RWBandTriDiagDecomp<T>

Module:  Linear Algebra   Group:  Decomposition classes

Does not inherit

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

Members

cols() diagonal() offDiagonal()

rows() RWBandTriDiagDecomp<DComplex>::RWBandTriDiagDecomp() RWBandTriDiagDecomp<double>::RWBandTriDiagDecomp ()

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

#include <rw/lapack/td.h>

RWBandTriDiagDecomp<double>(A);  // A is a DoubleSymMat

The class RWBandTriDiagDecomp<T> encapsulates a symmetric tridiagonal decomposition of a symmetric banded matrix A:

where Q is orthogonal and T is real tridiagonal symmetric. This class is used internally by the symmetric eigenvalue classes.

#include <rw/lapack/sbndmat.h>
#include <rw/lapack/td.h>
#include <iostream>

int main()
{
    RWSymBandMat<double> A;
    std::cin >> A;
    RWSymBandTriDiagDecomp<double> decomp(A);
    std::cout << "T's diagonal is" << decomp.diagonal() << std::endl;
    std::cout << "T's off diagonal is " << decomp.offDiagonal() 
               << std::endl;
    return 0;
}

RWBandTriDiagDecomp<double>::RWBandTriDiagDecomp
  (const RWSymMat<double>& A, bool keepQ=true);
RWBandTriDiagDecomp<float>::RWBandTriDiagDecomp(const
  RWSymMat<float>& A, bool keepQ=true);
RWBandTriDiagDecomp<DComplex>::RWBandTriDiagDecomp(const
   RWHermBandMat<DComplex>& A, bool keepQ=true);

Constructs a tridiagonal decomposition of A. By setting the optional boolean parameter to false, the data necessary to transform via Q is not stored. This can save substantial storage costs, but an exception is thrown if you attempt to use the member function transform.

unsigned
cols() const;

Returns the number of columns in the decomposition.

const RWMathVec<T>
diagonal() const;

Returns the diagonal of the symmetric tridiagonal matrix T.

const RWMathVec<T>
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
set(const RWMathVec<T>& diag,const RWMathVec<T>& offdiag);

Sets the tridiagonal matrix directly.

virtual RWMathVec<T>
transform(const RWMathVec<T>& x);
virtual RWGenMat<T>
transform(const RWGenMat<T>& 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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