public class CholeskyDecomposition extends Object
The Cholesky decomposition of a real symmetric positive-definite matrix A consists of a lower triangular matrix L with same size such that: A = LLT. In a sense, this is the square root of A.
This class is based on the class with similar name from the JAMA library, with the following changes:
getLT
method has been added,isspd
method has been removed, since the constructor of
this class throws a MathIllegalArgumentException
when a
matrix cannot be decomposed,getDeterminant
method has been added,solve
method has been replaced by a getSolver
method and the equivalent method provided by the returned
DecompositionSolver
.Modifier and Type | Field | Description |
---|---|---|
static double |
DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD |
Default threshold below which diagonal elements are considered null
and matrix not positive definite.
|
static double |
DEFAULT_RELATIVE_SYMMETRY_THRESHOLD |
Default threshold above which off-diagonal elements are considered too different
and matrix not symmetric.
|
Constructor | Description |
---|---|
CholeskyDecomposition(RealMatrix matrix) |
Calculates the Cholesky decomposition of the given matrix.
|
CholeskyDecomposition(RealMatrix matrix,
double relativeSymmetryThreshold,
double absolutePositivityThreshold) |
Calculates the Cholesky decomposition of the given matrix.
|
Modifier and Type | Method | Description |
---|---|---|
double |
getDeterminant() |
Return the determinant of the matrix
|
RealMatrix |
getL() |
Returns the matrix L of the decomposition.
|
RealMatrix |
getLT() |
Returns the transpose of the matrix L of the decomposition.
|
DecompositionSolver |
getSolver() |
Get a solver for finding the A × X = B solution in least square sense.
|
public static final double DEFAULT_RELATIVE_SYMMETRY_THRESHOLD
public static final double DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD
public CholeskyDecomposition(RealMatrix matrix)
Calling this constructor is equivalent to call CholeskyDecomposition(RealMatrix, double, double)
with the
thresholds set to the default values DEFAULT_RELATIVE_SYMMETRY_THRESHOLD
and DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD
matrix
- the matrix to decomposeMathIllegalArgumentException
- if the matrix is not square.MathIllegalArgumentException
- if the matrix is not symmetric.MathIllegalArgumentException
- if the matrix is not
strictly positive definite.CholeskyDecomposition(RealMatrix, double, double)
,
DEFAULT_RELATIVE_SYMMETRY_THRESHOLD
,
DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD
public CholeskyDecomposition(RealMatrix matrix, double relativeSymmetryThreshold, double absolutePositivityThreshold)
matrix
- the matrix to decomposerelativeSymmetryThreshold
- threshold above which off-diagonal
elements are considered too different and matrix not symmetricabsolutePositivityThreshold
- threshold below which diagonal
elements are considered null and matrix not positive definiteMathIllegalArgumentException
- if the matrix is not square.MathIllegalArgumentException
- if the matrix is not symmetric.MathIllegalArgumentException
- if the matrix is not
strictly positive definite.CholeskyDecomposition(RealMatrix)
,
DEFAULT_RELATIVE_SYMMETRY_THRESHOLD
,
DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD
public RealMatrix getL()
L is an lower-triangular matrix
public RealMatrix getLT()
LT is an upper-triangular matrix
public double getDeterminant()
public DecompositionSolver getSolver()
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