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The `RectSphereBivariateSpline` object\nonly takes 1-D arrays as input, therefore we need to do some reshaping.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "data_interp = lut.ev(new_lats.ravel(),\n new_lons.ravel()).reshape((360, 180)).T\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nLooking at the original and the interpolated data, one can see that the\ninterpolant reproduces the original data very well:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "import matplotlib.pyplot as plt\nfig = plt.figure()\nax1 = fig.add_subplot(211)\n", "execution_status": "success" }, { "__type": "Code", "__tag": 4050, "value": "ax1.imshow(data, interpolation='nearest')\n", "execution_status": "failure" }, { "__type": "Code", "__tag": 4050, "value": "ax2 = fig.add_subplot(212)\n", "execution_status": "success" }, { "__type": "Code", "__tag": 4050, "value": "ax2.imshow(data_interp, interpolation='nearest')\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-d150f23273c76031.png" } }, { "__type": "Text", "__tag": 4046, "value": "\nChoosing the optimal value of ``s`` can be a delicate task. Recommended\nvalues for ``s`` depend on the accuracy of the data values. If the user\nhas an idea of the statistical errors on the data, she can also find a\nproper estimate for ``s``. By assuming that, if she specifies the\nright ``s``, the interpolator will use a spline ``f(u,v)`` which exactly\nreproduces the function underlying the data, she can evaluate\n``sum((r(i,j)-s(u(i),v(j)))**2)`` to find a good estimate for this ``s``.\nFor example, if she knows that the statistical errors on her\n``r(i,j)``-values are not greater than 0.1, she may expect that a good\n``s`` should have a value not larger than ``u.size * v.size * (0.1)**2``.\n\nIf nothing is known about the statistical error in ``r(i,j)``, ``s`` must\nbe determined by trial and error. The best is then to start with a very\nlarge value of ``s`` (to determine the least-squares polynomial and the\ncorresponding upper bound ``fp0`` for ``s``) and then to progressively\ndecrease the value of ``s`` (say by a factor 10 in the beginning, i.e.\n``s = fp0 / 10, fp0 / 100, ...`` and more carefully as the approximation\nshows more detail) to obtain closer fits.\n\nThe interpolation results for different values of ``s`` give some insight\ninto this process:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "fig2 = plt.figure()\ns = [3e9, 2e9, 1e9, 1e8]\n", "execution_status": "success" }, { "__type": "Code", "__tag": 4050, "value": "for idx, sval in enumerate(s, 1):\n lut = RectSphereBivariateSpline(lats, lons, data, s=sval)\n data_interp = lut.ev(new_lats.ravel(),\n new_lons.ravel()).reshape((360, 180)).T\n ax = fig2.add_subplot(2, 2, idx)\n ax.imshow(data_interp, interpolation='nearest')\n ax.set_title(f\"s = {sval:g}\")\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-92a3c19ad8a86df4.png" } } ], "title": [], "level": 0, "target": null }, "see_also": [ { "__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": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "a base class for bivariate splines." } ] } ], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "LSQBivariateSpline", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": 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