org.ujmp.core.doublematrix.calculation.general.decomposition

Interface Eig<T>

public interface Eig<T>

Eigenvalues and eigenvectors of a real matrix.

If A is symmetric, then A = V*D*V' where the eigenvalue matrix D is diagonal and the eigenvector matrix V is orthogonal. I.e. A = V.times(D.times(V.transpose())) and V.times(V.transpose()) equals the identity matrix.

If A is not symmetric, then the eigenvalue matrix D is block diagonal with the real eigenvalues in 1-by-1 blocks and any complex eigenvalues, lambda + i*mu, in 2-by-2 blocks, [lambda, mu; -mu, lambda]. The columns of V represent the eigenvectors in the sense that A*V = V*D, i.e. A.times(V) equals V.times(D). The matrix V may be badly conditioned, or even singular, so the validity of the equation A = V*D*inverse(V) depends upon V.cond().

Nested Class Summary

Nested Classes

Modifier and Type	Interface and Description
static class	Eig.EigMatrix

Field Summary

Fields

Modifier and Type	Field and Description
static Eig<Matrix>	INSTANCE
static Eig<Matrix>	MATRIX
static Eig<Matrix>	MATRIXLARGEMULTITHREADED
static Eig<Matrix>	MATRIXLARGESINGLETHREADED
static Eig<Matrix>	MATRIXSMALLMULTITHREADED
static Eig<Matrix>	MATRIXSMALLSINGLETHREADED
static int	THRESHOLD
static Eig<Matrix>	UJMP

Method Summary

Modifier and Type	Method and Description
T[]	calc(T source)

Field Detail

THRESHOLD

static final int THRESHOLD

See Also:

Constant Field Values

MATRIX

static final Eig<Matrix> MATRIX

MATRIXLARGESINGLETHREADED

static final Eig<Matrix> MATRIXLARGESINGLETHREADED

MATRIXLARGEMULTITHREADED

static final Eig<Matrix> MATRIXLARGEMULTITHREADED

INSTANCE

static final Eig<Matrix> INSTANCE

UJMP

static final Eig<Matrix> UJMP

MATRIXSMALLMULTITHREADED

static final Eig<Matrix> MATRIXSMALLMULTITHREADED

MATRIXSMALLSINGLETHREADED

static final Eig<Matrix> MATRIXSMALLSINGLETHREADED

Method Detail

calc

T[] calc(T source)