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DigitalRuneCholeskyDecompositionD Class
Computes the Cholesky Decomposition of a matrix (double-precision).
Inheritance Hierarchy
SystemObject
  DigitalRune.Mathematics.AlgebraCholeskyDecompositionD

Namespace: DigitalRune.Mathematics.Algebra
Assembly: DigitalRune.Mathematics (in DigitalRune.Mathematics.dll) Version: 1.14.0.0 (1.14.0.14427)
Syntax
public class CholeskyDecompositionD

The CholeskyDecompositionD type exposes the following members.

Constructors
  NameDescription
Public methodCholeskyDecompositionD
Creates the Cholesky decomposition of the given matrix.
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Methods
  NameDescription
Public methodEquals
Determines whether the specified Object is equal to the current Object.
(Inherited from Object.)
Protected methodFinalize
Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.
(Inherited from Object.)
Public methodGetHashCode
Serves as a hash function for a particular type.
(Inherited from Object.)
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Protected methodMemberwiseClone
Creates a shallow copy of the current Object.
(Inherited from Object.)
Public methodSolveLinearEquations
Solves the equation A * X = B.
Public methodToString
Returns a string that represents the current object.
(Inherited from Object.)
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Properties
  NameDescription
Public propertyIsSymmetricPositiveDefinite
Gets a value indicating whether the original matrix is symmetric and positive definite.
Public propertyL
Gets the lower triangular matrix L. (This property returns the internal matrix, not a copy.)
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Remarks

The Cholesky Decomposition can be used on a square matrix A that is symmetric and positive definite (SPD).

Positive definite means that: vT * A * v > 0 for all vectors v. (The equivalent interpretation is that A has all positive eigenvalues.)

The matrix is decomposed into a lower triangular matrix L so that A = L * LT

If the matrix is not symmetric and positive definite, L will be a partial decomposition and the flag IsSymmetricPositiveDefinite is set to .

Applications:

  • Cholesky Decomposition can be used to solve linear equations for matrices that are SPD. This method is about a factor of 2 faster than other methods.
  • It can be used to determine efficiently if a matrix is SPD.

See Also