{ "__type": "IngestedDoc", "__tag": 4010, "_content": { "Notes": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Admonition", "__tag": 4056, "kind": "versionadded", "base_type": "neutral", "children": [ { "__type": "AdmonitionTitle", "__tag": 4055, "children": [ { "__type": "Text", "__tag": 4046, "value": "versionadded 0.9" } ] } ] }, { "__type": "Admonition", "__tag": 4056, "kind": "note", "base_type": "note", "children": [ { "__type": "AdmonitionTitle", "__tag": 4055, "children": [ { "__type": "Text", "__tag": 4046, "value": "note For data on a regular grid use `interpn` instead." } ] } ] } ], "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": "", "annotation": "ndarray", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Array of interpolated values." } ] } ] } ] } ], "title": [], "level": 0, "target": null }, "Summary": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Convenience function for interpolating unstructured data in multiple dimensions." } ] } ], "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": "points", "annotation": "2-D ndarray of floats with shape (n, D), or length D tuple of 1-D ndarrays with shape (n,).", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Data point coordinates." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "values", "annotation": "ndarray of float or complex, shape (n,)", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Data values." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "xi", "annotation": "2-D ndarray of floats with shape (m, D), or length D tuple of ndarrays broadcastable to the same shape.", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Points at which to interpolate data." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "method", "annotation": "{'linear', 'nearest', 'cubic'}, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Method of interpolation. One of" } ] }, { "__type": "DefList", "__tag": 4033, "children": [ { "__type": "DefListItem", "__tag": 4037, "dt": { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "InlineCode", "__tag": 4051, "value": "nearest" } ] }, "dd": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "return the value at the data point closest to the point of interpolation. See " }, { "__type": "CrossRef", "__tag": 4002, "value": "NearestNDInterpolator", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.interpolate._ndgriddata:NearestNDInterpolator" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " for more details." } ] } ] }, { "__type": "DefListItem", "__tag": 4037, "dt": { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "InlineCode", "__tag": 4051, "value": "linear" } ] }, "dd": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "tessellate the input point set to N-D simplices, and interpolate linearly on each simplex. See " }, { "__type": "CrossRef", "__tag": 4002, "value": "LinearNDInterpolator", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.interpolate._interpnd:LinearNDInterpolator" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " for more details." } ] } ] }, { "__type": "DefListItem", "__tag": 4037, "dt": { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "InlineCode", "__tag": 4051, "value": "cubic" }, { "__type": "Text", "__tag": 4046, "value": " (1-D)" } ] }, "dd": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "return the value determined from a cubic spline." } ] } ] }, { "__type": "DefListItem", "__tag": 4037, "dt": { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "InlineCode", "__tag": 4051, "value": "cubic" }, { "__type": "Text", "__tag": 4046, "value": " (2-D)" } ] }, "dd": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "return the value determined from a piecewise cubic, continuously differentiable (C1), and approximately curvature-minimizing polynomial surface. 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This option has no effect for the 'nearest' method." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "rescale", "annotation": "bool, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Rescale points to unit cube before performing interpolation. This is useful if some of the input dimensions have incommensurable units and differ by many orders of magnitude." } ] }, { "__type": "Admonition", "__tag": 4056, "kind": "versionadded", "base_type": "neutral", "children": [ { "__type": "AdmonitionTitle", "__tag": 4055, "children": [ { "__type": "Text", "__tag": 4046, "value": "versionadded 0.14.0" } ] } ] } ] } ] } ], "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/_ndgriddata.py", "item_line": 171, "item_type": "function", "aliases": [ "scipy.interpolate.griddata" ], "example_section_data": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Text", "__tag": 4046, "value": "Suppose we want to interpolate the 2-D function\n\n" }, { "__type": "Code", "__tag": 4050, "value": "import numpy as np\ndef func(x, y):\n return x*(1-x)*np.cos(4*np.pi*x) * np.sin(4*np.pi*y**2)**2\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\non a grid in [0, 1]x[0, 1]\n\n" }, { "__type": "Code", "__tag": 4050, "value": "grid_x, grid_y = np.mgrid[0:1:100j, 0:1:200j]\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nbut we only know its values at 1000 data points:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "rng = np.random.default_rng()\npoints = rng.random((1000, 2))\nvalues = func(points[:,0], points[:,1])\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nThis can be done with `griddata` -- below we try out all of the\ninterpolation methods:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "from scipy.interpolate import griddata\ngrid_z0 = griddata(points, values, (grid_x, grid_y), method='nearest')\ngrid_z1 = griddata(points, values, (grid_x, grid_y), method='linear')\ngrid_z2 = griddata(points, values, (grid_x, grid_y), method='cubic')\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nOne can see that the exact result is reproduced by all of the\nmethods to some degree, but for this smooth function the piecewise\ncubic interpolant gives the best results:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "import matplotlib.pyplot as plt\n", "execution_status": "success" }, { "__type": "Code", "__tag": 4050, "value": "plt.subplot(221)\nplt.imshow(func(grid_x, grid_y).T, extent=(0,1,0,1), origin='lower')\nplt.plot(points[:,0], points[:,1], 'k.', ms=1)\nplt.title('Original')\nplt.subplot(222)\nplt.imshow(grid_z0.T, extent=(0,1,0,1), origin='lower')\nplt.title('Nearest')\nplt.subplot(223)\nplt.imshow(grid_z1.T, extent=(0,1,0,1), origin='lower')\nplt.title('Linear')\nplt.subplot(224)\nplt.imshow(grid_z2.T, extent=(0,1,0,1), origin='lower')\nplt.title('Cubic')\n", "execution_status": "failure" }, { "__type": "Code", "__tag": 4050, "value": "plt.gcf().set_size_inches(6, 6)\nplt.show()\n", "execution_status": "success" }, { "__type": "Figure", "__tag": 4024, "value": { "__type": "RefInfo", "__tag": 4000, "module": "scipy", "version": "1.17.1", "kind": "assets", "path": "fig-0a5d6f9175994fc8.png" } } ], "title": [], "level": 0, "target": null }, "see_also": [ { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "CloughTocher2DInterpolator", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.interpolate._interpnd:CloughTocher2DInterpolator" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Piecewise cubic, C1 smooth, curvature-minimizing interpolator in 2D." } ] } ], "type": null }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "LinearNDInterpolator", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.interpolate._interpnd:LinearNDInterpolator" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Piecewise linear interpolator in N dimensions." } ] } ], "type": null }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "NearestNDInterpolator", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.interpolate._ndgriddata:NearestNDInterpolator" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Nearest-neighbor interpolator in N dimensions." } ] } ], "type": null }, { 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