How To Fix TE255 - Cholesky decomposition is successful after adding &1 to diagonal elements

SAP Error Message - Details

• Message type: E = Error

• Message class: TE - Market Risk Management

• Message number: 255

• Message text: Cholesky decomposition is successful after adding &1 to diagonal elements

What causes this issue?

Cholesky decomposition of the original covariance matrix could not be
performed successfully. Subsequently, the system automatically altered
the covariance matrix to achieve positive definiteness, but not in the
material sense.
This was achieved by adding a small number (epsilon) to all diagonal
elements of the matrix. When epsilon = &V1& is added, Cholesky
decomposition is performed successfully.

System Response

The system issues an error message and will not allow you to continue with this transaction until the error is resolved.

How to fix this error?

Procedure for System Administrators

Error message extract from SAP system. Copyright SAP SE.

Smart SAP Assistant

• What is the cause and solution for SAP error message TE255 - Cholesky decomposition is successful after adding &1 to diagonal elements ?

  The SAP error message TE255 indicates that a Cholesky decomposition was successful after adding a value to the diagonal elements of a matrix. This typically occurs in the context of financial calculations, such as when dealing with covariance matrices in risk management or portfolio optimization.
  Cause:
  The Cholesky decomposition is a method used to decompose a positive definite matrix into a lower triangular matrix and its transpose. If the matrix is not positive definite, the decomposition cannot be performed directly. The error message suggests that the matrix was not positive definite initially, and a small value (denoted as &1 in the message) was added to the diagonal elements to make it positive definite. This adjustment is often necessary in numerical computations to ensure stability and convergence.
  Solution:
  
  
  Review the Matrix: Check the matrix that is being decomposed. Ensure that it is supposed to be positive definite. If it is not, investigate why it is not. This could be due to data issues, such as incorrect input values or correlations that do not make sense.
  
  
  Adjust Input Data: If the input data is incorrect, correct it. This may involve revising the data sources or the calculations that lead to the creation of the matrix.
  
  
  Regularization: If the matrix is inherently not positive definite due to the nature of the data, consider using regularization techniques. Adding a small value to the diagonal (as indicated by the error message) is a common approach, but ensure that this does not significantly alter the results.
  
  
  Consult Documentation: Review SAP documentation or consult with SAP support for specific guidance related to the module you are working with. There may be specific configurations or settings that can help avoid this issue.
  
  
  Testing: After making adjustments, test the calculations again to ensure that the Cholesky decomposition can be performed without needing to add values to the diagonal.
  
  
  Related Information:
  
  Positive Definite Matrix: A matrix is positive definite if all its eigenvalues are positive. This property is crucial for many mathematical and statistical methods, including Cholesky decomposition.
  Numerical Stability: In numerical computations, ensuring stability is important. Adding a small value to the diagonal can help, but it should be done judiciously to avoid skewing results.
  SAP Modules: This error may be encountered in various SAP modules, particularly those related to finance, risk management, or analytics. Understanding the context in which the error occurs can help in troubleshooting.
  
  If the problem persists after following these steps, it may be beneficial to engage with SAP support or a consultant who specializes in the specific SAP module you are using.