Package org.apache.commons.math3.linear
Class CholeskyDecomposition
java.lang.Object
org.apache.commons.math3.linear.CholeskyDecomposition
Calculates the Cholesky decomposition of a matrix.
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:
- a
getLTmethod has been added, - the
isspdmethod has been removed, since the constructor of this class throws aNonPositiveDefiniteMatrixExceptionwhen a matrix cannot be decomposed, - a
getDeterminantmethod has been added, - the
solvemethod has been replaced by agetSolvermethod and the equivalent method provided by the returnedDecompositionSolver.
- Since:
- 2.0 (changed to concrete class in 3.0)
- See Also:
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Field Summary
FieldsModifier and TypeFieldDescriptionstatic final doubleDefault threshold below which diagonal elements are considered null and matrix not positive definite.static final doubleDefault threshold above which off-diagonal elements are considered too different and matrix not symmetric. -
Constructor Summary
ConstructorsConstructorDescriptionCholeskyDecomposition(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. -
Method Summary
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Field Details
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DEFAULT_RELATIVE_SYMMETRY_THRESHOLD
public static final double DEFAULT_RELATIVE_SYMMETRY_THRESHOLDDefault threshold above which off-diagonal elements are considered too different and matrix not symmetric.- See Also:
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DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD
public static final double DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLDDefault threshold below which diagonal elements are considered null and matrix not positive definite.- See Also:
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Constructor Details
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CholeskyDecomposition
Calculates the Cholesky decomposition of the given matrix.Calling this constructor is equivalent to call
CholeskyDecomposition(RealMatrix, double, double)with the thresholds set to the default valuesDEFAULT_RELATIVE_SYMMETRY_THRESHOLDandDEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD- Parameters:
matrix- the matrix to decompose- Throws:
NonSquareMatrixException- if the matrix is not square.NonSymmetricMatrixException- if the matrix is not symmetric.NonPositiveDefiniteMatrixException- if the matrix is not strictly positive definite.- See Also:
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CholeskyDecomposition
public CholeskyDecomposition(RealMatrix matrix, double relativeSymmetryThreshold, double absolutePositivityThreshold) Calculates the Cholesky decomposition of the given matrix.- Parameters:
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 definite- Throws:
NonSquareMatrixException- if the matrix is not square.NonSymmetricMatrixException- if the matrix is not symmetric.NonPositiveDefiniteMatrixException- if the matrix is not strictly positive definite.- See Also:
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Method Details
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getL
Returns the matrix L of the decomposition.L is an lower-triangular matrix
- Returns:
- the L matrix
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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
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getDeterminant
public double getDeterminant()Return the determinant of the matrix- Returns:
- determinant of the matrix
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getSolver
Get a solver for finding the A × X = B solution in least square sense.- Returns:
- a solver
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