototype: RealSymmetricMatrix ConvertToSymmetricMatrix ()
description:store hermitian matrix into a real symmetric matrix (real part as block diagonal element and imaginary part as block off-diagonal element )
input parameters:
return value: real symmetric matrix associated to the hermitian matrix
operator << :
prototype: friend ostream& operator << (ostream& , const HermitianMatrix& P )
description:Output Stream overload
input parameters:
Str = reference on output stream
P = matrix to print
return value: reference on output stream
operator << :
prototype: friend MathematicaOutput& operator << (MathematicaOutput& , const HermitianMatrix& P )
description:Mathematica Output Stream overload
input parameters:
Str = reference on Mathematica output stream
P = matrix to print
return value: reference on output stream
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