{ "__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": "Rbf", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.interpolate._rbf:Rbf" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " is not in-scope for support of Python Array API Standard compatible backends other than NumPy." } ] }, { "__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": [], "title": [], "level": 0, "target": null }, "Summary": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Class for radial basis function interpolation of functions from N-D scattered data to an M-D domain (legacy)." } ] } ], "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": [ { "__type": "Parameters", "__tag": 4026, "children": [ { "__type": "DocParam", "__tag": 4016, "name": "N", "annotation": "int", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The number of data points (as determined by the input arrays)." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "di", "annotation": "ndarray", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The 1-D array of data values at each of the data coordinates " }, { "__type": "CrossRef", "__tag": 4002, "value": "xi", "reference": { "__type": "RefInfo", "__tag": 4000, "module": null, "version": null, "kind": "local", "path": "xi" }, "kind": "local" }, { "__type": "Text", "__tag": 4046, "value": "." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "xi", "annotation": "ndarray", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The 2-D array of data coordinates." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "function", "annotation": "str or callable", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The radial basis function. See description under Parameters." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "epsilon", "annotation": "float", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Parameter used by gaussian or multiquadrics functions. See Parameters." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "smooth", "annotation": "float", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Smoothing parameter. See description under Parameters." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "norm", "annotation": "str or callable", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The distance function. See description under Parameters." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "mode", "annotation": "str", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Mode of the interpolation. See description under Parameters." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "nodes", "annotation": "ndarray", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "A 1-D array of node values for the interpolation." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "A", "annotation": "internal property, do not use", "desc": [] } ] } ], "title": [], "level": 0, "target": null }, "Parameters": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Parameters", "__tag": 4026, "children": [ { "__type": "DocParam", "__tag": 4016, "name": "*args", "annotation": "arrays", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "x, y, z, ..., d, where x, y, z, ... are the coordinates of the nodes and d is the array of values at the nodes" } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "function", "annotation": "str or callable, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The radial basis function, based on the radius, r, given by the norm (default is Euclidean distance); the default is 'multiquadric' " } ] }, { "__type": "Code", "__tag": 4050, "value": "'multiquadric': sqrt((r/self.epsilon)**2 + 1)\n'inverse': 1.0/sqrt((r/self.epsilon)**2 + 1)\n'gaussian': exp(-(r/self.epsilon)**2)\n'linear': r\n'cubic': r**3\n'quintic': r**5\n'thin_plate': r**2 * log(r)", "execution_status": null }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "If callable, then it must take 2 arguments (self, r). The epsilon parameter will be available as self.epsilon. Other keyword arguments passed in will be available as well." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "epsilon", "annotation": "float, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Adjustable constant for gaussian or multiquadrics functions - defaults to approximate average distance between nodes (which is a good start)." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "smooth", "annotation": "float, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Values greater than zero increase the smoothness of the approximation. 0 is for interpolation (default), the function will always go through the nodal points in this case." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "norm", "annotation": "str, callable, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "A function that returns the 'distance' between two points, with inputs as arrays of positions (x, y, z, ...), and an output as an array of distance. E.g., the default: 'euclidean', such that the result is a matrix of the distances from each point in " }, { "__type": "InlineCode", "__tag": 4051, "value": "x1" }, { "__type": "Text", "__tag": 4046, "value": " to each point in " }, { "__type": "InlineCode", "__tag": 4051, "value": "x2" }, { "__type": "Text", "__tag": 4046, "value": ". For more options, see documentation of " }, { "__type": "InlineRole", "__tag": 4003, "value": "scipy.spatial.distances.cdist", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": "." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "mode", "annotation": "str, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Mode of the interpolation, can be '1-D' (default) or 'N-D'. When it is '1-D' the data " }, { "__type": "InlineRole", "__tag": 4003, "value": "d", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " will be considered as 1-D and flattened internally. When it is 'N-D' the data " }, { "__type": "InlineRole", "__tag": 4003, "value": "d", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " is assumed to be an array of shape (n_samples, m), where m is the dimension of the target domain." } ] } ] } ] } ], "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/interpolate/_rbf.py", "item_line": 56, "item_type": "class", "aliases": [ "scipy.interpolate.Rbf" ], "example_section_data": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Code", "__tag": 4050, "value": "import numpy as np\nfrom scipy.interpolate import Rbf\nrng = np.random.default_rng()\nx, y, z, d = rng.random((4, 50))\nrbfi = Rbf(x, y, z, d) # radial basis function interpolator instance\nxi = yi = zi = np.linspace(0, 1, 20)\ndi = rbfi(xi, yi, zi) # interpolated values\ndi.shape\n", "execution_status": "success" } ], "title": [], "level": 0, "target": null }, "see_also": [ { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "RBFInterpolator", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.interpolate._rbfinterp:RBFInterpolator" }, "kind": "module" }, "descriptions": [], "type": "func" } ], "signature": null, "references": null, "qa": "scipy.interpolate._rbf:Rbf", "arbitrary": [], "local_refs": [ "*args", "A", "N", "di", "epsilon", "function", "mode", "nodes", "norm", "smooth", "xi" ] }