{
  "__type": "IngestedDoc",
  "__tag": 4010,
  "_content": {
    "Notes": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "The input array "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "a"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " may represent a single matrix or a collection (a.k.a. a \"batch\") of square matrices. For example, if "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "a.shape == (4, 3, 2, 2)"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ", it is interpreted as a "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "(4, 3)"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "-shaped batch of "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "2\\times 2"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " matrices."
            }
          ]
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "This routine checks the condition number of the "
            },
            {
              "__type": "ParamRef",
              "__tag": 4071,
              "name": "a"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " matrix and emits a "
            },
            {
              "__type": "CrossRef",
              "__tag": 4002,
              "value": "LinAlgWarning",
              "reference": {
                "__type": "LocalRef",
                "__tag": 4022,
                "kind": "module",
                "path": "scipy.linalg._misc:LinAlgWarning"
              },
              "kind": "module"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " for ill-conditioned inputs."
            }
          ]
        }
      ],
      "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": "",
              "annotation": "LinAlgError",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "If "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "a"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " is singular."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "",
              "annotation": "ValueError",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "If "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "a"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " is not square, or not 2D."
                    }
                  ]
                }
              ]
            }
          ]
        }
      ],
      "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": "ainv",
              "annotation": "ndarray",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Inverse of the matrix "
                    },
                    {
                      "__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 inverse 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": "array_like, shape (..., M, M)",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Square matrix (or a batch of matrices) to be inverted."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "overwrite_a",
              "annotation": "bool, optional",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Discard data in "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "a"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " (may improve performance). Default is False."
                    }
                  ]
                }
              ]
            },
            {
              "__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 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."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "assume_a",
              "annotation": "str, optional",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Valid entries are described above. If omitted or "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "None"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": ", checks are performed to identify structure so the appropriate solver can be called."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "lower",
              "annotation": "bool, optional",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Ignored unless "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "assume_a"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " is one of 'sym', 'her', or 'pos'. If True, the calculation uses only the data in the lower triangle of "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "a"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "; entries above the diagonal are ignored. If False (default), the calculation uses only the data in the upper triangle of "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "a"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "; entries below the diagonal are ignored."
                    }
                  ]
                }
              ]
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Extended Summary": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "If the data matrix is known to be a particular type then supplying the corresponding string to "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "assume_a"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " key chooses the dedicated solver. The available options are"
            }
          ]
        },
        {
          "__type": "Code",
          "__tag": 4050,
          "value": "=============================  ================================\n general                        'general' (or 'gen')\n diagonal                       'diagonal'\n upper triangular               'upper triangular'\n lower triangular               'lower triangular'\n symmetric positive definite    'pos'\n symmetric                      'sym'\n Hermitian                      'her'\n=============================  ================================",
          "execution_status": null
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "For the 'pos' option, only the triangle of the input matrix specified in the "
            },
            {
              "__type": "ParamRef",
              "__tag": 4071,
              "name": "lower"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " argument is used, and the other triangle is not referenced. Likewise, an explicit "
            },
            {
              "__type": "InlineRole",
              "__tag": 4003,
              "value": "assume_a='diagonal'",
              "domain": null,
              "role": null,
              "inventory": null
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " means that off-diagonal elements are not referenced."
            }
          ]
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "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."
            }
          ]
        }
      ],
      "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/_basic.py",
  "item_line": 1353,
  "item_type": "function",
  "aliases": [
    "scipy.linalg.inv"
  ],
  "example_section_data": {
    "__type": "Section",
    "__tag": 4015,
    "children": [
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "import numpy as np\nfrom scipy import linalg\na = np.array([[1., 2.], [3., 4.]])\nlinalg.inv(a)\n",
        "execution_status": "success"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "np.dot(a, linalg.inv(a))\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": "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"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "assume_a",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "KEYWORD_ONLY",
        "default": "None"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "lower",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "KEYWORD_ONLY",
        "default": "False"
      }
    ],
    "return_annotation": {
      "__type": "Empty",
      "__tag": 4031
    },
    "target_name": "inv"
  },
  "references": null,
  "qa": "scipy.linalg._basic:inv",
  "arbitrary": [],
  "local_refs": [
    "a",
    "ainv",
    "assume_a",
    "check_finite",
    "lower",
    "overwrite_a"
  ]
}