Class Decomposition

java.lang.Object

org.episteme.core.mathematics.linearalgebra.Decomposition

public final class Decomposition
extends Object

High-level utility for matrix decompositions.

This class abstracts the provider system, automatically selecting the most efficient implementation (Native LAPACK, EJML, or Core) based on matrix characteristics and available hardware.

Since:

1.2

Author:

Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

Method Summary

Modifier and Type	Method	Description
static <E> Vector<E>	bicgstab(Matrix<E> a, Vector<E> b, Vector<E> x0, E tolerance, int maxIterations)	Solves Ax = b using BiCGSTAB.
static <E> CholeskyResult<E>	cholesky(Matrix<E> matrix)	Computes the Cholesky decomposition of the specified matrix.
static <E> Vector<E>	conjugateGradient(Matrix<E> a, Vector<E> b, Vector<E> x0, E tolerance, int maxIterations)	Solves Ax = b using Conjugate Gradient.
static <E> EigenResult<E>	eigen(Matrix<E> matrix)	Computes the eigenvalue decomposition of the specified matrix.
static <E> Vector<E>	gmres(Matrix<E> a, Vector<E> b, Vector<E> x0, E tolerance, int maxIterations, int restarts)	Solves Ax = b using GMRES.
static <E> LUResult<E>	lu(Matrix<E> matrix)	Computes the LU decomposition of the specified matrix.
static <E> QRResult<E>	qr(Matrix<E> matrix)	Computes the QR decomposition of the specified matrix.
static <E> Vector<E>	solve(Matrix<E> a, Vector<E> b)	Solves Ax = b using the most appropriate decomposition.
static <E> SVDResult<E>	svd(Matrix<E> matrix)	Computes the Singular Value Decomposition (SVD) of the specified matrix.

Methods inherited from class Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Details

qr

public static <E> QRResult<E> qr(Matrix<E> matrix)

Computes the QR decomposition of the specified matrix.

Type Parameters:

E - the element type

Parameters:

matrix - the matrix to decompose

Returns:

the QR result

svd

public static <E> SVDResult<E> svd(Matrix<E> matrix)

Computes the Singular Value Decomposition (SVD) of the specified matrix.

Type Parameters:

E - the element type

Parameters:

matrix - the matrix to decompose

Returns:

the SVD result

eigen

public static <E> EigenResult<E> eigen(Matrix<E> matrix)

Computes the eigenvalue decomposition of the specified matrix.

Type Parameters:

E - the element type

Parameters:

matrix - the matrix to decompose

Returns:

the eigenvalue result

lu

public static <E> LUResult<E> lu(Matrix<E> matrix)

Computes the LU decomposition of the specified matrix.

Type Parameters:

E - the element type

Parameters:

matrix - the matrix to decompose

Returns:

the LU result

cholesky

public static <E> CholeskyResult<E> cholesky(Matrix<E> matrix)

Computes the Cholesky decomposition of the specified matrix.

Type Parameters:

E - the element type

Parameters:

matrix - the matrix to decompose

Returns:

the Cholesky result

solve

public static <E> Vector<E> solve(Matrix<E> a,
 Vector<E> b)

Solves Ax = b using the most appropriate decomposition.

Type Parameters:

E - the element type

Parameters:

a - the coefficient matrix A

b - the right-hand side vector B

Returns:

the solution vector X

bicgstab

public static <E> Vector<E> bicgstab(Matrix<E> a,
 Vector<E> b,
 Vector<E> x0,
 E tolerance,
 int maxIterations)

Solves Ax = b using BiCGSTAB.

conjugateGradient

public static <E> Vector<E> conjugateGradient(Matrix<E> a,
 Vector<E> b,
 Vector<E> x0,
 E tolerance,
 int maxIterations)

Solves Ax = b using Conjugate Gradient.

gmres

public static <E> Vector<E> gmres(Matrix<E> a,
 Vector<E> b,
 Vector<E> x0,
 E tolerance,
 int maxIterations,
 int restarts)

Solves Ax = b using GMRES.