{
  "__type": "IngestedDoc",
  "__tag": 4010,
  "_content": {
    "Notes": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "The Leslie matrix is used to model discrete-time, age-structured population growth "
            },
            {
              "__type": "FootnoteReference",
              "__tag": 4066,
              "label": "1"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " "
            },
            {
              "__type": "FootnoteReference",
              "__tag": 4066,
              "label": "2"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ". In a population with "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "n"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " age classes, two sets of parameters define a Leslie matrix: the "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "n"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " \"fecundity coefficients\", which give the number of offspring per-capita produced by each age class, and the "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "n - 1"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " \"survival coefficients\", which give the per-capita survival rate of each age class."
            }
          ]
        }
      ],
      "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": "L",
              "annotation": "(N, N) ndarray",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "The array is zero except for the first row, which is "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "f"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": ", and the first sub-diagonal, which is "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "s"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": ". The data-type of the array will be the data-type of "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "f[0]+s[0]"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "."
                    }
                  ]
                }
              ]
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Summary": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "Create a Leslie matrix."
            }
          ]
        }
      ],
      "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": "f",
              "annotation": "(N,) array_like",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "The \"fecundity\" coefficients."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "s",
              "annotation": "(N-1,) array_like",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "The \"survival\" coefficients. The length of "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "s"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " must be one less than the length of "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "f"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": ", and it must be at least 1."
                    }
                  ]
                }
              ]
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Extended Summary": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "Given the length "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "n"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " array of fecundity coefficients "
            },
            {
              "__type": "ParamRef",
              "__tag": 4071,
              "name": "f"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " and the length "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "n - 1"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " array of survival coefficients "
            },
            {
              "__type": "ParamRef",
              "__tag": 4071,
              "name": "s"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ", return the associated Leslie matrix."
            }
          ]
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "The documentation is written assuming array arguments are of specified \"core\" shapes. However, array argument(s) of this function may have additional \"batch\" dimensions prepended to the core shape. In this case, the array is treated as a batch of lower-dimensional slices; see "
            },
            {
              "__type": "InlineRole",
              "__tag": 4003,
              "value": "linalg_batch",
              "domain": null,
              "role": "ref",
              "inventory": null
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " for details. The NEP 5 signature of this function is (i),(j)->(i,i)."
            }
          ]
        }
      ],
      "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": "build-install/usr/lib/python3.14/site-packages/scipy/linalg/_special_matrices.py",
  "item_line": 279,
  "item_type": "function",
  "aliases": [
    "scipy.linalg.leslie"
  ],
  "example_section_data": {
    "__type": "Section",
    "__tag": 4015,
    "children": [
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "from scipy.linalg import leslie\n",
        "execution_status": "success",
        "out": ""
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "leslie([0.1, 2.0, 1.0, 0.1], [0.2, 0.8, 0.7])\n",
        "execution_status": "failure",
        "out": "array([[0.1, 2. , 1. , 0.1],\n       [0.2, 0. , 0. , 0. ],\n       [0. , 0.8, 0. , 0. ],\n       [0. , 0. , 0.7, 0. ]])\n"
      }
    ],
    "title": [],
    "level": 0,
    "target": null
  },
  "see_also": [],
  "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": "s",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": {
          "__type": "Empty",
          "__tag": 4031
        }
      }
    ],
    "return_annotation": {
      "__type": "Empty",
      "__tag": 4031
    },
    "target_name": "leslie"
  },
  "references": [
    ".. [1] P. H. Leslie, On the use of matrices in certain population",
    "       mathematics, Biometrika, Vol. 33, No. 3, 183--212 (Nov. 1945)",
    ".. [2] P. H. Leslie, Some further notes on the use of matrices in",
    "       population mathematics, Biometrika, Vol. 35, No. 3/4, 213--245",
    "       (Dec. 1948)"
  ],
  "qa": "scipy.linalg._special_matrices:leslie",
  "arbitrary": [],
  "local_refs": [
    "L",
    "f",
    "s"
  ]
}