RWDenseTriDiagDecomp<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()

RWDenseTriDiagDecomp() set()

transform()

#include <rw/lapack/td.h>

RWDenseTriDiagDecomp<double> QTQ(A);    // A is a
                                  // RWSymMat<double>

The class RWDenseTriDiagDecomp<T> encapsulates the symmetric tri-
diagonal decomposition of a dense symmetric matrix A, where:

and Q is orthogonal and T is real tridiagonal symmetric. These classes are used internally by the symmetric eigenvalue classes.

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

int main()
{
    RWSymMat<double> A;
    std::cin >> A;
    RWDenseTriDiagDecomp<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;
}

RWDenseTriDiagDecomp(const RWSymMat<T>& A);

Constructs a tridiagonal decomposition of A.

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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