org.hipparchus.optim.nonlinear.vector.leastsquares

Enum GaussNewtonOptimizer.Decomposition

java.lang.Object

java.lang.Enum<GaussNewtonOptimizer.Decomposition>

org.hipparchus.optim.nonlinear.vector.leastsquares.GaussNewtonOptimizer.Decomposition

All Implemented Interfaces:

Serializable, Comparable<GaussNewtonOptimizer.Decomposition>

Enclosing class:

GaussNewtonOptimizer

public static enum GaussNewtonOptimizer.Decomposition
extends Enum<GaussNewtonOptimizer.Decomposition>

The decomposition algorithm to use to solve the normal equations.

Enum Constant Summary

Enum Constants

Enum Constant and Description
CHOLESKY Solve by forming the normal equations (JTJx=JTr) and using the CholeskyDecomposition.
LU Solve by forming the normal equations (JTJx=JTr) and using the LUDecomposition.
QR Solve the linear least squares problem (Jx=r) using the QRDecomposition.
SVD Solve the linear least squares problem using the SingularValueDecomposition.

Method Summary

Modifier and Type	Method and Description
protected abstract RealVector	solve(RealMatrix jacobian, RealVector residuals) Solve the linear least squares problem Jx=r.
static GaussNewtonOptimizer.Decomposition	valueOf(String name) Returns the enum constant of this type with the specified name.
static GaussNewtonOptimizer.Decomposition[]	values() Returns an array containing the constants of this enum type, in the order they are declared.

Methods inherited from class java.lang.Enum

clone, compareTo, equals, finalize, getDeclaringClass, hashCode, name, ordinal, toString, valueOf

Methods inherited from class java.lang.Object

getClass, notify, notifyAll, wait, wait, wait

Enum Constant Detail

LU

public static final GaussNewtonOptimizer.Decomposition LU

Solve by forming the normal equations (J^TJx=J^Tr) and using the LUDecomposition.

Theoretically this method takes mn²/2 operations to compute the normal matrix and n³/3 operations (m > n) to solve the system using the LU decomposition.

QR

public static final GaussNewtonOptimizer.Decomposition QR

Solve the linear least squares problem (Jx=r) using the QRDecomposition.

Theoretically this method takes mn² - n³/3 operations (m > n) and has better numerical accuracy than any method that forms the normal equations.

CHOLESKY

public static final GaussNewtonOptimizer.Decomposition CHOLESKY

Solve by forming the normal equations (J^TJx=J^Tr) and using the CholeskyDecomposition.

Theoretically this method takes mn²/2 operations to compute the normal matrix and n³/6 operations (m > n) to solve the system using the Cholesky decomposition.

SVD

public static final GaussNewtonOptimizer.Decomposition SVD

Solve the linear least squares problem using the SingularValueDecomposition.

This method is slower, but can provide a solution for rank deficient and nearly singular systems.

Method Detail

values

public static GaussNewtonOptimizer.Decomposition[] values()

Returns an array containing the constants of this enum type, in the order they are declared. This method may be used to iterate over the constants as follows:

for (GaussNewtonOptimizer.Decomposition c : GaussNewtonOptimizer.Decomposition.values())
    System.out.println(c);

Returns:

an array containing the constants of this enum type, in the order they are declared

valueOf

public static GaussNewtonOptimizer.Decomposition valueOf(String name)

Returns the enum constant of this type with the specified name. The string must match exactly an identifier used to declare an enum constant in this type. (Extraneous whitespace characters are not permitted.)

Parameters:

name - the name of the enum constant to be returned.

Returns:

the enum constant with the specified name

Throws:

IllegalArgumentException - if this enum type has no constant with the specified name

NullPointerException - if the argument is null

solve

protected abstract RealVector solve(RealMatrix jacobian,
                                    RealVector residuals)

Solve the linear least squares problem Jx=r.

Parameters:

jacobian - the Jacobian matrix, J. the number of rows >= the number or columns.

residuals - the computed residuals, r.

Returns:

the solution x, to the linear least squares problem Jx=r.

Throws:

MathIllegalStateException - if the matrix properties (e.g. singular) do not permit a solution.