RWTriDiagDecomp<T>

Module:  Linear Algebra   Group:  Symmetric Eigenvalue Decomposition classes

Does not inherit

• Local Index
• Synopsis
• Description
• Example
• Public Member Functions

Members

cols() rows() RWTriDiagDecomp<DComplex>::diagonal() RWTriDiagDecomp<DComplex>::offDiagonal()

RWTriDiagDecomp<DComplex>::set() RWTriDiagDecomp<DComplex>::transform () RWTriDiagDecomp<double>::diagonal() RWTriDiagDecomp<double>::offDiagonal()

RWTriDiagDecomp<double>::set() RWTriDiagDecomp<double>::transform () RWTriDiagDecomp<float>::diagonal() RWTriDiagDecomp<float>::offDiagonal()

RWTriDiagDecomp<float>::set() RWTriDiagDecomp<float>::transform ()

#include <rw/lapack/td.h>

The class RWTriDiagDecomp<T> encapsulates the tridiagonal decomposition of a symmetric matrix A:

where Q is orthogonal and T is tridiagonal and real, even in the complex case. This decomposition is often done as a precursor to computing eigenvalues, since the eigenvalues of T and A are the same, and those of T are easier to compute. This class is used internally by the symmetric eigenvalue classes.

The class RWTriDiagDecomp<T> is an abstract base class. Subclasses must implement the pure virtual function decompose. This separates the implementation of the storage of Q from the interface, so that band and dense decompositions can use different storage techniques. The Linear Algebra Module provides the derived classes RWDenseTriDiagDecomp<T> and RWBandTriDiagDecomp<T>.

See specific subclasses for examples.

unsigned
cols() const;

Returns the number of columns in the decomposition.

const RWMathVec<float>
RWTriDiagDecomp<float>::diagonal() const;
const RWMathVec<double>
RWTriDiagDecomp<double>::diagonal() const;
const RWMathVec<double>
RWTriDiagDecomp<DComplex>::diagonal() const;

Returns the diagonal of the symmetric tridiagonal matrix T.

const RWMathVec<float>
RWTriDiagDecomp<float>::offDiagonal() const;
const RWMathVec<double>
RWTriDiagDecomp<double>::offDiagonal() const;
const RWMathVec<double>
RWTriDiagDecomp<DComplex>::offDiagonal() const;

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

unsigned
rows() const;

Returns the number of rows in the decomposition.

void
RWTriDiagDecomp<float>::set(const RWMathVec<float>&
             diag, const RWMathVec<float>& offdiag);
void
RWTriDiagDecomp<double>::set(const RWMathVec<double>&
             diag, const RWMathVec<double>& offdiag);
void
RWTriDiagDecomp<DComplex>::set(const
                RWMathVec<double>& diag,
                 const RWMathVec<double>& offdiag);

Sets the tridiagonal matrix directly.

virtual RWMathVec<float> 
RWTriDiagDecomp<float>::transform
          (const RWMathVec<float>& x);
virtual RWMathVec<double> 
RWTriDiagDecomp<double>::transform
          (const RWMathVec<double>& x);
virtual RWMathVec<DComplex>     RWTriDiagDecomp<DComplex>::transform
          (const RWMathVec<double>& x);
virtual RWGenMat<float>
RWTriDiagDecomp<float>::transform
          (const RWGenMat<float>& x);
virtual RWGenMat<double> 
RWTriDiagDecomp<double>::transform
          (const RWGenMat<double>& x);
virtual RWGenMat<DComplex> 
RWTriDiagDecomp<DComplex>::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.

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