﻿ JaggedCholeskyDecomposition Class

# JaggedCholeskyDecomposition Class

Cholesky Decomposition of a symmetric, positive definite matrix.
Inheritance Hierarchy
SystemObject
Accord.Math.DecompositionsJaggedCholeskyDecomposition

Namespace:  Accord.Math.Decompositions
Assembly:  Accord.Math (in Accord.Math.dll) Version: 3.8.0
Syntax
```[SerializableAttribute]
public sealed class JaggedCholeskyDecomposition : ICloneable,
ISolverArrayDecomposition<double>```

The JaggedCholeskyDecomposition type exposes the following members.

Constructors
NameDescription
JaggedCholeskyDecomposition
Constructs a new Cholesky Decomposition.
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Properties
NameDescription
Determinant
Gets the determinant of the decomposed matrix.
Diagonal
Gets the one-dimensional array of diagonal elements in a LDLt decomposition.
DiagonalMatrix
Gets the block diagonal matrix of diagonal elements in a LDLt decomposition.
IsPositiveDefinite
Gets whether the decomposed matrix was positive definite.
IsUndefined
Gets a value indicating whether the LDLt factorization has been computed successfully or if it is undefined.
LeftTriangularFactor
Gets the left (lower) triangular factor L so that A = L * D * L'.
LogDeterminant
If the matrix is positive-definite, gets the log-determinant of the decomposed matrix.
Nonsingular
Gets a value indicating whether the decomposed matrix is non-singular (i.e. invertible).
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Methods
NameDescription
Clone
Creates a new object that is a copy of the current instance.
Equals
Determines whether the specified object is equal to the current object.
(Inherited from Object.)
FromLeftTriangularMatrix
Creates a new Cholesky decomposition directly from an already computed left triangular matrix L.
GetHashCode
Serves as the default hash function.
(Inherited from Object.)
GetInformationMatrix
Computes (Xt * X)^1 (the inverse of the covariance matrix). This matrix can be used to determine standard errors for the coefficients when solving a linear set of equations through any of the Solve(Double) methods.
GetType
Gets the Type of the current instance.
(Inherited from Object.)
Inverse
Solves a set of equation systems of type A * X = I.
InverseDiagonal(Boolean)
Computes the diagonal of the inverse of the decomposed matrix.
InverseDiagonal(Double, Boolean)
Computes the diagonal of the inverse of the decomposed matrix.
InverseTrace
Computes the trace of the inverse of the decomposed matrix.
Reverse
Reverses the decomposition, reconstructing the original matrix X.
Solve(Double)
Solves a set of equation systems of type A * x = b.
Solve(Double)
Solves a set of equation systems of type A * X = B.
Solve(Double, Boolean)
Solves a set of equation systems of type A * x = b.
Solve(Double, Boolean)
Solves a set of equation systems of type A * X = B.
SolveForDiagonal
Solves a set of equation systems of type A * X = B where B is a diagonal matrix.
ToString
Returns a string that represents the current object.
(Inherited from Object.)
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Extension Methods
NameDescription
HasMethod
Checks whether an object implements a method with the given name.
(Defined by ExtensionMethods.)
IsEqual
Compares two objects for equality, performing an elementwise comparison if the elements are vectors or matrices.
(Defined by Matrix.)
Converts an object into another type, irrespective of whether the conversion can be done at compile time or not. This can be used to convert generic types to numeric types during runtime.
(Defined by ExtensionMethods.)
Converts an object into another type, irrespective of whether the conversion can be done at compile time or not. This can be used to convert generic types to numeric types during runtime.
(Defined by ExtensionMethods.)
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Remarks

For a symmetric, positive definite matrix A, the Cholesky decomposition is a lower triangular matrix L so that A = L * L'. If the matrix is not positive definite, the constructor returns a partial decomposition and sets two internal variables that can be queried using the IsUndefined and IsPositiveDefinite properties.

Any square matrix A with non-zero pivots can be written as the product of a lower triangular matrix L and an upper triangular matrix U; this is called the LU decomposition. However, if A is symmetric and positive definite, we can choose the factors such that U is the transpose of L, and this is called the Cholesky decomposition. Both the LU and the Cholesky decomposition are used to solve systems of linear equations.

When it is applicable, the Cholesky decomposition is twice as efficient as the LU decomposition.