{ "__type": "IngestedDoc", "__tag": 4010, "_content": { "Notes": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "See " }, { "__type": "InlineRole", "__tag": 4003, "value": "splev", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " for evaluation of the spline and its derivatives. The number of dimensions N must be smaller than 11." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The number of coefficients in the " }, { "__type": "InlineRole", "__tag": 4003, "value": "c", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " array is " }, { "__type": "InlineCode", "__tag": 4051, "value": "k+1" }, { "__type": "Text", "__tag": 4046, "value": " less than the number of knots, " }, { "__type": "InlineCode", "__tag": 4051, "value": "len(t)" }, { "__type": "Text", "__tag": 4046, "value": ". This is in contrast with " }, { "__type": "InlineRole", "__tag": 4003, "value": "splrep", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": ", which zero-pads the array of coefficients to have the same length as the array of knots. These additional coefficients are ignored by evaluation routines, " }, { "__type": "InlineRole", "__tag": 4003, "value": "splev", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " and " }, { "__type": "CrossRef", "__tag": 4002, "value": "BSpline", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.interpolate._bsplines:BSpline" }, "kind": "module" }, { "__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": "splprep", "domain": null, "role": null, "inventory": null }, { "__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": [ { "__type": "Parameters", "__tag": 4026, "children": [ { "__type": "DocParam", "__tag": 4016, "name": "tck", "annotation": "tuple", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "A tuple, " }, { "__type": "InlineCode", "__tag": 4051, "value": "(t,c,k)" }, { "__type": "Text", "__tag": 4046, "value": " containing the vector of knots, the B-spline coefficients, and the degree of the spline." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "u", "annotation": "array", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "An array of the values of the parameter." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "fp", "annotation": "float", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The weighted sum of squared residuals of the spline approximation." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "ier", "annotation": "int", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "An integer flag about splrep success. Success is indicated if ier<=0. If ier in [1,2,3] an error occurred but was not raised. Otherwise an error is raised." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "msg", "annotation": "str", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "A message corresponding to the integer flag, ier." } ] } ] } ] } ], "title": [], "level": 0, "target": null }, "Summary": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Find the B-spline representation of an N-D curve." } ] } ], "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": "A list of sample vector arrays representing the curve." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "w", "annotation": "array_like, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Strictly positive rank-1 array of weights the same length as " }, { "__type": "InlineRole", "__tag": 4003, "value": "x[0]", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": ". The weights are used in computing the weighted least-squares spline fit. If the errors in the " }, { "__type": "ParamRef", "__tag": 4071, "name": "x" }, { "__type": "Text", "__tag": 4046, "value": " values have standard-deviation given by the vector d, then " }, { "__type": "ParamRef", "__tag": 4071, "name": "w" }, { "__type": "Text", "__tag": 4046, "value": " should be 1/d. Default is " }, { "__type": "InlineCode", "__tag": 4051, "value": "ones(len(x[0]))" }, { "__type": "Text", "__tag": 4046, "value": "." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "u", "annotation": "array_like, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "An array of parameter values. If not given, these values are calculated automatically as " }, { "__type": "InlineCode", "__tag": 4051, "value": "M = len(x[0])" }, { "__type": "Text", "__tag": 4046, "value": ", where" } ] }, { "__type": "Blockquote", "__tag": 4059, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "v[0] = 0" } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "v[i] = v[i-1] + distance(" }, { "__type": "InlineRole", "__tag": 4003, "value": "x[i]", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": ", " }, { "__type": "InlineRole", "__tag": 4003, "value": "x[i-1]", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": ")" } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "u[i] = v[i] / v[M-1]" } ] } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "ub, ue", "annotation": "int, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The end-points of the parameters interval. Defaults to u[0] and u[-1]." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "k", "annotation": "int, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Degree of the spline. Cubic splines are recommended. Even values of " }, { "__type": "ParamRef", "__tag": 4071, "name": "k" }, { "__type": "Text", "__tag": 4046, "value": " should be avoided especially with a small s-value. " }, { "__type": "InlineCode", "__tag": 4051, "value": "1 <= k <= 5" }, { "__type": "Text", "__tag": 4046, "value": ", default is 3." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "task", "annotation": "int, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "If task==0 (default), find t and c for a given smoothing factor, s. If task==1, find t and c for another value of the smoothing factor, s. There must have been a previous call with task=0 or task=1 for the same set of data. If task=-1 find the weighted least square spline for a given set of knots, t." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "s", "annotation": "float, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "A smoothing condition. The amount of smoothness is determined by satisfying the conditions: " }, { "__type": "InlineCode", "__tag": 4051, "value": "sum((w * (y - g))**2,axis=0) <= s" }, { "__type": "Text", "__tag": 4046, "value": ", where g(x) is the smoothed interpolation of (x,y). The user can use " }, { "__type": "ParamRef", "__tag": 4071, "name": "s" }, { "__type": "Text", "__tag": 4046, "value": " to control the trade-off between closeness and smoothness of fit. Larger " }, { "__type": "ParamRef", "__tag": 4071, "name": "s" }, { "__type": "Text", "__tag": 4046, "value": " means more smoothing while smaller values of " }, { "__type": "ParamRef", "__tag": 4071, "name": "s" }, { "__type": "Text", "__tag": 4046, "value": " indicate less smoothing. Recommended values of " }, { "__type": "ParamRef", "__tag": 4071, "name": "s" }, { "__type": "Text", "__tag": 4046, "value": " depend on the weights, w. If the weights represent the inverse of the standard-deviation of y, then a good " }, { "__type": "ParamRef", "__tag": 4071, "name": "s" }, { "__type": "Text", "__tag": 4046, "value": " value should be found in the range " }, { "__type": "InlineCode", "__tag": 4051, "value": "(m-sqrt(2*m),m+sqrt(2*m))" }, { "__type": "Text", "__tag": 4046, "value": ", where m is the number of data points in x, y, and w." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "t", "annotation": "array, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The knots needed for " }, { "__type": "InlineCode", "__tag": 4051, "value": "task=-1" }, { "__type": "Text", "__tag": 4046, "value": ". There must be at least " }, { "__type": "InlineCode", "__tag": 4051, "value": "2*k+2" }, { "__type": "Text", "__tag": 4046, "value": " knots." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "full_output", "annotation": "int, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "If non-zero, then return optional outputs." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "nest", "annotation": "int, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "An over-estimate of the total number of knots of the spline to help in determining the storage space. By default nest=m/2. Always large enough is nest=m+k+1." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "per", "annotation": "int, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "If non-zero, data points are considered periodic with period " }, { "__type": "InlineCode", "__tag": 4051, "value": "x[m-1] - x[0]" }, { "__type": "Text", "__tag": 4046, "value": " and a smooth periodic spline approximation is returned. Values of " }, { "__type": "InlineCode", "__tag": 4051, "value": "y[m-1]" }, { "__type": "Text", "__tag": 4046, "value": " and " }, { "__type": "InlineCode", "__tag": 4051, "value": "w[m-1]" }, { "__type": "Text", "__tag": 4046, "value": " are not used." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "quiet", "annotation": "int, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Non-zero to suppress messages." } ] } ] } ] } ], "title": [], "level": 0, "target": null }, "Extended Summary": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Given a list of N rank-1 arrays, " }, { "__type": "ParamRef", "__tag": 4071, "name": "x" }, { "__type": "Text", "__tag": 4046, "value": ", which represent a curve in N-dimensional space parametrized by " }, { "__type": "ParamRef", "__tag": 4071, "name": "u" }, { "__type": "Text", "__tag": 4046, "value": ", find a smooth approximating spline curve g(" }, { "__type": "ParamRef", "__tag": 4071, "name": "u" }, { "__type": "Text", "__tag": 4046, "value": "). Uses the FORTRAN routine parcur from FITPACK." } ] } ], "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/_fitpack_py.py", "item_line": 14, "item_type": "function", "aliases": [ "scipy.interpolate.splprep" ], "example_section_data": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Text", "__tag": 4046, "value": "Generate a discretization of a limacon curve in the polar coordinates:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "import numpy as np\nphi = np.linspace(0, 2.*np.pi, 40)\nr = 0.5 + np.cos(phi) # polar coords\nx, y = r * np.cos(phi), r * np.sin(phi) # convert to cartesian\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nAnd interpolate:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "from scipy.interpolate import splprep, splev\ntck, u = splprep([x, y], s=0)\nnew_points = splev(u, tck)\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nNotice that (i) we force interpolation by using ``s=0``,\n(ii) the parameterization, ``u``, is generated automatically.\nNow plot the result:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "import matplotlib.pyplot as plt\nfig, ax = plt.subplots()\n", "execution_status": "success" }, { "__type": "Code", "__tag": 4050, "value": "ax.plot(x, y, 'ro')\nax.plot(new_points[0], new_points[1], 'r-')\n", "execution_status": "failure" }, { "__type": "Code", "__tag": 4050, "value": "plt.show()\n", "execution_status": "success" }, { "__type": "Figure", "__tag": 4024, "value": { "__type": "RefInfo", "__tag": 4000, "module": "scipy", "version": "1.17.1", "kind": "assets", "path": "fig-0fe642de2da1bdfc.png" } } ], "title": [], "level": 0, "target": null }, "see_also": [ { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "BSpline", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.interpolate._bsplines:BSpline" }, "kind": "module" }, "descriptions": [], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "BivariateSpline", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.interpolate._fitpack2:BivariateSpline" }, "kind": "module" }, "descriptions": [], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "UnivariateSpline", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.interpolate._fitpack2:UnivariateSpline" }, "kind": "module" }, "descriptions": [], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "bisplev", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.interpolate._fitpack_impl:bisplev" }, "kind": "module" }, "descriptions": [], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "bisplrep", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.interpolate._fitpack_impl:bisplrep" }, "kind": "module" }, "descriptions": [], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "make_interp_spline", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.interpolate._bsplines:make_interp_spline" }, "kind": "module" }, "descriptions": [], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "spalde", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.interpolate._fitpack_py:spalde" }, "kind": "module" }, "descriptions": [], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "splev", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "current-module", "version": "current-version", "kind": "to-resolve", "path": "splev" }, "kind": "module" }, "descriptions": [], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "splint", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "current-module", "version": "current-version", "kind": "to-resolve", "path": "splint" }, "kind": "module" }, "descriptions": [], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "splrep", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "current-module", "version": "current-version", "kind": "to-resolve", "path": "splrep" }, "kind": "module" }, "descriptions": [], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "sproot", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "current-module", "version": "current-version", "kind": "to-resolve", "path": "sproot" }, "kind": "module" }, "descriptions": [], "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": "w", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "u", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "ub", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "ue", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "k", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "3" }, { "__type": "SigParam", "__tag": 4030, "name": "task", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "0" }, { "__type": "SigParam", "__tag": 4030, "name": "s", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "t", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "full_output", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "0" }, { "__type": "SigParam", "__tag": 4030, "name": "nest", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "per", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "0" }, { "__type": "SigParam", "__tag": 4030, "name": "quiet", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "1" } ], "return_annotation": { "__type": "Empty", "__tag": 4031 }, "target_name": "splprep" }, "references": [ ".. [1] P. Dierckx, \"Algorithms for smoothing data with periodic and", " parametric splines, Computer Graphics and Image Processing\",", " 20 (1982) 171-184.", ".. [2] P. Dierckx, \"Algorithms for smoothing data with periodic and", " parametric splines\", report tw55, Dept. Computer Science,", " K.U.Leuven, 1981.", ".. [3] P. Dierckx, \"Curve and surface fitting with splines\", Monographs on", " Numerical Analysis, Oxford University Press, 1993." ], "qa": "scipy.interpolate._fitpack_py:splprep", "arbitrary": [], "local_refs": [ "fp", "full_output", "ier", "k", "msg", "nest", "per", "quiet", "s", "t", "task", "tck", "u", "ub", "ue", "w", "x" ] }