# Class SemiDefinitePositiveCholeskyDecomposition

java.lang.Object
org.hipparchus.linear.SemiDefinitePositiveCholeskyDecomposition

public class SemiDefinitePositiveCholeskyDecomposition extends Object
Calculates the Cholesky decomposition of a positive semidefinite matrix.

The classic Cholesky decomposition (CholeskyDecomposition) applies to real symmetric positive-definite matrix. This class extends the Cholesky decomposition to positive semidefinite matrix. The main application is for estimation based on the Unscented Kalman Filter.

Since:
2.2
• "J. Hartikainen, A. Solin, and S. Särkkä. Optimal ﬁltering with Kalman ﬁlters and smoothers, Dept. of Biomedica Engineering and Computational Sciences, Aalto University School of Science, Aug. 2011."
• ## Field Details

• ### POSITIVITY_THRESHOLD

public static final double POSITIVITY_THRESHOLD
Default threshold below which elements are not considered positive.
• ## Constructor Details

• ### SemiDefinitePositiveCholeskyDecomposition

public SemiDefinitePositiveCholeskyDecomposition(RealMatrix matrix)
Calculates the Cholesky decomposition of the given matrix.
Parameters:
matrix - the matrix to decompose
Throws:
MathIllegalArgumentException - if the matrix is not square.
• ### SemiDefinitePositiveCholeskyDecomposition

public SemiDefinitePositiveCholeskyDecomposition(RealMatrix matrix, double positivityThreshold)
Calculates the Cholesky decomposition of the given matrix.
Parameters:
matrix - the matrix to decompose
positivityThreshold - threshold below which elements are not considered positive
Throws:
MathIllegalArgumentException - if the matrix is not square.
• ## Method Details

• ### getL

public RealMatrix getL()
Returns the matrix L of the decomposition.

L is an lower-triangular matrix

Returns:
the L matrix
• ### getLT

public RealMatrix getLT()
Returns the transpose of the matrix L of the decomposition.

LT is an upper-triangular matrix

Returns:
the transpose of the matrix L of the decomposition