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See " }, { "__type": "InlineRole", "__tag": 4003, "value": "Note2", "domain": null, "role": null, "inventory": null }, { "__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 True, return the evaluation grid and the objective function's values on it." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "finish", "annotation": "callable, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "An optimization function that is called with the result of brute force minimization as initial guess. " }, { "__type": "ParamRef", "__tag": 4071, "name": "finish" }, { "__type": "Text", "__tag": 4046, "value": " should take " }, { "__type": "ParamRef", "__tag": 4071, "name": "func" }, { "__type": "Text", "__tag": 4046, "value": " and the initial guess as positional arguments, and take " }, { "__type": "ParamRef", "__tag": 4071, "name": "args" }, { "__type": "Text", "__tag": 4046, "value": " as keyword arguments. It may additionally take " }, { "__type": "ParamRef", "__tag": 4071, "name": "full_output" }, { "__type": "Text", "__tag": 4046, "value": " and/or " }, { "__type": "ParamRef", "__tag": 4071, "name": "disp" }, { "__type": "Text", "__tag": 4046, "value": " as keyword arguments. Use None if no \"polishing\" function is to be used. 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Requires that " }, { "__type": "ParamRef", "__tag": 4071, "name": "func" }, { "__type": "Text", "__tag": 4046, "value": " be pickleable." } ] }, { "__type": "Admonition", "__tag": 4056, "kind": "versionadded", "base_type": "neutral", "children": [ { "__type": "AdmonitionTitle", "__tag": 4055, "children": [ { "__type": "Text", "__tag": 4046, "value": "versionadded 1.3.0" } ] } ] } ] } ] } ], "title": [], "level": 0, "target": null }, "Extended Summary": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Uses the \"brute force\" method, i.e., computes the function's value at each point of a multidimensional grid of points, to find the global minimum of the function." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The function is evaluated everywhere in the range with the datatype of the first call to the function, as enforced by the " }, { "__type": "InlineCode", "__tag": 4051, "value": "vectorize" }, { "__type": "Text", "__tag": 4046, "value": " NumPy function. The value and type of the function evaluation returned when " }, { "__type": "InlineCode", "__tag": 4051, "value": "full_output=True" }, { "__type": "Text", "__tag": 4046, "value": " are affected in addition by the " }, { "__type": "InlineCode", "__tag": 4051, "value": "finish" }, { "__type": "Text", "__tag": 4046, "value": " argument (see Notes)." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The brute force approach is inefficient because the number of grid points increases exponentially - the number of grid points to evaluate is " }, { "__type": "InlineCode", "__tag": 4051, "value": "Ns ** len(x)" }, { "__type": "Text", "__tag": 4046, "value": ". Consequently, even with coarse grid spacing, even moderately sized problems can take a long time to run, and/or run into memory limitations." } ] } ], "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": 3673, "item_type": "function", "aliases": [ "scipy.optimize.brute" ], "example_section_data": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Text", "__tag": 4046, "value": "We illustrate the use of `brute` to seek the global minimum of a function\nof two variables that is given as the sum of a positive-definite\nquadratic and two deep \"Gaussian-shaped\" craters. Specifically, define\nthe objective function `f` as the sum of three other functions,\n``f = f1 + f2 + f3``. We suppose each of these has a signature\n``(z, *params)``, where ``z = (x, y)``, and ``params`` and the functions\nare as defined below.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "import numpy as np\nparams = (2, 3, 7, 8, 9, 10, 44, -1, 2, 26, 1, -2, 0.5)\ndef f1(z, *params):\n x, y = z\n a, b, c, d, e, f, g, h, i, j, k, l, scale = params\n return (a * x**2 + b * x * y + c * y**2 + d*x + e*y + f)\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\n" }, { "__type": "Code", "__tag": 4050, "value": "def f2(z, *params):\n x, y = z\n a, b, c, d, e, f, g, h, i, j, k, l, scale = params\n return (-g*np.exp(-((x-h)**2 + (y-i)**2) / scale))\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\n" }, { "__type": "Code", "__tag": 4050, "value": "def f3(z, *params):\n x, y = z\n a, b, c, d, e, f, g, h, i, j, k, l, scale = params\n return (-j*np.exp(-((x-k)**2 + (y-l)**2) / scale))\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\n" }, { "__type": "Code", "__tag": 4050, "value": "def f(z, *params):\n return f1(z, *params) + f2(z, *params) + f3(z, *params)\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nThus, the objective function may have local minima near the minimum\nof each of the three functions of which it is composed. To\nuse `fmin` to polish its gridpoint result, we may then continue as\nfollows:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "rranges = (slice(-4, 4, 0.25), slice(-4, 4, 0.25))\nfrom scipy import optimize\nresbrute = optimize.brute(f, rranges, args=params, full_output=True,\n finish=optimize.fmin)\n", "execution_status": "success" }, { "__type": "Code", "__tag": 4050, "value": "resbrute[0] # global minimum\nresbrute[1] # function value at global minimum\n", "execution_status": "failure" }, { "__type": "Text", "__tag": 4046, "value": "\nNote that if `finish` had been set to None, we would have gotten the\ngridpoint [-1.0 1.75] where the rounded function value is -2.892." } ], "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": 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": null } ], "signature": { "__type": "SignatureNode", "__tag": 4029, "kind": "function", "parameters": [ { "__type": "SigParam", "__tag": 4030, "name": "func", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": { "__type": "Empty", "__tag": 4031 } }, { "__type": "SigParam", "__tag": 4030, "name": "ranges", "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": "Ns", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "20" }, { "__type": "SigParam", "__tag": 4030, "name": "full_output", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "0" }, { "__type": "SigParam", "__tag": 4030, "name": "finish", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "" }, { "__type": "SigParam", "__tag": 4030, "name": "disp", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "False" }, { "__type": "SigParam", "__tag": 4030, "name": "workers", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "1" } ], "return_annotation": { "__type": "Empty", "__tag": 4031 }, "target_name": "brute" }, "references": null, "qa": "scipy.optimize._optimize:brute", "arbitrary": [], "local_refs": [ "Jout", "Ns", "args", "disp", "finish", "full_output", "func", "fval", "grid", "ranges", "workers", "x0" ] }