{ "__type": "IngestedDoc", "__tag": 4010, "_content": { "Notes": { "__type": "Section", "__tag": 4015, "children": [], "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": "nit", "annotation": "int", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The number of iterations. Used to keep an accurate iteration total in the two-phase problem." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "status", "annotation": "int", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "An integer representing the exit status of the optimization " } ] }, { "__type": "Code", "__tag": 4050, "value": "0 : Optimization terminated successfully\n1 : Iteration limit reached\n2 : Problem appears to be infeasible\n3 : Problem appears to be unbounded\n4 : Serious numerical difficulties encountered", "execution_status": null } ] } ] } ], "title": [], "level": 0, "target": null }, "Summary": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Solve a linear programming problem in \"standard form\" using the Simplex Method. Linear Programming is intended to solve the following problem form:" } ] } ], "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": "T", "annotation": "2-D array", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "A 2-D array representing the simplex tableau, T, corresponding to the linear programming problem. It should have the form:" } ] }, { "__type": "DefList", "__tag": 4033, "children": [ { "__type": "DefListItem", "__tag": 4037, "dt": { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "[[A[0, 0], A[0, 1], ..., A[0, n_total], b[0]]," } ] }, "dd": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "[A[1, 0], A[1, 1], ..., A[1, n_total], b[1]], . . . [A[m, 0], A[m, 1], ..., A[m, n_total], b[m]], [c[0], c[1], ..., c[n_total], 0]]" } ] } ] } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "for a Phase 2 problem, or the form:" } ] }, { "__type": "DefList", "__tag": 4033, "children": [ { "__type": "DefListItem", "__tag": 4037, "dt": { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "[[A[0, 0], A[0, 1], ..., A[0, n_total], b[0]]," } ] }, "dd": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "[A[1, 0], A[1, 1], ..., A[1, n_total], b[1]], . . . [A[m, 0], A[m, 1], ..., A[m, n_total], b[m]], [c[0], c[1], ..., c[n_total], 0], [c'[0], c'[1], ..., c'[n_total], 0]]" } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "for a Phase 1 problem (a problem in which a basic feasible solution is sought prior to maximizing the actual objective. " }, { "__type": "InlineCode", "__tag": 4051, "value": "T" }, { "__type": "Text", "__tag": 4046, "value": " is modified in place by " }, { "__type": "InlineCode", "__tag": 4051, "value": "_solve_simplex" }, { "__type": "Text", "__tag": 4046, "value": "." } ] } ] } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "n", "annotation": "int", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The number of true variables in the problem." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "basis", "annotation": "1-D array", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "An array of the indices of the basic variables, such that basis[i] contains the column corresponding to the basic variable for row i. Basis is modified in place by _solve_simplex" } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "callback", "annotation": "callable, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "If a callback function is provided, it will be called within each iteration of the algorithm. The callback must accept a " }, { "__type": "CrossRef", "__tag": 4002, "value": "scipy.optimize.OptimizeResult", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "scipy", "version": "*", "kind": "api", "path": "scipy.optimize._optimize:OptimizeResult" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " consisting of the following fields:" } ] }, { "__type": "Blockquote", "__tag": 4059, "children": [ { "__type": "DefList", "__tag": 4033, "children": [ { "__type": "DefListItem", "__tag": 4037, "dt": { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "x" } ] }, "dd": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "x" } ] } ] }, { "__type": "DefListItem", "__tag": 4037, "dt": { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "fun" } ] }, "dd": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "fun" } ] } ] }, { "__type": "DefListItem", "__tag": 4037, "dt": { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "success" } ] }, "dd": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "success" } ] } ] }, { "__type": "DefListItem", "__tag": 4037, "dt": { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "slack" } ] }, "dd": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "slack" } ] } ] }, { "__type": "DefListItem", "__tag": 4037, "dt": { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "con" } ] }, "dd": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "con" } ] } ] }, { "__type": "DefListItem", "__tag": 4037, "dt": { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "phase" } ] }, "dd": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "phase" } ] } ] }, { "__type": "DefListItem", "__tag": 4037, "dt": { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "status" } ] }, "dd": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "status" } ] } ] }, { "__type": "DefListItem", "__tag": 4037, "dt": { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "nit" } ] }, "dd": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "nit" } ] } ] }, { "__type": "DefListItem", "__tag": 4037, "dt": { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "message" } ] }, "dd": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "message" } ] } ] } ] } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "postsolve_args", "annotation": "tuple", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Data needed by _postsolve to convert the solution to the standard-form problem into the solution to the original problem." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "maxiter", "annotation": "int", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The maximum number of iterations to perform before aborting the optimization." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "tol", "annotation": "float", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The tolerance which determines when a solution is \"close enough\" to zero in Phase 1 to be considered a basic feasible solution or close enough to positive to serve as an optimal solution." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "phase", "annotation": "int", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The phase of the optimization being executed. In phase 1 a basic feasible solution is sought and the T has an additional row representing an alternate objective function." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "bland", "annotation": "bool", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "If True, choose pivots using Bland's rule " }, { "__type": "FootnoteReference", "__tag": 4066, "label": "3" }, { "__type": "Text", "__tag": 4046, "value": ". In problems which fail to converge due to cycling, using Bland's rule can provide convergence at the expense of a less optimal path about the simplex." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "nit0", "annotation": "int", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The initial iteration number used to keep an accurate iteration total in a two-phase problem." } ] } ] } ] } ], "title": [], "level": 0, "target": null }, "Extended Summary": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Minimize " } ] }, { "__type": "Code", "__tag": 4050, "value": "c @ x", "execution_status": null }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Subject to " } ] }, { "__type": "Code", "__tag": 4050, "value": "A @ x == b\n x >= 0", "execution_status": null } ], "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/_linprog_simplex.py", "item_line": 232, "item_type": "function", "aliases": [ "scipy.optimize._linprog_simplex._solve_simplex" ], "example_section_data": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "see_also": [], "signature": { "__type": "SignatureNode", "__tag": 4029, "kind": "function", "parameters": [ { "__type": "SigParam", "__tag": 4030, "name": "T", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": { "__type": "Empty", "__tag": 4031 } }, { "__type": "SigParam", "__tag": 4030, "name": "n", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": { "__type": "Empty", "__tag": 4031 } }, { "__type": "SigParam", "__tag": 4030, "name": "basis", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": { "__type": "Empty", "__tag": 4031 } }, { "__type": "SigParam", "__tag": 4030, "name": "callback", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": { "__type": "Empty", "__tag": 4031 } }, { "__type": "SigParam", "__tag": 4030, "name": "postsolve_args", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": { "__type": "Empty", "__tag": 4031 } }, { "__type": "SigParam", "__tag": 4030, "name": "maxiter", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "1000" }, { "__type": "SigParam", "__tag": 4030, "name": "tol", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "1e-09" }, { "__type": "SigParam", "__tag": 4030, "name": "phase", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "2" }, { "__type": "SigParam", "__tag": 4030, "name": "bland", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "False" }, { "__type": "SigParam", "__tag": 4030, "name": "nit0", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "0" } ], "return_annotation": { "__type": "Empty", "__tag": 4031 }, "target_name": "_solve_simplex" }, "references": null, "qa": "scipy.optimize._linprog_simplex:_solve_simplex", "arbitrary": [], "local_refs": [ "T", "basis", "bland", "callback", "maxiter", "n", "nit", "nit0", "phase", "postsolve_args", "status", "tol" ] }