{ "__type": "IngestedDoc", "__tag": 4010, "_content": { "Notes": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "This section describes the available solvers that can be selected by the 'method' parameter. The default method is the " }, { "__type": "InlineCode", "__tag": 4051, "value": "\"Bounded\"" }, { "__type": "Text", "__tag": 4046, "value": " Brent method if " }, { "__type": "ParamRef", "__tag": 4071, "name": "bounds" }, { "__type": "Text", "__tag": 4046, "value": " are passed and unbounded " }, { "__type": "InlineCode", "__tag": 4051, "value": "\"Brent\"" }, { "__type": "Text", "__tag": 4046, "value": " otherwise." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Method " }, { "__type": "InlineRole", "__tag": 4003, "value": "Brent ", "domain": null, "role": "ref", "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " uses Brent's algorithm " }, { "__type": "FootnoteReference", "__tag": 4066, "label": "1" }, { "__type": "Text", "__tag": 4046, "value": " to find a local minimum. The algorithm uses inverse parabolic interpolation when possible to speed up convergence of the golden section method." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Method " }, { "__type": "InlineRole", "__tag": 4003, "value": "Golden ", "domain": null, "role": "ref", "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " uses the golden section search technique " }, { "__type": "FootnoteReference", "__tag": 4066, "label": "1" }, { "__type": "Text", "__tag": 4046, "value": ". It uses analog of the bisection method to decrease the bracketed interval. It is usually preferable to use the " }, { "__type": "Emphasis", "__tag": 4047, "children": [ { "__type": "Text", "__tag": 4046, "value": "Brent" } ] }, { "__type": "Text", "__tag": 4046, "value": " method." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Method " }, { "__type": "InlineRole", "__tag": 4003, "value": "Bounded ", "domain": null, "role": "ref", "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " can perform bounded minimization " }, { "__type": "FootnoteReference", "__tag": 4066, "label": "2" }, { "__type": "Text", "__tag": 4046, "value": " " }, { "__type": "FootnoteReference", "__tag": 4066, "label": "3" }, { "__type": "Text", "__tag": 4046, "value": ". It uses the Brent method to find a local minimum in the interval x1 < xopt < x2." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Note that the Brent and Golden methods do not guarantee success unless a valid " }, { "__type": "InlineCode", "__tag": 4051, "value": "bracket" }, { "__type": "Text", "__tag": 4046, "value": " triple is provided. If a three-point bracket cannot be found, consider " }, { "__type": "CrossRef", "__tag": 4002, "value": "scipy.optimize.minimize", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "scipy", "version": "*", "kind": "api", "path": "scipy.optimize._minimize:minimize" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": ". Also, all methods are intended only for local minimization. When the function of interest has more than one local minimum, consider " }, { "__type": "InlineRole", "__tag": 4003, "value": "global_optimization", "domain": null, "role": "ref", "inventory": null }, { "__type": "Text", "__tag": 4046, "value": "." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Strong", "__tag": 4048, "children": [ { "__type": "Text", "__tag": 4046, "value": "Custom minimizers" } ] } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "It may be useful to pass a custom minimization method, for example when using some library frontend to minimize_scalar. You can simply pass a callable as the " }, { "__type": "InlineCode", "__tag": 4051, "value": "method" }, { "__type": "Text", "__tag": 4046, "value": " parameter." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The callable is called as " }, { "__type": "InlineCode", "__tag": 4051, "value": "method(fun, args, **kwargs, **options)" }, { "__type": "Text", "__tag": 4046, "value": " where " }, { "__type": "InlineCode", "__tag": 4051, "value": "kwargs" }, { "__type": "Text", "__tag": 4046, "value": " corresponds to any other parameters passed to " }, { "__type": "InlineRole", "__tag": 4003, "value": "minimize", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " (such as " }, { "__type": "ParamRef", "__tag": 4071, "name": "bracket" }, { "__type": "Text", "__tag": 4046, "value": ", " }, { "__type": "ParamRef", "__tag": 4071, "name": "tol" }, { "__type": "Text", "__tag": 4046, "value": ", etc.), except the " }, { "__type": "ParamRef", "__tag": 4071, "name": "options" }, { "__type": "Text", "__tag": 4046, "value": " dict, which has its contents also passed as " }, { "__type": "ParamRef", "__tag": 4071, "name": "method" }, { "__type": "Text", "__tag": 4046, "value": " parameters pair by pair. The method shall return an " }, { "__type": "CrossRef", "__tag": 4002, "value": "OptimizeResult", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.optimize._optimize:OptimizeResult" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " object." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The provided " }, { "__type": "ParamRef", "__tag": 4071, "name": "method" }, { "__type": "Text", "__tag": 4046, "value": " callable must be able to accept (and possibly ignore) arbitrary parameters; the set of parameters accepted by " }, { "__type": "InlineRole", "__tag": 4003, "value": "minimize", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " may expand in future versions and then these parameters will be passed to the method. You can find an example in the scipy.optimize tutorial." } ] }, { "__type": "Admonition", "__tag": 4056, "kind": "versionadded", "base_type": "neutral", "children": [ { "__type": "AdmonitionTitle", "__tag": 4055, "children": [ { "__type": "Text", "__tag": 4046, "value": "versionadded 0.11.0" } ] } ] } ], "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": "res", "annotation": "OptimizeResult", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The optimization result represented as a " }, { "__type": "InlineCode", "__tag": 4051, "value": "OptimizeResult" }, { "__type": "Text", "__tag": 4046, "value": " object. Important attributes are: " }, { "__type": "InlineCode", "__tag": 4051, "value": "x" }, { "__type": "Text", "__tag": 4046, "value": " the solution array, " }, { "__type": "InlineCode", "__tag": 4051, "value": "success" }, { "__type": "Text", "__tag": 4046, "value": " a Boolean flag indicating if the optimizer exited successfully and " }, { "__type": "InlineCode", "__tag": 4051, "value": "message" }, { "__type": "Text", "__tag": 4046, "value": " which describes the cause of the termination. See " }, { "__type": "CrossRef", "__tag": 4002, "value": "OptimizeResult", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.optimize._optimize:OptimizeResult" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " for a description of other attributes." } ] } ] } ] } ], "title": [], "level": 0, "target": null }, "Summary": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Local minimization of scalar function of one variable." } ] } ], "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": "fun", "annotation": "callable", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Objective function. Scalar function, must return a scalar." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Suppose the callable has signature " }, { "__type": "InlineCode", "__tag": 4051, "value": "f0(x, *my_args, **my_kwargs)" }, { "__type": "Text", "__tag": 4046, "value": ", where " }, { "__type": "InlineCode", "__tag": 4051, "value": "my_args" }, { "__type": "Text", "__tag": 4046, "value": " and " }, { "__type": "InlineCode", "__tag": 4051, "value": "my_kwargs" }, { "__type": "Text", "__tag": 4046, "value": " are required positional and keyword arguments. Rather than passing " }, { "__type": "InlineCode", "__tag": 4051, "value": "f0" }, { "__type": "Text", "__tag": 4046, "value": " as the callable, wrap it to accept only " }, { "__type": "InlineCode", "__tag": 4051, "value": "x" }, { "__type": "Text", "__tag": 4046, "value": "; e.g., pass " }, { "__type": "InlineCode", "__tag": 4051, "value": "fun=lambda x: f0(x, *my_args, **my_kwargs)" }, { "__type": "Text", "__tag": 4046, "value": " as the callable, where " }, { "__type": "InlineCode", "__tag": 4051, "value": "my_args" }, { "__type": "Text", "__tag": 4046, "value": " (tuple) and " }, { "__type": "InlineCode", "__tag": 4051, "value": "my_kwargs" }, { "__type": "Text", "__tag": 4046, "value": " (dict) have been gathered before invoking this function." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "bracket", "annotation": "sequence, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "For methods 'brent' and 'golden', " }, { "__type": "ParamRef", "__tag": 4071, "name": "bracket" }, { "__type": "Text", "__tag": 4046, "value": " defines the bracketing interval and is required. Either a triple " }, { "__type": "InlineCode", "__tag": 4051, "value": "(xa, xb, xc)" }, { "__type": "Text", "__tag": 4046, "value": " satisfying " }, { "__type": "InlineCode", "__tag": 4051, "value": "xa < xb < xc" }, { "__type": "Text", "__tag": 4046, "value": " and " }, { "__type": "InlineCode", "__tag": 4051, "value": "func(xb) < func(xa) and func(xb) < func(xc)" }, { "__type": "Text", "__tag": 4046, "value": ", or a pair " }, { "__type": "InlineCode", "__tag": 4051, "value": "(xa, xb)" }, { "__type": "Text", "__tag": 4046, "value": " to be used as initial points for a downhill bracket search (see " }, { "__type": "CrossRef", "__tag": 4002, "value": "scipy.optimize.bracket", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "scipy", "version": "*", "kind": "api", "path": "scipy.optimize._optimize:bracket" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": "). The minimizer " }, { "__type": "InlineCode", "__tag": 4051, "value": "res.x" }, { "__type": "Text", "__tag": 4046, "value": " will not necessarily satisfy " }, { "__type": "InlineCode", "__tag": 4051, "value": "xa <= res.x <= xb" }, { "__type": "Text", "__tag": 4046, "value": "." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "bounds", "annotation": "sequence, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "For method 'bounded', " }, { "__type": "ParamRef", "__tag": 4071, "name": "bounds" }, { "__type": "Text", "__tag": 4046, "value": " is mandatory and must have two finite items corresponding to the optimization bounds." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "args", "annotation": "tuple, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Extra arguments passed to the objective function." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "method", "annotation": "str or callable, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Type of solver. Should be one of:" } ] }, { "__type": "BulletList", "__tag": 4053, "ordered": false, "start": 1, "children": [ { "__type": "ListItem", "__tag": 4054, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "InlineRole", "__tag": 4003, "value": "Brent ", "domain": null, "role": "ref", "inventory": null } ] } ] }, { "__type": "ListItem", "__tag": 4054, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "InlineRole", "__tag": 4003, "value": "Bounded ", "domain": null, "role": "ref", "inventory": null } ] } ] }, { "__type": "ListItem", "__tag": 4054, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "InlineRole", "__tag": 4003, "value": "Golden ", "domain": null, "role": "ref", "inventory": null } ] } ] }, { "__type": "ListItem", "__tag": 4054, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "custom - a callable object (added in version 0.14.0), see below" } ] } ] } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Default is \"Bounded\" if bounds are provided and \"Brent\" otherwise. See the 'Notes' section for details of each solver." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "tol", "annotation": "float, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Tolerance for termination. For detailed control, use solver-specific options." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "options", "annotation": "dict, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "A dictionary of solver options." } ] }, { "__type": "DefList", "__tag": 4033, "children": [ { "__type": "DefListItem", "__tag": 4037, "dt": { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "maxiter" } ] }, "dd": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "maxiter" } ] } ] }, { "__type": "DefListItem", "__tag": 4037, "dt": { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "disp" } ] }, "dd": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "disp" } ] } ] } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "See " }, { "__type": "InlineRole", "__tag": 4003, "value": "show_options()", "domain": null, "role": "func", "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " for solver-specific options." } ] } ] } ] } ], "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/_minimize.py", "item_line": 831, "item_type": "function", "aliases": [ "scipy.optimize.minimize_scalar" ], "example_section_data": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Text", "__tag": 4046, "value": "Consider the problem of minimizing the following function.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "def f(x):\n return (x - 2) * x * (x + 2)**2\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nUsing the *Brent* method, we find the local minimum as:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "from scipy.optimize import minimize_scalar\nres = minimize_scalar(f)\n", "execution_status": "success" }, { "__type": "Code", "__tag": 4050, "value": "res.fun\n", "execution_status": "failure" }, { "__type": "Text", "__tag": 4046, "value": "\nThe minimizer is:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "res.x\n", "execution_status": "failure" }, { "__type": "Text", "__tag": 4046, "value": "\nUsing the *Bounded* method, we find a local minimum with specified\nbounds as:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "res = minimize_scalar(f, bounds=(-3, -1), method='bounded')\n", "execution_status": "success" }, { "__type": "Code", "__tag": 4050, "value": "res.fun # minimum\nres.x # minimizer\n", "execution_status": "failure" } ], "title": [], "level": 0, "target": null }, "see_also": [ { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "minimize", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "current-module", "version": "current-version", "kind": "to-resolve", "path": "minimize" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Interface to minimization algorithms for scalar multivariate functions" } ] } ], "type": null }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "show_options", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.optimize._optimize:show_options" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Additional options accepted by the solvers" } ] } ], "type": null } ], "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": "bracket", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "bounds", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "args", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "()" }, { "__type": "SigParam", "__tag": 4030, "name": "method", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "tol", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "options", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" } ], "return_annotation": { "__type": "Empty", "__tag": 4031 }, "target_name": "minimize_scalar" }, "references": [ ".. [1] Press, W., S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery.", " Numerical Recipes in C. Cambridge University Press.", ".. [2] Forsythe, G.E., M. A. Malcolm, and C. B. Moler. \"Computer Methods", " for Mathematical Computations.\" Prentice-Hall Series in Automatic", " Computation 259 (1977).", ".. [3] Brent, Richard P. Algorithms for Minimization Without Derivatives.", " Courier Corporation, 2013." ], "qa": "scipy.optimize._minimize:minimize_scalar", "arbitrary": [], "local_refs": [ "args", "bounds", "bracket", "fun", "method", "options", "res", "tol" ] }