{ "__type": "IngestedDoc", "__tag": 4010, "_content": { "Notes": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The transform for real input is performed over the last transformation axis, as by " }, { "__type": "InlineRole", "__tag": 4003, "value": "ihfft", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": ", then the transform over the remaining axes is performed as by " }, { "__type": "InlineRole", "__tag": 4003, "value": "ifftn", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": ". The order of the output is the positive part of the Hermitian output signal, in the same format as " }, { "__type": "InlineRole", "__tag": 4003, "value": "rfft", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": "." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Strong", "__tag": 4048, "children": [ { "__type": "Text", "__tag": 4046, "value": "Array API Standard Support" } ] } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "InlineRole", "__tag": 4003, "value": "ihfftn", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable " }, { "__type": "InlineCode", "__tag": 4051, "value": "SCIPY_ARRAY_API=1" }, { "__type": "Text", "__tag": 4046, "value": " and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported." } ] }, { "__type": "Code", "__tag": 4050, "value": "==================== ==================== ====================\nLibrary CPU GPU\n==================== ==================== ====================\nNumPy ✅ n/a \nCuPy n/a ✅ \nPyTorch ✅ ✅ \nJAX ✅ ✅ \nDask ⚠️ computes graph n/a \n==================== ==================== ====================", "execution_status": null }, { "__type": "Blockquote", "__tag": 4059, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "See " }, { "__type": "InlineRole", "__tag": 4003, "value": "dev-arrayapi", "domain": null, "role": "ref", "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " for more information." } ] } ] } ], "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 the number of axes of " }, { "__type": "ParamRef", "__tag": 4071, "name": "x" }, { "__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": "complex 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": " and " }, { "__type": "ParamRef", "__tag": 4071, "name": "x" }, { "__type": "Text", "__tag": 4046, "value": ", as explained in the parameters section above. The length of the last axis transformed will be " }, { "__type": "InlineCode", "__tag": 4051, "value": "s[-1]//2+1" }, { "__type": "Text", "__tag": 4046, "value": ", while the remaining transformed axes will have lengths according to " }, { "__type": "ParamRef", "__tag": 4071, "name": "s" }, { "__type": "Text", "__tag": 4046, "value": ", or unchanged from the input." } ] } ] } ] } ], "title": [], "level": 0, "target": null }, "Summary": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Compute the N-D inverse discrete Fourier Transform for a real spectrum." } ] } ], "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": "x", "annotation": "array_like", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Input array, taken to be real." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "s", "annotation": "sequence of ints, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Shape (length along each transformed axis) to use from the input. (" }, { "__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.). Along any axis, if the given shape is smaller than that of the input, the input is cropped. If it is larger, the input is padded with zeros. 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 " }, { "__type": "ParamRef", "__tag": 4071, "name": "axes" }, { "__type": "Text", "__tag": 4046, "value": " is used." } ] } ] }, { "__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 FFT. If not given, the last " }, { "__type": "InlineCode", "__tag": 4051, "value": "len(s)" }, { "__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." } ] } ] }, { "__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": "fft", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.fft" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": "). Default is \"backward\"." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "overwrite_x", "annotation": "bool, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "If True, the contents of " }, { "__type": "ParamRef", "__tag": 4071, "name": "x" }, { "__type": "Text", "__tag": 4046, "value": " can be destroyed; the default is False. See " }, { "__type": "CrossRef", "__tag": 4002, "value": "fft", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.fft" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " for more details." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "workers", "annotation": "int, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Maximum number of workers to use for parallel computation. If negative, the value wraps around from " }, { "__type": "InlineCode", "__tag": 4051, "value": "os.cpu_count()" }, { "__type": "Text", "__tag": 4046, "value": ". See " }, { "__type": "CrossRef", "__tag": 4002, "value": "fft", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "scipy", "version": "*", "kind": "api", "path": "scipy.fft._basic:fft" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " for more details." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "plan", "annotation": "object, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "This argument is reserved for passing in a precomputed plan provided by downstream FFT vendors. It is currently not used in SciPy." } ] }, { "__type": "Admonition", "__tag": 4056, "kind": "versionadded", "base_type": "neutral", "children": [ { "__type": "AdmonitionTitle", "__tag": 4055, "children": [ { "__type": "Text", "__tag": 4046, "value": "versionadded 1.5.0" } ] } ] } ] } ] } ], "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 N-D inverse discrete Fourier Transform over any number of axes in an M-D real array by means of the Fast Fourier Transform (FFT). By default, all axes are transformed, with the real transform performed over the last axis, while the remaining transforms are complex." } ] } ], "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/fft/_basic.py", "item_line": 1529, "item_type": "_Function", "aliases": [ "scipy.fft.ihfftn" ], "example_section_data": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Code", "__tag": 4050, "value": "import scipy.fft\nimport numpy as np\nx = np.ones((2, 2, 2))\n", "execution_status": "success" }, { "__type": "Code", "__tag": 4050, "value": "scipy.fft.ihfftn(x)\nscipy.fft.ihfftn(x, axes=(2, 0))\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": "scipy.fft" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The 1-D FFT, with definitions and conventions used." } ] } ], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "fftn", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "current-module", "version": "current-version", "kind": "to-resolve", "path": "fftn" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The N-D FFT." } ] } ], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "hfft", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "current-module", "version": "current-version", "kind": "to-resolve", "path": "hfft" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The 1-D FFT of Hermitian input." } ] } ], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "hfft2", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "current-module", "version": "current-version", "kind": "to-resolve", "path": "hfft2" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The 2-D FFT of Hermitian input." } ] } ], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "hfftn", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "current-module", "version": "current-version", "kind": "to-resolve", "path": "hfftn" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The forward N-D FFT of Hermitian input." } ] } ], "type": "func" } ], "signature": { "__type": "SignatureNode", "__tag": 4029, "kind": "function", "parameters": [ { "__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": "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": "overwrite_x", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "False" }, { "__type": "SigParam", "__tag": 4030, "name": "workers", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "plan", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "KEYWORD_ONLY", "default": "None" } ], "return_annotation": { "__type": "Empty", "__tag": 4031 }, "target_name": "ihfftn" }, "references": null, "qa": "scipy.fft._basic:ihfftn", "arbitrary": [], "local_refs": [ "axes", "norm", "out", "overwrite_x", "plan", "s", "workers", "x" ] }