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
static class Eig.EigMatrix
           
 
Field Summary
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
 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)


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