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The function is unimodal,\nso `bracket_minium` will easily find a bracket.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "from scipy.optimize import elementwise\nres_bracket = elementwise.bracket_minimum(f, 0)\n", "execution_status": "success", "out": "" }, { "__type": "Code", "__tag": 4050, "value": "res_bracket.success\nres_bracket.bracket\n", "execution_status": "failure", "out": "(np.float64(0.0), np.float64(0.5), np.float64(1.5))\n" }, { "__type": "Text", "__tag": 4046, "value": "\nIndeed, the bracket points are ordered and the function value\nat the middle bracket point is less than at the surrounding\npoints.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "xl, xm, xr = res_bracket.bracket\nfl, fm, fr = res_bracket.f_bracket\n", "execution_status": "success", "out": "" }, { "__type": "Code", "__tag": 4050, "value": "(xl < xm < xr) and (fl > fm <= fr)\n", "execution_status": "failure", "out": "np.True_\n" }, { "__type": "Text", "__tag": 4046, "value": "\nOnce we have a valid bracket, `find_minimum` can be used to provide\nan estimate of the minimizer.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "res_minimum = elementwise.find_minimum(f, res_bracket.bracket)\n", "execution_status": "success", "out": "" }, { "__type": "Code", "__tag": 4050, "value": "res_minimum.x\n", "execution_status": "failure", "out": "np.float64(1.0000000149011612)\n" }, { "__type": "Text", "__tag": 4046, "value": "\n`bracket_minimum` and `find_minimum` accept arrays for most arguments.\nFor instance, to find the minimizers and minima for a few values of the\nparameter ``c`` at once:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "import numpy as np\nc = np.asarray([1, 1.5, 2])\nres_bracket = elementwise.bracket_minimum(f, 0, args=(c,))\nres_bracket.bracket\nres_minimum = elementwise.find_minimum(f, res_bracket.bracket, args=(c,))\n", "execution_status": "success", "out": "" }, { "__type": "Code", "__tag": 4050, "value": "res_minimum.x\n", "execution_status": "failure", "out": "array([1. , 1.5, 2. ])\n" }, { "__type": "Code", "__tag": 4050, "value": "res_minimum.f_x\n", "execution_status": "success", "out": "array([2., 2., 2.])\n" } ], "title": [], "level": 0, "target": null }, "see_also": [ { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "scipy.optimize.bracket", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.optimize._optimize:bracket" }, "kind": "module" }, "descriptions": [], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "scipy.optimize.elementwise.find_minimum", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "current-module", "version": "current-version", "kind": "to-resolve", "path": "scipy.optimize.elementwise.find_minimum" }, "kind": "module" }, "descriptions": [], "type": "func" } ], "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": "xm0", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": { "__type": "Empty", "__tag": 4031 } }, { "__type": "SigParam", "__tag": 4030, "name": "xl0", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "KEYWORD_ONLY", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "xr0", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "KEYWORD_ONLY", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "xmin", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "KEYWORD_ONLY", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "xmax", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "KEYWORD_ONLY", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "factor", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "KEYWORD_ONLY", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "args", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "KEYWORD_ONLY", "default": "()" }, { "__type": "SigParam", "__tag": 4030, "name": "kwargs", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "KEYWORD_ONLY", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "maxiter", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "KEYWORD_ONLY", "default": "1000" } ], "return_annotation": { "__type": "Empty", "__tag": 4031 }, "target_name": "bracket_minimum" }, "references": null, "qa": "scipy.optimize._elementwise:bracket_minimum", "arbitrary": [], "local_refs": [ "args", "f", "factor", "kwargs", "maxiter", "res", "xl0", "xm0", "xmax", "xmin", "xr0" ] }