RWBalanceTransform<T>

Module:  Linear Algebra   Group:  Decomposition Classes

Does not inherit

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

Members

cols() highIndex()

invTransform() lowIndex()

operator=() rows()

RWBalanceTransform() transform()

#include <rw/lapack/bal.h>

RWBalanceTransform<double> dtrans;

A permutation and balance transformation is often performed on a nonsymmetric matrix before computing its eigenvalues. The permutation attempts to break the matrix into three independent blocks such that the first and last block are triangular, and the balance transformation is a diagonal scaling transformation that attempts to make the row and column norms close to each other. The class RWBalanceTransform<T> encapsulates these two transformations.

The class RWBalanceTransform<T> is not often required explicitly; most often it is used implicitly by the nonsymmetric eigenvalue decompositions and servers. If you do need to use this class explicitly, it is usually best to construct an object and extract the transform from the object.

RWBalanceTransform();

Constructs an empty transformation.

unsigned
cols() const;

Returns the number of columns in the transformation matrix.

unsigned
highIndex() const;

If a permutation breaks the matrix into three independent blocks, this function returns the index where the middle block ends. The part of the matrix below this block is triangular, so its eigenvalues need not be computed.

RWGenMat<T>
invTransform(const RWGenMat<T>& x);
RWMathVec<T>
invTransform(const RWMathVec<T>& x);

Computes the inner product of the inverse transpose of the transform and x. This is typically used to transform left eigenvectors.

unsigned
lowIndex() const;

If a permutation breaks the matrix into three independent blocks, this function returns the index where the middle block begins. The part of the matrix above this block is triangular, so its eigenvalues need not be computed.

unsigned
rows() const;

Returns the number of rows in the transformation matrix.

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

Computes the inner product of the transform and x. This is typically used to transform right eigenvectors.

void  operator=(const DComplexBalanceTransform&);

Initializes the transformation.

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