RWSymEigDecomp<T>, RWHermEigDecomp<T>

Module:  Linear Algebra   Group:  Symmetric Eigenvalue Decomposition classes

Does not inherit

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

Members

RWHermEigDecomp<DComplex>::eigenValue() RWHermEigDecomp<DComplex>::eigenValues() RWHermEigDecomp<T>::cols() RWHermEigDecomp<T>::eigenVector() RWHermEigDecomp<T>::eigenVectors() RWHermEigDecomp<T>::factor() RWHermEigDecomp<T>::fail()

RWHermEigDecomp<T>::good() RWHermEigDecomp<T>::inaccurate() RWHermEigDecomp<T>::numEigenValues() RWHermEigDecomp<T>::numEigenVectors() RWHermEigDecomp<T>::operator= () RWHermEigDecomp<T>::rows() RWHermEigDecomp()

RWSymEigDecomp<T>::cols() RWSymEigDecomp<T>::eigenValue() RWSymEigDecomp<T>::eigenValues() RWSymEigDecomp<T>::eigenVector() RWSymEigDecomp<T>::eigenVectors() RWSymEigDecomp<T>::factor() RWSymEigDecomp<T>::fail()

RWSymEigDecomp<T>::good() RWSymEigDecomp<T>::inaccurate() RWSymEigDecomp<T>::numEigenValues() RWSymEigDecomp<T>::numEigenVectors() RWSymEigDecomp<T>::operator= () RWSymEigDecomp<T>::rows() RWSymEigDecomp()

#include <rw/lapack/symeig.h>    // RWSymEigDecomp<T>
#include <rw/lapack/hermeig.h>  // RWHermEigDecomp<T>

RWSymEigDecomp<double> eig(A);  // A is an
                                 // RWGenMat<double>

The class RWSymEigDecomp<T> encapsulates the eigenvalues and eigenvectors of a symmetric matrix, a Hermitian in the complex case. You can construct an eigenvalue decomposition object in two ways:

• Use the decomposition class constructor. This has the advantage of simplicity, but allows only limited control over the computation. Your only choice is whether or not to compute eigenvectors.

• Use an eigenvalue server object. This gives you more precise control over the computation. See RWSymEigServer<T> in this manual for details.

#include <iostream>
#include <rw/lapack/eig.h>

int main()
{
    RWSymMat<double> A;
    std::cin >> A;
    RWSymEigDecomp<double> eig(A);
    std::cout << "eigenvalues: " << eig.eigenValues() << std::endl;
    std::cout << "eigenvectors: " << eig.eigenVectors() << std::endl;
   return 0;
}

RWSymEigDecomp();
RWHermEigDecomp();

Default constructor. Builds a decomposition of a 0 x 0 matrix.

RWSymEigDecomp(const RWSymEigDecomp<T>& A);
RWHermEigDecomp(const RWHermEigDecomp<T>& A);
RWHermEigDecomp(const RWHermEigDecomp<double>& A);

Copy and precision conversion constructors. Where possible, data is referenced for efficiency.

RWSymEigDecomp(const RWSymMat<T>& A, 
                bool computeVecs=true);
RWHermEigDecomp(const RWHermMat<T>& A, 
                bool computeVecs=true);
RWSymEigDecomp(const RWSymBandMat<T>& A, 
                bool cv=true);
RWHermEigDecomp(const RWHermBandMat<T>& A, 
                bool =true);

Constructs a representation of the eigenvalues and eigenvectors of the matrix A. The boolean parameter controls whether eigenvectors are computed.

unsigned
RWSymEigDecomp<T>::cols();
unsigned
RWHermEigDecomp<T>::cols();

Returns the number of columns in the decomposed matrix.

T
RWSymEigDecomp<T>::eigenValue(int i) const;
double
RWHermEigDecomp<DComplex>::eigenValue(int i) const;

Returns the i^th eigenvalue.

RWMathVec<T>
RWSymEigDecomp<T>::eigenValues() const;
RWMathVec<double>
RWHermEigDecomp<DComplex>::eigenValues() const;

Returns a vector of all computed eigenvalues.

RWMathVec<T>
RWSymEigDecomp<T>::eigenVector(int i) const;
RWMathVec<T>
RWHermEigDecomp<T>::eigenVector(int i) const;

Returns the i^th eigenvector.

RWGenMat<T>
RWSymEigDecomp<T>::eigenVectors() const;
RWGenMat<T>
RWHermEigDecomp<T>::eigenVectors() const;

Returns a matrix whose columns are the eigenvectors.

void
RWSymEigDecomp<T>::factor(const RWSymMat<T>& A,
    bool computeVecs=true);
void 
RWHermEigDecomp<T>::factor(const RWHermMat<T>& A,
    bool computeVecs =true);
void
RWSymEigDecomp<T>::factor(const RWSymBandMat<T>& A,
    bool computeVecs=true);
void
RWHermEigDecomp<T>::factor(RWHermBandMat<T>& A,
    bool computeVecs=true);

Constructs a representation of the eigenvalues and eigenvectors of the matrix A. The boolean parameter controls whether eigenvectors are computed. The current contents of the decomposition are lost.

bool
RWSymEigDecomp<T>::fail() const;
bool
RWHermEigDecomp<T>::fail() const;

Returns true if an eigenvalue or eigenvector that is supposed to be computed fails to be computed.

bool
RWSymEigDecomp<T>::good() const;
bool
RWHermEigDecomp<T>::good() const;

Returns true if all desired eigenvalues and eigenvectors are successfully computed to full desired accuracy.

bool
RWSymEigDecomp<T>::inaccurate() const;
bool
RWHermEigDecomp<T>::inaccurate() const;

Returns true if either an eigenvalue or eigenvector that is supposed to be computed fails to be computed, or some of the computed quantities are not computed to full desired accuracy.

unsigned
RWSymEigDecomp<T>::numEigenValues() const;
unsigned
RWHermEigDecomp<T>::numEigenValues() const;

Returns the number of eigenvalues in this object.

unsigned
RWSymEigDecomp<T>::numEigenVectors() const;
unsigned
RWHermEigDecomp<T>::numEigenVectors() const;

Returns the number of eigenvectors in this object.

unsigned
RWSymEigDecomp<T>::rows();
unsigned
RWHermEigDecomp<T>::rows();

Returns the number of rows in the decomposed matrix.

void  RWSymEigDecomp<T>::operator=
        (const RWSymEigDecomp<T>&);
void  RWHermEigDecomp<T>::operator=
        (const RWHermEigDecomp<T>&);

Assigns this decomposition the passed value. The current contents of the decomposition are lost.

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