{
  "__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": "",
              "annotation": "Search directions as defined in [4]",
              "desc": []
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Summary": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "Given standard form problem defined by "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "A"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ", "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "b"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ", and "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "c"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "; current variable estimates "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "x"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ", "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "y"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ", "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "z"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ", "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "tau"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ", and "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "kappa"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "; algorithmic parameters "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "gamma and ``eta; and options ``sparse"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ", "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "lstsq"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ", "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "sym_pos"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ", "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "cholesky"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ", "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "pc"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " (predictor-corrector), and "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "ip"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " (initial point improvement), get the search direction for increments to the variable estimates."
            }
          ]
        }
      ],
      "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": "As defined in [4], except:",
              "annotation": "",
              "desc": []
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "sparse",
              "annotation": "bool",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "True if the system to be solved is sparse. This is typically set True when the original "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "A_ub"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " and "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "A_eq"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " arrays are sparse."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "lstsq",
              "annotation": "bool",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "True if the system is ill-conditioned and/or (nearly) singular and thus a more robust least-squares solver is desired. This is sometimes needed as the solution is approached."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "sym_pos",
              "annotation": "bool",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "True if the system matrix is symmetric positive definite Sometimes this needs to be set false as the solution is approached, even when the system should be symmetric positive definite, due to numerical difficulties."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "cholesky",
              "annotation": "bool",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "True if the system is to be solved by Cholesky, rather than LU, decomposition. This is typically faster unless the problem is very small or prone to numerical difficulties."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "pc",
              "annotation": "bool",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "True if the predictor-corrector method of Mehrota is to be used. This is almost always (if not always) beneficial. Even though it requires the solution of an additional linear system, the factorization is typically (implicitly) reused so solution is efficient, and the number of algorithm iterations is typically reduced."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "ip",
              "annotation": "bool",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "True if the improved initial point suggestion due to [4] section 4.3 is desired. It's unclear whether this is beneficial."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "permc_spec",
              "annotation": "str (default = 'MMD_AT_PLUS_A')",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "(Has effect only with "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "sparse = True"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": ", "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "lstsq = False"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": ", "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "sym_pos = True"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": ".) A matrix is factorized in each iteration of the algorithm. This option specifies how to permute the columns of the matrix for sparsity preservation. Acceptable values are:"
                    }
                  ]
                },
                {
                  "__type": "BulletList",
                  "__tag": 4053,
                  "ordered": false,
                  "start": 1,
                  "children": [
                    {
                      "__type": "ListItem",
                      "__tag": 4054,
                      "children": [
                        {
                          "__type": "Paragraph",
                          "__tag": 4045,
                          "children": [
                            {
                              "__type": "InlineCode",
                              "__tag": 4051,
                              "value": "NATURAL"
                            },
                            {
                              "__type": "Text",
                              "__tag": 4046,
                              "value": ": natural ordering."
                            }
                          ]
                        }
                      ]
                    },
                    {
                      "__type": "ListItem",
                      "__tag": 4054,
                      "children": [
                        {
                          "__type": "Paragraph",
                          "__tag": 4045,
                          "children": [
                            {
                              "__type": "InlineCode",
                              "__tag": 4051,
                              "value": "MMD_ATA"
                            },
                            {
                              "__type": "Text",
                              "__tag": 4046,
                              "value": ": minimum degree ordering on the structure of A^T A."
                            }
                          ]
                        }
                      ]
                    },
                    {
                      "__type": "ListItem",
                      "__tag": 4054,
                      "children": [
                        {
                          "__type": "Paragraph",
                          "__tag": 4045,
                          "children": [
                            {
                              "__type": "InlineCode",
                              "__tag": 4051,
                              "value": "MMD_AT_PLUS_A"
                            },
                            {
                              "__type": "Text",
                              "__tag": 4046,
                              "value": ": minimum degree ordering on the structure of A^T+A."
                            }
                          ]
                        }
                      ]
                    },
                    {
                      "__type": "ListItem",
                      "__tag": 4054,
                      "children": [
                        {
                          "__type": "Paragraph",
                          "__tag": 4045,
                          "children": [
                            {
                              "__type": "InlineCode",
                              "__tag": 4051,
                              "value": "COLAMD"
                            },
                            {
                              "__type": "Text",
                              "__tag": 4046,
                              "value": ": approximate minimum degree column ordering."
                            }
                          ]
                        }
                      ]
                    }
                  ]
                },
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "This option can impact the convergence of the interior point algorithm; test different values to determine which performs best for your problem. For more information, refer to "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "scipy.sparse.linalg.splu"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "."
                    }
                  ]
                }
              ]
            }
          ]
        }
      ],
      "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/_linprog_ip.py",
  "item_line": 147,
  "item_type": "function",
  "aliases": [
    "scipy.optimize._linprog_ip._get_delta"
  ],
  "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": "A",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": {
          "__type": "Empty",
          "__tag": 4031
        }
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "b",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": {
          "__type": "Empty",
          "__tag": 4031
        }
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "c",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": {
          "__type": "Empty",
          "__tag": 4031
        }
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "x",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": {
          "__type": "Empty",
          "__tag": 4031
        }
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "y",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": {
          "__type": "Empty",
          "__tag": 4031
        }
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "z",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": {
          "__type": "Empty",
          "__tag": 4031
        }
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "tau",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": {
          "__type": "Empty",
          "__tag": 4031
        }
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "kappa",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": {
          "__type": "Empty",
          "__tag": 4031
        }
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "gamma",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": {
          "__type": "Empty",
          "__tag": 4031
        }
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "eta",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": {
          "__type": "Empty",
          "__tag": 4031
        }
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "sparse",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "False"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "lstsq",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "False"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "sym_pos",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "True"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "cholesky",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "True"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "pc",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "True"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "ip",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "False"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "permc_spec",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "MMD_AT_PLUS_A"
      }
    ],
    "return_annotation": {
      "__type": "Empty",
      "__tag": 4031
    },
    "target_name": "_get_delta"
  },
  "references": [
    ".. [4] Andersen, Erling D., and Knud D. Andersen. \"The MOSEK interior point",
    "       optimizer for linear programming: an implementation of the",
    "       homogeneous algorithm.\" High performance optimization. Springer US,",
    "       2000. 197-232."
  ],
  "qa": "scipy.optimize._linprog_ip:_get_delta",
  "arbitrary": [],
  "local_refs": [
    "As defined in [4]",
    "cholesky",
    "except:",
    "ip",
    "lstsq",
    "pc",
    "permc_spec",
    "sparse",
    "sym_pos"
  ]
}