python runtime_error ai_generated true

numpy.linalg.LinAlgError: Matrix is not positive definite

ID: python/scipy-linalg-singular

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80%Fix Rate
87%Confidence
0Evidence
2024-07-01First Seen

Version Compatibility

VersionStatusIntroducedDeprecatedNotes
3.x active — — —

Root Cause

Cholesky decomposition (np.linalg.cholesky / scipy.linalg.cholesky) requires a symmetric positive-definite matrix. Numerical noise, non-symmetric input, or a truly indefinite matrix breaks this.

generic

中文

Cholesky 分解（np.linalg.cholesky / scipy.linalg.cholesky）要求对称正定矩阵。数值噪声、非对称输入或真正非正定的矩阵会导致失败。

Workarounds

  1. 90% success 
    A = (A + A.T) / 2; A += 1e-8 * np.eye(A.shape[0]); L = np.linalg.cholesky(A)
  2. 85% success 
    Use scipy.linalg.ldl(A) or np.linalg.eigh(A) for indefinite matrices

Dead Ends

Common approaches that don't work:

  1. 70% fail

    Regularization too small for ill-conditioned matrices

  2. 90% fail

    Triangular part isn't symmetric