{
  "__type": "IngestedDoc",
  "__tag": 4010,
  "_content": {
    "Notes": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "Parameters "
            },
            {
              "__type": "ParamRef",
              "__tag": 4071,
              "name": "c1"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " and "
            },
            {
              "__type": "ParamRef",
              "__tag": 4071,
              "name": "c2"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " must satisfy "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "0 < c1 < c2 < 1"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "."
            }
          ]
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "If minimization doesn't complete successfully, with an error message of "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "Desired error not necessarily achieved due to precision loss"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ", then consider setting "
            },
            {
              "__type": "ParamRef",
              "__tag": 4071,
              "name": "gtol"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " to a higher value. This precision loss typically occurs when the (finite difference) numerical differentiation cannot provide sufficient precision to satisfy the "
            },
            {
              "__type": "ParamRef",
              "__tag": 4071,
              "name": "gtol"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " termination criterion. This can happen when working in single precision and a callable jac is not provided. For single precision problems a "
            },
            {
              "__type": "ParamRef",
              "__tag": 4071,
              "name": "gtol"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " of 1e-3 seems to work."
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Warns": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Raises": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "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": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Summary": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "Minimization of scalar function of one or more variables using the BFGS algorithm."
            }
          ]
        }
      ],
      "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": "disp",
              "annotation": "bool",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Set to True to print convergence messages."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "maxiter",
              "annotation": "int",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Maximum number of iterations to perform."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "gtol",
              "annotation": "float",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Terminate successfully if gradient norm is less than "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "gtol"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "norm",
              "annotation": "float",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Order of norm (Inf is max, -Inf is min)."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "eps",
              "annotation": "float or ndarray",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "If "
                    },
                    {
                      "__type": "InlineRole",
                      "__tag": 4003,
                      "value": "jac is None",
                      "domain": null,
                      "role": null,
                      "inventory": null
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " the absolute step size used for numerical approximation of the jacobian via forward differences."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "return_all",
              "annotation": "bool, optional",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Set to True to return a list of the best solution at each of the iterations."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "finite_diff_rel_step",
              "annotation": "None or array_like, optional",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "If "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "jac in ['2-point', '3-point', 'cs']"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " the relative step size to use for numerical approximation of the jacobian. The absolute step size is computed as "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "h = rel_step * sign(x) * max(1, abs(x))"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": ", possibly adjusted to fit into the bounds. For "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "jac='3-point'"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " the sign of "
                    },
                    {
                      "__type": "InlineRole",
                      "__tag": 4003,
                      "value": "h",
                      "domain": null,
                      "role": null,
                      "inventory": null
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " is ignored. If None (default) then step is selected automatically."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "xrtol",
              "annotation": "float, default: 0",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Relative tolerance for "
                    },
                    {
                      "__type": "InlineRole",
                      "__tag": 4003,
                      "value": "x",
                      "domain": null,
                      "role": null,
                      "inventory": null
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": ". Terminate successfully if step size is less than "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "xk * xrtol"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " where "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "xk"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " is the current parameter vector."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "c1",
              "annotation": "float, default: 1e-4",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Parameter for Armijo condition rule."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "c2",
              "annotation": "float, default: 0.9",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Parameter for curvature condition rule."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "hess_inv0",
              "annotation": "None or ndarray, optional",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Initial inverse hessian estimate, shape (n, n). If None (default) then the identity matrix is used."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "workers",
              "annotation": "int, map-like callable, optional",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "A map-like callable, such as "
                    },
                    {
                      "__type": "InlineRole",
                      "__tag": 4003,
                      "value": "multiprocessing.Pool.map",
                      "domain": null,
                      "role": null,
                      "inventory": null
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " for evaluating any numerical differentiation in parallel. This evaluation is carried out as "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "workers(fun, iterable)"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "."
                    }
                  ]
                },
                {
                  "__type": "Admonition",
                  "__tag": 4056,
                  "kind": "versionadded",
                  "base_type": "neutral",
                  "children": [
                    {
                      "__type": "AdmonitionTitle",
                      "__tag": 4055,
                      "children": [
                        {
                          "__type": "Text",
                          "__tag": 4046,
                          "value": "versionadded 1.16.0"
                        }
                      ]
                    }
                  ]
                }
              ]
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Extended Summary": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "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/optimize/_optimize.py",
  "item_line": 1345,
  "item_type": "function",
  "aliases": [
    "scipy.optimize._minimize._minimize_bfgs"
  ],
  "example_section_data": {
    "__type": "Section",
    "__tag": 4015,
    "children": [],
    "title": [],
    "level": 0,
    "target": null
  },
  "see_also": [],
  "signature": {
    "__type": "SignatureNode",
    "__tag": 4029,
    "kind": "function",
    "parameters": [
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "fun",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": {
          "__type": "Empty",
          "__tag": 4031
        }
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "x0",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": {
          "__type": "Empty",
          "__tag": 4031
        }
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "args",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "()"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "jac",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "None"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "callback",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "None"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "gtol",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "1e-05"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "norm",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "inf"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "eps",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "1.4901161193847656e-08"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "maxiter",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "None"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "disp",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "False"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "return_all",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "False"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "finite_diff_rel_step",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "None"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "xrtol",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "0"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "c1",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "0.0001"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "c2",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "0.9"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "hess_inv0",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "None"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "workers",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "None"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "unknown_options",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "VAR_KEYWORD",
        "default": {
          "__type": "Empty",
          "__tag": 4031
        }
      }
    ],
    "return_annotation": {
      "__type": "Empty",
      "__tag": 4031
    },
    "target_name": "_minimize_bfgs"
  },
  "references": null,
  "qa": "scipy.optimize._optimize:_minimize_bfgs",
  "arbitrary": [],
  "local_refs": [
    "c1",
    "c2",
    "disp",
    "eps",
    "finite_diff_rel_step",
    "gtol",
    "hess_inv0",
    "maxiter",
    "norm",
    "return_all",
    "workers",
    "xrtol"
  ]
}