{
  "__type": "IngestedDoc",
  "__tag": 4010,
  "_content": {
    "Notes": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "During the finiteness check (if selected), the entire matrix "
            },
            {
              "__type": "ParamRef",
              "__tag": 4071,
              "name": "a"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " is checked. During decomposition, "
            },
            {
              "__type": "ParamRef",
              "__tag": 4071,
              "name": "a"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " is assumed to be symmetric or Hermitian (as applicable), and only the half selected by option "
            },
            {
              "__type": "ParamRef",
              "__tag": 4071,
              "name": "lower"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " is referenced. Consequently, if "
            },
            {
              "__type": "ParamRef",
              "__tag": 4071,
              "name": "a"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " is asymmetric/non-Hermitian, "
            },
            {
              "__type": "InlineRole",
              "__tag": 4003,
              "value": "cholesky",
              "domain": null,
              "role": null,
              "inventory": null
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " may still succeed if the symmetric/Hermitian matrix represented by the selected half is positive definite, yet it may fail if an element in the other half is non-finite."
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Warns": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Raises": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Parameters",
          "__tag": 4026,
          "children": [
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "LinAlgError",
              "annotation": "if decomposition fails.",
              "desc": []
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Yields": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Methods": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Returns": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Parameters",
          "__tag": 4026,
          "children": [
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "c",
              "annotation": "(M, M) ndarray",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Upper- or lower-triangular Cholesky factor of "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "a"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "."
                    }
                  ]
                }
              ]
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Summary": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "Compute the Cholesky decomposition of a matrix."
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Receives": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Warnings": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Attributes": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Parameters": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Parameters",
          "__tag": 4026,
          "children": [
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "a",
              "annotation": "(M, M) array_like",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Matrix to be decomposed"
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "lower",
              "annotation": "bool, optional",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Whether to compute the upper- or lower-triangular Cholesky factorization. During decomposition, only the selected half of the matrix is referenced. Default is upper-triangular."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "overwrite_a",
              "annotation": "bool, optional",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Whether to overwrite data in "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "a"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " (may improve performance)."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "check_finite",
              "annotation": "bool, optional",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Whether to check that the entire input matrix contains only finite numbers. Disabling may give a performance gain, but may result in problems (crashes, non-termination) if the inputs do contain infinities or NaNs."
                    }
                  ]
                }
              ]
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Extended Summary": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "Returns the Cholesky decomposition, "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "A = L L^*"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " or "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "A = U^* U"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " of a Hermitian positive-definite matrix A."
            }
          ]
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "The documentation is written assuming array arguments are of specified \"core\" shapes. However, array argument(s) of this function may have additional \"batch\" dimensions prepended to the core shape. In this case, the array is treated as a batch of lower-dimensional slices; see "
            },
            {
              "__type": "InlineRole",
              "__tag": 4003,
              "value": "linalg_batch",
              "domain": null,
              "role": "ref",
              "inventory": null
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " for details. Note that calls with zero-size batches are unsupported and will raise a "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "ValueError"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "."
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Other Parameters": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    }
  },
  "_ordered_sections": [
    "Summary",
    "Extended Summary",
    "Parameters",
    "Attributes",
    "Methods",
    "Returns",
    "Yields",
    "Receives",
    "Other Parameters",
    "Raises",
    "Warns",
    "Warnings",
    "Notes"
  ],
  "item_file": "/scipy/linalg/_decomp_cholesky.py",
  "item_line": 50,
  "item_type": "function",
  "aliases": [
    "scipy.linalg.cholesky"
  ],
  "example_section_data": {
    "__type": "Section",
    "__tag": 4015,
    "children": [
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "import numpy as np\nfrom scipy.linalg import cholesky\na = np.array([[1,-2j],[2j,5]])\nL = cholesky(a, lower=True)\n",
        "execution_status": "success"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "L\nL @ L.T.conj()\n",
        "execution_status": "failure"
      }
    ],
    "title": [],
    "level": 0,
    "target": null
  },
  "see_also": [],
  "signature": {
    "__type": "SignatureNode",
    "__tag": 4029,
    "kind": "function",
    "parameters": [
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "a",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": {
          "__type": "Empty",
          "__tag": 4031
        }
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "lower",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "False"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "overwrite_a",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "False"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "check_finite",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "True"
      }
    ],
    "return_annotation": {
      "__type": "Empty",
      "__tag": 4031
    },
    "target_name": "cholesky"
  },
  "references": null,
  "qa": "scipy.linalg._decomp_cholesky:cholesky",
  "arbitrary": [],
  "local_refs": [
    "LinAlgError",
    "a",
    "c",
    "check_finite",
    "lower",
    "overwrite_a"
  ]
}