Class : RealSymmetricMatrix

class deriving from Matrix

RealSymmetricMatrix :

prototype: RealSymmetricMatrix ()

description:default constructor



RealSymmetricMatrix :

prototype: RealSymmetricMatrix (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



RealSymmetricMatrix :

prototype: RealSymmetricMatrix (double* , double* , int dimension )

description:constructor from matrix elements (without duplicating datas)


input parameters:
diagonal = pointer to diagonal element array
offDiagonal = pointer to off-diagonal element array
dimension = matrix dimension



RealSymmetricMatrix :

prototype: RealSymmetricMatrix (const RealMatrix& Q )

description:constructor from a real matrix Q (new matrix = Qt * Q)



RealSymmetricMatrix :

prototype: RealSymmetricMatrix (const RealSymmetricMatrix& M )

description:copy constructor (without duplicating datas)


input parameters:
M = matrix to copy



RealSymmetricMatrix :

prototype: RealSymmetricMatrix (const RealTriDiagonalSymmetricMatrix& M )

description:copy constructor from a real tridiagonal symmetric matrix (without duplicating diagonal elements)


input parameters:
M = matrix to copy



~RealSymmetricMatrix :

prototype: ~RealSymmetricMatrix ()

description:destructor



operator = :

prototype: RealSymmetricMatrix& operator = (const RealSymmetricMatrix& M )

description:assignement (without duplicating datas)


input parameters:
M = matrix to copy


return value: reference on modified matrix



operator = :

prototype: RealSymmetricMatrix& 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



operator :

prototype: double& operator ( )

description:get reference of a given matrix element


input parameters:
i = line position
j = column position


return value: reference om matrix elememt



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



Project :

prototype: Matrix* Project (SubspaceSpaceConverter& subspace )

description:project matrix into a given subspace


input parameters:
subspace = reference on subspace structure


return value: pointer to projected matrix



operator + :

prototype: friend RealSymmetricMatrix operator + (const RealSymmetricMatrix& , const RealSymmetricMatrix& M2 )

description:add two matrices


input parameters:
M1 = first matrix
M2 = second matrix


return value: sum of the two matrices



operator + :

prototype: friend RealSymmetricMatrix operator + (const RealTriDiagonalSymmetricMatrix& , const RealSymmetricMatrix& 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 RealSymmetricMatrix operator + (const RealSymmetricMatrix& , 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 RealSymmetricMatrix operator - (const RealSymmetricMatrix& , const RealSymmetricMatrix& 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 RealSymmetricMatrix operator - (const RealTriDiagonalSymmetricMatrix& , const RealSymmetricMatrix& 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 RealSymmetricMatrix operator - (const RealSymmetricMatrix& , 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 RealSymmetricMatrix operator * (const RealSymmetricMatrix& , 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 RealSymmetricMatrix operator * (double , const RealSymmetricMatrix& 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 RealSymmetricMatrix operator / (const RealSymmetricMatrix& , 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: RealSymmetricMatrix& operator += (const RealSymmetricMatrix& M )

description:add two matrices


input parameters:
M = matrix to add to current matrix


return value: reference on current matrix



operator += :

prototype: RealSymmetricMatrix& 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: RealSymmetricMatrix& operator -= (const RealSymmetricMatrix& M )

description:substract two matrices


input parameters:
M = matrix to substract to current matrix


return value: reference on current matrix



operator -= :

prototype: RealSymmetricMatrix& 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: RealSymmetricMatrix& 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: RealSymmetricMatrix& 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: double MatrixElement (RealVector& , RealVector& 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 an hermitian matrix with an unitary matrix (Ut M U)


input parameters:
UnitaryM = unitary matrix to use


return value: pointer to conjugated matrix



Conjugate :

prototype: Matrix* Conjugate (BlockDiagonalMatrix& UnitaryM )

description:conjugate an hermitian matrix with an unitary matrix (Ut M U)


input parameters:
UnitaryM = unitary matrix to use


return value: pointer to conjugated matrix



Conjugate :

prototype: void Conjugate (RealMatrix& , int , int , RealSymmetricMatrix& matrix )

description:conjugate a block of the matrix with an unitary matrix (Ut M U)


input parameters:
UnitaryM = unitary matrix to use
sourcePosition = index of the row where the block to conjugate starts
destinationPosition = index of the row where the conjugated block has to be stored
matrix = matrix where result has to be stored



Conjugate :

prototype: void Conjugate (RealMatrix& , RealMatrix& , int , int , int , int , RealSymmetricMatrix& matrix )

description:conjugate a block of the matrix (in the upper diagonal part) with two matrix matrix (Vt M U)


input parameters:
UnitaryMl = unitary matrix to use at the left hand side
UnitaryMr = unitary matrix to use at the right hand side
sourceRowIndex = index of the row where the block to conjugate starts
sourceColumnIndex = index of the column where the block to conjugate starts
destinationRowIndex = index of the row where the conjugated block has to be stored
destinationColumnIndex = index of the column where the conjugated block has to be stored
matrix = matrix where result has to be stored



AddAAAtAt :

prototype: RealSymmetricMatrix& AddAAAtAt (RealMatrix& , RealMatrix& , RealMatrix& , RealMatrix& , double coefficient = 1.0 )

description:add the symmetric matrix m1.m2.m3^t.m4^t + m4.m3.m2^t.m1^t to current symmetric matrix


input parameters:
m1 = first matrix
m2 = second matrix
m3 = third matrix
m4 = fourth matrix
coefficient = optional global multiplicative factor in front of m1.m2.m3^t.m4^t + m4.m3.m2^t.m1^t



AddAAAtAt :

prototype: RealSymmetricMatrix& AddAAAtAt (RealMatrix& , RealMatrix& , RealMatrix& , RealMatrix& , int , int , int , double coefficient = 1.0 )

description:add the symmetric matrix m1.m2.m3^t.m4^t + m4.m3.m2^t.m1^t to current symmetric matrix within a given range of indices


input parameters:
m1 = first matrix
m2 = second matrix
m3 = third matrix
m4 = fourth matrix
rowIndex = row index of the first element to add
columnIndex = column index of the first element to add
nbrElement = number of element to add (starting from first element knowing that line i contains n - i + 1)
coefficient = optional global multiplicative factor in front of m1.m2.m3^t.m4^t + m4.m3.m2^t.m1^t



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& , RealVector& 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& , RealMatrix& 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& , RealMatrix& , 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 err )

description:Tridiagonalize a real symmetric matrix using Householder algorithm


input parameters:
M = reference on real tridiagonal symmetric matrix where result has to be stored
err = absolute error on matrix element


return value: reference on real tridiagonal symmetric matrix



Householder :

prototype: RealTriDiagonalSymmetricMatrix& Householder (RealTriDiagonalSymmetricMatrix& , double , RealMatrix& Q )

description:Tridiagonalize a real symmetric 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



operator << :

prototype: friend ostream& operator << (ostream& , const RealSymmetricMatrix& 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 RealSymmetricMatrix& P )

description:Mathematica Output Stream overload


input parameters:
Str = reference on Mathematica output stream
P = matrix to print


return value: reference on output stream



operator >> :

prototype: friend ifstream& operator >> (ifstream& , RealSymmetricMatrix& matrix )

description:output file stream overload


input parameters:
file = reference on output file stream
matrix = reference on matrix to save


return value: reference on output file stream
friend ofstream& operator << (ofstream& file, const RealSymmetricMatrix& matrix);
input file stream overload


input parameters:
file = reference on output file stream
matrix = reference on matrix to load


return value: reference on output file stream



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