Class EpistemeLinearAlgebraBackend<E>

java.lang.Object

org.episteme.core.mathematics.linearalgebra.backends.EpistemeLinearAlgebraBackend<E>

All Implemented Interfaces:

AutoCloseable, LinearAlgebraProvider<E>, SparseLinearAlgebraProvider<E>, AlgorithmProvider, Backend, ComputeBackend, CPUBackend, SIMDBackend

@AutoService({Backend.class,LinearAlgebraProvider.class})
public class EpistemeLinearAlgebraBackend<E>
extends Object
implements SparseLinearAlgebraProvider<E>, SIMDBackend, CPUBackend

Unified CPU backend for Episteme linear algebra.

This backend acts as a foundation (socle) and relay, delegating to optimized dense and sparse providers while ensuring a robust Java environment.

Since:

1.2

Author:

Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

Constructor Summary

Constructors

Constructor	Description
EpistemeLinearAlgebraBackend()
EpistemeLinearAlgebraBackend(Ring<E> ring)

Method Summary

Modifier and Type	Method	Description
Matrix<E>	add(Matrix<E> a, Matrix<E> b)
Vector<E>	bicgstab(Matrix<E> a, Vector<E> b, Vector<E> x0, E tolerance, int maxIterations)	Solves Ax = b using BiCGSTAB (BiConjugate Gradient Stabilized) method.
CholeskyResult<E>	cholesky(Matrix<E> a)	Computes the Cholesky decomposition of the specified matrix.
void	close()
Vector<E>	conjugateGradient(Matrix<E> a, Vector<E> b, Vector<E> x0, E tolerance, int maxIterations)	Solves Ax = b using Conjugate Gradient method.
Object	createBackend()	Creates and returns the backend instance (or returns self if it is the backend).
ExecutionContext	createContext()	Creates an execution context for running operations.
E	determinant(Matrix<E> a)
E	dot(Vector<E> a, Vector<E> b)
EigenResult<E>	eigen(Matrix<E> a)	Computes the eigenvalue decomposition of the specified matrix.
HardwareAccelerator	getAcceleratorType()	Returns the type of hardware accelerator used by this backend.
String	getDescription()	Returns a description of the backend.
String	getId()	Returns the unique identifier for this backend (e.g., "javafx", "jmol", "cuda").
String	getName()	Returns the display name for UI presentation.
int	getPreferredVectorWidth()	Returns the preferred vector width in bytes for double operations.
int	getPriority()	Priority of this provider (higher means more preferred).
String	getSimdLevel()	Returns the SIMD instruction set level available.
String	getType()	Returns the backend type category (e.g., "plotting", "molecular", "tensor", "math").
Vector<E>	gmres(Matrix<E> a, Vector<E> b, Vector<E> x0, E tolerance, int maxIterations, int restarts)	Solves Ax = b using GMRES (Generalized Minimal Residual) method.
Matrix<E>	inverse(Matrix<E> a)
boolean	isAvailable()	Checks if the provider is available in the current environment.
boolean	isCompatible(Ring<?> ring)	Checks if this provider is compatible with the given ring.
LUResult<E>	lu(Matrix<E> a)	Computes the LU decomposition of the specified matrix.
Matrix<E>	multiply(Matrix<E> a, Matrix<E> b)
Vector<E>	multiply(Matrix<E> a, Vector<E> b)
Vector<E>	multiply(Vector<E> vector, E scalar)
E	norm(Vector<E> a)
QRResult<E>	qr(Matrix<E> a)	Computes the QR decomposition of the specified matrix.
Matrix<E>	scale(E scalar, Matrix<E> a)
void	shutdown()	Called when the provider is no longer needed (e.g., application shutdown).
Vector<E>	solve(CholeskyResult<E> cholesky, Vector<E> b)	Solves Ax = b using a previously computed Cholesky decomposition.
Vector<E>	solve(LUResult<E> lu, Vector<E> b)	Solves Ax = b using a previously computed LU decomposition.
Vector<E>	solve(QRResult<E> qr, Vector<E> b)	Solves Ax = b using a previously computed QR decomposition.
Vector<E>	solve(Matrix<E> a, Vector<E> b)
Vector<E>	solveTriangular(Matrix<E> a, Vector<E> b, boolean upper, boolean transpose, boolean conjugate, boolean unit)	Solves the triangular system Ax = b.
Matrix<E>	subtract(Matrix<E> a, Matrix<E> b)
SVDResult<E>	svd(Matrix<E> a)	Computes the Singular Value Decomposition (SVD) of the specified matrix.
E	trace(Matrix<E> a)
Matrix<E>	transpose(Matrix<E> a)

Methods inherited from class Object

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

Methods inherited from interface AlgorithmProvider

description, getMetadata

Methods inherited from interface Backend

getAlgorithmProviders, getStatusMessage, isExplicitlyDisabled

Methods inherited from interface CPUBackend

supportsComplexNumbers, supportsFloatingPoint, supportsParallelOps

Methods inherited from interface LinearAlgebraProvider

acos, acosh, add, angle, asin, asinh, atan, atanh, cbrt, configure, conjugateTranspose, cos, cosh, cross, exp, getEnvironmentInfo, log, log10, normalize, pow, projection, score, sin, sinh, sqrt, subtract, tan, tanh

Methods inherited from interface SparseLinearAlgebraProvider

conditionNumber, fromDense, getAlgorithmType, rank, toDense

Constructor Details

EpistemeLinearAlgebraBackend

public EpistemeLinearAlgebraBackend()

EpistemeLinearAlgebraBackend

public EpistemeLinearAlgebraBackend(Ring<E> ring)

Method Details

getId

public String getId()

Description copied from interface: Backend

Returns the unique identifier for this backend (e.g., "javafx", "jmol", "cuda").

Specified by:

getId in interface Backend

Specified by:

getId in interface ComputeBackend

getName

public String getName()

Description copied from interface: Backend

Returns the display name for UI presentation.

Specified by:

getName in interface AlgorithmProvider

Specified by:

getName in interface Backend

Specified by:

getName in interface LinearAlgebraProvider<E>

getAcceleratorType

public HardwareAccelerator getAcceleratorType()

Description copied from interface: ComputeBackend

Returns the type of hardware accelerator used by this backend.

Specified by:

getAcceleratorType in interface ComputeBackend

Specified by:

getAcceleratorType in interface CPUBackend

Specified by:

getAcceleratorType in interface SIMDBackend

Returns:

the accelerator type

getType

public String getType()

Description copied from interface: Backend

Returns the backend type category (e.g., "plotting", "molecular", "tensor", "math").

Specified by:

getType in interface Backend

Specified by:

getType in interface ComputeBackend

Specified by:

getType in interface CPUBackend

Specified by:

getType in interface SIMDBackend

getDescription

public String getDescription()

Description copied from interface: Backend

Returns a description of the backend.

Specified by:

getDescription in interface Backend

Specified by:

getDescription in interface ComputeBackend

isAvailable

public boolean isAvailable()

Description copied from interface: AlgorithmProvider

Checks if the provider is available in the current environment.

Specified by:

isAvailable in interface AlgorithmProvider

Specified by:

isAvailable in interface Backend

getPriority

public int getPriority()

Description copied from interface: LinearAlgebraProvider

Priority of this provider (higher means more preferred). Used for automatic backend selection.

Specified by:

getPriority in interface AlgorithmProvider

Specified by:

getPriority in interface Backend

Specified by:

getPriority in interface LinearAlgebraProvider<E>

isCompatible

public boolean isCompatible(Ring<?> ring)

Description copied from interface: LinearAlgebraProvider

Checks if this provider is compatible with the given ring.

Specified by:

isCompatible in interface LinearAlgebraProvider<E>

createContext

public ExecutionContext createContext()

Description copied from interface: ComputeBackend

Creates an execution context for running operations.

The context should be used within a try-with-resources block to ensure proper cleanup of resources.

Specified by:

createContext in interface ComputeBackend

Returns:

new execution context

createBackend

public Object createBackend()

Description copied from interface: Backend

Creates and returns the backend instance (or returns self if it is the backend).

Specified by:

createBackend in interface Backend

Specified by:

createBackend in interface ComputeBackend

Returns:

The backend implementation object

shutdown

public void shutdown()

Description copied from interface: AlgorithmProvider

Called when the provider is no longer needed (e.g., application shutdown). Use this to release local resources or close native segments.

Specified by:

shutdown in interface AlgorithmProvider

Specified by:

shutdown in interface Backend

getSimdLevel

public String getSimdLevel()

Description copied from interface: SIMDBackend

Returns the SIMD instruction set level available.

Examples: "AVX2", "AVX-512", "NEON", "SVE", "GENERIC"

Specified by:

getSimdLevel in interface SIMDBackend

getPreferredVectorWidth

public int getPreferredVectorWidth()

Description copied from interface: SIMDBackend

Returns the preferred vector width in bytes for double operations.

Typical values: 32 (AVX2), 64 (AVX-512), 16 (NEON)

Specified by:

getPreferredVectorWidth in interface SIMDBackend

add

public Matrix<E> add(Matrix<E> a,
 Matrix<E> b)

Specified by:

add in interface LinearAlgebraProvider<E>

subtract

public Matrix<E> subtract(Matrix<E> a,
 Matrix<E> b)

Specified by:

subtract in interface LinearAlgebraProvider<E>

multiply

public Matrix<E> multiply(Matrix<E> a,
 Matrix<E> b)

Specified by:

multiply in interface LinearAlgebraProvider<E>

multiply

public Vector<E> multiply(Matrix<E> a,
 Vector<E> b)

Specified by:

multiply in interface LinearAlgebraProvider<E>

scale

public Matrix<E> scale(E scalar,
 Matrix<E> a)

Specified by:

scale in interface LinearAlgebraProvider<E>

multiply

public Vector<E> multiply(Vector<E> vector,
 E scalar)

Specified by:

multiply in interface LinearAlgebraProvider<E>

dot

public E dot(Vector<E> a,
 Vector<E> b)

Specified by:

dot in interface LinearAlgebraProvider<E>

norm

public E norm(Vector<E> a)

Specified by:

norm in interface LinearAlgebraProvider<E>

transpose

public Matrix<E> transpose(Matrix<E> a)

Specified by:

transpose in interface LinearAlgebraProvider<E>

trace

public E trace(Matrix<E> a)

Specified by:

trace in interface LinearAlgebraProvider<E>

determinant

public E determinant(Matrix<E> a)

Specified by:

determinant in interface LinearAlgebraProvider<E>

inverse

public Matrix<E> inverse(Matrix<E> a)

Specified by:

inverse in interface LinearAlgebraProvider<E>

lu

public LUResult<E> lu(Matrix<E> a)

Description copied from interface: LinearAlgebraProvider

Computes the LU decomposition of the specified matrix.

Specified by:

lu in interface LinearAlgebraProvider<E>

qr

public QRResult<E> qr(Matrix<E> a)

Description copied from interface: LinearAlgebraProvider

Computes the QR decomposition of the specified matrix.

Specified by:

qr in interface LinearAlgebraProvider<E>

cholesky

public CholeskyResult<E> cholesky(Matrix<E> a)

Description copied from interface: LinearAlgebraProvider

Computes the Cholesky decomposition of the specified matrix.

Specified by:

cholesky in interface LinearAlgebraProvider<E>

eigen

public EigenResult<E> eigen(Matrix<E> a)

Description copied from interface: LinearAlgebraProvider

Computes the eigenvalue decomposition of the specified matrix.

Specified by:

eigen in interface LinearAlgebraProvider<E>

svd

public SVDResult<E> svd(Matrix<E> a)

Description copied from interface: LinearAlgebraProvider

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

Specified by:

svd in interface LinearAlgebraProvider<E>

solve

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

Specified by:

solve in interface LinearAlgebraProvider<E>

solve

public Vector<E> solve(LUResult<E> lu,
 Vector<E> b)

Description copied from interface: LinearAlgebraProvider

Solves Ax = b using a previously computed LU decomposition.

Specified by:

solve in interface LinearAlgebraProvider<E>

solve

public Vector<E> solve(QRResult<E> qr,
 Vector<E> b)

Description copied from interface: LinearAlgebraProvider

Solves Ax = b using a previously computed QR decomposition.

Specified by:

solve in interface LinearAlgebraProvider<E>

solve

public Vector<E> solve(CholeskyResult<E> cholesky,
 Vector<E> b)

Description copied from interface: LinearAlgebraProvider

Solves Ax = b using a previously computed Cholesky decomposition.

Specified by:

solve in interface LinearAlgebraProvider<E>

solveTriangular

public Vector<E> solveTriangular(Matrix<E> a,
 Vector<E> b,
 boolean upper,
 boolean transpose,
 boolean conjugate,
 boolean unit)

Description copied from interface: LinearAlgebraProvider

Solves the triangular system Ax = b.

Specified by:

solveTriangular in interface LinearAlgebraProvider<E>

Parameters:

a - the triangular matrix

b - the right-hand side vector

upper - true if A is upper triangular, false if lower

transpose - true if solving A^T x = b

conjugate - true if solving A^H x = b (only if transpose is true and complex)

unit - true if A is unit triangular (diagonal is all ones)

bicgstab

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

Description copied from interface: SparseLinearAlgebraProvider

Solves Ax = b using BiCGSTAB (BiConjugate Gradient Stabilized) method.

Specified by:

bicgstab in interface SparseLinearAlgebraProvider<E>

gmres

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

Description copied from interface: SparseLinearAlgebraProvider

Solves Ax = b using GMRES (Generalized Minimal Residual) method.

Specified by:

gmres in interface SparseLinearAlgebraProvider<E>

conjugateGradient

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

Description copied from interface: SparseLinearAlgebraProvider

Solves Ax = b using Conjugate Gradient method.

Specified by:

conjugateGradient in interface SparseLinearAlgebraProvider<E>

close

public void close()

Specified by:

close in interface AutoCloseable

Specified by:

close in interface LinearAlgebraProvider<E>