{ "__type": "IngestedDoc", "__tag": 4010, "_content": { "Notes": { "__type": "Section", "__tag": 4015, "children": [ { "__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": "CrossRef", "__tag": 4002, "value": "is_isomorphic", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.cluster.hierarchy:is_isomorphic" }, "kind": "module" }, { "__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 ✅ 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": [], "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": "b", "annotation": "bool", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Whether the flat cluster assignments " }, { "__type": "ParamRef", "__tag": 4071, "name": "T1" }, { "__type": "Text", "__tag": 4046, "value": " and " }, { "__type": "ParamRef", "__tag": 4071, "name": "T2" }, { "__type": "Text", "__tag": 4046, "value": " are equivalent." } ] } ] } ] } ], "title": [], "level": 0, "target": null }, "Summary": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Determine if two different cluster assignments are equivalent." } ] } ], "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": "T1", "annotation": "array_like", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "An assignment of singleton cluster ids to flat cluster ids." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "T2", "annotation": "array_like", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "An assignment of singleton cluster ids to flat cluster ids." } ] } ] } ] } ], "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/cluster/hierarchy.py", "item_line": 3813, "item_type": "function", "aliases": [ "scipy.cluster.hierarchy.is_isomorphic" ], "example_section_data": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Code", "__tag": 4050, "value": "from scipy.cluster.hierarchy import fcluster, is_isomorphic\nfrom scipy.cluster.hierarchy import single, complete\nfrom scipy.spatial.distance import pdist\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nTwo flat cluster assignments can be isomorphic if they represent the same\ncluster assignment, with different labels.\n\nFor example, we can use the `scipy.cluster.hierarchy.single` method\nand flatten the output to four clusters:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "X = [[0, 0], [0, 1], [1, 0],\n [0, 4], [0, 3], [1, 4],\n [4, 0], [3, 0], [4, 1],\n [4, 4], [3, 4], [4, 3]]\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\n" }, { "__type": "Code", "__tag": 4050, "value": "Z = single(pdist(X))\nT = fcluster(Z, 1, criterion='distance')\nT\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nWe can then do the same using the\n`scipy.cluster.hierarchy.complete`: method:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "Z = complete(pdist(X))\nT_ = fcluster(Z, 1.5, criterion='distance')\nT_\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nAs we can see, in both cases we obtain four clusters and all the data\npoints are distributed in the same way - the only thing that changes\nare the flat cluster labels (3 => 1, 4 =>2, 2 =>3 and 4 =>1), so both\ncluster assignments are isomorphic:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "is_isomorphic(T, T_)\n", "execution_status": "failure" } ], "title": [], "level": 0, "target": null }, "see_also": [ { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "fcluster", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.cluster.hierarchy:fcluster" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "for the creation of flat cluster assignments." } ] } ], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "linkage", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "current-module", "version": "current-version", "kind": "to-resolve", "path": "linkage" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "for a description of what a linkage matrix is." } ] } ], "type": "func" } ], "signature": { "__type": "SignatureNode", "__tag": 4029, "kind": "function", "parameters": [ { "__type": "SigParam", "__tag": 4030, "name": "T1", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": { "__type": "Empty", "__tag": 4031 } }, { "__type": "SigParam", "__tag": 4030, "name": "T2", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": { "__type": "Empty", "__tag": 4031 } } ], "return_annotation": { "__type": "Empty", "__tag": 4031 }, "target_name": "is_isomorphic" }, "references": null, "qa": "scipy.cluster.hierarchy:is_isomorphic", "arbitrary": [], "local_refs": [ "T1", "T2", "b" ] }