{
  "__type": "IngestedDoc",
  "__tag": 4010,
  "_content": {
    "Notes": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "ParamRef",
              "__tag": 4071,
              "name": "f"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " must be continuous.  f(a) and f(b) must have opposite signs."
            }
          ]
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "As mentioned in the parameter documentation, the computed root "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "x0"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " will satisfy "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "np.isclose(x, x0, atol=xtol, rtol=rtol)"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ", where "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "x"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " is the exact root. In equation form, this terminating condition is "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "abs(x - x0) <= xtol + rtol * abs(x0)"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "."
            }
          ]
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "The default value "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "xtol=2e-12"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " may lead to surprising behavior if one expects "
            },
            {
              "__type": "CrossRef",
              "__tag": 4002,
              "value": "brentq",
              "reference": {
                "__type": "LocalRef",
                "__tag": 4022,
                "kind": "module",
                "path": "scipy.optimize._zeros_py:brentq"
              },
              "kind": "module"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " to always compute roots with relative error near machine precision. Care should be taken to select "
            },
            {
              "__type": "ParamRef",
              "__tag": 4071,
              "name": "xtol"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " for the use case at hand. Setting "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "xtol=5e-324"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ", the smallest subnormal number, will ensure the highest level of accuracy. Larger values of "
            },
            {
              "__type": "ParamRef",
              "__tag": 4071,
              "name": "xtol"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " may be useful for saving function evaluations when a root is at or near zero in applications where the tiny absolute differences available between floating point numbers near zero are not meaningful."
            }
          ]
        }
      ],
      "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": [
        {
          "__type": "Parameters",
          "__tag": 4026,
          "children": [
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "root",
              "annotation": "float",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Root of "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "f"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " between "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "a"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " and "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "b"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "r",
              "annotation": "`RootResults` (present if ``full_output = True``)",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Object containing information about the convergence. In particular, "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "r.converged"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " is True if the routine converged."
                    }
                  ]
                }
              ]
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Summary": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "Find a root of a function in a bracketing interval using Brent's method."
            }
          ]
        }
      ],
      "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": "f",
              "annotation": "function",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Python function returning a number. The function "
                    },
                    {
                      "__type": "InlineMath",
                      "__tag": 4057,
                      "value": "f"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " must be continuous, and "
                    },
                    {
                      "__type": "InlineMath",
                      "__tag": 4057,
                      "value": "f(a)"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " and "
                    },
                    {
                      "__type": "InlineMath",
                      "__tag": 4057,
                      "value": "f(b)"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " must have opposite signs."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "a",
              "annotation": "scalar",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "One end of the bracketing interval "
                    },
                    {
                      "__type": "InlineMath",
                      "__tag": 4057,
                      "value": "[a, b]"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "b",
              "annotation": "scalar",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "The other end of the bracketing interval "
                    },
                    {
                      "__type": "InlineMath",
                      "__tag": 4057,
                      "value": "[a, b]"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "xtol",
              "annotation": "number, optional",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "The computed root "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "x0"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " will satisfy "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "np.isclose(x, x0, atol=xtol, rtol=rtol)"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": ", where "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "x"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " is the exact root. The parameter must be positive. For nice functions, Brent's method will often satisfy the above condition with "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "xtol/2"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " and "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "rtol/2"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": ". "
                    },
                    {
                      "__type": "CitationReference",
                      "__tag": 4063,
                      "label": "Brent1973"
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "rtol",
              "annotation": "number, optional",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "The computed root "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "x0"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " will satisfy "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "np.isclose(x, x0, atol=xtol, rtol=rtol)"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": ", where "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "x"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " is the exact root. The parameter cannot be smaller than its default value of "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "4*np.finfo(float).eps"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": ". For nice functions, Brent's method will often satisfy the above condition with "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "xtol/2"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " and "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "rtol/2"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": ". "
                    },
                    {
                      "__type": "CitationReference",
                      "__tag": 4063,
                      "label": "Brent1973"
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "maxiter",
              "annotation": "int, optional",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "If convergence is not achieved in "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "maxiter"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " iterations, an error is raised. Must be >= 0."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "args",
              "annotation": "tuple, optional",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Containing extra arguments for the function "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "f"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": ". "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "f"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " is called by "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "apply(f, (x)+args)"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "full_output",
              "annotation": "bool, optional",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "If "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "full_output"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " is False, the root is returned. If "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "full_output"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " is True, the return value is "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "(x, r)"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": ", where "
                    },
                    {
                      "__type": "InlineRole",
                      "__tag": 4003,
                      "value": "x",
                      "domain": null,
                      "role": null,
                      "inventory": null
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " is the root, and "
                    },
                    {
                      "__type": "CrossRef",
                      "__tag": 4002,
                      "value": "r",
                      "reference": {
                        "__type": "RefInfo",
                        "__tag": 4000,
                        "module": null,
                        "version": null,
                        "kind": "local",
                        "path": "r"
                      },
                      "kind": "local"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " is a "
                    },
                    {
                      "__type": "CrossRef",
                      "__tag": 4002,
                      "value": "RootResults",
                      "reference": {
                        "__type": "LocalRef",
                        "__tag": 4022,
                        "kind": "module",
                        "path": "scipy.optimize._zeros_py:RootResults"
                      },
                      "kind": "module"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " object."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "disp",
              "annotation": "bool, optional",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "If True, raise RuntimeError if the algorithm didn't converge. Otherwise, the convergence status is recorded in any "
                    },
                    {
                      "__type": "CrossRef",
                      "__tag": 4002,
                      "value": "RootResults",
                      "reference": {
                        "__type": "LocalRef",
                        "__tag": 4022,
                        "kind": "module",
                        "path": "scipy.optimize._zeros_py:RootResults"
                      },
                      "kind": "module"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " return object."
                    }
                  ]
                }
              ]
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Extended Summary": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "Uses the classic Brent's method to find a root of the function "
            },
            {
              "__type": "ParamRef",
              "__tag": 4071,
              "name": "f"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " on the sign changing interval [a , b]. Generally considered the best of the rootfinding routines here. It is a safe version of the secant method that uses inverse quadratic extrapolation. Brent's method combines root bracketing, interval bisection, and inverse quadratic interpolation. It is sometimes known as the van Wijngaarden-Dekker-Brent method. Brent (1973) claims convergence is guaranteed for functions computable within [a,b]."
            }
          ]
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "CitationReference",
              "__tag": 4063,
              "label": "Brent1973"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " provides the classic description of the algorithm. Another description can be found in a recent edition of Numerical Recipes, including "
            },
            {
              "__type": "CitationReference",
              "__tag": 4063,
              "label": "PressEtal1992"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ". A third description is at http://mathworld.wolfram.com/BrentsMethod.html. It should be easy to understand the algorithm just by reading our code. Our code diverges a bit from standard presentations: we choose a different formula for the extrapolation step."
            }
          ]
        }
      ],
      "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/_zeros_py.py",
  "item_line": 712,
  "item_type": "function",
  "aliases": [
    "scipy.optimize.brentq"
  ],
  "example_section_data": {
    "__type": "Section",
    "__tag": 4015,
    "children": [
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "def f(x):\n    return (x**2 - 1)\n",
        "execution_status": "success"
      },
      {
        "__type": "Text",
        "__tag": 4046,
        "value": "\n"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "from scipy import optimize\n",
        "execution_status": "success"
      },
      {
        "__type": "Text",
        "__tag": 4046,
        "value": "\n"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "root = optimize.brentq(f, -2, 0)\nroot\n",
        "execution_status": "success"
      },
      {
        "__type": "Text",
        "__tag": 4046,
        "value": "\n"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "root = optimize.brentq(f, 0, 2)\nroot\n",
        "execution_status": "success"
      }
    ],
    "title": [],
    "level": 0,
    "target": null
  },
  "see_also": [
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "basinhopping",
        "reference": {
          "__type": "LocalRef",
          "__tag": 4022,
          "kind": "module",
          "path": "scipy.optimize._basinhopping:basinhopping"
        },
        "kind": "module"
      },
      "descriptions": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "global optimizers"
            }
          ]
        }
      ],
      "type": null
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "bisect",
        "reference": {
          "__type": "LocalRef",
          "__tag": 4022,
          "kind": "module",
          "path": "scipy.optimize._zeros_py:bisect"
        },
        "kind": "module"
      },
      "descriptions": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "1-D root-finding"
            }
          ]
        }
      ],
      "type": null
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "bracket",
        "reference": {
          "__type": "LocalRef",
          "__tag": 4022,
          "kind": "module",
          "path": "scipy.optimize._optimize:bracket"
        },
        "kind": "module"
      },
      "descriptions": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "local scalar minimizers"
            }
          ]
        }
      ],
      "type": null
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "brent",
        "reference": {
          "__type": "LocalRef",
          "__tag": 4022,
          "kind": "module",
          "path": "scipy.optimize._optimize:brent"
        },
        "kind": "module"
      },
      "descriptions": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "local scalar minimizers"
            }
          ]
        }
      ],
      "type": null
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "brenth",
        "reference": {
          "__type": "LocalRef",
          "__tag": 4022,
          "kind": "module",
          "path": "scipy.optimize._zeros_py:brenth"
        },
        "kind": "module"
      },
      "descriptions": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "1-D root-finding"
            }
          ]
        }
      ],
      "type": null
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "brute",
        "reference": {
          "__type": "LocalRef",
          "__tag": 4022,
          "kind": "module",
          "path": "scipy.optimize._optimize:brute"
        },
        "kind": "module"
      },
      "descriptions": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "global optimizers"
            }
          ]
        }
      ],
      "type": null
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "differential_evolution",
        "reference": {
          "__type": "LocalRef",
          "__tag": 4022,
          "kind": "module",
          "path": "scipy.optimize._differentialevolution:differential_evolution"
        },
        "kind": "module"
      },
      "descriptions": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "global optimizers"
            }
          ]
        }
      ],
      "type": null
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "elementwise.find_root",
        "reference": {
          "__type": "RefInfo",
          "__tag": 4000,
          "module": "current-module",
          "version": "current-version",
          "kind": "to-resolve",
          "path": "elementwise.find_root"
        },
        "kind": "module"
      },
      "descriptions": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "efficient elementwise 1-D root-finder"
            }
          ]
        }
      ],
      "type": null
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "fixed_point",
        "reference": {
          "__type": "LocalRef",
          "__tag": 4022,
          "kind": "module",
          "path": "scipy.optimize._minpack_py:fixed_point"
        },
        "kind": "module"
      },
      "descriptions": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "scalar fixed-point finder"
            }
          ]
        }
      ],
      "type": null
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "fmin",
        "reference": {
          "__type": "LocalRef",
          "__tag": 4022,
          "kind": "module",
          "path": "scipy.optimize._optimize:fmin"
        },
        "kind": "module"
      },
      "descriptions": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "multivariate local optimizers"
            }
          ]
        }
      ],
      "type": null
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "fmin_bfgs",
        "reference": {
          "__type": "LocalRef",
          "__tag": 4022,
          "kind": "module",
          "path": "scipy.optimize._optimize:fmin_bfgs"
        },
        "kind": "module"
      },
      "descriptions": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "multivariate local optimizers"
            }
          ]
        }
      ],
      "type": null
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "fmin_cg",
        "reference": {
          "__type": "LocalRef",
          "__tag": 4022,
          "kind": "module",
          "path": "scipy.optimize._optimize:fmin_cg"
        },
        "kind": "module"
      },
      "descriptions": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "multivariate local optimizers"
            }
          ]
        }
      ],
      "type": null
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "fmin_cobyla",
        "reference": {
          "__type": "LocalRef",
          "__tag": 4022,
          "kind": "module",
          "path": "scipy.optimize._cobyla_py:fmin_cobyla"
        },
        "kind": "module"
      },
      "descriptions": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "constrained multivariate optimizers"
            }
          ]
        }
      ],
      "type": null
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "fmin_l_bfgs_b",
        "reference": {
          "__type": "LocalRef",
          "__tag": 4022,
          "kind": "module",
          "path": "scipy.optimize._lbfgsb_py:fmin_l_bfgs_b"
        },
        "kind": "module"
      },
      "descriptions": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "constrained multivariate optimizers"
            }
          ]
        }
      ],
      "type": null
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "fmin_ncg",
        "reference": {
          "__type": "LocalRef",
          "__tag": 4022,
          "kind": "module",
          "path": "scipy.optimize._optimize:fmin_ncg"
        },
        "kind": "module"
      },
      "descriptions": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "multivariate local optimizers"
            }
          ]
        }
      ],
      "type": null
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "fmin_powell",
        "reference": {
          "__type": "LocalRef",
          "__tag": 4022,
          "kind": "module",
          "path": "scipy.optimize._optimize:fmin_powell"
        },
        "kind": "module"
      },
      "descriptions": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "multivariate local optimizers"
            }
          ]
        }
      ],
      "type": null
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "fmin_tnc",
        "reference": {
          "__type": "LocalRef",
          "__tag": 4022,
          "kind": "module",
          "path": "scipy.optimize._tnc:fmin_tnc"
        },
        "kind": "module"
      },
      "descriptions": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "constrained multivariate optimizers"
            }
          ]
        }
      ],
      "type": null
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "fminbound",
        "reference": {
          "__type": "LocalRef",
          "__tag": 4022,
          "kind": "module",
          "path": "scipy.optimize._optimize:fminbound"
        },
        "kind": "module"
      },
      "descriptions": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "local scalar minimizers"
            }
          ]
        }
      ],
      "type": null
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "fsolve",
        "reference": {
          "__type": "LocalRef",
          "__tag": 4022,
          "kind": "module",
          "path": "scipy.optimize._minpack_py:fsolve"
        },
        "kind": "module"
      },
      "descriptions": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "N-D root-finding"
            }
          ]
        }
      ],
      "type": null
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "golden",
        "reference": {
          "__type": "LocalRef",
          "__tag": 4022,
          "kind": "module",
          "path": "scipy.optimize._optimize:golden"
        },
        "kind": "module"
      },
      "descriptions": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "local scalar minimizers"
            }
          ]
        }
      ],
      "type": null
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "leastsq",
        "reference": {
          "__type": "LocalRef",
          "__tag": 4022,
          "kind": "module",
          "path": "scipy.optimize._minpack_py:leastsq"
        },
        "kind": "module"
      },
      "descriptions": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "nonlinear least squares minimizer"
            }
          ]
        }
      ],
      "type": null
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "newton",
        "reference": {
          "__type": "LocalRef",
          "__tag": 4022,
          "kind": "module",
          "path": "scipy.optimize._zeros_py:newton"
        },
        "kind": "module"
      },
      "descriptions": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "1-D root-finding"
            }
          ]
        }
      ],
      "type": null
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "ridder",
        "reference": {
          "__type": "LocalRef",
          "__tag": 4022,
          "kind": "module",
          "path": "scipy.optimize._zeros_py:ridder"
        },
        "kind": "module"
      },
      "descriptions": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "1-D root-finding"
            }
          ]
        }
      ],
      "type": null
    }
  ],
  "signature": {
    "__type": "SignatureNode",
    "__tag": 4029,
    "kind": "function",
    "parameters": [
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "f",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": {
          "__type": "Empty",
          "__tag": 4031
        }
      },
      {
        "__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": "b",
        "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": "xtol",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "2e-12"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "rtol",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "8.881784197001252e-16"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "maxiter",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "100"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "full_output",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "False"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "disp",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "True"
      }
    ],
    "return_annotation": {
      "__type": "Empty",
      "__tag": 4031
    },
    "target_name": "brentq"
  },
  "references": [
    ".. [Brent1973]",
    "   Brent, R. P.,",
    "   *Algorithms for Minimization Without Derivatives*.",
    "   Englewood Cliffs, NJ: Prentice-Hall, 1973. Ch. 3-4.",
    "",
    ".. [PressEtal1992]",
    "   Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T.",
    "   *Numerical Recipes in FORTRAN: The Art of Scientific Computing*, 2nd ed.",
    "   Cambridge, England: Cambridge University Press, pp. 352-355, 1992.",
    "   Section 9.3:  \"Van Wijngaarden-Dekker-Brent Method.\""
  ],
  "qa": "scipy.optimize._zeros_py:brentq",
  "arbitrary": [],
  "local_refs": [
    "a",
    "args",
    "b",
    "disp",
    "f",
    "full_output",
    "maxiter",
    "r",
    "root",
    "rtol",
    "xtol"
  ]
}