 | CholeskyDecompositionD Class |
Computes the Cholesky Decomposition of a matrix (double-precision).
Inheritance HierarchyNamespace: DigitalRune.Mathematics.Algebra
Assembly: DigitalRune.Mathematics (in DigitalRune.Mathematics.dll) Version: 1.14.0.0 (1.14.0.14427)
SyntaxThe CholeskyDecompositionD type exposes the following members.
Constructors| Name | Description | |
|---|---|---|
 | CholeskyDecompositionD |
Creates the Cholesky decomposition of the given matrix.
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Methods| Name | Description | |
|---|---|---|
| Equals | (Inherited from Object.) |
 | Finalize | Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.) |
| GetHashCode | Serves as a hash function for a particular type. (Inherited from Object.) |
| GetType | Gets the Type of the current instance. (Inherited from Object.) |
| MemberwiseClone | Creates a shallow copy of the current Object. (Inherited from Object.) |
| SolveLinearEquations |
Solves the equation A * X = B.
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| ToString | Returns a string that represents the current object. (Inherited from Object.) |
Properties| Name | Description | |
|---|---|---|
 | IsSymmetricPositiveDefinite |
Gets a value indicating whether the original matrix is symmetric and positive definite.
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| L |
Gets the lower triangular matrix L. (This property returns the internal matrix, not a copy.)
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RemarksThe 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