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Chapter 4: Matrix and Vector Operations 29

This document describes various matrix factorization operations including: - AEPBALANCE for balancing a matrix or complex matrix - DET for computing the determinant of a matrix or complex matrix - GEPBALANCE for generalized balancing of two matrices or complex matrices - CHOL for Cholesky factorization of a matrix or complex matrix - HESS for Hessenberg factorization of a matrix It provides the function definitions and descriptions for these matrix factorization classes and operations.

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Fernando Moreira Lagos
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46 views8 pages

Chapter 4: Matrix and Vector Operations 29

This document describes various matrix factorization operations including: - AEPBALANCE for balancing a matrix or complex matrix - DET for computing the determinant of a matrix or complex matrix - GEPBALANCE for generalized balancing of two matrices or complex matrices - CHOL for Cholesky factorization of a matrix or complex matrix - HESS for Hessenberg factorization of a matrix It provides the function definitions and descriptions for these matrix factorization classes and operations.

Uploaded by

Fernando Moreira Lagos
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Chapter 4: Matrix and Vector Operations 29

ComplexColumnVector operator + (const ComplexColumnVector &a, const


ColumnVector &b)
ComplexColumnVector operator - (const ComplexColumnVector &a, const
ColumnVector &b)
ComplexColumnVector product (const ComplexColumnVector &a, const
ColumnVector &b)
ComplexColumnVector quotient (const ComplexColumnVector &a, const
ColumnVector &b)
ComplexColumnVector map (c c Mapper f, const ComplexColumnVector &a)
ColumnVector map (d c Mapper f, const ComplexColumnVector &a)
void map (c c Mapper f)
Complex min (void) const
Complex max (void) const
ostream& operator << (ostream &os, const ComplexColumnVector &a)
ComplexRowVector (void)
ComplexRowVector (int n)
ComplexRowVector (int n, const Complex &val)
ComplexRowVector (const RowVector &a)
ComplexRowVector (const Array<Complex> &a)
ComplexRowVector (const ComplexRowVector &a)
ComplexRowVector& operator = (const ComplexRowVector &a)
int operator == (const ComplexRowVector &a) const
int operator != (const ComplexRowVector &a) const
ComplexRowVector& insert (const RowVector &a, int c)
ComplexRowVector& insert (const ComplexRowVector &a, int c)
ComplexRowVector& fill (double val)
ComplexRowVector& fill (const Complex &val)
ComplexRowVector& fill (double val, int c1, int c2)
ComplexRowVector& fill (const Complex &val, int c1, int c2)
ComplexRowVector append (const RowVector &a) const
ComplexRowVector append (const ComplexRowVector &a) const
ComplexColumnVector transpose (void) const
RowVector real (const ComplexRowVector &a)
RowVector imag (const ComplexRowVector &a)
ComplexRowVector conj (const ComplexRowVector &a)
ComplexRowVector extract (int c1, int c2) const
ComplexRowVector& operator += (const RowVector &a)
ComplexRowVector& operator -= (const RowVector &a)
ComplexRowVector& operator += (const ComplexRowVector &a)
ComplexRowVector& operator -= (const ComplexRowVector &a)
ComplexRowVector operator + (const ComplexRowVector &a, double s)
Chapter 4: Matrix and Vector Operations 30

ComplexRowVector operator - (const ComplexRowVector &a, double s)


ComplexRowVector operator * (const ComplexRowVector &a, double s)
ComplexRowVector operator / (const ComplexRowVector &a, double s)
ComplexRowVector operator + (double s, const ComplexRowVector &a)
ComplexRowVector operator - (double s, const ComplexRowVector &a)
ComplexRowVector operator * (double s, const ComplexRowVector &a)
ComplexRowVector operator / (double s, const ComplexRowVector &a)
Complex operator * (const ComplexRowVector &a, const ColumnVector &b)
Complex operator * (const ComplexRowVector &a, const
ComplexColumnVector &b)
ComplexRowVector operator * (const ComplexRowVector &a, const
ComplexMatrix &b)
ComplexRowVector operator + (const ComplexRowVector &a, const
RowVector &b)
ComplexRowVector operator - (const ComplexRowVector &a, const
RowVector &b)
ComplexRowVector product (const ComplexRowVector &a, const RowVector
&b)
ComplexRowVector quotient (const ComplexRowVector &a, const
RowVector &b)
ComplexRowVector map (c c Mapper f, const ComplexRowVector &a)
RowVector map (d c Mapper f, const ComplexRowVector &a)
void map (c c Mapper f)
Complex min (void) const
Complex max (void) const
ostream& operator << (ostream &os, const ComplexRowVector &a)
ComplexDiagMatrix (void)
ComplexDiagMatrix (int n)
ComplexDiagMatrix (int n, const Complex &val)
ComplexDiagMatrix (int r, int c)
ComplexDiagMatrix (int r, int c, const Complex &val)
ComplexDiagMatrix (const RowVector &a)
ComplexDiagMatrix (const ComplexRowVector &a)
ComplexDiagMatrix (const ColumnVector &a)
ComplexDiagMatrix (const ComplexColumnVector &a)
ComplexDiagMatrix (const DiagMatrix &a)
ComplexDiagMatrix (const DiagArray<Complex> &a)
ComplexDiagMatrix (const ComplexDiagMatrix &a)
ComplexDiagMatrix& operator = (const ComplexDiagMatrix &a)
int operator == (const ComplexDiagMatrix &a) const
int operator != (const ComplexDiagMatrix &a) const
ComplexDiagMatrix& fill (double val)
Chapter 4: Matrix and Vector Operations 31

ComplexDiagMatrix& fill (const Complex &val)


ComplexDiagMatrix& fill (double val, int beg, int end)
ComplexDiagMatrix& fill (const Complex &val, int beg, int end)
ComplexDiagMatrix& fill (const ColumnVector &a)
ComplexDiagMatrix& fill (const ComplexColumnVector &a)
ComplexDiagMatrix& fill (const RowVector &a)
ComplexDiagMatrix& fill (const ComplexRowVector &a)
ComplexDiagMatrix& fill (const ColumnVector &a, int beg)
ComplexDiagMatrix& fill (const ComplexColumnVector &a, int beg)
ComplexDiagMatrix& fill (const RowVector &a, int beg)
ComplexDiagMatrix& fill (const ComplexRowVector &a, int beg)
ComplexDiagMatrix transpose (void) const
DiagMatrix real (const ComplexDiagMatrix &a)
DiagMatrix imag (const ComplexDiagMatrix &a)
ComplexDiagMatrix conj (const ComplexDiagMatrix &a)
ComplexMatrix extract (int r1, int c1, int r2, int c2) const
ComplexRowVector row (int i) const
ComplexRowVector row (char *s) const
ComplexColumnVector column (int i) const
ComplexColumnVector column (char *s) const
ComplexDiagMatrix inverse (int &info) const
ComplexDiagMatrix inverse (void) const
ComplexDiagMatrix& operator += (const DiagMatrix &a)
ComplexDiagMatrix& operator -= (const DiagMatrix &a)
ComplexDiagMatrix& operator += (const ComplexDiagMatrix &a)
ComplexDiagMatrix& operator -= (const ComplexDiagMatrix &a)
ComplexMatrix operator + (const ComplexDiagMatrix &a, double s)
ComplexMatrix operator - (const ComplexDiagMatrix &a, double s)
ComplexMatrix operator + (const ComplexDiagMatrix &a, const Complex
&s)
ComplexMatrix operator - (const ComplexDiagMatrix &a, const Complex
&s)
ComplexDiagMatrix operator * (const ComplexDiagMatrix &a, double s)
ComplexDiagMatrix operator / (const ComplexDiagMatrix &a, double s)
ComplexMatrix operator + (double s, const ComplexDiagMatrix &a)
ComplexMatrix operator - (double s, const ComplexDiagMatrix &a)
ComplexMatrix operator + (const Complex &s, const ComplexDiagMatrix
&a)
ComplexMatrix operator - (const Complex &s, const ComplexDiagMatrix
&a)
ComplexDiagMatrix operator * (double s, const ComplexDiagMatrix &a)
32

ComplexColumnVector operator * (const ComplexDiagMatrix &a, const


ColumnVector &b)
ComplexColumnVector operator * (const ComplexDiagMatrix &a, const
ComplexColumnVector &b)
ComplexDiagMatrix operator + (const ComplexDiagMatrix &a, const
DiagMatrix &b)
ComplexDiagMatrix operator - (const ComplexDiagMatrix &a, const
DiagMatrix &b)
ComplexDiagMatrix product (const ComplexDiagMatrix &a, const
DiagMatrix &b)
ComplexMatrix operator + (const ComplexDiagMatrix &a, const Matrix &b)
ComplexMatrix operator - (const ComplexDiagMatrix &a, const Matrix &b)
ComplexMatrix operator * (const ComplexDiagMatrix &a, const Matrix &b)
ComplexMatrix operator + (const ComplexDiagMatrix &a, const
ComplexMatrix &b)
ComplexMatrix operator - (const ComplexDiagMatrix &a, const
ComplexMatrix &b)
ComplexMatrix operator * (const ComplexDiagMatrix &a, const
ComplexMatrix &b)
ComplexColumnVector diag (void) const
ComplexColumnVector diag (int k) const
ostream& operator << (ostream &os, const ComplexDiagMatrix &a)
33

5 Matrix Factorizations

AEPBALANCE (void)
AEPBALANCE (const Matrix &a, const char *balance_job)
AEPBALANCE (const AEPBALANCE &a)
AEPBALANCE& operator = (const AEPBALANCE &a)
Matrix balanced_matrix (void) const
Matrix balancing_matrix (void) const
ostream& operator << (ostream &os, const AEPBALANCE &a)
ComplexAEPBALANCE (void)
ComplexAEPBALANCE (const ComplexMatrix &a, const char *balance_job)
ComplexAEPBALANCE (const ComplexAEPBALANCE &a)
ComplexAEPBALANCE& operator = (const ComplexAEPBALANCE &a)
ComplexMatrix balanced_matrix (void) const
ComplexMatrix balancing_matrix (void) const
ostream& operator << (ostream &os, const ComplexAEPBALANCE &a)
DET (void)
DET (const DET &a)
DET& operator = (const DET &a)
int value_will_overflow (void) const
int value_will_underflow (void) const
double coefficient (void) const
int exponent (void) const
double value (void) const
ostream& operator << (ostream &os, const DET &a)
ComplexDET (void)
ComplexDET (const ComplexDET &a)
ComplexDET& operator = (const ComplexDET &a)
int value_will_overflow (void) const
int value_will_underflow (void) const
Complex coefficient (void) const
int exponent (void) const
Complex value (void) const
ostream& operator << (ostream &os, const ComplexDET &a)
GEPBALANCE (void)
GEPBALANCE (const Matrix &a, const Matrix &, const char *balance_job)
GEPBALANCE (const GEPBALANCE &a)
GEPBALANCE& operator = (const GEPBALANCE &a)
Chapter 5: Matrix Factorizations 34

Matrix balanced_a_matrix (void) const


Matrix balanced_b_matrix (void) const
Matrix left_balancing_matrix (void) const
Matrix right_balancing_matrix (void) const
ostream& operator << (ostream &os, const GEPBALANCE &a)
CHOL (void)
CHOL (const Matrix &a)
CHOL (const Matrix &a, int &info)
CHOL (const CHOL &a)
CHOL& operator = (const CHOL &a)
Matrix chol_matrix (void) const
ostream& operator << (ostream &os, const CHOL &a)
ComplexCHOL (void)
ComplexCHOL (const ComplexMatrix &a)
ComplexCHOL (const ComplexMatrix &a, int &info)
ComplexCHOL (const ComplexCHOL &a)
ComplexCHOL& operator = (const ComplexCHOL &a)
ComplexMatrix chol_matrix (void) const
ostream& operator << (ostream &os, const ComplexCHOL &a)
HESS (void)
HESS (const Matrix &a)
HESS (const Matrix&a, int &info)
HESS (const HESS &a)
HESS& operator = (const HESS &a)
Matrix hess_matrix (void) const
Matrix unitary_hess_matrix (void) const
ostream& operator << (ostream &os, const HESS &a)
ComplexHESS (void)
ComplexHESS (const ComplexMatrix &a)
ComplexHESS (const ComplexMatrix &a, int &info)
ComplexHESS (const ComplexHESS &a)
ComplexHESS& operator = (const ComplexHESS &a)
ComplexMatrix hess_matrix (void) const
ComplexMatrix unitary_hess_matrix (void) const
ostream& operator << (ostream &os, const ComplexHESS &a)
SCHUR (void)
SCHUR (const Matrix &a, const char *ord)
SCHUR (const Matrix &a, const char *ord, int &info)
SCHUR (const SCHUR &a, const char *ord)
SCHUR& operator = (const SCHUR &a)
Chapter 5: Matrix Factorizations 35

Matrix schur_matrix (void) const


Matrix unitary_matrix (void) const
ostream& operator << (ostream &os, const SCHUR &a)
ComplexSCHUR (void)
ComplexSCHUR (const ComplexMatrix &a, const char *ord)
ComplexSCHUR (const ComplexMatrix &a, const char *ord, int &info)
ComplexSCHUR (const ComplexSCHUR &a, const char *ord)
ComplexSCHUR& operator = (const ComplexSCHUR &a)
ComplexMatrix schur_matrix (void) const
ComplexMatrix unitary_matrix (void) const
ostream& operator << (ostream &os, const ComplexSCHUR &a)
SVD (void)
SVD (const Matrix &a)
SVD (const Matrix &a, int &info)
SVD (const SVD &a)
SVD& operator = (const SVD &a)
DiagMatrix singular_values (void) const
Matrix left_singular_matrix (void) const
Matrix right_singular_matrix (void) const
ostream& operator << (ostream &os, const SVD &a)
ComplexSVD (void)
ComplexSVD (const ComplexMatrix &a)
ComplexSVD (const ComplexMatrix &a, int &info)
ComplexSVD (const ComplexSVD &a)
ComplexSVD& operator = (const ComplexSVD &a)
DiagMatrix singular_values (void) const
ComplexMatrix left_singular_matrix (void) const
ComplexMatrix right_singular_matrix (void) const
ostream& operator << (ostream &os, const ComplexSVD &a)
EIG (void)
EIG (const Matrix &a)
EIG (const Matrix &a, int &info)
EIG (const ComplexMatrix &a)
EIG (const ComplexMatrix &a, int &info)
EIG (const EIG &a)
EIG& operator = (const EIG &a)
ComplexColumnVector eigenvalues (void) const
ComplexMatrix eigenvectors (void) const
ostream& operator << (ostream &os, const EIG &a)
36

LU (void)
LU (const Matrix &a)
LU (const LU &a)
LU& operator = (const LU &a)
Matrix L (void) const
Matrix U (void) const
Matrix P (void) const
ostream& operator << (ostream &os, const LU &a)
ComplexLU (void)
ComplexLU (const ComplexMatrix &a)
ComplexLU (const ComplexLU &a)
ComplexLU& operator = (const ComplexLU &a)
ComplexMatrix L (void) const
ComplexMatrix U (void) const
Matrix P (void) const
ostream& operator << (ostream &os, const ComplexLU &a)
QR (void)
QR (const Matrix &A)
QR (const QR &a)
QR& operator = (const QR &a)
Matrix Q (void) const
Matrix R (void) const
ostream& operator << (ostream &os, const QR &a)
ComplexQR (void)
ComplexQR (const ComplexMatrix &A)
ComplexQR (const ComplexQR &a)
ComplexQR& operator = (const ComplexQR &a)
ComplexMatrix Q (void) const
ComplexMatrix R (void) const
ostream& operator << (ostream &os, const ComplexQR &a)

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