{ "__type": "IngestedDoc", "__tag": 4010, "_content": { "Notes": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Finite difference schemes {'2-point', '3-point', 'cs'} may be used for approximating either the Jacobian or the Hessian. We, however, do not allow its use for approximating both simultaneously. Hence whenever the Jacobian is estimated via finite-differences, we require the Hessian to be estimated using one of the quasi-Newton strategies." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The scheme 'cs' is potentially the most accurate, but requires the function to correctly handles complex inputs and be analytically continuable to the complex plane. The scheme '3-point' is more accurate than '2-point' but requires twice as many operations." } ] } ], "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": [], "title": [], "level": 0, "target": null }, "Summary": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Nonlinear constraint on the variables." } ] } ], "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": "The function defining the constraint. The signature is " }, { "__type": "InlineCode", "__tag": 4051, "value": "fun(x) -> array_like, shape (m,)" }, { "__type": "Text", "__tag": 4046, "value": "." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "lb, ub", "annotation": "array_like", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Lower and upper bounds on the constraint. Each array must have the shape (m,) or be a scalar, in the latter case a bound will be the same for all components of the constraint. Use " }, { "__type": "InlineCode", "__tag": 4051, "value": "np.inf" }, { "__type": "Text", "__tag": 4046, "value": " with an appropriate sign to specify a one-sided constraint. Set components of " }, { "__type": "ParamRef", "__tag": 4071, "name": "lb" }, { "__type": "Text", "__tag": 4046, "value": " and " }, { "__type": "ParamRef", "__tag": 4071, "name": "ub" }, { "__type": "Text", "__tag": 4046, "value": " equal to represent an equality constraint. Note that you can mix constraints of different types: interval, one-sided or equality, by setting different components of " }, { "__type": "ParamRef", "__tag": 4071, "name": "lb" }, { "__type": "Text", "__tag": 4046, "value": " and " }, { "__type": "ParamRef", "__tag": 4071, "name": "ub" }, { "__type": "Text", "__tag": 4046, "value": " as necessary." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "jac", "annotation": "{callable, '2-point', '3-point', 'cs'}, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Method of computing the Jacobian matrix (an m-by-n matrix, where element (i, j) is the partial derivative of f[i] with respect to x[j]). The keywords {'2-point', '3-point', 'cs'} select a finite difference scheme for the numerical estimation. A callable must have the following signature " } ] }, { "__type": "Code", "__tag": 4050, "value": "jac(x) -> {ndarray, sparse array}, shape (m, n)", "execution_status": null }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Default is '2-point'." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "hess", "annotation": "{callable, '2-point', '3-point', 'cs', HessianUpdateStrategy, None}, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Method for computing the Hessian matrix. The keywords {'2-point', '3-point', 'cs'} select a finite difference scheme for numerical estimation. Alternatively, objects implementing " }, { "__type": "CrossRef", "__tag": 4002, "value": "HessianUpdateStrategy", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.optimize._hessian_update_strategy:HessianUpdateStrategy" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " interface can be used to approximate the Hessian. Currently available implementations are:" } ] }, { "__type": "BulletList", "__tag": 4053, "ordered": false, "start": 1, "children": [ { "__type": "ListItem", "__tag": 4054, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "CrossRef", "__tag": 4002, "value": "BFGS", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.optimize._hessian_update_strategy:BFGS" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " (default option)" } ] } ] }, { "__type": "ListItem", "__tag": 4054, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "CrossRef", "__tag": 4002, "value": "SR1", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.optimize._hessian_update_strategy:SR1" }, "kind": "module" } ] } ] } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "A callable must return the Hessian matrix of " }, { "__type": "InlineCode", "__tag": 4051, "value": "dot(fun, v)" }, { "__type": "Text", "__tag": 4046, "value": " and must have the following signature: " }, { "__type": "InlineCode", "__tag": 4051, "value": "hess(x, v) -> {LinearOperator, sparse array, array_like}, shape (n, n)" }, { "__type": "Text", "__tag": 4046, "value": ". Here " }, { "__type": "InlineCode", "__tag": 4051, "value": "v" }, { "__type": "Text", "__tag": 4046, "value": " is ndarray with shape (m,) containing Lagrange multipliers." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "keep_feasible", "annotation": "array_like of bool, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Whether to keep the constraint components feasible throughout iterations. A single value sets this property for all components. Default is False. Has no effect for equality constraints." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "finite_diff_rel_step: None or array_like, optional", "annotation": "", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Relative step size for the finite difference approximation. Default is None, which will select a reasonable value automatically depending on a finite difference scheme." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "finite_diff_jac_sparsity: {None, array_like, sparse array}, optional", "annotation": "", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Defines the sparsity structure of the Jacobian matrix for finite difference estimation, its shape must be (m, n). If the Jacobian has only few non-zero elements in " }, { "__type": "Emphasis", "__tag": 4047, "children": [ { "__type": "Text", "__tag": 4046, "value": "each" } ] }, { "__type": "Text", "__tag": 4046, "value": " row, providing the sparsity structure will greatly speed up the computations. A zero entry means that a corresponding element in the Jacobian is identically zero. If provided, forces the use of 'lsmr' trust-region solver. If None (default) then dense differencing will be used." } ] } ] } ] } ], "title": [], "level": 0, "target": null }, "Extended Summary": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The constraint has the general inequality form " } ] }, { "__type": "Code", "__tag": 4050, "value": "lb <= fun(x) <= ub", "execution_status": null }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Here the vector of independent variables x is passed as ndarray of shape (n,) and " }, { "__type": "InlineCode", "__tag": 4051, "value": "fun" }, { "__type": "Text", "__tag": 4046, "value": " returns a vector with m components." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "It is possible to use equal bounds to represent an equality constraint or infinite bounds to represent a one-sided constraint." } ] } ], "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/_constraints.py", "item_line": 22, "item_type": "class", "aliases": [ "scipy.optimize.NonlinearConstraint" ], "example_section_data": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Text", "__tag": 4046, "value": "Constrain ``x[0] < sin(x[1]) + 1.9``\n\n" }, { "__type": "Code", "__tag": 4050, "value": "from scipy.optimize import NonlinearConstraint\nimport numpy as np\ncon = lambda x: x[0] - np.sin(x[1])\nnlc = NonlinearConstraint(con, -np.inf, 1.9)\n", "execution_status": "success" } ], "title": [], "level": 0, "target": null }, "see_also": [], "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": "lb", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": { "__type": "Empty", "__tag": 4031 } }, { "__type": "SigParam", "__tag": 4030, "name": "ub", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": { "__type": "Empty", "__tag": 4031 } }, { "__type": "SigParam", "__tag": 4030, "name": "jac", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "2-point" }, { "__type": "SigParam", "__tag": 4030, "name": "hess", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "keep_feasible", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "False" }, { "__type": "SigParam", "__tag": 4030, "name": "finite_diff_rel_step", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "finite_diff_jac_sparsity", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" } ], "return_annotation": { "__type": "Empty", "__tag": 4031 }, "target_name": "NonlinearConstraint" }, "references": null, "qa": "scipy.optimize._constraints:NonlinearConstraint", "arbitrary": [], "local_refs": [ "array_like", "finite_diff_jac_sparsity: {None", "finite_diff_rel_step: None or array_like", "fun", "hess", "jac", "keep_feasible", "lb", "optional", "sparse array}", "ub" ] }