Cholesky Decomposition¶
Cholesky decomposition is a matrix factorization technique that decomposes a symmetric positive-definite matrix into a product of a lower triangular matrix and its conjugate transpose.
Because of numerical stability and superior efficiency in comparison with other methods, Cholesky decomposition is widely used in numerical methods for solving symmetric linear systems. It is also used in non-linear optimization problems, Monte Carlo simulation, and Kalman filtration.
Details¶
Given a symmetric positive-definite matrix
Batch Processing¶
Algorithm Input¶
Cholesky decomposition accepts the input described below.
Pass the Input ID
as a parameter to the methods that provide input for your algorithm.
For more details, see Algorithms.
Input ID |
Input |
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|
Pointer to the The input can be an object of any class derived from |
Algorithm Parameters¶
Cholesky decomposition has the following parameters:
Parameter |
Default Value |
Description |
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|
|
The floating-point type that the algorithm uses for intermediate computations. Can be |
|
|
Performance-oriented computation method, the only method supported by the algorithm. |
Algorithm Output¶
Cholesky decomposition calculates the result described below.
Pass the Result ID
as a parameter to the methods that access the results of your algorithm.
For more details, see Algorithms.
Result ID |
Result |
---|---|
|
Pointer to the By default, the result is an object of the |
Examples¶
Batch Processing:
Performance Considerations¶
To get the best overall performance when Cholesky decomposition:
If input data is homogeneous, for input matrix
and output matrix use homogeneous numeric tables of the same type as specified in thealgorithmFPType
class template parameter.If input data is non-homogeneous, use AOS layout rather than SOA layout.
Product and Performance Information |
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Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex. Notice revision #20201201 |