{
  "id": "python/scipy-linalg-singular",
  "signature": "numpy.linalg.LinAlgError: Matrix is not positive definite",
  "signature_zh": "numpy.linalg.LinAlgError: 矩阵不是正定的",
  "regex": "numpy\\.linalg\\.LinAlgError:\\ Matrix\\ is\\ not\\ positive\\ definite",
  "domain": "python",
  "category": "runtime_error",
  "subcategory": null,
  "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.",
  "root_cause_type": "generic",
  "root_cause_zh": "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。",
  "versions": [
    {
      "version": "3.x",
      "introduced": null,
      "deprecated": null,
      "removed": null,
      "behavior_change": null,
      "status": "active"
    }
  ],
  "os_specific": {},
  "dead_ends": [
    {
      "action": "",
      "why_fails": "Regularization too small for ill-conditioned matrices",
      "fail_rate": 0.7,
      "condition": "",
      "sources": []
    },
    {
      "action": "",
      "why_fails": "Triangular part isn't symmetric",
      "fail_rate": 0.9,
      "condition": "",
      "sources": []
    }
  ],
  "workarounds": [
    {
      "action": "",
      "success_rate": 0.9,
      "how": "A = (A + A.T) / 2; A += 1e-8 * np.eye(A.shape[0]); L = np.linalg.cholesky(A)",
      "condition": "",
      "sources": []
    },
    {
      "action": "",
      "success_rate": 0.85,
      "how": "Use scipy.linalg.ldl(A) or np.linalg.eigh(A) for indefinite matrices",
      "condition": "",
      "sources": []
    }
  ],
  "workarounds_zh": [],
  "transition_graph": {
    "leads_to": [],
    "preceded_by": [],
    "frequently_confused_with": []
  },
  "official_doc_url": null,
  "official_doc_section": null,
  "error_code": null,
  "verification_tier": "ai_generated",
  "confidence": 0.87,
  "fix_success_rate": 0.8,
  "resolvable": "true",
  "first_seen": "2024-07-01",
  "last_confirmed": "2025-01-01",
  "last_updated": "2025-01-01",
  "evidence_count": 0,
  "tags": [],
  "locale": "en",
  "aliases": []
}