org.apache.ignite.ml.math.decompositions

Class CholeskyDecomposition

java.lang.Object

org.apache.ignite.ml.math.decompositions.CholeskyDecomposition

All Implemented Interfaces:

Destroyable

public class CholeskyDecomposition
extends Object
implements Destroyable

Calculates the Cholesky decomposition of a matrix.

This class inspired by class from Apache Common Math with similar name.

See Also:

MathWorld, Wikipedia

Field Summary

Fields

Modifier and Type	Field and Description
static double	DFLT_ABS_POSITIVITY_THRESHOLD Default threshold below which diagonal elements are considered null and matrix not positive definite.
static double	DFLT_REL_SYMMETRY_THRESHOLD Default threshold above which off-diagonal elements are considered too different and matrix not symmetric.

Constructor Summary

Constructors

Constructor and Description
CholeskyDecomposition(Matrix mtx) Calculates the Cholesky decomposition of the given matrix.
CholeskyDecomposition(Matrix mtx, double relSymmetryThreshold, double absPositivityThreshold) Calculates the Cholesky decomposition of the given matrix.

Method Summary

Modifier and Type	Method and Description
void	destroy() Destroys object if managed outside of JVM.
double	getDeterminant() Return the determinant of the matrix
Matrix	getL() Returns the matrix L of the decomposition.
Matrix	getLT() Returns the transpose of the matrix L of the decomposition.
Matrix	solve(Matrix b) Solve the linear equation A × X = B for matrices A.
Vector	solve(Vector b) Solve the linear equation A × X = B for matrices A.

Methods inherited from class java.lang.Object

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

Field Detail

DFLT_REL_SYMMETRY_THRESHOLD

public static final double DFLT_REL_SYMMETRY_THRESHOLD

Default threshold above which off-diagonal elements are considered too different and matrix not symmetric.

See Also:

Constant Field Values

DFLT_ABS_POSITIVITY_THRESHOLD

public static final double DFLT_ABS_POSITIVITY_THRESHOLD

Default threshold below which diagonal elements are considered null and matrix not positive definite.

See Also:

Constant Field Values

Constructor Detail

CholeskyDecomposition

public CholeskyDecomposition(Matrix mtx)

Calculates the Cholesky decomposition of the given matrix.

Calling this constructor is equivalent to call CholeskyDecomposition(Matrix, double, double) with the thresholds set to the default values DFLT_REL_SYMMETRY_THRESHOLD and DFLT_ABS_POSITIVITY_THRESHOLD.

Parameters:

mtx - the matrix to decompose.

Throws:

CardinalityException - if matrix is not square.

See Also:

CholeskyDecomposition(Matrix, double, double), DFLT_REL_SYMMETRY_THRESHOLD, DFLT_ABS_POSITIVITY_THRESHOLD

CholeskyDecomposition

public CholeskyDecomposition(Matrix mtx,
                             double relSymmetryThreshold,
                             double absPositivityThreshold)

Calculates the Cholesky decomposition of the given matrix.

Parameters:

mtx - the matrix to decompose.

relSymmetryThreshold - threshold above which off-diagonal elements are considered too different and matrix not symmetric

absPositivityThreshold - threshold below which diagonal elements are considered null and matrix not positive definite

See Also:

CholeskyDecomposition(Matrix), DFLT_REL_SYMMETRY_THRESHOLD, DFLT_ABS_POSITIVITY_THRESHOLD

Method Detail

destroy

public void destroy()

Destroys object if managed outside of JVM. It's a no-op in all other cases.

Specified by:

destroy in interface Destroyable

getL

public Matrix getL()

Returns the matrix L of the decomposition.

L is an lower-triangular matrix

Returns:

the L matrix

getLT

public Matrix getLT()

Returns the transpose of the matrix L of the decomposition.

L^T is an upper-triangular matrix

Returns:

the transpose of the matrix L of the decomposition

getDeterminant

public double getDeterminant()

Return the determinant of the matrix

Returns:

determinant of the matrix

solve

public Vector solve(Vector b)

Solve the linear equation A × X = B for matrices A.

Parameters:

b - right-hand side of the equation A × X = B

Returns:

a vector X that minimizes the two norm of A × X - B

Throws:

CardinalityException - if the vectors dimensions do not match

solve

public Matrix solve(Matrix b)

Solve the linear equation A × X = B for matrices A.

Parameters:

b - right-hand side of the equation A × X = B

Returns:

a matrix X that minimizes the two norm of A × X - B

Throws:

CardinalityException - if the matrices dimensions do not match