{ "__type": "IngestedDoc", "__tag": 4010, "_content": { "Notes": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "SciPy uses a C-translated and modified version of the Fortran code, L-BFGS-B v3.0 (released April 25, 2011, BSD-3 licensed). Original Fortran version was written by Ciyou Zhu, Richard Byrd, Jorge Nocedal and, Jose Luis Morales." } ] } ], "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": "x", "annotation": "array_like", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Estimated position of the minimum." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "f", "annotation": "float", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Value of " }, { "__type": "ParamRef", "__tag": 4071, "name": "func" }, { "__type": "Text", "__tag": 4046, "value": " at the minimum." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "d", "annotation": "dict", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Information dictionary." } ] }, { "__type": "BulletList", "__tag": 4053, "ordered": false, "start": 1, "children": [ { "__type": "ListItem", "__tag": 4054, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "d['warnflag'] is" } ] }, { "__type": "BulletList", "__tag": 4053, "ordered": false, "start": 1, "children": [ { "__type": "ListItem", "__tag": 4054, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "0 if converged," } ] } ] }, { "__type": "ListItem", "__tag": 4054, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "1 if too many function evaluations or too many iterations," } ] } ] }, { "__type": "ListItem", "__tag": 4054, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "2 if stopped for another reason, given in d['task']" } ] } ] } ] } ] }, { "__type": "ListItem", "__tag": 4054, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "d['grad'] is the gradient at the minimum (should be 0 ish)" } ] } ] }, { "__type": "ListItem", "__tag": 4054, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "d['funcalls'] is the number of function calls made." } ] } ] }, { "__type": "ListItem", "__tag": 4054, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "d['nit'] is the number of iterations." } ] } ] } ] } ] } ] } ], "title": [], "level": 0, "target": null }, "Summary": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Minimize a function func using the L-BFGS-B 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": "func", "annotation": "callable f(x,*args)", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Function to minimize." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "x0", "annotation": "ndarray", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Initial guess." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "fprime", "annotation": "callable fprime(x,*args), optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The gradient of " }, { "__type": "ParamRef", "__tag": 4071, "name": "func" }, { "__type": "Text", "__tag": 4046, "value": ". If None, then " }, { "__type": "ParamRef", "__tag": 4071, "name": "func" }, { "__type": "Text", "__tag": 4046, "value": " returns the function value and the gradient (" }, { "__type": "InlineCode", "__tag": 4051, "value": "f, g = func(x, *args)" }, { "__type": "Text", "__tag": 4046, "value": "), unless " }, { "__type": "ParamRef", "__tag": 4071, "name": "approx_grad" }, { "__type": "Text", "__tag": 4046, "value": " is True in which case " }, { "__type": "ParamRef", "__tag": 4071, "name": "func" }, { "__type": "Text", "__tag": 4046, "value": " returns only " }, { "__type": "InlineCode", "__tag": 4051, "value": "f" }, { "__type": "Text", "__tag": 4046, "value": "." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "args", "annotation": "sequence, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Arguments to pass to " }, { "__type": "ParamRef", "__tag": 4071, "name": "func" }, { "__type": "Text", "__tag": 4046, "value": " and " }, { "__type": "ParamRef", "__tag": 4071, "name": "fprime" }, { "__type": "Text", "__tag": 4046, "value": "." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "approx_grad", "annotation": "bool, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Whether to approximate the gradient numerically (in which case " }, { "__type": "ParamRef", "__tag": 4071, "name": "func" }, { "__type": "Text", "__tag": 4046, "value": " returns only the function value)." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "bounds", "annotation": "list, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "InlineCode", "__tag": 4051, "value": "(min, max)" }, { "__type": "Text", "__tag": 4046, "value": " pairs for each element in " }, { "__type": "InlineCode", "__tag": 4051, "value": "x" }, { "__type": "Text", "__tag": 4046, "value": ", defining the bounds on that parameter. Use None or +-inf for one of " }, { "__type": "InlineCode", "__tag": 4051, "value": "min" }, { "__type": "Text", "__tag": 4046, "value": " or " }, { "__type": "InlineCode", "__tag": 4051, "value": "max" }, { "__type": "Text", "__tag": 4046, "value": " when there is no bound in that direction." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "m", "annotation": "int, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The maximum number of variable metric corrections used to define the limited memory matrix. (The limited memory BFGS method does not store the full hessian but uses this many terms in an approximation to it.)" } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "factr", "annotation": "float, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The iteration stops when " }, { "__type": "InlineCode", "__tag": 4051, "value": "(f^k - f^{k+1})/max{|f^k|,|f^{k+1}|,1} <= factr * eps" }, { "__type": "Text", "__tag": 4046, "value": ", where " }, { "__type": "InlineCode", "__tag": 4051, "value": "eps" }, { "__type": "Text", "__tag": 4046, "value": " is the machine precision, which is automatically generated by the code. Typical values for " }, { "__type": "ParamRef", "__tag": 4071, "name": "factr" }, { "__type": "Text", "__tag": 4046, "value": " are: 1e12 for low accuracy; 1e7 for moderate accuracy; 10.0 for extremely high accuracy. See Notes for relationship to " }, { "__type": "InlineRole", "__tag": 4003, "value": "ftol", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": ", which is exposed (instead of " }, { "__type": "ParamRef", "__tag": 4071, "name": "factr" }, { "__type": "Text", "__tag": 4046, "value": ") by the " }, { "__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": " interface to L-BFGS-B." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "pgtol", "annotation": "float, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The iteration will stop when " }, { "__type": "InlineCode", "__tag": 4051, "value": "max{|proj g_i | i = 1, ..., n} <= pgtol" }, { "__type": "Text", "__tag": 4046, "value": " where " }, { "__type": "InlineCode", "__tag": 4051, "value": "proj g_i" }, { "__type": "Text", "__tag": 4046, "value": " is the i-th component of the projected gradient." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "epsilon", "annotation": "float, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Step size used when " }, { "__type": "ParamRef", "__tag": 4071, "name": "approx_grad" }, { "__type": "Text", "__tag": 4046, "value": " is True, for numerically calculating the gradient" } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "iprint", "annotation": "int, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Deprecated option that previously controlled the text printed on the screen during the problem solution. Now the code does not emit any output and this keyword has no function." } ] }, { "__type": "Admonition", "__tag": 4056, "kind": "deprecated", "base_type": "neutral", "children": [ { "__type": "AdmonitionTitle", "__tag": 4055, "children": [ { "__type": "Text", "__tag": 4046, "value": "deprecated 1.15.0" } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "This keyword is deprecated and will be removed from SciPy 1.18.0." } ] } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "disp", "annotation": "int, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Deprecated option that previously controlled the text printed on the screen during the problem solution. Now the code does not emit any output and this keyword has no function." } ] }, { "__type": "Admonition", "__tag": 4056, "kind": "deprecated", "base_type": "neutral", "children": [ { "__type": "AdmonitionTitle", "__tag": 4055, "children": [ { "__type": "Text", "__tag": 4046, "value": "deprecated 1.15.0" } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "This keyword is deprecated and will be removed from SciPy 1.18.0." } ] } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "maxfun", "annotation": "int, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Maximum number of function evaluations. Note that this function may violate the limit because of evaluating gradients by numerical differentiation." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "maxiter", "annotation": "int, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Maximum number of iterations." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "callback", "annotation": "callable, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Called after each iteration, as " }, { "__type": "InlineCode", "__tag": 4051, "value": "callback(xk)" }, { "__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": "maxls", "annotation": "int, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Maximum number of line search steps (per iteration). Default is 20." } ] } ] } ] } ], "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/_lbfgsb_py.py", "item_line": 94, "item_type": "function", "aliases": [ "scipy.optimize.fmin_l_bfgs_b" ], "example_section_data": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Text", "__tag": 4046, "value": "Solve a linear regression problem via `fmin_l_bfgs_b`. To do this, first we\ndefine an objective function ``f(m, b) = (y - y_model)**2``, where `y`\ndescribes the observations and `y_model` the prediction of the linear model\nas ``y_model = m*x + b``. The bounds for the parameters, ``m`` and ``b``,\nare arbitrarily chosen as ``(0,5)`` and ``(5,10)`` for this example.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "import numpy as np\nfrom scipy.optimize import fmin_l_bfgs_b\nX = np.arange(0, 10, 1)\nM = 2\nB = 3\nY = M * X + B\ndef func(parameters, *args):\n x = args[0]\n y = args[1]\n m, b = parameters\n y_model = m*x + b\n error = sum(np.power((y - y_model), 2))\n return error\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\n" }, { "__type": "Code", "__tag": 4050, "value": "initial_values = np.array([0.0, 1.0])\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\n" }, { "__type": "Code", "__tag": 4050, "value": "x_opt, f_opt, info = fmin_l_bfgs_b(func, x0=initial_values, args=(X, Y),\n approx_grad=True)\n", "execution_status": "success" }, { "__type": "Code", "__tag": 4050, "value": "x_opt, f_opt\n", "execution_status": "failure" }, { "__type": "Text", "__tag": 4046, "value": "\nThe optimized parameters in ``x_opt`` agree with the ground truth parameters\n``m`` and ``b``. Next, let us perform a bound constrained optimization using\nthe `bounds` parameter.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "bounds = [(0, 5), (5, 10)]\nx_opt, f_op, info = fmin_l_bfgs_b(func, x0=initial_values, args=(X, Y),\n approx_grad=True, bounds=bounds)\n", "execution_status": "success" }, { "__type": "Code", "__tag": 4050, "value": "x_opt, f_opt\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 multivariate functions. See the 'L-BFGS-B' " }, { "__type": "InlineRole", "__tag": 4003, "value": "method", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " in particular. Note that the " }, { "__type": "InlineRole", "__tag": 4003, "value": "ftol", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " option is made available via that interface, while " }, { "__type": "InlineRole", "__tag": 4003, "value": "factr", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " is provided via this interface, where " }, { "__type": "InlineRole", "__tag": 4003, "value": "factr", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " is the factor multiplying the default machine floating-point precision to arrive at " }, { "__type": "InlineRole", "__tag": 4003, "value": "ftol", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": ": " }, { "__type": "InlineCode", "__tag": 4051, "value": "ftol = factr * numpy.finfo(float).eps" }, { "__type": "Text", "__tag": 4046, "value": "." } ] } ], "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": "x0", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": { "__type": "Empty", "__tag": 4031 } }, { "__type": "SigParam", "__tag": 4030, "name": "fprime", "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": "approx_grad", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "0" }, { "__type": "SigParam", "__tag": 4030, "name": "bounds", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "m", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "10" }, { "__type": "SigParam", "__tag": 4030, "name": "factr", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "10000000.0" }, { "__type": "SigParam", "__tag": 4030, "name": "pgtol", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "1e-05" }, { "__type": "SigParam", "__tag": 4030, "name": "epsilon", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "1e-08" }, { "__type": "SigParam", "__tag": 4030, "name": "iprint", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "" }, { "__type": "SigParam", "__tag": 4030, "name": "maxfun", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "15000" }, { "__type": "SigParam", "__tag": 4030, "name": "maxiter", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "15000" }, { "__type": "SigParam", "__tag": 4030, "name": "disp", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "" }, { "__type": "SigParam", "__tag": 4030, "name": "callback", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "maxls", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "20" } ], "return_annotation": { "__type": "Empty", "__tag": 4031 }, "target_name": "fmin_l_bfgs_b" }, "references": [ "* R. H. Byrd, P. Lu and J. Nocedal. A Limited Memory Algorithm for Bound", " Constrained Optimization, (1995), SIAM Journal on Scientific and", " Statistical Computing, 16, 5, pp. 1190-1208.", "* C. Zhu, R. H. Byrd and J. Nocedal. L-BFGS-B: Algorithm 778: L-BFGS-B,", " FORTRAN routines for large scale bound constrained optimization (1997),", " ACM Transactions on Mathematical Software, 23, 4, pp. 550 - 560.", "* J.L. Morales and J. Nocedal. L-BFGS-B: Remark on Algorithm 778: L-BFGS-B,", " FORTRAN routines for large scale bound constrained optimization (2011),", " ACM Transactions on Mathematical Software, 38, 1." ], "qa": "scipy.optimize._lbfgsb_py:fmin_l_bfgs_b", "arbitrary": [], "local_refs": [ "approx_grad", "args", "bounds", "callback", "d", "disp", "epsilon", "f", "factr", "fprime", "func", "iprint", "m", "maxfun", "maxiter", "maxls", "pgtol", "x", "x0" ] }