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A\nperiodic boundary condition is used. You can see that the first derivative\nvalues, ds/dx=0, ds/dy=1 at the periodic point (1, 0) are correctly\ncomputed. Note that a circle cannot be exactly represented by a cubic\nspline. To increase precision, more breakpoints would be required.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "theta = 2 * np.pi * np.linspace(0, 1, 5)\ny = np.c_[np.cos(theta), np.sin(theta)]\ncs = CubicSpline(theta, y, bc_type='periodic')\nprint(\"ds/dx={:.1f} ds/dy={:.1f}\".format(cs(0, 1)[0], cs(0, 1)[1]))\nxs = 2 * np.pi * np.linspace(0, 1, 100)\nfig, ax = plt.subplots(figsize=(6.5, 4))\n", "execution_status": "success" }, { "__type": "Code", "__tag": 4050, "value": "ax.plot(y[:, 0], y[:, 1], 'o', label='data')\nax.plot(np.cos(xs), np.sin(xs), label='true')\nax.plot(cs(xs)[:, 0], cs(xs)[:, 1], label='spline')\n", "execution_status": "failure" }, { "__type": "Code", "__tag": 4050, "value": "ax.axes.set_aspect('equal')\n", "execution_status": "success" }, { "__type": "Code", "__tag": 4050, "value": "ax.legend(loc='center')\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-c0e00826152c43f6.png" } }, { "__type": "Text", "__tag": 4046, "value": "\nThe third example is the interpolation of a polynomial y = x**3 on the\ninterval 0 <= x<= 1. A cubic spline can represent this function exactly.\nTo achieve that we need to specify values and first derivatives at\nendpoints of the interval. Note that y' = 3 * x**2 and thus y'(0) = 0 and\ny'(1) = 3.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "cs = CubicSpline([0, 1], [0, 1], bc_type=((1, 0), (1, 3)))\nx = np.linspace(0, 1)\nnp.allclose(x**3, cs(x))\n", "execution_status": "success" } ], "title": [], "level": 0, "target": null }, "see_also": [ { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "Akima1DInterpolator", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.interpolate._cubic:Akima1DInterpolator" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Akima 1D interpolator." } ] } ], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "PPoly", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.interpolate._interpolate:PPoly" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Piecewise polynomial in terms of coefficients and breakpoints." } ] } ], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "PchipInterpolator", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.interpolate._cubic:PchipInterpolator" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "PCHIP 1-D monotonic cubic interpolator." } ] } ], "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": "y", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": { "__type": "Empty", "__tag": 4031 } }, { "__type": "SigParam", "__tag": 4030, "name": "axis", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "0" }, { "__type": "SigParam", "__tag": 4030, "name": "bc_type", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "not-a-knot" }, { "__type": "SigParam", "__tag": 4030, "name": "extrapolate", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" } ], "return_annotation": { "__type": "Empty", "__tag": 4031 }, "target_name": "CubicSpline" }, "references": [ ".. 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