Package org.flag4j.linalg

Class PositiveDefiniteness

java.lang.Object

org.flag4j.linalg.PositiveDefiniteness

public class PositiveDefiniteness
extends Object

This class contains several methods for determining the positive definiteness of a matrix.

Constructor Summary

Constructors

Modifier	Constructor	Description
private	PositiveDefiniteness()

Method Summary

Modifier and Type	Method	Description
static boolean	isPosDef(CMatrix src)	Checks if the matrix is positive definite.
static boolean	isPosDef(Matrix src)	Checks if the matrix is positive definite.
static boolean	isPosSemiDef(CMatrix src)	Checks if the matrix is positive semi-definite.
static boolean	isPosSemiDef(Matrix src)	Checks if the matrix is positive semi-definite.
static boolean	isSymmPosDef(CMatrix src)	Checks if the matrix is symmetric positive definite.
static boolean	isSymmPosDef(Matrix src)	Checks if the matrix is symmetric positive definite.

Methods inherited from class java.lang.Object

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

Constructor Details

PositiveDefiniteness

private PositiveDefiniteness()

Method Details

isPosDef

public static boolean isPosDef(Matrix src)

Checks if the matrix is positive definite. A matrix M is positive definite iff x^TMx > 0 for any vector x, or equivalently, if all eigenvalues are strictly greater than zero.

Parameters:

src - Matrix to check if it is positive definite.

Returns:

True if the matrix is positive definite. Otherwise, returns false.

See Also:

• isPosSemiDef(Matrix)

isSymmPosDef

public static boolean isSymmPosDef(Matrix src)

Checks if the matrix is symmetric positive definite. A matrix M is positive definite iff x^TMx > 0 for any vector x, or equivalently, if all eigenvalues are strictly greater than zero.

Parameters:

src - Matrix to check if it is positive definite.

Returns:

True if the matrix is positive definite. Otherwise, returns false.

See Also:

• isPosSemiDef(Matrix)

isPosDef

public static boolean isPosDef(CMatrix src)

Checks if the matrix is positive definite. A matrix M is positive definite iff x^TMx > 0 for any vector x, or equivalently, if the matrix is hermitian and all eigenvalues are strictly greater than zero.

Parameters:

src - Matrix to check if it is positive definite.

Returns:

True if the matrix is positive definite. Otherwise, returns false.

See Also:

• isPosSemiDef(CMatrix)

isSymmPosDef

public static boolean isSymmPosDef(CMatrix src)

Checks if the matrix is symmetric positive definite. A matrix M is positive definite iff x^TMx > 0 for any vector x, or equivalently, if all eigenvalues are strictly greater than zero.

Parameters:

src - Matrix to check if it is positive definite.

Returns:

True if the matrix is positive definite. Otherwise, returns false.

See Also:

• isPosSemiDef(Matrix)

isPosSemiDef

public static boolean isPosSemiDef(Matrix src)

Checks if the matrix is positive semi-definite. A matrix M is positive semi-definite iff x^TMx >= 0 for any vector x, or equivalently, if the matrix is symmetric and all eigenvalues are greater than or equal to zero.

Parameters:

src - Matrix to check if it is positive semi-definite.

Returns:

True if the matrix is positive semi-definite. Otherwise, returns false.

See Also:

• isPosSemiDef(Matrix)

isPosSemiDef

public static boolean isPosSemiDef(CMatrix src)

Checks if the matrix is positive semi-definite. A matrix M is positive semi-definite iff x^TMx >= 0 for any vector x, or equivalently, if the matrix is hermitian and all eigenvalues are greater than or equal to zero.

Parameters:

src - Matrix to check if it is positive semi-definite.

Returns:

True if the matrix is positive semi-definite. Otherwise, returns false.

See Also:

• isPosSemiDef(CMatrix)