{
  "__type": "IngestedDoc",
  "__tag": 4010,
  "_content": {
    "Notes": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "See "
            },
            {
              "__type": "CrossRef",
              "__tag": 4002,
              "value": "fft",
              "reference": {
                "__type": "LocalRef",
                "__tag": 4022,
                "kind": "module",
                "path": "numpy.fft"
              },
              "kind": "module"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " for definitions and conventions used."
            }
          ]
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "See "
            },
            {
              "__type": "CrossRef",
              "__tag": 4002,
              "value": "rfft",
              "reference": {
                "__type": "LocalRef",
                "__tag": 4022,
                "kind": "module",
                "path": "numpy.fft:rfft"
              },
              "kind": "module"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " for definitions and conventions used for real input."
            }
          ]
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "The correct interpretation of the hermitian input depends on the shape of the original data, as given by "
            },
            {
              "__type": "ParamRef",
              "__tag": 4071,
              "name": "s"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ". This is because each input shape could correspond to either an odd or even length signal. By default, "
            },
            {
              "__type": "CrossRef",
              "__tag": 4002,
              "value": "irfftn",
              "reference": {
                "__type": "LocalRef",
                "__tag": 4022,
                "kind": "module",
                "path": "numpy.fft:irfftn"
              },
              "kind": "module"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " assumes an even output length which puts the last entry at the Nyquist frequency; aliasing with its symmetric counterpart. When performing the final complex to real transform, the last value is thus treated as purely real. To avoid losing information, the correct shape of the real input "
            },
            {
              "__type": "Strong",
              "__tag": 4048,
              "children": [
                {
                  "__type": "Text",
                  "__tag": 4046,
                  "value": "must"
                }
              ]
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " be given."
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Warns": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Raises": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Parameters",
          "__tag": 4026,
          "children": [
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "",
              "annotation": "ValueError",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "If "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "s"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " and "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "axes"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " have different length."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "",
              "annotation": "IndexError",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "If an element of "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "axes"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " is larger than than the number of axes of "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "a"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "."
                    }
                  ]
                }
              ]
            }
          ]
        }
      ],
      "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": "out",
              "annotation": "ndarray",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "The truncated or zero-padded input, transformed along the axes indicated by "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "axes"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": ", or by a combination of "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "s"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " or "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "a"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": ", as explained in the parameters section above. The length of each transformed axis is as given by the corresponding element of "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "s"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": ", or the length of the input in every axis except for the last one if "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "s"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " is not given.  In the final transformed axis the length of the output when "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "s"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " is not given is "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "2*(m-1)"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " where "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "m"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " is the length of the final transformed axis of the input.  To get an odd number of output points in the final axis, "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "s"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " must be specified."
                    }
                  ]
                }
              ]
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Summary": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "Computes the inverse of "
            },
            {
              "__type": "CrossRef",
              "__tag": 4002,
              "value": "rfftn",
              "reference": {
                "__type": "LocalRef",
                "__tag": 4022,
                "kind": "module",
                "path": "numpy.fft:rfftn"
              },
              "kind": "module"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "."
            }
          ]
        }
      ],
      "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": "a",
              "annotation": "array_like",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Input array."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "s",
              "annotation": "sequence of ints, optional",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Shape (length of each transformed axis) of the output ("
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "s[0]"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " refers to axis 0, "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "s[1]"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " to axis 1, etc.). "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "s"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " is also the number of input points used along this axis, except for the last axis, where "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "s[-1]//2+1"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " points of the input are used. Along any axis, if the shape indicated by "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "s"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " is smaller than that of the input, the input is cropped.  If it is larger, the input is padded with zeros."
                    }
                  ]
                },
                {
                  "__type": "Admonition",
                  "__tag": 4056,
                  "kind": "versionchanged",
                  "base_type": "neutral",
                  "children": [
                    {
                      "__type": "AdmonitionTitle",
                      "__tag": 4055,
                      "children": [
                        {
                          "__type": "Text",
                          "__tag": 4046,
                          "value": "versionchanged 2.0"
                        }
                      ]
                    },
                    {
                      "__type": "Paragraph",
                      "__tag": 4045,
                      "children": [
                        {
                          "__type": "Text",
                          "__tag": 4046,
                          "value": "If it is "
                        },
                        {
                          "__type": "InlineCode",
                          "__tag": 4051,
                          "value": "-1"
                        },
                        {
                          "__type": "Text",
                          "__tag": 4046,
                          "value": ", the whole input is used (no padding/trimming)."
                        }
                      ]
                    }
                  ]
                },
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "If "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "s"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " is not given, the shape of the input along the axes specified by axes is used. Except for the last axis which is taken to be "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "2*(m-1)"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " where "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "m"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " is the length of the input along that axis."
                    }
                  ]
                },
                {
                  "__type": "Admonition",
                  "__tag": 4056,
                  "kind": "deprecated",
                  "base_type": "neutral",
                  "children": [
                    {
                      "__type": "AdmonitionTitle",
                      "__tag": 4055,
                      "children": [
                        {
                          "__type": "Text",
                          "__tag": 4046,
                          "value": "deprecated 2.0"
                        }
                      ]
                    },
                    {
                      "__type": "Paragraph",
                      "__tag": 4045,
                      "children": [
                        {
                          "__type": "Text",
                          "__tag": 4046,
                          "value": "If "
                        },
                        {
                          "__type": "ParamRef",
                          "__tag": 4071,
                          "name": "s"
                        },
                        {
                          "__type": "Text",
                          "__tag": 4046,
                          "value": " is not "
                        },
                        {
                          "__type": "InlineCode",
                          "__tag": 4051,
                          "value": "None"
                        },
                        {
                          "__type": "Text",
                          "__tag": 4046,
                          "value": ", "
                        },
                        {
                          "__type": "ParamRef",
                          "__tag": 4071,
                          "name": "axes"
                        },
                        {
                          "__type": "Text",
                          "__tag": 4046,
                          "value": " must not be "
                        },
                        {
                          "__type": "InlineCode",
                          "__tag": 4051,
                          "value": "None"
                        },
                        {
                          "__type": "Text",
                          "__tag": 4046,
                          "value": " either."
                        }
                      ]
                    }
                  ]
                },
                {
                  "__type": "Admonition",
                  "__tag": 4056,
                  "kind": "deprecated",
                  "base_type": "neutral",
                  "children": [
                    {
                      "__type": "AdmonitionTitle",
                      "__tag": 4055,
                      "children": [
                        {
                          "__type": "Text",
                          "__tag": 4046,
                          "value": "deprecated 2.0"
                        }
                      ]
                    },
                    {
                      "__type": "Paragraph",
                      "__tag": 4045,
                      "children": [
                        {
                          "__type": "ParamRef",
                          "__tag": 4071,
                          "name": "s"
                        },
                        {
                          "__type": "Text",
                          "__tag": 4046,
                          "value": " must contain only "
                        },
                        {
                          "__type": "InlineCode",
                          "__tag": 4051,
                          "value": "int"
                        },
                        {
                          "__type": "Text",
                          "__tag": 4046,
                          "value": " s, not "
                        },
                        {
                          "__type": "InlineCode",
                          "__tag": 4051,
                          "value": "None"
                        },
                        {
                          "__type": "Text",
                          "__tag": 4046,
                          "value": " values. "
                        },
                        {
                          "__type": "InlineCode",
                          "__tag": 4051,
                          "value": "None"
                        },
                        {
                          "__type": "Text",
                          "__tag": 4046,
                          "value": " values currently mean that the default value for "
                        },
                        {
                          "__type": "InlineCode",
                          "__tag": 4051,
                          "value": "n"
                        },
                        {
                          "__type": "Text",
                          "__tag": 4046,
                          "value": " is used in the corresponding 1-D transform, but this behaviour is deprecated."
                        }
                      ]
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "axes",
              "annotation": "sequence of ints, optional",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Axes over which to compute the inverse FFT. If not given, the last "
                    },
                    {
                      "__type": "InlineRole",
                      "__tag": 4003,
                      "value": "len(s)",
                      "domain": null,
                      "role": null,
                      "inventory": null
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " axes are used, or all axes if "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "s"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " is also not specified. Repeated indices in "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "axes"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " means that the inverse transform over that axis is performed multiple times."
                    }
                  ]
                },
                {
                  "__type": "Admonition",
                  "__tag": 4056,
                  "kind": "deprecated",
                  "base_type": "neutral",
                  "children": [
                    {
                      "__type": "AdmonitionTitle",
                      "__tag": 4055,
                      "children": [
                        {
                          "__type": "Text",
                          "__tag": 4046,
                          "value": "deprecated 2.0"
                        }
                      ]
                    },
                    {
                      "__type": "Paragraph",
                      "__tag": 4045,
                      "children": [
                        {
                          "__type": "Text",
                          "__tag": 4046,
                          "value": "If "
                        },
                        {
                          "__type": "ParamRef",
                          "__tag": 4071,
                          "name": "s"
                        },
                        {
                          "__type": "Text",
                          "__tag": 4046,
                          "value": " is specified, the corresponding "
                        },
                        {
                          "__type": "ParamRef",
                          "__tag": 4071,
                          "name": "axes"
                        },
                        {
                          "__type": "Text",
                          "__tag": 4046,
                          "value": " to be transformed must be explicitly specified too."
                        }
                      ]
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "norm",
              "annotation": "{\"backward\", \"ortho\", \"forward\"}, optional",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Normalization mode (see "
                    },
                    {
                      "__type": "CrossRef",
                      "__tag": 4002,
                      "value": "numpy.fft",
                      "reference": {
                        "__type": "LocalRef",
                        "__tag": 4022,
                        "kind": "module",
                        "path": "numpy.fft"
                      },
                      "kind": "module"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "). Default is \"backward\". Indicates which direction of the forward/backward pair of transforms is scaled and with what normalization factor."
                    }
                  ]
                },
                {
                  "__type": "Admonition",
                  "__tag": 4056,
                  "kind": "versionadded",
                  "base_type": "neutral",
                  "children": [
                    {
                      "__type": "AdmonitionTitle",
                      "__tag": 4055,
                      "children": [
                        {
                          "__type": "Text",
                          "__tag": 4046,
                          "value": "versionadded 1.20.0"
                        }
                      ]
                    },
                    {
                      "__type": "Paragraph",
                      "__tag": 4045,
                      "children": [
                        {
                          "__type": "Text",
                          "__tag": 4046,
                          "value": "The \"backward\", \"forward\" values were added."
                        }
                      ]
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "out",
              "annotation": "ndarray, optional",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "If provided, the result will be placed in this array. It should be of the appropriate shape and dtype for the last transformation."
                    }
                  ]
                },
                {
                  "__type": "Admonition",
                  "__tag": 4056,
                  "kind": "versionadded",
                  "base_type": "neutral",
                  "children": [
                    {
                      "__type": "AdmonitionTitle",
                      "__tag": 4055,
                      "children": [
                        {
                          "__type": "Text",
                          "__tag": 4046,
                          "value": "versionadded 2.0.0"
                        }
                      ]
                    }
                  ]
                }
              ]
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Extended Summary": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "This function computes the inverse of the N-dimensional discrete Fourier Transform for real input over any number of axes in an M-dimensional array by means of the Fast Fourier Transform (FFT).  In other words, "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "irfftn(rfftn(a), a.shape) == a"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " to within numerical accuracy. (The "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "a.shape"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " is necessary like "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "len(a)"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " is for "
            },
            {
              "__type": "CrossRef",
              "__tag": 4002,
              "value": "irfft",
              "reference": {
                "__type": "LocalRef",
                "__tag": 4022,
                "kind": "module",
                "path": "numpy.fft:irfft"
              },
              "kind": "module"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ", and for the same reason.)"
            }
          ]
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "The input should be ordered in the same way as is returned by "
            },
            {
              "__type": "CrossRef",
              "__tag": 4002,
              "value": "rfftn",
              "reference": {
                "__type": "LocalRef",
                "__tag": 4022,
                "kind": "module",
                "path": "numpy.fft:rfftn"
              },
              "kind": "module"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ", i.e. as for "
            },
            {
              "__type": "CrossRef",
              "__tag": 4002,
              "value": "irfft",
              "reference": {
                "__type": "LocalRef",
                "__tag": 4022,
                "kind": "module",
                "path": "numpy.fft:irfft"
              },
              "kind": "module"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " for the final transformation axis, and as for "
            },
            {
              "__type": "CrossRef",
              "__tag": 4002,
              "value": "ifftn",
              "reference": {
                "__type": "LocalRef",
                "__tag": 4022,
                "kind": "module",
                "path": "numpy.fft:ifftn"
              },
              "kind": "module"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " along all the other axes."
            }
          ]
        }
      ],
      "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/numpy/fft/_pocketfft.py",
  "item_line": 1473,
  "item_type": "_ArrayFunctionDispatcher",
  "aliases": [
    "numpy.fft.irfftn"
  ],
  "example_section_data": {
    "__type": "Section",
    "__tag": 4015,
    "children": [
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "import numpy as np\na = np.zeros((3, 2, 2))\na[0, 0, 0] = 3 * 2 * 2\n",
        "execution_status": "success"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "np.fft.irfftn(a)\n",
        "execution_status": "failure"
      }
    ],
    "title": [],
    "level": 0,
    "target": null
  },
  "see_also": [
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "fft",
        "reference": {
          "__type": "LocalRef",
          "__tag": 4022,
          "kind": "module",
          "path": "numpy.fft"
        },
        "kind": "module"
      },
      "descriptions": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "The one-dimensional FFT, with definitions and conventions used."
            }
          ]
        }
      ],
      "type": null
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "irfft",
        "reference": {
          "__type": "LocalRef",
          "__tag": 4022,
          "kind": "module",
          "path": "numpy.fft:irfft"
        },
        "kind": "module"
      },
      "descriptions": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "The inverse of the one-dimensional FFT of real input."
            }
          ]
        }
      ],
      "type": null
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "irfft2",
        "reference": {
          "__type": "LocalRef",
          "__tag": 4022,
          "kind": "module",
          "path": "numpy.fft:irfft2"
        },
        "kind": "module"
      },
      "descriptions": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "The inverse of the two-dimensional FFT of real input."
            }
          ]
        }
      ],
      "type": null
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "rfftn",
        "reference": {
          "__type": "LocalRef",
          "__tag": 4022,
          "kind": "module",
          "path": "numpy.fft:rfftn"
        },
        "kind": "module"
      },
      "descriptions": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "The forward n-dimensional FFT of real input, of which "
            },
            {
              "__type": "InlineRole",
              "__tag": 4003,
              "value": "ifftn",
              "domain": null,
              "role": null,
              "inventory": null
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " is the inverse."
            }
          ]
        }
      ],
      "type": null
    }
  ],
  "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": "s",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "None"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "axes",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "None"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "norm",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "None"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "out",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "None"
      }
    ],
    "return_annotation": {
      "__type": "Empty",
      "__tag": 4031
    },
    "target_name": "irfftn"
  },
  "references": null,
  "qa": "numpy.fft:irfftn",
  "arbitrary": [],
  "local_refs": [
    "a",
    "axes",
    "norm",
    "out",
    "s"
  ]
}