How To Fix TE253 - Cholesky decomposition cannot be processed due to negative square root

SAP Error Message - Details

• Message type: E = Error

• Message class: TE - Market Risk Management

• Message number: 253

• Message text: Cholesky decomposition cannot be processed due to negative square root

What causes this issue?

During calculation of Cholesky decomposition, the argument below the
square root becomes negative. In detail, the matrix is not positive
definite.

System Response

The negative square root has no solution in the expected range.
Therefore, the Cholesky decomposition cannot be calculated.

How to fix this error?

Check the market data, especially the data for risk factor &V1& and
above.
Check the market data for same validation date. If this is not
fulfilled, it could be the reason for inconsistencies in the values for
the correlation coefficient.

Procedure for System Administrators

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

Error message extract from SAP system. Copyright SAP SE.

Smart SAP Assistant

• What is the cause and solution for SAP error message TE253 - Cholesky decomposition cannot be processed due to negative square root ?

  The SAP error message TE253, which states "Cholesky decomposition cannot be processed due to negative square root," typically occurs in the context of financial or statistical calculations, particularly when dealing with covariance matrices or similar mathematical constructs. This error indicates that the matrix being processed is not positive definite, which is a requirement for Cholesky decomposition.
  Cause:
  
  Negative Eigenvalues: The matrix may have one or more negative eigenvalues, which means it is not positive definite.
  Data Issues: The underlying data used to create the matrix may contain errors, such as outliers or incorrect values.
  Model Specification: The model or assumptions used to generate the covariance matrix may be incorrect or inappropriate for the data.
  Numerical Instability: In some cases, numerical precision issues can lead to this error, especially with large datasets or poorly scaled data.
  
  Solution:
  
  Check Data Quality: Review the input data for any anomalies, outliers, or incorrect values that could affect the covariance matrix.
  Adjust Model: Re-evaluate the model specifications and assumptions. Ensure that the model is appropriate for the data being analyzed.
  Regularization: If applicable, consider adding a small positive value (regularization) to the diagonal elements of the covariance matrix to make it positive definite.
  Use Alternative Methods: If Cholesky decomposition is not feasible, consider using other decomposition methods that can handle non-positive definite matrices, such as Singular Value Decomposition (SVD) or Principal Component Analysis (PCA).
  Matrix Conditioning: Improve the conditioning of the matrix by scaling or transforming the data appropriately.
  
  Related Information:
  
  Cholesky Decomposition: This is a method for decomposing a positive definite matrix into a lower triangular matrix and its transpose. It is widely used in numerical analysis and statistics.
  Positive Definite Matrix: A matrix is positive definite if all its eigenvalues are positive, which is a requirement for certain mathematical operations, including Cholesky decomposition.
  Eigenvalues and Eigenvectors: Understanding the properties of eigenvalues and eigenvectors can help diagnose issues with matrix decomposition.
  SAP Documentation: Refer to SAP's official documentation or support resources for specific guidance related to the error in the context of the SAP application you are using.
  
  If the problem persists after trying the above solutions, it may be beneficial to consult with a technical expert or SAP support for further assistance.