{ "__type": "IngestedDoc", "__tag": 4010, "_content": { "Notes": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Given a set of " }, { "__type": "InlineMath", "__tag": 4057, "value": "m" }, { "__type": "Text", "__tag": 4046, "value": " data points in " }, { "__type": "InlineMath", "__tag": 4057, "value": "D" }, { "__type": "Text", "__tag": 4046, "value": " dimensions, " }, { "__type": "InlineMath", "__tag": 4057, "value": "\\vec{x}_j" }, { "__type": "Text", "__tag": 4046, "value": ", with " }, { "__type": "InlineMath", "__tag": 4057, "value": "j=1, ..., m" }, { "__type": "Text", "__tag": 4046, "value": " and " }, { "__type": "InlineMath", "__tag": 4057, "value": "\\vec{x}_j = (x_{j; 1}, ..., x_{j; D})" }, { "__type": "Text", "__tag": 4046, "value": ", this routine constructs the parametric spline curve " }, { "__type": "InlineMath", "__tag": 4057, "value": "g_a(u)" }, { "__type": "Text", "__tag": 4046, "value": " with " }, { "__type": "InlineMath", "__tag": 4057, "value": "a=1, ..., D" }, { "__type": "Text", "__tag": 4046, "value": ", to minimize the sum of jumps, " }, { "__type": "InlineMath", "__tag": 4057, "value": "D_{i; a}" }, { "__type": "Text", "__tag": 4046, "value": ", of the " }, { "__type": "InlineCode", "__tag": 4051, "value": "k" }, { "__type": "Text", "__tag": 4046, "value": "-th derivative at the internal knots (" }, { "__type": "InlineMath", "__tag": 4057, "value": "u_b < t_i < u_e" }, { "__type": "Text", "__tag": 4046, "value": "), where" } ] }, { "__type": "Math", "__tag": 4058, "value": "D_{i; a} = g_a^{(k)}(t_i + 0) - g_a^{(k)}(t_i - 0)" }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Specifically, the routine constructs the spline function " }, { "__type": "InlineMath", "__tag": 4057, "value": "g(u)" }, { "__type": "Text", "__tag": 4046, "value": " which minimizes" } ] }, { "__type": "Math", "__tag": 4058, "value": "\\sum_i \\sum_{a=1}^D | D_{i; a} |^2 \\to \\mathrm{min}" }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "provided that" } ] }, { "__type": "Math", "__tag": 4058, "value": "\\sum_{j=1}^m \\sum_{a=1}^D (w_j \\times (g_a(u_j) - x_{j; a}))^2 \\leqslant s" }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "where " }, { "__type": "InlineMath", "__tag": 4057, "value": "u_j" }, { "__type": "Text", "__tag": 4046, "value": " is the value of the parameter corresponding to the data point " }, { "__type": "InlineMath", "__tag": 4057, "value": "(x_{j; 1}, ..., x_{j; D})" }, { "__type": "Text", "__tag": 4046, "value": ", and " }, { "__type": "InlineMath", "__tag": 4057, "value": "s > 0" }, { "__type": "Text", "__tag": 4046, "value": " is the input parameter." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "In other words, we balance maximizing the smoothness (measured as the jumps of the derivative, the first criterion), and the deviation of " }, { "__type": "InlineMath", "__tag": 4057, "value": "g(u_j)" }, { "__type": "Text", "__tag": 4046, "value": " from the data " }, { "__type": "InlineMath", "__tag": 4057, "value": "x_j" }, { "__type": "Text", "__tag": 4046, "value": " (the second criterion)." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Note that the summation in the second criterion is over all data points, and in the first criterion it is over the internal spline knots (i.e. those with " }, { "__type": "InlineCode", "__tag": 4051, "value": "ub < t[i] < ue" }, { "__type": "Text", "__tag": 4046, "value": "). The spline knots are in general a subset of data, see " }, { "__type": "CrossRef", "__tag": 4002, "value": "generate_knots", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.interpolate._fitpack_repro:generate_knots" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " for details." } ] }, { "__type": "Admonition", "__tag": 4056, "kind": "versionadded", "base_type": "neutral", "children": [ { "__type": "AdmonitionTitle", "__tag": 4055, "children": [ { "__type": "Text", "__tag": 4046, "value": "versionadded 1.15.0" } ] } ] }, { "__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": "make_splprep", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.interpolate._fitpack_repro:make_splprep" }, "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 ⚠️ no JIT ⛔ \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": [], "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": "spl", "annotation": "a `BSpline` instance", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "For " }, { "__type": "InlineRole", "__tag": 4003, "value": "s=0", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": ", " }, { "__type": "InlineCode", "__tag": 4051, "value": "spl(u) == x" }, { "__type": "Text", "__tag": 4046, "value": ". For non-zero values of " }, { "__type": "InlineCode", "__tag": 4051, "value": "s" }, { "__type": "Text", "__tag": 4046, "value": ", " }, { "__type": "CrossRef", "__tag": 4002, "value": "spl", "reference": { "__type": "RefInfo", "__tag": 4000, "module": null, "version": null, "kind": "local", "path": "spl" }, "kind": "local" }, { "__type": "Text", "__tag": 4046, "value": " represents the smoothed approximation to " }, { "__type": "InlineCode", "__tag": 4051, "value": "x" }, { "__type": "Text", "__tag": 4046, "value": ", generally with fewer knots." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "u", "annotation": "ndarray", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The values of the parameters" } ] } ] } ] } ], "title": [], "level": 0, "target": null }, "Summary": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Create a smoothing parametric B-spline curve with bounded error, minimizing derivative jumps." } ] } ], "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, shape (ndim, m)", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Sampled data points representing the curve in " }, { "__type": "InlineCode", "__tag": 4051, "value": "ndim" }, { "__type": "Text", "__tag": 4046, "value": " dimensions. The typical use is a list of 1D arrays, each of length " }, { "__type": "InlineCode", "__tag": 4051, "value": "m" }, { "__type": "Text", "__tag": 4046, "value": "." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "w", "annotation": "array_like, shape(m,), optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Strictly positive 1D array of weights. 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": "np.ones(m)" }, { "__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 for the curve in the parametric form. If not given, these values are calculated automatically, according to " } ] }, { "__type": "Code", "__tag": 4050, "value": "v[0] = 0\nv[i] = v[i-1] + distance(x[i], x[i-1])\nu[i] = v[i] / v[-1]", "execution_status": null } ] }, { "__type": "DocParam", "__tag": 4016, "name": "ub, ue", "annotation": "float, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The end-points of the parameters interval. Default to " }, { "__type": "InlineCode", "__tag": 4051, "value": "u[0]" }, { "__type": "Text", "__tag": 4046, "value": " and " }, { "__type": "InlineCode", "__tag": 4051, "value": "u[-1]" }, { "__type": "Text", "__tag": 4046, "value": "." } ] } ] }, { "__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, " }, { "__type": "InlineCode", "__tag": 4051, "value": "k=3" }, { "__type": "Text", "__tag": 4046, "value": ", are recommended. Even values of " }, { "__type": "ParamRef", "__tag": 4071, "name": "k" }, { "__type": "Text", "__tag": 4046, "value": " should be avoided especially with a small " }, { "__type": "InlineCode", "__tag": 4051, "value": "s" }, { "__type": "Text", "__tag": 4046, "value": " value. Default is " }, { "__type": "InlineCode", "__tag": 4051, "value": "k=3" } ] } ] }, { "__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": "Code", "__tag": 4050, "value": "sum((w * (g(u) - x))**2) <= s,", "execution_status": null }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "where " }, { "__type": "InlineCode", "__tag": 4051, "value": "g(u)" }, { "__type": "Text", "__tag": 4046, "value": " is the smoothed approximation to " }, { "__type": "InlineCode", "__tag": 4051, "value": "x" }, { "__type": "Text", "__tag": 4046, "value": ". 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": "InlineCode", "__tag": 4051, "value": "s" }, { "__type": "Text", "__tag": 4046, "value": " means more smoothing while smaller values of " }, { "__type": "InlineCode", "__tag": 4051, "value": "s" }, { "__type": "Text", "__tag": 4046, "value": " indicate less smoothing. Recommended values of " }, { "__type": "InlineCode", "__tag": 4051, "value": "s" }, { "__type": "Text", "__tag": 4046, "value": " depend on the weights, " }, { "__type": "InlineCode", "__tag": 4051, "value": "w" }, { "__type": "Text", "__tag": 4046, "value": ". If the weights represent the inverse of the standard deviation of " }, { "__type": "InlineCode", "__tag": 4051, "value": "x" }, { "__type": "Text", "__tag": 4046, "value": ", then a good " }, { "__type": "InlineCode", "__tag": 4051, "value": "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 " }, { "__type": "InlineCode", "__tag": 4051, "value": "m" }, { "__type": "Text", "__tag": 4046, "value": " is the number of data points in " }, { "__type": "InlineCode", "__tag": 4051, "value": "x" }, { "__type": "Text", "__tag": 4046, "value": " and " }, { "__type": "InlineCode", "__tag": 4051, "value": "w" }, { "__type": "Text", "__tag": 4046, "value": "." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "t", "annotation": "array_like, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The spline knots. If None (default), the knots will be constructed automatically. There must be at least " }, { "__type": "InlineCode", "__tag": 4051, "value": "2*k + 2" }, { "__type": "Text", "__tag": 4046, "value": " and at most " }, { "__type": "InlineCode", "__tag": 4051, "value": "m + k + 1" }, { "__type": "Text", "__tag": 4046, "value": " knots." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "nest", "annotation": "int, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The target length of the knot vector. Should be between " }, { "__type": "InlineCode", "__tag": 4051, "value": "2*(k + 1)" }, { "__type": "Text", "__tag": 4046, "value": " (the minimum number of knots for a degree-" }, { "__type": "InlineCode", "__tag": 4051, "value": "k" }, { "__type": "Text", "__tag": 4046, "value": " spline), and " }, { "__type": "InlineCode", "__tag": 4051, "value": "m + k + 1" }, { "__type": "Text", "__tag": 4046, "value": " (the number of knots of the interpolating spline). The actual number of knots returned by this routine may be slightly larger than " }, { "__type": "ParamRef", "__tag": 4071, "name": "nest" }, { "__type": "Text", "__tag": 4046, "value": ". Default is None (no limit, add up to " }, { "__type": "InlineCode", "__tag": 4051, "value": "m + k + 1" }, { "__type": "Text", "__tag": 4046, "value": " knots)." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "bc_type", "annotation": "str, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Boundary conditions. Default is " }, { "__type": "InlineRole", "__tag": 4003, "value": "\"not-a-knot\"", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": ". The following boundary conditions are recognized:" } ] }, { "__type": "BulletList", "__tag": 4053, "ordered": false, "start": 1, "children": [ { "__type": "ListItem", "__tag": 4054, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "InlineCode", "__tag": 4051, "value": "\"not-a-knot\"" }, { "__type": "Text", "__tag": 4046, "value": " (default): The first and second segments are the same polynomial. This is equivalent to having " }, { "__type": "InlineCode", "__tag": 4051, "value": "bc_type=None" }, { "__type": "Text", "__tag": 4046, "value": "." } ] } ] }, { "__type": "ListItem", "__tag": 4054, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "InlineCode", "__tag": 4051, "value": "\"periodic\"" }, { "__type": "Text", "__tag": 4046, "value": ": The values and the first " }, { "__type": "InlineCode", "__tag": 4051, "value": "k-1" }, { "__type": "Text", "__tag": 4046, "value": " derivatives at the ends are equivalent." } ] } ] } ] } ] } ] } ], "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 1D 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 " }, { "__type": "InlineCode", "__tag": 4051, "value": "g(u)" }, { "__type": "Text", "__tag": 4046, "value": "." } ] } ], "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_repro.py", "item_line": 1168, "item_type": "function", "aliases": [ "scipy.interpolate.make_splprep" ], "example_section_data": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "see_also": [ { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "generate_knots", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.interpolate._fitpack_repro:generate_knots" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "is used under the hood for generating the knots" } ] } ], "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": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "construct an interpolating spline (" }, { "__type": "InlineCode", "__tag": 4051, "value": "s = 0" }, { "__type": "Text", "__tag": 4046, "value": ")" } ] } ], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "make_lsq_spline", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.interpolate._bsplines:make_lsq_spline" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "construct the least-squares spline given the knot vector" } ] } ], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "make_splrep", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.interpolate._fitpack_repro:make_splrep" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "the analog of this routine 1D functions" } ] } ], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "splprep", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "current-module", "version": "current-version", "kind": "to-resolve", "path": "splprep" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "a FITPACK analog of this routine" } ] } ], "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": "KEYWORD_ONLY", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "u", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "KEYWORD_ONLY", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "ub", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "KEYWORD_ONLY", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "ue", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "KEYWORD_ONLY", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "k", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "KEYWORD_ONLY", "default": "3" }, { "__type": "SigParam", "__tag": 4030, "name": "s", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "KEYWORD_ONLY", "default": "0" }, { "__type": "SigParam", "__tag": 4030, "name": "t", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "KEYWORD_ONLY", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "nest", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "KEYWORD_ONLY", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "bc_type", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "KEYWORD_ONLY", "default": "None" } ], "return_annotation": { "__type": "Empty", "__tag": 4031 }, "target_name": "make_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, \"Curve and surface fitting with splines\", Monographs on", " Numerical Analysis, Oxford University Press, 1993." ], "qa": "scipy.interpolate._fitpack_repro:make_splprep", "arbitrary": [], "local_refs": [ "bc_type", "k", "nest", "s", "spl", "t", "u", "ub", "ue", "w", "x" ] }