{type}SymDenseTriDiagDecomp, DComplexHermDenseTriDiagDecomp

Data Type and Member Function Indexes
Synopsis
Description
Example
Public Constructors
Public Member Functions

Data Type and Member Function Indexes
(exclusive of constructors and destructors)

Member Functions
DComplexHermDenseTriDiagDecomp::cols() DComplexHermDenseTriDiagDecomp::diagonal() DComplexHermDenseTriDiagDecomp::offDiagonal() DComplexHermDenseTriDiagDecomp::rows() DComplexHermDenseTriDiagDecomp::set() DComplexHermDenseTriDiagDecomp::transform()	DoubleSymDenseTriDiagDecomp::cols() DoubleSymDenseTriDiagDecomp::diagonal() DoubleSymDenseTriDiagDecomp::offDiagonal() DoubleSymDenseTriDiagDecomp::rows() DoubleSymDenseTriDiagDecomp::set() DoubleSymDenseTriDiagDecomp::transform()	FloatSymDenseTriDiagDecomp::cols() FloatSymDenseTriDiagDecomp::diagonal() FloatSymDenseTriDiagDecomp::offDiagonal() FloatSymDenseTriDiagDecomp::rows() FloatSymDenseTriDiagDecomp::set() FloatSymDenseTriDiagDecomp::transform()

Synopsis

#include <rw/dtd.h>          // DoubleSymDenseTriDiagDecomp
#include <rw/ftd.h>          // FloatSymDenseTriDiagDecomp
#include <rw/ctd.h>          // DComplexHermDenseTriDiagDecomp

DoubleSymDenseTriDiagDecomp QTQ(A);    // A is a DoubleSymMat

Description

The classes {TYPE}SymDenseTriDiagDecomp encapsulate the symmetric tri-
diagonal decomposition of a dense symmetric matrix A, where:

and Q is orthogonal and T is real tridiagonal symmetric. Class DComplexHermDenseTriDiagDecomp does the same for Hermitians. These classes are used internally by the symmetric eigenvalue classes.

Example

#include <rw/dsymmat.h>
#include <rw/dtd.h>

main()
{
    DoubleSymMat A;
    cin >> A;
    DoubleSymDenseTriDiagDecomp decomp(A);
    cout << "T's diagonal is" << decomp.diagonal() << endl;
    cout << "T's off diagonal is " << decomp.offDiagonal() << endl;
}

Public Constructors

FloatSymDenseTriDiagDecomp(const FloatSymMat& A);
DoubleSymDenseTriDiagDecomp(const DoubleSymMat& A);
DComplexHermDenseTriDiagDecomp(const DComplexSymMat& A);

Constructs a tridiagonal decomposition of A.

Public Member Functions

unsigned
FloatSymDenseTriDiagDecomp::cols() const;
unsigned
DoubleSymDenseTriDiagDecomp::cols() const;
unsigned
DComplexHermDenseTriDiagDecomp::cols() const;

Returns the number of columns in the decomposition.

const RWMathVec<float>
FloatSymDenseTriDiagDecomp::diagonal() const;
const RWMathVec<double>
DoubleSymDenseTriDiagDecomp::diagonal() const;
const RWMathVec<double>
DComplexHermDenseTriDiagDecomp::diagonal() const;

Returns the diagonal of the symmetric tridiagonal matrix T.

const RWMathVec<float>
FloatSymDenseTriDiagDecomp::offDiagonal() const;
const RWMathVec<double>
DoubleSymDenseTriDiagDecomp::offDiagonal() const;
const RWMathVec<double>
DComplexHermDenseTriDiagDecomp::offDiagonal() const;

Returns the subdiagonal or superdiagonal of the symmetric tridiagonal matrix T.

unsigned
FloatSymDenseTriDiagDecomp::rows() const;
unsigned
DoubleSymDenseTriDiagDecomp::rows() const;
unsigned
DComplexHermDenseTriDiagDecomp::rows() const;

Returns the number of rows in the decomposition.

void
FloatSymDenseTriDiagDecomp::set
          (const RWMathVec<float>& diag,
           const RWMathVec<float>& offdiag);
void
DoubleSymDenseTriDiagDecomp::set
          (const RWMathVec<double>& diag,
           const RWMathVec<double>& offdiag);
void
DComplexHermDenseTriDiagDecomp::set
          (const RWMathVec<double>&diag,
           const RWMathVec<double>& offdiag);

Sets the tridiagonal matrix directly.

virtual RWMathVec<float>
FloatSymDenseTriDiagDecomp::transform
          (const RWMathVec<float>& x);
virtual RWMathVec<double>
DoubleSymDenseTriDiagDecomp::transform
          (const RWMathVec<double>& x);
virtual RWMathVec<DComplex> 
DComplexHermDenseTriDiagDecomp::transform
          (const RWMathVec<double>& x);
virtual RWGenMat<float> 
FloatSymDenseTriDiagDecomp::transform
          (const RWGenMat<float>& x);
virtual RWGenMat<double> 
DoubleSymDenseTriDiagDecomp::transform
          (const RWGenMat<double>& x);
virtual RWGenMat<DComplex>
DComplexHermDenseTriDiagDecomp::transform
          (const RWGenMat<double>& x);

Transforms the vector from tridiagonal decomposition space back to the original matrix space. This amounts to multiplying it by the matrix Q.