org.ojalgo.matrix.decomposition
Interface SingularValue<N extends Number>

All Superinterfaces:

MatrixDecomposition<N>

All Known Implementing Classes:

JamaSingularValue, SingularValueDecomposition

public interface SingularValue<N extends Number>
extends MatrixDecomposition<N>

Decomposes [this] into [Q1], [D] and [Q2] where:

• [Q1] is an orthogonal matrix. The columns are the left, orthonormal, singular vectors of [this]. Its columns are the eigenvectors of [A][A]^T, and therefore has the same number of rows as [this].
• [D] is a diagonal matrix. The elements on the diagonal are the singular values of [this]. It is either square or has the same dimensions as [this]. The singular values of [this] are the square roots of the nonzero eigenvalues of [A][A]^T and [A]^T[A] (they are the same)
• [Q2] is an orthogonal matrix. The columns are the right, orthonormal, singular vectors of [this]. Its columns are the eigenvectors of [A][A]^T, and therefore has the same number of rows as [this] has columns.
• [this] = [Q1][D][Q2]^T

A singular values decomposition always exists.

Author:

apete

Method Summary

double	getCondition() The condition number.
MatrixStore<N>	getD()
double	getFrobeniusNorm() Sometimes also called the Schatten 2-norm or Hilbert-Schmidt norm.
double	getKyFanNorm(int k) Ky Fan k-norm.
double	getOperatorNorm()
MatrixStore<N>	getQ1()
MatrixStore<N>	getQ2()
int	getRank() Effective numerical matrix rank.
Array1D<Double>	getSingularValues()
double	getTraceNorm()
boolean	isOrdered()

Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition

compute, equals, equals, getInverse, invert, isComputed, isFullSize, isSolvable, reconstruct, reset, solve, solve

Method Detail

getCondition

double getCondition()

The condition number.

Returns:

The largest singular value divided by the smallest singular value.

getD

MatrixStore<N> getD()

Returns:

The diagonal matrix of singular values.

getFrobeniusNorm

double getFrobeniusNorm()

Sometimes also called the Schatten 2-norm or Hilbert-Schmidt norm.

Returns:

The square root of the sum of squares of the singular values.

getKyFanNorm

double getKyFanNorm(int k)

Ky Fan k-norm.

The first Ky Fan k-norm is the operator norm (the largest singular value), and the last is called the trace norm (the sum of all singular values).

Parameters:

k - The number of singular values to add up.

Returns:

The sum of the k largest singular values.

getOperatorNorm

double getOperatorNorm()

getQ1

MatrixStore<N> getQ1()

getQ2

MatrixStore<N> getQ2()

getRank

int getRank()

Effective numerical matrix rank.

Returns:

The number of nonnegligible singular values.

getSingularValues

Array1D<Double> getSingularValues()

Returns:

The singular values ordered in descending order.

getTraceNorm

double getTraceNorm()

isOrdered

boolean isOrdered()